journal in electronics

54 IEEE REVIEWS IN BIOMEDICAL ENGINEERING, VOL. 2, 2009

Diabetes: Models, Signals, and ControlClaudio Cobelli, Chiara Dalla Man, Giovanni Sparacino, Lalo Magni, Giuseppe De Nicolao, and

Boris P. Kovatchev

Methodological Review

Abstract—The control of diabetes is an interdisciplinary en-deavor, which includes a significant biomedical engineeringcomponent, with traditions of success beginning in the early1960s. It began with modeling of the insulin-glucose system, andprogressed to large-scale in silico experiments, and automatedclosed-loop control (artificial pancreas). Here, we follow theseengineering efforts through the last, almost 50 years. We beginwith the now classic minimal modeling approach and discuss anumber of subsequent models, which have recently resulted in thefirst in silico simulation model accepted as substitute to animaltrials in the quest for optimal diabetes control. We then reviewmetabolic monitoring, with a particular emphasis on the newcontinuous glucose sensors, on the analyses of their time-seriessignals, and on the opportunities that they present for automationof diabetes control. Finally, we review control strategies thathave been successfully employed in vivo or in silico, presenting apromise for the development of a future artificial pancreas and, inparticular, discuss a modular architecture for building closed-loopcontrol systems, including insulin delivery and patient safetysupervision layers. We conclude with a brief discussion of theunique interactions between human physiology, behavioral events,engineering modeling and control relevant to diabetes.

Index Terms—Artificial pancreas, automatic control, identifica-tion, parameter estimation, physiological systems, sensors, signalprocessing.

I. INTRODUCTION

D IABETES is a common metabolic disorder characterizedby chronic hyperglycemia that leads to microvascular and

macrovascular complications [1]–[5]. These complications in-clude limb loss, blindness, ischemic heart disease, and end-stagerenal disease. Diabetes is broadly classified into two categories,type 1 diabetes and type 2 diabetes. Both arise from complexinteractions between genes and the environment, however theirpathogenesis is distinct. Type 1 diabetes is the result of immune-

Manuscript received October 15, 2009; revised October 25, 2009. Currentversion published December 09, 2009. This work was supported in part by PRIN2007, in part by the JDRF Artificial Pancreas project at the University of Vir-ginia, and in part under Grant RO1 DK 51562 from the National Institutes ofHealth.

C. Cobelli, C. Dalla Man, and G. Sparacino are with the Department of Infor-mation Engineering, University of Padova, Via Gradenigo 6B, 35131 Padova,Italy (e-mail: [email protected]).

L. Magni and G. De Nicolao are with the Department of Computer Engi-neering and Systems Science, University of Pavia, Via Ferrata 1, 27100 Pavia,Italy.

B. P. Kovatchev is with the Department of Psychiatry and NeurobehavioralSciences, P.O. Box 40888, University of Virginia, Charlottesville, VA 22903USA.

Digital Object Identifier 10.1109/RBME.2009.2036073

mediated destruction of the beta-cells in the islets of Langer-hans—the site of insulin secretion and production. In general,the disease occurs in childhood and adolescence (although itcan occur at all ages) and is characterized by absolute insulindeficiency. Consequently, affected individuals require insulintherapy to control hyperglycemia and sustain life. As a rule, obe-sity does not play a part in the pathogenesis of type 1 diabetes,although obesity in type 1 diabetes is associated with the devel-opment of cardiovascular complications. In contrast, type 2 dia-betes occurs because insulin secretion is inadequate and cannotovercome the prevailing defects in insulin action, resulting inhyperglycemia. Excess caloric intake, inactivity, and obesity allplay parts in the pathogenesis of type 2 diabetes. In general, it isa disease that occurs with increasing frequency with increasingage and is uncommon before age 40 (although there are impor-tant exceptions). In addition, people with type 2 diabetes aremore likely to have associated adverse cardiovascular risk fac-tors such as dyslipidemia and hypertension. Prediabetes, i.e.,impaired fasting glucose (IFG) and impaired glucose tolerance(IGT), is an intermediate condition in the transition betweennormality and diabetes. People with IGT or IFG are at high riskof progressing to type 2 diabetes, although this is not inevitable.Both type 2 diabetes and prediabetes are recognized risk factorsfor overt cardiovascular disease and related metabolic complica-tions and are major components of health care spending [6], [7].Rapid urbanization and societal affluence of global migratingpopulations has been suggested as major risk factors for the ob-served exploding prevalence of prediabetes and type 2 diabeteswith consequent rising trends in cardiovascular risks [8]. IFG isa rapidly emerging form of prediabetes with a 20%–30% risk ofprogression to diabetes over 5–10 years. This risk is even greaterif individuals have both IFG and IGT. Furthermore, both IFGand IGT are linked to increased risk for cardiovascular events[6], [7] in the Caucasian population. Ninety percent of the worldpopulation with diabetes is type 2 with type 1 diabetes com-prising between 5%–10%. It is plausible that the relative fre-quency of type 1 and type 2 diabetes will change with risingtrends in the prevalence of type 2 diabetes, obesity, and predia-betes in the developing world.

Over time, diabetes leads to complications, in particular: dia-betic retinopathy, which leads to blindness; diabetic neuropathy,which increases of the risk of foot ulceration and limb loss; anddiabetic nephropathy leading to kidney failure. In addition, thereis an increased risk of heart disease and stroke with 50% ofpeople with diabetes dying of cardiovascular disease and stroke.Finally, the overall risk of dying among people with diabetesis at least double the risk of their peers without diabetes. The

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COBELLI et al.: DIABETES: MODELS, SIGNALS, AND CONTROL 55

Fig. 1. Disciplines which contribute to diabetes control.

World Health Organization (WHO) estimates than more than180 million people worldwide have diabetes. This number islikely to more than double by 2030. In 2005, an estimated 1.1million people died from diabetes. When ranked by cause-spe-cific mortality, diabetes is the fifth cause of death, after com-municable diseases, cardiovascular diseases, cancer and injury[8]. Almost 80% of diabetes death occurs in low- and middle-in-come countries. WHO projects that diabetes deaths will increaseby more than 50% in the next ten years without urgent action.Most notably, diabetes is projected to increase by over 80% inupper-middle income countries between 2006 and 2015. Dia-betes and its complications impose significant economic conse-quences on individuals, families, health systems, and countries.WHO estimates that over the next ten years (2005–2015) Chinawill lose $558 billion in national income due to heart disease,stroke, and diabetes alone.

Given the complexity of the disease it is not surprising thatdiabetes is fought with a battery of tools spanning over severaldisciplines, from cellular biology to pathophysiology to phar-macology to chemistry, physics,and engineering to transplan-tation to patient management to health care (Fig. 1). Dynamicsystem models are an essential ingredient of virtually all of thesestrategies. However, in this review we have to limit our scope;thus, we will not be able to discuss modeling in the areas of pa-tient management [9], [10] and health care intervention strate-gies [11]–[14], or in the emerging area of systems biology [15],[16]. We will first focus on two mechanistic, physiologicallybased classes of models: minimal (coarse) models which de-scribe the key components of the system functionality and arecapable of measuring crucial processes of glucose metabolismand insulin control in health and diabetes; maximal (fine-grain)models which include comprehensively all available knowledgeabout system functionality and are capable to simulate the glu-cose-insulin system in diabetes, thus making it possible to createsimulation scenarios whereby cost effective experiments can beconducted in silico to assess the efficacy of various treatmentstrategies. Then, we discuss the crucial role of models to en-hance the interpretation of glucose and insulin time-series sig-nals. Finally, we discuss recent strategies, in particular ModelPredictive Control aiming for closed-loop control of type 1 dia-betes (known as artificial pancreas), where models also play animportant role.

Fig. 2. Scheme of the glucose-insulin system.

II. GLUCOSE-INSULIN CONTROL SYSTEM

Glucose concentration is tightly regulated in health by a com-plex neuro-hormonal control system [1], [2]. Insulin is the pri-mary regulator of glucose homeostasis, i.e., it promotes glucoseutilization and inhibits glucose production. A battery of counter-regulatory hormones are also at work, i.e., glucagon, epineph-rine, cortisol, and growth hormone, which defend, on differenttime scales, the body from life-threatening hypoglycemia. Bothhypoglycemia counterregulation and insulin control are neuro-mediated.

In this review, we focus on the glucose-insulin control systemwhich is not only the most studied in terms of modeling, but alsothe one where modeling has had major impact in diabetes re-search and therapy. A high-level scheme of this system is shownin Fig. 2. Glucose is produced (mainly by the liver), distributed,and utilized in both insulin-independent (e.g., central nervoussystem and red blood cells) and insulin-dependent (muscle andadipose tissues) tissues. Insulin is secreted by pancreatic beta-cells, reaches the system circulation after liver degradation, andis peripherally cleared primarily by the kidneys. The glucoseand insulin systems interact by feedback control signals, e.g., ifa glucose perturbation occurs (after a meal), beta-cells secretemore insulin in response to increased plasma glucose concen-tration and in turn insulin signaling promotes glucose utiliza-tion and inhibits glucose production so as to bring rapidly andeffectively plasma glucose to the preperturbation level. Thesecontrol interactions are usually referred to as insulin sensitivityand beta-cell responsivity. In pathophysiology, the control isdegraded. In type 2 diabetes this degradation is initially pre-sented as prediabetes, characterized by progressive deteriora-tion of both insulin sensitivity and beta-cell responsivity. In type1 diabetes, beta-cells rapidly become virtually silent and in-sulin must be provided exogenously by the patient attemptingto compensate for hyperglycemia. However, insulin treatmentmay risk potentially severe hypoglycemia and thus people withtype 1 diabetes face a life-long behavior-controlled optimizationproblem: to maintain strict glycemic control and reduce hyper-glycemia, without increasing their risk for hypoglycemia. Bloodglucose is both the measurable result of this optimization andthe principal feedback signal to the patient for his/her controlof diabetes. Several types of models assist the optimization ofdiabetes control.


III. MINIMAL MODELS

A. Rationale

Minimal models must be parsimonious and describe the keycomponents of system functionality. Thus, a sound modelingmethodology must be used to select a valid model, i.e., a wellfounded and useful model which fulfills the purpose for whichit was formulated [17]. Briefly, it is reasonable to assumethat a good minimal model will not be a large-scale one: notevery known substrate/hormone needs to be included becausethe macro-level response of the system would be relativelyinsensitive to many micro-level relationships. In addition,because it is not possible to estimate the values of all systemparameters from in vivo dynamic data, many of the unit pro-cesses must be lumped together. Therefore, desirable featuresof a minimal model include: 1) physiologically based; 2) pa-rameters that can be estimated with reasonable precision froma single dynamic response of the system; 3) parameters thatvary within physiologically plausible ranges; and 4) ability todescribe the dynamics of the system with the smallest numberof identifiable parameters. Given a set of dynamic data, e.g.,plasma concentration measurements after a perturbation, onegenerally proceeds by proposing a series of system models,beginning with the simplest and systematically increasing thecomplexity by including more known physiological detail.Each of the series of system models is then tested for a prioriidentifiability and subsequently numerically identified fromexperimental data in which samples are taken at frequent inter-vals, and for which measurements are made with utmost care(to reduce the influence of measurement error on the choiceof a model). A number of quantitative tools are available toselect the most parsimonious from a series of models, includingtesting the residuals, parameter precision, parsimony criteria,and parameter plausibility. Also of importance is the validationof the model-derived measures against those provided by anindependent technique. All these methodological aspects havereceived systematic attention; books are available which coverin details all aspects of model identification and validation[17], [18]. In Section III-B, we discuss minimal models usedto understand/measure glucose metabolism and insulin control;in Section III-C we discuss insulin secretion and glucose con-trol; Section III-D reviews briefly some recent clinical studieswhere certain models discussed below have been successfullyemployed.

B. Glucose System

Understanding quantitatively the glucose system requires dy-namic data, e.g., glucose or a tracer-glucose perturbation, and asystem model, e.g., a compartmental model [18].

1) Insulin Action: Steady State: To study glucose kinetics insteady state, a tracer is needed. Tracer theory shows that lineartime-variant compartmental models are accurate [19], thus al-lowing the use of a sum of exponential models (input–outputmodels) to understand the number of compartments needed todescribe the system. Insel et al. [20] were the first showing that athree compartment model is required to describe basal glucosekinetics (Fig. 3, top panel). This was later confirmed by Co-belli et al. [21], albeit a different model structure was postulated

Fig. 3. Compartmental model of glucose kinetics in steady state. Upper panel:three compartment model with glucose utilization taking place in plasma andrapidly equilibrating tissues; Middle panel: three compartment model with glu-cose utilization taking place in slowly and rapidly equilibrating tissues; Lowerpanel: compartment model with glucose utilization taking place in plasma +rapidly equilibrating tissue and slowly equilibrating tissues.

(Fig. 3, middle panel). The compartmental structure has beenvalidated in animal experiments [22]. Both models incorporateda priori physiological knowledge to achieve unique identifia-bility. As noted in [21], the exchange kinetics between com-partment 1 and 2 is much faster than between 1 and 3; thus, itis reasonable to use a simpler model (Fig. 3, bottom panel) withcompartments 1 and 2 aggregated into a new single compart-ment 1 (e.g., after the first 2–3 min following tracer injection,only a two-compartment model is resolvable from the data).

Steady state allows a safe use of linear modeling strategies,so it is not surprising that the first quantitative studies on theeffect of insulin on glucose kinetics were performed by arti-ficially inducing an elevated insulin steady state with glucoseclamp at basal level and performing a tracer study. As an ex-ample, Fig. 4 shows the model-derived parametric representa-tions of basal and elevated-insulin state obtained in [21] and[23] by identifying the tracer model of Fig. 3 (middle panel).If one compares the parameter values in the two steady states,an insulin effect on the rate constants into and out of compart-ment 3 is detected, slowly equilibrating tissues, presumably in-sulin-dependent tissues. In fact, not only parameter , whichdescribes irreversible removal, increases, but also the exchange


Fig. 4. Model of glucose kinetics in steady state: model-derived parametricrepresentation at basal (upper panel) and elevated insulin (lower panel). EGPdenotes endogenous glucose production.

parameters with the accessible pool, and , increase anddecrease, respectively.

Multiple steady-state tracer data allow not only inference ofthe effect of insulin on glucose masses, fluxes, and rate param-eters, but also on the timing and magnitude of insulin control[20]. A model of insulin kinetics was studied at basal glucosewith the glucose clamp technique and it was shown, for the firsttime, that it is not plasma insulin but insulin in a large slowlyequilibrating compartment that mimics the time course of glu-cose utilization (Fig. 5). The authors performed three separateexperiments in each individual: primed continuous infusion ofinsulin, primed continuous infusion of a glucose tracer, and glu-cose clamp with a variable infusion, and were able to identifythe 12-parameter combined glucose (tracer and trace) and in-sulin model of Fig. 6. The two steady-state glucose systemswere quantified in detail and the model revealed their ability toquantify the action of insulin on glucose utilization (with glu-cose production suppressed). In order to describe glucose uti-lization (equal to the glucose infusion rate), this approach fol-lowed Sherwin et al. finding [24] where glucose utilization fromcompartment 2 was related to insulin in the remote compartment3 by a linear function, compartment 3, thus derivinga measure of insulin effectiveness, defined as the derivative ofglucose utilization with respect to insulin in the remote com-partment 3.

2) Insulin Action: Nonsteady State: Multiple steady-statetracer studies have been very informative, but also very complexin terms of required protocols and models. Is there a possibilityto take advantage of the rich information content of a glucosedynamic perturbation, illustrated in Fig. 7, e.g., an intravenousglucose tolerance test (IVGTT), or a meal or an oral glucose

Fig. 5. Comparison among insulin concentration in plasma (compartment 1),rapidly (compartment 2) and slowly (compartment 3) equilibrating tissues withglucose utilization measured with glucose clamp technique. Compartment 3mimics the time course of glucose infusion (=utilization).

Fig. 6. Compartmental models of insulin (upper panel), glucose (middlepanel), and tracer glucose (lower panel) kinetics.

tolerance test (OGTT)? In other words, is it possible to derive ameasure of key control points of the glucose regulatory system,such as insulin sensitivity, i.e., the ability of insulin to controlglucose production and utilization (Fig. 2), by simply exploitingthe information content of the measured plasma glucose and in-sulin concentrations after the perturbation? The quest for an-swers inspired the minimal modeling strategy development atthe end of the 1970s/early 1980s [25], [26], which has been,and still is, very successful [27], [28]. The simplest model de-scribing the responses of plasma glucose and insulin to an oral or


Fig. 7. Plasma glucose (upper) and insulin (lower) concentrations measured during IVGTT (right), OGTT (middle), and MTT (left, panel).

intravenous administration of glucose, was the pioneering studyof Bolie in 1961 [29]

(1)

where denote plasma glucose and insulin, respectively, andis glucose input which can be either an intravenous injection

or the absorption rate of glucose during a meal or an oral glu-cose tolerance test. The model assumed that glucose disappear-ance was a linear function of both glucose and insulin, that in-sulin secretion was proportional to glucose, and that insulin dis-appeared in proportion to plasma insulin concentration. Withvarious minor modifications this model has been used in con-junction with intravenous injections or infusions [29]–[31] andalso during an oral glucose tolerance test [32]–[34] to obtain afour-parameter representation of glucose metabolism in variousstates of glucose intolerance, including diabetes. This model isa priori and a posteriori (numerically) identifiable, but it is toosimple to be an adequate representation of the glucose-insulinsystem. First, the assumed linear relationship between insulinsecretion and glucose has no experimental basis; in fact, therelationship between insulin secretion rate and glucose is dy-namically very complex. Second, this model does not explicitlyconsider the complex interactive control of hepatic glucose pro-duction and uptake by glucose and insulin. Thus, this first modelcan be criticized as representing complex metabolic interactionsin too simplistic terms to adequately represent the complex dy-namical patterns that characterize the response of the metabolicsystem to exogenous perturbation.

Dynamic perturbations: The modeling methodologyoutlined in the Section III-A was first employed to define theso-called glucose minimal model, the goal being the estimationof insulin sensitivity from an IVGTT [25]. To facilitate themodel selection process, system decomposition or partitionanalysis was introduced [35]. In fact, to describe plasma glucoseand insulin data measured in an organism there is the need tosimultaneously model not only the glucose but also the insulin

Fig. 8. Decomposition of glucose-insulin system into glucose and insulin sub-systems.

system and their interactions. This means that, in addition tomodel insulin action, one also has to model glucose-stimulatedinsulin secretion. Since models are, by definition, “wrong,”an error in the insulin secretion model would be compensatedby an error in the insulin action model, thus introducing abias in insulin sensitivity. To avoid this interference that is socommon in physiological studies, the dynamic contribution ofa subsystem can be eliminated. Such a “loop-opening” can beaccomplished in a several ways by gross surgical manipulationof the systems, by using an external feedback loop to clampthe level of specific system variables, or by infusing certainsubstances that inhibit the endogenous elaboration of somefeedback signals. All of these techniques are invasive, and mostare not applicable to humans, at least on a routine basis. Incontrast, model-based system decomposition [25], [35] is an ar-tificial “loop cut”: the system is decomposed in two subsystemswhich are linked together by measured variables (Fig. 8); theinsulin subsystem represents all tissues secreting, distributingand degrading insulin, and the glucose subsystem representsall tissues producing, distributing and metabolizing glucose.When the system is perturbed, e.g., by a glucose injection,and the time courses of plasma glucose, and insulin , aremeasured, then the time courses of and can be considered


Fig. 9. Left panel: IVGTT glucose minimal model. Right panel: OGTT/MTT glucose minimal model.

in terms as “input” (assumed known) and “output” (assumednoisy) of the beta-cell and glucose subsystems, respectively.Models are then proposed not for the whole system but for eachof the subsystems, independently, thus considerably reducingthe difficulties of the modeling exercise. This way, the difficul-ties of modeling the beta-cell do not interfere with modellinginsulin action on glucose-consuming tissues and vice versa(see Section III-C). Seven models of increasing complexitywere proposed to explain plasma glucose concentration byusing plasma insulin as the known input. The chosen minimalmodel (Fig. 9, left panel) assumes that glucose kinetics can bedescribed with one compartment (the early portion of glucosedata is not considered) and that remote (with respect to plasma)insulin controls both net hepatic glucose balance and peripheralglucose disposal:

(2)

where is plasma glucose mass, with denoting its basalvalue; is plasma insulin concentration, with denoting itsbasal value, above basal remote insulin; is the glucosedose; is the glucose distribution volume, and and arerate parameters.

NHGB is the net hepatic glucose balance, which dependsupon plasma glucose and remote insulin

NHGB (3)

and the rate of glucose disappearance form the peripheraltissues, also function of plasma glucose and remote insulin,

(4)

This nonlinear model requires a reparameterization in order tobecome a priori uniquely identifiable (details in [17])

(5)with ; ; ;

; . is insulinaction, is the fractional (i.e., per unit distribution volume) glu-cose effectiveness measuring glucose ability per se to promoteglucose disposal and inhibit glucose production; is the rateconstant of the remote insulin compartment from which insulinaction is emanated; is a scale factor governing the amplitudeof insulin action. The model allows the estimation of insulinsensitivity as

dl/kg/min per U/ml (6)

A novel feature of the model was that insulin action did not em-anate from plasma but from a compartment remote from plasma.This was a model ingredient requested by data and modelingmethodology, in agreement with [24]. Only later this remotecompartment was experimentally proven in dog studies to bethe interstitial fluid [27].

In numerous studies reviewed in [27], insulin sensitivity esti-mated with the minimal model has been shown to strongly cor-relate to that measured with the euglycemic-hyperinsulinemicclamp [36], calculated as the steady-state glucose infusion ratedivided by basal glucose times the above basal increase in in-sulin concentration. This technique is usually considered thegold standard to measure insulin sensitivity in humans. How-ever, it is labor-intensive and requires glucose and insulin pumpsto be frequently manipulated by a trained physician; moreover,the method is “nonphysiological” since in normal life conditionsa constantly elevated insulin concentration not coordinated witha concomitant rise in glucose is never experienced. The minimal


model has been widely employed by more than one thousand pa-pers since its introduction in 1979 (counted until mid 2009); inthe last five years alone around 55 papers/year have been pub-lished.

is essentially a steady-state measure, i.e., it does notaccount for how fast or slow insulin action takes place. Recently,a new dynamic insulin sensitivity index, , was intro-duced and shown to provide a more comprehensive picture ofinsulin action on glucose metabolism than , especiallyin diabetic subjects who exhibit both low and slow insulin ac-tion [37].

Glucose kinetics requires at least a two compartment descrip-tion [21]. Undermodeling the system, i.e., using one insteadof two compartments during the highly dynamic IVGTT per-turbation, can introduce bias in glucose effectiveness and in-sulin sensitivity, being over- and under-estimated, respectively[38]–[40]. A two compartment glucose minimal model has beenproposed [41], [42], but this requires a priori knowledge on thetwo glucose exchange parameters [21], [23], [43], [44]. By in-corporating this a priori knowledge and using a Bayesian Max-imum a posteriori estimator, the accuracy of both glucose ef-fectiveness and insulin sensitivity has been shown to improve.

Like the glucose clamp technique, the IVGTT is nonphysio-logical, albeit to a lesser extent. Because it is important to mea-sure insulin sensitivity in the presence of physiological changesin glucose and insulin concentrations, e.g., during a meal orOGTT, a different approach is needed to describe glucose ki-netics in the gastrointestinal tract. The oral glucose minimalmodel (OMM) builds on the IVGTT minimal model by paramet-rically describing the rate of appearance of glucose into plasma(Ra) [45]. The model (Fig. 9, right panel) has a new mass bal-ance equation

(7)

with the parameter vector describing .Insulin sensitivity, , can be derived from model param-eters as reported in (6). A piecewise linear description forwith eight parameters is reasonably flexible to accommodatemeal or OGTT data. The addition of parameters renders themodel more complex and it can be shown that the OMM is nota priori uniquely identifiable because is nonidentifiable and

is nonuniquely identifiable (two solutions). Thus, there is theneed to assume and to be known, usually fixed to popu-lation values. To improve numerical identifiability, a Maximuma Posteriori Bayesian estimator is used exploiting some prioron and a constraint on , related to the total amount ofglucose appearing in the circulation. has been preciselyestimated and has been validated by comparison with both mul-tiple tracer [46] and glucose clamp [47] techniques. Given thepotential of the method for large scale clinical trials, a reducesprotocol, e.g., a 2h-7 samples OGTT, has been designed andshow to perform as well as a full protocol, e.g., a 5h-11 samplesOGTT [54].

For both OGTT and MTT the new dynamic indexhas been shown to have the same beneficial effects on assessinginsulin action as for IVGTT [37].

Fig. 10. Two compartment model of tracer glucose kinetics. The insulin-in-dependent glucose utilization takes place in the accessible compartment �� while insulin-dependent glucose utilization consists of two components, oneconstant, � , and the other proportional to glycemia. Insulin-dependent glu-cose utilization is parametrically controlled by insulin in a compartment remotefrom plasma �� .

Dynamic perturbations with tracer: The IVGTT and oralminimal models are providing a composite “liver plus periph-eral tissues” measure of insulin action (Fig. 9). Is it possible todissect insulin action on the liver and peripheral tissues? Yes, ifa glucose tracer is added to the IVGTT or meal/OGTT, thanks tothe tracer’s ability to separate glucose utilization from produc-tion. The labeled IVGTT, both radio- (e.g., -glucose)and stable- (e.g., -glucose) label, was first interpretedwith one [48]–[51] and, subsequently, with a two-compartmentminimal model [52], [53], [55], [56] which has been shownto be more accurate. The model proposed in [52] and [53] isshown in Fig. 10. It is assumed that insulin-independent glucoseutilization takes place in the accessible compartment while in-sulin-dependent glucose utilization consists of two components,one constant, , and the other proportional to glycemia. In-sulin-dependent glucose utilization is parametrically controlledby insulin in a compartment remote from plasma. Details onmodel identifiability can be found in [52] and [53]. From theuniquely identifiable parameterization important indices such asglucose effectiveness, glucose clearance, and insulin sensitivity,can be estimated.

More recently, a labeled meal/OGTT was introduced and in-terpreted with the oral tracer minimal model [57]. A stable iso-tope glucose tracer (e.g., C -glucose or -glu-cose) is normally used and from the oral tracer dose and plasmameasurements of glucose tracer one can calculate the exogenousglucose , i.e., coming from the meal/OGTT.

The model describing data is given by [57]

(8)where denotes tracer variables and parameters.

The disposal insulin sensitivity index, , i.e., insulinaction on glucose disposal only, is



The model shares the same input, , of the oral min-imal model [(7)]. Thus, these two models can be simultaneouslyidentified from the measurements and and there is noneed for using Bayesian priors for and to improve numer-ical identifiability. However, knowledge of and is stillneeded.

has been validated against the multiple tracer [57]and the glucose clamp [47] techniques.

An unexpected finding commented in [47] was tobe very close to (sometimes higher than) , which im-plies a negligible (or negative) action of insulin on the liversince hepatic insulin sensitivity .The principal suspect was the mechanistic description of en-dogenous glucose production (EGP), an ingredient of[58]. To address this issue, model-independent EGP profiles[59] were used.

The minimal model EGP description is

(10)

where is the basal EGP, liver glucose effective-ness, is glucose concentration, its basal value, is liverinsulin action (deviation from basal) which follows the dynamicequation

(11)

where is a rate constant describing the dynamics of insulinaction on glucose production (assumed the same as on glucoseutilization) and is the scale factor governing the amplitudeof hepatic insulin action.

When tested against EGP data, the model failed, i.e., it wasunable to fit the data, and provided imprecise and physiolog-ically implausible parameter estimates. This finding supportedour hypothesis that the mechanistic description of EGP includedin the minimal model is incorrect, and this may be the cause ofthe unreliable (negative) estimate of hepatic insulin sensitivityobtained with the minimal model.

Other models were tested, with the goal to find an EGP de-scription that is suitable for incorporation in the minimal modelinstead of (10); the best one was

(12)

with defined as

(13)

and

if

if(14)

where is a rate constant describing the dynamics of insulinaction on glucose production (assumed here to be different fromthat on glucose utilization), is the scale factor governing theamplitude of hepatic insulin action, and is a parameter gov-erning the magnitude of glucose derivative control.

This model is different from the minimal-model EGP descrip-tion. First, insulin action it is not multiplied by glucose concen-tration, which means that glucose and insulin act independentlyon the liver. In fact, while insulin modulates glucose utilizationby moving the glucose transporter GLUT-4 to cell membraneand thus the glucose utilization clearly depends on glucose level,the insulin-stimulated inhibition of production follows differentpaths. In addition, insulin action on glucose production has a dif-ferent time course from insulin signalling on glucose disposal.Finally, the model incorporates the accepted notion that a portalinsulin signal (here is approximated by glucose derivative) con-trols the rapid suppression of EGP [60]. Hepatic insulin sensi-tivity is given by


with basal glucose concentration and and definedabove.

This model has been recently coupled with oral tracer min-imal model (unpublished); thus, hepatic [ , (15)] anddisposal insulin sensitivity ( , (9)] can be simultaneouslyestimated from a single-tracer experiment using total glucose,exogenous glucose, and insulin concentrations. The whole-bodyinsulin sensitivity is , thus, the rela-tive role of the liver versus periphery can be determined in per-centage. Our results show that during a meal repre-sents 34% of total insulin action.

Both unlabelled and tracer IVGTT and oral minimal modelsare powerful tools to measure a number of indices character-izing the control that glucose and insulin exert on glucose me-tabolism. These indices are of utmost importance for the under-standing and treatment of pathophysiology, from glucose intol-erance to diabetes. Even more importantly, the combined useof the unlabelled and labeled minimal models, thanks to thetracer-to-tracee indistinguishability principle [19], allows us tomove from a parametric indices to a flux portrait.

Consider the IVGTT probe. Glucose utilization can be cal-culated from the uniquely identifiable parameterization of themodel of Fig. 10 as

(16)

where and are glucose masses in compartments 1 and 2,respectively.


Fig. 11. Endogenous glucose production estimated with the dual tracer tech-nique (open circles, vertical bars represents standard deviation) and with decon-volution (continuous line).

Endogenous glucose production can be calculated by usingthe endogenous glucose concentration, , i.e., the compo-nent of total glucose concentration measured in plasma due toglucose production, which can be calculated in a model-inde-pendent fashion [61]. is related to the endogenous glucoseproduction, EGP, by the integral equation

(17)

where is the time-varying impulse response of the glu-cose system, given by the tracer minimal model of Fig. 10,and is basal glucose. EGP can be estimated by deconvo-lution, e.g., the stochastic deconvolution method [62]. In [61],EGP estimation has been validated against that obtained by adual tracer-to-tracee clamp technique, which provided a virtu-ally model-independent estimation (Fig. 11). A similar mod-eling strategy has also been used in [63].

Recently, Krudys et al. [64] have proposed a structuralmodel of EGP during an IVGTT. EGP depends on the amountof releasable glucose in the liver and has an inhibitory functionwhich is related to remote insulin. The model reconstructedEGP was validated against that obtained via deconvolutionand the tracer-to-tracee clamp technique [64]. The model alsoprovided some indices of glucose and insulin control on EGPwhich have been recently refined [65].

As for the IVGTT, relevant glucose fluxes can also be derivedfrom meal and OGTT data. Glucose rate of appearance, ,can be reconstructed from the simultaneous identification of thetwo models of (7) and (8). Moreover, glucose utilization can becalculated as

(18)

The time course of endogenous glucose productioncan be reconstructed with the model described in [58] and re-ported in (12). In this case, in addition to EGP profile, the modelprovides quantitative indices of hepatic insulin sensitivity [(15)]

Fig. 12. Comparison between endogenous glucose production (upper panel)and rate of appearance of glucose (lower panel) during a meal reconstructedwith models and triple tracer model-independent method.

and glucose effectiveness as well as (unlike the Krudys model)an index quantifying hepatic insulin sensitivity.

Alternatively, EGP(t) can also be estimated by stochastic de-convolution from endogenous glucose concentration data,[66]. Unlike IVGTT, during meal and OGTT the single com-partment model can be used to describe glucose kinetics; thus,

is the impulse response of the system of (8). Moreover,if a single glucose tracer is orally administered, can bedetermined by fixing and to population values.

EGP and time courses reconstructed with both modelsand deconvolution have been validated against the triple tracertechnique [59], [67], [68] which provided virtually model-inde-pendent estimates of such glucose fluxes (Fig. 12) [58].

3) From Whole-Body to Organ/Tissue: While whole-bodymodels can provide important quantitative information on in-sulin action, it is important but at the same time remarkably dif-ficult, to noninvasively measure the processes of glucose trans-port and metabolism at the organ level. A crucial target tissueof glucose metabolism is the skeletal muscle. Impaired insulintransport within the muscle is a well-recognized characteristicof a number of metabolic diseases, including type 2 diabetes,obesity, hypertension, and cardiovascular disease [69]. Under-standing its causes requires us to segregate and quantify in situthe major individual steps of glucose processing, particularlythose of glucose delivery, transport in and out of the cell, andphosphorylation (Fig. 13).

There are two major experimental techniques to tackle thisproblem, both employing tracers with glucose metabolism at


Fig. 13. Major glucose processing: diffusion to/from the intersitium, activetransport in and out of the cell, and phosphorylation/metabolism.

steady state. The classical experimental approach is based onthe multiple tracer dilution [70]. This model consists of the si-multaneous injection, upstream of the organ, of more than onetracer which allows the separate monitoring of the individualsteps of glucose metabolism. For example, in the case when theobjective of the experiment is the measure of all the elementaryprocesses (convection, diffusion, transport, and metabolism),usually one can simultaneously inject upstream of the organ(artery) and measure downstream (vein) a first tracer that is dis-tributed only in the capillary bed (intravascular tracer), a secondthat is subject to the bidirectional exchange through the capil-lary membrane (extracellular tracer), a third that also perme-ates the cell through the sarcolemma (permeating not metabo-lizable tracer), and, finally, a fourth that is also metabolized (per-meating metabolizable tracer). These tracers must obviously bedistinguishable once they reach the organ outflow. The venousoutflow curves must then be analyzed by means of a physio-logical system model. More recently, the positron emission to-mography (PET) noninvasive imaging technique was proposed.Using appropriate tracers, PET can provide highly specific andrich biochemical information if applied in dynamic mode, i.e.,sequential tissue images acquired following a bolus injection oftracer so that the time course of the tissue metabolism can bemonitored. Again, a physiological system model is needed tointerpret the data. Unlike the multiple tracer dilution technique,here tracers cannot be injected simultaneously but only sequen-tially.

Multiple tracer dilution data can be interpreted with bothlinear distributed parameter (see reviews [18] and [71] andcompartmental organ models [72]. The only application toglucose metabolism of distributed parameter models has beenin an isolated and perfused heart [70]. In contrast and despiteshort history, compartmental organ models have been moreintensively applied to interpret multiple tracer dilution datain the human skeletal muscle. A compartmental model hasbeen proposed [73] describing the transmembrane transport ofglucose. The model has been developed from multiple tracerdilution data obtained in human skeletal muscle in vivo usingtwo tracers, one extracellular ( -glucose) and the otherpermeant, nonmetabolizable ( C -3-O-methyl-D-glucose).This allows us to estimate with very good precision the rate

constants of glucose transport into and out of the cell. Conse-quently, this model allowed us to study the enhancing effect ofinsulin on muscle glucose transport parameters in nondiabeticsubjects [73] and identified the presence of a localized defectin insulin control in non-insulin-dependent diabetic (NIDD)patients [74]. This compartmental model has been extended[76] to describe the kinetics of a third tracer, permeant nonme-tabolizable ( -glucose). The gain obtained by adding to theexperimental protocol a third tracer is immense. This ultimatelyallowed us to quantify a model of the tracee and therefore studynot only the rate constants of transport and phosphorylation butalso the bidirectional glucose flux through the cell membrane,the phosphorylation flux, and the intracellular concentration,in nondiabetic, obese and diabetic subjects [75]–[77]. Thisallowed important physiological results to be obtained. Amongthese, it was possible to show that the insulin control on bothtransmembrane transport and phosphorylation flux in subjectsaffected by NIDDM is much less efficient with respect tonondiabetic subjects [76], [77]. Therefore, the model enableddemonstration of the fact that cellular transport plays a veryimportant role in the insulin resistance associated with NIDDM.

PET data can be analyzed by several modeling strategieswith regional compartmental modeling being the most pow-erful approach to connect organ or tissue concentration datainto measures of physiological parameters. In this respect,the brain glucose model by Sokoloff et al. [78] has been alandmark. The selected tracer for studying glucose metabolismin skeletal muscle (but also in the brain and myocardium) is

F fluorodeoxyglucose F FDG , a glucose analog. Theideal tracer would be C -glucose but the interpretative modelby having to account for all metabolic products along theglycolysis and glycogen synthetic pathways would be unrea-sonable from the limited information content of PET data. Theadvantage of F FDG is that a simpler model can be adopted.In fact, F FDG once in the tissue, similarly to glucose, caneither be transported back to plasma or can be phosphorilated to

F FDG , F FDG . The advantageis that F FDG is trapped in the tissue and releasedvery slowly. In other words, F FDG cannot be metab-olized further, while glucose-6-P does so along the glycolysisand glycogenosynthesis pathways. The major disadvantageof F FDG is the necessity to correct for the differences intransport and phosphorylation between the analog F FDGand glucose. A correction factor called lumped constant (LC)can be employed to convert F FDG fractional uptake (butnot the F FDG transport rate parameters) to that of glucose.LC values in human skeletal muscle are available [79], [80]. Inorder to provide rate constants of transport and phosphorylationof F FDG in skeletal muscle, a four-compartment model(plasma, extracellular, tissue F FDG, and F FDG )with five rate constants has been proposed [81]. The model(Fig. 14) is described by

C C C C C

C C C C

C C C (19)


Fig. 14. The 5 k model of � F�FDG in skeletal muscle: C is � F�FDG plasmaarterial concentration, C extracellular concentration of � F�FDG normalizedto tissue volume, C � F�FDG tissue concentration, C � F�FDG � � � �tissue concentration, total F activity concentration in the ROI, � [ml/ml/min] and � �� the exchange between plasma and extracellular space,� �� and � �� transport in and out of cell, � �� phospho-rylation.

C C C C C (20)

where C is F FDG plasma arterial concentration, C is extra-cellular concentration of F FDG normalized to tissue volume,C F FDG is tissue concentration, C F FDGis tissue concentration, C is total F activity concentration inthe ROI, [ml/ml/min] and are the exchanges be-tween plasma and extracellular space, ,is the rate of transport in and out of cell, and is therate of phophorylation. is the fractional blood volume in theregion of interest, and C is the whole blood tracer concentra-tion. From the model one can calculate the fractional uptake of

F FDG, K [ml/ml/min]

(21)

and, by using LC value and the glucose basal plasma concen-tration value, the glucose fractional uptake. F FDG rate con-stants of transport and phosphorylation are inefficient in obesityand type 2 diabetes, but these defects can be substantially re-versed with weight loss [82].

To move to a glucose representation a multi-tracer positronemission tomography (PET) imaging method is needed [83],which allows the simultaneous assessment of blood flow, glu-cose transport, and phosphorylation in the skeletal muscle. Themethod employs three different PET tracers (Fig. 15) injectedat different times, and allows us to quantify blood flow from

H O images with one- compartment two-rate constantmodel; glucose transport from C -OMG images with a threecompartment four-rate constant model; and, finally, glucosephosphorylation by combining F FDG fractional uptakewith C -OMG rate constants. The C -OMG model is asimpler version of that of (19), (20) since C -OMG is notphosphorylated. This multi-tracer model-based PET imagingmethod has shown that glucose transport from plasma intointerstitial space is virtually identical to tissue perfusion andnot affected by insulin; insulin significantly increases bothglucose transport and phosphorylation modulating distributionof control among delivery, transport, and phosphorylation(glucose delivery and transport contribute nearly equally to the

Fig. 15. Employment of PET tracers to study glucose diffusion through capil-lary membrane, active transport into the cells and metabolism.

control of glucose uptake accounting for 90% of control to-gether); predominately oxidative muscles (soleus) have higherperfusion and higher capacity for glucose phosphorylation thanless oxidative muscles (tibialis).

C. Insulin System

Here, we describe some models of the insulin system and thecontrol exerted by glucose on insulin secretion.

1) Insulin Kinetics: To study insulin kinetics in the steadystate a tracer would be the ideal probe. Tracer studies have beenperformed, e.g., by using radioactive isotopes of iodine or hy-drogen, but ideal tracer prerequisites such as tracer-tracee in-distinguishability and nonnegligible perturbation, are not com-pletely met. The majority of insulin kinetic studies have beenperformed by pulse injection or infusion. However, the admin-istration of a nontrace amount of insulin has two undesired ef-fects: first, it may induce hypoglycemia, which in turn couldtrigger counterregulatory response that may affect insulin ki-netics; second, it inhibits insulin secretion, thus the measuredinsulin concentration contains a time-varying endogenous com-ponent. These confounding effects can be avoided by designinga rather complex experiment, where hypoglycemia is preventedby variable glucose infusion (glucose clamp technique), and en-dogenous insulin secretion is suppressed by somatostatin infu-sion.

In the physiological concentration range (up to 100–150U/ml) where insulin kinetic is approximately linear, various

linear compartmental models have been proposed [84], fol-lowing the landmark model of Sherwin et al. [24] (alreadydiscussed, see Fig. 6, upper panel). Some of these models areshown in Fig. 16. The two-compartment structure is derived bynoting that compartments 1 and 2 in the model of Fig. 6 (upperpanel) are in rapid equilibrium. is the posthepaticinsulin secretion rate, i.e., the flux of newly secreted insulin thatreaches plasma after the first passage through the liver. The twomodels differ in terms of the site of irreversible loss: plasma(Fig. 17, top panel), or peripheral tissues (Fig. 16, middlepanel). Both models are a priori uniquely identifiable. Typicalnumerical values of their parameters are shown in the figure.In the situation where a two-compartment model cannot beresolved from the data, the single compartment model (Fig. 16,bottom panel) can be used.

In the supraphysiological range, nonlinear or lineartime-varying insulin kinetics model are more appropriate.


Fig. 16. Compartmental models of insulin kinetics. Upper panel: two com-partment model with insulin degradation in the accessible compartment; Upperpanel: two compartment model with insulin degradation in the remote compart-ment; Upper panel: one compartment model.

Fig. 17. Schematic representation of insulin (upper) and C-peptide (lower) pan-creatic secretion and kinetics. Insulin is secreted by the beta-cells in the portalvein and extracted by the liver before it appears in plasma; C-peptide is secretedby the beta-cells, equimolarly to insulin, passes through the liver, before it ap-pears in plasma, but is not extracted.

A relatively simple nonlinear two-compartment model, similarto that of Fig. 16, upper panel, has been proposed by Frost etal. [85], with linear transfer rate and but nonlinear irre-versible loss described by the Michaelis-Menten relation.However, the relatively high number of model parameters (six)poses some problems in deriving precise estimates for all ofthem. A nonlinear five-compartment model has been proposedby Hovorka et al. [86], which also incorporates a descriptionof insulin kinetic at the receptor level. Alternatively, linear

time-varying models has also been formulated, e.g., that ofMorishima et al. [87], which assumes constant and andtime-varying .

2) Insulin Secretion: The problem of estimating the secretionprofile in vivo during perturbation from plasma concentrationmeasurements is a classic input estimation problem for whichdeconvolution offers the classic solution. However, it is not pos-sible to infer on pancreatic secretion from plasma insulin con-centration data; it is only possible to derive its component ap-pearing in plasma, or the posthepatic insulin secretion, whichis approximately equal to 50% of the pancreatic secretion. Thisproblem can be bypassed if C-peptide concentration is measuredduring the perturbation and used to estimate insulin secretionsince C-peptide is secreted equimolarly with insulin, but it isextracted by the liver to a negligible extent (Fig. 17). In otherwords, plasma C-peptide concentration well reflects, apart fromthe rapid liver dynamics, C-peptide pancreatic secretion, whichcoincides with insulin secretion.

Since there is solid evidence that C-peptide kinetics are linearin a wide range of concentration, the relationship between abovebasal pancreatic secretion (SR, the input), and the above basalC-peptide concentration measurements (C, the output) is theconvolution integral

(22)

where is the impulse response function of the system. SR pro-file during a perturbation can be reconstructed by solving theinverse problem, which is deriving SR by deconvolution, givenC and . The knowledge of the impulse response is a prereq-uisite. This requires an additional experiment on the same sub-ject, consisting of a bolus of C-peptide and a concomitant infu-sion of somatostatin to inhibit endogenous C-peptide secretion.Usually, C-peptide concentration data are then approximatedby a sum of two exponential models that, after normalizationto the C-peptide dose, provide the impulse response function[88], [96]. Deconvolution methods have been applied to esti-mate the secretion profile in various physiological states [89],[90] and during both intravenous and oral glucose tolerance tests[91]–[93].

To eliminate the need for a separate experiment to evaluatethe impulse response function, a method has been proposed [94]to derive C-peptide kinetic parameters in an individual basedon data about his or her age, weight, height and gender. Secre-tion reconstructed by deconvolution, whith the impulse func-tion evaluated from either the C-peptide bolus experiment or thepopulation parameters are similar [94], indicating that the pop-ulation values allow a good prediction of individual secretionprofiles.

As for pancreatic insulin secretion, an indirect measurementapproach is essential to quantify hepatic insulin extraction in hu-mans since the direct measurement requires invasive protocols,with catheters placed in a artery and hepatic vein [84]. Deconvo-lution offers a possible solution since by comparing pancreatic


Fig. 18. Left panel: IVGTT C-peptide minimal model. Right panel: OGTT/MTT C-peptide minimal model.

Fig. 19. Disposition index paradigm. Left panel: a normal individual could be represent by state I; if beta-cells respond to a decrease in insulin sensitivity byadequately increasing insulin secretion (state II) the product of beta-cell function and insulin sensitivity (the disposition index) is unchanged, and normal glucosetolerance is retained. In contrast, if there is not an adequate compensatory increase in beta-cell function to the decreased insulin sensitivity (state 2) the individualdevelops glucose intolerance. Right panel: importance of segregating glucose tolerance into its individual components of beta-cell responsivity and insulin sensi-tivity. Subject x is intolerant due to its poor beta-cell function while subject y has poor insulin sensitivity; these two individuals need opposite therapy vectors.

secretion rate (SR) obtained from C-peptide data and posthep-atic secretion obtained from insulin data—one can es-timate hepatic extraction as

(23)

Estimation of by deconvolution is straightforward ifinsulin levels are in the physiological range since the kineticmodel is linear, while it becomes more problematic if insulinlevels are supraphysiological. In this last case, the link between

and insulin concentration (I) is given by

(24)

with representing the impulsive response of the lineartime-varying insulin kinetic system.

3) Beta-Cell Function: Deconvolution allows us to measurein a virtually model-independent way insulin secretion after aglucose stimulus. However, giving a mechanistic description of

pancreatic insulin secretion as a function of plasma glucose con-centration has the advantage to provide quantitative indices ofbeta-cell function.

The minimal modeling methodology is similar to that em-ployed to derive the glucose minimal model: the system is de-composed in two subsystems (Fig. 8.), but this time we look atthe insulin subsystem with plasma glucose, G, considered the“input” (assumed known) and C-peptide, C, the “output” (as-sumed noisy).

Since the secretion model is identified on C-peptide measure-ments taken in plasma, it must be integrated into a model ofwhole-body C-peptide kinetics, which has two compartments[88].

During IVGTT, the above-basal insulin secretion [97] is givenby (Fig. 18, left)

(25)

with the ready releasable insulin described by

(26)


with the amount of insulin released immediately after theglucose stimulus; is the provision of new insulin, whichdepends on glucose level

(27)

and

(28)

In other words, insulin secretion consists of two components:first and second phase secretion. First phase secretion is por-trayed by a rapidly turning-over compartment (2 min) andlikely represents exocytosis of previously primed insulin secre-tory granules (commonly called readily releasable). It exertsderivative control, since it is proportional to the rate of increaseof glucose from basal up to the maximum through a parameter[28], , which defines the first responsivity index

(29)

with the difference between peak and basal glucose con-centration.

Second phase insulin secretion is believed to be derived fromthe provision and/or docking of new insulin secretory granulesthat occurs in response to a given (i.e., proportional to) glu-cose concentration, through a parameter , which defines thesecond phase responsivity index, and reaching the releasablepool with a delay time constant,

(30)

The meaning of and can be explained by analyzing modelparameters under the above-basal step increase of glucose: pro-vision tends with time constant towards a steady state, whichis linearly related to the glucose step size through parameter .

presumably represents the time required for new “readily re-leasable” granules to dock, be primed, then exocytosed. In ad-dition to and , a basal responsivity index can also be cal-culated, . Finally, a single total index of stimulated beta-cellresponsivity, , can be derived by combining and .Of note, in [97] it has been shown that population values are alsoa good predictor of the individual kinetic parameters. However,additional uncertainty is brought in by the population approach[98], which can be taken into account into a Bayesian setting viaMarkov Chain Monte Carlo [99].

Beta-cell function can also be assessed from an oral test, suchas meal or OGTT. An oral glucose test differs from IVGTT inseveral important aspects including the route of delivery withthe associated incretin hormone secretion, the more physiolog-ical and smoother changes in glucose, insulin, and C-peptideconcentrations, and, during a mixed meal, the presence of non-glucose nutrients stimulation, i.e., amino acids and fat. Var-ious models have been proposed to assess beta-cell function

during a meal and OGTT [95], [100]–[102]. All of them sharethe model of C-peptide kinetics described above, but differ onthe assumption on how glucose controls the secretion. The oralC-peptide minimal model proposed by Breda et al. [101] Fig. 18(right) maintains basically all of the previous model ingredientsemployed in the IVGTT model, with the exception of the fastturning over insulin releasable pool ( , which is not evidentunder these conditions) to describe the data. In particular, botha rate of change of glucose component of insulin secretion anda delay between glucose stimulus and beta-cell response havebeen shown to be necessary to fit the data [103]. Model equa-tions are

(31)

with described by (27) and (28), also called a staticcomponent of insulin secretion, and the dynamiccomponent of insulin secretion

if

if(32)

Thus, this model features a dynamic component that senses therate of change of glucose concentration, and a static componentthat represents the release of insulin that, after a delay, occursin proportion to prevailing glucose concentration. Similarly tothe IVGTT, where first, , and second phase, , beta-cell re-sponsivity indices were defined, from the oral model dynamic,

, and static responsivity indices can be de-rived. Basal responsivity index, , can be obtained as a ratiobetween basal secretion and basal glucose. A total responsivityindex, , which combines and , can also be derived.

The model has been successfully used by Toffolo et al. [104]during “up&down” intravenous glucose infusion and by Steilet al. [105] for describing hyperglycemic clamp C-peptide dataas well as meals, thus providing further independent evidencefor its validity. In contrast to the IVGTT model where thederivative component of first phase secretion was operativeonly during the first few minutes as the plasma glucose concen-tration increased from a “basal” to “maximal” concentration,the relatively gradual pattern of glucose appearance observedduring oral tests necessitated the presence of a secretion com-ponent proportional to glucose rate of change that contributedto the model for the first 60–90 minutes. In addition, and similarto IVGTT, a component of insulin secretion proportional toglucose, characterized by a delay time (presumably reflectingat least in part the time it takes for new granules to reach thereleasable pool), that contributed throughout the experimentalperiod, was also necessary. As discussed above, is markedlydifferent from its IVGTT counterparts . In fact, duringIVGTT first phase component only contributed during the first4–6 minutes and the proportional component for the rest oftest. Thus, it is probable that and are assessing differentaspects of the insulin secretory pathway. In particular,presumably could also reflect multiple distal steps includingthe rate of granule docking, priming as well as exocytosis.


Fig. 20. Scheme of the glucose-insulin control system which relates measured plasma concentrations, i.e., glucose and insulin, to glucose fluxes, i.e., rate ofappearance, production, utilization, renal extraction, and insulin fluxes, i.e., secretion and degradation.

The model proposed by Hovorka et al. [95] assumes an in-stantaneous linear control of glucose on insulin secretion; i.e.,there is no delay between glucose stimulus and beta-cell re-sponse. The model proposed by Cretti et al. [100] describes in-sulin secretion with the static component of glucose control ofthe C-peptide minimal model; thus, it is characterized by a delaybut does not include any dynamic, i.e., rate of change, glucosecontrol. Interestingly, the same authors have recently included adynamic control to describe first phase secretion in a subsequentreport [106]. The model proposed by Mari et al. [102], similarlyto the oral model shown in Fig. 18 right, has both a proportionalcomponent and a component responsive to the rate of changeof glucose, but there is no delay between glucose signaling andsupply of new insulin to the circulation. The authors choose toaccount for the expected inability of a proportional plus deriva-tive glucose control to account for C-peptide measurements witha time-varying term correcting only the static component of in-sulin secretion, which has been called the potentiation factor. Insimple words, the potentiation factor is a time-varying correc-tion term that mathematically compensates for the proportionalplus derivative description deficiency.

4) Disposition Index: It is worth noting that beta-cell func-tion needs to be interpreted in light of the prevailing insulinsensitivity. One possibility is to resort to a normalization ofbeta-cell function based on the disposition index paradigm,first introduced in 1981 [35], and recently revisited in [28],where beta-cell function is multiplied by insulin sensitivity.This concept, self-evident in Fig. 8, is more clearly illustratedin Fig. 20 (left). While regulation of carbohydrate toleranceis undoubtedly more complex, it is conceived that glucose

tolerance of an individual is related to the product of beta-cellfunction and insulin sensitivity. In essence, different valuesof tolerance are represented by different hyperbolas, i.e.,DI beta-cell function insulin sensitivity const. If an indi-vidual’s beta-cells respond to a decrease in insulin sensitivityby adequately increasing insulin secretion (state II) the productof beta-cell function and insulin sensitivity (the dispositionindex) is unchanged, and normal glucose tolerance is retained.In contrast, if there is an inadequate compensatory increasein beta-cell function to the decreased insulin sensitivity (state2), the individual develops glucose intolerance. Thanks to itsintuitive and reasonable grounds, this measure of beta-cell func-tionality, which was first introduced for IVGTT, has become themethod of choice also with the meal and OGTT test. Thus, dis-position indices , , or , ,can be calculated by multiplying responsivity indices , ,

by (for IVGTT) or by multiplying respon-sivity indices , , by (for meal/OGTT) todetermine if the first phase, second phase, global beta-cell func-tion is appropriate in light of the prevailing insulin sensitivity.Another important use of the disposition index paradigm is themonitoring in time of the individual components of toleranceand the assessment of different treatment strategies. It is easilyappreciated from Fig. 20 (right) the importance of segregatingglucose tolerance into its individual components of beta-cellresponsivity and insulin sensitivity: subject x is intolerant dueto its poor beta-cell function while subject y has a poor insulinsensitivity and these two individuals need opposite therapyvectors. However, the glucose-insulin feedback system is morecomplex than the hyperbola paradigm. The relation between


beta-cell function and insulin sensitivity is certainly describableby a nonlinear inverse relationship but is in all likelihood morecomplex than a simple hyperbola, i.e., the relation is more likelyDI beta-cell function insulin sensitivity constant.In addition, this simple concept hides several methodologicalissues which, unless fully appreciated, could lead to errors ininterpretation. Some critical questions are: is it true that thehyperbolic relationship holds in a population? How shouldthe disposition indices be used in comparing populations,i.e., should the individual values be averaged, or should thedisposition index be estimated directly in the population? Howshould the population variability accounted for? Also, sincethe effect of insulin on peripheral tissues is also determined bythe amount of insulin to which the tissue is exposed, hepaticinsulin extraction may come into play (see the following) andprovide yet another dimension to the relationship betweeninsulin secretion and action portrayed in Fig. 20. Some of theseaspects have been recently examined in [28] and [107].

5) Hepatic Insulin Extraction: Minimal models also providean approach to assess hepatic insulin extraction. In fact, SR canbe assessed from the model of C-peptide kinetics and secretionidentified from C-pepide and glucose measured during IVGTTor meal or OGTT. By following a similar approach,can be assessed by insulin and glucose data. In particular, in-sulin-modified IVGTT experiment, i.e., an IVGTT associatedwith short insulin infusion given between 20 and 25 minutesafter the glucose bolus, offers definitive advantages with respectto the standard IVGTT since the insulin infusion generates anadditional disappearance curve that greatly facilitates the simul-taneous estimation of insulin kinetic and secretion parameters.Hepatic insulin extraction can then be calculated from SR and

profiles [106]. During meal and OGTT the situationis more complicated, however, a recent study [108] proposesa population model, which, similarly to the widely used VanCauter formulas [94], allows us to calculate insulin kinetic pa-rameters from subject anthropometric characteristic, such age,gender, body surface area, etc., avoiding the necessity to infuseexogenous insulin. From pre- and post-hepatic insulin secretionrates, hepatic insulin extraction time course can be derived asfor the IVGTT. In addition, from pre- and post-hepatic modelparameters an index of hepatic extraction can also be calculated[108], [109].

D. Clinical Studies

It is well beyond the scope of this contribution to reviewmodel-based phathophysiological studies. However, it may behelpful for the reader to refer to specific instances where an an-swer to a diabetes-related question has been provided by a sys-tematic use of models. For instance, the battery of oral glucose,C-peptide, and insulin models have been used in studying: theeffect of age and gender on glucose metabolism [59]; the ef-fect of anti-aging drugs [110]; the influence of ethnicity [111];insulin sensitivity and beta-cell function in nondiabetic [112]and obese [113] adolescents; the pathogenesis of prediabetes[114]–[116] and type 2 diabetes [117], [118].

IV. MAXIMAL MODELS

A. Rationale

In contrast to minimal, maximal (fine-grain) models are com-prehensive descriptions attempting to fully implement the bodyof knowledge about metabolic regulation into a generally large,nonlinear model of high order, with a large number of param-eters. This class of models cannot, in general, be identified,i.e., without massive experimental investigation on a single in-dividual it is not possible to relate with confidence alterationsin the dynamics of blood-borne substances to specific changesin parameters of a comprehensive model. This means that thesemodels are not generally useful for the quantification of spe-cific metabolic relationships—their utility is in the possibilityfor system simulation.

Simulation is a powerful investigative tool, particularly in theengineering disciplines where the system structure and functionis usually “known” and equations can be written based on firstprinciples. In contrast, a physiological system is largely “un-known” in terms of structure and function, i.e., equations canalways be written but the problem is model validity. Althoughstrategies for validation of a complex (versus simple) modelhave been delineated [17], [119], the difficulties of the problemremain.

In metabolism and diabetes, large scale models have been ofvalue as research tool, i.e., to test a theory or incompatibilitiesof theories. A classic is the insulin secretion model of Grodsky[120] where in order to describe insulin secretion patterns in re-sponse to a variety of glucose stimuli, he postulated that insulingranules were not a homogeneous pool. While the threshold hy-pothesis he introduced (i.e., each granule has a certain glucosethreshold above which it releases the content) has gained littlesupport from subsequent experiments, the non-homogeneity ofinsulin—containing granules pool is today an accepted notionand various beta-cell biology theories have been put forward.Another example is the glucose-insulin simulation model bySturis et al. [121], which offered an explanation of why wideultradian oscillations (period of 120 min in humans) occur ininsulin and glucose profiles in various physiological conditions,stating that they can originate from the interaction between theglucose and insulin subsystems without the need to invoke thepresence of a pancreatic pacemaker operating at these frequen-cies.

Another important area for maximal models is their use as testbeds for examining the empirical validity of models intendedfor clinical applications. For instance, in [122] and [123] theconsequences of undermodeling the glucose system by usingthe classic IVGTT single compartment minimal model has beenstudied by using a richer IVGTT two compartment glucose-in-sulin simulation model.

Finally, simulation models have been proven useful in ateaching setting as heuristic devices providing easy and quickanswers to “what if” questions. Some good examples on sim-ulators being an efficient library of physiological knowledgeare [124]–[126].

A classic simulation is in silico experimentation, which in dis-ciplines like engineering is carried out in everyday life; a recentsuccess is the Boeing 777 jetliner, which has been recognized


as the first airplane to be 100% digitally designed and assem-bled in a computer simulation environment. This important useof simulation has not had the expected impact in metabolismand diabetes. However, there are situations where in silico ex-periments with complex models could be of enormous value. Infact, it is often not possible, appropriate, convenient, or desir-able to perform an experiment on the glucose system, becauseit cannot be done at all, or it is too difficult, too dangerous, orunethical. In such cases, simulation offers an alternative wayof in silico experimenting on the system. Simulation modelshave been published and used to examine various aspects of dia-betes control, e.g., for assessing different control algorithms anddifferent insulin infusion routes [122], [127]–[138]. Althoughthe confidence in their results is certainly higher than that ob-tained using as simulator the glucose minimal model [25] (ex-tensively misused for this purpose and recently being the coreof the Medtronic Virtual Patient [139]), the impact has beenvery modest. All these models are average population modelsand as a result their capabilities are generally limited to pre-diction of population averages that would be observed duringclinical trials. An average-model approach is not realistic for insilico experimentation. A different approach is needed in orderto provide valuable information about the safety and the limita-tions of control algorithms, or to guide and focus emphasis ofclinical studies, or to rule out ineffective control scenarios in acost-effective manner prior to human use. It is necessary to havea diabetes simulator equipped with a cohort of in silico subjectsthat spans sufficiently well the observed interperson variabilityof key metabolic parameters in the general population of people,say with type 1 or type 2 diabetes.

In the following, we discuss in detail a whole-body glucose-insulin simulator and an organ/cellular-level insulin secretionsimulator. The healthy state glucose-insulin simulator is pre-sented first, then prediabetes and type 2 diabetes version arediscussed. Finally, we describe the type 1 diabetes simulator,which was recently accepted by FDA as a substitute of preclin-ical animal trials for certain insulin treatments [140].

B. Healthy State Simulator

The rationale was to identify the glucose-insulin meal simu-lation model [137], developed on average data, in each of 204nondiabetic individuals. All these subjects underwent a tripletracer meal protocol which provided virtually model-indepen-dent estimates of crucial fluxes of the system, i.e., the rate ofappearance in plasma of ingested glucose, glucose production,glucose utilization, and insulin secretion [59]. This flux infor-mation was key to developing with confidence a large scale max-imal model, i.e., with only plasma glucose and insulin concen-tration this exercise is practically impossible since one cannotobtain a good description of the multiple system fluxes (Fig. 20).Fig. 21 shows the database and allows appreciation of the rel-evance of interindividual variability. Thanks to this rich “con-centration and flux” representation, the glucose-insulin systemmodel was identified by resorting to a subsystem forcing func-tion strategy, which minimizes structural uncertainties in mod-eling the various subsystems. The rationale is shown in Fig. 22.As an example consider the glucose utilization subsystem (see

[137] for details). Glucose kinetics is described with a two com-partment model. Insulin-independent utilization takes place inthe first compartment, is constant, and represents glucose up-take by the brain and erythrocytes

(33)

Insulin-dependent utilization takes place in the remote compart-ment and depends nonlinearly (Michaelis–Menten) from glu-cose in the tissues

(34)

where is glucose mass in the insulin-dependent tissuesand is assumed to be linearly dependent on a remoteinsulin

(35)

(pmol/L) is insulin in the interstitial fluid described by

(36)

where is plasma insulin, suffix denotes basal state, andis rate constant of insulin action on the peripheral glucose uti-lization.

Total glucose utilization is thus

(37)

For each of the 204 subjects included in the database, the glu-cose kinetics model equipped with (33)–(37) was numericallyidentified using the measured glucose utilization (U) and con-centration (G) as output and plasma insulin, endogenous glu-cose production and glucose rate of appearance as known inputs(Fig. 22, bottom left panel).

The other subsystems of Fig. 22 have been identified fol-lowing a similar strategy (more details can be found in [137]).

The model consists of 12 differential equations and 35 param-eters, 26 of which are free and nine derived from steady-stateconstraints.

From the 204 subjects model parameters and their joint prob-ability distribution in the healthy population were reconstructed.Since most parameters were approximately log-normally dis-tributed, this probability distribution is uniquely defined by theaverage vector and the covariance matrix of the log-transformedparameter vector. Given the joint distribution, virtual subjectscan be generated, i.e., say 1000 realizations of the log-trans-formed parameter vector can be sampled randomly from themultivariate normal distribution, thereby producing 1000 virtualin silico “subjects.”

Fig. 23 shows examples of daily glucose patterns in somegenerated in silico subjects.


Fig. 21. Mixed meal data base (average of 204 nondiabetic subjects, grey area represents mean�1SD range). Top panel: glucose (left) and insulin (right) concen-trations. Middle panel: endogenous glucose production (left) and glucose rate of appearance (right). Bottom panel: glucose utilization (left) and insulin secretion(right).

C. Prediabetes and Type 2 Diabetes Simulator

A prediabetes and type 2 diabetes simulators would be veryuseful to assess the efficacy of various drug therapies before per-forming experiments in humans. A triple tracer protocol mealdata base, similar to that available in nondiabetics, was avail-able for 35 prediabetic and 23 type 2 diabetic subjects. Thesame modeling strategy developed for the Healthy State Sim-ulator was adopted. The model consists of 12 differential equa-tion and 35 parameters (26 of which are free) [137], [138]. Thesimulator can generate cohorts of virtual subjects, thus enabling

various diabetes treatments to be assessed rapidly in cost-effec-tive in silico experiments.

D. Type 1 Diabetes Simulator

A type 1 diabetes version of the simulator would be criticalfor the preclinical testing of control strategies in artificial pan-creas studies. Arguably, large-scale simulations would accountbetter for intersubject variability than small-size animal trialsand would allow for more extensive testing of the limits and ro-bustness of control algorithms. A first necessary modification


Fig. 22. Unit process models and forcing function strategy: endogenous glucose production (top left panel); glucose rate of appearance (top right panel); glucoseutilization (bottom left panel); insulin secretion (bottom right panel). Entering arrows represent forcing function variables, outgoing arrows are model output.

Fig. 23. Example of daily glucose concentration in some generated in silico subjects.

was the substitution of insulin secretion subsystem with an ex-ogenous insulin delivery subsystem, e.g., a subcutaneous (sc)insulin pump an associated model of insulin kinetics and ab-sorption. Subcutaneous insulin transport has been extensivelymodeled and quantitative models exist [142], [285], [286] whichallowed both the estimation of the timing and duration of insulinaction from insulin pump data, and their computer simulationin in silico experiments. One approach includes a two-compart-ment model approximating nonmonomeric and monomeric in-sulin fractions in the subcutaneous space [285], which can serve

as a base for the translation of the insulin signal from the pumpto insulin in the circulation.

A much more difficult task was the description of the inter-subject variability, since even single-tracer studies in type 1 dia-betes are scarce. In order to obtain parameter joint distributionsin type 1 diabetes from those in the healthy state, we assumedthat the intersubject variability was the same (same covariancematrix), but certain clinically relevant modifications were intro-duced in the average vector. The model consists of 13 differen-tial equation and 35 parameters (26 of which are free and nine


Fig. 24. Employment of the type 1 diabetes simulator for testing closed-loop control algorithm for insulin infusion.

derived from steady-state constraints). The simulator has beentested by several experiments in adults, adolescents, and chil-dren to assess the validity of the cohort of in silico subjects. Thesimulator (Fig. 24) is equipped with 100 virtual adults, 100 ado-lescents, and 100 children, spanning the variability of the T1DMpopulation observed in vivo. In addition to virtual “subjects,”the simulator is equipped with mechanisms reproducing CGMerrors, e.g., virtual “sensors” that can be placed on the “sub-jects” for in silico closed-loop control experiments. Subcuta-neous insulin delivery is modeled as well, which allows placingvirtual “insulin pumps” on the subjects for full-scale open- orclosed-loop control experiments with any predefined treatmentscenario. In January 2008, the simulator was accepted by theFood and Drug Administration (FDA) as a substitute to animaltrials for the preclinical testing of control strategies in artificialpancreas studies and has been adopted by the JDRF ArtificialPancreas Consortium as a primary test bed for new closed-loopcontrol algorithms. The simulator was immediately put to itsintended use with the in silico testing of a new Model Predic-tive Control algorithm [141], and in April 2008, an investiga-tional device exemption (IDE) was granted by the FDA for aclosed-loop control clinical trial (see Section VI). This IDE wasissued solely on the basis of in silico testing of the safety andeffectiveness of the proposed artificial pancreas algorithm, anevent that sets a precedent for future preclinical studies. Thus,the following paradigm has emerged: 1) in silico modeling couldproduce credible preclinical results that could substitute certainanimal trials and 2) in silico testing yields these results in a frac-tion of the time and the cost required for animal trials. However,one needs to emphasize that good in silico performance of a con-trol algorithm does not guarantee in vivo performance; it onlyhelps to test extreme situations and the stability of the algorithm

and to rule out inefficient scenarios. Thus, computer simulationis only a prerequisite to, but not a substitute for, clinical trials.

In addition to the simulator described above [137], [247], an-other simulation environment has been developed with the coreglucose-insulin model detailed in [136] which is used by theUniversity of Cambridge in the JDRF Artificial Pancreas Pro-gram. The model [136] has been built for being the model in-gredient of a closed loop MPC algorithm. The model, coupled toa subcutaneous insulin kinetic model [142], consists of 11 dif-ferential equations and 20 parameters. The strategy to describethe population variability differs from that described above. Thesimulator presently includes 18 type 1 synthetic subjects de-fined by 20 parameter sets. A subset of six parameters was es-timated from experimental data collected in type 1 subjects andthe remaining 14 obtained from the literature. An important usehas been the assessment of hypoglycemia and hyperglycemiarisk during overnight with closed-loop Model Predictive Con-trol versus open-loop insulin delivery [143].

E. Insulin Secretion

Another useful application of simulation models is hypoth-esis pilot testing. For instance, simulation models have beenused to investigate the cellular mechanisms which lead pancre-atic beta-cells to secrete insulin. Beta-cells show bursting elec-trical activity and oscillatory calcium levels and insulin secre-tion and modeling has contributed significantly to the under-standing of the generation of these rhythmic patterns (see re-views in [144] and [145]). However, surprisingly little work hasbeen done on detailed modeling insulin secretion. Already inthe 1970s, Grodsky [120] and Cerasi et al. [146], among others,modeled the pancreatic insulin response to various kinds of glu-cose stimuli, but these models were phenomenological due to


the limited knowledge of the beta-cell biology at that time. Onlyrecently has the knowledge of the control of the movement andfusion of insulin granules increased to a level where it is pos-sible to formulate mechanistically based models. Here, we dis-cuss some recent developments on cellular simulation modelsof insulin secretion serving as research tool at organ level topilot-test new theories.

Grodsky [120] proposed that insulin was located in “packets,”plausibly the insulin containing granules, but also possibly en-tire beta-cells. Some of the insulin was stored in a reservepool, while other insulin packets were located in a labilepool, ready for release in response to glucose. The labilepool was responsible for the first phase of insulin secretion[120], while the reserve pool was responsible for creating asustained second phase. This basic distinction has been, atleast partly, confirmed when the packets are identified withgranules [147], [148]. Moreover, Grodsky [120] assumed thatthe labile pool is heterogeneous in the sense that the packetsin the pool have different thresholds with respect to glucose,beyond which they release their content. This assumption wasnecessary for explaining the so-called staircase experiment,where the glucose concentration was stepped up and each stepgave rise to a peak of insulin. There is no supporting evidencefor granules having different thresholds [149], but Grodsky[120] mentioned that cells apparently have different thresholdsbased on electro-physiological measurements. Later, Jonkersand Henquin [150] showed that the number of active cells is asigmoidal function of the glucose concentration, as assumed byGrodsky [120] or the threshold distribution.

Recently, Pedersen et al. [151] unified the threshold distri-bution for cells with the pool description for granules, thus pro-viding an updated version of Grodsky’s model, which also takesinto account recent knowledge of beta-cell biology. The modelscheme is shown in Fig. 25 (top panel). It includes mobiliza-tion of secretory granules from a very large reserve pool tothe cell periphery, where they attach to the plasma membrane(docking). The granules can mature further (priming) and attachto calcium channels, thus entering the “readily releasable pool”(RRP). Calcium influx provides the signal triggering membranefusion, and the insulin molecules can then be released into theextracellular space. Also included is the possibility of so-calledkiss-and-run exocytosis, where the fusion pore reseals beforethe granule cargo is released. For the mathematical formulationthe mobilized and docked pools have been lumped into a single“intermediate pool” (Fig. 25, lower panel). The glucose-depen-dent increase in the number of cells showing a calcium signal[150] was included by distinguishing between readily releasablegranules in silent and active cells. Therefore, the RRP is hetero-geneous in the sense that only granules residing in cells with athreshold for calcium activity below the ambient glucose con-centration are allowed to fuse. Hence, the model provides a bi-ologically founded explanation for the heterogeneity assumedby Grodsky [120] and it is able to simulate the characteristicbiphasic insulin secretion pattern in response to a step in glucosestimulation, as well as the secretory profile of the staircase stim-ulation protocol (Fig. 26). The model is a classic compartmental

Fig. 25. Upper panel: overview of the in silico model of insulin secretion whichincludes mobilization of secretory granules from a very large reserve pool to thecell periphery, where they attach to the plasma membrane (docking). The gran-ules can mature further (priming) and attach to calcium channels, thus enteringthe “readily releasable pool” (RRP). Calcium influx provides the signal trig-gering membrane fusion. Lower panel: mathematical formulation of the model.

one, except from the description of the RRP. The intermediatepool develops according to the mass-balance equation

(38)

where is the mobilization flux, and is the rate of reinter-nalization. The last term describes the flux of granules loosingthe capacity of rapid exocytosis. Mobilization has been modeledsimilarly to Grodsky (1972) by a first-order differential equa-tion.

The RRP is described by a time-varying density functionindicating the amount of insulin in the RRP in beta-cells

with a threshold between and . Granules are primedwith rate and are assumed to loose the capacity of rapid ex-ocytosis with rate . Moreover, if the granule is in a triggeredbeta-cell it will fuse with rate . This leads to the equation

(39)

Here, is the Heaviside step function, which is 1 forand zero otherwise, indicating that fusion only occurs

when the threshold is reached. is total intermediate pool, andthe priming flux distributes among cells according to thefraction of cells with threshold described by the time-constantfunction . Thus, priming is assumed to occur with the same


Fig. 26. Simulation results: insulin secretion (SR) in response to the staircaseglucose stimulation (G).

rate in all cells, but the model takes into account the fractionof cells with the corresponding threshold. The secretion rate isproportional to the size of the fused pool (Fig. 25, bottompanel).

An interesting property of beta-cells that was included inGrodsky’s model is so-called derivative control, i.e., the fact thatthe pancreas senses not only the glucose concentration but alsoits rate of change. Modeling at whole-body level has shown thatthis property is necessary for explaining data, e.g., both IVGTTand OGTT&MTT [101], [152]. Derivative control arises fromthe threshold hypothesis as explained by Grodsky [120] and ingreater detail by Licko [153]. Due to the threshold on cells,the model by Pedersen [151] also possesses derivative control,which is only active when . It is of interest to un-derstand, and is currently under investigation, how the subcel-lular parameters relate to beta-cell responsivity measured bywhole-body minimal models, i.e., , for IVGTT and ,

for OGTT&MTT, e.g., which steps of glucose stimulated in-sulin secretion are impaired in diabetics.

V. SIGNALS

A. Rationale

Historically, the use of signal analysis techniques in thestudy of diabetes physiology started in the late 1970s with thequantification of blood glucose (BG) concentration and othersubstances, such as insulin, C-peptide, and glucagon duringin-hospital monitoring. Some of the principal approaches arediscussed in Section V-B.

Routine field observation of BG fluctuation began with theadvent of self-monitoring (SMBG), which typically provides2–5 BG capillary BG samples per day analyzed by portable glu-cometers. This opened the possibility of studying individuals’glucose fluctuation (and thus the effectiveness of their therapy)

during natural conditions for extended periods of time. The prin-cipal methods for analysis of SMBG data include statistical ap-proaches and risk assessment and are presented in Section V-C.

In the last ten years, new continuous glucose monitoring(CGM) systems capable of monitoring glucose concentrationfrequently (e.g., every 5 minutes) for several days have begunto emerge. Most of CGM systems are minimally invasive andportable, measuring glucose subcutaneously and assessing BGconcentration indirectly via interstitial fluid sampling. Even ifcertain accuracy issues are still unsolved, CGM sensors opennew possibilities in diabetes management, showing encour-aging treatment results and potential for real-time preventionof hypo- and hyper-glycemia. Methodologies and applicationsconcerning CGM sensor data are discussed in Section V-D.

B. Physiological Signals

1) Glucose-Insulin Oscillations: According to a recent re-view, for glucose concentration measured in blood four timescales of BG fluctuation have been identified: 5–15 min cor-responding to pulsatile secretion of insulin; 60–120 min corre-sponding to intrinsic oscillatory phenomena; 150–500 min ac-counting for meals, insulin injection, and other external sched-ules, and 700 min corresponding to circadian rhythm [154].The Nyquist sampling period sufficient to follow the intrinsicblood glucose dynamics in diabetes was estimated at 10 min-utes [155]. The temporal relationship between insulin oscilla-tion and plasma glucose excursions has been attributed to a feed-back loop between beta cell action and endogenous glucose pro-duction [156]. It has been established that the ability of glucoseto entrain ultradian insulin secretion patterns is disturbed in dia-betic and prediabetic individuals [157]–[159], but the exact roleof oscillations in the glucose regulation systems is still underinvestigation [160].

2) Peak Detection and Spectral/Correlation Analysis: Mostof the approaches employed in the 1980s and early 1990s tostudy glucose and insulin oscillations can be traced back topeak-detection methods and spectral/correlation analysis. Peak-detection methods provide information on pulse amplitude andlocation [161]–[164], while spectral/correlation analysis seeksto identify cycles in time series [165], [166]. These methodscan be easily modified to assess the concordance of peaks andthe cross-spectrum/correlation function in order to study the dy-namic relationship between paired time series, e.g., glucose andinsulin [167]–[170]. However, in situations where pulses arebrief, small in amplitude, and irregular, peak detection is dif-ficult. Spectral/correlation analysis is hard to apply to short andnoisy time series, or when the observed cycles are inherentlyirregular. Finally, both peak-detection and spectral/correlationanalysis ignore the morphology of the pulses and cannot de-tect e.g., changes in the pattern of episodic insulin release whichis characteristic of some physiological and patho-physiologicalstates. Overcoming these limitations may require the use of dif-ferent data analysis tools, such as the ApEn described as follows.

3) Hormone Pulsatility and Approximate Entropy: Approx-imate Entropy (ApEn) is a method developed in the early 1990s[171] to quantify the “regularity” of a time series. ApEn detectschanges in underlying episodic behavior not reflected in peak


occurrences or amplitudes. To do so, ApEn assigns a nonnega-tive number to a time series, with larger values correspondingto greater apparent temporal irregularity in the hormone releasepattern over time. Two input parameters, m and r, must be spec-ified to compute ApEn, which then measures the logarithmiclikelihood that runs in the patterns that are close (within r) form contiguous observations remain close (within the same toler-ance r) on the next incremental comparisons [172]. An extensionof this theory has also been proposed to analyze the synchronyof two time series belonging to the same physiologic networkthrough the Cross Approximate Entropy index [173].

To a large extent, ApEn is complementary to peak detectionand spectral analysis in that it evaluates both dominant and sub-ordinate patterns in concentration-time series [174]. Given itsability to detect changes in underlying episodic behavior whichwill not be reflected in pulse occurrences or their characteristics,ApEn acts as a “barometer” of feedback system change in manycoupled systems. ApEn has been utilized to probe the regulationof several hormones including growth hormone [175], aldos-terone [176], cortisol [177], insulin [178], and glucagon [179].Specific to diabetes, it has been reported that insulin secretionpatterns are more irregular in healthy older and obese individ-uals and patients with prediabetes or type II diabetes mellitusthan in young, nonobese, nondiabetic subjects [156]–[159]. Itwas hypothesized that this may in part reflect failure of nega-tive feedback by glucose, and that disorderly insulin secretionpatterns in aging and prediabetes accompany insulin resistance[160]. Methodologically it has also been discussed how, e.g., inhormone secretion studies, the discrimination power of ApEnfrom plasma concentration time series can be influenced by theirkinetics [180], [181].

C. Self Monitoring of Blood Glucose

1) Blood Glucose Self-Monitoring: Blood glucose self-mon-itoring (SMBG) is typically comprised of several episodic BGreadings per day. When rather large time intervals are moni-tored in a given patient, several tools can be used to analyzeSMBG time series. For instance, in [182] and [183], the ex-pected cyclo-stationary behavior of glucose was investigatedby decomposing the SMBG time series into a cyclic compo-nent, that expresses the daily pattern, and a trend component,that describes long-term variations, by a Bayesian method im-plemented by Monte Carlo Markov chains. Another approach,widely accepted to analyze SMBG time series, is risk analysis.A key element to the interpretation of SMBG signals is the use ofthe BG Risk Space, which was introduced over ten years ago andwas based on a transformation of the BG scale that corrects aninherent asymmetry of the hypoglycemic versus hyperglycemicranges [184]. The steps of the SMBG data risk analysis are asfollows.

2) Symmetrization of BG Scale: The BG measurementscale is asymmetric: the hypoglycemic range (below 70 mg/dl)is much narrower numerically than the hyperglycemic rangeBG 180 mg/dl . This asymmetry creates a number of

computational problems and challenges. For example, a BG ex-cursion from 180 to 240 mg/dl is much larger numerically thana BG excursion from 70 to 50 mg/dl, yet the second excursion

carries much greater risk to the patient. The asymmetry of theBG scale can be corrected by using

(40)

where , are parameters determined from the assump-tions

(41)

and

(42)

By multiplying by a third parameter we fix the minimal andmaximal values of the transformed BG range at andrespectively. When solved numerically under the restriction

, these equations give: , , and. These parameters are sample independent and were

fixed in 1997 [184].3) BG Risk Space: After fixing the parameters of f(BG),

we define the quadratic function ,which defines the BG risk space. The function r(BG) rangesfrom 0 to 100. Its minimum value is 0 and is achieved atBG mg/dl, a safe euglycemic BG reading, whileits maximum is reached at the extreme ends of the BG scale20 mg/dl and 600 mg/dl. Thus, r(BG) can be interpreted as ameasure of the risk associated with a certain BG level. Theleft branch of this parabola identifies the risk of hypoglycemia,while the right branch identifies the risk of hyperglycemia[185]. Fig. 27 visualizes this concept by a 72-hour CGM traceof a patient with T1DM: each CGM reading is processed intwo steps: 1) application of the symmetrization formula [184],and 2) application of the quadratic risk function that assignsincreasing weights to larger BG deviations towards hypo- orhyper-glycemia [185]. As seen in Fig. 27, a hypoglycemicepisode occurring at hour 30 of observation is hardly visible inBG scale, but is well pronounced in risk space. Conversely, ahyperglycemic excursion at hour 54 is numerically reduced inrisk space, which corresponds to the notion of relative risk itcarries.

The conversion of the BG data into risk values has profoundimplications not only for the interpretation of the BG signal, butfor control as well because similar emphasis is placed on thehypoglycemic and hyperglycemic ranges; the normal BG range(70–180 mg/dl) is given less weight, thus variability containedwithin normal range carries less risk than excursions outside ofthis range; excursions into extreme hypo- and hyper-glycemiaget progressively increasing risk values.

4) SMBG-Based Risk Metrics: In addition, the conversion ofBG data into risk space has resulted in established metrics forthe risk for hypoglycemia and glucose variability in general. Let

be a series of n BG readings, and let:1) if and 0 otherwise;2) if and 0 otherwise.


Fig. 27. Transforming BG data into risk space equalizing the hypoglycemic and hyperglycemic blood glucose ranges.

The Low Blood Glucose [Risk] Index (LBGI) and the HighBG [Risk] Index (HBGI) are then defined as:

LBGI (43)

and

HBGI (44)

respectively.The LBGI, which is based on the left branch of the BG Risk

Function r(BG) has been validated as an excellent predictor offuture significant hypoglycemia [186], [187]. The LBGI alsoprovides means for classification of the subjects with regard totheir long-term risk for hypoglycemia into: minimal, low, mod-erate and high-risk groups, with LBGI of below 1.1, 1.1–2.5,2.5–5.0, and above 5.0, respectively [187], and has been usedfor short term prediction of hypoglycemia as well [188], [189].By definition, the LBGI is independent from hyperglycemicepisodes.

Further, we define the Average Daily Risk Range (ADRR),which is a measure of overall glycemic variability based onr(BG) and computed as follows.

1) Let be a series of SMBG readings takenon Day 1.

2) Let be a series of SMBG readings takenon Day 2.

3) Let be a series of SMBG readingstaken on Day M.

Thus, and the number of days of observa-tion M is between 14 and 42 (two to six weeks). Further, let

and

for day

The Average Daily Risk Range is then defined as

ADRR (45)

The ADRR has been shown superior to traditional measures interms of risk assessment and prediction of extreme glycemic ex-cursions [190]. Specifically, it has been demonstrated that clas-sification of risk for hypoglycemia based on four ADRR cat-egories: low risk: ADRR ; low-moderate risk:ADRR ; moderate-high risk: ADRR , andhigh risk: ADRR , resulted in over six-fold increase in risk


for hypoglycemia from the lowest to the highest risk category[190].

D. Continuous Glucose Monitoring Time Series

Subcutaneous continuous glucose monitors (CGM) assist thetreatment of diabetes by providing frequent data for the dy-namics of BG. Recent studies have documented the benefits ofCGM [191]–[193] and charted guidelines for clinical use [194]and its future as a precursor to closed-loop control [195]. How-ever, while CGM has the potential to revolutionize the controlof diabetes, it also generates data streams that are both volu-minous and complex. The utilization of such data requires anunderstanding of the physical, biochemical, and mathematicalprinciples and properties involved in this new technology. It isimportant to know that CGM devices measure glucose concen-tration in a different compartment—the interstitium. Interstitialglucose (IG) fluctuations are related to BG presumably via dif-fusion process [196], [197]. This leads to a number of issues, in-cluding distortion (which incorporate a time lag) and calibrationerrors, and necessitates the development of methods for theirmitigation. In particular, it is necessary to consider that, sincethe BG to IG kinetics acts as a low-pass filter, the frequency con-tent of interstitial glucose is different from that of blood glucose[198], [199].

1) CGM Sensor Calibration: CGM sensor calibration ac-counts for the gradient between BG and IG. Typically, CGMdevices are calibrated with capillary glucose, which bringsthe (generally lower) IG concentration to BG levels. Thefactors pertinent to successful calibration and the effects ofcalibration errors have been extensively studied in the past fewyears [200]–[203]. Alternative calibration methods based ondecomposition of the sensor errors and on the use of diffusionmodels have been studied as well [204], [205]. Various cali-bration functions are adopted by researchers and industry, butmost have a certain linear component using a 2-point linearregression model: , where and are calibrationparameters which are determined by fitting them against acouple of reference and raw CGM currentlevels collected at the same time. However, this procedure canbe suboptimal, because it does not take into account distortionsintroduced by BG-to-IG kinetics. The DirecNet Study Group[200], analyzed the improvement in CGMS sensor accuracyby retrospectively modifying the number and timing of thecalibration points and established that the timing of the cal-ibration points is quite important. In particular, performingcalibrations during periods of relative glucose stability, i.e.,where the point-to-point difference due to the BG-to-IG ki-netics is minimized, significantly improves the accuracy. Anapproach presented by Kuure-Kinsey et al. [206] uses dual-rateKalman filter to improve the accuracy of CGM data. Theprocedure exploits episodic SMBG readings and estimates inreal-time the sensor gain. A critical aspect of this algorithm isthat it does not embed any BG-to-IG kinetics model. A morecomprehensive description of the CGM measurement processwas done by Knobbe and Buckingham [201]. In their work,BG-to-IG kinetics model was explicitly taken into account in

order to reconstruct BG levels in continuous time from CGMmeasurements by an Extended Kalman Filter potentially able todeal with a multiplicative calibration error. However, successfulcalibration would adjust the amplitude of IG fluctuations withrespect to BG, but would not eliminate the possible time lagdue to BG-to-IG glucose transport and the sensor processingtime (instrument delay).

2) CGM versus BG: Because the time lag typicallyassociated with CGM could greatly influence CGM applica-tions, a number of studies were dedicated to its investigation[207]–[211], yielding various results. For example, it washypothesized that if glucose fall is due to peripheral glucoseconsumption the physiologic time lag would be negative, i.e.,fall in IG would precede fall in BG [196], [212]. In moststudies, however, IG lagged behind BG by 4–10 min, regardlessof the direction of BG change [196], [207], [208]. The for-mulation of the push-pull phenomenon offered reconciliationof these results and provided arguments for a more complexBG-IG relationship than a simple constant or directional timelag [211]. In addition, loss of sensitivity and random noiseconfound CGM data [213]–[215]. Thus, while the accuracy ofCGM is increasing, it is still below the accuracy of direct BGmeasurement [216]–[219] and may be reaching a physiologicallimit of s.c. glucose monitoring.

Consequently, it is now recognized that the glucose monitorremains the main limiting factor in the development of diabetescontrol systems [220]–[223]. Less recognized is the fact that thealgorithms retrieving CGM data also have a major contributionto the clinical success of these devices. In order to provide thebest data possible, CGM signal processing is needed. Of pri-mary importance are methods for: tracking CGM data integrity,including CGM data filtering (denoising); predicting glucosefluctuations which has the potential to mitigate the effects of atime lag; generating predictive alarms that could produce appro-priate warning for upcoming extreme glycemic events (e.g., hy-poglycemia) and would thereby assist the behavioral self-regu-lation of diabetes. Available techniques for filtering, prediction,and alert generation have been recently reviewed in [224].

3) Filtering: In general, denoising filters start from the fol-lowing equation:

(46)

where is the glucose level measured at time , is thetrue, unknown, glucose level and is random additive noise.The purpose of filtering is then recovering from . Giventhe expected spectral characteristics of signal and noise, e.g.,signal is lowpass and noise is white, (causal) low-pass filteringrepresents the most natural candidate to separate signal fromnoise in online applications. One major problem in low-passfiltering is that, because signal and noise spectra overlap, it isnot possible to remove noise from the measured signalwithout distorting the true signal . In particular, distortionresults in a delay affecting the estimate with respect to thetrue : the more the filtering, the larger the delay. Thus, aclinically significant filtering issue is reaching a compromise


Fig. 28. Two simulated CGM profiles obtained with different noise variance. Noisy (gray line) versus Kalman filtered (black) signals. Shaded areas correspondto the burn-in intervals.

between the regularity of and its delay with respect to thetrue .

In the literature, real-time denoising of CGM signals hasbeen addressed, both by sensor manufacturers and universityresearchers. The information of signal processing in commer-cial CGM devices is generally proprietary, but some resultsseem to indicate that moving-average (MA) filters with fixedparameters are often used. Methods which indirectly can ad-dress the denoising issue can be found in Chase et al. [214],Knobbe et al. [201] Palerm et al. [226], and Kuure-Kinsey etal. [206]. An explicit dealing with the denoising problem ismade in the recent work by Facchinetti et al. [225]. In thispaper, a Bayesian estimation approach was implemented byKalman filtering for the real-time denoising of CGM signals. Akey feature of the method is that, thanks to the incorporation ofa stochastically based smoothing criterion, it can individualizefilter parameters and hence the regularization amount accordingto the signal-to-noise ratio (SNR) of the specific CGM signal.In particular, the approach is able to cope with different sensors,interindividual and intraindividual SNR variability of CGMdata. The performance of this new approach was assessed usingMonte Carlo simulations and 24 CGM datasets and comparedto a moving average filtering with fixed parameters. Fig. 28shows two CGM time series (gray profiles) taken from theMonte Carlo simulation of [225] and obtained by adding,to a reference profile, a white Gaussian noise sequence withvariance mg dl (top panel) and mg dl(bottom panel). Data from a burn-in interval (shaded box) wereused to estimate : notably, the numerical values estimatedfor (reported in the shaded box) are very close to the trueones. Thanks to the self-tunable parameters individualization,

in both simulations the Kalman filter denoises optimally noisyCGM data (black lines in Fig. 28). On real data, results showedthat, for comparable signal denoising, the delay introduced bythe Kalman filter is about 35% less than that obtained by MA[225].

4) Prediction: A multitude of methods has been proposedfor the near-term (up to 45 minutes) prediction of glucose fluc-tuations. Most of these methods are based on time-series mod-eling techniques [227]–[233], but neural networks [234], [235]and other physiological structural models [236] have been usedas well. Some of the approaches based on time-series modelingare briefly described as follows.

A typical CGM-based predictor would be based on a localapproximation of the CGM time series by a first-order polyno-mial:

(47)

or by a first-order autoregressive (AR) model corresponding tothe following time-domain difference equation

(48)

where is the order of glucose samples collecteduntil the th sampling time and is a random white noiseprocess with zero mean and variance . The prediction strategythen works as follows: Let be the vector of the parametersof the model employed to describe the glucose time series, ateach sampling time . A new value of is determined by fit-ting past glucose data by weighted linear


least squares. Once is determined, the model is used to cal-culate the prediction of glucose level Q steps ahead, i.e., .The product , where is the sensor sampling period,gives the so-called prediction horizon (PH). The necessity ofhaving a time-varying is obvious in the model of (47). For theAR model of (48), the use of a time-invariant , e.g., identifiedin a burn-in interval, would produce inaccurate predictions be-cause of nonstationarity of CGM time series, which, in the caseof low-order model, calls for a time-varying modeling strategy[230]. In the estimation of , the past data participate with dif-ferent relative weights. A typical choice is to employ exponen-tial weighting, i.e., is the weight of the sample taken in-stants before the actual sampling time, with the forgetting factor

within the range (0,1) termed forgetting factor. In [233], theforgetting factor is modulated in order to account for suddenchanges of glucose dynamics.

Reifman et al. [228] employed a different approach, whichexploited a high-order AR model (order 10) which was firstfitted, in each subject, in a burn-in interval and then used withinthe prediction algorithm for the rest of the time series. A priceto be paid for this approach is an increased model complexitywhich requires the use of a rather long burn-in interval (about2000 samples, or 36 h). Moreover, given the high number ofparameters to be estimated, this AR model would be overly sen-sitive to noise. Indeed, a “regularization constraint” was placedon the AR coefficients in order to decrease their sensitivity to thedata. Furthermore, the prediction algorithm of [228] has beenassessed on retrospectively smoothed CGM data.

A stochastic nonparametric approach, similar to that em-ployed in [225] for denoising, was proposed for predictionpurposes in [237]. The idea of the method is to exploit theavailable a priori information on the smoothness of CGMsignal, formalized through a stochastic model including themultiple integration of a white noise process. After havingplaced the problem in a state-space setting, a Kalman Filteringmethodology is used to predict glucose level within a given PH.The approach was tested on 13 data sets of Minimed CGM data(5 min sampling) during a hypoglycemic clamp (4 hour data).Three different PH were tested, PH and min. Theparameters of the Kalman filter were empirically determined,in a retrospective fashion, in order to “maximize” sensitivityand specificity. The authors reported that the prediction perfor-mance, in this well-controlled hypoglycaemic clamp situation,was satisfactory in terms of sensitivity and specificity. Noquantitative estimates of the prediction delays were reported.

5) Hypoglycemia and Hyperglycemia Alerts: A specialclass of predictive methods concerns the generation of alarmsforewarning the patient about upcoming extreme glycemicevents, e.g., hypo- or hyper-glycemia. These methods haverapidly evolved from a concept [238] to implementation inCGM devices, such as the GuardianRT (Medtronic, Norhtridge,CA) [239] and the Freestyle Navigator (Abbott Diabetes Care,Alameda, CA) [178]. Discussion of the methods for testing ofthe accuracy and the utility of such alarms has been initiated[178], [240], [241], and the next logical step—preventionof hypoglycemia via shutoff of the insulin pump—has beenundertaken [242].

VI. CONTROL

A. Rationale

As already noted in Section II, a patient with type 1 diabetesfaces a life-long behavior-controlled optimization problem: theadministration of external insulin to control glycemia entersa stochastic scenario where hyperglycemia and hypoglycemiamay not be easily prevented by open-loop therapy. The adjust-ment of therapy, i.e., basal insulin delivery and premeal boluses,on the basis of a few daily fingerstick blood glucose measure-ments, can be seen as rudimentary way to close the loop. Clearly,the few daily measurements, albeit very important, considerablylimit the effectiveness of the feedback action.

Closed-loop glucose control uses in contrast frequent mea-surements. This subject has been discussed by numerousresearch papers since the 1960s, and several surveys are nowavailable [223], [243]. The purpose here is to review recentdevelopments by taking into account some guidelines. In par-ticular, attention is focused on the subcutaneous sc-to-sc controlroute, i.e., on control systems adopting noninvasive sc insulinpumps and sc CGM devices. Therefore, contributions specificto intensive care patients or those dealing with glucagon pumpsare not dealt with. Recent years have witnessed the develop-ment of more realistic models of glucose metabolism, as wellas the first trials testing closed-loop glucose control systemsin people. In view of this, another inclusion criterion is thevalidation platform: we will only consider control algorithmsvalidated in clinical in vivo trials or in advanced in silicoexperiments, which provide accurate description of dynamicphenomena and/or incorporate interindividual variability [137],[244], [245]. The ideal in silico experiment not only provides adetailed simulation of metabolic processes but is also capableof running simulations on a large virtual population of patients.The importance of these models for testing glucose controlalgorithms is confirmed by the fact that the FDA has acceptedin silico trials conducted with a large-scale in silico modelas a substitute of the preclinical animals studies, which areusually needed to authorize clinical trials in humans [140]. In[246] and [247], some guidelines for in silico proof-of-concepttesting of artificial pancreas control algorithms are proposed. Acritical step of a full-scale in silico testing should involve notonly controller software but also hardware elements, includingthe communication interface between the controller and theglucose sensor and insulin pump [248].

The problem of maintaining glucose levels within a prede-fined range by acting on insulin delivery is a control problemwith a number of more or less specific features. The controlledvariable is glucose utilization, the measured output is the sc glu-cose provided by the CGM, and the clinical criterion for suc-cess is plasma glucose. There is one manipulated variable (alsocalled control input), namely the insulin delivered by the scpump that can be acted upon by either the patient or the con-trol systems to regulate plasma glucose. The system is subjectedto disturbances, the most important one being the meals. It isimportant to note that this disturbance may be announced, ap-proximately known, or even predictable. Such knowledge is rou-tinely exploited in conventional insulin therapy in order to com-


pute premeal boluses. Among other disturbance inputs, one maymention physical exercise that is known to acutely increase glu-cose utilization and chronically modify insulin sensitivity.

The dynamics of the system linking sc insulin to sc glucoseconsist of a cascade of three subsystems: the sc insulin havingplasma insulin as output, the insulin-glucose metabolism non-linear model having plasma glucose as output, and the sc glu-cose subsystem having sc glucose as output. As a result, sc in-sulin infusion poses major challenges to control algorithms dueto the significant time needed for insulin absorption, diffusion,and action. With the advent of new rapid-acting insulin ana-logues that have been developed to more closely approximatethe physiology of meal-related insulin secretion (e.g., lispro, as-part, glulisine) this time is now one hour or less [287], [288],which is still far inferior to the rate of insulin response in health.Such large time delays are relatively inconsequential in a steady(fasting) state, but have a major impact during system distur-bances (e.g., meals, exercise). Recently, it has been found that,due to the “smoothing” inherent with sc insulin transport, small15-min insulin boluses are indistinguishable from continuousbasal rate [289], which allows designing control algorithms withup to a 15-min actuation rate, an approach that may be superiorto the traditional bolus + continuous basal rate in terms of bothcomputational and insulin pump energy efficiency. Further, theeffect of meals on plasma glucose is characterized by an absorp-tion delay whose time constant is in the order of hours. Overall,the sc system dynamics is nonlinear and affected by substantialdelays, making the design of effective sc closed-loop control al-gorithms all but a trivial task. In addition, control must also facethe significant inter- and intra-patient variability, meaning thatit may be virtually impossible to apply the same controller todifferent patients and that even the same patient may show largevariations at different days. Another issue is the presence of in-trinsic input constraints, in that the manipulated input variable,e.g., insulin, is nonnegative. Moreover, there are also output con-straints on the controlled variable in that plasma glucose shouldnever go below a hypoglycaemia threshold, e.g., 60 or 70 mg/dl.On the other hand, in order to prevent long-term complications,hyperglycemia should be avoided as well. Finally, it is impor-tant to realize that closed-loop control is not without risks. Forinstance, in presence of hyperglycemia following a meal the reg-ulator is likely to react by delivering more insulin, whose effectwill not be immediately apparent due to intrinsic system delays.Then, insulin given in excess and too late may act when mealeffect has ceased, so that hypoglycemia becomes unavoidableeven if the insulin pump is shut off.

B. Architecture of Glucose Control

The availability of CGM measurements opens the way todifferent types of closed-loop control strategies, ranging fromsimple short-term safety-oriented interventions to long-termtherapy-optimization schemes. In order to classify and organizethe review of the literature, we refer to a recent paper that hasproposed a layered architecture for artificial pancreas systems[249] (Fig. 29). The layers are characterized by the time-scaleof their operations. At the bottom, the fastest layer is in charge

of safety requirements. Possible algorithms include pumpshutoff, insulin on board (IOB), and the so-called “brakes.”Immediately above, there is the real-time control layer that de-cides insulin delivery on the basis of latest CGM data, previousinsulin delivery, and meal information. Typical algorithms areeither Proportional Integral Derivative (PID) or Model Predic-tive Control (MPC) regulators. The top layer, called offlinecontrol tuning, uses clinical parameters and historical datato tune the real-time control layer. In this case, the methodsinclude individual controller calibration strategies, run-to-run(R2R) control algorithms, and behavioral analysis of patientlifestyle. Each layer processes available information (experi-mental measurements and patient’s inputs) to take decisionsthat are passed to a lower layer. Each layer can override com-mands from an upper layer if this is either useful or necessary:a typical example may be provided by the safety layer zeroinginsulin administration decided by the real-time control module.

It is interesting to note that activation of all layers is notstrictly necessary. Within a traditional therapy consisting ofbasal insulin and meal-compensating boluses, use of the CGMinformation may be limited to safety interventions when thepatient is at risk of hypoglycemia. For instance, the real-timecontrol layer may be omitted, in which case the offline layerwould just be in charge of adjusting basal insulin and premealinsulin boluses using historical information.

C. Safety Algorithms

The idea behind control algorithms pertaining to the safetylayer is to exploit CGM data to improve patient’s safety. Sincethe main short-term risk is hypoglycemia, the safety algorithmsdiscontinue or reduce basal insulin to prevent dangerous de-creases of blood glucose level.

The simplest strategy is pump shutoff when hypoglycemia ispredicted. This approach has been shown to reduce the risk ofnocturnal hypoglycemia [242], [250]. A possible drawback isthat the use of an on–off control law for basal insulin, similar tobang-bang or relay control, may induce undesired oscillationsof plasma glucose. In fact, if the basal insulin is higher thanthat needed to keep the glycemic target, the recovery from hy-poglycemia would be followed by application of the basal thatwill cause a new shut-off occurrence. The cycle of shut-off in-terventions yields an insulin square wave that induces periodicoscillation of plasma glucose.

An alternative approach relies on insulin-on-board (IOB)computation [251]. The amount of IOB should never exceed aquantity that can cause future hyperglycemia. This assessmentof the amount of on-board insulin, though approximate, offersa practical way to prevent hypo phenomena. Moreover, the IOBcomputation is simple enough to be included within a safetymodule that should act when upper layers have failed.

The third approach, the so-called “brakes” [252], which as-sess the risk associated with glucose values and reduce the deliv-ered insulin accordingly. The main advantage, compared to theshut-off approach, is the ability to finely adapt intervention tothe estimated risk. A possible improvement may regard risk as-sessment that could take into account past CGM and insulin his-tory and not only the current CGM value. With this respect, the


Fig. 29. Modular layered architecture of the artificial pancreas. The layers work on different time scales: the fastest one deal with safety maintenance, the middleone with real-time closed-loop control, and the top one with tuning and supervision on a daily or longer time scale. Three main functionalities are included in eachlayer: control, estimation, and data management. Decision flow is from top to bottom and information flow is from bottom to top. A layer can override decisionssuggested by its upper layer, e.g., for safety reasons.

complex risk prediction algorithms may be incompatible withsimplicity and robustness requirements of a safety module.

Recently, it has been proposed that implementation of “semiclosed-loop” glucose control, only using the safety module,without the real-time control, could offer a first step towardsfull-closed loop control [253]. However, the philosophy ofpure safety (act only to prevent hypoglycemia) needs to beadopted with caution, particularly in a system characterizedby slow dynamics where prevention is much more efficientthan correction. Nevertheless, in the presence of a real-timecontrol module, safety algorithms may play an important role,especially if they are based on simple and physically groundedcomputations and offer a recovery strategy from physical oralgorithmic failures of real-time controllers.

D. Real-Time Control

1) Feedback and Feedforward Control: There are two classesof control schemes: open- and closed-loop. Both classes of con-trol schemes aim to keep the controlled variable (e.g., bloodglucose) within the admissible or desired range, compensatingfor disturbances and uncertainties by acting on the manipulatedvariable (e.g., insulin). The main difference is that open-loopmethods do not employ real-time measurements in order to taketheir decisions, whereas closed-loop control exploits measure-ments correlated with the variable under control to react to un-certainties and disturbances.

A fully open-loop scheme would correspond to a fixedtherapy (for instance consisting of basal insulin administrationthroughout the day and insulin boluses at meal times), based onpatient characteristics, without plasma glucose measurements.The open-loop therapy could, however, exploit knowledgeof external disturbances, e.g., adapting the boluses to thepredicted meal amount. The use of knowledge on an externaldisturbance in order to compensate in advance for its effectsis a feedforward action. In principle, if the patient dynamicsand external disturbances were perfectly known, it would bepossible to design an open-loop insulin profile ensuring thedesired glycemic control. In real life, however, both the patientdynamics and presence and size of external disturbances arefar from being perfectly known. Hence, there is the need ofcorrections that must be based to the actual patient state. Infact, in the conventional therapy, occasional fingerstick glucosemeasurements are used to trigger corrective actions in order toreact to deviations from the nominal profile that the open-loopcontrol is expected to produce. This gives rise to a kind ofpartially closed-loop control scheme. However, few dailymeasurements are insufficient to change the nature of a controlstrategy which relies heavily on feedforward compensation.

With the commercial availability of CGM, it has become pos-sible to design minimally invasive closed-loop control schemesbased on frequent output measurements. In particular, the ef-fect of external disturbances (e.g., meal and exercise, but alsochanges of insulin sensitivity) can be corrected based on theireffect on glucose levels. In presence of an excessive rise of glu-


cose, the controller is alerted by the CGM signal and can in-crease insulin delivery. Conversely, an undesired decrease ofglycemia can trigger the reduction of basal insulin delivery.

A purely closed-loop control scheme would decide instanta-neous insulin delivery on the basis of CGM signal alone. Thiswould bring several advantages. First, any undesired glucoselevel would be accounted for in real time by suitable correc-tions of insulin rate. Moreover, being based on the measuredeffects of disturbances, corrections are applied without need forexplicit knowledge or modeling of such disturbances. For ex-ample, an unexpected meal would be dealt with by reactingto the consequent glucose rise. If all this were possible andeffective, improved quality of life would be apparent, as anychange of meals and habits would be dealt with similarly to glu-cose control in health. Unfortunately, the sc delays describedabove present a major stumbling block on the way to a purelyclosed-loop control strategy: The action of insulin on plasmaglucose is subject to significant delays so that effects of reac-tions to undesired glucose level may arrive too late to preventhyper- or hypo-glycemic episodes. This problem is further ex-acerbated by the inherent delay between plasma glucose andthe CGM signal. For a closed-loop controller, the worst casescenario is when a fast acting disturbance has to be counter-acted by a manipulated variable whose action is delayed by thesystem dynamics. In this context, attempts to speed up the re-sponsiveness of the closed-loop system may even result in an un-stable behavior. For example, an excessive closed-loop insulinadministration following postprandial hyperglycemia is likelyto cause a hypoglycemic episode. This kind of intrinsic perfor-mance limitation is well known in control: in presence of signif-icant delays in the route from manipulated (s.c. insulin) to thecontrolled variable (plasma glucose), the designer must settlefor a relatively slow response time (i.e., the time needed for de-sired glycemia to be restored). These considerations suggest thatthe closed-loop control action should not be abrupt and favourgradual corrections. However, a poorly aggressive control is notlikely to provide good postprandial glycaemic attenuation, whena large and sudden disturbance is to be counteracted.

The problem of finding a tradeoff between nocturnal reg-ulation, well suited to mild control actions, and postprandialregulation, calling for prompt and energic correction has beenpointed out in [254] with reference to previous closed-loop trials[255]–[257] where good nocturnal regulation was to the detri-ment of breakfast control quality. This dilemma can be escapedby a control scheme that combines feedforward and feedbackactions [254], [258] (Fig. 30). In particular, feedback control ac-tions are applied only as corrections that are summed to a “con-ventional” insulin administration (feedforward action) made ofa basal profile and premeal boluses calibrated on the presumedmeal amount. Associated with the feedforward action is a nom-inal glucose profile which represents the expected consequenceof the conventional therapy. The closed-loop regulator basesits actions on the difference between the CGM signal and thisnominal profile. If the difference is zero, no closed-loop cor-rection is applied and the patient is subject to the conventionaltherapy alone. Although in practice the difference will always benonzero, a well-designed feedforward action will require small-

Fig. 30. Block diagram of a closed-loop glucose control systems including afeedforward action. Information on meal time and amount is used to generatea feedforward action, typically under the form of a premeal bolus. The insulincontrol signal is obtained as the sum of the feedforward action and the feedbackcomputed by the controller on the basis of glucose sensing.

size feedback corrections. The major advantage is the possi-bility of combining prompt and energic compensation of meals(through the feedforward bolus) with the robustness of closed-loop control capable of adapting to unpredicted events, distur-bances, and changes in patient’s dynamics.

2) Models for Control: The deployment of a controller, espe-cially a closed-loop one, relies heavily on mathematical models.It is worth noting that the requirements posed to models mayvary depending on the different phases: design, tuning, and val-idation.

Most control design methods make use of compact models,whose main task is capturing system dynamics on the time scaleregulation is concerned with. In this respect, linear time-in-variant models may be obtained by linearization of either theaverage insulin-glucose in silico model or the minimal model.In the former case, order reduction methods may be employedto eliminate redundant state variables. Another way to obtaina linear time-invariant model is by black-box identificationtechniques applied to patient’s data, e.g., to identify ARMAXmodels. Some nonlinear control strategies such as NonlinearModel Predictive Control, described as follows, can rely di-rectly on nonlinear models such as the insulin-glucose in silicomodel or the minimal model (nonlinear black-box models, e.g.,Nonlinear ARMAX, can be considered as well).

In the tuning and validation stages, it is convenient to run sim-ulations that mimic the real system dynamics as faithfully aspossible, so that large scale simulation models are particularlyuseful. In control engineering, it is a common practice to designa controller on some simple model (low-order linear time-in-variant, for instance) and validate it on a detailed simulator of thesystem under control. Recalling that the insulin-glucose in silicomodel characterizes a population of virtual patients it is evenpossible to tune the controller parameters through in silico trialsthat compare the performances of different parameters values onthe whole in silico population.

In the following review of glucose control strategies, the roleand type of associated models will be pinpointed for each con-trol method. In any case, a common feature of models for controldesign is instrumental to the achievement of satisfactory regula-tion performances rather than striving for the best possible de-scription of all physiological phenomena.


3) PID Control: The classical PID control scheme is the mostwidespread in the control of industrial processes due to its sim-plicity, flexibility, and ease of tuning. In particular, the tuning ofthe controller parameters can be done without a mathematicalmodel of patient’s metabolism, simply using empirical rules.

It is therefore not surprising that some of the first sc-to-sccontrol experiments used a PID controller [259], [260], [290],[291]. Among its pros, there is the possibility of relating thePID tuning parameters to the biometric parameters of the patient[259]–[261].

However, one issue concerning PID is the merit of the inte-gral action. In fact, integral action is usually included in indus-trial regulators because, provided that the closed-loop systemis stable, its presence guarantees asymptotic zero-error regu-lation. In the case of glucose control, this would correspondto the asymptotic convergence of glycemia, in absence distur-bances, towards the assigned setpoint. Recalling that meals areto be regarded as disturbances, the assumption is unrealistic,which makes the asymptotic zero-error property much less ap-pealing. There is a further concern, relative to the transient re-sponse to disturbances, which is even more critical: Considera closed-loop stable linear system having in the loop a con-troller with an integral action and assume that the initial stateis at the equilibrium with output equal to the setpoint. If an ex-ternal transient disturbance is applied, it can be easily demon-strated that the integral over time of the difference between theresulting output and the equilibrium output is equal to zero. Theglucose metabolism is nonlinear but nevertheless it may be ap-proximated by a linear system in a neighborhood of the equilib-rium point. As observed by [243], this means that after a meal,which makes glycemia exceed the desired value, there will al-ways be an undershoot, i.e., a glucose transient that takes valuesbelow the glycemia setpoint and whose area is comparable thearea of the previous overshoot above the setpoint. For these rea-sons, it may be convenient to turn to PD controllers, i.e., withoutthe integral action. In particular, [262] can be regarded as a PDcontroller, in that is adapts the basal insulin depending of glu-cose value (proportional action) and its variation in the past 30min (which replaces the derivative action).

PID control suffers from the same problems already high-lighted. Due to the presence of substantial delays in theinsulin-to-glucose route, one has to design a scarcely aggres-sive controller which, however, may react less promptly andeffectively to meals than the usual premeal boluses of the con-ventional therapy. As already mentioned, in order to improveperformance, a possibility is to add a feedforward action, soas to recover the promptness of meal compensation. AlthoughMPC strategies appear better suited to incorporate predictionson the future effects of meals, an attempt has been made alongthis direction by [261], where the authors present a controllerswitching between PID regulation and bolus administration inproximity of meals. In any case, irrespective of the adoptedtuning procedure or the presence of a feedforward action,PID controller will be subject to saturations and therefore ananti-windup implementation is always needed.

4) MPC: In recent years MPC [263] has emerged as the mostpromising approach to glucose control. The main ingredients of

MPC are: the model, the cost function, and the constraints. Themodel is needed in order to be able to predict the future statesand outputs of the system as a function of the current state, futurevalues of the manipulated variables, and future values of mea-surable or predictable disturbances (Fig. 31). It can be linearor nonlinear, continuous-time or discrete-time, state-space orinput–output, black-box, grey-box, or white-box. The cost func-tion measures the quality of closed-loop control. Usually, but notnecessarily, it is a quadratic penalty

(49)

on future deviations (whose number is a design parameter calledprediction horizon) of the output from the setpoint and mayinclude also a quadratic penalty on future control actions thatcan be the difference of the input with respect to a reference

or the variation along the time .Finally, there may be constraints on the manipulated variables(insulin delivery rates by the pump is greater than zero and lessthan some maximal value)

(50)

(51)

and also on the controlled ones (glycemia in the admissiblerange)

(52)

The rationale behind MPC is rather simple: at each time pointwe compute the sequence of future input moves optimizing thecost function subject to the constraints. Then, only the first con-trol move is applied. At the next step, the procedure is repeatedby translating the predictions and control horizons: an optimiza-tion is again performed and only the first input move is applied.The principal merit of MPC is that it reduces the control designproblem to a sequence of finite-horizon optimization problems,which makes it possible to deal with nonlinear system models,input and output constraints, multiple inputs and outputs, andpossible knowledge regarding the dynamics of disturbances. Fi-nally, the tuning of the regulator can follow a rather straight-forward trial-and-error procedure: if the control action is slug-gish, it suffices to adjust the cost function increasing the weighton the controlled output, i.e., glycemia. In the simplest imple-mentation, after finding reasonable values for the control andprediction horizons (e.g., a unique value covering the durationof typical post-meal transients), the tuning reduces to the cali-bration of a scalar aggressiveness parameter [270]. As alreadymentioned, the core of MPC is a mathematical model able topredict the future evolution of the system under control. In fact,


Fig. 31. MPC prediction scheme: given the model, past inputs and outputs, thefuture outputs are predicted as a function of future inputs.

different MPC schemes are obtained depending on the natureand complexity of the adopted model.

Nonlinear Model Predictive Control (NMPC) assumes a non-linear patient model and keeps into account input and outputconstraints. In this case, explicit solution of the finite-horizonoptimization problem does not exist, and the price to pay foran accurate description of the nonlinear dynamics is the needfor online iterative optimization within the algorithm. This maypreclude the adoption of NMPC within commercial devices, forboth engineering and regulatory reasons. Moreover, standardNMPC algorithms assume knowledge of the current state vari-ables, so that it is necessary to include also a state observer or aKalman filter whose design and tuning may not be straightfor-ward. A final problem is the difficulty of obtaining reliable in-dividual models of insulin-glucose dynamics, as interindividualvariability may hinder the use of an average model.

NMPC is however of particular interest as a touchstone forother simpler MPC schemes. A study has indeed demonstrateda distinct improvement over linear MPC [141] on the averagein silico patient of the insulin-glucose in silico model. Experi-ments on real patients using NMPC have also been performed[136], [264], [265]. The need for an individual model has beenovercome by online recursive identification of model param-eters within a Bayesian setting. Given that experimental dataalone may not guarantee parameter identifiability, the Bayesianpriors play a key role. Moreover, a formal demonstration ofstability and robustness properties of the closed-loop system isobstructed by the complex interplay between on line recursiveidentification and nonlinear control.

Linear Model Predictive Control (LMPC) uses an approxi-mate linear model of the insulin-glucose dynamics, which pro-duces a substantial algorithmic simplification. The linear modelcan have different sources. For instance, it may be obtained fromthe linearization of a more complex nonlinear average patientmodel around a suitable working point; however such an ap-proach would suffer from the lack of individualization. To over-come this limitation, one possibility is to resort to black-boxidentification of an individual patient model from data collectedon the same individual subject to conventional therapy. In prac-tice, time series of insulin, CGM data, and meal informationare used to identify an ARMAX model with two inputs (sc in-sulin and meals) and one output (sc glucose). A necessary condi-tion to ensure good identifiability properties of ARMAX modelsis the so-called persistent excitation property of input signals,which should not be collinear between each other and whosespectrum should excite an adequate number of frequencies. Un-fortunately, the meals and insulin boluses of the conventionaltherapy turn out to be collinear and, due to this lack of excita-tion, the identification algorithm may even fail to correctly esti-mate the sign of the gains from insulin and meals to sc glucose[266]. As a remedy, it has been proposed to use split and/or de-layed insulin boluses to improve the joint excitation propertiesof the inputs [254], [266] (see also [267] for further optimal de-sign issues in the identification of insulin-glucose models).

A remarkable property of constrained LMPC is the existenceof a closed-form solution under the form of a piecewise constantcontrol law that can be computed off line, e.g., in [268] an ap-plication to simulated patients is reported. The main drawbackof this LMPC scheme, that goes under the name of explicit mul-tiparametric MPC, is the need of finding the appropriate controlgain for the current state, a task that involves searching amonga potentially very high number of regions in the state space.This can be avoided by computing on line the optimal solutionvia quadratic programming methods [258], which could be acomputationally advantageous alternative to explicit multipara-metric MPC. It is worth noting the possibility of including IOBamong the constraints of the optimization problem, to embedcertain safety constraints already within the real-time controlmodule [258], [269].

It is unlikely that the first commercial realizations of anartificial pancreas will include overly complex computationalalgorithms. This motivates the interest for the simplest pos-sible LMPC scheme, which is input–output unconstrainedLMPC. This particular MPC scheme neglects constraints anduses a linear model in input–output form, e.g., an ARX- orARMAX-type model. There is no need for online optimizationalgorithms, because the unconstrained optimization problemadmits a closed-form solution that calculates the insulin rateas a simple linear combination of previous insulin rates, pre-vious CGM values, and meal amounts (when known). Theuse of an input–output model, instead of state-space model,alleviates the need for a state observer, which is a furthersimplification. A clinical trial on 20 patients has been recentlycarried out using unconstrained LMPC [255]–[257], showinga five-fold reduction of nocturnal hypoglycemia episodes andan improvement of overnight percent time within the target


Fig. 32. Results of a recent clinical trial that compared conventional open-looptherapy to closed-loop glucose control using Linear Model Predictive Control.Closed-loop control achieved an increase of overnight percent time within thetarget range and an almost five-fold reduction of the number of nocturnal hypo-glycemic episodes.

range of 70–140 mg/dl, with respect to conventional open-loopcontrol [255] (Fig. 32). The LMPC controller was based onan average patient model, but the regulator aggressiveness waspersonalized keeping into account easy-to-measure individualclinical parameters. To improve breakfast regulation, whichwas slightly worse than open-loop, an unconstrained LMPCwith feedforward action has been proposed [249]. GeneralizedPredictive Control (GPC), a classic type of input–output un-constrained LMPC, has been experimented with on diabeticswine using both insulin and glucagon as inputs. A first trialused an adaptive GPC (i.e., with model parameters adapted online) employing insulin or glucagon depending on the sign ofthe difference between measured glycemia and its target value[271]. In a second trial, GPC was used to compute the insulinrate while, to speed up glucagon administration, the regulationof this second input was decided by a PD controller [272].The main drawbacks of unconstrained LMPC are the use ofa simplified linear model and the neglect of constraints, espe-cially the one on minimal admissible glycemia. However, thesedrawbacks may be compensated by the advantage of a verysimple implementation, especially if this real-time controlleris part of a modular architecture including a safety moduleresponsible for hyperglycemia prevention.

5) Real-Time Detection and Estimation: As already men-tioned, controllers based on state feedback require the knowl-edge of the state of the insulin-glucose system. Even for thesimplest models, the available measurements do not give accessto the full state vector, so that real time algorithms for state ob-servation are needed (see [143], [273], and [292]). State esti-mation is important not only for control properties, but can alsobe easily extended to prediction. In particular, it can be used topredict hypoglycemia [274], [275] and possibly trigger safetyactions such as pump shutoff or attenuation. Nevertheless, in-sofar as a state observer or a Kalman filter rely heavily on acomplex model not easily personalized to the specific patient,caution should be used in their use as safety algorithms.

The knowledge of meal time and amount plays an impor-tant role in that it can substantially help choosing the correctinsulin profile for restoring glycemic control. An ideal artifi-cial pancreas would be completely automatic, dispensing thepatient from providing meal information to the device. In this

Fig. 33. An example of CVGA plot. Each patient is represented by a point inthe CVGA plane whose coordinates correspond to the minimal and maximalglycemia reached during the monitored time period (note that the axis of theminimal glycemia is reverted). Regulation improves as the points get closer tothe lower left corner, corresponding to ideal euglycemia. The glycemic regu-lation of two populations (white and black circles) is compared. The greaterpercentage of patients within the A region indicates that the white-dot popula-tion achieves better glycemic control compared to the black-dot population.

context, a meal detection and estimation module [258], [276],[277] could greatly help the controller reacting properly to theglucose rise following a meal. However, in an s.c.-s.c. glucosecontrol system, the delay introduced by meal detection and esti-mation would add to the intrinsic delays in the sc-to-sc route,thus degrading the effectiveness of meal compensation com-pared to the use of an appropriate premeal bolus. In any case,even if the patient were asked to provide meal confirmation tothe control device, it would still be necessary to recover from auser’s error by giving the device the capability to automaticallydetect unannounced meals.

E. Strategies for Control Tuning

1) Measuring Control Performance on Population: Al-though several classic control metrics exist for assessing thequality of glycemic control [278], some additional issuesemerge. In particular, it does not suffice to develop an algorithmthat performs satisfactorily on a single subject either real orsimulated. As a matter of fact, given the great interindividualvariability, it is of paramount importance to guarantee satis-factory performance on the entire population of patients. Thismotivated the introduction of the so-called Control VariabilityGrid Analysis (CVGA) [279], which associates to each patient apoint in a plane (Fig. 33). The two coordinates correspond, via anonlinear transformation, to the minimal and maximal glucosevalue in the considered time interval. The lower left corneris associated with ideal glycemic control while high -valuescorrespond to hypoglycemic episodes and high -values tohyperglycemic episodes. The plane is partitioned into nineregions corresponding to different levels of glycemic control


quality, from A (best) to E (worst). In this way, the resultsfrom a real or simulated trial can be visualized by plotting thepatients as a cloud of points onto the CVGA and summarized bycounting the percentage of points in the nine regions. Using theCVGA, comparison with either conventional open-loop controlor another closed-loop controller is immediate. Of course, agood controller will bring as many patients as possible in the Aand B regions. Preliminary to a clinical study, the controller canbe applied to an in silico population, representative of the realpopulation, and the performance assessed on the CVGA. If theyare unsatisfactory, the controller can be modified and testedagain by repeating the in silico trial. The procedure is iterateduntil glycemic control is acceptable for all the virtual patients.

2) Robustness versus Personalization of Controller Pa-rameters: The ideal artificial pancreas should perform safelyand satisfactorily in all patients. To achieve this, the designedcontroller should be highly robust against uncertainties in thesystem dynamics, either due to interindividual or intraindi-vidual variability. Experiments conducted in in silico patientshave shown that, a fixed controller yields largely disparateperformances when applied to different patients; hence, thereis need for a personalization of the control algorithm. Giventhe difficulty of identifying accurate individual models, thedirect tuning of controller parameters has been investigatedon the basis of few biometric and clinical parameters (bodyweight, total daily insulin, basal insulin delivery, carb ratio,etc.) characterizing the physiology of each individual. Thiscan be done for both PID regulators [261] and MPC ones[143], [255]–[257]. In particular, for MPC the relation betweenbiometric and physiological patient’s parameters and the op-timal scalar aggressiveness parameter of the controller can bedetermined through a sequence of in silico trials [255]–[257].

3) Run-to-Run Control and Behavioral Analysis: An offlinemodule may be in charge of adapting the control strategy on adaily or weekly basis through the monitoring of the outcomesachieved by the real-time control module. This corresponds to afurther closed-loop working on a coarser time scale. This type ofproblem, called run-to-run (R2R) control, has been extensivelystudied in the control of chemical and manufacturing processes[293]. The rationale of R2R control is rather simple: the param-eter to be adjusted is corrected on the basis of the outcome of thelast run. Proportional and proportional-integral control schemesare the most widely used ones. The first applications to glucosecontrol regarded the iterative adjustment of the basal and bo-luses forming the conventional open-loop therapy [280]–[282].It goes without saying that if the glucose controller includes afeedforward action, it may still benefit from this kind of R2Rcontrol. More recently, R2R control has been applied also to thetuning of the controller parameters [254] where adjustment ofthe controller aggressiveness is considered. An iterative tuningbased on the last 24 hours may also be performed continuouslyvia iterative learning control techniques [283].

Finally, stochastic models of patient’s behavior may be veryhelpful in order to design and recursively update the parame-ters (basal and boluses) of the conventional therapy. A formalstochastic model of the process of self-treatment in diabetes(e.g., regular meals, exercise, as well as random treatment de-viations) and its potential to generate system challenges can bevery useful in that regard, giving a probabilistic interpretation

Fig. 34. Dual-layer bio-behavioral structure of diabetes modeling and control:Layer 1 includes the puzzle of physiologic and behavioral characteristics thatdetermine the specifics of each individual. Layer 2 includes the engineering ap-proaches available to support the optimization of diabetes control.

of the observed patterns [294], [295]. Specifically, behavioralself-regulation of diabetes can be approximated by a periodicrenewal process that has a significant random component. Sucha periodic pattern causes downward and upward BG shifts that,with certain probability, can result in extreme events, such assevere hypoglycemia or major hyperglycemia. The parametersof this process are individual, contingent on behavioral inter-pretation (a person’s ability to control his/her BG within near-normal limits) and physiology (e.g., a hypoglycemic episodewould increase the risk for recurrent hypoglycemia). It has beenshown that such an approach is capable of quantifying patternsof diabetes self-management [296] and is particularly usefulfor understanding the causes of severe hypoglycemia. Thesestudies have demonstrated a quantifiable relationship betweenstochastic patterns of self-treatment behavior and subsequentoccurrence of hypoglycemic episodes [297], [298]. Integratingbehavior and physiology into a common framework has also en-abled the computer simulation of patterns related to countereg-ulatory depletion, HAAF, and recurrent hypoglycemia [299].

VII. CONCLUSION

Approached from a biomedical engineering point of view,the bio-behavioral control of insulin-dependent diabetes (type1 or insulin-treated type 2) is therefore comprised of: 1)physiologic processes depending on a person’s metabolicparameters such as insulin sensitivity and counterregulation,which could suffer from occasional depletion of counterreg-ulatory reserves occurring with repeated hypoglycemia, and2) behaviorally triggered processes of glucose fluctuations(e.g., regular postprandial glucose excursions) interrupted bygenerally random hypoglycemia-triggering behavioral events(e.g., insulin overdose, missed food, or excessive exercise).Fig. 34 presents the dual-layer structure of the engineeringunderstanding of diabetes and places in context the uniquecombination of mathematical modeling, signal processing,and optimal control reviewed in this contribution. Specifically,Layer 1 represents the puzzle of physiological and behavioralinteractions predetermining the specific parameters of each


individual with diabetes. Each puzzle piece represents a specificsubsystem pertinent to glycemic control: the glucose system,reflecting the appearance and the elimination of exogenousor endogenous carbohydrates, the insulin system that controlsthe dynamics of insulin-mediated carbohydrate metabolism,the counterregulatory system which is of enormous relevanceto diabetes and is presented by hypoglycemia—the primaryobstacle to diabetes control, and the patient behavior, whichserves as a generator of events (e.g., meals, physical activity,human errors) resulting in metabolic perturbations. Completingthe puzzle, the processing of these perturbations depends onindividual physiologic parameters of glucose appearance, in-sulin sensitivity, and counterregulation. The interplay betweenbehavior and biology results in glucose variability, which is theprimary observable signal for optimal diabetes control. Layer2 represents the engineering tools available to contemporarydiabetes control. We have discussed several types of mathe-matical models which over the past 40–50 years have becomeincreasingly elaborate, with recent trends also moving fromsingle individual to population [300] by describing inter-sub-ject variability in a stochastic framework where individualdata and anthropometric and metabolic characteristics areexplicitly taken into account [301]–[304]. A milestone in thisline of research was the introduction of the minimal modelingconcept, which established in 1979, the framework for a host ofsubsequent studies of the human glucose metabolism. A morecontemporary milestone has been achieved in 2008, when thefirst model-based computer simulator of the human metabolicsystem was accepted as a viable tool for the preclinical testingof control algorithms, essentially alleviating the need for costlyand time-consuming animal trials. The progress in modelingwas supported by other technological developments, mostimportantly by the advent of continuous glucose monitoring,which provided detailed signals that could be used as inputsfor optimizing glucose control. Finally, a number of controlalgorithms have been used and are recently under developmentwith the goal to assist, and ultimately automate, the glycemiccontrol in diabetes.

We can therefore conclude that the formal understanding anddescription of glucose-insulin metabolism in health and diabetesis, arguably, one of the most advanced applications of biomed-ical engineering to the life sciences. A rich background exists ofmodels, metrics, and algorithms, and this contribution attemptsto provide a systematic review of a number of them. We haveto admit, however, that many more metabolic models exist thatfall out of the scope of this review. This is because our goal isto follow a specific line of research that led from the first com-prehensive model of glucose-insulin dynamics, through detailedsimulation of the human physiology, to the first attempts for au-tomated closed-loop control. Future reviews will therefore dis-cuss problems not addressed by this manuscript.

ACKNOWLEDGMENT

The authors thank Dr. A. Vella and Dr. A. Basu, Mayo Clinic,Rochester, MN; Dr. A. Avogaro, Dr. G. Toffolo, Dr. A. Bertoldo,and Dr. A. Facchinetti, University of Padova, Padova, Italy; Dr.L. Farhi, Dr. M. Breton, and Dr. S. Patek, University of Virginia,Charlottesville, VA, for their contributions to this review.

REFERENCES

[1] J. C. Pickup and G. Williams, Textbook of Diabetes 2. Oxford, U.K.:Blackwell , 1991.

[2] R. H. Wilson, D. W. Foster, H. N. Kronenberg, and P. R. Larsen,William Textbook of Endocrinology, 9th ed. Philadelphia, PA: Saun-ders, 1998.

[3] [Online]. Available: www.ada.org[4] [Online]. Available: www.easd.ord[5] [Online]. Available: www.idf.org[6] J. B. Meigs, D. M. Nathan, R. B. D’Agostino, and P. W. Wilson,

“Fasting and postchallenge glycemia and cardiovascular diseaserisk: The Framingham offspring study,” Diabetes Care, vol. 25, pp.1845–1850, 2002.

[7] The DECODE Study Group, “Glucose tolerance and mortality: Com-parison of WHO and American Diabetes Association diagnostic cri-teria,” Lancet, vol. 354, pp. 617–621, 1999.

[8] P. Zimmet, K. G. Alberti, and J. Shaw, “Global and societal implica-tions of the diabetes epidemic,” Nature, vol. 414, pp. 782–787, 2001.

[9] E. R. Carson, T. Deutsch, H. J. Leicester, A. V. Roudsari, and P. H.Sönksen, “Challenges for measurement science and measurement prac-tice: The collection and interpretation of home-monitored blood,” Mea-surement, vol. 24, pp. 281–293, 1998.

[10] S. Montani, P. Magni, R. Bellazzi, C. Larizza, A. V. Roudsari, and E.R. Carson, “Integrating model-based decision support in a multi-modalreasoning system for managing type 1 diabetic patients,” Artificial In-tell. Medicine, vol. 29, pp. 131–151, 2003.

[11] A. J. Palmer, C. Weiss, P. P. Sendi, K. Neeser, A. Brandt, G. Singh, H.Wenzel, and G. A. Spinas, “The cost-effectiveness of different manage-ment strategies for type 1 diabetes: A Swiss perspective,” Diabetologia,vol. 43, pp. 13–26, 2000.

[12] W. J. Valentine, A. J. Palmer, L. Nicklasson, D. Cobden, and S. Roze,“Improving life expectancy and decreasing the incidence of compli-cations associated with type 2 diabetes: A modelling study of HbA1ctargets,” Int. J. Clin. Pract., vol. 60, pp. 1138–1145, 2006.

[13] D. M. Eddy and L. Schlessinger, “Archimedes: A trial-validate modelof diabetes,” Diabetes Care, vol. 26, pp. 3093–3101, 2003.

[14] D. M. Eddy and L. Schlessinger, “Validation of the Archimedes dia-betes model,” Diabetes Care, vol. 26, pp. 3102–3110, 2003.

[15] H. Kitano, K. Oda, T. Kimura, Y. Matsuoka, M. Csete, J. Doyle, and M.Muramatsu, “Metabolic syndrome and robustness tradeoffs,” Diabetes,vol. 53, pp. S6–S15, 2004.

[16] E. E. Schadt, “Molecular networks as sensors and drivers of commonhuman diseases,” Nature, vol. 46, pp. 218–223, 2009.

[17] C. Cobelli and E. R. Carson, Introduction to Modeling in Physiologyand Medicine. New York: Elsevier/Academic, 2008.

[18] E. R. Carson and C. Cobelli, Modelling Methodology for Physiologyand Medicine. San Diego, CA: Academic, 2001.

[19] C. Cobelli, D. Foster, and G. Toffolo, Tracer Kinetics in BiomedicalResearch. Boston, MA: Kluwer, 2000.

[20] P. A. Insel, J. E. Liljenquist, J. D. Tobin, R. S. Sherwin, P. Watkins,R. Andres, and M. Berman, “Insulin control of glucose metabolism inman: A new kinetic analysis,” J. Clin. Invest., vol. 55, pp. 1057–1066,1975.

[21] C. Cobelli, G. Toffolo, and E. Ferrannini, “A model of glucose kineticsand their control by insulin, compartmental and noncompartmental ap-proaches,” Math. Biosci., vol. 72, pp. 291–315, 1984.

[22] A. Gastaldelli, J. M. Schwarz, E. Caveggion, L. D. Traber, D. L. Traber,J. Rosenblatt, G. Toffolo, C. Cobelli, and R. R. Wolfe, “Glucose ki-netics in interstitial fluid can be predicted by compartmental modeling,”Amer. J. Physiol., vol. 272, pp. E494–E505, 1997.

[23] E. Ferrannini, D. J. Smith, C. Cobelli, G. Toffolo, A. Pilo, and R. A.DeFronzo, “Effect of insulin on the distribution and disposition of glu-cose in man,” J. Clin. Invest., vol. 76, pp. 357–364, 1995.

[24] R. S. Sherwin, K. J. Kramer, J. D. Tobin, P. A. Insel, J. E. Liljenquist,M. Berman, and R. Andres, “A model of the kinetics of insulin in man,”J. Clin. Invest., vol. 53, pp. 1481–1492, 1974.

[25] R. N. Bergman, Y. Z. Ider, C. R. Bowden, and C. Cobelli, “Quantita-tive estimation of insulin sensitivity,” Amer. J. Physiol., vol. 236, pp.E667–E677, 1979.

[26] R. N. Bergman and C. Cobelli, “Minimal modeling, partition anal-ysis, and the estimation of insulin sensitivity,” Fed. Proc., vol. 39, pp.110–115, 1980.

[27] R. N. Bergman, “Lilly lecture 1989. Toward physiological under-standing of glucose tolerance. Minimal-model approach,” Diabetes,vol. 38, pp. 1512–1527, 1989, Review.

[28] C. Cobelli, G. M. Toffolo, C. Dalla Man, M. Campioni, P. Denti, A.Caumo, P. Butler, and R. Rizza, “Assessment of beta-cell function inhumans, simultaneously with insulin sensitivity and hepatic extraction,from intravenous and oral glucose tests,” Amer. J. Physiol. Endocrinol.Metab. Jul., vol. 293, no. 1, pp. E1–E15, 2007.

[29] V. W. Bolie, “Coefficients of normal blood glucose regulation,” J. Appl.Physiol., vol. 16, pp. 783–788, 1961.


[30] G. Segre, G. L. Turco, and G. Vercellone, “Modeling blood glucose andinsulin kinetics in normal, diabetic and obese subjects,” Diabetes, vol.22, pp. 94–103, 1973.

[31] F. Ceresa, F. Ghemi, P. F. Martini, P. Martino, G. Segre, and A. Vitelli,“Control of blood glucose in normal and in diabetic subjects. Studiesby compartmental analysis and digital computer technics,” Diabetes,vol. 17, pp. 570–578, 1968.

[32] Ackerman, J. W. Rosevear, and W. F. McGucking, “A mathematicalmodel of the glucose tolerance test,” Phys. Medicine Biol., vol. 9, pp.203–213, 1964.

[33] L. C. Gatewood, E. Ackerman, J. W. Rosevear, G. D. Molnar, and T. W.Burns, “Tests of a mathematical model of the blood-glucose regulatorysystem,” Comput. Biomed. Res., vol. 2, pp. 1–14, 1968.

[34] L. C. Gatewood, E. Ackerman, J. W. Rosevear, and G. D. Molnar,“Simulation studies of blood-glucose regulation: Effect of intestinalglucose absorption,” Comput. Biomed. Res., vol. 2, pp. 15–27, 1968.

[35] R. N. Bergman, L. S. Phillips, and C. Cobelli, “Physiologic evaluationof factors controlling glucose tolerance in man: Measurement of insulinsensitivity and beta-cell sensitivity from the response to intravenousglucose,” J. Clin. Invest., vol. 68, pp. 1456–1467, 1981.

[36] R. A. De Fronzo, J. D. Tobin, and R. Andres, “Glucose clamp tech-nique: A method for quantifying insulin secretion and resistance,”Amer. J. Physiol., vol. 237, pp. E214–E223, 1979.

[37] G. Pillonetto, A. Caumo, and C. Cobelli, “Dynamic insulin sensitivityindex: Importance in diabetes,” Amer. J. Physiol. PMID: 19920215, tobe published.

[38] C. Cobelli, F. Bettini, A. Caumo, and M. J. Quon, “Overestimation ofminimal model glucose effectiveness in presence of insulin response isdue to undermodeling,” Amer. J. Physiol., vol. 275, pp. E1031–E1036,1998.

[39] D. T. Finegood and D. Tzur, “Reduced glucose effectiveness associatedwith reduced insulin release: An artifact of the minimal model method,”Amer. J. Physiol., vol. 271, pp. E485–E495, 1996.

[40] M. J. Quon, C. Cochran, S. Y. Taylor, and R. C. Eastman, “Non-insulin-mediated glucose disappearance in subjects with IDDM. Discordancebetween experimental results and minimal model analysis,” Diabetes,vol. 43, pp. 890–896, 1994.

[41] C. Cobelli, A. Caumo, and M. Omenetto, “Minimal model SG over-estimation and SI underestimation: Improved accuracy by a Bayesiantwo-compartment model,” Amer. J. Physiol., vol. 277, pp. E481–E488,1999.

[42] T. Callegari, A. Caumo, and C. Cobelli, “Bayesian two-compartmentand classic single-compartment minimal models: Comparison oninsulin modified IVGTT and effect of experiment reduction,” IEEETrans. Biomed. Eng., vol. 50, no. 12, pp. 1301–1309, Dec. 2003.

[43] C. Cobelli and A. Ruggeri, “Optimal design of sampling schedules forstudying glucose kinetics with tracers,” Amer. J. Physiol., vol. 257, En-docrinol. Metab. 20, pp. E444–E450, 1989.

[44] R. Hovorka, D. J. A. Eckland, D. Halliday, S. Lettis, C. E. Robinson,P. Bannister, M. A. Young, and A. Bye, “Constant infusion and bolusinjection of stable-label tracer give reproducible and comparablefasting HGO,” Amer. J. Physiol., vol. 273, Endocrinol. Metab., pp.E192–E201, 1997.

[45] C. Dalla Man, A. Caumo, and C. Cobelli, “The oral glucose minimalmodel: Estimation of insulin sensitivity from a meal test,” IEEE Trans.Biomed. Eng., vol. 49, no. 3, pp. 419–429, Mar. 2002.

[46] C. Dalla Man, A. Caumo, R. Basu, R. A. Rizza, G. Toffolo, and C.Cobelli, “Minimal model estimation of glucose absorption and insulinsensitivity from oral test: Validation with a tracer method,” Amer. J.Physiol., vol. 287, pp. E637–E643, 2004.

[47] C. Dalla Man, K. E. Yarasheski, A. Caumo, H. Robertson, G. Toffolo,K. S. Polonsky, and C. Cobelli, “Insulin sensitivity by oral glucoseminimal models: Validation against clamp,” Amer. J. Physiol., vol. 289,pp. E954–E959, 2005.

[48] C. Cobelli, G. Pacini, G. Toffolo, and L. Saccà, “Estimation of insulinsensitivity and glucose clearance from minimal model: New insightsfrom labeled IVGTT,” Amer. J. Physiol., vol. 250, pp. E591–E598,1986.

[49] A. Avogaro, J. D. Bristow, D. M. Bier, C. Cobelli, and G. Toffolo,“Stable-label intravenous glucose tolerance test minimal model,” Di-abetes, vol. 38, pp. 1048–1055, 1989.

[50] A. Caumo, A. Giacca, M. Morgese, G. Pozza, P. Micossi, and C. Co-belli, “Minimal models of glucose disappearance: Lessons from thelabelled IVGTT,” Diabet. Med., vol. 8, pp. 822–832, 1991.

[51] A. Avogaro, P. Vicini, A. Valerio, A. Caumo, and C. Cobelli, “Thehot but not the cold minimal model allows precise assessment of in-sulin sensitivity in NIDDM subjects,” Amer. J. Physiol., vol. 270, pp.E532–E540, 1996.

[52] P. Vicini, A. Caumo, and C. Cobelli, “The hot IVGTT two-compart-ment minimal model: Indexes of glucose effectiveness and insulin sen-sitivity,” Amer. J. Physiol., vol. 273, pp. E1024–E1032, 1997.

[53] G. Toffolo and C. Cobelli, “The hot IVGTT two-compartment minimalmodel: An improved version,” Amer. J. Physiol. Endocrinol. Metab.,vol. 284, pp. E317–E321, 2003.

[54] C. Dalla Man, M. Campioni, K. S. Polonsky, R. Basu, R. A. Rizza,G. Toffolo, and C. Cobelli, “Two-hour seven-sample oral glucose tol-erance test and meal protocol: Minimal model assessment of beta-cellresponsivity and insulin sensitivity in nondiabetic individuals,” Dia-betes, vol. 54, pp. 3265–3273, 2005.

[55] A. Caumo and C. Cobelli, “Hepatic glucose production during thelabeled IVGTT: Estimation by deconvolution with a new minimalmodel,” Amer. J. Physiol., vol. 264, no. 5, pt. 1, pp. E829–E841, 1993.

[56] R. Hovorka, F. Shojaee-Moradie, P. V. Carroll, L. J. Chassin, I. J.Gowrie, N. C. Jackson, R. S. Tudor, A. M. Umpleby, and R. H. Jonesl,“Partitioning glucose distribution/transport, disposal, and endogenousproduction during IVGTT,” Amer. J. Physiol. Endocrinol. Metab., vol.282, no. 5, pp. E992–E1007, 2002.

[57] C. Dalla Man, A. Caumo, R. Basu, R. A. Rizza, G. Toffolo, and C. Co-belli, “Measurement of selective effect of insulin on glucose disposalfrom labeled glucose oral test minimal model,” Amer. J. Physiol., vol.289, pp. E909–E914, 2005.

[58] C. Dalla Man, G. Toffolo, R. Basu, R. A. Rizza, and C. Cobelli, “Useof labeled oral minimal model to measure hepatic insulin sensitivity,”Amer. J. Physiol. Endocrinol Metab., vol. 295, pp. E1152–E1159,2008.

[59] R. Basu, C. Dalla Man, M. Campioni, A. Basu, G. Klee, G. Jenkins, G.Toffolo, C. Cobelli, and R. A. Rizza, “Mechanisms of postprandial hy-perglycemia in elderly men and women: Gender specific differences ininsulin secretion and action,” Diabetes, vol. 55, pp. 2001–2014, 2006.

[60] A. D. Cherrington, “Control of glucose uptake and release by the liverin vivo,” Diabetes, vol. 48, pp. 1198–1214, 1999.

[61] P. Vicini, J. J. Zachwieja, K. E. Yarasheski, D. M. Bier, A. Caumo,and C. Cobelli, “Glucose production during an IVGTT by deconvo-lution: Validation with the tracer-to-tracee clamp technique,” Amer. J.Physiol., vol. 276, pp. E285–E294, 1999.

[62] G. De Nicolao, G. Sparacino, and C. Cobelli, “Nonparametric inputestimation in physiological systems: Problems, methods, case studies,”Automatica, vol. 33, pp. 851–870, 1997.

[63] R. Hovorka, H. Jayatillake, E. Rogatsky, V. Tomuta, T. Hovorka, andD. T. Stein, “Calculating glucose fluxes during meal tolerance test: Anew computational approach,” Amer. J. Physiol. Endocrinol. Metab.,vol. 293, no. 2, pp. E610–E619, 2007.

[64] K. M. Krudys, M. G. Dodds, S. M. Nissen, and P. Vicini, “Integratedmodel of hepatic and peripheral glucose regulation for estimation of en-dogenous glucose production during the hot IVGTT,” Amer. J. Physiol.Endocrinol. Metab., vol. 288, pp. E1038–E1046, 2005.

[65] K. Tokuyama, S. Nagasaka, S. Mori, N. Takahashi, I. Kusaka, A. Kiy-onaga, H. Tanaka, M. Shindo, and S. Ishibashi, “Hepatic insulin sen-sitivity assessed by integrated model of hepatic and peripheral glu-cose regulation,” Diabetes Technol. Therapeutics, vol. 11, no. 8, pp.487–492, 2009.

[66] M. Chierici, G. Toffolo, R. Basu, R. A. Rizza, and C. Cobelli, “Post-prandial endogenous glucose production from a single tracer labeledmeal: Validation against a triple tracer protocol,” Diabetes, vol. 56, no.supp. 1, p. 155-OR, 2007.

[67] G. Toffolo, R. Basu, C. Dalla Man, R. A. Rizza, and C. Cobelli,“Assessment of postprandial glucose metabolism: Conventional dualversus triple tracer method,” Amer. J. Physiol. Endocrinol. Metab.,vol. 291, pp. E800–E806, 2006.

[68] G. Toffolo, C. Dalla Man, C. Cobelli, and A. L. Sunehag, “Glucosefluxes during OGTT in adolescents assessed by a stable isotope tripletracer method,” J. Pediatr. Endocrinol. Metab., vol. 21, pp. 31–45,2008.

[69] E. Bonora, P. Moghetti, C. Zancanaro, M. Cigolini, M. Querena, V.Cacciatori, A. Corgnati, and M. Muggeo, “Estimates of in vivo insulinaction in man: Comparison of insulin tolerance tests with euglycemicand hyperglycemic glucose clamp studies,” J. Clin. Endocrinol.Metab., vol. 68, pp. 374–378, 1989.

[70] J. Kuikka, M. Levin, and J. B. Bassingthwaighte, “Multiple tracer dilu-tion estimates of D- and 2-deoxy-D-glucose uptake by the heart,” Amer.J. Physiol., vol. 250, pp. H29–H42, 1986.

[71] J. B. Bassingthwaighte and C. A. Goresky, “Modeling in the anal-ysis of solute and water exchange in the microvasculature,” in Hand-book of Physiology—The Cardiovascular System. Microcirculation.Bethesda, MD: Amer. Soc. Physiology, 1984.

[72] J. A. Jacquez, Compartmental Analysis in Biology and Medicine, 2nded. Ann Arbor, MI: Univ. Michigan Press, 1985.

[73] C. Cobelli, M. P. Saccomani, E. Ferrannini, R. A. DeFronzo, R.Gelfand, and R. C. Bonadonna, “A compartmental model to quantitatein vivo glucose transport in the human forearm,” Amer. J. Physiol.,vol. 257, pp. E943–E958, 1989.


[74] R. C. Bonadonna, M. P. Saccomani, L. Seely, K. Starick Zych, E. Fer-rannini, C. Cobelli, and R. A. DeFronzo, “Glucose transport in humanskeletal muscle: The in vivo response to insulin,” Diabetes, vol. 42, pp.191–198, 1993.

[75] M. P. Saccomani, R. C. Bonadonna, D. M. Bier, R. A. De Fronzo, andC. Cobelli, “A compartmental model to measure the effects of insulinon glucose transport and phosphorylation in human skeletal muscle. Atriple tracer study,” Amer. J. Physiol., vol. 270, pp. E170–E185, 1996.

[76] R. C. Bonadonna, S. Del Prato, E. Bonora, M. P. Saccomani, G. Gulli,A. Natali, S. Frascerra, N. Pecori, E. Ferrannini, D. M. Bier, C. Cobelli,and R. A. De Fronzo, “Roles of glucose transport and glucose phospho-rylation in muscle insulin resistance of NIDDM,” Diabetes, vol. 45, pp.915–925, 1996.

[77] M. Pendergrass, A. Bertoldo, R. C. Bonadonna, G. Nucci, L. Man-darino, C. Cobelli, and R. A. DeFronzo, “Muscle glucose transport andphosphorylation in type 2 diabetic, obese nondiabetic, and geneticallypredisposed individuals,” Amer. J. Physiol. Endocrinol. Metab., vol.292, pp. E92–E100, 2007.

[78] L. Sokoloff, M. Reivich, C. Kennedy, M. H. Des-Rosiers, C. S. Patlak,K. D. Pettigrew, O. Sakurada, and M. Shinohara, “The [14C]deoxyglu-cose method for the measurement of local cerebral glucose utilization:Theory, procedure, and normal values in the conscious and anesthetizedalbino rat,” J. Neurochem., vol. 28, pp. 897–916, 1977.

[79] T. Utriainen, S. Mäkimattilla, S. Lovisatti, A. Bertoldo, R. C.Bonadonna, S. Weintraub, R. De Fronzo, C. Cobelli, and H.Yki-Järvinen, “Lumped constant for [14C]deoxy-D-glucose inhuman skeletal muscle,” Diabetologia, vol. 41, p. A187, 1998.

[80] D. E. Kelley, K. V. Williams, J. C. Price, and B. Goodpaster, “Determi-nation of the lumped constant for [18F]FDG in human skeletal muscle,”J. Nucl. Med., vol. 40, pp. 1798–1804, 1999.

[81] A. Bertoldo, P. Peltoniemi, V. Oikonen, J. Knuuti, P. Nuutila, and C.Cobelli, “Kinetic modeling of [(18)F]FDG in skeletal muscle by PET:A four-compartment five-rate-constant model,” Amer. J. Physiol. En-docrinol. Metab., vol. 281, pp. E524–E536, 2001.

[82] K. V. Williams, A. Bertoldo, P. Kinahan, C. Cobelli, and D. E. Kelley,Diabetes, vol. 52, pp. 1619–1626, 2003.

[83] A. Bertoldo, R. R. Pencek, K. Azuma, J. C. Price, C. Kelley, C. Co-belli, and D. E. Kelley, “Interactions between delivery, transport, andphosphorylation of glucose in governing uptake into human skeletalmuscle,” Diabetes, vol. 55, pp. 3028–3037, 2006.

[84] E. Ferrannini and C. Cobelli, “The kinetics of insulin in man. I. Generalaspects,” Diabetes Metab. Rev., vol. 3, pp. 335–363, 1987.

[85] D. P. Frost, M. C. Srivastava, R. H. Jones, J. D. Nabarro, and P. H.Sonksen, “The kinetics of insulin metabolism in diabetes mellitus,”Postgrad. Med. J., vol. 49, no. Suppl 7, pp. 949–954, 1973.

[86] R. Hovorka, J. K. Powrie, G. D. Smith, P. H. Sönksen, E. R. Carson,and R. H. Jones, “Five-compartment model of insulin kinetics and itsuse to investigate action of chloroquine in NIDDM,” Am J. Physiol.,vol. 265, pp. E162–E175, 1993.

[87] T. Morishima, S. Pye, C. Bradshaw, and J. Radziuk, “Posthepatic rateof appearance of insulin: Measurement and validation in the nonsteadystate,” Amer. J. Physiol., vol. 263, pp. E772–E779, 1992.

[88] R. P. Eaton, R. C. Allen, D. S. Schade, K. M. Erickson, and J. Standefer,“Prehepatic insulin production in man: Kinetic analysis using periph-eral connecting peptide behavior,” J. Clin. Endocrinol. Metab., vol. 51,pp. 520–528, 1980.

[89] K. S. Polonsky, J. Licinio-Paixao, B. D. Given, B. D. W. Pugh, P. Rue,J. Galloway, T. Karrison, and B. Frank, “Use of biosynthetic humanC-peptide in the measurement of insulin secretion rates in normalvolunteers and type I diabetic patients,” J. Clin. Invest., vol. 51, pp.98–105, 1986.

[90] K. S. Polonsky, B. D. Given, and E. Van Cauter, “Twenty-four-hourprofiles and pulsatile patterns of insulin secretion in normal and obesesubjects,” J. Clin. Invest., vol. 81, no. 2, pp. 442–448, 1988.

[91] E. T. Shapiro, H. Tillil, A. H. Rubenstein, and K. S. Polonsky, “Pe-ripheral insulin parallels changes in insulin secretion more closely thanC-peptide after bolus intravenous glucose administration,” J. Clin. En-docrinol. Metab., vol. 67, no. 5, pp. 1094–1099, 1988.

[92] H. E. Tillil, E. T. Shapiro, M. A. Miller, T. Karrison, B. H. Frank, J.A. Galloway, A. H. Rubenstein, and K. S. Polonsky, “Dose-dependenteffects of oral and intravenous glucose on insulin secretion and clear-ance in normal humans,” Amer. J. Physiol., vol. 254, no. 3, pt. 1, pp.E349–E357, 1988.

[93] G. Sparacino and C. Cobelli, “A stochastic deconvolution approach toreconstruct insulin secretion rate after a glucose stimulus,” IEEE Trans.Biomed. Eng., vol. 42, no. 4, pp. 512–529, Apr. 1996.

[94] E. Van Cauter, F. F. Mestrez, J. Sturis, and K. S. Polonsky, “Estima-tion of insulin secretion rates from C-peptide levels. Comparison ofindividual and standard kinetic parameters for C-peptide clearance,”Diabetes, vol. 41, pp. 368–377, 1992.

[95] R. Hovorka, L. Chassin, S. D. Luzio, R. Playle, and D. R. Owens, “Pan-creatic beta-cell responsiveness during meal tolerance test: Model as-sessment in normal subjects and subjects with newly diagnosed non-in-sulin-dependent diabetes mellitus,” Clin. Endocrinol. Metab., vol. 83,pp. 744–750, 1998.

[96] K. S. Polonsky, B. D. Given, W. Pugh, J. Licinio-Paixao, J. E.Thompson, T. Karrison, and A. H. Rubenstein, “Calculation of thesystemic delivery rate of insulin in normal man,” J. Clin. Endocrinol.Metab., vol. 63, pp. 113–118, 1986.

[97] G. Toffolo, F. De Grandi, and C. Cobelli, “Estimation of beta-cell sen-sitivity from intravenous glucose tolerance test C-peptide data. Knowl-edge of the kinetics avoids errors in modeling the secretion,” Diabetes,vol. 44, pp. 845–854, 1995.

[98] P. Magni, R. Bellazzi, G. Sparacino, and C. Cobelli, “Bayesian iden-tification of a population compartmental model of C-peptide kinetics,”Ann. Biomed. Eng., vol. 28, pp. 812–823, 2000.

[99] P. Magni, G. Sparacino, R. Bellazzi, G. M. Toffolo, and C. Cobelli,“Insulin minimal model indexes and secretion: Proper handling of un-certainty by a bayesian approach,” Ann. Biomed. Eng., vol. 32, pp.1027–1037, 2004.

[100] A. Cretti, M. Lehtovirta, E. Bonora, B. Brunato, M. G. Zenti, F. Tosi,M. Caputo, B. Caruso, L. C. Groop, M. Muggeo, and R. C. Bonadonna,“Assessment of beta-cell function during the oral glucose tolerance testby a minimal model of insulin secretion,” Eur. J. Clin. Invest., vol. 31,pp. 405–416, 2001.

[101] E. Breda, M. K. Cavaghan, G. Toffolo, K. S. Polonsky, and C. Cobelli,“Oral glucose tolerance test minimal model indexes of �-cell functionand insulin sensitivity,” Diabetes, vol. 50, pp. 150–158, 2001.

[102] A. Mari, O. Schmitz, A. Gastaldelli, T. Oestergaard, B. Nyholm, andE. Ferrannini, “Meal and oral glucose tests for assessment of beta-cellfunction: Modeling analysis in normal subjects,” Am J Physiol. En-docrinol. Metab., vol. 283, pp. E1159–E1166, 2002.

[103] E. Breda, G. Toffolo, K. S. Polonsky, and C. Cobelli, “Insulin releasein impaired glucose tolerance: Oral minimal model predicts normalsensitivity to glucose but defective response times,” Diabetes, vol. 51,pp. S227–S233, 2002.

[104] G. Toffolo, E. Breda, M. K. Cavaghan, D. A. Ehrmann, K. S. Polonsky,and C. Cobelli, “Quantitative indexes of beta-cell function duringgraded up&down glucose infusion from C-peptide minimal models,”Amer. J. Physiol. Endocrinol. Metab., vol. 280, pp. E2–E10, 2001.

[105] G. M. Steil, C. Hwu, R. Janowski, F. Hariri, S. Jinagouda, C. Darwin,S. Tadros, K. Rebrin, and M. F. Saad, “Evaluation of insulin sensitivityand beta-cell function indexes obtained from minimal model analysisof a meal tolerance test,” Diabetes, vol. 53, pp. 1201–1207, 2004.

[106] R. Weiss, S. Caprio, M. Trombetta, S. E. Taksali, W. V. Tamborlane,and R. C. Bonadonna, “Beta-cell function across the spectrum of glu-cose tolerance in obese youth,” Diabetes, vol. 54, pp. 1735–1743, 2005.

[107] P. Denti, D. Salinger, P. Vicini, G. Toffolo, and C. Cobelli, “A non-linear mixed-effects approach to the estimation of the glucose disposi-tion index,” in Proc. PAGE 2009 Meeting, St. Petersburg, Russia, Jun.23–26, 2009.

[108] M. Campioni, G. M. Toffolo, R. Basu, R. A. Rizza, and C. Cobelli,“Minimal model assessment of hepatic insulin extraction during an oraltest from standard insulin kinetic parameters,” Amer. J. Physiol. En-docrinol. Metab., Aug. 11 [Epub ahead of print], 2009.

[109] G. Toffolo, M. Campioni, R. Basu, R. A. Rizza, and C. Cobelli, “Aminimal model of insulin secretion and kinetics to assess hepatic in-sulin extraction,” Amer. J. Physiol. Endocrinol. Metab., vol. 290, no.1, pp. E169–E176, 2006.

[110] K. S. Nair, R. A. Rizza, P. O’Brein, K. R. Short, A. Nehra, J. L. Vit-tone, G. G. Klee, A. Basu, R. Basu, C. Cobelli, G. Toffolo, C. DallaMan, D. J. Tindall, L. J. Melton, G. E. Smith, S. Khosla, and M. D.Jensen, “Effect of two years dehydropiandosterone in elderly men andwomen and testosterone in elderly men on physiological performance,body composition and bone density,” New England J Med., vol. 355,pp. 1647–1659, 2006.

[111] K. F. Petersen, S. Dufour, J. Feng, D. Befroy, J. Dzuira, C. Dalla Man,C. Cobelli, and G. Shulman, “Increased prevalence of insulin resistanceand non-alcholic fatty liver disease in asian indian men,” PNAS, vol.103, pp. 18273–18277, 2006.

[112] A. L. Sunehag, C. Dalla Man, G. Toffolo, M. W. Haymond, D. M. Bier,and C. Cobelli, “Beta-Cell function and insulin sensitivity in adoles-cents from an OGTT,” Obesity, vol. 17, pp. 233–239, 2009.

[113] A. M. Cali, C. Dalla Man, C. Cobelli, J. Dziura, A. Seyal, M. Shaw, K.Allen, S. Chen, and S. Caprio, “Primary defects in beta-cell functionfurther exacerbated by worsening of insulin resistance mark the devel-opment of impaired glucose tolerance in obese adolescents,” DiabetesCare, vol. 32, pp. 456–461, 2009.

[114] G. Bock, C. Dalla Man, M. Campioni, E. Chittilapilly, R. Basu, G.Toffolo, C. Cobelli, and R. A. Rizza, “Pathogenesis of pre-diabetes:Mechanisms of fasting and postprandial hyperglycemia in people withimpaired fasting glucose and/or impaired glucose tolerance,” Diabetes,vol. 55, pp. 3536–3549, 2006.


[115] G. Bock, E. Chittilapilly, R. Basu, G. Toffolo, C. Cobelli, V. Chan-dramouli, B. R. Landau, and R. A. Rizza, “Contribution of hepatic andextrahepatic insulin resistance to the pathogenesis of impaired fastingglucose: Role of increased rates of gluconeogenesis,” Diabetes, vol. 56,pp. 1703–1711, 2007.

[116] G. Bock, C. Dalla Man, M. Campioni, E. Chittilapilly, R. Basu, G.Toffolo, C. Cobelli, and R. A. Rizza, “Effects of nonglucose nutrientson insulin secretion and action in people with pre-diabetes,” Diabetes,vol. 56, pp. 1113–1119, 2007.

[117] A. Basu, C. Dalla Man, R. Basu, G. Toffolo, C. Cobelli, and R. A.Rizza, “Effects of type 2 diabetes on insulin secretion, insulin action,glucose metabolism,” Diabetes Care, vol. 32, pp. 866–872, 2009.

[118] C. Dalla Man, G. Bock, P. D. Giesler, D. B. Serra, M. Saylan Ligueros,J. E. Foley, M. Camilleri, G. Toffolo, C. Cobelli, R. A. Rizza, and A.Vella, “Dipeptidyl peptidase-4 inhibition by vidagliptin and the effectof insulin secretion and action in response to meal ingestion in type 2diabetes,” Diabetes Care, vol. 32, pp. 14–18, 2008.

[119] C. Cobelli, E. R. Carson, L. Finkelstein, and M. S. Leaning, “Validationof simple and complex models in physiology and medicine,” Amer. J.Physiol. Endocrinol. Metab., vol. 246, pp. R259–R266, 1984.

[120] G. M. Grodsky, “A threshold distribution hypothesis for packet storageof insulin and its mathematical modeling,” J. Clin. Invest., vol. 51, pp.2047–2059, Aug. 1972.

[121] J. Sturis, K. S. Polonsky, E. Mosekilde, and E. Van Cauter, “Computermodel for mechanisms underlying ultradian oscillations of insulin andglucose,” Amer. J. Physiol., vol. 260, pp. E801–E809, 1991.

[122] P. Vicini, A. Caumo, and C. Cobelli, “Glucose effectiveness and insulinsensitivity from the minimal models: Consequence of undermodelingassessed by Monte Carlo simulation,” IEEE Trans. Biomed. Eng., vol.46, no. 1, pp. 130–137, Jan. 1999.

[123] A. Caumo, P. Vicini, J. Zachwieja, A. Avogaro, K. Yarasheski, D. Bier,and C. Cobelli, “Undermodeling affects minimal model indexes: In-sights from a two-compartment model,” Amer. J. Physiol., vol. 276,pp. E1171–E1193, 1999.

[124] E. D. Lehmann, S. S. Chatu, and S. S. Hashmy, “Retrospective pilotfeedback survey of 200 users of the AIDA Version 4 Educational Dia-betes Program. 1—Quantitative survey data,” Diabetes Technol. Ther.,vol. 8, pp. 419–432, 2006.

[125] A. Rutscher, E. Salzsieder, U. Thierbach, U. Fischer, and G. Albrecht,“Kadis—A computer-aided decision support system for improving themanagement of type-1 diabetes,” Exp. Clin. Endocrinol.., vol. 95, pp.137–147, 1990.

[126] E. Salzsieder, U. Fischer, H. Stoewhas, U. Thierbach, A. Rutscher, R.Menzel, and G. Albrecht, “A model-based system for the individualprediction of metabolic responses to improve therapy in type I dia-betes,” Horm. Metab. Res. Suppl., vol. 24, pp. 10–19, 1990.

[127] R. Srinivasan, A. H. Kadish, and R. Sridhar, “A mathematical model forthe control mechanism of free fatty acid-glucose metabolism in normalhumans,” Comput. Biomed. Res., vol. 3, pp. 146–166, 1970.

[128] L. E. Fridlyand, M. C. Harbeck, M. W. Roe, and L. H. Philipson, “Reg-ulation of cAMP dynamics by Ca2+ and G protein-coupled receptors inthe pancreatic beta-cell: A computational approach,” Amer. J. Physiol.Cell Physiol., vol. 293, pp. C1924–C1933, Dec. 2007.

[129] C. Cobelli, G. Federspil, G. Pacini, A. Salvan, and C. Scandellari, “Anintegrated mathematical model of the dynamics of blood glucose andits hormonal control,” Math. Biosci., vol. 58, pp. 27–60, 1982.

[130] C. Cobelli and A. Mari, “Validation of mathematical models of com-plex endocrine-metabolic systems: A case study on a model of glucoseregulation,” Med. Biol. Eng. Comput., vol. 21, pp. 390–399, 1983.

[131] C. Cobelli and A. Ruggeri, “Evaluation of portal/peripheral route and ofalgorithms for insulin delivery in the closed-loop control of glucose indiabetes. A modeling study,” IEEE Trans. Biomed. Eng., vol. BME-30,no. 1, pp. 93–103, Jan. 1983.

[132] E. Salzsieder, G. Albrecht, U. Fischer, and E. J. Freys, “Kinetic mod-eling of the glucoregulatory system to improve insulin therapy,” IEEETrans. Biomed. Eng., vol. 32, no. 6, pp. 846–855, Jun. 1985.

[133] J. T. Sorensen, “A physiologic model of glucose metabolism in manand its use to design and assess improved insulin therapies for dia-betes,” Ph.D. dissertation, Dept. Chemical Eng., Massachusetts Inst.Technology, , 1985.

[134] E. D. Lehmann and T. Deutsch, “A physiological model of glucose-insulin interaction in type 1 diabetes mellitus,” J. Biomed. Eng., vol.14, pp. 235–242, 1992.

[135] S. Andreassen, J. J. Benn, R. Hovorka, K. G. Olesen, and E. R. Carson,“A probabilistic approach to glucose prediction and insulin dose ad-justment: Description of metabolic model and pilot evaluation study,”Comput. Methods Programs Biomed., vol. 41, pp. 153–165, 1994.

[136] R. Hovorka, V. Canonico, L. J. Chassin, U. Haueter, M. Massi-Benedetti, M. O. Federici, T. R. Pieber, H. C. Schaller, L. Schaupp,T. Vering, and M. E. Wilinska, “Nonlinear model predictive controlof glucose concentration in subjects with type 1 diabetes,” Physiol.Meas., vol. 25, pp. 905–920, 2004.

[137] C. Dalla Man, R. A. Rizza, and C. Cobelli, “Meal simulation model ofthe glucose-insulin system,” IEEE Trans. Biomed. Eng., vol. 54, no. 8,pp. 1740–1749, Aug. 2007.

[138] C. Dalla Man and C. Cobelli, “A pre & type 2 diabetes simulator for insilico trials,” in Proc. Ninth Diabetes Technology Meeting, San Fran-cisco, CA, 2009, accepted for publication.

[139] S. S. Kanderian, S. Weinzimer, G. Voskanyan, and G. M. Steil, “Identi-fication of intraday metabolic profiles during closed-loop glucose con-trol in individuals with type 1 diabetes,” J. Diabetes Sci. Technol., vol.3, pp. 1047–1057, 2009.

[140] B. P. Kovatchev, M. D. Breton, C. Dalla Man, and C. Cobelli, In silicomodel and computer simulation environment approximating the humanglucose/insulin utilization Food and Drug Administration Master FileMAF 1521, 2008.

[141] L. Magni, D. M. Raimondo, C. Dalla Man, G. De Nicolao, B. Ko-vatchev, and C. Cobelli, “Model predictive control of glucose concen-tration in type I diabetec patients: An in silico trial,” Biomed. SignalProcessing Contr., vol. 4, pp. 338–346, 2009.

[142] M. Wilinska, L. J. Chassin, H. C. Schaller, L. Schaupp, T. R. Pieber,and R. Hovorka, “Insulin kinetics in type-I diabetes: Continuous andbolus delivery of rapid acting insulin,” IEEE Trans. Biomed. Eng., vol.52, no. 1, pp. 3–12, Jan. 2005.

[143] M. E. Wilinska, E. S. Budiman, M. B. Taub, D. Elleri, J. M. Allen,C. L. Acerini, D. B. Dunger, and R. Hovorka, “Overnight closed-loopinsulin delivery with model predictive control: Assessment of hypo-glycemia and hyperglycemia risk using simulation studies,” J. DiabetesSci. Technol., vol. 3, pp. 1109–1120, 2009.

[144] R. Bertram, A. Sherman, and L. S. Satin, “Metabolic and electricaloscillations: Partners in controlling pulsatile insulin secretion,” Amer.J. Physiol. Endocrinol. Metab., vol. 293, pp. E890–E900, Oct. 2007.

[145] M. G. Pedersen, “Contributions of mathematical modeling of beta-cellsto the understanding of beta-cell oscillations and insulin secretion,” J.Diabetes Sci. Technol., vol. 3, pp. 12–20, Jan. 2009.

[146] E. Cerasi, G. Fick, and M. Rudemo, “A mathematical model for theglucose induced insulin release in man,” Eur. J. Clin. Invest., vol. 4,pp. 267–278, Aug. 1974.

[147] S. Daniel, M. Noda, S. G. Straub, and G. W. Sharp, “Identificationof the docked granule pool responsible for the first phase of glucose-stimulated insulin secretion,” Diabetes, vol. 48, pp. 1686–1690, Sep.1999.

[148] C. S. Olofsson, S. O. Göpel, S. Barg, J. Galvanovskis, X. Ma, A. Salehi,P. Rorsman, and L. Eliasson, “Fast insulin secretion reflects exocytosisof docked granules in mouse pancreatic B-cells,” Pflugers Arch., vol.444, pp. 43–51, May 2002.

[149] R. Nesher and E. Cerasi, “Modeling phasic insulin release: Immediateand time-dependent effects of glucose,” Diabetes, vol. 51, no. Suppl.1, pp. S52–S59, Feb. 2002.

[150] F. C. Jonkers and J.-C. Henquin, “Measurements of cytoplasmic Ca2+in islet cell clusters show that glucose rapidly recruits beta-cells andgradually increases the individual cell response,” Diabetes, vol. 50, pp.540–550, Mar. 2001.

[151] M. G. Pedersen, A. Corradin, G. M. Toffolo, and C. Cobelli, “A subcel-lular model of glucose-stimulated pancreatic insulin secretion,” Philos.Transact. Roy. Soc. A, vol. 366, pp. 3525–3543, Oct. 2008.

[152] G. Toffolo, E. Breda, M. K. Cavaghan, D. A. Ehrmann, K. S. Polonsky,and C. Cobelli, “Quantitative indexes of beta-cell function duringgraded up&down glucose infusion from C-peptide minimal models,”Am. J. Physiol. Endocrinol. Metab., vol. 280, pp. E2–E10, Jan. 2001.

[153] V. Licko, “Threshold secretory mechanism: A model of derivative el-ement in biological control,” Bull. Math. Biol., vol. 35, pp. 51–58,Feb.–Apr. 1973.

[154] F. N. Rahaghi and D. A. Gough, “Blood glucose dynamics,” DiabetesTechnol. Therapeutics, vol. 10, no. 2, pp. 81–94, 2008.

[155] D. A. Gough, K. Kreutz-Delgado, and T. M. Bremer, “Frequency char-acterization of blood glucose dynamics,” Ann. Biomed. Eng., vol. 31,no. 1, pp. 91–97, 2003.

[156] N. Porksen, M. Hollingdal, C. B. Juhl, P. Butler, J. D. Veldhuis, and O.Schmitz, “Pulsatile insulin secretion: Detection, regulation and role indiabetes,” Diabetes, vol. 51, pp. S245–S254, 2002.

[157] G. S. Meneilly, A. S. Ryan, J. D. Veldhuis, and D. Elahi, “Increaseddisorderliness of basal insulin release, attenuated insulin secretoryburstmass, and reduced ultradian rhythmicity of insulin secretion in olderindividuals,” J. Clinical Endocrinol. Metab., vol. 82, pp. 4088–4093,1997.

[158] G. S. Meneilly, J. D. Veldhuis, and D. Elahi, “Disruption of the pul-satile and entropic modes of insulin release during an unvarying glu-cose stimulus in elderly individuals,” J. Clin. Endocrinol. Metab., vol.84, pp. 1938–1943, 1999.

[159] O. Schmitz, N. Porksen, B. Nyholm, C. Skjaerback, P. C. Butler, J.D. Veldhuis, and S. M. Pincus, “Disorderly and nonstationary insulinsecretion in relatives of patients with NIDDM,” Amer. J. Physiol., vol.272, pp. E218–E226, 1997.


[160] J. D. Veldhuis, D. M. Keenan, and S. M. Pincus, “Motivations andmethods for analyzing pulsatile hormone secretion,” Endocrine Rev.,vol. 29, pp. 823–864, 2008.

[161] G. Merriam and K. Wachter, “Algorithms for the study of episodic hor-mone secretion,” Amer. J. Physiol., vol. 243, pp. E310–E318, 1982.

[162] K. E. Oerter, V. Guardabasso, and D. Rodbard, “Detection and char-acterization of peaks and estimation of instantaneous secretory rate forepisodic pulsatile hormone secretion,” Comput. Biomed. Res., vol. 19,pp. 170–191, 1986.

[163] E. Van Cauter, “Estimating false positive and false negative errorsin analysis of hormone pulsatility,” Amer. J. Physiol., vol. 254, pp.E786–E794, 1988.

[164] R. J. Urban, D. L. Kaiser, E. Van Cauter, M. L. Johnson, and J. D.Veldhuis, “Comparative assessments of objective peak-detection algo-rithms. II. Studies in men,” Amer. J. Physiol., vol. 254, no. 1 Pt 1, pp.E113–E119, Jan. 1988.

[165] J. Sturis, E. Van Cauter, J. D. Blackman, and K. S. Polonsky, “Entrain-ment of pulsatile insulin secretion by oscillatory glucose infusion,” J.Clin. Invest., vol. 87, pp. 439–445, 1991.

[166] P. Grambsch, M. H. Meller, and P. V. Grambsch, “Periodograms andpulse detection methods for pulsatile hormone data,” Stat. Med.. 30,vol. 21, no. 16, pp. 2331–2344, 2002.

[167] C. Simon, C. Brandenberger, M. Follenius, and J. Schlienger, “Alter-ation in the temporal organization of insulin secretion in type 2 diabeticpatients under continuous enteral nutrition,” Diabetologia, vol. 34, pp.435–440, 1991.

[168] J. Sturis, K. S. Polonsky, T. Shapiro, J. D. Blackman, N. O’Meara, andE. Van Cauter, “Abnormalities in the ultradian oscillations of insulinsecretion and glucose levels in type 2 diabetic patients,” Diabetologia,vol. 35, pp. 681–689, 1992.

[169] N. M. O’Meara, J. Sturis, E. Van Cauter, and K. S. Polonsky, “Lackof control by glucose of ultradian insulin secretory oscillations in im-paired glucose tolerance and in non-insulin-dependent diabetes mel-litus,” J. Clin. Invest., vol. 92, pp. 262–271, 1993.

[170] M. Hollingdal, C. B. Juhl, S. M. Pincus, J. Sturis, J. D. Veldhuis, K.S. Polonsky, N. Pørksen, and O. Schmitz, “Failure of physiologicalplasma glucose excursions to entrain high-frequency pulsatile insulinsecretion in type 2 diabetes,” Diabetes, vol. 49, no. 8, pp. 1334–1340,Aug. 2000.

[171] S. M. Pincus, “Approximate entropy as a measure of system com-plexity,” Proc Nat. Acad. Sci. USA, vol. 88, pp. 2297–2301, 1991.

[172] S. M. Pincus, “Quantification of evolution from order to randomness inpractical time series analysis,” Methods Enzymol., vol. 240, pp. 68–89,2004.

[173] S. M. Pincus, T. Mulligan, A. Iranmanesh, S. Gheorghiu, M. God-schalk, and J. D. Veldhuis, “Older males secrete luteinizing hormoneand testosterone more irregularly, and jointly more asynchronously,than younger males,” Proc. Nat. Acad. Sci. USA, vol. 93, no. 24, pp.14100–14105, 1996.

[174] W. S. Evans, L. S. Farhy, and M. L. Johnson, “Biomathematicalmodeling of pulsatile hormone secretion: A historical perspective,”Methods Enzymol., vol. 454, pp. 345–366, 2009.

[175] K. Friend, A. Iranmanesh, and J. D. Veldhuis, “The orderliness of thegrowth hormone (GH) release process and the mean mass of GH se-creted per burst are highly conserved in individual men on successivedays,” J. Clin.Endocrinol. Metab., vol. 81, pp. 3746–3753, 1996.

[176] H. M. Siragy, W. V. Vieweg, S. Pincus, and J. D. Veldhuis, “Increaseddisorderliness and amplified basal and pulsatile aldosterone secretionin patients with primary aldosteronism,” J. Clin. Endocrinol. Metab.,vol. 80, pp. 28–33, 1995.

[177] G. Van den Berg, S. M. Pincus, J. D. Veldhuis, M. Frolich, and F. Roelf-sema, “Greater disorderliness of ACTH and cortisol release accompa-nies pituitary-dependent Cushing’s disease,” Eur. J. Endocrinol., vol.136, pp. 394–400, 1997.

[178] G. McGarraugh and R. Bergenstal, “Detection of hypoglycemia withcontinuous interstitial and traditional blood glucose monitoring usingthe FreeStyle Navigator Continuous Glucose Monitoring System,” Di-abetes Technol. Therapeutics, vol. 11, no. 3, pp. 145–150, 2009.

[179] J. J. Meier, L. L. Kjems, J. D. Veldhuis, P. Lefèbvre, and P. C. Butler,“Postprandial suppression of glucagon secretion depends on intact pul-satile insulin secretion: Further evidence for the intraislet insulin hy-pothesis,” Diabetes, vol. 55, no. 4, pp. 1051–1056, 2006.

[180] G. Sparacino, F. Bardi, and C. Cobelli, “Approximate entropy studiesof hormone pulsatility from plasma concentration time series: Influenceof the kinetics assessed by simulation,” Ann. Biomed. Eng., vol. 28, no.6, pp. 665–676, Jun. 2000.

[181] J. D. Veldhuis, M. L. Johnson, O. L. Veldhuis, M. Straume, and S. M.Pincus, “Impact of pulsatility on the ensemble orderliness (approxi-mate entropy) of neurohormone secretion,” Amer. J. Physiol. Regul.Integr. Comp. Physiol., vol. 281, no. 6, pp. R1975–R1985, Dec. 2001.

[182] R. Bellazzi, P. Magni, and G. De Nicolao, “Bayesian analysis of bloodglucose time series from diabetes home monitoring,” IEEE Trans.Biomed. Eng., vol. 47, no. 7, pp. 971–975, Jul. 2000.

[183] P. Magni and R. Bellazzi, “A stochastic model to assess the variabilityof blood glucose time series in diabetic patients self-monitoring,” IEEETrans. Biomed. Eng., vol. 53, no. 6, pp. 977–985, Jun. 2006.

[184] B. P. Kovatchev, D. J. Cox, L. A. Gonder-Frederick, and W. L. Clarke,“Symmetrization of the blood glucose measurement scale and its ap-plications,” Diabetes Care, vol. 20, pp. 1655–1658, 1997.

[185] B. P. Kovatchev, M. Straume, D. J. Cox, and L. S. Farhy, “Risk anal-ysis of blood glucose data: A quantitative approach to optimizing thecontrol of insulin dependent diabetes,” J. Theoretical Medicine, vol. 3,pp. 1–10, 2001.

[186] B. P. Kovatchev, D. J. Cox, L. A. Gonder-Frederick, D. Young-Hyman,D. Schlundt, and W. L. Clarke, “Assessment of risk for severe hypo-glycemia among adults with IDDM: Validation of the low blood glu-cose index,” Diabetes Care, vol. 21, pp. 1870–1875, 1998.

[187] B. P. Kovatchev, D. J. Cox, A. Kumar, L. A. Gonder-Frederick, and W.L. Clarke, “Algorithmic evaluation of metabolic control and risk of se-vere hypoglycemia in type 1 and type 2 diabetes using Self-MonitoringBlood Glucose (SMBG) Data,” Diabetes Technol. Therapeutics, vol. 5,no. 5, pp. 817–828, 2003.

[188] D. J. Cox, L. A. Gonder-Frederick, L. Ritterband, W. L. Clarke, andB. P. Kovatchev, “Prediction of severe hypoglycemia,” Diabetes Care,vol. 30, pp. 1370–1373, 2007.

[189] B. P. Kovatchev, D. J. Cox, L. S. Farhy, M. Straume, L. A. Gonder-Frederick, and W. L. Clarke, “Episodes of severe hypoglycemia in type1 diabetes are preceded, and followed, within 48 hours by measurabledisturbances in blood glucose,” J. Clin. Endocrinol. Metab., vol. 85,pp. 4287–4292, 2000.

[190] B. P. Kovatchev, E. Otto, D. J. Cox, L. A. Gonder-Frederick, and W.L. Clarke, “Evaluation of a new measure of blood glucose variabilityin diabetes,” Diabetes Care, vol. 29, pp. 2433–2438, 2006.

[191] D. Deiss, J. Bolinder, J. Riveline, T. Battelino, E. Bosi, N. Tubiana-Rufi, D. Kerr, and M. Phillip, “Improved glycemic control in poorlycontrolled patients with type 1 diabetes using real-time continuous glu-cose monitoring,” Diabetes Care, vol. 29, pp. 2730–2732, 2006.

[192] K. Garg, H. Zisser, S. Schwartz, T. Bailey, R. Kaplan, S. Ellis, andL. Jovanovic, “Improvement in glycemic excursions with a transcuta-neous, real-time continuous glucose sensor,” Diabetes Care, vol. 29,pp. 44–50, 2006.

[193] The Juvenile Diabetes Research Foundation Continuous Glucose Mon-itoring Study Group, “Continuous glucose monitoring and intensivetreatment of type 1 diabetes,” New England J. Medicine, vol. 359, pp.1464–1476, 2008.

[194] I. B. Hirsch, D. Armstrong, R. M. Bergenstal, B. Buckingham, B. P.Childs, W. L. Clarke, A. Peters, and H. Wolpert, “Clinical applicationof emerging sensor technologies in diabetes management: Consensusguidelines for continuous glucose monitoring,” Diabetes Technol.Therapeutics, vol. 10, pp. 232–246, 2008.

[195] R. Hovorka, “The future of continuous glucose monitoring: Closedloop,” Current Diabetes Rev., vol. 4, pp. 269–279, 2008.

[196] K. Rebrin, G. M. Steil, W. P. van Antwerp, and J. J. Mastrototaro,“Subcutaneous glucose predicts plasma glucose independent of insulin:Implications for continuous monitoring,” Amer. J. Physiol. Endocrinol.Metab., vol. 277, pp. E561–E571, 1999.

[197] G. M. Steil, K. Rebrin, F. Hariri, S. Jinagonda, S. Tadros, C. Darwin,and M. F. Saad, “Interstitial fluid glucose dynamics during insulin-in-duced hypoglycemia,” Diabetologia, vol. 48, pp. 1833–1840, 2005.

[198] M. D. Breton, D. P. Shields, and B. P. Kovatchev, “Optimum subcu-taneous glucose sampling and Fourier analysis of continuous glucosemonitors,” J Diabetes Sci. Technol., vol. 2, pp. 495–500, 2008.

[199] M. Miller and P. Strange, “Use of Fourier models for analysis and in-terpretation of continuous glucose monitoring glucose profiles,” J. Di-abetes Sci. Technol., vol. 1, pp. 630–638, 2007.

[200] B. A. Buckingham, C. Kollman, R. Beck, A. Kalajian, R. Fi-allo-Scharer, M. J. Tansey, L. A. Fox, D. M. Wilson, S. A. Weinzimer,K. J. Ruedy, and W. V. Tamborlane, Diabetes Research In ChildrenNetwork (Direcnet) Study Group, “Evaluation of factors affectingCGMS calibration,” Diabetes Technol. Therapeutics, vol. 8, no. 3, pp.318–325, 2006.

[201] E. J. Knobbe and B. Buckingham, “The extended Kalman filter forcontinuous glucose monitoring,” Diabetes Technol. Therapeutics, vol.7, no. 1, pp. 15–27, 2005.

[202] L. M. Lesperance, A. Spektor, and K. J. McLeod, “Calibration of thecontinuous glucose monitoring system for transient glucose moni-toring,” Diabetes Technol. Therapeutics, vol. 9, no. 2, pp. 183–190,2007.

[203] V. Lodwig and L. Heinemann, “Glucose Monitoring Study Group.Continuous glucose monitoring with glucose sensors: Calibration andassessment criteria,” Diabetes Technol. Therapeutics, vol. 5, no. 4, pp.572–586, 2003.

[204] A. Facchinetti, G. Sparacino, and C. Cobelli, “Reconstruction of glu-cose in plasma from interstitial fluid continuous glucose monitoringdata: Role of sensor calibration,” J. Diabetes Sci. Technol., vol. 1, no.5, pp. 617–623, 2007.


[205] C. R. King, S. M. Anderson, M. D. Breton, W. L. Clarke, and B. P.Kovatchev, “Modeling of calibration effectiveness and blood-to-inter-stitial glucose dynamics as potential confounders of the accuracy ofcontinuous glucose sensors during hyperinsulinemic clamp,” J. Dia-betes Sci. Technol., vol. 1, pp. 317–322, 2007.

[206] M. Kuure-Kinsey, C. C. Palerm, and B. W. Bequette, “A dual-rateKalman filter for continuous glucose monitoring,” in Proc. IEEE Conf.Eng. Medicine Biology Soc., 2006, vol. 1, pp. 63–66.

[207] M. Boyne, D. Silver, J. Kaplan, and C. Saudek, “Timing of changesin interstitial and venous blood glucose measured with a continuoussubcutaneous glucose sensor,” Diabetes, vol. 52, pp. 2790–2794, 2003.

[208] B. P. Kovatchev, D. P. Shields, and M. D. Breton, “Graphical and nu-merical evaluation of continuous glucose sensing time lag,” DiabetesTechnol. Therapeutics, vol. 11, pp. 139–143, 2009.

[209] E. Kulcu, J. A. Tamada, G. Reach, R. O. Potts, and M. J. Lesho, “Phys-iological differences between interstitial glucose and blood glucosemeasured in human subjects,” Diabetes Care, vol. 26, pp. 2405–2409,2003.

[210] G. Voskanyan, D. B. Keenan, J. J. Mastrototaro, and G. M. Steil, “Pu-tative delays in interstitial fluid (ISF) glucose kinetics can be attributedto the glucose sensing systems used to measure them rather than thedelay in ISF glucose itself,” J. Diabetes Sci. Technol., vol. 1, no. 5, pp.639–644, 2007.

[211] I. M. E. Wentholt, A. A. M. Hart, J. B. L. Hoekstra, and J. H. De-Vries, “Relationship between interstitial and blood glucose in type 1diabetes patients: Delay and the push-pull phenomenon revisited,” Di-abetes Technol. Therapeutics, vol. 9, pp. 169–175, 2004.

[212] K. J. Wientjes and A. J. Schoonen, “Determination of time delaybetween blood and interstitial adipose tissue glucose concentrationchange by microdialysis in healthy volunteers,” Int. J. ArtificialOrgans, vol. 24, pp. 884–889, 2001.

[213] M. D. Breton and B. P. Kovatchev, “Analysis, modeling, and simula-tion of the accuracy of continuous glucose sensors,” J. Diabetes Sci.Technol., vol. 2, pp. 853–862, 2008.

[214] J. G. Chase, C. E. Hann, M. Jackson, J. Lin, T. Lotz, X. W. Wong,and G. M. Shaw, “Integral-based filtering of continuous glucosesensor measurements for glycaemic control in critical care,” ComputerMethods and Programs in Biomedicine, vol. 82, no. 3, pp. 238–247,2006.

[215] B. P. Kovatchev and W. L. Clarke, “Peculiarities of the continuousglucose monitoring data stream and their impact on developing closed-loop control technology,” J. Diabetes Sci. Technol., vol. 2, pp. 158–163,2008.

[216] W. L. Clarke and B. P. Kovatchev, “Continuous glucose sensors—Con-tinuing questions about clinical accuracy,” J. Diabetes Sci. Technol.,vol. 1, pp. 164–170, 2007.

[217] S. K. Garg, J. Smith, C. Beatson, B. Lopez-Baca, M. Voelmle, and P. A.Gottlieb, “Comparison of accuracy and safety of the SEVEN and thenavigator continuous glucose monitoring systems,” Diabetes Technol.Therapeutics, vol. 11, pp. 65–72, 2009.

[218] B. P. Kovatchev, S. M. Anderson, L. Heinemann, and W. L. Clarke,“Comparison of the numerical and clinical accuracy of four continuousglucose monitors,” Diabetes Care, vol. 31, pp. 1160–1164, 2008.

[219] The Diabetes Research in Children Network (DirecNet) Study Group,“The accuracy of the guardian RT continuous glucose monitor in chil-dren with type 1 diabetes,” Diabetes Technol. Therapeutics, vol. 10, pp.266–272, 2008.

[220] C. De Block, J. Vertommen, B. Manuel-y-Keenoy, and L. Van Gaal,“Minimally-invasive and non-invasive continuous glucose monitoringsystems: Indications, advantages, limitations and clinical aspects,”Current Diabetes Rev., vol. 4, no. 3, pp. 159–168, 2008.

[221] B. H. Ginsberg, “The current environment of CGM technologies,” J.Diabetes Sci. Technol., vol. 1, no. 1, pp. 118–121, 2007.

[222] D. C. Klonoff, “Continuous glucose monitoring: Roadmap for 21stcentury diabetes therapy,” Diabetes Care, vol. 28, pp. 1231–1239,2005.

[223] R. Hovorka, “Continuous glucose monitoring and closed-loop sys-tems,” Diabetic Medicine, vol. 23, pp. 1–12, 2005.

[224] G. Sparacino, A. Facchinetti, A. Maran, and C. Cobelli, “Continuousglucose monitoring time series and hypo/hyperglycemia prevention:Requirements, methods, open problems,” Current Diabetes Rev., vol.4, no. 3, pp. 181–192, 2008.

[225] A. Facchinetti, G. Sparacino, and C. Cobelli, “An on-line self-tune-able method to denoise CGM sensor data,” IEEE Trans. Biomed. Eng.10.1109/TBME.2009.2033264, to be published.

[226] C. C. Palerm, J. P. Willis, J. Desemone, and B. W. Bequette, “Hypo-glycemia prediction and detection using optimal estimation,” DiabetesTechnol. Therapeutics, vol. 7, pp. 3–14, 2005.

[227] A. Gani, A. V. Gribok, S. Rajaraman, W. K. Ward, and J. Reifman,“Predicting subcutaneous glucose concentration in humans:Data-driven glucose modeling,” IEEE Trans. Biomed. Eng., vol.56, no. 2, pp. 246–254, Feb. 2009.

[228] J. Reifman, S. Rajaraman, A. Gribok, and W. K. Ward, “Predictivemonitoring for improved management of glucose levels,” J. DiabetesSci. Technol., vol. 1, no. 4, pp. 478–486, 2007.

[229] G. Sparacino, F. Zanderigo, S. Corazza, A. Maran, A. Facchinetti, andC. Cobelli, “Glucose concentration can be predicted ahead in timefrom continuous glucose monitoring sensor time-series,” IEEE Trans.Biomed. Eng., vol. 54, no. 5, pp. 931–937, 2007.

[230] G. Sparacino, F. Zanderigo, A. Maran, and C. Cobelli, “Continuousglucose monitoring and hypo/hyperglycemia prediction,” DiabetesRes. Clin. Pract., vol. 74, no. Suppl 2, pp. S160–S163, 2006.

[231] C. Choleau, P. Dokladal, J. C. Klein, W. K. Ward, G. S. Wilson, andG. Reach, “Prevention of hypoglycemia using risk assessment with acontinuous glucose monitoring system,” Diabetes, vol. 51, no. 11, pp.3263–3273, Nov. 2002.

[232] F. Cameron, G. Niemayer, K. Gundy-Burlet, and B. Buckingham, “Sta-tistical hypoglycemia prediction,” J. Diabetes Sci. Technol., vol. 2, no.4, pp. 612–621, 2008.

[233] M. Eren-Oruklu, A. Cinar, L. Quinn, and D. Smith, “Estimation offuture glucose concentrations with subject-specific recursive linearmodels,” Diabetes Technol. Therapeutics, vol. 11, no. 4, pp. 243–253,2009.

[234] S. M. Pappada, B. D. Cameron, and P. M. Rosman, “Development ofa neural network for prediction of glucose concentration in type 1 di-abetes patients,” J. Diabetes Sci. Technol., vol. 2, no. 5, pp. 792–801,2008.

[235] C. Pérez-Gandía, A. Facchinetti, G. Sparacino, C. Cobelli, E. J.Gómez, and M. E. Hernando, “Artificial neural network algorithmfor on-line glucose prediction from continuous glucose monitoring,”Diabetes Technol. Ther., 2009, in press.

[236] F. Stahl and R. Johansson, “Diabetes mellitus modeling and short-termprediction based on blood glucose measurements,” Math. Biosci., vol.217, no. 2, pp. 101–117, 2009.

[237] C. Palerm and W. Bequette, “Hypoglycemia detection and predictionusing continuous glucose monitoring—A study on hypoglycemicclamp data,” J. Diabetes Sci. Technol., vol. 1, pp. 624–629, 2007.

[238] T. Heise, T. Koschinsky, L. Heinemann, and V. Lodwig, Glucose Mon-itoring Study Group, “Hypoglycemia warning signal and glucose sen-sors: Requirements and concepts,” Diabetes Technol. Theraputics, vol.5, no. 4, pp. 563–571, 2003.

[239] B. Bode, K. Gross, N. Rikalo, S. Schwartz, T. Wahl, C. Page, T. Gross,and J. Mastrototaro, “Alarms based on real-time sensor glucose valuesalert patients to hypo- and hyperglycemia: The Guardian continuousmonitoring system,” Diabetes Technol. Therapeutics, vol. 6, no. 2, pp.105–113, 2004.

[240] S. E. Noujaim, D. Horwitz, M. Sharma, and J. Marhoul, “Accuracy re-quirements for a hypoglycemia detector: An analytical model to eval-uate the effects of bias, precision, and rate of glucose change,” J. Dia-betes Sci. Technol., vol. 1, no. 5, pp. 653–668, 2007.

[241] W. K. Ward, “The role of new technology in the early detection ofhypoglycemia,” Diabetes Technol. Therapeutics, vol. 6, no. 2, pp.115–117, 2004.

[242] B. Buckingham, E. Cobry, P. Clinton, V. Gage, K. Caswell, E. Kun-selman, F. Cameron, and H. P. Chase, “Preventing hypoglycemia usingpredictive alarm algorithms and insulin pump suspension,” DiabetesTechnol. Therapeutics, vol. 11, no. 2, pp. 93–97, 2009.

[243] B. W. Bequette, “A critical assessment of algorithms and challenges inthe development of a closed-loop artificial pancreas,” Diabetes Technol.Therapeutics, vol. 7, pp. 28–47, 2005.

[244] M. E. Wilinska, L. J. Chassin, and R. Hovorka, “In silico testing—Im-pact on the progress of the closed loop insulin infusion for critical illpatient project,” J. Diabetes Technol., vol. 2, no. 3, pp. 417–423, 2008.

[245] R. Hovorka, L. J. Chassin, M. Ellmerer, J. Plank, and M. E. Wilinska,“A simulation model of glucose regulation in the critically ill,” Physiol.Meas., vol. 29, pp. 959–978, 2008.

[246] S. D. Patek, B. W. Bequette, M. Breton, B. A. Buckingham, E. Dassau,F. J. Doyle, III, J. Lum, L. Magni, and H. Zisser, “In silico preclinicaltrials: Methodology and engineering guide to closed-loop control inT1DM,” J. Diabetes Sci. Technol., vol. 3, no. 2, pp. 269–282, 2009.

[247] B. P. Kovatchev, C. Dalla Man, and C. Cobelli, “In silico preclinicaltrials: A proof of concept in closed-loop control of type 1 diabetes,” J.Diabetes Sci. Technol., vol. 3, pp. 44–55, 2009.

[248] E. Dassau, C. C. Palerm, H. Zisser, B. A. Buckingham, L. Jovanovic,and F. J. Doyle, III, “In silico evaluation platform for artificial pancre-atic �-cell development—A dynamic simulator for closed-loop controlwith hardware-in-the-loop,” Diabetes Technol. Ther., vol. 11, no. 3, pp.187–194, 2009.

[249] B. P. Kovatchev, S. Patek, E. Dassau, F. J. Doyle, III, L. Magni, G. DeNicolao, and C. Cobelli, “Control-to-range for diabetes functionalityand modular architecture,” J. Diabetes Sci. Technol., vol. 3, no. 5, pp.1058–1065, 2009.


[250] E. Cengiz, K. L. Swan, W. V. Tamborlane, G. M. Steil, A. T. Steffen,and S. A. Weinzimer, “Is an automatic pump suspension feature safe forchildren with type 1 diabetes? An exploratory analysis with closed-loopsystem,” Diabetes Technol. Therapeutics, vol. 11, no. 4, pp. 207–210,2009.

[251] H. Zisser, L. Robinson, W. Bevier, E. Dassau, C. Ellingsen, F. J. Doyle,III, and L. Jovanovic, “Bolus calculator: A review of four “smart” in-sulin pumps,” Diabetes Technol. Ther., vol. 10, no. 6, pp. 441–444,2008.

[252] S. D. Patek, M. D. Breton, C. Hughes, and B. P. Kovatchev, “Control ofhypoglycemia via estimation of active insulin, glucose forecasts, andrisk-based insulin reduction,” in Proc. 2nd Advanced Technol. Treat-ment for Diabetes, Athens, Greece, 2009.

[253] A. J. Kowalski, “Can we really close the loop and how soon? Accel-erating the availability of an artificial pancreas: A roadmap to betterdiabetes outcomes,” Diabetes Technol. Therapeutics, vol. 11, pp.S113–S119, 2009.

[254] L. Magni, M. Forgione, C. Toffanin, C. Dalla Man, G. De Nicolao,B. Kovatchev, and C. Cobelli, “Run-to-run tuning of model predictivecontrol for type I diabetic subjects: An in silico trial,” J. Diabetes Sci.Technol., vol. 3, no. 5, pp. 1091–1098, 2009.

[255] B. P. Kovatchev, S. Anderson, M. Breton, S. Patek, W. Clarke, D. Brut-tomesso, A. Maran, S. Costa, A. Avogaro, C. Dalla Man, A. Facchinetti,S. Guerra, L. Magni, D. M. Raimondo, G. De Nicolao, E. Renard, andC. Cobelli, “Personalized subcutaneous model-predictive closed-loopcontrol of T1DM: Pilot studies in the USA and Italy,” Diabetes, vol.58, no. Suppl. 1, pp. A60–A60, Jun. 2009.

[256] D. Bruttomesso, A. Farret, S. Costa, M. C. Marescotti, M. Vettore,A. Avogaro, A. Tiengo, C. Dalla Man, J. Place, A. Facchinetti, S.Guerra, L. Magni, G. De Nicolao, C. Cobelli, E. Renard, and A.Maran, “Closed-loop artificial pancreas using subcutaneous glucosesensing & insulin delivery, and a model predictive control algorithm:Preliminary studies in Padova and Montpellier,” J. Diabetes Sci.Technol., vol. 3, no. 5, pp. 1014–1021, 2009.

[257] W. L. Clarke, S. M. Anderson, M. D. Breton, S. D. Patek, L. Kashmer,and B. P. Kovatchev, “Closed-loop artificial pancreas using subcuta-neous glucose sensing and insulin delivery and a model predictive con-trol algorithm: The Virginia experience,” J. Diabetes Sci. Technol., vol.3, no. 5, pp. 1031–1038, 2009.

[258] H. Lee, B. A. Buckingham, D. M. Wilson, and B. W. Bequette, “Aclosed-loop artificial pancreas using model predictive control and asliding meal size estimation,” J. Diabetes Sci. Technol., vol. 3, no. 5,pp. 1082–1090, 2009.

[259] G. M. Steil, A. E. Panteleon, and K. Rebrin, “Closed-loop insulin de-livery—The path to physiological glucose control,” Adv. Drug Deliv.Rev., vol. 56, pp. 125–144, 2004.

[260] G. M. Steil, K. Rebrin, C. Darwin, F. Hariri, and M. F. Saad, “Fea-sibility of automating insulin delivery for the treatment of type 1 dia-betes,” Diabetes, vol. 55, no. 12, pp. 3344–3350, 2006.

[261] G. Marchetti, M. Barolo, L. Jovanovic, H. Zisser, and D. E. Seborg,“An improved PID switching control strategy for type 1 diabetes,”IEEE Trans. Biomed. Eng., vol. 55, no. 3, pp. 857–865, 2008.

[262] Y. Wang, M. W. Percival, E. Dassau, H. C. Zisser, L. Jovanovic, andF. J. Doyle, III, “A novel adaptive basal therapy based on the value andrate of change of blood glucose,” J. Diabetes Technol., vol. 3, no. 5, pp.1099–1108, 2009.

[263] Nonlinear Model Predictive Control: Towards New Challenging Ap-plications, L. Magni, D. M. Raimondo, and F. Allgower, Eds. NewYork: Springer Verlag, 2009, vol. 384, Springer Lecture Notes in Con-trol and Information Sciences series.

[264] R. Hovorka, L. J. Chassin, M. E. Wilinska, V. Canonico, J. A. Akwi, M.O. Federici, M. Massi-Benedetti, I. Hutzli, C. Zaugg, H. Kaufmann, M.Both, T. Vering, H. C. Schaller, L. Schaupp, M. Bodenlenz, and T. R.Pieber, “Closing the loop: The adicol experience,” Diabetes Technol.Therapeutics, vol. 8, no. 3, pp. 307–318, 2004.

[265] H. C. Schaller, L. Schaupp, M. Bodenlenz, M. E. Wilinska, L. J.Chassin, P. Wach, T. Vering, R. Hovorka, and T. R. Pieber, “On-lineadaptive algorithm with glucose prediction capacity for subcutaneousclosed loop control of glucose: Evaluation under fasting conditions inpatients with type 1 diabetes,” Diabetic Medicine, vol. 23, pp. 90–93,2006.

[266] D. A. Finan, C. C. Palerm, F. J. Doyle, III, D. E. Seborg, H. Zisser, W.C. Bevier, and L. Jovanovic, “Effect of input excitation on the qualityof empirical dynamic models for type 1 diabetes,” AIChE J, vol. 55,pp. 1135–1146, 2009.

[267] F. Galvanin, M. Barolo, S. Macchietto, and F. Bezzo, “Optimal designof clinical tests for the identification of physiological models of type 1diabetes mellitus,” Ind. Eng. Chem. Res., vol. 48, no. 4, pp. 1989–2002,2009.

[268] P. Dua, F. J. Doyle, III, and E. N. Pistikopoulos, “Model-based bloodglucose control for type 1 diabetes via parametric programming,” IEEETrans. Biomed. Eng., vol. 53, no. 6, pp. 1478–1491, Jun. 2006.

[269] C. Ellingsen, E. Dassau, H. Zisser, B. Grosman, M. W. Percival, L. Jo-vanovic, and F. J. Doyle, III, “Safety constraints in an artificial pancreasbeta cell: An implementation of model-predictive control with insulinon board,” J. Diabetes Sci . Technol., vol. 3, pp. 536–544, 2009.

[270] L. Magni, D. M. Raimondo, L. Bossi, C. Dalla Man, G. De Nicolao,B. Kovatchev, and C. Cobelli, “Model predictive control of type 1 dia-betes: An in silico trial,” J. Diabetes Sci. Technol., vol. 1, pp. 804–812,2007.

[271] F. H. El-Khatib, J. Jiang, and E. R. Damiano, “Adaptive closed-loopcontrol provides blood glucose regulation using dual subcutaneousinsulin and glucagon infusion in diabetic swine,” J. Diabetes Sci.Technol., vol. 1, pp. 181–192, 2007.

[272] F. H. El-Khatib, J. Jiang, and E. R. Damiano, “A feasibility study of bi-hormonal closed-loop blood glucose control using dual subcutaneousinfusion of insulin and glucagon in ambulatory diabetic swine,” J. Di-abetes Sci. Technol., vol. 3, no. 4, pp. 789–803, 2009.

[273] R. Gillis, C. C. Palerm, H. Zisser, L. Jovanovic, D. E. Seborg, and F.J. Doyle, “Glucose estimation and prediction through meal responsesusing ambulatory subject data for advisory mode model predictive con-trol,” J. Diabetes Sci. Technol., vol. 1, no. 6, pp. 825–833, 2007.

[274] C. C. Palerm, J. P. Willis, J. Desemone, and B. W. Bequette, “Hypo-glycemia prediction and detection using optimal estimation,” DiabetesTechnol. Therapeutics, vol. 7, no. 1, pp. 3–15, 2005.

[275] C. C. Palerm and B. W. Bequette, “Hypoglycemia detection and predic-tion using continuous monitoring—A study on hypoglycaemic clampdata,” J. Diabetes Sci. Technol., vol. 1, no. 5, pp. 624–629, 2009.

[276] E. Dassau, B. A. Buckingham, B. W. Bequette, and F. J. Doyle, III,“Detection of a meal using continuous glucose monitoring: Implica-tions for an artificial�-cell,” Diabetes Care, vol. 31, no. 2, pp. 295–300,2008.

[277] F. Cameron, G. Niemeyer, and B. A. Buckingham, “Probabilisticevolving meal detection and estimation of meal total glucose appear-ance,” J. Diabetes Sci. Technol., vol. 3, no. 5, pp. 1022–1030, 2009.

[278] W. L. Clarke and B. P. Kovatchev, “Statistical tools to analyze CGMdata,” Diabetes Technol. Therapeutics, vol. 11, pp. S45–S54, 2009.

[279] L. Magni, D. M. Raimondo, C. Dalla Man, M. Breton, S. Patek, G.De Nicolao, C. Cobelli, and B. Kovatchev, “Evaluating the efficacyof closed-loop glucose regulation via control-variability grid analysis(CVGA),” J. Diabetes Sci. Technol., vol. 2, pp. 630–635, 2008.

[280] H. Zisser, L. Jovanovic, F. J. Doyle, III, P. Ospina, and C. Owens,“Run-to-run control of meal-related insulin dosing,” Diabetes Technol.Ther., vol. 7, no. 1, pp. 48–57, 2005.

[281] C. C. Palerm, H. Zisser, L. Jovanovic, and F. J. Doyle, III, “A run-to-runframework for prandial insulin dosing: Handling real-life uncertainty,”Int. J. Robust Nonlin., vol. 17, no. 13, pp. 1194–1213, Sep. 2007.

[282] C. C. Palerm, H. Zisser, L. Jovanovic, and F. J. Doyle, III, “A run-to-runcontrol strategy to adjust basal insulin infusion rates in type 1 diabetes,”J. Process Contr., vol. 18, no. 3–4, pp. 258–265, Mar.–Apr. 2008.

[283] Y. Wang, E. Dassau, and F. J. Doyle, III, “Closed-loop control of artifi-cial pancreatic �-cell in type 1 diabetes mellitus using model predictiveiterative learning control,” IEEE Trans. Biomed. Eng., to appear.

[284] G. Roglic, N. Unwin, P. H. Bennett, C. Mathers, J. Tuomilehto, S. Nag,V. Connolly, and H. King, “The burden of mortality attributable todiabetes: Realistic estimates for the year 2000,” Diabetes Care, vol.28, pp. 2130–2135, 2005.

[285] C. Dalla Man, D. M. Raimondo, R. A. Rizza, and C. Cobelli, “GIM,simulation software of meal glucose-insulin model,” J. Diabetes Sci.Technol., vol. 1, pp. 323–330, 2007.

[286] G. Nucci and C. Cobelli, “Models of subcutaneous insulin kinetics.A critical review,” Comput Methods Programs Biomed., vol. 62, pp.249–257, 2000.

[287] P. Roach, “New insulin analogues and routes of delivery: Pharmacody-namic and clinical considerations,” Clin Pharmacokinet., vol. 47, pp.595–610, 2008.

[288] P. Rossetti, F. Porcellati, C. G. Fanelli, G. Perriello, E. Torlone, and G.B. Bolli, “Superiority of insulin analogues versus human insulin in thetreatment of diabetes mellitus,” Arch. Physiol. Biochem., vol. 114, pp.3–10, 2008.

[289] A. Chan, M. D. Breton, and B. P. Kovatchev, “Effects of pulsatile sub-cutaneous injections of insulin lispro on plasma insulin concentrationlevels,” J Diabetes Sci. Technol., vol. 2, pp. 844–852, 2008.

[290] S. A. Weinzimer, G. M. Steil, K. L. Swan, J. Dziura, N. Kurtz, and W.V. Tamborlane, “Fully automated closed-loop insulin delivery versussemi-automated hybrid control in pediatric patients with type 1 dia-betes using an artificial pancreas,” Diabetes Care, vol. 31, pp. 934–939,2008.

[291] A. E. Panteleon, M. Loutseiko, G. M. Steil, and K. Rebrin, “Evaluationof the effect of gain on the meal response of an automated closed-loopinsulin delivery system,” Diabetes, vol. 55, pp. 1995–2000, 2006.

[292] S. D. Patek, M. D. Breton, Y. Chen, C. Solomon, and B. Kovatchev,“Linear quadratic gaussian-based closed-loop control of type 1 dia-betes,” J. Diabetes Sci. Technol., vol. 1, no. 6, pp. 834–841, 2007.


[293] J. Moyne, E. del Castillo, and A. M. Hurwitz, Run-to-Run Control inSemiconductor Manufacturing. Boca Raton, FL: CRC, 2001.

[294] L. A. Gonder-Frederick, D. J. Cox, B. P. Kovatchev, D. Schlundt, andW. L. Clarke, “Biopsychobehavioral model of risk of severe hypo-glycemia,” Diabetes Care, vol. 20, pp. 661–669, 1997.

[295] B. P. Kovatchev, D. J. Cox, L. A. Gonder-Frederick, D. Schlundt, andW. L. Clarke, “Stochastic model of self-regulation decision makingexemplified by decisions concerning hypoglycemia,” Health Psychol.,vol. 17, pp. 277–284, 1998.

[296] S. D. Patek, M. D. Breton, C. Cobelli, C. Dalla Man, and B. P. Ko-vatchev, “Adaptive meal detection algorithm enabling closed-loop con-trol in type 1 diabetes,” in Proc. 7th Diabetes Technology Meeting, SanFrancisco, CA, 2007.

[297] W. L. Clarke, D. J. Cox, L. A. Gonder-Frederick, D. M. Julian, B. P.Kovatchev, and D. Young-Hyman, “The bio-psycho-behavioral modelof severe hypoglycemia II: Self-management behaviors,” DiabetesCare, vol. 22, pp. 580–584, 1999.

[298] D. J. Cox, L. A. Gonder-Frederick, B. P. Kovatchev, D. Young-Hyman,D. Schlundt, D. M. Julian, and W. L. Clarke, “Bio-psycho-behavioralmodel of severe hypoglycemia: II understanding causes of severe hy-poglycemia,” Diabetes Care, vol. 22, pp. 2018–2025, 1999.

[299] M. D. Breton, W. L. Clarke, L. S. Farhy, and B. P. Kovatchev, “A modelof self-treatment behavior, glucose variability, and hypoglycemia-asso-ciated autonomic failure in type 1 diabetes,” J. Diabetes Sci. Technol.,vol. 1, pp. 331–357, 2007.

[300] M. Davidian and D. M. Giltinan, Nonlinear Models for Repeated Mea-surement Data. Boca Raton, FL: Chapman & Hall/CRC, 1998.

[301] P. Denti, A. Bertoldo, P. Vicini, and C. Cobelli, “Nonlinear mixed ef-fects to improve glucose minimal model parameter estimation: a sim-ulation study in intensive and sparse sampling,” IEEE Trans. Biomed.Eng., vol. 56, no. 9, pt. 1, pp. 2156–2166, Sep. 2009.

[302] P. Denti, A. Bertoldo, P. Vicini, and C. Cobelli, “Covariate Selec-tion for the IVGTT Minimal Model of Glucose Disappearance,” inProc. 18th Population Approach Group in Europe Meeting, St. Peters-burg, Russia, 2009 [Online]. Available: http://www.page-meeting.org/default.asp?abstract=1642

[303] H. E. Silber, P. M. Jauslin, N. Frey, R. Gieschke, U. S. Simonsson,and M. O. Karlsson, “An integrated model for glucose and insulin reg-ulation in healthy volunteers and type 2 diabetic patients followingintravenous glucose provocations,” J. Clin. Pharmacol., vol. 47, pp.1159–1171, 2007.

[304] P. M. Jauslin, H. E. Silber, N. Frey, R. Gieschke, U. S. Simonsson, K.Jorga, and M. O. Karlsson, “An integrated glucose-insulin model todescribe oral glucose tolerance test data in type 2 diabetics,” J. Clin.Pharmacol., vol. 47, pp. 1244–1255, 2007.

Claudio Cobelli (M’84–SM’90–F’01) was born inBressanone (Bolzano), Italy, on February 21, 1946.He received the Ph.D. degree (Laurea) in electricalengineering from the University of Padova, Padova,Italy, in 1970.

From 1970 to 1980, he was a Research Fellow ofthe Institute of System Science and Biomedical En-gineering, National Research Council, Padova. From1973 to 1975 and 1975 to 1981, he was an AssociateProfessor of biological systems at the University ofFlorence and Associate Professor of biomedical engi-

neering at the University of Padova, respectively. In 1981, he became a Full Pro-fessor of biomedical engineering at the University of Padova. Since 2000, he hasbeen an Affiliate Professor of bioengineering at the University of Washington,Seattle. Since 2000, he has been Chairman of the Graduate and Ph.D. Programon bioengineering at the University of Padova. His main research activity isin the field of modeling and identification of physiological systems, especiallyendocrine-metabolic systems. He has published around 280 papers in interna-tionally refereed journals. He is Coeditor of Carbohydrate Metabolism: Quanti-tative Physiology and Mathematical Modeling (Chichester: Wiley, 1981), Mod-eling and Control of Biomedical Systems (Oxford: Pergamon, 1989), and Mod-eling Methodology for Physiology and Medicine (New York: Academic, 2000).He is Coauthor of The Mathematical Modeling of Metabolic and Endocrine Sys-tems (New York: Wiley, 1983); Tracer Kinetics in Biomedical Research: fromData to Model (London: Kluwer Academic/Plenum, 2001) and Introduction toModeling in Physiology and Medicine (San Diego: Academic, 2008).

Dr. Cobelli is currently an Associate Editor of IEEE TRANSACTIONS ON

BIOMEDICAL ENGINEERING and Diabetes. He is on the Editorial Board of theAmerican Journal of Physiology: Endocrinology and Metabolism, Diabetes,and Journal of Diabetes Science & Technology. In the past he has been Asso-ciate Editor of Mathematical Biosciences and on the Editorial Board of Control

Engineering Practice, Diabetes, Nutrition and Metabolism, Diabetologia,and American Journal of Physiology: Modeling in Physiology. He has beenChairman (1999–2004) of the Italian Biomedical Engineering Group and hasbeen Chairman (1990–1993 and 1993–1996) of IFAC TC on Modeling andControl of Biomedical Systems. He is Fellow of BMES.

Chiara Dalla Man was born in Venice, Italy, onMarch 2, 1977. She received the Ph.D. degree(Laurea) cum laude in electronics engineering fromthe University of Padova, Padova, Italy, in 2000.She also received the Ph.D degree in biomedicalengineering from the University of Padova, and CityUniversity London, U.K., in 2005.

From March to September 2004, she was a VisitingPh.D. Student at the Centre of Measurements andInformation in Medicine, City University London,U.K. From 2005 to 2007, she was a Post-Doctoral

Research Fellow with the Department of Information Engineering of PadovaUniversity. Since October 2007, she has been an Assistant Professor in theFaculty of Engineering of Padova University. Her research interests include thefield of mathematical modeling of metabolic and endocrine systems.

Dr. Dalla Man is on the Editorial Board of Journal of Diabetes Science andTechnology.

Giovanni Sparacino was born in Pordenone, Italy,on November 11, 1967. He received the Doctoraldegree in electronics engineering cum laude fromthe University of Padua, Padua, Italy, in 1992, andthe Ph.D. degree in biomedical engineering from thePolytechnic of Milan, Milan, Italy, in 1996.

Since 1997, he has been with the Universityof Padua: from 1997 to 1998, he was a ResearchEngineer at the Faculty of Medicine; from 1999 to2004, he was an Assistant Professor at the Faculty ofEngineering; since 2005, he has been an Associate

Professor of biomedical engineering at the Faculty of Engineering. His scien-tific interests include deconvolution and parameter estimation techniques forthe study of physiological systems, hormone time-series analysis, continuousglucose monitoring, and measurement and processing of evoked potentials.

Lalo Magni was born in Bormio, Italy, in 1971. Hegraduated with full marks and honors (summa cumlaude) in computer engineering from the Universityof Pavia, Pavia, Italy, in 1994. He received the Ph.D.degree in electronic and computer engineering in1998.

From January 1999 to December 2004, he wasan Assistant Professor at the University of Pavia,where he has been an Associate Professor sinceJanuary 2005. From October 1996 to February1997 and in March 1998, he was at CESAME,

Universitè Catholique de Louvain, Louvain La Neuve, Belgium. From Octoberto November 1997, he was at the University of Twente with the System andControl Group in the Faculty of Applied Mathematics. His current researchinterests include nonlinear control, predictive control, robust control, processcontrol and glucose concentration control in subjects with diabetes. His re-search is witnessed by more than 40 papers published in international journals.

Dr. Magni was a Plenary Speaker at the 2nd IFAC Conference “Control Sys-tems Design” (CSD’03), in 2003. In 2005, he was a Keynote Speaker at theNMPC Workshop on Assessment and Future Direction. In 2003, he was a GuestEditor of the Special Issue “Control of Nonlinear Systems with Model Predic-tive Control” in the International Journal of Robust and Nonlinear Control.He served as an Associate Editor of the IEEE TRANSACTIONS ON AUTOMATIC

CONTROL. He is an Associate Editor of Automatica. He was subarea Chair forthe area “Nonlinear systems optimal and predictive control” at the IFAC Sympo-sium on Nonlinear Control Systems (NOLCOS 2007). He organized the NMPCWorkshop on Assessment and Future Direction in September 2008 in Pavia.


Giuseppe De Nicolao (SM’01) received the degreein electronic engineering from the Polytechnic ofMilan, Italy.

From 1987 to 1988, he was with the Biomathe-matics and Biostatistics Unit of the Institute of Phar-macological Researches “Mario Negri”, Milano. In1988, he joined the Italian National Research Council(CNR) as a Research Scientist at the Center of SystemTheory in Milan, Italy. From 1992 to 2000, he wasan Associate Professor and, since 2000, he has beena full Professor of model identification in the Depart-

ment of Computer Science and Systems Engineering of the University of Pavia,Pavia, Italy. In 1991, he held a visiting fellowship at the Department of Sys-tems Engineering of the Australian National University, Canberra. His researchinterests include Bayesian learning, neural networks, model predictive control,optimal and robust filtering and control, deconvolution techniques, modeling,identification and control of biomedical systems, advanced process control andfault diagnosis for semiconductor manufacturing. On these subjects he has au-thored or coauthored more than 100 journal papers and is coinventor of twopatents.

Dr. De Nicolao was a Keynote Speaker at the IFAC workshop on “Non-linear model predictive control: Assessment and future directions for research”.From 1999 to 2001, he was an Associate Editor of the IEEE TRANSACTIONS

ON AUTOMATIC CONTROL and, since 2007, he has been an Associate Editor ofAutomatica.

Boris P. Kovatchev received the Ph.D. degree inmathematics (probability and statistics) from SofiaUniversity “St. Kliment Ohridski,” Bulgaria, in1989.

Currently, he is a Professor in the Departmentof Psychiatry and Neurobehavioral Sciences andAdjunct Professor of Systems and InformationEngineering, University of Virginia, Charlottesville.He is Head of Section Computational Neuroscienceand Director of the University of Virginia DiabetesTechnology Program. His research expertise is in

biomathematics, specifically modeling of biologic and behavioral processes. Inthe past 15 years he has been involved in various aspects of diabetes technologydevelopment, as well as in the development of quantitative strategies forneurobiological problems. Currently, he is the Principal Investigator of twolarge projects funded by the National Institutes of Health, and the Principal In-vestigator of the JDRF Artificial Pancreas Project at the University of Virginia.He is also involved in industry-sponsored translational research. He is authorof over 100 scientific publications and coauthor of the textbook Invitation toBiomathematics (Academic, 2008). His academic work includes participationin several international boards and NIH study sections. He holds five patentsand is author of 15 other inventions that are currently at various stages of thepatenting process.

Dr. Kovatchev is an Associate Editor of IEEE TRANSACTIONS ON

BIOMEDICAL ENGINEERING and member of the Editorial board of theJournal of Diabetes Science and Technology.

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