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

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*

7*

i*=*1*

pref*–*pj*pref*

j*

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*

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*

97 28 P63 15 TRR

652 84 IP385 123 AS421 171 S374 128 DS400 177 SQP

82 19 P79 21 TRR

1101 736 IP424 105 AS874 345 S314 29 DS521 49 SQP

03

1003

2003

3003

4003

5003

6003

7003

8003

P3 TRR3 IP3 AS3 S3 DS3 SQP3

032003400360038003100031200314003160031800320003

P3 TRR3 IP3 AS3 S3 DS3 SQP3

Number*of*func)on*evalua)ons*

97 28 P63 15 TRR

652 84 IP385 123 AS421 171 S374 128 DS400 177 SQP

82 19 P79 21 TRR

1101 736 IP424 105 AS874 345 S314 29 DS521 49 SQP

03

1003

2003

3003

4003

5003

6003

7003

8003

P3 TRR3 IP3 AS3 S3 DS3 SQP3

032003400360038003

100031200314003160031800320003

P3 TRR3 IP3 AS3 S3 DS3 SQP3

Number*of*func)on*evalua)ons*

A.Pironet@ulg.ac.be*TDesaive@ulg.ac.be*

Contact*

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