Model Mathematics

k_fca = \{\begin{matrix} 0 if x_fca_inf_inact > X_fca_inact \land v > - 60 \\ 1 otherwise \end{matrix}

\frac{d}{d t} (v) = 0 \frac{d}{d t} (ca_SR) = 0 \frac{d}{d t} (ca_i) = 0 \frac{d}{d t} (X_ca_act) = \frac{x_ca_inf_act - X_ca_act}{tau_ca_act} \frac{d}{d t} (X_ca_inact) = \frac{x_ca_inf_inact - X_ca_inact}{tau_ca_inact} \frac{d}{d t} (X_fca_inact) = \frac{k_fca (x_fca_inf_inact - X_fca_inact)}{tau_fca} p_CaL = d_0 p_CaL_shannonTot = p_CaL_shannonCa + p_CaL_shannonNa + p_CaL_shannonK p_CaL_shannonCap = \frac{p_CaL_shannonCa}{p_CaL_shannonTot} p_CaL_shannonNap = \frac{p_CaL_shannonNa}{p_CaL_shannonTot} p_CaL_shannonKp = \frac{p_CaL_shannonK}{p_CaL_shannonTot} p_CaL_Ca = p_CaL_shannonCap p_CaL p_CaL_Na = p_CaL_shannonNap p_CaL p_CaL_K = p_CaL_shannonKp p_CaL ibarca = \frac{\frac{p_CaL_Ca 4.0 v F^{2}}{R T} (0.341 ca_i ⅇ^{\frac{2.0 v F}{R T}} - (0.341 Cao))}{ⅇ^{\frac{2.0 v F}{R T}} - 1.0} i_CaL_Ca = ibarca X_ca_act X_ca_inact X_fca_inact ibarna = \frac{\frac{p_CaL_Na v F^{2}}{R T} (0.75 Na_i ⅇ^{\frac{2.0 v F}{R T}} - (0.75 Nao))}{ⅇ^{\frac{2.0 v F}{R T}} - 1.0} i_CaL_Na = ibarna X_ca_act X_ca_inact X_fca_inact ibark = \frac{\frac{p_CaL_K v F^{2}}{R T} (0.75 Ki ⅇ^{\frac{2.0 v F}{R T}} - (0.75 Ko))}{ⅇ^{\frac{2.0 v F}{R T}} - 1.0} i_CaL_K = ibark X_ca_act X_ca_inact X_fca_inact i_CaL = i_CaL_Ca + i_CaL_Na + i_CaL_K

V_tot_tenT = Vc_tenT + VSR_tenT Vc = \frac{V_tot Vc_tenT}{V_tot_tenT} V_SR = \frac{V_tot VSR_tenT}{V_tot_tenT}

d_3 = d_5 d_1 f_3 = f_5 f_1 d_4 = \frac{1}{\frac{1}{d_2} + \frac{1}{d_6}} f_4 = \frac{1}{\frac{1}{f_2} + \frac{1}{f_6}} alpha_act = d_1 ⅇ^{\frac{v}{d_2}} beta_act = d_3 ⅇ^{\frac{v}{d_4}} x_ca_inf_act = \frac{alpha_act}{alpha_act + beta_act} tau_ca_act = \frac{1}{alpha_act + beta_act} + tau_d_const alpha_inact = f_1 ⅇ^{\frac{v}{f_2}} beta_inact = f_3 ⅇ^{\frac{v}{f_4}} x_ca_inf_inact = \frac{alpha_inact}{alpha_inact + beta_inact} tau_ca_inact = \frac{1}{alpha_inact + beta_inact} + tau_f_const scale_Ical_Fca_Cadep = 1.2 alpha_fCa = \frac{1.0}{1.0 + {(\frac{scale_Ical_Fca_Cadep ca_i}{.000325})}^{8}} beta_fCa = \frac{0.1}{1.0 + ⅇ^{\frac{scale_Ical_Fca_Cadep ca_i - .0005}{0.0001}}} gamma_fCa = \frac{0.2}{1.0 + ⅇ^{\frac{scale_Ical_Fca_Cadep ca_i - 0.00075}{0.0008}}} x_fca_inf_inact = \frac{alpha_fCa + beta_fCa + gamma_fCa + 0.23}{1.46}