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*
[email protected]*[email protected]*
Contact*
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