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