Model Mathematics

\frac{d}{d time} (Vm) = - (\frac{I_iCa + I_iNa}{Cm}) I_iCa = I_Ca + I_NSCC_Ca + I_PM I_iNa = I_NSCC_Na + I_Na

ECa = \frac{R T}{2.0 F} \ln (\frac{CO}{CS1}) I_Ca = gCa (Vm - ECa)

gNSCC_Ca = gNSCC_Ca_\frac{{KNSCC}^{hNSCC}}{{KNSCC}^{hNSCC} + {CS1}^{hNSCC}} I_NSCC_Ca = gNSCC_Ca (Vm - ENSCC)

gNSCC_Na = gNSCC_Na_\frac{{KNSCC}^{hNSCC}}{{KNSCC}^{hNSCC} + {CS1}^{hNSCC}} I_NSCC_Na = gNSCC_Na (Vm - ENSCC)

I_PM = gPM \frac{{CS1}^{2.0}}{{KPM}^{2.0} + {CS1}^{2.0}}

I_Na = gNa \frac{{NS1}^{hNa}}{{KNa}^{hNa} + {NS1}^{hNa}}

JSERCA = \frac{VSERCA (CS1 - (A2 CER))}{1.0 + A4 CS1 + A5 CER + A6 CS1 CER}

JMCU = VMCU \frac{{CS2}^{2.0}}{{KMCU}^{2.0} + {CS2}^{2.0}} epsilon_INH epsilon_INH = \frac{{KINH}^{hINH}}{{KINH}^{hINH} + {CMT}^{hINH}}

JNCX = VNCX \frac{CMT}{CMT + KNCX}

JS1S2 = mu_S1S2 (CS2 - CS1)

\frac{d}{d time} (H) = phi3 (1.0 - H) - (\frac{P phi1 phi2}{P phi1 + phi_1} H) JIPR = kIPR {(\frac{P phi1 H}{P phi1 + phi_1})}^{4.0} (CER - CS2) phi1 = \frac{k1 R1 + r2 CS2}{R1 + CS2} phi_1 = \frac{(k_1 + r_2) R3}{R3 + CS2} phi2 = \frac{k2 R3 + r4 CS2}{R3 + CS2} \frac{d}{d time} (phi3) = alpha_phi3 - (beta_phi3 phi3) alpha_phi3 = g_alpha beta_phi3 = g_beta \frac{{CS2}^{h_beta}}{{K_beta}^{h_beta} + {CS2}^{h_beta}}

\frac{d}{d time} (CS1) = JS1S2 + lambda_MT_S1 JNCX - (\frac{delta_s}{2.0} I_iCa + lambda_ER_S1 JSERCA) lambda_MT_S1 = \frac{gamma_MT}{gamma_S1} lambda_ER_S1 = \frac{gamma_ER}{gamma_S1}

\frac{d}{d time} (CS2) = lambda_ER_S2 JIPR - (lambda_S1_S2 JS1S2 + lambda_MT_S2 JMCU) lambda_MT_S2 = \frac{gamma_MT}{gamma_S2} lambda_ER_S2 = \frac{gamma_ER}{gamma_S2} lambda_S1_S2 = \frac{gamma_S1}{gamma_S2}

\frac{d}{d time} (CER) = JSERCA - JIPR

\frac{d}{d time} (CMT) = fm (JMCU - JNCX) fm = \frac{1.0}{1.0 + \frac{Km Bm}{{(Km + CMT)}^{2.0}}}

\frac{d}{d time} (NS1) = (- (\frac{delta_s}{1.0})) I_iNa