Computer Control of Propofol Infusion using Quantitative and Qualitative Approaches

Computer Control of Propofol Infusion using Quantitative and Qualitative Approaches

Copyright © IFAC Modelling and Control in Biomedical Systems, Warwick, UK, 1997 Computer Control of Propofol Infusion Using Quantitative and Qualitat...

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Copyright © IFAC Modelling and Control in Biomedical Systems, Warwick, UK, 1997

Computer Control of Propofol Infusion Using Quantitative and Qualitative Approaches Jiann-Shing Shieh*, Liang-Wey Chang*, Shou-Zen Fan**, Chien-Chiang Liu**

* Center for Biomedical Engineering. College of Medicine. National Taiwan University

** Depanment of Anestilesiology. College of Medicine, National Taiwan University

Abstract: A two-level hierarchical slructure using quantitative and qualitative approaches for cOlltrolling propofol infusion rate is proposed in this paper. The first level merges online measurements (i.e. systolic arterial pressure and heart rate) to interpret the primary depth of anaesthesia. The second level uses an average three-comparanent pharmacokinetic model to predict the propofol concentration in the blood of the patienl Then, using fuzzy set theory to combine these two levels, a lookup table to administer the propofol infusion rate is obtained. This lookup table has given confidence of anaesthetists to perform automatic. control of propofol in clinical trials at the next stage.

Keywords: Hierarchical Slructure, quantitative, qualitative, pharmacokinetic model, propofol concentration, propotol infusion rate.

plasma concentration of the drug. Also, using this

1. INTRODUCTION

model, tbe infusion of propofol can be designed to The development of a computerized system of

achieve constant drug concentration in the blood as a

propofol infusion \\.'as designed to achieve constalll

feed forward conlroller which is totally quantitative

drug concentration in the blood rapidly in order to

approach.

minimize

tbe

unwanted

haemodynrunic

and

respiratory effects. Numerous investigators have

However. in order to provide satisfactory anaesthesia,

evaluated the pharmacokinetics of propofol following

the depth of anaesthesia (DOA) need to be defined

a wide range of doses as well as continuous infusions.

and decided. Unfortunately, DOA is much harder to

The kinetics have been described by two and three-

be defined and not readily measurable. In practice,

compartment models and the three-compartment

anaesthetists have a number of clinical signs and on-

structure seems to be betler than the former ones in

line measurements which can be used selectively for

most of the studies as it reflects more closely the drug

the determination of the patient's state. Therefore,

metabolism in the body (Marsh, et aJ.. 1991). Hence,

many methods have been used for feedback control of

it is easy to use a model based on an average

anaesthetic

pharmacokinetic population to predict the blood or

measurements,

199

depth

based such

on as

different blood

clinical pressure,

electroencephalograph alveolar

concentration

2. THE PHARMACOKINETIC MODEL

(EEG) signals, minimum (MAC)

values,

plasma

DESCRIBING PROPOFOL

concentration of propofol and auditory evoked response (AER) (Linkens, et al., 1996).

Propofol is a relatively new intravenous anaesthetic induction agent introduced for clinical use in 1986.

From the above it is clear that. the interpretation and

The

kinetics

have

been

described

by

three-

control of DOA is complex and dependent on many

compartment models as it reflects more closely the

factors which vary between patients and operating

drug metabolism in the body. Hence, the blood

procedures. However, anaesthetists in the operating

concentration of infusion propofol is assumed to be

theater can manage patients very well based on their

described by an equation representing a linear three-

experience and knowledge. Much of human problem

compartment model as figure 1 illustrates (Linkens,

solving and inference is uncertain, inexact and

et al., 1993).

partial, i.e. it is fuzzy (Zadeb, 1965). In many Bolus Dos.

circumstances where decisions have to be made, the facts are far from precise. This paradigm seems to be specially suitable for medical processes, since it depends upon expert experiences which are not precisely quantifiable. such as patient'S subjective Fig. 1. Diagram representing the three-compartment model associated with propofol

sensations, interpretation of clinical signs and effects of instrument accuracy.

Following a propofol injection into tile central comparunent, elimination and inter-compartment

In this paper, a feedforward-feedback controller has

distribution can be detined by the following system

been designed to administer the propofol infusion

equation:

using quantitative and qualitative approaches. An

.

average three-compartment pharrnacokinetic model

XI

=k!IX2 +k31X3

-kJ!x J -kJJx l -kJOx J ~u

acts as a feed forward controller to roughly administer

(1)

the drug infusion of propofol into tile patient. Meanwhile, a fuzzy logic controller can be designed to fine tune propofol infusion rate as a feedback Using Laplace transforms. equation (I) becomes:

·controller. After extensive discussion of ulis system with anaesthetists. reasonable results have given confidence to perform on-line clinical trials in

XI (s)

s~

+ (k~1 + k-;!)s + k~lk}1

U(s)

S3

+ PPIS~ + PP~s + pp}

---=

operating uleater. Not only can tilis system keep

(:2)

constant drug concentration in ule blood, but it could where:

be used to fine tune propofol infusion rale (PIR) due to varying and surgical disturbances.

200

PPI

=k3\ + k Z\ + k lz + k\; + kw

PP:

=kZ\k3\ + klZ k

PP3

= k Z\ k3\ kiO

3J

+ k\3 k 21 + kiO k 31 + k\o.k:l

Hence, equation (2) describes the amount of drug in

central comparunent at 5.1IIlple "k" can be written as

the central compartment at any moment in time

being equal to:

given a dose U. The propofol concentration (PC) can be obtained by dividing XI by VcM p where

Vc is the central comparunent volume per

kg of

+Bp(J; -1) + BPCk - 2) + BP(k - 3»

(5)

patient's weight and Mp is the pmielll's mass in kg. In order to obtain the plasma concentration during In order to obtain an accurate description of the drug

the previous sample-time, it is necessary to divide Xl by (~ . Mp) as already mentioned above.

distribution in the body at regular intervals, bilinear transformation can be used to derive the propofol concentration or the central comparunent drug amount from equation (2). Hence, using

3. A TWO-LEVEL HIERARCHICAL

the

STRUCTURE FOR CONTROLLING

following expression:

PROPOFOL INFUSION RATE

(3)

In order to make the problem manageable, the concept of hierarchical structure is inside the

where

T:

anaesthetist's brain. The most influential parameters

is the sampling interval. The expression (2)

for monitoring are chosen as the system variables for

becomes:

the tirst level and

BB-I 1 + ~.: + B3': -~ + B~.: -3 -U"':"(---:-I-) = A A -I A -~ A -3 Z 1 + ~.: + 3': + ~.: XI (_~. -I )

paramelers are chosen as the system variables for the

(4)

where:

hierarchiL'a1

using

structure

Hence. a two-level quantitative

and

for controlling propofol

figure 2.

T:3 pp;

=-24 -

3

4TsPP 1 + 2T;:- PP2 + 3T: PP3 2 A3 = 24 - 4T:PPI - 2T: PP2 + 3T/ PP: 2 A~ =-8 + 4T:PPI - 2T: PP,! + T:' PP3 A2

011.

infusion rate is proposed in this paper as shown in

B3 =-4 Ts -2T}(k 21 +k,I)+3T/k 2I k 31 B~ =4Ts -2T/(k: 1 +k31)+T}k2Ik31 2

second level, and so

qualitative approaches

BI = 4T: + 2T/ (k~1 + k,l) + T:~ k2lk'l B2 = -4 Ts + 2Ts2 (k 21 + k31 ) + 3T:' k2lk31

Al = 8+ 4T:PPI + 2T: PP2 +

the next most important

Fig. 2. The diagram offeedforward-feedback controller of administering propofol infusion

3.1 First level of rule-base of monitoring PDO.J.

PPI = k'l + k21 + kl2 + k l3 + k lO PP1 =

k2lk31

The first level estimates the primary depth of

+ kl1 k 31 + kl;k~l + klOk31 + klOk~1

anaesthesia (PDOA) from Oil-line signals such as

PP3 = k21 k31 klO

systolic arterial pressure (SAP) and heart rate (HR), as shown in Fig. 2. At this level, the rules can come

Hence, using the equation (4) the drug amount in the

from anaesthetists' experience and a simple fuzzy

201

modelling system is used to model the PDOA. The

l,lble (as shown in Table 2) from Table 1 and Figure

rules to decide PDOA can be expressed verbally.

3

SAP and HR are divided into tllree different ranges

defuzzification method.

to

decide PDOA using centre of area as a

i.e. High, Medium and Low. High means the SAP Table 2 The lookup table of PDOA

and HR values of the patient are higher than nonna! values and vice versa for Low. Medium means the SAP

~d

SAP

HR values of the patient are in the nonna!

PDOA

range. There are also tluee states of anaesthesia i.e., Anaesthetic Light (AL), Anaesthetic OK (AO) and

0

-I

1

0.8

0.67

0.33

0

0.71

0.33

0

-1

0.6

0.14

-0.4

Anaesthetic Deep (AD). The details of the rule-base

HR

and membership function derived from anaesthetists' experience are shown in the Table 1 and Figure 3.

Table 1 Anaesthetist's rule-base for PDOA SAP PDOA

High

Medium

3.2 Second level of rule-base of adminisrering Low

propofol High

HR Medium Low

AL

AL

AL

AO

AO

AL

AO

AD

Using the previous section of 3.1 for measuring SAP and HR to decide PDOA and from pharmacokinetic model to predict the propofol concentration in the blood, these two factors have been merged to decide the propafol infusion rate. There are three levels of

La ..·

~!
High

propofol concentration i.e., High. Medium and Low.

=>OC ·1

i.e. I (Increase), Z (no change) and D (Decrease).

0

~I
Low

Also, there are Lhree states of change of propafol rate

From extensive discussion with anaesthetists. the

Junction of SAP

)'I
rule-base to decide the change of propofo! rate has

High

=>OC ·1

been elicited, as sho\\11 in Table 3.

Tahle 3 Anaesthetist's rule-base for DPR

o

~kmb.... hlp

JWlclioo of HR

PDOA AD

AO

AL

=>OC ·1

o

~!
APIR

AL

AO

AD

High

z

z

D

z

D

z

D

PC Medium

function of P';:;QA

Low

Fig. 3. The membership function of the first level

Using fuzzy logic theory, one can ob[.'lin a lookup

202

Regarding the membership function, it is quite

tbepatient; at this point, the rapid infusion is stopped.

similar to previous section of 3.1 in Figure 3.

The infusion is altered according

Therefore, using fuzzy logic theory, one can also

requirements as judged by patient blood pressure and

obtain a lookup table (as shown in Table 4) from

cardiovascular

Table 3 to decide change of propofol infusion rate

concentration. The

using centre of area as a defuzzification method.

discontinued just before the end of surgery. /ul the

response

as

infusion

well of

to clinical

as

propofol

propofol

was

trials used a Dinamap instrument to measure Table 4 The lookup table of 6PIR

patients' SAP and HR. The propofol concentration is obtained from

PDOA clIR

PC

0

the pharmacokinetic model.

A

Ohmeda 9000 syringe pump which can pump from -1

0.2

- 0.14

- 0.6

o

0.43

- 0.1

- 0.57

-1

0.6

0

- 0.6

0.1 to 1200 mlJbr is used to pump propofoI. Fentanyl is injected by syringe manUally. Meanwhile, an automatic control of muscle relaxation is applied in this system (Shieh, et al., 1996a). The muscle relaxants

can

be

used

either

Atracuriurn

or

Mivacurium. The infusion of muscle rela."{aJlts is altered according to EMG signals which js measured

4. PATIENTS AND l\1ETHODS

by Datex Relaxograph . Also. another Ohmeda 9000 syringe pump is used to pump the muscle relaxant.

This preliminary study will focus on some simple

Meanwhile. a pulse oximetry and end-tidal of CO~

and short operations. Hence, dilatation and curellage,

are also monitored by Datex Capnomac.

tubal ligmion. and myomectomy will be studied during intravenous anaesthesia. All the patients

The whole system is programmed in tile language

belong to ASA I and II and age is between 15 to 50.

Borland C++. The IBM compatible notebook is

Meanwhile, the blood loss during tbe operation must

connected via the RS232 com 1 port for Dinamap and

be less than 500 cc. Patients are excluded if they have

com2 port for the Ohmeda 9000 syringe pump. The

uncontrolled

Dinamap is set to provide arterial pressure and heart

hypertension. autonomic nervous disease, or previous

rate information at I-min intervals. the sbortest

adverse response to general anaesthesia. If there are

iIHerval possible with this instrument. The Ohmeda

taking any drug likely to inHuence the autonomic

pump administers and monitors the rate and total

nervous system or haemodynamic response they are

amount of prepofol during the operation. Also. the

also excluded.

IBM compatible notebook is connected "ia the

clinical

evidence

of

diabetes.

RS232 com3 port for Datex Relaxograpb and com4 Patients are given fentanyl 2 -

4 J.lg/kg (i.e.

port for another Ohmeda 9000 syTinge pump for

intravenous) 5 min before induction of anaesthesia

monitoring and controlling the muscle relaxation.

according to surgery and patient. They receive propofol 600 ml/hr for induction of anaesthesia.

5. CONCLUSION

Anaesthesia is defined as loss of verbal contact with

203

At the moment, this monitoring and controlling of

changeable system, it is dangerous and not reliable

multi-input and multi-output system in anaesthesia is

from point view of control. Hence, a more complete

still in preliminary study and not yet going to clinical

and safe system has been proposed in this study. Not

trials. However, the automatic control of muscle

only can it predict propofol infusion rate to control

relaxation

in

tile patient from 3-compartrnent mathematical model

Atracurium after extensive clinical trials in our

as a feedforwatd controller but also it is able to use

previous

on-line clinical signs (i.e.

has

studies

been

finished

(Shieh,

successfully

et al.,

1996b). The

SAP and

HR)

to

measurement of muscle relaxation is considerably

administer propofol infusion rate as a feedback

easier but the depth of anaesthesia (DO A) is much

controller.

harder to define and not readily measurable. In this

controller will give confidence of anaesthetists to go

study, the SAP and HR are merged to PDOA and

to clinical trials at the next stage.

Hence,

this

feedforward-feedback

combined with propofol concentration to administer the propofol infusion rate. It is still far away to say

6. REFERENCES

that this system can monitor the depth of anaesthesia.

1. Marsh, B., M. White. N. Morton and G.N.C.

But, it can be act as the lowest level to guard the

Kenny

unconsciousness. If this stage does not work, further

infusion of propofol in children. Br. J. Anaeslh .. 67,

level to monitor the DOA need to consider carefully

41-48.

from brain signals (such as EEG, AEP and SEP) or

2. Linkens. D.A., 1.S. Shieh and 1.E. Peacock (1996).

other clinical signs (such as sweating, pupil response

Hierarchical fuzzy modelling for monitoring depth of

and lacrimation).

allaestilesia. Fu:::y Sets and SYSTems, 79. 43-57.

(1991).

Phannacokinetic

mcxlel

driven

3. Zadeh, L.A. (1965). Fuzzy Sets. Information and Kenny's

group

cooperated

witil

Control, 8, 338-353.

le!neca

Pharmaceuticals has designed a prototype! infusion

4. Linkens, D.A.. M. Mallfouf and 1.E. Peacock

system which controls a Graseby 3400 syringe pump.

(1993). Propofol induced anaesthesia: a comparative

The control programme consists of a 3-comparunent

control study using a derived pharmacokinetic-

matilematical

phannaccxlynrunic

model.

pharmacokinetics of propofol. routines for data en try.

Automatic

and

subroutines to control the Graseby pump and a

SheftieJd University.

display of tile predicted blood concentration and

5. Shieh, 1.S., L.W. Chang, S.l. Fang and

infusion rate . The advantage of this system is

(1996a). Hierarchical monitoring and fuzzy logic

designed to provide target-controlled infusion of

control

drug (TCI) which permits tile anaestiletist to achieve

Engineering-Applications,Basis & COllultll1ZiCalions

and maintain the required target concentration in tile

(Submitted).

blood rather than altering infusion rates manually.

6. Shieh. 1.S .. S.l. Fang. L.W. Chang and

However. they still have some problems about the

(l996b). Computer monitoring and fuzzy logic

accuracy of 3-compartrnent matilematicaJ model for

control of neuromuscular block with atracurium.

individual patient. Meanwhile. using a open-loop

ACla Anaesthesial Sill (Submitted).

model

describing

the

system to control a non-linear, complicated and

204

Control

of

muscle!

IlHernal Systems

relaxation.

Report,

Engineering.

c.c. Liu

Biollledical

c.c. Liu