closed loop muscle relaxant infusion

Closed loop infusion of

muscle relaxantsClaudio Melloni

Anestesia e Rianimazione

Ospedale di Faenza(RA)

Why?

Perfetto adattamento alle necessità» 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 atracurium-induced 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).

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.

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Martineau RJ,Jean BSt,Kitts JB, Curran MC,Lindsay P, Hull A, Miller DR.Cumulatioon

and reversalwith 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 infusions of both ATR and VEC were titrated in increments or decrements of 12.5% to maintain first twitch (T1) suppression of 90–95%. Neuromuscular block was measured by recording the integrated evoked electromyographic response (EMG) of the first dorsal interosseous muscle in response to supramaximal TOF stimuli on the ulnar nerve. The durations of infusion were similar for the two groups (164 ± 42 and 183 ± 67 min for ATR and VEC, respectively). The infusion rates of ATR (mean ± SD) remained between 4.0 ± 0.7 and 5.0 ± 1.0 mg × kg-1 × min-1 throughout the study period. In contrast, a progressive decrease (P < 0.05) in the infusion rate of VEC, from 1.0 to 0.47 ± 0.13 mg × kg-1 × min-1, was observed during the study period. The number of adjustments required to maintain 90–95% T1 suppression decreased between the second and fourth hours of administration, but were similar at corresponding times when comparing the two groups. The times to recover to a TOF ratio >70% following reversal with neostigmine 40 mg × kg-1 and atropine 15 mg × kg-1 were also similar for the two groups (13.4 ± 4.9 and 14.4 ± 8.0 min for ATR and VEC, respectively). We conclude that a constant infusion of vecuronium adjusted to maintain T

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

Dosi richieste per il mantenimentoDosi richieste per il mantenimento+ difficile che in induzione...+ difficile che in induzione...

farmaci cumulativifarmaci cumulativicompensare per ladistribuzione nel tempocompensare per ladistribuzione nel tempo

variabilitàinterindividuale

variabilitàinterindividuale

covariate:età,funzioneepatica,renale,enzimi(covariate:età,funzioneepatica,renale,enzimi(

variabilitàintraindividuale

variabilitàintraindividuale

ICU (Segredo BJA1998,80,715-9)ICU (Segredo BJA1998,80,715-9)

Obbiettivi del closed loopObbiettivi del closed loop

da dimostrare....da dimostrare....

+sicurezza+sicurezza

diminuire lafatica per

l'anestesista

diminuire lafatica per

l'anestesista

abbreviare itempi diripresa

abbreviare itempi diripresa

migliorare lecondizionichirurgiche

migliorare lecondizionichirurgiche

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

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mason 1Eagermason2mason3martineau

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

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

??

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

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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.

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.

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.

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etomidatefentanylmidazolampropofolthiopentalisoflurane 0,7%

*

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.

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The goals of automated controlThe goals of automated controlThe accuracy of the control depends on the accuracy

of the sensors used to measure the controlled variableThe 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 withindefined limits. These limits may be fixed in advance or may be

varied if the system is to adapt to changes in conditions.

To keep the average value of the controlled variable withindefined 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 controlledvariable. The system must remain stable, so that over time the

size of the oscillations either becomes smaller or remainsconstant at an acceptable level, rather than increasing, which

would allow the controlled variable to swing wildly.

Within these limits, to minimize oscillations in the controlledvariable. The system must remain stable, so that over time the

size of the oscillations either becomes smaller or remainsconstant 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;

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

isteresi

Pump off

Pump on

DeVries JW, Ros HH, Booij LHD: Infusion of vecuronium controlled by a closed-loop system. Br J Anaesth 58:1100-1103, 1986

DeVries JW, Ros HH, Booij LHD: Infusion of 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 5-

22 pts awakened at T1 70% & tof 50% antagonism 3/28

Controllers type TYPE Problems: On/off: 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 proportional-integral-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 (derivative component)

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 closed-

loop 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.

Muscle relaxant controllers

Model driven

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 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.

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

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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 closed-loop 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.

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.

Black box conceptBlack box conceptproposta di controllo.....proposta di controllo.....

Controller:Controller:

Dose ofnmb

Dose ofnmb

bodybody blockadeblockade

desireddesiredexpectedexpected

AlgorythmAlgorythm EE

P/ID....P/ID....

ControllerControllercalculates 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.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.

ErrorError

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 valueerror signal (E) between the actual and desired TI value

is processed first to form the differential (D = dE/dt) andis processed first to form the differential (D = dE/dt) and

integral (I) components. The error signal (E) gives theintegral (I) components. The error signal (E) gives the

proportional component (P) directlyproportional component (P) directly

parametersparameters

Initial infusion rateInitial infusion rate

time rom initial bolus to 5% recovery....sensitivity....time rom initial bolus to 5% recovery....sensitivity....

additional bolusesadditional boluses

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

requirement of a fast increase in the nmblockaderequirement of a fast increase in the nmblockade

When the set point was reduced from 20% to 10%, an additional bolus dose of atracurium wasadministered equal to 10% of the value of the current mg h-1 integral (I) component of the fuzzy controlleroutput.

When the set point was reduced from 20% to 10%, an additional bolus dose of atracurium wasadministered equal to 10% of the value of the current mg h-1 integral (I) component of the fuzzy controlleroutput.

Dose limits:Dose limits:

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

Rules of functioningRules of functioningfuzzy logicfuzzy logic

IF T1 is greater than the set point by a LARGE amountIF T1 is greater than the set point by a LARGE amount

AND T1 is moving towards the set point but onlyAND T1 is moving towards the set point but only

SLOWLYSLOWLY

THEN set the atracurium infusion rate to a HIGH level.”THEN set the atracurium infusion rate to a HIGH level.”

The first line of this rule is a proportional (P) controller component, thesecond a differential (D) component. These antecedent components are

fuzzy rule inputs. The final line is the fuzzy rule output.

The first line of this rule is a proportional (P) controller component, thesecond 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 rate required.

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 self-organizing fuzzy logic controllers . For this study, however, a fuzzy rulebase was hand-crafted based on a simulation involving the non-linear atracurium dose-response characteristic comprising pharmacokinetics and pharmacodynamics .

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 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 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 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.

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 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 h-1, the patient's lungs ventilated with 66% nitrous oxide in oxygen and morphine administered as appropriate. Neuromuscular block was controlled by the closed-loop fuzzy atracurium controller throughout the operation.

The time taken after administration of the atracurium loading dose for T1 to start recovering and reach at least 5% of baseline was used to assess patient sensitivity to atracurium and thus determine its initial infusion rate. If this recovery time was fast (slow) the patient was judged insensitive (sensitive) to atracurium and therefore required a high (low) initial infusion rate. If T1 was above the initial 10% set point when neuromuscular block started to recover, the computer was programmed to give an additional 5-mg bolus over 3 min and repeat as necessary until T1 was less than the initial 10% T1 set point level. When T1 had recovered to 5-10%, the fuzzy controller commenced operation.


The fuzzy controller used the median of the last three T1 values. The Datex Relaxograph performed a train-of-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 output. This was introduced to represent the situation where a prompt increase in neuromuscular block is required to improve surgical conditions while avoiding the problem of overshooting the degree of block required. During all phases the atracurium infusion rate was subject to an upper limit of 100 mg h-1. In addition, the atracurium infusion was temporarily stopped if the median T1 value was more than 5% below the set point.

To assess the performance of the fuzzy controller, raw T1 values were analysed (i.e. not three-term median T1 values) to allow comparison of performance with previously reported controllers. T1 errors, defined as the raw T1 value minus the set point T1 value, were calculated for each phase with each patient. These T1 errors were analysed for each phase as follows: mean (SD); root mean square deviation (RMSD); point count (PC), proportion of T1 errors above the T1 set point (i.e. those with positive value); integral square error (ISE); and integral time absolute error (ITAE) (appendix).

The latter two calculations are standard control engineering performance measures . The first, ISE, is similar to RMSD, a measure of variation about the set point. The second, ITAE, is a measure which penalizes errors more heavily the further they are from the time origin of each phase. Both of these measures are sensitive to the period of analysis (appendix). We therefore selected the first 30 min of each phase for analysis. Clearly, for good control performance we need values for each of these calculations to be close to zero, except PC which needs to be close to 50%. Mean (SD) mg kg-1 h-1 atracurium infusion rates were also calculated for each phase. These values were then analysed for the 10 patients and expressed as mean (SD) and range.


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 control rule drawn from expert experience in the control of atracurium-induced neuromuscular block or just plain common sense could be:

“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. This friendly designer interface for the fuzzy controller implies there is no need to understand complex mathematical formulae nor is there a need to interpret pharmacokinetic data. The fuzzy controller simply takes the T1 measurement and

goes through some basic processing steps: 1. Input scaling Scale each of the error inputs, that is proportional, differential and integral components. 2. Fuzzification Assign fuzzy sets centred about these scaled values. This transforms error inputs from the real world to the fuzzy domain. 3. Fuzzy inferencing Determine the degree of membership (DOM) of each error input with overlapping fuzzy sets. These calculated DOM values are used in combination with the fuzzy rules to calculate the DOM value for each fuzzy rule output. 4. Defuzzification Combine the outputs of the fuzzy rules using a weighting method such as “centre of gravity”. This transforms data from the fuzzy domain back to the real world. 5. Output scaling This defuzzified value is scaled to give the real output value in terms of mg h-1 atracurium infusion rate. Each of these steps requires simple calculations only. This low computational cost means it is simple to implement in terms of hardware and software. The only other atracurium controller to report the point count (PC) performance measure also found that T1 was below a 20% set point (our phase II) for most of the time (PC = 25%) . This may be a reflection of the non-linear atracurium dose-

response characteristic in this region. No previous clinical study has analysed the performance of an automated atracurium drug delivery system using ISE and ITAE but we report them here in the hope that future performance assessments will use them. It is noted that ITAE and

ISE performance measures are sensitive to the duration of analysis (appendix). It is therefore important to compare these values over the same period (30 min in our study). The ISE is similar to the commonly reported RMSD as a measure of variation about the set point. However, ITAE has greater value because it measures the accuracy of the controller in reducing any error from the set point in proportion to the length of time as the controller commenced operation after receiving a new set point.

The consistently high SD atracurium infusion rate () indicates high controller activity, that is fluctuating infusion rates. This controller over-activity was not expected from computer simulation studies and suggests that the fuzzy PD (dynamic) component of the controller needed further testing with computer simulation under high system noise level conditions. Interestingly, however, Young and Hsiao suggested that this pseudo-bolus action is required to promptly bring second compartment concentrations to desired levels in a three-compartment pharmacokinetic open model of neuromuscular blocking agents. The apparent over-activity of this fuzzy controller might be overcome by reducing the output scaling factor of the dynamic (PD) component of the fuzzy controller.

It may be argued that the fuzzy controller reported here could easily be implemented as a simple PID controller without the need for fuzzy logic. This would imply simply limiting the ranges for the PID error components in a piece-wise linear manner. This is true with this particular fuzzy controller but overlooks the potential for fuzzy logic controllers to provide a smooth and arbitrarily non-linear control surface with no additional computational burden. This holds particular promise with self-organizing fuzzy logic controllers which can modify the fuzzy rulebase online so as to match the needs of each individual patient, which may change during the course of an operation.

Clinically this system was useful. It provided stable surgical operating conditions, minimized the amount of neuromuscular blocker required by each patient, reduced the need for the anaesthetist to spend time controlling neuromuscular block, and allowed reliable antagonism of neuromuscular block at the end of surgery.

In conclusion, this simple fuzzy controller with fixed variables provided stable control of neuromuscular block and its performance was insensitive to set point changes.

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

Ross JJ, Mason DG, Linkens DA, Edwards ND. Self-learning 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.

Ross JJ, Mason DG, Linkens DA, Edwards ND. Self-learning fuzzy logic control of neuromuscular block. British Journal of Anaesthesia 1997; 78: 412-5. 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 60 s, was then used for action by the controller. In addition, the supervising anaesthetist could administer an atracurium bolus should neuromuscular block be inadequate, alter the T1 set point or quit the programme as required.

The performance of the fuzzy controller was analysed by raw T1 values. T1 errors (measured T1 value-the set point T1 value) were analysed for mean and root mean square deviation (RMSD) for the entire duration of control. In addition, these values were determined for the initial 30 min of control to allow comparison with our previous controller. Mean (SD) atracurium infusion rates delivered every 1 min during control in each individual case were also calculated and then summarized for all 20 patients as mean (SD) and range.

Ross JJ, Mason DG, Linkens DA, Edwards ND. Self-learning fuzzy logic control of neuromuscular block. 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 real-time. 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 rule-base, 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 achieved by adding a performance index which measures the error from a desired trajectory and modifies recently generated control rules so making the controller self-learning. In addition an ageing process was added to the rules generated so that those recently generated carried more weight, or were considered “more relevant” than older rules. This helps eliminate steady state error and continually improves controller performance.

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.

Kansanaho M, Olkkola KT, Wierda JM. Dose-response and concentration-response relation of rocuronium infusion during propofol-nitrous oxide and isoflurane-

nitrous oxide anaesthesia. Eur J Anaesthesiol 1997; 14: 488-94.

Ross JJ, Mason DG, Linkens DA, Edwards ND. Self-learning fuzzy logic control of neuromuscular block. British Journal of

Anaesthesia 1997; 78: 412-5.

Asbury AJ, Tzabar Y. Fuzzy logic: new ways of thinking for anaesthesia. British Journal of Anaesthesia 1995; 75: 1-

2.

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 interpreted as “low” but 100 mm Hg as “normal”. When we now divide the values into fuzzy sets (, where the ordinate indicates the extent of membership), each value can belong to one or more sets (but usually two sets). Thus a pressure of 85 mm Hg can be seen as belonging 75% to a set termed “low” and at the same time 25% to a set termed “normal” (). This fuzzy set membership concept should not be confused with probability. We are not saying that there is a 75% chance that an arterial pressure of 85 mm Hg is low, but that arterial pressure is low to some extent and at the same time normal to some extent. We now have a way of expressing imprecise information in a way a computer can understand.

Although the use of fuzzy logic in medicine as a whole and anaesthesia in particular is in its infancy, fuzzy logic techniques are already present in consumer products. Many of these products originate from Japan where much of the research and development have been carried out and include camcorders that reduce image jitter, washing machines that automatically adjust the wash cycle to suit the clothes and microwave ovens that determine how best to cook the food. Fuzzy logic makes these appliances very easy to operate—just one button. Fuzzy logic has even been used to control a Japanese subway system. It does this so well that humans are only allowed to drive the trains during off peak hours to maintain their skills .

In medicine, fuzzy logic techniques have obvious potential roles in automatic control and expert systems. The reader can be forgiven for reading this far and asking of what use is fuzzy logic to anaesthetists? By way of an answer, a real–life anaesthetic problem is described. The control of arterial pressure in patients after cardiac surgery using an infusion of sodium nitroprusside (SNP) imposes on the nursing staff the task of frequent monitoring of mean arterial pressure (MAP) and adjustments of the infusion rate. Because nurses have many duties, manual control of the infusion can lead to poor control of MAP. Automatic closed–loop control SNP delivery systems have been developed to improve the quality of control. These systems, usually using standard engineering self–tuning algorithms, rely on a mathematical model of the human body's cardiovascular system which is inevitably complex. Much of the complexity arises from the fact that the response of the cardiovascular system to an infusion of SNP is non–linear, involves a time delay before any response occurs, and the body's responsiveness can change over time. An alternative using fuzzy logic control employs a series of rules described in imprecise terms. Examples of such rules might be:

“If the arterial pressure is slightly above the desired range, increase the infusion rate a little” or “If the arterial pressure falls catastrophically,stop the infusion temporarily.” These rules would be formulated by questioning an anaesthetist or another expert. An engineer can then convert the rules and imprecise data into a computer program which fuzzifies the

incoming MAP data, applies the rules and then calculates a definitive drug infusion setting (this process is termed “defuzzification”), and automatically sets it on the SNP pump. The system devised by Ying and co–workers used four control rules. Their system resulted in closer control of MAP than conventional logic control. It coped with a wide variety of patient sensitivity to SNP and allowed for events such as tracheal suction or sedation, which had effects on arterial pressure.

Other anaesthesia–related applications of fuzzy logic are in the interpretation of Apgar scores and in the control of an alfentanil infusion for postoperative pain , although the latter has only been used on simulated patients so far. Fuzzy logic also appears in other branches of medicine. Current applications include expert systems for medical diagnosis , interpretation of cytological smears and identification of tumour areas on mammograms .

The Achilles' heel of fuzzy logic is its rules which have to be extracted from an expert. Unfortunately, many experts such as anaesthetists, who are highly efficient in their clinical work, do not realize the extent of their own knowledge, and particularly how their knowledge is structured . An engineer then needs to optimize the rules and the boundaries of the fuzzy sets in collaboration with the experts for best system performance; this is costly and time–consuming. On the positive side, fuzzy logic techniques can be simpler, less affected by artefacts and more intuitive in design than traditional engineering methods. In addition, fuzzy methods applied to control systems can cope with non–linearities; the initial dose of neuromuscular blocker when the “margin of safety” is being filled, as opposed to every subsequent dose.

The use of fuzzy logic control is growing. Increasingly, it is becoming the way to model real world imprecision and complexity. The future of anaesthesia may be fuzzier than we think.

Uys PC, Morrell DF, Bradlow HS, Rametti LB. Self-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, microprocessor-based closed-loop control of atracurium- induced neuromuscular blockade. British Journal of Anaesthesia 1988; 61:654-692.

11: Webster NR, Cohen AT. Closed-loop administration of atracurium: steady-state neuromuscular blockade during surgery using a computer controlled closed-loop atracurium infusion. Anaesthesia 1987; 42:1085-1091.

Mason, D. G.; Edwards, N. D.; Linkens, D. A.; Reilly, C. S.

Performance assessment of a fuzzy controller for atracurium-induced

neuromuscular block. Br. J. Anaesth. 1996; 76:396-400.

Devys JM, Billard V, Barreau-Pouhaer Let al. 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.

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 / 532-537

[email protected] 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 the propofol group, anesthesia was maintained by a continuous infusion of 6–8 mg×kg-1×hr-1 propofol. After bolus application of 0.1 mg×kg-1 cisatracurium, a T1%-level of 10% of control level (train-of-four stimulation every 20 sec) was maintained using closed-loop feedback controlled infusion of cisatracurium. The effective therapeutic infusion rate (ETI) was estimated from the asymptotic steady-state infusion rate Iss. The Iss was derived from fitting an asymptotic line to the measured cumulative dose requirement curve. The ETI of the different groups was compared using Kruskal-Wallis- test, followed by rank sum test, corrected for the number of comparisons, P <0.05 was regarded as showing significant difference.Results: ETI in the isoflurane group was 35.6 ± 8.6 mg×m-2×min-1, in the sevoflurane group 36.4-± 11.9 mg m-2×min-1, in the desflurane group 23.8 ± 6.3 mg×m-2×min-1. The ETI of the volatile anesthetic groups were all significantly lower than the ETI in the propofol group at 61.7 ± 25.3 mg×m-2×min-1 (P <0.002). The ETI in the desflurane group was significantly lower than in all other groups (P <0.02).Conclusion: In comparison to propofol, isoflurane, sevoflurane and desflurane reduce the cumulative dose requirements of cisatracurium to maintain a 90% neuromuscular blockade by 42%, 41% and 60%, respectively.

Time course of the nmblockade and cumulative 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 / 532-537

Effective therapeutic infusion rate (microgr/m2/min) of cisatracurium in

the 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 / 532-537

Isoflurane, sevoflurane and desflurane at 1.3 MAC reduce the cumulative

dose requirements of cisatracuriumby 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.

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 / 532-537

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.

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 / 532-537

The controller performance for cisatracurium was different from those found for other non-depolarizing 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, the additive effect of nitrous oxide might be different, limiting the comparability of the studies. In the current study, all volatile anesthetics were compared in a breathing gas mixture consisting of air/oxygen (30% oxygen).

It could be assumed that the significant 20% reduction of the cumulative cisatracurium dose requirement of desflurane in comparison to isoflurane and sevoflurane is due to a different depth of anesthesia achieved by 1.3 MAC of desflurane. 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 atracurium requirements by 20%, 1 MAC by 25% and 1.3 MAC reduced the Iss of atracurium by 28%. The assumption that 1 MAC of desflurane might create a different depth of anesthesia than 1 MAC of sevoflurane or isoflurane cannot, however, be supported by a recent study by Rehberg et al. In a study of pharmacodynamic modelling of the EEG slowing effect of isoflurane, sevoflurane and desflurane, these authors have shown that MAC and MAC multiples are valid representations of the concentration response curve for the anesthetic suppression of the 95th percentile of the power spectrum with no significant difference of the EC50 values.

The effect of desflurane on cumulative dose requirements using closed loop feedback systems had not been studied previously. Several studies, however, have determined the effect of desflurane on the recovery of neuromuscular blockade of vecuronium, mivacurium and rapacuronium. Desflurane prolonged the recovery of neuromuscular blockade of those non-depolarizing blocking drugs in a degree similar to sevoflurane or isoflurane.

One reason for the significantly higher ETI reduction by desflurane in comparison to sevoflurane or isoflurane might be the need for a much higher partial pressure to achieve the same MAC multiples because of its weaker anesthetic potency.

In our study, isoflurane, sevoflurane and desflurane at 1.3 MAC reduced the cumulative dose requirements of cisatracurium by 42%, 41% and 60% in comparison to propofol at 6–8 mg×kg-1×hr-1. Our findings did not differ from other investigators who - in contrast to animal studies - could not show any interaction between iv anesthetic agents such as midazolam, etomidate, thiopental or fentanyl and muscle relaxants. Propofol seems to show an interaction similar to these other agents.

The clinical implication of this study is that the dose of cisatracurium required to maintain a given degree of neuromuscular blockade is influenced by volatile anesthetics as much as for other muscle relaxants such as vecuronium, rocuronium or atracurium and needs to be adjusted accordingly. It is noteworthy that desflurane reduced the ETI of cisatracurium in comparison to sevoflurane or isoflurane by a further 20%; this might have economic implications in surgeries such as neurosurgical procedures where a high degree of neuromuscular blockade must be maintained for a long period of time but short awakening times are desirable. Large interindividual differences, however, and the absence of any correlation between patient characteristics, such as age, weight or even body surface area, and the ETI to maintain the desired level of neuromuscular blockade make monitoring of the neuromuscular function mandatory. When monitoring neuromuscular blockade at the adductor pollicis muscle, one should remember the shorter onset, faster recovery and less intense block at the orbicularis oculi muscle for appropriate site-related relaxation.

10: Olkkola KT, Schwilden H. Adaptive closed-loop 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 mass. During the first 90 min, anaesthesia was maintained with nitrous oxide in oxygen (2:1) and fentanyl. For the following 90 min the patients were randomly assigned to receive enflurane at different end-tidal concentrations: Group I, control, fentanyl-nitrous oxide anaesthesia; Group II, enflurane 0.3%-nitrous oxide; Group III, enflurane 0.6%-nitrous oxide; Group IV, enflurane 0.9%-nitrous oxide. The possible interaction of atracurium with enflurane was quantified by determining the asymptotic steady-state rate of infusion (Iss) of atracurium necessary to produce a constant 90% neuromuscular block. This was accomplished by applying nonlinear curve fitting to data on the cumulative dose requirements. Every patient served as his/her own control and the changes in the infusion rates were determined individually. Patient characteristics and controller performance, i.e., the ability of the controller to maintain the neuromuscular blockade constant at the setpoint, did not differ among groups. In Group II Iss decreased from 0.33 ± 0.12 to 0.26 ± 0.08 mg × kg-1 hr-1 (P < 0.01), in Group III from 0.32 ± to 0.12 to 0.24 ± 0.08 mg kg-1 × hr-1 (P < 0.001) and in Group IV from 0.29 ± 0.09 to 0.21 ± 0.09 mg × kg-1 × hr-1(P < 0.001). In the control group atracurium requirements remained unchanged throughout the study. Enflurane reduces atracurium requirements in a dose-dependent manner. During enflurane anaesthesia the rate of atracurium infusion should be reduced but because of interindividual differences the monitoring of the neuromuscular function is important to ensure the appropriate level of neuromuscular block.

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 the atracurium infusion requirements was quantified by determining the asymptotic steady-state infusion rates necessary to produce 90% neuromuscular blockade at different levels of enflurane anaesthesia.

Kansanaho M, Olkkola KT. Quantifying the effect of

enflurane on atracurium infusion requirements. Can J Anaesth

1995; 42:103-8.

Rate of atracurium infusion during the first 90-min study period when no volatile anaesthetic was

given and during the second study period, when enflurane was added(every patient served 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.

0.00

0.07

0.14

0.21

0.28

0.36

mg/kg/h

Ist 90 min IInd 90 min

N2O/O2

enflurane 0.3%

enflurane 0.6%

enflurane 0.9%



Analg 1994; 78:691-6.

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 mg×kg-1×h-1 in the etomidate, fentanyl, midazolam, propofol, thiopental, and isoflurane groups, respectively. The isoflurane group had a lower steady-state rate of infusion of rocuronium than the other five groups (P < 0.05). Compared to intravenous anesthetics, etomidate, fentanyl, midazolam, propofol, or thiopental, isoflurane reduced the infusion requirement of rocuronium by 35%–40%.



Analg 1994; 78:691-6.

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 width, 0.1 ms) by means of stimulating surface electrodes placed adjacent to the ulnar nerve at the wrist. Recording electrodes were placed on first dorsal interosseus muscle and second finger . The stimulus output is a rectangular wave with a current range of 0–70 mA, and the machine calibrated automatically by searching for the optimum signal levels before setting the supramaximal level. The calibration of the neuromuscular monitoring device was performed 5–10 min after induction of anesthesia. A stable baseline calibration signal was awaited before administration of rocuronium. The degree of neuromuscular block, assessed every 20 s with the RelaxographÒ, was defined as the ratio of the measurement of first twitch in the train-of-four sequence (T1) to the corresponding control value.

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 volume, k = relative rate of distribution of rocuronium, Iss = asymptotic steady-state rate of infusion of rocuronium, and t = duration of rocuronium administration.

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 alfentanil 50–100 mg kg-1 h-1. Neuromuscular block was produced by repeated bolus doses of mivacurium 0.1 mg kg-1; subsequently the target neuromuscular block was maintained by a closed loop infusion. Dose potency of mivacurium was similar to that previously published in children with a similar anaesthetic technique. Mean mivacurium requirement for 95% neuromuscular block was 820 (SD 300) mg kg-1 h-1, which represented an hourly requirement of 6.6 (1.5) individual ED95 doses. Infusion requirement for 50% neuromuscular block was 320 (150) mg kg-1 h-1. These infusion rates were similar to those in children. No side effects of mivacurium were noticed.



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 open model, frequent rate adjustments have been required during the first 15 min of infusion . In the present study, achieving a stable neuromuscular response took only a few minutes, even less than in our previous study in 1–15 yr old children .

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. The targeted neuromuscular block was reached within mean 5 (SD 3) min from initiation of an infusion. Mivacurium requirement for 95% neuromuscular block was 950 (350) mg kg-1 h-1, which represented an hourly requirement of 6.8 (1.6) individual ED95 doses. Infusion requirement for 50% neuromuscular block averaged 350 (150) mg kg-1 h-1. There was a significant negative correlation between infusion rate and age of a patient. Great individual variation of the infusion rate makes a computerized infusion an easy method to achieve and maintain a desired level of neuromuscular block. No side effects of mivacurium were noticed.

Infusion requirement of mivacurium to maintain a 95% neuromuscular block averaged 950 (350) mg kg-1 h-1. This represents an hourly requirement of 6.8 (1.6) individual ED95 doses (). Infusion requirement of mivacurium to maintain a 50% neuromuscular block was 350 (150) mg kg-1 h-1. shows a time-course of the mean neuromuscular block targeted to 95% and 50%, and simultaneous cumulative infusion requirements of mivacurium. There was a negative correlation between age and infusion requirement of mivacurium to maintain a 50% neuromuscular block: infusion requirement decreases by 170 (70) mg kg-1 h-1 for every 10 yr of age (P = 0.0197). Age appeared to correlate also with infusion requirement of mivacurium to maintain a 95% neuromuscular block (P = 0.0553) ().

Timew course of targeted 95%(upper graph) and 50%(lower graph) nmblockades and cumulatroive infusione requirements of

mivacurium Meretoja, O. A.; Olkkola, K. T.Pharmacodynamics of

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

Correlation between age of child and mivacurium infusion requirement to

maintain a 50% (upopoer 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 min-1) 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-controlled infusion device does not confer smaller requirements for mivacurium than a conventional infusion device. Also, the variability of individual infusion requirements (a 40% coefficient of variation) and the range of individual infusion rates (four- to five-fold differences) were similar to those of earlier studies using a conventional infusion service.

We included a greater age range of patients in our study than have previous paediatric infusion studies (1–15 yr vs 2–10 or 2–12 yr ). Our finding of a significant correlation between infusion requirement and age is clinically important. All studies have found that children require greater infusion rates of mivacurium than adults ; it is not clear why younger children required even greater infusion rates than older children. Mivacurium is degraded by plasma cholinesterase; this enzyme has similar activity in the age range from young infants to adolescents , therefore variations in its activity cannot be used to explain the greater maintenance requirement of mivacurium in children. There may, however, be routes of elimination of mivacurium other than via degradation by this enzyme . Plasma clearance of mivacurium, in common with that of atracurium , may, indeed, be greater in children than in adults and result in greater maintenance requirements when these are calculated on a body weight basis. However, it is noteworthy that the infusion rate when calculated as mg m-2 h-1 was not related to patient age (r = 0.088, P = 0.704), and does not differ between children and adults.

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 after bolus administration of a unit dose : where A and B = zero-time intercepts; a and b = exponential disposition rate constants describing the decay of plasma concentrations Cp(t) after bolus administration of a unit dose [Cp(t) = Ae-at + Be-bt]; keo = elimination rate constant for the effect compartment;

Emax = maximum effect; Co = concentration at half-maximal effect; g = a value describing the steepness of the concentration-response curve. The initial values used for the variables were as follows: A = 5.2 x 10 By applying the superposition principle, it is possible to calculate the concentration of mivacurium in the effect compartment at any moment and during any drug administration scheme. Equations (1) to (3) give a full description of the drug input-effect

relationship. Given a target, equation (2) may be solved for the necessary concentration in the effect compartment. The pharmacokinetic model, equation (1), may be used subsequently for the calculation of the drug input function . If the measured neuromuscular block was within 2% of the desired neuromuscular block, an infusion scheme was used to maintain the current effect of mivacurium, as predicted by the pharmacokinetic-dynamic model (formulae (1) and (2)). Otherwise, the

difference between the measured and predicted neuromuscular block was used to correct the model variables. The updated values were used to calculate the new infusion scheme for achieving and maintaining the desired neuromuscular block. This cycle was performed every 20 s. Adjustment of the variables of the pharmacokinetic-dynamic model was begun 2 min after activation of the closed-loop system.

ADAPTATION ALGORITHM It is apparent that equation (2) is scale invariant with respect to the transformation (Ce, Co)®(lCe,lCo) for any number l¹ 0. Consequently, the insertion of equation (1) to equation (2) does not depend on A, B and Co, but only on the ratios A/Co and B/Co, thus

allowing an estimate not of clearance or volume of distribution, but only of the microconstants k10, k12, k21 and the amount of drugs in diverse compartments. This is, however, sufficient for determining the drug input function. A complete adaptation would require the estimation of A/Co, B/Co, a, b, keo. We chose to update during the feedback control only the variables A/Co and B/Co. This allowed adaptation of the initial bolus to achieve a certain effect (short term control) and the steady state infusion rate to maintain the given effect (long term control).

The effect E may be regarded as a function of A and B and the drug input I(t): Denoting by A + dA and B + dB the true hybrid constants for an individual subject, the difference between measured and predicted effect (DE) can be expanded in a Taylor series, as follows: In conjunction with the condition to minimize the expression dA2 + dB2, equation (4) was used to solve for dA and dB. A change in the range of ± 10% of the previous values was allowed in each update. From the updated values, new microconstants were

calculated that served to correct the drug input function. CONTROLLER PERFORMANCE Controller performance was measured by calculating the mean offset from target and mean SD from target during feedback infusion. Feedback infusion was said to begin when block returned from overshoot to target of 95% after the initial bolus. The variables

describing the controller performance were calculated for two periods: the first lasted from the beginning of the feedback infusion until the target was changed to 50%; the second lasted from the time when neuromuscular block of 50% was reached for the first time after the change of target until the closed-loop control was relinquished at the end of surgery. Both variables were calculated every 20 s. Mean offset was calculated by:

where s = set-point (target); bi = neuromuscular block measured every 20 s during feedback infusion; n = number of measurements. Mean SD from target was SD for mean offset defined above. ASYMPTOTIC STEADY-STATE RATE OF INFUSION OF MIVACURIUM To estimate the asymptotic steady-state rate of infusion of mivacurium (ISS), we used non-linear curve-fitting to fit the following formula to the curve representing the cumulative dose requirement of mivacurium : where D = amount of mivacurium contained its apparent distribution volume; k = relative rate of distribution of mivacurium; ISS =

Meretoja OA, Brown TCK. Maintenance requirement of alcuronium in paediatric patients. Anaesthesia and Intensive Care 1990; 18:452-454.

15: Meretoja OA, Luosto T. Dose-response characteristics of pancuronium in neonates, infants and children. Anaesthesia and Intensive Care 1990; 18:455-459.

16: Kalli I, Meretoja OA. Infusion of atracurium in neonates, infants and children: a study of dose requirements. British Journal of Anaesthesia 1988; 60:651-654.

17: Meretoja OA. Vecuronium infusion requirement in pediatric patients during fentanyl-N2O-O2 anesthesia. Anesthesia and Analgesia 1989; 68:20-24.

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.

Correspondence to K.T.O.

ABSTRACT: We have studied the effect of prior administration of suxamethonium on the infusion

requirements of atracurium at 50% neuromuscular block in patients undergoing elective general surgery. Anaesthesia was maintained with nitrous oxide in oxygen, propofol and fentanyl. Of 20 patients given atracurium, only 10 were given prior administration of suxamethonium 1 mg kg-1. At the beginning of the infusion, atracurium 0.3 mg kg-1 was given by bolus administration. Interaction between the two drugs was assessed by determining the steady state rate of infusion necessary to produce a constant 50% neuromuscular block. This was accomplished by applying non–linear curve fitting to data on the cumulative dose requirements during anaesthesia. The neuromuscular blocking effect was found to be similar with or without prior administration of suxamethonium. The mean steady–state rate of infusion for atracurium was 0.19 (SD 0.03) mg kg-1 h-1 for patients given suxamethonium and 0.18 (0.09) mg kg-1 h-1 for those who were not given suxamethonium. Thus prior administration of suxamethonium did not affect the infusion requirements of atracurium at 50% neuromuscular block, unlike the situation at constant 90% neuromuscular block.

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, University of Helsinki, SF-00290 Helsinki, Finland. Accepted for Publication: January 21, 1993.

ABSTRACT: 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. The targeted neuromuscular block was reached within mean 5 (SD 3) min from initiation of an infusion. Mivacurium requirement for 95% neuromuscular block was 950 (350) mg kg-1 h-1, which represented an hourly requirement of 6.8 (1.6) individual ED95 doses. Infusion requirement for 50% neuromuscular block averaged 350 (150) mg kg-1 h-1. There was a significant negative correlation between infusion rate and age of a patient. Great individual variation of the infusion rate makes a computerized infusion an easy method to achieve and maintain a desired level of neuromuscular block. No side effects of mivacurium were noticed.

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 atracurium requirements by 20%, 1 MAC by 25% and 1.3 MAC reduced the Iss of atracurium by 28%.

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 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 (derivative component).

Although the muscle relaxant controllers used in previous studies were effective, they did have some problems. The on-off controller was associated both with overshoot and with oscillation about the setpoint. The proportional controller was associated with a significant steady-state offset error, a poor response time, and some overshoot. In a clinical trial, the PID controller designed by Ritchie et al. was found to regulate succinylcholine-induced block effectively in humans, and in 1987 Jaklitsch and Westenskow improved Ritchie's model by developing a two-phase controller for the infusion of vecuronium. The two phases allowed a rapid bolus of the relaxant to be followed by a lower level of continuous infusion. This controller was not studied in a clinical trial, but when tested by computer simulation, the controller had a steady-state error of less than 1% and overshoot of 4%.

Although a number of controllers have been used with a variety of anesthetic agents and muscle relaxants, no single controller has been tested with a series of anesthetic agents to compare their different effects. In addition, the speed and reliability of a controller have not yet been used as research tools. Because a controller can rapidly achieve and maintain a desired degree of neuromuscular blockade, it also should be useful for estimating infusion rates rapidly and under a variety of conditions. This study was conducted to test the clinical efficacy of a new PID infusion controller using atracurium in conjunction with four different anesthetics (halothane, enflurane, isoflurane, and N2O/morphine) and to measure the effects of these anesthetics on atracurium-induced neuromuscular blockade with the controller.

A series of different anesthetics was tested in this study for two reasons: 1) It provides a substantial test of the controller, since different inhalation anesthetics have been shown to potentiate the effects of muscle relaxants differently. Isoflurane and enflurane show the most potentiation, and halothane and N2O/opioid show less potentiation. There is also evidence for an additional time-dependent increase in blockade by curare, at constant end-tidal enflurane concentration and at constant plasma curare concentration. This effect may occur also with atracurium. Therefore, an effective controller would need to be able to compensate for highly variable anesthetic effects as well as individual patient variation. 2) It provides a test of the controller as a means of estimating mean infusion rates to maintain desired degrees of blockade for groups of patients, anesthetized with different anesthetics.

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

4: Bradlow HS, Uys PC, Rametti LB: On-line control of atracurium induced muscle relaxation. J Biomed Eng 8:72-75, 1985

5: Ritchie G, Ebert JP, Jannett TC, Kissin I, Sheppard LC: A microcomputer based controller for neuromuscular block during surgery. Ann Biomed Eng 13:3-15, 1985

6: Jaklitsch RR, Westenskow DR: A model-based self-adjusting two-phase controller for vecuronium-induced muscle relaxation during anesthesia. IEEE Trans Biomed Eng 34:583-594, 1987

Asbury AJ, Linkens DA: Clinical automatic 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 comparison of computer-controlled versus manual administration of vecuronium in humans. J Clin Monit 3:269-276, 1987

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

3: Gramstad L, Lilleasen P. Neuromuscular blocking effects of atracurium, vecuronium and pancuronium during bolus and infusion administration. Br J Anaesth 1985; 57:1052-9.

4: Madsen JV, Anderson BN, Schurizek BA, Jensen OV, Juhl B. Atracurium administered by infusion for long neurosurgical procedures. Br J Anaesth 1986; 58:605-15.

5: Nilsson A, Tamsen A, Persson MP. Atracurium infusion in total intravenous anaesthesia. Acta Anaesthesiol Scand 1987; 31:205-8.

6: Fisher DM, Canfell C, Miller RD. Stability of atracurium administered by infusion. Anesthesiology 1984; 61:347-8.

7: Cannon JE, Fahey MR, Castagnoli KP, et al. Continuous infusion of vecuronium: the effect of anesthetic agents. Anesthesiology 1987; 67:503-6.

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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.

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control. IEEE engineering in medicine and biology 1994; 678-86. 25. Edwards ND, Mason DG, Ross JJ. A portable self-learning fuzzy logic control system for muscle relaxation. Anaesthesia

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The use of computers for controlling the

delivery of anesthesia.Anesthesiol

ogy 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 2. Closed-loop 3. Closed-loop proportional-integral-derivative 4. Adaptive 5. State estimation C. Validation of control systems D. Drugs delivered by controller 1. Antihypertensive agents 2. Muscle relaxants 3. Barbiturates 4. Anesthetic gases 5. Fluids III. History of Control of Anesthesia and Related Drugs IV. Applications of Control System Strategies A. Open-loop control B. Closed-loop feedback control 1. On-off 2. Proportional-integral-derivative 3. Adaptive V. Incorporation of Modeling into Anesthetic Control VI. Expert Systems Applications

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 (derivative component).

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

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neuromuscular blockade. British Journal of Anaesthesia 1988; 61:685-692. 7: Denai M, Linkens DA, Asbury AJ, MacLeod AD, Gray WM. Self-tuning PID control of atracurium-induced muscle relaxation in

surgical patients. IEEE Proceedings 1990; 137:261-272. 8: O'Hara DA, Derbyshire GJ, Overdyk FJ, Bogen DK, Marshall BE. Closed-loop infusion of atracurium with four different

anesthetic techniques. Anesthesiology 1991; 74:258-263. 9: Schwilden H, Olkkola KT. Use of a pharmacokinetic-dynamic model for the automatic feedback control of atracurium.

European Journal of Pharmacology 1991; 40:293-296. 10: Mahfouf M, Linkens DA, Asbury AJ, Gray WM, Peacock JE. Generalised predictive control (GPC) in the operating-theatre.

IEEE Proceedings 1992; 139:404-420. 11: Assef SJ, Lennon RL, Jones KA, Burke MJ, Behrens TL. A versatile, computer-controlled, closed)loop system for

continuous infusion of muscle relaxant. Mayo Clinic Proceedings 1993; 68:1074-1080. 13: Mason DG, Linkens DA, Edwards ND, Reilly CS. Automated delivery of muscle relaxants using buzzy-logic control. IEEE

Engineering in Medicine and Biology 1994; 13:678-686. 14: Linkens DA, Hasnain SB. Self-organizing fuzzy logic control and application to muscle relaxant anaesthesia. IEEE

Proceedings 1991; 138:274-284. 15: Linkens DA, Mahfouf M, Abbod M. Self-adaptive and self-organizing control applied to nonlinear multivariable anaesthesia:

A comparative model-based study. IEEE Proceedincs 1992; 139:381-394. 16: Mason DG, Linkens DA, Edwards ND, Reilly CS. Development of a portable closed-loop atracurium infusion system:

Systems methodology and safety issues. International Monitoring and Computing (in press) 17: Asbury AJ, Tzabar Y. Fuzzy logic: new ways of thinking for anaesthesia. British Journal of Anaesthesia 1995; 75:1-2. <ldn>! 18: Martin JF. Fuzzy control in anaesthesia. Journal of Clinical Monitoring 1994; 10:77-80.

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