Direct parameter identification in a model of the cardiovascular system

(1)

A. Pironet

1

_{,
P.C.
Dauby}

1

_{,
T.
Desaive}

1

_{University
of
Liège
(ULg),
GIGA-‐Cardiovascular
Sciences,
Liège,
Belgium}

DIRECT PARAMETER IDENTIFICATION

IN A MODEL OF THE CARDIOVASCULAR SYSTEM

IntroducAon

Methods

•  Parameter idenAﬁcaAon is crucial if models are to be used to track an individual paAent’s condiAon.

•  In cardiovascular system modeling, model-‐dependent iden,ﬁca,on methods can ﬁnd the best set of parameters, whereas in general nonlinear regression methods cannot*.

•  In this work, a model-‐dependent method is developed which allows compuAng model parameters without requiring any model simulaAon.

P_pu Plv, Vlv LV E_lv R_mt P_ao, V_ao Aorta E_ao R_av P_vc R_sys Model outputs:

•  leO ventricle pressure P_lv(t), •  aorAc pressure P_ao(t), •  stroke volume SV,

Lumped model of the leK ventricle (LV) and systemic circulaNon* Model inputs: LV driver funcAon e(t), heart rate HR

EquaNons for direct parameter computaNon:

•  opening Ame of the mitral valve t_MVO, •  closing Ame of the mitral valve t_MVC, •  opening Ame of the aorAc valve t_AVO, •  closing Ame of the aorAc valve t_AVC.

Results

•  The equaAons permit us to directly and exactly retrieve model parameters without any model simulaAon. •  This work proves that the model is structurally globally idenNﬁable from the selected model outputs. •  Finding bounds on the equaAons provides physiological limits on the parameter values.

Reference

*Hann, C. E. et al. Unique parameter idenAﬁcaAon for cardiac diagnosis in criAcal care using minimal data sets.

Comput Methods Programs Biomed,

99(1), 75-‐87, 2010. •  This method is not clinically applicable as it relies on ventricular

pressure, which is not available in a clinical se]ng.

•  This invasive measurement can easily be replaced by the result of model simulaAons, implying iteraAons of the method*.

This work was ﬁnancially supported by the FederaAon Wallonia-‐ Brussels (AcAons de Recherches Concertées).

Conclusion

Acknowledgments

[email protected]

Contact

Pulmonary

vein Mitral valve AorAc valve resistance Systemic Vena cava Ppu=Plv(tMVO) =Plv(tMVC) Rmt= RtMVC tMVOPpu Plv(t)dt SV Rav= RtAVC tAVOPlv(t) Pao(t)dt SV Rsys= ¯ Pao Pvc HR·SV Eao= Rsys tAVO tAVCln ✓ Pmaxao Pvc Pmin ao Pvc ◆ Elv= 1 SV ✓ Pao(tAVO) e(tAVO) Pao(tAVC) e(tAVC) ◆ 1