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Component: environment

Component: heart_parameters

Component: driver_function

tau = time mod period e_t = A ⅇ^{(- B) {(\frac{tau HR}{60} - C)}^{2}}

Component: pericardium

V_pcd = V_lv + V_rv P_pcd = P_0_pcd (ⅇ^{lambda_pcd (V_pcd - V_0_pcd)} - 1) P_peri = P_pcd + P_pl

Component: left_ventricle

V_lvf = V_lv - V_spt P_lvf = e_t P_es_lvf + (1 - e_t) P_ed_lvf P_lv = P_lvf + P_peri \frac{d}{d time} (V_lv) = \{\begin{matrix} 0 if P_pu - P_lv < 0 \land P_lv - P_ao < 0 \\ \frac{- (P_lv - P_ao)}{R_av} if P_pu - P_lv < 0 \\ \frac{P_pu - P_lv}{R_mt} if P_lv - P_ao < 0 \\ \frac{P_pu - P_lv}{R_mt} - (\frac{P_lv - P_ao}{R_av}) otherwise \end{matrix}

Component: lvf_calculator

P_es_lvf = E_es_lvf (V_lvf - V_d_lvf) P_ed_lvf = P_0_lvf (ⅇ^{lambda_lvf (V_lvf - V_0_lvf)} - 1)

Component: right_ventricle

V_rvf = V_rv + V_spt P_rvf = e_t P_es_rvf + (1 - e_t) P_ed_rvf P_rv = P_rvf + P_peri \frac{d}{d time} (V_rv) = \{\begin{matrix} 0 if P_vc - P_rv < 0 \land P_rv - P_pa < 0 \\ \frac{- (P_rv - P_pa)}{R_pv} if P_vc - P_rv < 0 \\ \frac{P_vc - P_rv}{R_tc} if P_rv - P_pa < 0 \\ \frac{P_vc - P_rv}{R_tc} - (\frac{P_rv - P_pa}{R_pv}) otherwise \end{matrix}

Component: rvf_calculator

P_es_rvf = E_es_rvf (V_rvf - V_d_rvf) P_ed_rvf = P_0_rvf (ⅇ^{lambda_rvf (V_rvf - V_0_rvf)} - 1)

Component: septum

P_sept = P_lv - P_rv P_lvf = e_t E_es_spt (V_spt - V_d_spt) + (one - e_t) P_0_spt (ⅇ^{lambda_spt (V_spt - V_0_spt)} - one) - P_rvf

Component: pulmonary_artery

P_pa = E_es_pa (V_pa - V_d_pa) \frac{d}{d time} (V_pa) = \{\begin{matrix} 0 if P_rv - P_pa < 0 \land P_pa - P_pu < 0 \\ \frac{- (P_pa - P_pu)}{R_pul} if P_rv - P_pa < 0 \\ \frac{P_rv - P_pa}{R_pv} if P_pa - P_pu < 0 \\ \frac{P_rv - P_pa}{R_pv} - (\frac{P_pa - P_pu}{R_pul}) otherwise \end{matrix}

Component: pulmonary_vein

P_pu = E_es_pu (V_pu - V_d_pu) \frac{d}{d time} (V_pu) = \{\begin{matrix} 0 if P_pa - P_pu < 0 \land P_pu - P_lv < 0 \\ \frac{- (P_pu - P_lv)}{R_mt} if P_pa - P_pu < 0 \\ \frac{P_pa - P_pu}{R_pul} if P_pu - P_lv < 0 \\ \frac{P_pa - P_pu}{R_pul} - (\frac{P_pu - P_lv}{R_mt}) otherwise \end{matrix}

Component: aorta

P_ao = E_es_ao (V_ao - V_d_ao) \frac{d}{d time} (V_ao) = \{\begin{matrix} 0 if P_lv - P_ao < 0 \land P_ao - P_vc < 0 \\ \frac{- (P_ao - P_vc)}{R_sys} if P_lv - P_ao < 0 \\ \frac{P_lv - P_ao}{R_av} if P_ao - P_vc < 0 \\ \frac{P_lv - P_ao}{R_av} - (\frac{P_ao - P_vc}{R_sys}) otherwise \end{matrix}

Component: vena_cava

P_vc = E_es_vc (V_vc - V_d_vc) \frac{d}{d time} (V_vc) = \{\begin{matrix} 0 if P_ao - P_vc < 0 \land P_vc - P_rv < 0 \\ \frac{- (P_vc - P_rv)}{R_tc} if P_ao - P_vc < 0 \\ \frac{P_ao - P_vc}{R_sys} if P_vc - P_rv < 0 \\ \frac{P_ao - P_vc}{R_sys} - (\frac{P_vc - P_rv}{R_tc}) otherwise \end{matrix}

Source: Derived from workspace Shaw, Chase, Starfinger, Smith, Hann, Desaive, Ghuysen, 2007 at changeset 34beaab48984.

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Modeling the Cardiovascular System