Closed loop muscle relaxant infusion

Closed loop infusion
of muscle relaxants
Claudio Melloni
Anestesia e Rianimazione
Ospedale di Faenza(RA)

Why?
Perfetto adattamento alle necessità
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Onset rapido…..
Mantenimento ottimale
Rapido offset
Mancanza di PORC e delle sue sequele
Diminuzione del consumo di farmaco/i
Contenimento dei costi…
Riduzione dei tempi di ripresa
ottimizzazione turnover in sala op.

How deep is deep?
Per IOT:scomparsa di tutte 4 le risposte al TOF
Per mantenimento;1 solo del TOF presente ovvero
10% del T1.(. Viby-Mogensen J. Clinical assessment of neuromuscular

transmission. Br J Anaesth 1982; 54:209-23. , Brull SJ, Silverman DG. Intraoperative
use of muscle relaxants. Anesthesiology Clinics of North America 1993; 11:325-44. )

(On-demand, surgeon-controlled doses of mivacurium were injected at a mean of T1
42.3 ± 36%.while anesthesiologists maintained a 90% blockade Abdulatif M; Taylouni
E.Surgeon controlled mivacurium infusion during elective cesarean
section.CanAnesth.Soc.J.95:42;num 2.
Saddler JM, Marks LF, Norman J. Comparison of atracurium-induced neuromuscular
block in rectus abdominis and hand muscles of man. Br J Anaesth 1992; 69:26-8.

Esigenze particolari;chirurgia oculare,della
carena……..blocchi più profondi
-

Saddler JM, Marks LF, Norman J. Comparison of atracuriuminduced neuromuscular block in rectus abdominis and hand
muscles of man. Br J Anaesth 1992; 69:26-8.
- We have compared neuromuscular block in the rectus abdominis
and the hand muscles in 11 adult patients. Atracurium 0.5 mg kg-1
was administered by single bolus and anaesthesia maintained
with isoflurane and nitrous oxide in oxygen. Train-of-four (TOF)
stimulation was applied to the 10th intercostal space in the
anterior axillary line and to the ulnar nerve at the wrist.
Electromyographic (EMG) responses were recorded over the
rectus abdominis and hypothenar muscles. Neuromuscular block
had a significantly faster onset in the rectus abdominis (mean 1.6
(SEM 0.2) min) than in the hand (2.4 (0.3) min) (P less than 0.001).
Recovery occurred more rapidly in the rectus abdominis: time to
25% TOF recovery was 39 (3) min at rectus abdominis and 51 (4)
min at the hand (P less than 0.001). Time to 75% TOF recovery was
56 (4) min at rectus abdominis and 72 (6) min at the hand (P less
than 0.001).

Comparison of atracuriuminduced neuromuscular block in rectus abdominis and
hand muscles of man. Br J Anaesth 1992; 69:26-8.
Saddler JM, Marks LF, Norman J.

80
70
60
50
Rectus abd
AP

40
30
20
10
0

TOF25%

TOF 75%

Hull A, Miller DR.Cumulatioon and reversal
with prolonged infusion of atracurium or
vecuronium.Can.Anaesth.Soc.J 1992:39;num7
A randomized, double-blind study was undertaken to
compare the tendencies for cumulation, and reversal
characteristics of atracurium (ATR) and vecuronium
(VEC) when administered by continuous infusion for
long surgical procedures under balanced
anaesthesia. Eligible subjects were between 50 and
75 yr of age and were free of neuromuscular disease.
Patients in the ATR group (n = 25) received a loading
dose of atracurium 0.25 mg × kg-1, followed by an
infusion initially set at 5.0 mg × kg-1 × min-1. In the
VEC group (n = 25) patients received a loading dose
of vecuronium 0.05 mg × kg-1, followed by an
infusion at 1.0 mg × kg-1 × min-1. During surgery, the

Martineau RJ,Jean BSt,Kitts JB, Curran MC,Lindsay P, Hull
A, Miller DR.Cumulation and reversal
with prolonged infusion of atracurium or
vecuronium.Can.Anaesth.Soc.J 1992:39;num7

Dosi richieste per il mantenimento
Dosi richieste per il mantenimento
+ difficile che in induzione...
farmaci cumulativi

compensare per la
distribuzione nel tempo

variabilità
interindividuale

covariate:età,funzione
epatica,renale,enzimi(

variabilità
intraindividuale

ICU (Segredo BJA
1998,80,715-9)

Obbiettivi del closed loop
Obbiettivi del closed loop
da dimostrare....
diminuire la
diminuire la
fatica per
fatica per
l'anestesista
l'anestesista

+sicurezza
+sicurezza

migliorare le
migliorare le
condizioni
condizioni
chirurgiche
chirurgiche

abbreviare i
abbreviare i
tempi di
tempi di
ripresa
ripresa

Utilità del closed loop
Possibilità di studio delle
interferenze
farmacologiche(gas,vapori….)
nelle stesse condizioni
diminuzioni dei dosaggi???
(razionalizzazione????)

Advantages of closed loop vs manual
control of atracurium infusion
6
5
4
3

Eager BM, Flynn PJ, Hughes R.
Iufusion of atracurium for long
surgical procedures.
Br J Anaesth 1984; 56:447-52.

??
mason 1
Eager
mason2
mason3
martineau

Martineau RJ,Jean BSt,Kitts JB,
Curran MC,Lindsay P, Hull A, Miller DR.
Cumulatioon and reversal
with prolonged infusion of atracurium
or vecuronium.
Can.Anaesth.Soc.J 1992:39;num7

2
1
0

dose required to maintain T1 10%

Atracurium infusion rates to maintain 90% blockade
under 4 different anesthetic techniques.O'Hara DA, Derbyshire GJ,
Overdyk FJ, Bogen DK, Marshall BE. Closed-loop infusion of atracurium with four different
anesthetic techniques. Anesthesiology 1991; 74:258-63

8
6
microgr/kg/min

4
2
0

haloth
enflurane
isoflurane
morph/N2O

Olkkola KT, Tammisto T. Quantifying the interaction of
rocuronium (Org 9426) with etomidate, fentanyl, midazolam,
propofol, thiopental, and isoflurane using closed-loop
feedback control of rocuronium infusion. Anesth Analg 1994;
78:691-6.

propofol, thiopental, and isoflurane using closed-loop feedback
control of rocuronium infusion. Anesth Analg 1994; 78:691-6.

Steady state infusion of rocuronium controlled by a closed loop
feedback model during tiva (Olkkola KT, Tammisto T. Quantifyig the interaction of
rocuronium (Org 9426) with etomidate, fentanyl, midazolam, propofol, thiopental, and isoflurane
using closed-loop feedback control of rocuronium infusion. Anesth Analg 1994; 78:691-6.

0,70
0,60
0,50
mg/kg/h

0,40
0,30
0,20
0,10

*

etomidate
fentanyl
midazolam
propofol
thiopental
isoflurane 0,7%

0,00
Compared to IV anesthetics,
isoflurane decreases the rocuronium
infusion requirement by 35%–40%.

Abdulatif M; Taylouni E.Surgeon controlled
mivacurium infusion during elective cesarean
section.CanAnesth.Soc.J.95:42;num 2.

24 C/S,elettivi, a termine
TPS/Scc/IOT/Isofl/N2O/fent
MMG
2 gruppi;anestesista vs chirurgo
» Anestesista:mivacurium qb per T1 10%
» Chirurgo:mivacurium boli qb per rilasciamento
addominale

Comparison of anesthesiologist vs surgeon controlled
relaxation with mivacurium for C/S.
80,0
70,0
60,0

%

50,0
%

40,0
30,0

mg

20,0

%

10,0
0,0

dose tot

T1 end
surgery

Tof end of Antagonism
surgery

Anest
Chir

The goals of automated control
The goals of automated control
The accuracy of the control depends on the accuracy
of the sensors used to measure the controlled variable
To keep the average value of the controlled variable within
defined limits. These limits may be fixed in advance or may be
varied if the system is to adapt to changes in conditions.

Within these limits, to minimize oscillations in the controlled
variable. The system must remain stable, so that over time the
size of the oscillations either becomes smaller or remains
constant at an acceptable level, rather than increasing, which
would allow the controlled variable to swing wildly.

Modelli
On/OFF
Model based
Fuzzy logic

DeVries JW, Ros HH, Booij LHD: Infusion of
vecuronium controlled by a closed-loop
system. Br J Anaesth 58:1100-1103, 1986
Nicomorph+aloperidol:TPS/fent
vecu 0.07 mg/kg/N2O
iot
closed loop activated <16% control
EMG hypothenar

Schematic diagram of the control system and oscillations
around the preset value(DeVries JW, Ros HH, Booij LHD:
Infusion of vecuronium controlled by a closed-loop system.
Br J Anaesth 58:1100-1103, 1986)

passive element :adaptor between
NTM and comparator
Controller;solid state relay
and syringe pump;

Pump
on

isteresi
Pump off

swithched on
when the input of the comparator
>value A and switched off
when it was lower than B

vecuronium controlled by a closed-loop
system. Br J Anaesth 58:1100-1103, 1986

vecuronium controlled by a closed-loop system.
Br J Anaesth 58:1100-1103, 1986

Depression of nmt oscillated around
the preset value:13-17% of control;
no twitch height <10% or> 25%
avg vecu 1.1 microgr/kg /min(range
0.8-1.5)
rapid recovery:mean 11 min,range 522
pts awakened at T1 70% & tof 50%
antagonism 3/28

Controllers type
TYPE
On/off:

Problems:
overshoot , oscillation about
the setpoint.

PID:
the system react, not just to the magnitude of the error, but to the
accumulated error over time (integral of error) and the rate of
change of error (derivative of error). A control system that
reacts to all three attributes of error is known as a proportionalintegral-derivative (PID) controller.

steady-state offset error, a
poor response time, some
overshoot.

A feedback controller uses the error signal to calculate the
correct infusion rate of a drug for maintaining the response at
or near the chosen setpoint.
The error signal is the difference between the setpoint and the
desired response.
Closed-loop controllers require a specific monitor of the
desired response, which “feed back” to regulate the
controlling agent.
For muscle relaxant control, the measured response usually
is the electromyogram (EMG). A PID controller takes three
components of the measured response to increase the speed
and accuracy of control: the error signal itself (proportional
component), a summation of the area between the EMG
response curve and the EMG setpoint level (integral
component), and the rate of change of the error signal

Controllers type:II
PID 2 phases; better overshoot,shorter
response time(initial
bolus allowed…)
Adaptive
The tuning of a controller does not need to be permanently fixed.
Adaptive control systems are those in which the tuning is varied
to adapt to changing conditions.

proportional:input to the system is
proportional to the error

Controllers type:III
state estimation The output response of the
patient to an input is estimated by equations
that include the response in the “effect”
compartment and any time delays (i.e., the
kinetics and dynamics of the response). The
equations are rewritten to define the response
at time (t + Dt) in terms of the response at
time t and a state vector. The advantage of
state estimation is that all of the
characteristics of the system, including
nonlinear and time-varying responses, are
modeled into the system.

3. Adaptive
Rametti et al.( dTC),Bradlow et al.( atracurium )
using on-line state estimation. They initially estimated
the patient response to a bolus of drug, modeling the
response with a nonlinear least-squares method. The
model included the time delay in the onset of
relaxation and the nonlinear pharmacodynamics of
muscle relaxant agents. Depending on the patient
response, the parameters of the controller were
updated. The controller had both minimal overshoot
and minimal oscillation about the operating point.

O'Hara DA, Derbyshire GJ, Overdyk FJ, Bogen DK, Marshall
BE. Closed-loop infusion of atracurium with four

different anesthetic techniques. Anesthesiology 1991; 74:258-63.

32 patients
EMG
PID controller for the automated closedloop delivery of atracurium
Groups :halothane, enflurane, isoflurane,
or N2O/morphine anesthesia.
TPS/Atrac bolus
infusion calculated to maintain the (EMG)
at a setpoint of 90% nmb.

average overshoot for the controller was 10.1% and
the mean steady-state error 3.0%.
mean infusion rates for atracurium N2O/morphine,
halothane 0.8%, enflurane 1.7%, and isoflurane
1.4% at 90% blockade were 5.7 ± 0.6, 4.9 ± 0.3,
3.5 ± 0.3, and 4.1 ± 0.5 mg × kg-1 × min-1,
respectively (mean ± SE).
This controller performed well in comparison to
previously developed controllers, and in addition
was used as a research tool for rapid estimation of
infusion rates.

O'Hara DA, Derbyshire GJ, Overdyk FJ, Bogen DK, Marshall
BE. Closed-loop infusion of atracurium with four different
anesthetic techniques. Anesthesiology 1991; 74:258-63.

EMG with time(upper graph) and PID control(pump rate)(lower
graph) for one patient in the halothane group O'Hara DA, Derbyshire GJ,
Overdyk FJ, Bogen.DK, Marshall BE. Closed-loop infusion of atracurium with four different
anesthetic techniques. Anesthesiology 1991; 74:258-63.

EMG response to a bolus and PID control of atraurium under
narcotic/N2O anesthesia ;setpoint changed from 80 to 90%
blockade at time 45 min.O'Hara DA, Derbyshire GJ, Overdyk FJ, Bogen DK, Marshall
BE. Closed-loop infusion of atracurium with four different anesthetic techniques. Anesthesiology
1991; 74:258-63.

Performances of various muscle relaxant controllers
from the literature.O'Hara DA, Derbyshire GJ, Overdyk FJ, Bogen DK, Marshall BE.
Closed-loop infusion of atracurium with four different anesthetic techniques. Anesthesiology 1991;
74:258-63.

Olkkola KT, Schwilden H. Quantitation of the
interaction between atracurium and succinylcholine
using closed-loop feedback control of infusion of
atracurium. Anesthesiology 1990; 73:614-8.

TPS/N2= 60%,flunitrazepam,fent
EMG Datex relaxograph.
T1/Tc TOF q.20 sec.
Model driven closed feedback
system(Fresenius pump/Toshiba
computer/RS232
90% depression(T1 10%)set point

Model driven computerized infusion of atracurium

Olkkola KT, Schwilden H. Quantitation of the interaction between atracurium and succinylcholine
using closed-loop feedback control of infusion of atracurium. Anesthesiology 1990; 73:614-8.

2 compartment open mammillary
model;hypothetical effect compartment linked
to the central compartment
integrated PK-PD model with 2 formulas;
» 1st representing the relationship between drug input
and concentration of the drug in the effect
compartment
» 2nd representing the relationship between
concentration and effect

Model driven computerized infusion of atracurium


Rate of atracurium infusion(mg/kg/min) under balanced
i.v.anesthesia

0.43
0.36

+/-0.10

0.28
+/-0.06

0.21
0.14
0.07
0.00

atrac

ch+atrac

Cumulative dose + SE calculated as mg of atracurium /body
weight in the 2 groups given atracurium preceded by
succinylcholine( Sch+Atr) or without(ATR) to produce a
constant 90% nmblockade by closed loop administration of
atracurium. Olkkola KT, Schwilden H. Quantitation of the interaction between atracurium
and succinylcholine using closed-loop feedback control of infusion of atracurium. Anesthesiology
1990; 73:614-8.

Data for one patient in the group treated with atrac
only;infusion rate for a constant 90% block and cumulative
atrac dosage with fitted cumulative dose(straight line) Olkkola KT,

Schwilden H. Quantitation of the interaction between atracurium and succinylcholine using closedloop feedback control of infusion of atracurium. Anesthesiology 1990; 73:614-8.

Data for one patient in the group given Scc before atrac:rate of
infusion for a 90% blockade and cumulative dosage of atrc with
fitted cumulative dose(sraight line) of atrac .( Olkkola KT, Schwilden H.

Quantitation of the interaction between atracurium and succinylcholine using closed-loop feedback
control of infusion of atracurium. Anesthesiology 1990; 73:614-8.

Black box concept
Black box concept
proposta di controllo.....

Controller:

Dose of
nmb

body

blockade

desired

expected

Algorythm

E

P/ID....

Controller
Controller
calculates the difference between the measured output and the desired output (let's call it the
error "e"), and correct the input according to a preset algorithm to minimize this difference.

Error
Error
how fast it changed (derivative)
how fast it changed (derivative)
what was its overall time course (integral).
what was its overall time course (integral).
infusion rate algorithm looks like ::
infusion rate algorithm looks like
v(t) = weight.[ kp.(e) + ki.ò edt+kd .. de/dt]
v(t) = weight.[ kp.(e) + ki.ò edt+kd de/dt]
Fuzzy logic:
Fuzzy logic:
error signal (E) between the actual and desired TI value
error signal (E) between the actual and desired TI value
is processed first to form the differential (D = dE/dt) and
is processed first to form the differential (D = dE/dt) and
integral (I) components. The error signal (E) gives the
integral (I) components. The error signal (E) gives the
proportional component (P) directly
proportional component (P) directly

parameters
parameters
Initial infusion rate
time rom initial bolus to 5% recovery....sensitivity....

additional boluses
if T1 >10% when nmb started to recover ;for atrac 5 mg over 3 min....

requirement of a fast increase in the nmblockade
When the set point was reduced from 20% to 10%, an additional bolus dose of atracurium was
administered equal to 10% of the value of the current mg h-1 integral (I) component of the fuzzy controller
output.

Dose limits:
atracurium infusion rate was subject to an upper limit of 100 mg h-1, the atracurium infusion was
temporarily stopped if the median T1 value was more than 5% below the set point.

Rules of functioning
fuzzy logic
IF T1 is greater than the set point by a LARGE amount
AND T1 is moving towards the set point but only
SLOWLY
THEN set the atracurium infusion rate to a HIGH level.”
The first line of this rule is a proportional (P) controller component, the
second a differential (D) component. These antecedent components are
fuzzy rule inputs. The final line is the fuzzy rule output.

Mason DG, Edwards ND, Linkens DA, Reilly CS.
Performances assessment of a fuzzy logic controller for
atracurium-induced neuromuscular block. Br. J. Anaesth. 1996;
76:396-400
fuzzy controller
atracurium-induced neuromuscular block
10 ASA I or II patients
Datex Relaxograph
T1 set point set at 10% of baseline for at least 30 min (phase I).
The T1 set point was then increased to 20% and then returned
to 10% for two further periods of at least 30 min duration
(phases II and III).
The mean (SD) of the mean T1 error in 10 patients for phases
I, II and III were 1.1 (1.4)%, -0.43 (1.2)% and 0.28 (0.94)%,
respectively.
The results show that a simple fuzzy logic controller can
provide good accuracy with insensitivity to set point changes
despite the considerable inter-individual variation in infusion

Mason DG, Edwards ND, Linkens DA, Reilly CS. Performances
assessment of a fuzzy logic controller for atracurium-induced
neuromuscular block. Br. J. Anaesth. 1996; 76:396-400

Fuzzy logic control is a simple, although effective,
technique for controlling non-linear and uncertain
processes . The effect of neuromuscular blockers is
non-linear and fuzzy logic provides a simple way to
create a non-linear controller. Fuzzy logic
accommodates uncertainty by dealing in imprecise,
qualitative terms such as low, medium and high.
This also provides control rules which are easy to
understand and therefore simple to modify.

The derivation of the fuzzy rules is a common
bottleneck in the application of fuzzy logic controllers.
Conventionally, these fuzzy rules are based on
emulating the control actions of an expert. Such a
case was reported recently with the clinical application
of fuzzy logic control to arterial pressure regulation
using isoflurane . However, with neuromuscular block
no such experience is readily available to draw on for
derivation of the fuzzy rulebase. This situation was the
main driving force behind the introduction of selforganizing fuzzy logic controllers . For this study,
however, a fuzzy rulebase was hand-crafted based on
a simulation involving the non-linear atracurium dose-


A particular configuration of fuzzy logic controller
known as PD+I (proportional, differential plus integral)
was found to be appropriate for this application via the
use of computer simulation studies . This fuzzy
controller comprises separate PD and I components
which correspond to dynamic and memory parts,
respectively. The error signal (E) between the actual
and desired TI value is processed first to form the
differential (D = dE/dt) and integral (I) components.
The error signal (E) gives the proportional component
(P) directly. These error signals which are input to the
fuzzy controller first need to be scaled to suit the
particular control application. The separate outputs of
the fuzzy PD and fuzzy I components also require

The error signal (E) gives the proportional component
(P) directly. These error signals which are input to the
fuzzy controller first need to be scaled to suit the
particular control application. The separate outputs of
the fuzzy PD and fuzzy I components also require
scaling to suit the specific application. These input and
output scaling factors for this fuzzy controller were
identified by iterative computer simulations until good
control performance was observed. We then assessed
the performance of this fuzzy atracurium controller in
clinical practice.


The initial T1 set point was entered as 10% of
baseline, a file name was entered for data storage and
the concentration of atracurium (2 mg ml-1) was
entered so that the computer could convert the
controller output from mass rate (mg h-1) to volume
flow rate (ml h-1). In addition, the patient's weight was
entered for calculation of the atracurium loading dose.
When the computer system was satisfied that no
alarm conditions were active, it delivered a loading
dose of atracurium 0.33 mg kg-1 at 1200 ml h-1 to
facilitate tracheal intubation. Anaesthesia was
maintained with a propofol infusion of 8-10 mg kg-1 h1, the patient's lungs ventilated with 66% nitrous oxide
in oxygen and morphine administered as appropriate.


The fuzzy controller used the median of the last three
T1 values. The Datex Relaxograph performed a trainof-four stimulation every 20 s to calculate the T1 error
values at 1-min intervals which the fuzzy controller
then used. The controller remained active at the initial
10% set point level for at least 30 min (phase I). The
set point was then increased to 20% by keyboard
entry and then returned to 10% again for two further
periods of at least 30 min duration (phases II and III)
(). When the set point was reduced from 20% to 10%,
an additional bolus dose of atracurium was
administered equal to 10% of the value of the current
mg h-1 integral (I) component of the fuzzy controller

Several different computer systems for feedback control of
atracurium infusions have been reported. The periods used for
performance analysis in these studies differ. Most have analysed
only steady state performance . We included transient phases in
our performance analysis. Unlike previously reported clinical
studies we tested the controller sensitivity to set point changes.
Most studies have used EMG to monitor neuromuscular block.
However, various different maintenance anaesthetics were used,
some of which potentiate the effects of neuromuscular blockers. It
is therefore not possible to provide a valid comparison of
performance across these different atracurium controllers in terms
of mean, SD and RMSD. However, there appears to be no
statistically or clinically significant difference in reported controller
performances. The main advantage the fuzzy controller offers
over previously reported controllers is its simplicity and its friendly
or intuitive designer interface. For example, a possible fuzzy

Ross JJ, Mason DG, Linkens DA, Edwards ND. Selflearning fuzzy logic control of neuromuscular block.
British Journal of Anaesthesia 1997; 78: 412-5.
performance of a “self-learning” fuzzy logic controller
atracurium
20 ASA I and II patients
Datex Relaxograph
control to a T1 twitch height set point of 10% of
baseline neuromuscular function
The controller commenced with a blank rule-base and
instructed a Graseby 3400 infusion pump to
administer an atracurium infusion to maintain this level
of block.

The system achieved stable control of neuromuscular
block with a mean T1 error of -0.52% (SD 0.55%)
accommodating a range in mean atracurium infusion
rate of 0.25–0.44 mg kg-1 h-1.
These results compare favourably with the more
computationally intensive and unwieldy adaptive
control strategies for atracurium infusion used
previously. There was less variation in infusion rates
than in our previously studied fixed rules fuzzy
controller.

Recovery of T1 was monitored every 20 s, giving
an indication of patient sensitivity to the drug,
allowing the controller to create its first control rule.
Thus, for instance, if recovery was rapid, a high
initial infusion rate was selected as T1 approached
10%, to a maximum rate of 100 mg h-1. If T1 failed
to decrease below the 10% set point, the computer
was programmed to deliver an additional 5-mg
bolus and repeat as necessary until T1 was less
than 10%. The fuzzy controller commenced
operation when T1 had recovered to between 5%
and 10%. To reduce spurious data from noisy
signals the median of the previous three readings
was used. This median T1 value, calculated each

British Journal of Anaesthesia 1997; 78: 412-5
Fuzzy logic is an appropriate, simple and effective
technique for controlling non-linear and unpredictable
processes, dealing in imprecise, qualitative (i.e.
“fuzzy”) terms such as “low”, “medium” or “high” rather
than precise measurements. This imprecision permits
very simple but effective control rules to be generated
which are easy to modify and update rapidly in realtime. Fuzzy logic control is intrinsically suited to the
control of physiological processes because it requires
little hard input data before it can begin functioning,
unlike other strategies such as “neural networks”.

For closed-loop control of neuromuscular block the
following features need to be addressed when
designing the system: recognition of the onset and,
more importantly, the rate of decay of neuromuscular
block; recognition of the difference between desired
and actual T1 value (error); recognition of the rate of
change in error from the desired T1 value; and
elimination of drift from the desired T1 value when
achieved, that is steady state error.

Using a fixed rule-base, we have demonstrated
previously that fuzzy logic control is appropriate for
controlling neuromuscular block. However, the
development of such a controller required the
construction of a hand-crafted rule-base which was
time and labour intensive. However, by incorporating a
“self-learning” layer to the fuzzy controller, it becomes
self-teaching in real-time in the clinical situation and
dispensed with the need for a pre-set fixed rule-base.
Our self-learning controller starts with a blank rulebase, and this is the first study to investigate the
clinical application of such an intelligent control
technique.

Ross et Self-learning fuzzy logic control of
neuromuscular block. British Journal of
Anaesthesia 1997; 78: 412-5
The “self-learning” strategy implemented in our
controller functioned by rapidly and repeatedly
measuring T1 twitch height and modifying the
atracurium infusion rate. This allowed the controller to
recognize the patient's drug requirements and select
infusion rates appropriate to maintain 90%
neuromuscular block. Initially, the fuzzy rule-base is
completely blank as the controller is unaware of its
first rule until control begins. This first rule is simple
and generated by assessing the return of
neuromuscular tone towards the desired T1 height.
The effect is then assessed and adapted by
generating new rules as control continues. This is

Ross et Self-learning fuzzy logic control of
neuromuscular block. British Journal of
Anaesthesia 1997; 78: 412-5
The results of this study showed improved
performance over previous controllers. Control was as
good as our previous fixed-rule controller with less
erratic infusion rates being demanded; the controller
delivered a mean SD atracurium infusion rate of 0.16
mg kg-1 h-1 for the first 30 min compared with 0.23
mg kg-1 h-1 in our previous study. Control was
implemented with a basic amount of information. At no
point did the controller have to administer a bolus in
order to regain control of a deteriorating situation and
in no case was a diverging or progressively unstable
oscillation entered.

While fuzzy logic has been used in other fields in
anaesthesia this is the first occasion where, by
application of a self-learning facility to the fuzzy logic
controller, a physiological process during anaesthesia
has been controlled entirely by machine alone. The
controller determined individual drug requirements
and administered atracurium accurately in each case,
demonstrating the ability to assess and respond to
fluctuating patient conditions during surgery. The
success of this self-learning control system should
encourage research into the control of other
physiological processes.

and concentration-response relation of rocuronium
infusion during propofol-nitrous oxide and isofluranenitrous oxide anaesthesia. Eur J Anaesthesiol 1997; 14:
488-94.

Asbury AJ, Tzabar Y. Fuzzy logic: new ways of thinking
for anaesthesia. British Journal of Anaesthesia 1995; 75: 12.
Although they might not like to admit it, anaesthetists use “rules of thumb” when managing
patients. Imagine a patient on the operating table: as the operation proceeds, changes in the
patient's physiological state are monitored by the anaesthetist who adjusts the drug inflow or
possibly ventilation. The anaesthetist probably uses a rule of thumb to determine the extent and
direction of his adjustments. That anaesthetists use imprecise, personal rules does not prevent
them from providing a safe and effective anaesthetic; every doctor uses some type of rules, but
sometimes simple rules are obscured by an aura of profundity. This is merely one aspect to
consider if computers are to assist anaesthetists in their work.
Consider a rule of thumb such as “If the end–tidal carbon dioxide concentration increases
slowly, then increase the minute ventilation a little”. In addition to a proposed action, this rule
contains imprecise terms such as “a little” and “slowly”, terms that are difficult to express and
manipulate in a computer. Humans have no difficulty with such imprecise information or even
uncertain value judgements such as “the blood pressure is high”, but they are the obstacles to
exploiting an expert's knowledge in a computer system simply because there is no language to
describe imprecise data in a way that a computer understands .
The key to this problem lies in an article published in 1965 by Lofti Zadeh, then Professor of
Electrical Engineering at the University of California at Berkeley who coined the term “fuzzy
sets”. A set is merely a group of distinguishable objects, or even distinguishable concepts such
as elephants, cars, whole numbers or good thoughts. In the classical understanding of sets, an
item would belong rigidly to one set or another. For example, a spoon would belong to the set
titled “spoons”, and everything else would belong to the set titled “not–spoons”, there is no
middle ground for spoon–like items (e.g. ladles and spades). The concept of a fuzzy set is one
where an item can simultaneously belong to several sets to different degrees, from not
belonging (or 0% membership) through to totally belonging (or 100% membership) to a set.
This is a reasonable concept as may be seen in the following example. Consider a collection
of systolic arterial pressure measurements from 20 to 220 mm Hg, and assign them into sets
such as “normal”, “very low”, “high”, etc. Using classical logic (), each value then takes on 100%
membership of one, and only one set. This logic becomes less reasonable when 99 mm Hg is

tuning, microprocessor-based closed-loop control of
atracurium- induced neuromuscular blockade. British
Journal of Anaesthesia 1988; 61: 685-92.

8: Bradlow HS, Uys PC, Rametti LB.
On-line control of atracurium induced
muscle relaxation. Journal of Biomedical
Engineering 1986; 8:72-75.
9: MacLeod, AD, Asbury AJ, Gray WM,
Linkens DA. Automatic control of
neuromuscular block with atracurium.
British Journal of Anaesthesia 1989;
63:31-35.
10: Uys PC, Morrell DF, Bradlow HS,
Rametti LB. Self-tuning, microprocessorbased closed-loop control of atracurium-

Performance assessment of a fuzzy controller for
atracurium-induced neuromuscular block.
Br. J. Anaesth. 1996; 76:396-400.

Administration des curares pour chirurgie plastique :
apports de l'adaptation bayésienne.
Ann.Fr.Anesth.Reanim. 15[6], R279. 1996.

J.A. Kuipers, F.Boer, E.Olofsen, J.G.Bovill and A.G.Burm,
Recirculatory Pharmacokinetics and Pharmacodynamics
of Rocuronium in Patients: The Influence of Cardiac
Output. Anesthesiology; 94: 47-55 2001.

rate (ETI) of cisatracurium more than isoflurane,
sevoflurane, or propofol Can J Anesth 2001 / 48 / 532537
thomashemmerling@hotmail.com
The present study investigated the
interaction between the cumulative dose
requirements of cisatracurium and
anesthesia with isoflurane, sevoflurane,
desflurane or propofol using closed-loop
feedback control.Methods: Fifty-six
patients (18–85 yr, vitrectomies of more
than one hour) were studied. In the
volatile anesthetics groups, anesthesia
was maintained by 1.3 MAC of
isoflurane, sevoflurane or desflurane; in

dose requirement for one patient (isoflurane
1.3 mac) Hemmerling TM, Schuettler J, Schwilden H. Desflurane reduces the effective therapeutic

infusion rate (ETI) of cisatracurium more than isoflurane, sevoflurane, or propofol Can J Anesth 2001 / 48 / 532537

desflurane,isoflurane,sevoflurane,propofol
groups. Hemmerling TM, Schuettler J, Schwilden H. Desflurane reduces the effective therapeutic

infusion rate (ETI) of cisatracurium more than isoflurane, sevoflurane, or propofol Can J Anesth 2001 / 48 / 532537

Isoflurane, sevoflurane and
desflurane
at 1.3 MAC reduce the cumulative
dose requirements of cisatracurium
by 42%, 41% and 60% in comparison
to propofol at 6–8 mg×kg-1×hr-1.
Desflurane significantly reduced
the cumulative dose requirements
of cisatracurium in comparison to
evoflurane and isoflurane .

rate (ETI) of cisatracurium more than isoflurane,
sevoflurane, or propofol Can J Anesth 2001 / 48 / 532537

The controller performance was
regarded as sufficient at an
average difference from 2.0%
(group D) to 3.2% (group I)
between the set point of T1%=10%
and the measured degree of
neuromuscular blockade.

cisatracurium more than isoflurane,
sevoflurane, or propofol Can J Anesth
2001 / 48 / 532-537
The controller performance for cisatracurium was different from those found for other nondepolarizing muscle relaxants such as vecuronium, atracurium or rocuronium. In the latter study,
Olkkola et al. investigated the interaction of rocuronium with several iv anesthetics or isoflurane; the
best controller performance values were achieved at 0.2% to 0.8% average offset from set point.
The controller performance found in our study could have been anticipated because cisatracurium
shows a more marked hysteresis and slower onset time than the other three non-depolarizing
muscle relaxants. Wulf et al. recently showed a significant decrease of ED50 and ED95 of
cisatracurium during anesthesia with 1.5 MAC (in a mixture of 70% nitrous oxide/30% oxygen) of
desflurane, sevoflurane or isoflurane in comparison to propofol. It is interesting to note that the time
to reach 25% of control level of
TOF stimulation was not statistically different between the groups, but recovery index and time to
reach a TOF ratio of 0.7 were significantly prolonged during anesthesia with desflurane and
sevoflurane in comparison to propofol, but not so for isoflurane. There are, however, several
limitations to that study. The cumulative dose technique might underestimate the potency of the
neuromuscular blocking drugs. Diffusion of the inhaled anesthetic requires more than 30 min to
reach equilibrium and this time span is different for the volatile anesthetic tested. Hendricks et al.
showed that uptake for desflurane and isoflurane might even take up to an hour. These findings
limit at least the interpretation of the degree of ED50 or ED95 reductions. Wulf et al. admit
themselves that the application of the total dose in increments could have underestimated the
effect of the duration of action of cisatracurium during continuous infusion of propofol. Finally, in
contrast to the current study, which used the algorithm presented by Mapleson
In contrast to the present study, most studies have compared cumulative dose requirements of
volatile anesthetics in breathing gas mixtures including nitrous oxide. A recent study, however,
shows by calculating isoboles for desflurane and cumulative doses of nitrous oxide, that the
decrease of the required desflurane concentrations by the administration of nitrous oxide might be
less than expected from their MAC values. This could mean that for different volatile anesthetics,

10: Olkkola KT, Schwilden H. Adaptive closedloop feedback control of vecuronium-induced
neuromuscular relaxation. Eur J Anaesth 1991;
8:7-12.
11: Olkkola KT, Kansanaho M. Quantifying the
interaction of vecuronium with enflurane using
closed-loop feedback control of vecuronium
infusion. Acta Anaesthesiol Scand 1995;
39:489-93.

Kansanaho M, Olkkola KT. Quantifying the effect of
enflurane on atracurium infusion requirements. Can J
Anaesth 1995; 42:103-8.

The present study was designed to
evaluate the interaction between
atracurium and enflurane in 40
adult surgical patients using
closed-loop feedback control of
infusions of atracurium.
Anaesthesia was induced with
thiopentone and fentanyl and
intubation was facilitated with
atracurium 0.5 mg × kg-1 lean body

This study was designed to quantify
the effect of clinically relevant
concentrations of enflurane on
atracurium infusion requirements
and to investigate the possible time
dependence of this interaction. We
used the technique of closed-loop
feedback control of atracurium
infusion to maintain a steady
neuromuscular blockade of 90%.

the effect of enflurane on atracurium
infusion requirements. Can J Anaesth
1995; 42:103-8.

as his/her own control)

Kansanaho M, Olkkola KT. Quantifying the effect of enflurane

on atracurium infusion requirements. Can J Anaesth 1995; 42:103-8.

0.36
0.28
N2O/O2
enflurane 0.3%
enflurane 0.6%
enflurane 0.9%

0.21

mg/kg/h
0.14
0.07
0.00

Ist 90 min

IInd 90 min

The present study was designed to evaluate the interactions of
rocuronium with etomidate, fentanyl, midazolam, propofol, thiopental, and
isoflurane using closed-loop feedback control of infusion of rocuronium.
Sixty patients were randomly assigned to one of six sequences where
anesthesia was maintained with etomidate, fentanyl, midazolam, propofol,
or thiopental and nitrous oxide, or with isoflurane and nitrous oxide. The
possible interaction of rocuronium with the anesthetics was quantified by
determining the asymptotic steady-state rate of infusion (Iss) of
rocuronium necessary to produce a constant 90% neuromuscular block.
This was accomplished by applying nonlinear curve fitting to data on the
cumulative dose requirement during the initial 90-min period after bolus
administration of rocuronium. Patient characteristics and controller
performance, i.e., the ability of the controller to maintain the
neuromuscular block constant at the set-point, did not differ significantly
between the groups. Iss values calculated per lean body mass were 0.64 ±
0.22, 0.60 ± 0.15, 0.61 ± 0.21, 0.67 ± 0.31, 0.63 ± 0.15, and 0.39 ± 0.17


After induction of anesthesia, but
before rocuronium for
neuromuscular block, we used a
RelaxographÒ neuromuscular
transmission monitor (Datex,
Helsinki, Finland) to obtain control
electromyographic values.
Specifically, the train-of-four
sequence was assessed
(frequency of stimuli, 2 Hz; pulse

nonlinear curve fitting to fit the
following formula to the curve
representing the cumulative dose
requirement of rocuronium during
the initial 90-min period after the
bolus administration of
rocuronium :
where D = amount of rocuronium
contained its apparent distribution

Meretoja, O. A.; Taivainen, T.; Wirtavuori, K.;
Olkkola, K. T.Pharmacodynamics of
mivacurium in infants.BJA 1994;73 :num4...
ABSTRACT: A computerized
infusion system was used to
determine mivacurium infusion
requirements to maintain 95% and
50% neuromuscular block in 15
infants less than 1 yr of age.
Neuromuscular block was
measured by adductor pollicis EMG
and anaesthesia maintained with
66% nitrous oxide in oxygen and

We have evaluated the
pharmacodynamics of mivacurium
in infants using a model–driven
computerized infusion device to
maintain two different levels of
neuromuscular block. The infusion
device was easy to use and
resulted in relatively rapid control of
the target neuromuscular block. If
mivacurium infusion is adjusted by

Meretoja, O. A.; Olkkola, K. T.Pharmacodynamics of
mivacvurium in children using a computer controlled
infusion.BJA 1993:71:

A computerized infusion system
was used to determine requirement
for a mivacurium infusion to
maintain a 95% and a 50%
neuromuscular block in 21 children
aged 1–15 yr. Neuromuscular block
was measured by adductor pollicis
EMG and anaesthesia maintained
with 66% nitrous oxide in oxygen
and alfentanil 50–100 mg kg-1 h-1.

infusione requirements of mivacurium

Meretoja, O. A.; Olkkola, K.

T.Pharmacodynamics of mivacvurium in children using a computer controlled infusion.BJA
1993:71

:

graph) and a 95%(lower graph) nmblockade.
Meretoja, O. A.; Olkkola, K. T.Pharmacodynamics of mivacvurium in children using a computer
controlled infusion.BJA 1993:71:

Meretoja, O. A.; Olkkola, K. T.Pharmacodynamics of mivacvurium in
children using a computer controlled infusion.BJA 1993:71:

During nitrous oxide in oxygen and
alfentanil anaesthesia, children
required an average of mivacurium
950 mg kg-1 h-1 (16 mg kg-1 min1) to maintain a 95%
neuromuscular block. This rate is
similar to that reported earlier for
children during open control of
mivacurium infusion . It seems,
therefore, that use of a computer-

Meretoja, O. A.; Olkkola, K. T.Pharmacodynamics of mivacvurium in
children using a computer controlled infusion.BJA 1993:71:
MODEL-DRIVEN COMPUTERIZED INFUSION OF MIVACURIUM
A two-compartment, open mammillary model with a hypothetical effect
compartment linked to the central compartment was assumed to
represent a valid model for the pharmacokinetics of mivacurium . The
integrated pharmacokinetic and pharmacodynamic model we used
consists of two formulae (both given as a function of time, t), one
representing the relationship between the function for drug input, I(t),
and the concentration of the drug in the effect compartment, Ce(t):

and one representing the relationship between concentration Ce(t) and
effect E(t) :

The function G(t) is given by the effect compartment concentration

Meretoja OA, Brown TCK.
Maintenance requirement of
alcuronium in paediatric patients.
Anaesthesia and Intensive Care
1990; 18:452-454.
15: Meretoja OA, Luosto T. Doseresponse characteristics of
pancuronium in neonates, infants
and children. Anaesthesia and

Olkkola, K. T.; Tammisto, T.
KLAUS T. OLKKOLA, M.D.,
TAPANI TAMMISTO, M.D.,
Department of Anaesthesia,
University of Helsinki,
Haartmaninkatu 4, FIN–00290
Helsinki, Finland. Accepted for
Publication: January 24, 1994.

AUTHOR(S): Meretoja, O. A.;
Olkkola, K. T.
OLLI A. MERETOJA, M.D.,
Department of Anaesthesia,
Children's Hospital University of
Helsinki, SF-00290 Helsinki,
Finland. KLAUS T. OLKKOLA,
M.D., Department of Anaesthesia,

Kansanaho M, Olkkola KT. Quantifying the effect of
enflurane on atracurium infusion requirements. Can J
Anaesth 1995; 42:103-8

Kansanaho et al. studied the
influence of several doses of
enflurane on the cumulative dose
requirements of atracurium to
maintain a constant 90%
neuromuscular block; this study
showed that enflurane decreased
the atracurium requirements in a
dose-dependant manner: 0.5 MAC
of enflurane reduced the

FFECTIVE FEEDBACK CONTROL systems for the
delivery of muscle relaxants in humans have been
introduced over the past few years. Methods for control
have included on-off, proportional infusion, state
estimation, and proportional-integral-derivative (PID).
A feedback controller uses the error signal to
calculate the correct infusion rate of a drug for
maintaining the response at or near the chosen setpoint.
The error signal is the difference between the setpoint
and the desired response. Closed-loop controllers
require a specific monitor of the desired response, which
“feed back” to regulate the controlling agent. For muscle
relaxant control, the measured response usually is the
electromyogram (EMG). A PID controller takes three
components of the measured response to increase the

2: 3: Rametti LB, Bradlow HS,
Uys PC: Online parameter
estimation and control of dtubocurarine-induced muscle
relaxation. Med Biol Eng Comput
23:556-564, 1985
4: Bradlow HS, Uys PC, Rametti
LB: On-line control of atracurium

control of neuromuscular blockade.
Anaesthesia 41:316-320, 1986

Shanks CA, Avram MJ, Fragen RJ,
O'Hara DA: Pharmacokinetics and
pharmacodynamics of vecuronium
infusion administered by bolus and
infusion during halothane or
balanced anesthesia. Clin
Pharmacol Ther 42:459-464, 1987
19: Jaklitsch RR, Westenskow DR,
Pace NL, Streisand JB, East KA: A

1: d'Hollander AA, Hennart DA, Barvais
L, Baurin M. Administration of
atracurium by infusion for long surgical
procedures. Simple techniques for
routine use. Br J Anaesth 1986; 58
(suppl 1):56S–59S.
2: Eager BM, Flynn PJ, Hughes R.
Iufusion of atracurium for long surgical
procedures. Br J Anaesth 1984; 56:44752.
3: Gramstad L, Lilleasen P.
Neuromuscular blocking effects of

15. Ebeling BJ, Muller W, Tonner P, Olkkola KT, Stoekel H.

Adaptative feedback-controlled infusion versus repetitive
injections of vecuronium in patients during isoflurane
anesthesia. Journal of Clinical Anesthesia 1991; 3: 181-5.
16. Schwilden H, Olkkola KT. Use of a pharmacokineticdynamic model for the automatic feedback control of
atracurium. Eur J Clin Pharmacol. 1991; 40: 293-6.
17. 18. Kansanaho M, Hynynen M, Olkkola KT. Model-driven
closed-loop feedback infusion of atracurium and vecuronium
during hypothermic cardiopulmonary bypass. J Cardiothorac
Vasc Anesth 1997; 11: 58-61.
21. Olkkola KT, Kansanaho M. Quantifying the interaction of
vecuronium with enflurane using closed- loop feedback control
of vecuronium infusion. Acta Anaesthesiol Scand. 1995; 39:
489-93.

anesthesia.Anesthesiology
1992:77 vol 3...
O'Hara, Dorene A., M.D. M.S.E.*;
Bogen, Daniel K., M.D. Ph.D.†;
Noordergraaf, Abraham, Ph.D.‡
I. Introduction
II. Background on Control Theory
A. Basic control system
components and terminology
B. Types of control systems
1. Open-loop

For muscle relaxant control, the
measured response usually is the
electromyogram (EMG). A PID
controller takes three components
of the measured response to
increase the speed and accuracy of
control: the error signal itself
(proportional component), a
summation of the area between the
EMG response curve and the EMG

1: Beemer GH. Continuous infusion of
muscle relaxants—why and how.
Anaesthesia and Intensive Care 1987;
15:83-89.
2: Bradlow HS, Uys PC, Rametti LB.
On-line control of atracurium induced
muscle relaxation. Journal of Biomedical
Engineering 1986; 8:72-75.
3: Webster NR, Cohen AT. Closed-loop
administration of atracurium: steadystate neuromuscular blockade during
surgery using a computer controlled

Closed loop muscle relaxant infusion

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