Structural identifiability analysis of a cardiovascular system model

Structural(iden-fiability(analysis(

of(a(cardiovascular(system(model(

A.#Pironet,(P.C.(Dauby,(J.G.(Chase,(

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_{To(be(clinically(relevant,(mathema-cal(models(}

have(to(be(made(pa-ent.specific.(

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have(to(be(made(pa-ent.specific.(

• 

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to#iden-fy#all#model#parameters?#

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_{Structural(iden-fiability(analysis.(}

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have(to(be(made(pa-ent.specific.(

• 

_{Can#we#find#a#measurement#set#which#allows#}

to#iden-fy#all#model#parameters?#

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_{Structural(iden-fiability(analysis.(}

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During(the(whole(cardiac(cycle(

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V_lv(=(Q_mt(–(Q_av( V_ao(=(Q_av(–(Q_sys( V_vc(=(Q_sys(–(Q_tc( V_rv(=(Q_tc(–(Q_pv( V_pa(=(Q_pv(–(Q_pul( V_pu(=(Q_pul(–(Q_mt( SBV(=(V_lv(+(V_ao(+(V_vc(+(V_rv(+(V_pa(+(V_pu( SV(=(∫((Q(dt( ( Q_mt(=(₍r(Ppu_R(–(Plv)( mt( Q_av(=(₍r(Plv_R(–(Pao)( av( Q_sys(=(₍Pao_R(–(Pvc( sys( Q_tc(=(₍r(Pvc_R(–(Prv)( tc( Q_pv(=(₍r(Prv_R(–(Ppa)( pv( Q_pul(=(₍Ppa_R(–(Ppu( pul( .( .( .( .( .( .( T( 0(

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During(the(whole(cardiac(cycle(

V_lv(=(Q_mt(–(Q_av( V_ao(=(Q_av(–(Q_sys( V_vc(=(Q_sys(–(Q_tc( V_rv(=(Q_tc(–(Q_pv( V_pa(=(Q_pv(–(Q_pul( V_pu(=(Q_pul(–(Q_mt( SBV(=(V_lv(+(V_ao(+(V_vc(+(V_rv(+(V_pa(+(V_pu( SV(=(∫((Q(dt( ( P_pu(=(E_pu((V_pu( P_lv(=(E_lv((e_lv((V_lv( P_ao(=(E_ao((V_ao( P_vc(=(E_vc((V_vc( P_rv(=(E_rv((e_rv((V_rv( P_pa(=(E_pa((V_pa( Q_mt(=(₍r(Ppu_R(–(Plv)( mt( Q_av(=(₍r(Plv_R(–(Pao)( av( Q_sys(=(₍Pao_R(–(Pvc( sys( Q_tc(=(₍r(Pvc_R(–(Prv)( tc( Q_pv(=(₍r(Prv_R(–(Ppa)( pv( Q_pul(=(₍Ppa_R(–(Ppu( pul( .( .( .( .( .( .( .( .( .( .( .( .( .( .( T( 0(

During(the(whole(cardiac(cycle(

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