Rev. Bras. Anestesiol. vol.67 número2

(1)

REVISTA

BRASILEIRA

DE

ANESTESIOLOGIA

PublicaçãoOficialdaSociedadeBrasileiradeAnestesiologia

www.sba.com.br

SCIENTIFIC

ARTICLE

Regulation

of

hypnosis

in

Propofol

anesthesia

administration

based

on

non-linear

control

strategy

Muhammad

Ilyas

a

_,

_Ali

_Khaqan

a

_,

_Jamshed

_Iqbal

b,∗

_,

_Raja

_Ali

_Riaz

a

a_COMSATS_Institute_of_Information_Technology,_Department_of_Electrical_Engineering,_Chak_Shahzad,_Pakistan

b_National_University_of_Computer_and_Emerging_Sciences_(FAST-NU),_Department_of_Electrical_Engineering,_Islamabad,_Pakistan

Received28May2015;accepted17August2015 Availableonline11May2016

KEYWORDS

Closed-loop anesthesia;

Moderncontrol;

Biocontrol;

Pharmacodynamics; Pharmacokinetics

Abstract ContinuousadjustmentofPropofol inmanual deliveryofanesthesiafor conduct-ing a surgical procedure overburdens the workload of an anesthetist who is working in a multi-taskingscenario.Going beyond manual administrationandTargetControlledInfusion, closed-loopcontrolofPropofolinfusionhasthepotentialtoofferseveralbenefitsintermsof handlingperturbationsandreducingtheeffectofinter-patientvariability.Thispaperproposes aclosed-loopautomateddrugadministrationapproachtocontrolDepthOfHypnosisin anes-thesia.Incontrastwithmostoftheexistingresearchonanesthesiacontrolwhichmakesuseof linearcontrolstrategiesortheirimprovedvariants,thenoveltyofthepresentresearchliesin applyingrobustcontrolstrategyi.e.SlidingModeControltoaccuratelycontroldruginfusion. Basedonthederivedpatient’smodel,thedesignedcontrollerusesmeasurementsfromEEG toregulateDOHonBispectralIndexbycontrollinginfusionrateofPropofol.Theperformance ofthecontroller isinvestigatedandcharacterized withreal datasetof8patients undergo-ingsurgery.Resultsofthisinsilicostudyindicatethatforallthepatients,with0%overshoot observed,thesteadystateerrorliesinbetween±5.Clinically,thisimpliesthatinallthecases, withoutanyoverdose,thecontrollermaintainsthedesiredDOHlevelforsmoothconductionof surgicalprocedures.

∗_{Corresponding}_author.

E-mail:jamshed.iqbal@nu.edu.pk(J.Iqbal).

http://dx.doi.org/10.1016/j.bjane.2015.08.011

(2)

PALAVRAS-CHAVE

Anestesiadecircuito fechado;

Controlemoderno;

Biocontrole; Farmacodinâmica; Farmacocinética

Controledahipnosenaadministrac¸ãodepropofolcombasenaestratégiadecontrole nãolinear

Resumo Oajustecontínuodepropofolnaadministraçãomanualdeanestesiaparaarealização deumprocedimentocirúrgicooneraacargadetrabalhodeanestesiologistasquetrabalhamem ambientemultitarefa.Indoalémdaadministraçãomanualedainfusãoalvo-controlada(IAC),o controledecircuitofechadodainfusãodepropofoltemopotencialdeoferecerváriosbenefícios emtermosdemanejodasperturbaçõesereduziroefeitodavariabilidadeinterpaciente.Este artigopropõeumaabordagemparaaadministraçãoautomatizadadedrogasemcircuitofechado paracontrolaraprofundidadedahipnose(PDH)emanestesia.Emcontrastecomamaioriadas pesquisasexistentessobreocontroledaanestesiaqueusamestratégiasdecontrolelinearou de suasvariantesmelhoradas,anovidade dapresentepesquisaresidenaaplicaçãodeuma estratégiadecontrolerobusto;istoé,oControleporModosDeslizantes(CMD)paracontrolar comprecisão ainfusãodadroga.Combasenomodeloderivado dopaciente,ocontrolador projetadousaasmediçõesdoEEGpararegularaPDHnoBispectralIndex(BIS),controlandoa taxadeinfusãodepropofol.Odesempenhodocontroladoréinvestigadoecaracterizadocom umconjuntodedadosreaisdeoitopacientessubmetidosàcirurgia.Osresultadosdesteestudo insilicoindicamque,paratodosospacientes,com0%deexcessoobservado,oerrodeestado estacionário ficaentre±5. Clinicamente,issoimplicaqueemtodosos casos,semqualquer sobredosagem,ocontroladormantémoníveldesejadodePDHparaaconduçãotranquilados procedimentoscirúrgicos.

Introduction

Thankstotechnologicaladvancements,thebenefitsoffered bymodernmedicinehave totallytransformedtheconcept of clinical surgery. Nowadays, surgical procedures can be performed with much ease and comfort. This incredible milestone has been achieved only through the research outcomesin modern anesthesia. Prior tothe discovery of anesthesia, surgery has to be conducted extremely fast. Historically, trivial techniques like application of cold, compression of nerve or reduction in cerebral perfusion wereemployedtokeeppatientunconscious.1_Undoubtedly,

invention of inhalation gases in 1840 by Hickman was a pivotal steptowarddiscovery of anesthesiatofinally per-mitconductionofinvasivesurgeries.Thefirstprocedureof anesthesia,basedondiethylether,wasperformed in1842 byC.W.Long.Thisnewrevolutionaryconceptwaslateron termedasanesthesiameaninglackofesthesiai.e.sense.

Anesthesia is intensively used particularly in medical domain in many applications including surgical operation withincision,dentalsurgery andintensivecare.2_The

pri-maryobjectiveofanesthesiaistoofferpainlessfeelingsto a patientunder operation bydriving him/her into uncon-sciousstatewithoutmemory.Theoverallfunctionalscenario ofanesthesiacanbecategorizedintothreetemporalphase insequence:induction,maintenanceandemergence. Dur-ing the firstphase, the objectiveis tobring apatient to areferenceDepthof Hypnosis(DOH). Itis thennecessary toadministerthe anestheticdrugin ordertomaintainan adequateDOH.Forinductionandmaintenanceof anesthe-sia,commonly usedintravenouslyadministeredanesthetic drugisPropofol.3_During_emergence _phase_in_post-surgery

activities,vaporizerandother infusion devicesareturned offsoastoenablepatientstoawakefast.

During general anesthesia, Propofol is usually used togetherwithfastactingopioidse.g.remifentaniltohave asynergisticeffect.4_Under-dosing_of_anesthetic_drugs_may

leadto insufficient analgesia or awareness. On the other hand,itisdangerousforpatientstohaveexcessiveamount ofdrug.Thuscarefulmanagementoftheintravenousdrug delivery is the key factor behind successful anesthesia practice.It is desirous to accessthe depth of anesthesia togetherwithautomaticandinteractivedrugadministration withlittlehumaninterventionsoastoadjustdrugdosage accordinglyfor balancingtheanesthetic state, autonomic functionandresponsetonoxiousstimuli.

The procedures to administer intravenous drug deliv-ery have been evolved from simple manual delivery and computer-assisted automated Target Controlled Infusion (TCI)tomoresophisticatedClosed-LoopANesthesia(CLAN). Traditionally, hypnotic drug delivery rates in intravenous anesthesiaaremanuallycontrolledbyananesthetist.Doses are principally decided based on patient demographics, qualitatively measured signs (e.g. presence of certain reflexes, movement) and quantitatively measured signals (e.g. oxygen saturation, blood pressure, heart rate). The dosage scheme is then tuned by hit and trial to opti-mizeanesthesiaand toevade toxicity.TCI,alsoknownas Computer Assisted Continuous Infusion (CACI),5 _relies _on

population-based pharmacokinetic (PK) and pharmacody-namic (PD) models6 _for _calculating _an _adequate _infusion

(3)

Awake state (100-90)

Light hypnotic

state

Moderate hypnotic state

Start deep hypnotic

state _{Flat line EEG} Increasing

burst suppression

0 20

40 60

Surgical procedure band

80 100

Figure1 BISscalingbandtoindicateDOHlevel.

of plasma concentration. This prediction is then used to trackthereferenceconcentrationthusdevisinganopenloop control paradigm. Instead of adjusting the infusion rate, the anesthetist manipulates the referenceconcentration, both reactivelyand proactively,usingcommercially avail-ableinfusionpumps.TCIsystemssufferfromdrawbacksof sensitivitytomodelnon-linearities anddisturbances since thereisnofeedbackofmeasurementondrugeffect.These drawbacks can be addressed by closing the control loop through DOH measurement, which is given by EEG-based monitors e.g. Bispectral Index (BIS).7 _The _value _of _BIS _is

mappedto theDOH level of apatient basedon the scal-ingbandshowninFig.1.Thevalueof100---90corresponds to a fully awake state while level of 90---60 and 60---40 indicatelight and moderate hypnosis levelsrespectively.8

Themoderatelevelrepresentsthesurgicalprocedureband in which general surgery is performed by clinical profes-sionals.Levelbeyonddeephypnoticstate (40---20)isquite dangerous.9

InaCLAN system,drugeffectismeasured inrealtime andiscomparedwiththereferenceDOHtoobtainanerror signal.Basedonwhich,thesystem subsequentlyadjustsa druginfusionrate.ACLANsystemoffersseveralbenefitsin comparisonwithaTCIsystemincludingautomatichandling ofperturbations,precisecontrolofdruginfusionrate, min-imizing the effectof patientvariability and reducing the needofanesthetistintervention.

TrendtorealizeaCLANsystemhasbeenbasedontrivial orlinearcontrolapproaches.10_Dong2_proposed_a_CLAN

sys-temfortotalintravenousanesthesiabasedonProportional, Integral, Derivative (PID) controller. With BIS as sensory feedbackand Digital Signal Processing (DSP) based super-visorysystem,therealizedsystemwastestedon21healthy volunteersand 15patients undergoingsurgery. Exceptfor the2patients,satisfactoryclinical resultswereobtained. Anotherstudy11 _based_on_PID_control_investigated_the

con-trolperformancewith10patientsundergoingelectivehipor kneesurgery. Themedianabsoluteperformance errorwas found tobe8%. The control strategywasable toprovide adequateanesthesiain9patientswithoscillatoryresponse recorded in BIS values for 3 patients. Other prominent studiesreportingPIDcontrolofanesthesiainclude.12,13

Com-paringconventionalPIDwithLinearModelPredictiveControl (LMPC),itisreportedinRef.14thatthelaterapproach out-performsinterms of robustnesstointraand inter-patient dynamicsandhandlingdisturbances,constraints and mea-surementnoise.Recent studies15---18 _aim _to_improve_linear

approaches by properly tuning the controllers to achieve sufficientrobustnessmarginsforidentifiableuncertainties. However,forcontrollawsbasedonthelinearapproaches, themodelofapatient,exhibitinganon-linearbehavior,is

linearized.Suchapproximationachievesgoodcontrol per-formance only if the difference between the predicted and actual closed-loop systems is small for the designed controller.19 _The _traditional _PID _controller _cannot _handle

disturbances like blood pressure changes, neural muscu-lar blockade and heart rate variability10 _and _may _result

in oscillatorybehavior during clinicaltrials. Alsofor wide acceptanceofaCLAN systembyclinical professionalsand regulatory bodies, guarantees of robuststability and per-formance are must. Employing a non-linear and robust control strategy is therefore need of the hour in clinical anesthesia.

This research is aimed at unleashing the potential of a sophisticated control strategy i.e. Sliding ModeControl (SMC) to manage Propofol anesthesia infusion rate. The paper is organized as follows: Section II derives patient model. Section III explains the design details of SMC while Section IVpresentsresults basedonclinical param-eters of actual patients. Finally Section V comments on conclusion.

Patient

model

Thedynamicsofthehypnoticdrugiscategorizedinits phar-macokinetics(PK)andpharmacodynamics(PD)parameters. The PK parameter is used to govern the behavior of the infused drug in the body over time includingits distribu-tion,metabolism,absorptionandclearance20_while_the_PD

parameter representsthe drugconcentrationintheblood andthecorrespondingimpactcausedattheeffectsite.21

Onthebasis ofblood flow indifferentorgans,medical literaturedivideshumanbodyintovariouscompartments.22

Compartmentalmodelrepresentsabasickineticapproach todescribedrugabsorption,distributionandelimination.23

Relating plasma druglevelstoPD parameters,this model is intensively used in variousbiomedical and biotechnical applicationsbecauseoftheirinherentflexibilityand simplic-ity. The integratedPKPD structurefollowscompartmental modeling. In the present study, a three compartment PK model with an additional effect compartment has been adoptedowingtoitssufficientprecisionandcomputational efficiency.24_Centred_on_a_primary_compartment

(intravascu-larblood)withvolumeV1,arapidperipheralcompartment (muscle)andaslowperipheralcompartment(fat),with vol-umesV2andV3respectively,areconnectedtotheprimary compartment.Thusdistributionandeliminationofthedrug betweenprimaryandperipheralcompartmentstakeplace withweightedrate constantsk12,k21,k13,k31 asdepicted inFig.2.Atanytime,thechangeinconcentrationofdrug in primary compartment is related tothe drug moved to andfromtherapidandslowperipheralcompartments.The induction and clearance of the drug takes place through the primary compartment. The drug eliminates from this compartmentinanexponentialfashion.17_At_the_effect_side

(brain),theconcentrationofthedrugismeasuredthrough thecorticalactivityinthebrainmeasuredthroughthe mod-ified form of EEGsignal.25 _The _extracted _information _can

thenbemappedtoDepthOfHypnosis(DOH)soastoanalyze patient’ssuitabilityforsurgicalprocedures.

(4)

2

Rapid peripheral compartment

(V2)

X2

Muscle

Fat

Intravascular blood Brain Slow peripheral

compartment

(V3)

X3

Primary compartment

(V1)

X1

Effect site compartment

Ce

k1e

k10

Infusion r

ate

u(t)

k

21

k

12

k31

k13

ke0

3

1

Figure2 BlockdiagramofPKandPDmodels.

ToderivethePKmodel,stateequationscorrespondingto thethreecompartmentscanbewrittenas(1)---(3)

˙

x1(t)=−k10x1(t)−k12x1(t)−k13x1(t)+k21x2(t)

+k31x3(t)+u(t) (1)

˙

x2(t)=−k12x1(t)−k21x2(t) (2)

˙

x3(t)=−k13x1(t)−k31x3(t) (3)

Laplacetransformof(1)---(3)yields(4)---(6)

sX1(s)=−(k10+K12+K13)X1(s)+k21X2(s)+k31X13(s)+(t)

(4)

sX2(s)=k12X1(s)−k21X2(s) (5)

sX23(s)=k13X1(s)−k31X3(s) (6)

Solving (4)---(6), the input---output relationship can be writtenas(7)

Dp(s)= X1(s)

U(s) =

(s2₊_s₍_k

21+k31)+k21k31)

(s3₊_s2₍_k

10+k12+k21+k13+k31)+s(k10k21+k10k31+k13k21+k31k21)+(k10k21k31))

(7)

where Dp(s) is the rate of drug absorption/metabolism withinthebodydefinedasdisposition rate.Rewriting(7), thegeneralformofPKmodelisobtainedas

Dp(s)= X1(s)

U(s) =

b2s2+b1s+b0 a3s3+a2s2+a1s+a0

(8)

where b2=1, b1=21+31, b0=2131, a3=1, a2=(10+12+13+31), a1=1021+1031+1231+ 1321+3121,a0=102131

The PD model indicating level of consciousnessrelates concentration of the drug in plasma to the effect site concentration andcan be derived based onthe state Eq.

(9)

˙

xe(t)=k1ex1(t)−ke0xe(t) (9)

ApplyingLaplacetransformon(9)

sXe(s)=k1eX1(s)−ke0Xe(s) (10)

Table1 Nomenclature.

Symbol Unit Name

u(t) mgseg−1 _Infusion_rate

k10 seg−1 Eliminationrateconstant

x1 mg Amountofdruginprimary

compartment

x2 mg Amountofdruginrapid

peripheralcompartment

x3 mg Amountofdruginslow

peripheralcompartment

xe mg Flowofhypnoticagentin

effectsite

k1e s−1 Rateconstantateffectsite

ke0 seg−1 Eliminationrateconstantat

effectsite

Ce mgL−1 Effectsiteconcentration

E0 --- Awakestage(100---90)

Emax --- Maximumeffectachieved

bydruginfusion

C50 mgL−1 Drugconcentrationathalf

ofthemaximumeffect

--- Sigmoidcurveslope

parameter

Consideringk1eandke0areequalbecauseofitsnegligible

volumeoftheeffectsitecompartment,thedispositionrate attheeffectsideisgivenby(11)

De(s)= Xe(s)

X1(s)

= ke0

(s+ke0)

(11)

BasedonthecascadednatureofPKandPDmodels,the overallpatientmodelcanfinallybewrittenas

Hp(s)= ke0 (s+Xe0)

∗ b2s

2₊_b 1s+b0 a3s3+a2s2+a1s+a0

(12)

BISis relatedwithanestheticeffectsiteconcentration

Ce(t)y throughnonlinearsigmoidmodeli.e.

BIS(t)=E0−Emax∗

Ce(t) Ce(t)

+C50

(13)

whereCe(t)canbecomputedbyintegrating(14)

˙

Ce(t)=−₀_.₁₀₆₈_x₁+₀_.₄₅₆_Ce ₍₁₄₎

Control

design

(5)

Patient model

Sigmoid

PD PK

BIS

S M C

b₂s2 ₊_b

1s + b0 ke0 Xe(s)

s + ke0

a₃s3 + a₂s2 + a₁s+a₀ R(s)

Figure3 Blockdiagramofoverallclosed-loopsystem.

toachievethedesiredDOHduringsurgicalprocedures.The overallobjectiveinthecontroldesignistominimizesteady stateerror soastomaintainDOHlevel withinacceptable rangeforsurgery.

The control law is based on SMC, which is one of the mosteffectiverobustcontroltechniquesfor highly nonlin-earsystemsoperatinginuncertainenvironmentssubjected todisturbances.SMCinvolvesdefiningaslidingsurface typ-ically a linear hyper-surface. The fundamental concept26

behindSMCistodrivethesystemdynamicsfromanyinitial statetotheslidingsurface(i.e.reachingphase).The sys-temisthenmaintainedonthissurfaceforallfuturevalues oftime(slidingphase).ThemajorbenefitofferedbySMCis itslowsensitivitytoplantdisturbancesanduncertainties.27

To designSMC,considering the slidingsurfacegivenby

(15)

=_a₁_x₁+_a₂_x₂+_a₃_x₃+_a₄_xe ₍₁₅₎

or

˙

=_a₁_˙_x₁+_a₂_˙_x₂+_a₃_x_˙₃+_a₄_˙_xe ₍₁₆₎

wherea1,a2,a3,a4aretuningparametersofthecontroller. With a1=1, values of other parameters are chosen in a

waythat0becomesHurwitzmonicpolynomial.This condi-tion ensures reduction in order of the system which can be represented with n−1 states. Such a system demon-stratesinsensitivitytomatcheduncertainties.Substituting thestateequations,(16)canbere-writtenas,

˙

=a1[(−k10−k12−k13)x1(t)+k21x2(t)+k31x3(t)+u(t)]

+_a₂_[_k₁₂_x₁₍_t₎−_k₂₁_x₂₍_t_)]+_a₃_[_k₁₃_x₁₍_t₎−_k₃₁_x₃₍_t_)]

+a4[k1ex1(t)−ke0xe(t)] (17)

The overall control law (u) consistsof equivalentcontrol (ueq)anddiscontinuouscontrol(udisc)i.e.

u=ueq+udisc (18)

The equivalent control forces the system dynamics to move tothe slidingsurface and dependsonthe states of the systemand state parameters.Itmakes thederivative ofslidingmanifoldequal tozero andcanbecomputedby putting=0alongthesystemdynamics(17).Thus,

ueq=−[(−k10−k12−k13)x1(t)+k21x2(t)+k31x3(t)]

−a2[k12x1(t)−k21x2(t)]−a3[k13x1(t)−k31x3(t)]

−a4[k1e1(t)−ke0xe(t)] (19)

Presence of disturbances or uncertainties may lead

=/ 0.Discontinuouscontrolhandlessuchdisturbancesand dependsongainandsignumfunction,whichexhibits switch-ingbehavior.Thus,

udisc=−ksign() (20)

wherek ∈ Rn×n_is_the_{discontinuity}_gain_matrix.

Mathemat-ically,

sign()=

1for>0

−₁_for<0

(21)

Toinvestigateandcharacterizetheperformanceofthe designed controller, clinical data including characteristic variablesofeightpatientsispresentedinTable2.8

Based on the patient’s attributes, clinical parameters computed using Schnider three compartmental model for Propofolaregivenbelow:

V1=4.27[l]

AV2=18.9−0.391(Age−53)[l]

AV3=238[l]

Table2 Clinicaldatasetshowingpatients’attributes.

Patient Ageyears Height(H),cm Weight(W),kg Gender C50 E0 Emax

1 40 163 54 F 6.33 98.80 94.10 2.24

2 36 163 50 F 6.76 98.60 86.00 4.29

3 34 172 58 F 4.95 96.20 90.80 1.84

4 28 164 60 M 4.96 94.70 85.30 2.46

5 37 187 75 M 8.02 92.00 104.00 2.10

6 42 179 78 M 4.82 91.80 77.90 1.85

7 38 174 80 F 6.56 95.50 76.40 4.12

(6)

a

b

0 50 100 150 200 250

–0.5 0 0.5 1

Time (sec.)

Plasma drug conc.

(mg/l)

Primary compartment Rapid peripheral compartment Slow peripheral compartment Effect site compartment

0 50 100 150 200 250

85 90 95 100

Time (sec.)

BIS

Figure4 Controller-lessadministrationofanestheticagentinpatient6:(a)drugconcentrationinvariouscompartmentsand(b) outputprofile.

Cl1=1.89+0.0456(W−77)−0.0681(LBM−59)

+₀_.₀₂₆₄₍_H−₁₇₇₎

Cl2=1.29−0.24(Age−53)

Cl3=0.836

whereLeanBodyMass(LBM)isafunctionofpatient’sgender, heightandweight.Formaleandfemale,itisrespectively givenas

LBM=₁.1∗W−₁₂₈∗W

2

H2

LBM=1.07∗W−148∗W

2

H2r 2

Therateconstantsk10,k12,k13,k21,k31dependonweight,

height,age,genderofthepatientandaregivenas:

k10=

Cl1

V1

k12=

Cl2

V1

k13=

Cl3

V1

b

a

c

0 50 100 150 200 250 1.4

1.6 1.8 2

Time (sec.)

Dr

ug

infus

ion

ra

te

(m

g/

s

)

0 50 100 150 200 250 –0.5

0 0.5 1 1.5 2

Time (sec.)

P

la

s

m

a

dr

ug

co

nc

.

(m

g

/l

)

0 50 100 150 200 250 40

50 60 70 80 90 100

Time (sec.)

BI

S

(7)

a

b

c

d

0 50 100 150 200 250 –0.5

0 0.5 1 1.5 2

Time (sec.)

P

la

s

m

a

dr

ug

c

o

n

c

.

(m

g

/l

)

0 50 100 150 200 250 –0.5

0 0.5 1 1.5 2

Time (sec.)

P

las

m

a

dr

ug

c

o

n

c

.

(m

g/

l)

0 50 100 150 200 250 –0.5

0 0.5 1 1.5 2

Time (sec.)

Pl

a

s

m

a

drug

c

on

c.

(m

g

/l

)

0 50 100 150 200 250 –1

0 1 2

Time (sec.)

Pl

a

s

m

a

d

rug

c

on

c.

(m

g

/l

)

Figure6 Plasmadrugconcentrationin(a)patient4,(b)patient8,(c)patient2,and(d)patient7.

0 50 100 150 200 250

40 50 60 70 80 90 100

Time (sec.)

BIS (DOH)

Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6 Patient 7 Patient 8

Maintenance phase Induction phase

(8)

k21=

Cl2

V2

k31=

Cl3

V3

Results

and

discussion

Thetrivialschemeofanestheticagentadministrationsimply consistsofacontroller-lessparadigm.Withsuchascheme,

Fig.4Apresentsplasmadrugconcentrationinvarious com-partmentswhileFig.4Bshowstheoutputprofileintheform ofBISsignal.BISvaluesarestillfarawayfromthedesired DOH level which is required for the general surgery. It is observed from theseresults that manipulatinganesthesia withoutadedicatedcontrollerintheloopcanbequiterisky andmaynotbesuitableinmanyoperationalscenarios.Using thisscheme,theaccuracyandprecisionofthedrug deliv-erytoapatientduringsurgeryistotallydependentonthe anesthesiologist experience. The critical response of this controllerbecomesmoreproblematicandcrucialespecially incaseofchildrenandcardiacpatients.

Employing a robust controllerin a closed-loop fashion completelychangestheresponse.Fig.5Apresentsthe con-trolleddruginfusionlevelusingSMCtechniqueforpatient6. PlasmadrugconcentrationinthecompartmentsofthePKPD structureisillustratedinFig.5B,wheretherateofchange ofdrug concentrationwithrespecttotimeinall thefour compartmentsofthebodyafterthedruginfusionisshown. Initiallythedrugconcentrationismaximumintheprimary compartment.Butasthedrugmovesbetweenprimaryand peripheral compartments, its level decays exponentially in the primary compartment and rises in the peripheral compartments.Thisflowofdruginthecompartmentsis rep-resentedthroughtheuseofrateconstants.TheoutputofBIS indicatorisplottedinFig.5C.Itclearlyshowsthatthe pres-enceofthecontrollerwithaclosed-loopfeedbacksystem dramatically improvesperformance ofanesthesiaprocess. TheoutputconvergestotherequiredlevelofBISforsurgery withinseconds.ThecontrollerthenmaintainsthisDOHlevel

–10 0 10 20 30 40 50 60

8 7 6 5 4 3 2 1

BI

S (

DOH

)

Patient no.

Reference Actual S/State error

Figure8 SteadystateerrorshowingthatDOHisunderdesired range.

soastoassistanesthesiologist in ensuringsafer regionof operation.

Plasmadrugconcentrationinvariouscompartmentsisa functionoffactorsincludingpatients’age.Lessertheageof apatient,fasteristhemetabolism/eliminationofthedrug. Asanexample,comparethedrugconcentrationofpatients 4and8illustratedinFig.6AandBrespectively.Itisevident thatpatient 4 beingcomparatively youngerdemonstrates fastmetabolismofthedrugoccurringinprimary compart-mentthanpatient8.Comparisonofyoungandoldpatients disclosesthat the concentrationin rapid peripheral com-partment increases substantially due to the fast flow of Propofol from primary compartment. The same effect is reflectedinslowperipheralcompartmentandtheeffectsite compartment.

Incontrasttoage,theweightofapatientdoesnot sig-nificantlyaffecttheplasma drugconcentrationprofile.To investigatethiseffect,theconcentrationinpatients’2and 7(weight=30kg)hasbeencompared(Fig.6CandD).Itcan beseenthat theconcentrationofPropofol inthe primary compartmentofpatient2decaysatarelativelysamerate asthatofpatient7.Theminordifferenceintheresponses isduetodifferenceinagesofthepatients.Samefashionis observedregardingflowofdrugtoothercompartments.

Thedesignedcontrollerwiththederivedpatient’smodel is then simulated as per the dataset (Table 2). Simula-tionresults shown in Fig. 7 present the hypnosis level of 8 patients after the infusion of drug for surgery. These

0 50 100 150 200 250

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

Time (sec.)

Dr

ug

infu

si

o

n

ra

te

(m

g/

s)

Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6 Patient 7 Patient 8

(9)

responses indicate both the induction and maintenance phases of anesthesia. Initially, during induction phase, patientisin awakestate(DOHlevelnear100)andthenit entersintomoderatehypnoticstate(DOHlevelof40---60). Thislevelismaintainedfor safeexecutionofsurgical pro-cedures.In thisstudy, allthe patients achievedthe ideal hypnosislevel.However,forthesakeofquantification,Fig.8

shows steady state error considering DOH level of 50 as reference.Theerrorboundedinbetween±5isstillwithin acceptablerangeforsurgicaloperations.

The designed SMC provides different rates of Propofol infusioncorrespondingtodifferentpatients(Fig.9)dueto differenceinpatients’parameterslikeage,weight,height, genderandLBMtomaintainthedesiredlevelofDOH.The controllerinitiallypermitsinjectionoflargeamountofdrug tobringthe patientin unconsciousness state in induction phase of anesthesia. Once the desired hypnosis level is achieved,thenthecontrollerstrictlymaintainsthespecific infusionratethroughoutthemaintenancephaseof anesthe-siaforeachpatient.

Conclusions

ThispaperproposesSMC-basedlawfor adequateandsafe deliveryofPropofolanesthesiaforachievingdesired hypno-sislevels.Simulationresultsbasedonthedatasetcomprising of8realpatientswithdifferentclinicalparametersclearly witnessefficacyofthepresentedapproach.Withthehelpof medicalprofessionalsat National InstituteofHealth(NIH) Pakistan,we are goingto test the proposed CLAN in real surgicalscenarioaftermeetingmedicalsafetystandards.It isimperativetodemonstratepracticalbenefitsofCLANto convinceclinicians.TheCLANtechnique,thoughpotentially theeventualgoalofanestheticdruginfusionisstillinearly stagesofresearch.ItisanticipatedthatsuchaCLANsystem basedonanon-linearandrobustcontrolwillreplacemanual administrationaswellasTCIsysteminverynearfuture.

Conflicts

of

interest

Theauthorsdeclarenoconflictsofinterest.

References

1.BibianS[PhDThesis]AutomationinClinicalAnesthesia.Canada: UniversityofBritishColumbia;2006.

2.DongC[PhDThesis]ClosedLoopControlledTotalIntravenous Anaesthesia.UK:UniversityofPlymouth;2003.

3.WarpechowskiP,SantosATL,PereiraPJI,etal.Effectsof propo-fol on the cardiac conduction system. Rev Bras Anestesiol. 2010;60:441---4.

4.Absalom AR, Sutcliffe N, Kenny GNC. Closed-loop control of anesthesia using bispectral index: performance assess-mentinpatientsundergoing majororthopedicsurgeryunder combined general and regional anesthesia. Anesthesiology. 2002;96:67---73.

5.LiuN,ChazotT,GentyA,etal.Titrationofpropofolfor anes-thetic induction and maintenance guided by the bispectral index:closed-loopversusmanualcontrol:aprospective, ran-domized,multicenterstudy.Anesthesiology.2006;104:686---95.

6.SimoniRF,MiziaraLEDPG,EstevesLO,etal.Pharmacodynamic evaluationandphysical/chemicalanalysisoftwoformulations

ofpropofolusedintarget-controlledinfusion.RevBras Aneste-siol.2013;63:66---72.

7.NunesRR, Chave IMM,Alencar JCGD,etal. Bispectral index andotherprocessedparametersofelectroencephalogram:an update.RevBrasAnestesiol.2012;62:111---7.

8.Ionescu CM, De Keyser R, Torrico BC, et al. Robust predic-tivecontrol strategyappliedfor propofoldosingusing BISas acontrolledvariableduringanesthesia.IEEETransBiomedEng. 2008;55:2161---70.

9.Struys M,Desmet T, GreenwaldS,et al. Performance eval-uation of two published closed-loop control systems using bispectralindexmonitoring:asimulationstudy.Anesthesiology. 2004;100:640---7.

10.LanJY,AbbodMF,YehRG,etal.Review:intelligentmodeling andcontrolinanesthesia.JMedBiolEng.2012;32:293---307.

11.Absalom AR, Struys MMRF. An overview of target controlled infusionsandtotalintravenousanaesthesia.SanDiego,CA,USA: AcademiaPress;2007.

12.SolteszK,HeusdenK,DumontGA,etal.Closed-loop anesthe-siainchildren using aPID controller: a pilotstudy.In: IFAC conferenceonadvancesinPIDcontrol.2012.

13.SakaiT, MatsukiA, WhitePF,etal. UseofanEEG-bispectral closed-loop deliverysystem for administering propofol.Acta AnaesthesiolScand.2000;44:1007---10.

14.IngoleDD,SonawaneDN,NaikVV,etal.Linearmodelpredictive controllerforclosed-loopcontrolofintravenousanesthesiawith timedelay.ACEEEIntJControlSystInstrum.2013;4:8---15.

15.ZhusubaliyevTZ,MedvedevA,SilvaMM.Bifurcationanalysisof PID-controlledneuromuscularblockadeinclosed-loop anesthe-sia.JProcessControl.2015;25:152---63.

16.Heusden KV, Dumont GA, Soltesz K, et al. Design and clinical evaluation of robust PID control of propofol anes-thesia inchildren. IEEETransControl Syst Technol.2014;22: 491---501.

17.Soltesz K,Dumont GA,Ansermino JM.Assessingcontrol per-formance in closed-loop anesthesia. In: 21st Mediterranean conferenceoncontrolandautomation.2013.p.191---6.

18.WestN,DumontGA,HeusdenKV,etal.Robustclosed-loop con-trol ofinduction and maintenance of propofol anesthesia in children.PediatrAnesth.2013;23:712---9.

19.AjwadSA,IqbalJ,UllahMI,etal.Asystematicreviewofcurrent andemergentmanipulatorcontrolapproaches.FrontMechEng. 2015;10:198---210.

20.Shargel L, Wu-PongS, Yu AB. Applied biopharmaceuticsand pharmacokinetics.NY,USA:McGraw-Hill;2007.

21.HeusdenKV,SolteszK,KhosraviS,etal.Quantificationofthe variabilityinresponsetopropofoladministrationinchildren. IEEETransBiomedEng.2013;60:2521---9.

22.CoppensMJ,EleveldDJ,ProostJH,etal.Anevaluationofusing populationpharmacokineticmodelstoestimate pharmacody-namicparametersforpropofolandbispectralindexinchildren. Anesthesiology.2011;115:83---93.

23.BibianS, RiesCR, Huzmezan M,et al.Introduction to auto-mated drug delivery in clinical anesthesia. Eur J Control. 2005;11:535---57.

24.Schnider TW, Minto CF, Cambus P, et al. The influence of methodofadministrationandcovariatesonthe pharmacoki-neticsofpropofolinadultvolunteers.Anesthesiology.1998;88: 1170---82.

25.Hendrickx JF [PhD Thesis] The Pharmacokinetics of Inhaled AnestheticsandCarrierGases.Belgium:GhentUniversity;2004.

26.IslamRU,IqbalJ,KhanQ.Designandcomparisonoftwocontrol strategiesformulti-DOFarticulatedroboticarmmanipulator. ControlEngApplInform.2014;16:28---39.