Anesthetic Machine

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


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


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.

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Anesthetic Machine