602 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 14, NO. 4, JULY 2006

Fluidic Operational Amplifier for MockCirculatory Systems

Kwan-Woong Gwak, Brad E. Paden, Fellow, IEEE, Myounggyu D. Noh, and James F. Antaki

Abstract—For the development of cardiovascular devices andthe study of the dynamics of blood flow through the cardiovas-cular system, hardware fluidic models are commonly used to min-imize animal experiments and clinical trials. These systems, called“mock circulatory systems,” are also critical for the development ofventricular assist devices. The passive and active elements in thesesystems are frequently “hard-plumbed” and are difficult to modifyin experimental studies. Therefore, we propose a concept of novelfluidic operational amplifier comprised of a high-gain feedback-controlled gear pump. With pressure being the analog of voltage,design with the fluidic op-amp is analogous to electrical op-ampcircuit design. Initial computer and hardware simulation resultsdemonstrate that the device may be programmed for use in mockcirculatory systems to emulate the function of the energy sources(the ventricles) or passive networks (hemodynamic loads).

Index Terms—Feedback-controlled gear pump, fluidic opera-tional amplifier, impedance, mock circulatory systems.

I. INTRODUCTION

MOCK CIRCULATORY systems (MCSs) are valuablelaboratory instruments for the understanding of blood

flow dynamics, or “hemodynamics,” in animal and humancardiovascular systems. Our particular interest is motivated bythe development and in vitro evaluation of ventricular assistdevices (VADs). As various types of VADs and related controlsystems are developed, new features must be evaluated beforeanimal testing and subsequent use in humans. This need isdriven by the obvious ethical and economic requirements,and also the scientific need to evaluate VADs over a widerange of operating conditions that would not be possible witha single in vivo trial. Conventional MCSs are not flexiblein modifying their characteristics because they are made of“hard-plumbed” (approximately) linear fluidic elements forsimulating resistances ( ), inertances ( ), compliances ( )

Manuscript received September 23, 2004. Manuscript received in finalform February 13, 2006. Recommended by Associate Editor F. Ghorbel.This work was supported in part by the National Institute of Health/NHLB1(1R43HL66656-01) and by the National Science Foundation—Control, Net-works, and Computational Intelligences (ECS-03000097).

K.-W. Gwak was with LaunchPoint Technologies, Goleta, CA 93117 USA.He is now with the Department of Mechanical Engineering, Sejong University,143-747 Seoul, Korea (e-mail: kwgwak@sejong.ac.kr).

B. E. Paden is with the Department of Mechanical Engineering, Universityof California, Santa Barbara, CA 93106 USA.

M. D. Noh is with the Mechanical and Environmental Engineering Depart-ment, University of California Santa Barbara, CA 93106 USA on sabbaticalleave from the Department of Mechatronics Engineering, Chungnam NationalUniversity, 305-764 Daejeon, Korea.

J. F. Antaki is with the Department of Biomedical Engineering, CarnegieMellon University, Pittsburgh, PA 15219 USA.

Digital Object Identifier 10.1109/TCST.2006.876624

of the cardiovascular system, and pumps for the heart (theand source analogs to electric circuits). Hence, the

MCS setup needs to be physically modified and recalibratedeach time a change is desired to its parameters and/or features.This is inefficient, time consuming, and costly. Moreover, it hasproven very difficult to simulate the precise nonlinear physicsobserved in the body with static fluidic elements.

Motivated by this need, we have designed an innovative flu-idic operational amplifier. Both passive and active elements of aconventional mock loop are replaced by a programmable servo-controlled gear pump. Pumps of this class behave analogous tocontrolled current sources. Thus, they may be programmed toprovide a prescribed dynamic relationship between pressure andflow depending on the sensing element and feedback control.A general configuration includes a pair of integrated pressuresensors.

An issue in the design of any operational amplifier (pneu-matic, mechanical, electronic, or fluidic) is the gain-bandwidthproduct. A high-impedance load for a fluidic op-amp is simplya short obstructed flow path. To obtain high-bandwidth pressureresponse, therefore, the output stage of the op-amp requires hightorque and low inertia in the motor, and low inductance in themotor coils. Given that cardiovascular simulation requires band-widths on the order of ten times the heart rate (i.e., 10–20 Hz),this is a reasonable requirement for such a fluidic element.

A complete mock circulatory system can be constructed withthree fluidic op-amps: one for left ventricle simulation, a secondfor combined right ventricle source and left atrium compliancesimulation, and the third for combined aortic compliance, sys-temic resistance, and inertance.

In this paper, we present the computer simulation resultsof the fluidic op-amp-based MCS to evaluate the performanceof the MCS in terms of physiological requirements. We alsoreport the initial experimental results from the prototype fluidicop-amp that was built from the off-the-shelf components toprovide the feasibility of hardware implementation as a pro-grammable element of MCS.

II. METHODS

A. Design of MCS

Mock circulatory systems have been used as test platformsfor in vitro evaluation of VADs and their feedback controllers[1]–[12]. The purpose of a MCS is to reproduce the in vivohemodynamic responses of the native circulatory system toVAD operation over a wide range of cardiac (dys)function [11].

The native human body cardiovascular circulatory systemcan be simply modeled and implemented in MCS using linear

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Fig. 1. Simplified cardiovascular circulatory system schematic.

lumped elements as in Fig. 1. This model is adopted and modi-fied from Loh et al. [10] and the proposed op-amp-based MCSis developed based on this model.

In the figure, LV and RV represents left and right ventricle, re-spectively. The time-varying flows and are the flows intoand out of the left ventricle, is the flow through the systemiccirculation, and represents the flow out of the right ventricle.The compliances , , and denote the complianceof the right atrium, left atrium, and aorta, respectively, and arerepresented schematically by compressible air volumes abovethe fluid circulating in the system. The impedances andrepresent the systemic resistance and inertance. , ,and represent left atrial pressure, aortic pressure, and rightatrial pressure.

Simulating the native ventricle’s pumping function is a keyingredient for the physiologically meaningful MCS. The nativeleft ventricle’s pressure and volume is influenced by the venousreturn to the ventrical (preload) and the arterial dynamics seenduring ejection (afterload). In rough terms, the ventricle isvery elastic during filling (diastole) and essentially accepts allthe blood supplied by the venous return. During systole, theventricles become inelastic and contract to a volume whichis roughly independent of the arterial pressure (pulmonary oraortic) against which they are pumping. This rough behaviorof pumping all blood that is returned to the heart is calledFrank–Starling’s law [13]. A more detailed model of the heartincorporates nonzero elastance during diastole, and finiteelastance during systole so that some effects of preload andafterload appear in simulation. A commonly used model of theventricles describes the ventricular behavior as linear, elastic,and time-varying so that, the left ventricular pressure isrelated to the left ventricular volume by

(1)

where is modeled, for example, as a raised cosine pulse[6]–[8]. Defining and as the minimum and max-imum values of over a cardiac cycle, one can capture thepressure–volume (P–V) loop between lines with correspondingslopes as shown in Fig. 2. The line iscalled the end-systolic pressure–volume relationship (ESPVR)and the line corresponding to is called the end-diastolicpressure–volume relationship (EDPVR). These two lines in ourmodel are replaced with somewhat convex nonlinearities in ac-tual physiologic data. The linear relationship, however, sufficesfor synthesizing realistic system behavior.

Fig. 2. Pressure–volume relationship (E(t)) of the left ventricle.

Fig. 3. Normalized elastance curve with T = 0:8 (solid: measured, dashed:approximated).

It has been observed [6]–[8] that scaling the elastance byand the time by the cardiac cycle time , yields the nor-

malized elastance whichis of nearly constant shape in vivo over a range of physiologicconditions as shown in Fig. 3 (solid line).

An approximation to normalized elastance curve inFig. 3 is, during systole

(2)

where, is the normalized time with respect to cardiaccycle period (s). Systole is taken to be the normalized timeinterval where empirically we have[14].

604 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 14, NO. 4, JULY 2006

Fig. 4. Cardiac output as a function of RAP.

Thus, the elastance function can be parameterized by ,, and to obtain

.(3)

A reduction in is a simple way of modeling an ailing heart.In developing and evaluating an MCS, controlling the load

conditions seen by the ventricle is critical since different loadcondition creates different hemodynamic responses (pressureand flow) due to our time-varying elastance model. Formal def-initions of “preload” and “afterload” vary, but for our purposes,we define preload as the venous return flow into the left ven-tricle and afterload as aortic pressure. Changes in these loadsoccur with exercise, sympathetic and parasympathetic stimuli,and VAD intervention, etc. In MCSs, a valve is frequently usedfor the mock systemic resistance and is manually adjusted forthe afterload variation.

Cardiac output (the average flow in Fig. 1) is known to bedependent on the as illustrated in Fig. 4 [14] and can bemodeled empirically as [10]

(4)

The gain is determined from the level of activity and/orsympathetic stimulation, thereby, controlling the cardiac output.By Frank–Starling’s law, the venous return flow is assumed tobe the same as the cardiac output, hence, (4) can be used for thepreload control ( ).

The mathematical model of the MCS in Fig. 1 can be devel-oped as follows using the electrical analogy.

Left Ventricle:

(5)

(6)

Mitral Valve:

otherwise(7)

Aortic Valve:

otherwise(8)

Fig. 5. Fluidic op-amp based MCS.

Aortic Compliance:

(9)

Vascular Inertance and Resistance:

(10)

Right Atrial Compliance:

(11)

Simplified Right Heart Model:

(12)

Left Atrial Compliance:

(13)

and represent the mitral and aortic valve resistance,respectively.

B. Gear Pump Element

As explained in the previous section, conventional MCSs arebuilt with hard-plumbed approximately linear lumped passiveelements. Therefore, it is difficult to modify the existing MCSto vary parameters or create nonlinear elements, etc. In thissection, we present an innovative fluidic operational amplifierbased on a gear-pump output stage.

As shown in Fig. 1, the whole MCS is divided into three sub-systems partitioned with dotted lines. Our approach is to simu-late the overall function of each subsystem with discrete fluidicop-amps shown in Fig. 5.

A more comprehensive model of the fluidic op-amp, in-cluding the instrumentation and control components, is shownin Fig. 6.

The central element of the op-amp is a gear pump [15]–[17],a positive displacement pumps in the sense that the displacedvolume is proportional to the pump rotation

(14)

where is the pump constant (volume per unit rotation). Dif-ferentiating, we have the flow relationship

(15)

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Fig. 6. Fluidic op-amp.

Assuming a frictionless pump, conservation of energy dictatesthat the input torque is related to the pressure across the outputports by the same constant

(16)

where and are the outlet and inlet pressures, respectively.A servo-position controlled motor will control volume, and

velocity-control will regulate volumetric flow rate. If we adddynamic terms for the pump and motor inertia , and combinethe gain of the current amplifier and the motor torque constantinto the single relationship the fluidic op-amp can bemodeled as

(17a)

(17b)

where is the combined inertia of the motor and the gear pumpand is the motor control input.

C. Configurations and Control of the Op-Amp

With the model of Fig. 6, we present below the design andcontrol of fluidic op-amps to simulate the physiological ele-ments of Fig. 1.

1) Left Ventricular Subsystem: The native left ventricleperiodically cycles the phases of filling (diastole; low elastance;high compliance) and ejection (systole, high elastance, lowcompliance). This periodic contraction of the native ventricleis implemented as an op-amp (gear pump output stage shownin Fig. 7). The subscript “gp” is used to denote “gear pump”to distinguish from the corresponding physiologic quantity.The net liquid volume change in the control volume of Fig. 7corresponds to the volume change of the native LV. Note thatthe pressure in the reservoir above the gear pump output stagehas no physiologic interpretation; only the pressure below thegear pump is relevant.

Fig. 7. Configuration of a subsystem for LV simulation.

The volume of the simulated LV, , can be related toflows using volume conservation

(18)

where and are as follows.Mitral Valve:

otherwise(19)

Aortic Valve:

otherwise(20)

The simulated left ventricular pressure , is the pressurebeneath the gear pump, internal to the fluid circuit. ismeasured using one of the pressure transducers of the op-ampshown in Fig. 6.

For numerical simulation, can be modeled as followsassuming there is no pump flow :

or (21)

However, due to the fixed boundary of the simulated LV, com-pliance of the simulated LV, is small and constant, hence(21) cannot replicate the time-varying elastance (compliance) ofthe native LV shown in (5). The fixed compliance of (21) mustbe compensated to simulate the native ventricle’s contraction.Given the time varying elastance waveform in (3) and ,the reference should be calculated as follows to simulatethe time-varying contraction of the native ventricle

(22)

With the controllable pump flow , in (21) is now mod-ified to (23) and can be controlled to track the desired ,thereby, compensating constant and reproducing thesame pressure-volume relation of the native ventricle

(23)

The pump flow is obtained from the pump dynamics

(24)

(25)

(26)

(27)

606 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 14, NO. 4, JULY 2006

where and represent the area and the height of the reservoirabove the gear pump.

Since should be controlled by (28), such that asubsystem shown in Fig. 7 is equivalent to the native ven-tricle, is a key state variable and should be includedin the subsystem dynamics. A subsystem that simulates thenative left ventricle in Fig. 1 can be represented in the stan-dard affine-in-control state space form with state vector being

as follows:

(28)

(29)

Note that the gear pump alone, which is a second-order linearsystem [(24)–(27)], does not have physiological meaning. Itis the subsystem defined in (28) that replaces native ventricle.However, this subsystem is a third-order nonlinear system dueto hard nonlinearities of the mitral and arotic valves included in

and [i.e., has nonlinear dynamics. Refer to(19) and (20)]. Therefore, a nonlinear control scheme is usedin this study to compensate the nonlinearities of the valves ofLV-replacing nonlinear subsystem.

Output vector is selected as (29) as only needs tobe controlled to simulate the time-varying elastance of thenative LV. Since only the output vector is nonlinear, outputfeedback linearization [18], [19] is a reasonable control law.The relative degree of the output is two. Following the standardrepresentation:

(30)

(31)

If we define the desired error dynamics as in (32) below, withthe definition of error in (33), we have

(32)

with

(33)

Parameters of the error dynamics are chosen to have its poles at200 and 300, such that (32) has much faster dynamics than

the LVPs.The fictitious input is defined from (32) as

(34)

We compute the actual input as follows:

(35)

(36)

(37)

Fig. 8. Concept of impedance matching gear pump.

The final form of the controller for a gear pump of a subsystemthat guarantees the equivalence to the native LV is now given asfollows:

(38)

2) – – Equivalent Gear Pump: The fluid circuit ofthe cardiovascular system has an impedance which can beapproximated by linear lumped passive elements ( , , ),and each of these elements has its own constitutive law (orimpedance) . Dynamic characteristics ofeach element are determined based on this relation.

Hence, for a given (measured) pressure, if we can control flowappropriately using the impedance or vice versa, then gear

pump creates dynamically equivalent responses to these passiveelements. The concept of impedance matching gear pump is il-lustrated in Fig. 8.

First, we consider the impedance for systemic resistanceand systemic inertance . For a given current pressure (and ) measured from the loop, the flow through the se-ries-connected and elements is determined from the fol-lowing relations:

(39)

(40)

(41)

(42)

Note that operator in (39)–(42) represents the Laplace op-erator. Equation (42) is the flow through the original passiveelements based on given pressure conditions. Hence, for afluidic op-amp to behave as a series – circuit, , shouldbehave the same way as does as in (42). Therefore, thecontrol strategy for the series – simulation would be toimpose a flow through the gear pump , equal to , asderived from (42).

The impedance for aortic compliance can be understood in asimilar manner

(43)

(44)

(45)

(46)

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Equation (46) implies that for given flows in theMCS, the aortic pressure should satisfy (46) for the gear pumpto be equivalent to the aortic compliance.

Proceeding to the simulation of combined elements, if wecombine the two (42) and (46), and substitute corre-sponding to series into (46) instead of , then thedynamics of will reproduce the dynamics of the systemicimpedance of the loop comprised of a series – – circuit.Finally, if one can control the gear pump such that current

, this gear pump will be equivalent to theoriginal passive elements.

In summary, the reference dynamics to guarantee the equiva-lence to a series – – are as follows:

(47)

(48)

where , , and are measurements from theMCS.

For the controller design and numerical simulations of com-bined elements, the mathematical model for cir-cuit-equivalent subsystem is derived as follows:

(49)

(50)

(51)

(52)

and represent the pump flow and aortic pressure.is the compliance of the aorta of the equiv-

alent circuit and is much smaller than . If ,equivalence of the subsystem to the circuit [i.e., sat-isfying (47) and (48)] can be simply achieved by driving

. However, due to compliance mismatch ,the bandwidth of response would be much higher than

, thereby, cannot be the same as merelyby driving . Therefore, the controller should be de-signed to drive to simulate thecircuit while compensating the compliance mismatch.

The subsystem that replaces circuit is rep-resented in the standard affine-in-control state space formwith state vector being asfollows:

(53)

(54)

As explained in the previous section, the gear pump alone,which is linear, does not represent any physiological quan-tity. It is the subsystem defined in (53) that corresponds tothe circuit. However, the subsystem of (53) isnonlinear due to hard nonlinearity of aortic valve includedin of AOP dynamics [refer to (20)]. Therefore, outputfeedback linearization is a reasonable choice of controller as inthe previous section.

Following the same controller design path in the previous sec-tion, the controller is derived by

and (55)

(56)

(57)

(58)

The final form of the controller for the op-amp of the subsystemthat simulates circuit is represented by

(59)

3) Equivalent Gear Pump: In this section, thedesign and control of a subsystem that replaces the right ven-tricle and the left atrium compliance is addressed. The de-sign and control logic is exactly the same as the one used for the

equivalent gear pump but is referenced to the pas-sive elements of the right ventricle and pulmonary circulation.

For a given , the right atrium creates venous return asfollows:

(60)The original passive left atrium , forms impedance to thisflow condition as follows:

(61)

Equations (60) and (61) are the reference impedance relationsfor the equivalent subsystem to mimic the load tothe ventricle.

The actual subsystem that replaces the with afluidic op-amp is modeled as follows with state vector being

:

(62)

is the compliance of the equivalent circuitand is smaller than the original passive . Due to this com-pliance mismatch, merely driving cannot achieve

as explained previously. Therefore, the con-troller should be designed to achieve and thisleads to the output dynamics as follows:

(63)

The subsystem for is also nonlinear due to the hardnonlinearity of the mitral valve included in of (62), hencethe same control law, output feedback, and design procedure isapplied as follows.

The desired error dynamics is defined as

(64)

(65)

608 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 14, NO. 4, JULY 2006

and

(66)

(67)

(68)

(69)

The final form of the controller for the op-amp of the subsystemthat replaces circuit is as follows:

(70)

In summary, the full MCS based on three op-amps in Fig. 5,is seventh-order nonlinear systems defined as (28), (29), (53),(54), (62), and (63).

D. Validation via Simulation

In this section, we validate the equivalence of proposed flu-idic op-amps to their physiological counterparts. Four sets ofconfigurations were studied:

1) native LV passive systemic impedance;2) op-amp LV passive systemic impedance;3) native LV op-amp systemic impedance;4) op-amp LV op-amp systemic impedance.Comparisons between cases 1 versus 2, and 3 versus 4

demonstrated an excellent match in their simulated pressureand flow waveforms. This was concluded to validate the equiv-alence of op-amp LV with the native LV.

For a – – equivalent op-amp to maintain the sameimpedance of passive systems, (flow in the loop withop-amp) should be different from (flow in the loop with

– – series) to maintain compensatinghigher bandwidth response of due to .This results in being different from RAP and it makesit difficult to validate both op-amps at the same time sincedifferent conditions create different impedances on theRV and left atrium. Hence, it was found to be advantageousto decouple each branch to validate each gear pump indepen-dently, before combining them together. This was achieved bysetting as constant—equivalent to tying it to ground, asdepicted in Fig. 9.

The final validation was performed for a tandem set ofgear pumps, representing the combination of the systemicload and the right ventricle and left atrium

. This was achieved in a similar fashion by com-paring the open circuit response, as shown in Fig. 9. Likewise,a near identical correspondence was observed between theconfiguration pairs 1 and 3, as well as, 2 and 4. (The responseplots for each set are omitted for consideration of space.)

III. RESULTS: SIMULATION OF CARDIAC DYNAMICS

Following the demonstration of the fluidic op-amp repro-ducing the response of the passive elements, we proceeded to

Fig. 9. Open mock loops for the validation of MCS equivalence for elementsin the circulatory path.

investigate the performance of the full mock circulatory system.Specifically, we investigated the hemodynamic response of theproposed fluidic op-amp MCS to changes in load as would beexperienced in the body. For any MCS to be physiologicallyvalid, the following performance objectives need to be satisfiedto the load changes:

• Frank–Starling law must hold—responsiveness to preloadchange;

• stroke work done by left ventricle shouldremain unchanged for afterload variation (responsivenessto afterload change);

• consistency of (ESPVR) regardless of preload andafterload changes.

Before validating the above performance objectives to the loadchanges, waveforms of key hemodynamic variables of the flu-idic op-amp MCS simulator need to be examined to confirmthe physiologic validity. Fig. 10 shows the wave forms gener-ated by the fluidic op-amp MCS simulator, corresponding toFig. 5 with nominal values of preload and afterload ( ,

). The hemodynamics appear to be physiologically rea-sonable as they closely match the nominal values established byliterature [13]. They also look reasonable in a qualitative sense:the ventricular pressure resembles the elastance waveform, withthe aortic pressure corresponding to LVP through systole, anddecaying according to a typical windkessel model. Likewise,LAP rises during systole and drops to correspond to LVP duringdiastole.

As hemodynamic waveforms are verified to be physiologi-cally reasonable, performance objectives are now to be verifiedwith respect to load changes. The subsequent preload and after-load responsiveness tests were performed using the same nom-inal values.

Step changes of preload were introduced by varying valueof as defined in (4). The resulting left ventricular pres-sure–volume (P–V) loops for three cases ( 65, 100, 150)are shown in Fig. 11. Here, it is observed that increased preloadresults in an increased end-diastolic volume (EDV), as expected

GWAK et al.: FLUIDIC OPERATIONAL AMPLIFIER FOR MOCK CIRCULATORY SYSTEMS 609

Fig. 10. Waveforms of hemodynamic variables in the proposed MCS.

Fig. 11. P–V loops for preload variation.

physiologically. Furthermore, the increased EDV causes an in-crease in the developed pressure, maintaining (ESPVR)constant indicated by the straight blue line. The slope of thisline is very close to the prescribed (2.24) of the elastancefunction, thereby verifying the consistency of with respectto preload changes. As a final validation of the Frank–Starlingresponse, the relationship of stroke work (the integral within thePV curve) and stroke volume was observed to follow a straightline, as shown in Fig. 12. The stroke work was calculated usingthe trapezoidal integration method.

Afterload changes were introduced by varying the systemicresistance value ( , 2.1, 2.8). Corresponding P–V loops

Fig. 12. Linearity of stroke (external) work to stroke volume (demonstratingFrank–Starling law).

are shown in Fig. 13. As is the case in preload changes, ESPVRis maintained constant for the afterload changes as well and itis found to be which is very close to of elastancefunction. It is verified that increased afterload reduces the re-turning volume, thereby reducing the stroke volume while main-taining end-diastolic volume as is observed in vivo. The workdone by the ventricle was maintained unchanged, as observedin the body.

Through Figs. 10–13, it has been shown that performance ob-jectives are satisfied successfully, thereby physiological validityof the op-amp MCS has been confirmed.

610 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 14, NO. 4, JULY 2006

Fig. 13. P–V loops and consistency ofE (ESPVR) for afterload variations.

Fig. 14. Block diagram of the flow control loop.

IV. PRELIMINARY EXPERIMENTS

A. Experimental Setup

In order to verify the concept of the fluidic op-amp, wehave assembled a prototype with the off-the-shelf components.This prototype consists of a magnetically-coupled gear pump(Model TXS79EEEV3WN; Tuthill Corp., Concord, CA) and abrushless servomotor (Model A0100-104-3; Applied MotionProducts, Montville, NJ). The servomotor is driven by aservoamplifier (Model B25A20FACQ; Advanced Motion Con-trols, Camarillo, CA). The inlet and outlet pressures of the gearpump are measured by the combination of the disposable pres-sure transducers (Model PX260; Edward Life Sciences, Irvine,CA) and the patient monitors (Model 78532A; Hewlet-Packard,Palo Alto, CA). An electromagnetic flow probe (Model 300A;Carolina Medical, King, NC) measures the flow rate either atthe inlet or the outlet of the pump. The mechanical hardwarewas combined into a feedback loop system that either controlsthe flow or the pressure difference at the pump. The blockdiagram shown in Fig. 14 controls the flow of the pump.

MatLab/Simulink (MathWorks Inc. Natick, MA) was used asthe software platform interfaced to the gear pump with a PCIinterface board (Quanser Inc., Markham, ON, Canada). Fig. 15shows the picture of the experimental setup.

B. Experimental Results

The prototype fluidic op-amp was used to simulate either theleft ventricle or the systemic resistance. In the case of the simu-lation for the left ventricle, the flow output of the pump mustmatch the physiologically relevant flow characteristics, whilefor the simulation of the systemic resistance, the pressure profilemust follow the hemodynamic data. Fig. 16 shows the resultsof the experiments, where the top graph compares the outlet

Fig. 15. Preliminary prototype assembled from off-the-shelf components.The displacement of the pump is 7.9 cc and the gears are made of PEEK. Theservomotor has the optical encoder which has the 2000 counts per revolution.

Fig. 16. Pressure and flow waveforms synthesized with the prototype (withpressure and flow feedback, respectively). The black lines represent the humandata found in [20] and the grey lines show the experimental results. Due to thedesign feature of the gear pump, the results exhibit ripples [17].

pressure of the pump with the pressure waveforms measured inthe human aorta [20]. The bottom graph contains the results ofthe flow control experiment, where the pump flow is forced tofollow the flow rate in the human left ventricle [20].

Although the experiments confirm the feasibility of the flu-idic op-amp concept, the results reveal several limitations ofthe system. Our prototype: 1) does not have tachometer feed-back and, hence, operates at limited bandwidth; 2) suffers fromdriveline compliance due to the magnetic coupling; 3) has rel-atively high friction due to high design pressures (tight toler-ances); and 4) has friction ripple due to the tight tolerances of thegear teeth and bearing eccentricity (“runout”) [17]. These limi-tations may only be overcome by the custom-made gear pumpsspecifically designed for the fluidic op-amp.

V. CONCLUSION

A concept of new and innovative mock circulatory systemusing feedback-controlled gear pumps has been presented. The

GWAK et al.: FLUIDIC OPERATIONAL AMPLIFIER FOR MOCK CIRCULATORY SYSTEMS 611

gear pumps are controlled to mimic the impedance of its cor-responding active/passive fluidic elements of the conventionalMCS, thereby guaranteeing the corresponding hemodynamiccharacteristics. Equivalence of gear pumps to the principle el-ements of the circulatory system: ventricle, compliance, and in-ertance were demonstrated and physiological validity of the pro-posed op-amp MCS was confirmed by computer simulations.

Initial experimental results with a prototype built with theoff-the-shelf components showed the feasibility of the fluidicop-amp concept, however, several limitations of the systemswere revealed also. Custom-made gear pumps specifically de-signed for the fluidic op-amp will be constructed to overcomethese limitations and they will be tested in the actual hardwareMCS in the future.

The advantages of the proposed fluidic op-amp MCS overexisting mock circulatory systems include its flexibility ofarbitrarily programmable fluidic components, simplicity, lowpriming volume, and repeatability. Furthermore, the proposedMCS may provide nonlinearity not currently achievable withcommon fluidic elements. This feature is particularly usefulfor evaluation of ventricular assist devices (VADs) and relatedphysiologic feedback control. This is the topic of our ongoingand future work.

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[2] G. Ferrari, C. De Lazzri, R. Mimmo, G. Tosti, D. Ambrosi, and K. Gor-czynska, “Mock circulatory system for in vitro reproduction of the leftventricle, the arterial tree and their interaction with a left ventricular as-sist device,” J. Med. Eng. Technol., vol. 18, pp. 87–95, 1994.

[3] L. A. Garrison, A. Frangos, D. B. Geselowitz, T. C. Lamson, and J. M.Tarbell, “A new mock circulatory loop and its application to the study ofchemical additive and aortic pressure effects on hemolysis in the PennState electric ventricular assist device,” Artif. Organs, vol. 18, no. 5, pp.397–407, 1994.

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Kwan-Woong Gwak received the B.S. and M.S. de-grees from Korea University, Seoul, Korea, in 1993and 1995, respectively, and the Ph.D. degree from theUniversity of Texas at Austin, Austin, in 2003, all inmechanical engineering.

From 1995 to 1996, he was a Research Scientistat the Robotics Lab., Korea Institute of Science andTechnology (KIST), Korea, working towards thedevelopment of the die polishing robot system. From2003 to 2004, he worked for LaunchPoint Technolo-gies, Inc., Santa Barbara, CA, as a Post-Doctoral

Fellow to develop the adaptive controller for the artificial heart. From 2004to 2006, he served as a Manager at Samsung SDI Production EngineeringResearch Laboratory, Suwon, Korea, to develop the fuel cell performance testsystem. In 2006, he joined the Department of Mechanical Engineering, SejongUniversity, Seoul, Korea, as an Assistant Professor. His main research interestsinclude nonlinear optimal control with application to electromechanical andbiomedical systems, as well as, adaptive control of artificial heart, mechatronicsystem for the biomedical engineering, and fuel cell performance test system.

Brad E. Paden (S’83–M’85–SM’02–F’05) receivedthe Ph.D. degree in electrical engineering from theUniversity of California, Berkeley, in 1985.

He is currently a Professor at the University ofCalifornia, Santa Barbara, in the Mechanical Engi-neering Department with a joint appointment in theElectrical and Computer Engineering Department.His research interests focus on nonlinear controltheory and its application to electromechanical sys-tems. He was a Visiting Fellow in the Department ofMathematics at the University of Western Australia

in 1988. In 2002, he was a distinguished foreign visitor and plenary speakerat the Brazilian Control Conference—the largest control conference in SouthAmerica. He is the co-founder and president of LaunchPoint Technologies—asystems firm specializing in venture engineering. He has 12 patents.

Dr. Paden received the Best Paper Award from the ASME Journal of DynamicSystems, Measurement, and Control in 1993, the IEEE Control System SocietyTechnology Award in 2001, and the James Yorke Red Sock Award given atthe SIAM Conference on Applications of Dynamical Systems for his work onexperimental chaos in 2001. He has consulted for industry on the design andcontrol of magnetic bearings, design of medical devices, and has served as anAssociate Editor for the Journal of Robotic Systems.

612 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 14, NO. 4, JULY 2006

Myounggyu D. Noh received the B.S. and M.S.degrees in mechanical design and production en-gineering from Seoul National University, Seoul,Korea, in 1986 and 1988, respectively, and thePh.D. degree in mechanical engineering from theUniversity of Virginia, Charlottesville, in 1996.

From 1996 to 1999, he was a Research Scientist inthe Department of Neurosurgery, University of Iowa,Ames, working in the areas of functional brain map-ping. In 1999, he joined the faculty of the Depart-ment of Mechatronics Engineering, Chungnam Na-

tional University, Daejeon, Korea, and currently holds the rank of AssociateProfessor. From 2004 to 2005, he was a Visiting Scholar at the University ofCalifornia, Santa Barbara, where he did consulting work for LaunchPoint Tech-nologies, LLC, Goleta, CA, in the areas of motor and magnetic suspension de-sign for pediatric ventricular assist device. His research interests include actu-ator and sensor design, magnetic bearings, and biomedical devices.

James F. Antaki received the B.S. degree in mechanical and electrical engi-neering from Rensselaer Polytechnic Institute, Troy, NY, in 1985 and the Ph.D.degree in mechanical engineering from the University of Pittsburgh, Pittsburgh,PA, in 1991.

Over the past 12 years, he has conducted research in the field of prostheticcardiovascular organs. In 1997, his team completed the development of anovel magnetically levitated turbodynamic blood pump, the Streamliner, whichrecorded the world’s first in vivo implant of such a device. He is currently anAssociate Professor of Biomedical Engineering with a courtesy appointmentin Computer Science at Carnegie Mellon University, Pittsburgh, PA. He alsoholds academic positions in the Departments of Surgery and Bioengineeringat the University of Pittsburgh. For the past three years, he has been teachingthe Capstone Design Course within the Department of Bioengineering. Heis a proponent of teaching methods that promote the integration of didacticcoursework with industrial mentorship, aimed at solving practical problems inbiomedicine with particular emphasis on engineering of medical devices. Afterjoining Carnegie Mellon University, he intensified his interest in advancing themethodology by which medical devices are designed. He recently founded theLaboratory for Innovation and Optimization of Medical Devices which seeksto promote creative collaborations between medical professionals, industrialpartners, and faculty experts in the field of design. He holds 12 patents relatedto artificial organs and 4 in other fields.

Dr. Antaki received an IEEE Control Systems Technology Award in 2001.He was recently recognized as one of the top 40 most influential people underage 40 in the Pittsburgh region.