parameter identification methods in a model of the … · 2015. 10. 8. · title: parameter...

A. Pironet 1 , T. Desaive 1 , P. C. Dauby 1 , J. G. Chase 2 , P. D. Docherty 2 PARAMETER IDENTIFICATION METHODS IN A MODEL OF THE CARDIOVASCULAR SYSTEM Introduc)on Methods • To be clinically relevant, the parameters p of a model have to be iden)fied from pa)ent data y. • To achieve realA)me monitoring, it is important to select the best parameter iden)fica)on method, in terms of speed, efficiency and reliability. • This work compares seven parameter iden)fica)on methods applied to a cardiovascular system (CVS) model. 1 University of Liège (ULg), GIGAACardiovascular Sciences, Liège, Belgium 2 Department of Mechanical Engineering, University of Canterbury, New Zealand The seven methods are tested using in silico and animal experimental reference data. Output vector (available in the ICU): y = (Aor)c pulse pressure, venous pulse pressure, stroke volume, mean aor)c pressure, mean venous pressure, mean leF ventricular (LV) volume, peak 1 st deriva)ve of aor)c pressure) SBV LV Vena cava E lv (t) E ao R i R o R c E vc Aorta ThreeAchamber CVS model: Experimental reference datasets y ref –y (p) y ref ^ Residual vector: r i = Objec)ve: minimise || r || 1 =∑ |r i | For in silico reference data: error w.r.t. the true parameters e j = i i i 7 i =1 p ref –p j p ref j j p =(E lv E ao E vc R i R o SBV) • P and TRR work on r; the others work on || r || 1 . • P, S and DS are deriva)ve free; the others are gradientAbased. In silico reference datasets Final |e j | < 0.05 V j Minimum || r || 1 Minimum || r || 1 A B C D A B C D E F G H Propor)onal (P) N Y N N 0.08 0.04 0.05 0.82 0.04 0.29 2.05 0.03 TrustAregion reflec)ve (TRR) Y Y N Y 0.00 0.00 0.40 0.00 0.02 0.23 1.65 0.00 Interior point (IP) N Y N N 0.08 0.00 0.14 0.10 0.14 0.65 1.48 0.00 Ac)ve set (AS) Y Y N N 0.00 0.00 1.59 0.12 0.02 0.19 1.44 0.00 Simplex (S) N N N N 0.32 0.09 0.57 0.39 0.42 0.64 2.51 0.00 Direct search (DS) N Y N N 0.80 0.05 0.32 1.24 0.69 1.44 2.67 0.75 Sequen)al quadra)c programming (SQP) Y Y N N 0.00 0.00 0.57 0.22 0.02 0.19 1.45 0.00 Results Acknowledgments • The best methods are the TRR, SQP and AS. AS and SQP are based on similar principles. • These best methods are all gradientAbased, indica)ng that the residual r is smooth. • The P method, designed for iden)fica)on of CVS models by Hann et al. (2010), is the second fastest. • Parameter iden)fica)on in this lumped CVS model can be performed in 2 to 3 minutes. Conclusions 0 2 4 6 8 10 5 25 125 625 Propor-onal TRR Interior point Ac-ve set Simplex Direct search SQP Func)on evalua)ons (log scale) Total error on the parameters 0 100 200 300 400 500 600 700 800 P TRR IP AS S DS SQP Number of func)on evalua)ons 0 200 400 600 800 1000 1200 1400 1600 1800 2000 P TRR IP AS S DS SQP Number of func)on evalua)ons [email protected] [email protected] Contact • • •

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Page 1: Parameter Identification Methods in a Model of the … · 2015. 10. 8. · Title: Parameter Identification Methods in a Model of the Cardiovascular System Author: Pironet, A., Desaive,

A.#Pironet1,#T.#Desaive1,#P.#C.#Dauby1,#J.#G.#Chase2,#P.#D.#Docherty2#

PARAMETER#IDENTIFICATION#METHODS##IN#A#MODEL#OF#THE#CARDIOVASCULAR#SYSTEM#

Introduc)on*

Methods*

•  To*be*clinically*relevant,*the*parameters*p*of*a*model*have*to*be*iden)fied*from*pa)ent*data*y.*•  To* achieve* realA)me*monitoring,* it* is* important* to* select* the* best* parameter* iden)fica)on*method,* in* terms* of*

speed,*efficiency*and*reliability.*•  This*work*compares*seven*parameter*iden)fica)on*methods*applied*to*a*cardiovascular*system*(CVS)*model.*

#1University*of*Liège*(ULg),*GIGAACardiovascular*Sciences,*Liège,*Belgium*

2Department*of*Mechanical*Engineering,*University*of*Canterbury,*New*Zealand*

The*seven*methods*are*tested*using*in*silico*and*animal*experimental*reference*data.*Output*vector*(available*in*the*ICU):*y*=*(Aor)c*pulse*pressure,*********venous*pulse*pressure,********stroke*volume,********mean*aor)c*pressure,********mean*venous*pressure,********mean*leF*ventricular*(LV)*volume,********peak*1st*deriva)ve*of*aor)c*pressure)*

SBV*LV*

Vena*cava*

Elv(t)*

Eao*

Ri*

Ro*

Rc*

Evc*

Aorta*

ThreeAchamber*CVS*model:*

Experimental*reference*datasets*

yref*–*y*(p)*yref*^*

Residual*vector:*ri*=**Objec)ve:*minimise*|| r"||1*=*∑**|ri|**For*in*silico*reference*data:*error***w.r.t.*the*true*parameters*ej*=*

i*i*

i*=*1*

pref*–*pj*pref*

j*p*=*(Elv*Eao*Evc*Ri*Ro*SBV)*

•  P*and*TRR*work*on*r;*the*others*work*on*|| r"||1.*

•  P,*S*and*DS*are*deriva)ve**free;*the*others*are*gradientAbased.*

In*silico*reference*datasets*Final*|ej|*<*0.05*V*j*** Minimum || r*||1* Minimum || r*||1*A* B* C* D* A* B* C* D* E* F* G* H*

Propor)onal*(P)* N* Y* N* N* 0.08* 0.04* 0.05* 0.82* 0.04* 0.29* 2.05* 0.03*TrustAregion*reflec)ve*(TRR)* Y* Y* N* Y* 0.00* 0.00* 0.40* 0.00* 0.02* 0.23* 1.65* 0.00*Interior*point*(IP)* N* Y* N* N* 0.08* 0.00* 0.14* 0.10* 0.14* 0.65* 1.48* 0.00*Ac)ve*set*(AS)* Y* Y* N* N* 0.00* 0.00* 1.59* 0.12* 0.02* 0.19* 1.44* 0.00*Simplex*(S)* N* N* N* N* 0.32* 0.09* 0.57* 0.39* 0.42* 0.64* 2.51* 0.00*Direct*search*(DS)* N* Y* N* N* 0.80* 0.05* 0.32* 1.24* 0.69* 1.44* 2.67* 0.75*Sequen)al*quadra)c*programming*(SQP)*

Y* Y* N* N* 0.00* 0.00* 0.57* 0.22* 0.02* 0.19* 1.45* 0.00*

Results*

Acknowledgments*•  The*best*methods*are*the*TRR,*SQP*and*AS.*

AS*and*SQP*are*based*on*similar*principles.*•  These*best*methods*are*all*gradientAbased,*

indica)ng*that*the*residual*r*is*smooth.**•  The* P* method,* designed* for* iden)fica)on*

of*CVS*models*by*Hann*et*al.*(2010),*is*the*second*fastest.*

•  Parameter*iden)fica)on*in*this*lumped*CVS*model*can*be*performed*in*2*to*3*minutes.*

Conclusions*

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5" 25" 125" 625"

Propor-onal"

TRR"