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Anesthetic Machine Closed-‐Loop Adaptive Control of Depth of Hypnosis
Kousha Talebian UBC ECEM | BC Children’s Hospital PART
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Table of Contents
List of Figures .............................................................................................................................................. 3 List of Abbreviation .................................................................................................................................. 4 1. Introduction ........................................................................................................................................ 5 1. PK/PD Model ....................................................................................................................................... 6 2. Control System ................................................................................................................................... 8 2.1. Open-‐Loop Control .................................................................................................................. 9 2.2. Closed-‐Loop Control ............................................................................................................. 10 2.3. Adaptive Control .................................................................................................................... 10
3. Pharmacology & Physiology of Anesthetic Drugs ............................................................ 12 3.1. Basics of Drugs ........................................................................................................................ 12 3.2. Receptors .................................................................................................................................. 14 3.3. Surface Receptors .................................................................................................................. 15 3.3.1. G-‐protein coupled .............................................................................................................. 15 3.3.2. Ligand-‐gated ion channel ............................................................................................... 15 3.3.3. Enzyme-‐linked .................................................................................................................... 16 3.4. Intercellular Receptors ....................................................................................................... 16
4. Current Measuring Indices ......................................................................................................... 18 5. Anesthetic Machine ....................................................................................................................... 18 5.1. Heart Rate Monitor ............................................................................................................... 19 5.2. Respiratory Monitor ............................................................................................................. 20 5.3. Measuring Node ..................................................................................................................... 20 5.4. CPU ............................................................................................................................................... 21 5.5. Intravenous Injection ........................................................................................................... 21 5.6. Volatile Distribution ............................................................................................................. 21
6. Target-‐Controlled Induction ..................................................................................................... 23 7. Closed-‐Loop Adaptive Control ................................................................................................. 24 7.1. Current Technology .............................................................................................................. 24 7.2. Adaptive Control .................................................................................................................... 24 7.3. Further Works ........................................................................................................................ 26
8. Conclusion ......................................................................................................................................... 27 Bibliography .............................................................................................................................................. 28
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List of Figures
Figure 1: PK/PD compartment model. ............................................................................................. 7 Figure 2: Settling time, rise time and overshoot .......................................................................... 9 Figure 3: Open-‐loop control system .................................................................................................. 9 Figure 4: A closed-‐loop control structure .................................................................................... 10 Figure 5: General MRAC control structure .................................................................................. 11 Figure 6: The plasma distribution of IV drug as a function of time .................................. 12 Figure 7: Alveolar partial pressure of an inhaling drug ......................................................... 13 Figure 8: A G-‐protein coupled receptor ........................................................................................ 15 Figure 9: A ligand-‐gated coupled receptor .................................................................................. 16 Figure 10: Enzyme-‐coupled receptor ............................................................................................ 16 Figure 11: A cytoplasm receptor ...................................................................................................... 17 Figure 12: A BIS Index measuring node ........................................................................................ 18 Figure 13: An inhaling anesthetic machine ................................................................................. 19 Figure 14: A single heartbeat ............................................................................................................ 20 Figure 15: A TCI IV drug injector ..................................................................................................... 21 Figure 16: An inhalable administration tube .............................................................................. 22 Figure 17: L1 adaptive control structure ...................................................................................... 25 Figure 18: Acceptable control scenario ........................................................................................ 25 Figure 19: Unacceptable scenario ................................................................................................... 26
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List of Abbreviation
BCCH BC Children’s Hospital BIS Bispectral BPM Beats per Minute CPU Central Processing Unit DOH Depth of Hypnosis ECG Electrocardiography EEG Electroencephalography HRM Heart Rate Monitor IV Intravenous MIMO Multi-‐Input Multi-‐Output MIAC Model Identification Adaptive Control MRAC Model Reference Adaptive Control SISO Single-‐Input Single-‐Output TCI Target-‐Controlled Induction Pa Artillery Partial Pressure PA Alveolar Partial Pressure Pbr Brain Partial Pressure PD Pharmacodynamics PID Proportional Integral Differential PK Pharmacokinetics
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1. Introduction Anesthetic machine is used to aid anesthesiologist to put a patient into a state of
anesthetic – hypnotic and sedative. The main component of the machine is the
Central Processing Unit (CPU) that performs the calculation of how much drug is
required to achieve the state. The two areas that require profound knowledge are
the PK/PD model describing the patient, and the control algorithm used. There is a
large variability amongst patients and that is an important issue regarding the
robustness of the controller.
This report will describe the PK/PD model in depth. It will describe the theory of
control structure. It will conclude by using these subjects to describe the methods
used to control depth of anesthetic.
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1. PK/PD Model
Pharmacokinetic/Pharmacodynamics modeling is a technique that combines the
two classical pharmacological studies into one. It integrates the two models into one
mathematical model that can successfully be used to predict the time course of
concentration of an administrated drug and the pharmacological effects (Stoelting &
Hillier, 2006).
Pharmacokinetics (PK) is concerned with what the body does to an administrated
drug. It is the quantitative study of the absorption, distribution, metabolism and
excretion of the injected/inhaled drug. PK will determine the concentration of drug
at anytime and its effect.
Pharmacodynamics (PD) is concerned with what the drug does to the body. It is the
study of the intrinsic sensitivity or responsiveness of receptors to a drug and the
mechanisms by which these effects occur. The structure-‐sensitive of the drug is
explored in this model. The responsiveness of the receptors to the drug is
determined by measuring the plasma concentration required to evoke a
pharmacological effect.
The combined PK/PD Model can be used to determine the full life cycle of the drug
and the patient. The model is simplified by considering the body to be composed of
different compartments. Known as “Compartment Model” (Stoelting & Hillier,
2006), each compartment represents a theoretical space that compromises of
different organs and functionalities. The more complicated the model, the more
compartments there are.
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Figure 1: PK/PD compartment model.
There are many methods used for determining PK/PD models; however, all are
empirical. Each compartment is separated, and the effect of age, sex, height, weight,
and etc. are tested on a large sample (Prinzlin, Campbell, & Sutcliffe). This will allow
an empirical formula to be postulated; the variability is also modeled.
Some model methods include: Schuttler, Schnider, Short, Marsh, Peadfusor, Kataria
(Knibbe, Della Pasqua, & Danhof). Schuttler is usually used as a default one.
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2. Control System
A control system is a device/algorithm that is used to manage, regulate and
maintain another system. The CPU controls the administrated drug to control the
anesthetic state. The controlled system is the patient.
Control systems are broken down to either non-‐adaptive, or adaptive. The non-‐
adaptive system can be open-‐loop or close-‐loop. Current anesthetic machines are
open-‐loop. The ECEM team at UBC has designed a closed-‐loop control machine, and
is working on the prototype of the adaptive version.
There are three important control engineering performance matrices. Settling time
denotes the time it takes for the output to settle within 5% of the set-‐point. Rise
time denotes the time it takes the output to initially reach to 10% of the set-‐point.
Overshoot is the maximum deviation from the set-‐point after the rise time (Astrom
& Murray, Feedback Systems An Introduction for Scientists and Engineers, 2008).
Figure below shows these matrices graphically.
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Figure 2: Settling time, rise time and overshoot
2.1. Open-‐Loop Control
An open-‐loop control system is achieved by attaching a controller to the system -‐
without providing any feedback. Such a structure lacks steady-‐state error
correction, and is only applicable if the system’s model is known.
Figure 3: Open-‐loop control system
Controller works by inverting the system. Defining the system as M, the
controller is then of the form Mc-‐1. Defining the desired state as r, the output as y,
result in:
y(t) = r(t)×C ×M = r(t)×Mc−1 ×M = r(t)
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If Mc-‐1 and M don’t match up, the output would not directly follow r(t). This
control loop cannot cancel out added noise. Most importantly, inverting a system
is a risky task; the zeros of M will become the poles and the system will have
singularities. This will cause instability and large unrealistic controller actuator
(while Mc-‐1 and M cancel out, the control output or the drug flow, is r(t)* Mc-‐1 and
this could take very large values).
2.2. Closed-‐Loop Control
Closed-‐loop control fixes the issues with the above algorithm by closing the loop
and providing feedback. Such a system can determine the current state of the
system, and the error of control. It can eliminate noise, and will not require
inverting the system. The most implemented closed-‐loop controller is a PID
(Proportional Integral Differential) and is very robust.
The closed-‐loop control is an active area of research. For more information, refer
to (Astrom & Murray, Feedback Systems An Introduction for Scientists and
Engineers, 2008).
Figure 4: A closed-‐loop control structure
2.3. Adaptive Control
Even the best-‐tuned PID controller has limited controllability on a system that
has high variability (such as PK/PD Model). Adaptive control is a new branch of
control algorithms that is designed to be adaptive –the controller changes as the
system changes. It is used for systems where the parameters vary considerably.
A PID controller, for instance, is continuously updated online to provide best
possible controller for the system currently in process.
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Adaptive control is broken down to either Model Reference Adaptive Control
(MRAC), or Model Identification Adaptive Control (MIAC) (Astrom &
Witternmark, 1994). In MRAC, a model (such as PK/PD) is defined. The
controller’s action is then to force the system to follow the model. In MIAC, the
system is identified, and the controller is altered to match the system. Both cases
run online, and are continuously updated and approach steady state. MRAC is
described below.
Figure 5: General MRAC control structure
The control architecture is shown above – it contains the Plant (Patient PK/PD
Model), Reference Model (a fixed PK/PD model that has ideal behavior),
Adjustment Mechanics, and the Controller. This architecture is able to
successfully cancel out the Plant, and cause the Plant to follow the Reference’s
output – this is without inverting the system.
The main disadvantage of the MRAC algorithm is the trade off between
robustness and the speed of adaption. Increasing the adaptation gain increases
the adaptation – this is required for stability reasons. However, high gain also
increases the noise, which can cause instability.
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3. Pharmacology & Physiology of Anesthetic Drugs
3.1. Basics of Drugs
Drugs are categorized as either intravenous (IV), or inhalable. IV drug is injected
into the blood stream directly, and causes a change in plasma concentration,
which can be used as a measuring index. The drug from the blood enters tissues
through concentration gradient.
Figure 6: The plasma distribution of IV drug as a function of time
Inhalable drug enters the capillary blood artery through the alveolar. Just as any
other gas, the exchange takes place due to partial pressure gradient between the
two gases in the alveolar and the capillary blood. Denoting the arterial blood
partial pressure as Pa, and the alveolar partial pressure as PA, the exchange of
gases occurs until Pa ⇔ PA . The blood acts as a reservoir of drug. This drug is
distributed in the body and is absorbed in tissues. The tissue and the blood will
exchange drug to equilibrate the partial pressures. In the case of hypnotic,
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denoting Pbr as the partial pressure of drug in the brain, this means PA ⇔ Pbr . A
simple equality describes these partial pressures:
Pa ⇔ PA ⇔ Pbr
This equality allows a convenient method of measuring the anesthetic drug;
knowing one of the partial pressures will identify the other partial pressures.
Measuring PA is the simplest and is used as an index for depth of anesthesia. It is
important to keep in mind that the drug is distributed due to partial pressure
and not absolute volume of drug.
Figure 7: Alveolar partial pressure of an inhaling drug
Solubility, degree of hydrophilic or lipophilic, concentration/partial pressure
gradient, cardiac output and other factors contribute to the speed and strength
of anesthetic.
The lower its solubility in blood, the faster the anesthetic acts. This seems
unintuitive. Solubility defines how much a drug can be dissolved in blood before
equilibrium is reached. If solubility is low, then equilibrium is reached faster,
and the drug enters the tissues faster. Solubility is analogous to heat capacitance.
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The higher the heat capacitance, the longer it takes for a material to heat up, just
as the higher the solubility, the longer it takes for the drug to show its
pharmacological effect.
Cardiac output corresponds to the volume of blood present in the alveoli artery.
The higher the output, the higher the amount of drug required bringing the
partial pressure of the blood to equilibrium with the alveolar pressure. In other
words, high cardiac output will delay the pharmacological effect.
3.2. Receptors
The pharmacological effect of a drug is contributed to the drug-‐receptor
interaction. This interaction alters the functionality or conformity of a specific
cellular component that results in number of steps that eventually lead to the
pharmacological effect.
Receptors are classified based on their physical locations: surface receptors are
found on the cell membrane, while intercellular receptors are found in the
cytoplasm. If a drug is hydrophilic, then it can only interact with the surface
receptors. These receptors will carry the neurotransmitter signal into the cell. If
the cell is lipophilic, then the drug may cross the cell membrane, and interact
with the receptors inside the cytoplasm. This complex acts as ligand-‐regulated
transcription factor to modulate gene expression by binding to the regulatory
DNA sequence.
The activity of a drug is categorized by its ability to activate receptors. A full
agonist will fully activate the receptor. A partial agonist can only activate some of
the receptors it attaches to. An antagonist cannot activate the receptor and will
prevent other agonists from activating the receptor.
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3.3. Surface Receptors
There are three types of surface receptors: G-‐protein coupled, ligand-‐gated ion
channel, and enzyme-‐linked.
3.3.1. G-‐protein coupled
In a G-‐protein coupled receptor, an exogenously administrated drug is
recognized by the receptor. This receptor-‐ligand interaction induces
conformation change, enabling the receptor to activate a specific G-‐protein
inside the cell. Hydrolysis of guanine triphosphate to guanosine diphosphate
provides energy for the activated G-‐protein to interact with effector molecule
to mediate the final cascade of steps that will lead to the pharmacological
response.
Figure 8: A G-‐protein coupled receptor
3.3.2. Ligand-‐gated ion channel
These receptors act as classical ion channels (such as sodium, calcium,
potassium). They function as receptor-‐ion channel complexes in which the
channel is an integral part of a larger and more complex transmembrane
protein. Each receptor is a pentamer, composed of 5 homologous subunits,
each with four transmembrane segment an ex extracellular terminus that
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contains residues that form the binding site. When a ligand activates the
receptor, the channel opens and allows the flow of ions into the cell.
Figure 9: A ligand-‐gated coupled receptor
3.3.3. Enzyme-‐linked
The enzyme-‐linked receptors behave similar to the ligand-‐gated receptors.
Once activated, they release an enzyme inside the cell.
Figure 10: Enzyme-‐coupled receptor
3.4. Intercellular Receptors
A lipophilic drug can cross the transmembrane of the cell and interact with the
cytoplasmic receptors. Hormones and steroids are examples of lipophilic
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exogenous neurotransmitter. As these ligands interact inside the cell, they bind
with the DNA sequence and regulate the gene of the cell, and can have genetic
effects.
Figure 11: A cytoplasm receptor
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4. Current Measuring Indices
For the IV drugs, plasma concentration is used as the measuring index. In the case of
inhaling drugs, PA is used. While these indices are informative, they do not convey
any direct information regarding the state of hypnosis. For instance, a PA value of
1.2% for isoflurane does not translate into an anesthetic state.
Using electroencephalography (EEG), depth of hypnosis (DOH) can be measured. A
value of 100 corresponds to fully awake, and a value of 0 corresponds to a dead
state. Bispectral Index (BIS) and the subsequent new version WAV Index are two of
the latest indices that are being widely recognized and used to measure DOH. The
main advantage of WAV is the use of only 4 nodes as opposed to other techniques
for measuring EEG as well as the direct description of the DOH.
Figure 12: A BIS Index measuring node
5. Anesthetic Machine
Any anesthetic machine can be broken down to the same components: Heart and
Respiratory monitors, measuring node, CPU, and a drug delivery instrument. The
difference between machines is either algorithm used to control the DOH or the
measuring index.
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Figure 13: An inhaling anesthetic machine
5.1. Heart Rate Monitor
A heart rate monitor (HRM) measures the electrocardiography (ECG) activity of
the heart over a period of time. A heartbeat has three intervals: PR Interval, QRS
Complex, and QT Interval. These correspond to the P, Q, R, S and T peaks.
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Figure 14: A single heartbeat
The HRM then needs to properly measure these intervals and these peaks to
calculate the beats per minute (BPM).
5.2. Respiratory Monitor
A respiratory monitor is used to measure the breathing pattern of the patient.
This usually works in parallel with the ventilator.
5.3. Measuring Node
A measuring index is required for controllability. Discussed in Section 4, there
are multiple different indices available for measuring. The alveolar pressure
measurement is implemented in the ventilator. The plasma concentration is
measured by calculating the amount of drug injected into the patient. The EEG,
and BIS index in particular, are performed by attaching nodes on the head of the
patient and measuring the EEG.
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5.4. CPU
The CPU runs the algorithm that determines the rate of flow, and the amount of
injection required. A control algorithm, either closed-‐loop or open-‐loop is used
for this purpose.
5.5. Intravenous Injection
The injection is performed via a piston that is attached to a syringe that pushes it
in.
Figure 15: A TCI IV drug injector
5.6. Volatile Distribution
The administration of the volatile drug is delivered via mask or tubes.
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Figure 16: An inhalable administration tube
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6. Target-‐Controlled Induction Target-‐Controlled Induction (TCI) is the latest anesthetic machine. It uses an open-‐
loop approach and relies heavily on the correctness of PK/PD model. Since the
algorithm is open-‐loop, it is not possible to reach zero steady state error, and any
slight mismatch between the patient and the PK/PD model will result in further
errors. The system is usually modified with a small feed-‐forward gain (less than 1),
ensuring that the algorithm always underperforms; the anesthesiologist can
manually inject a bolus if required.
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7. Closed-‐Loop Adaptive Control The ECEM team from UBC in collaboration with the PART team from BC Children
Hospital (BCCH) is working on the next generation of the anesthetic machine. The
system is designed to be adaptive. Propofol is used for delivering hypnotic state, and
remifentanil (remi) is used for bringing sedative state. Currently, only propofol
administration is being studied. The remi is controlled via TCI. The PK/PD models
then correspond to an input of propofol, with an output that denotes WAV index.
7.1. Current Technology
iControl is a closed-‐loop PID controller designed and in-‐use at BCCH. Of a large
sample, only 5 failed to control the patient. Another 10 showed oscillation, but
were still stable. Another 13 were non-‐oscillatory and stable, but were not
acceptable.
7.2. Adaptive Control
A new adaptive algorithm, known as L1 Adaptive Control, is promising to
provide fast adaptation, with robustness property (Hovakimyan & Cao, 2010).
By introducing a filter at a specific location in the MRAC design, they declare that
adaptation and robustness become decoupled. They claim this is possible since
the filter takes out high frequency components (noise) caused by high
adaptation gain. In theory, the adaptation can be tuned to infinity. Others,
however, are attacking this theory since filter adds phase lead that causes
instability.
The predictor model has a rise time of 3 minutes, with settling time of 10
minutes and overshoot of only 8BIS.
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Figure 17: L1 adaptive control structure
Below are two examples (input propofol, and output WAV index) controlling the
output based on some PK/PD models modeled by Dr. Bernhard MacLeod at UBC
Pharmacology Department. The system is able to control one of the examples,
but fails to reach the target for the other. Both examples are stable. No noise
placed on the system.
Figure 18: Acceptable control scenario
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Figure 19: Unacceptable scenario
7.3. Further Works
There are emerging evidences that L1 Adaptive Control cannot achieve what it
promises and under certain conditions, it will underperform (Ioannou, Jafari,
Rudd, Annaswamy, Ortega, & Narendra). Ioannou1 et. Al. has taken a strong
stance against the theory, and go as far as calling it a “scam.”
After the implementation of a working adaptive control, the next step is to
design a two-‐input control algorithm, for both propofol and remi. A multi-‐input
multi-‐output (MIMO) would be a simple expansion of single-‐input single-‐output
(SISO).
1 Ioannou is considered as one of the fathers of modern control theory.
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8. Conclusion The future of anesthetic machines lies in closed-‐loop control and adaptive theory.
Due to the large variability in patients, the adaptive theory is the only option for a
full robustness control structure. While L1 Adaptive Control may fail to hold up to its
promises of robustness and fast adaptation, adaptive control has come a long way
since its formulation in the 1960s and will definitely provide the degree of
robustness required in this field.
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Bibliography
Astrom, K. J., & Murray, R. M. (2008). Feedback Systems An Introduction for Scientists and Engineers. New York: Princeton University Press. Astrom, K. J., & Witternmark, B. (1994). Adaptive Control. Upper Saddle River: Prentice Hall. Hovakimyan, N., & Cao, C. (2010). L1 Adaptive Control Theory Gauranteed Robustness with Fast Adaptation. Philadelphia: SIAM. Ioannou, P. A., Jafari, S., Rudd, L., Annaswamy, A. M., Ortega, R., & Narendra, K. S. L1 Adaptive Control: Stability and Robustness Properties and Misperceptions. Ioannou, P., & Fidan, B. (2006). Adaptive Control Tutorial. Philadelphia: Siams. Keesman, K. J. (2011). System Identification An Introduction. New York: Springer. Knibbe, C., Della Pasqua, O., & Danhof, M. Introduction to population PKPD modelling in paediatric clinical pharmocology. Leiden/Amsterdam. Prinzlin, J., Campbell, A., & Sutcliffe, N. A Comparison of Four Pharmacokinetic/ Pharmacodynamic Models of Propofol TCI in an Older Population. Department of Anaesthesia, Golden Jubilee National Hospital, Clydebank. Stoelting, R. K., & Hillier, C. S. (2006). Pharmacology & Physiology in Anesthetic Practice. Philadelphia, Pennsylvania, USA: Lippincott Williams & Wilkins.