Model Mathematics

\frac{d}{d t} (q_Ca_i) = - v_CaB \frac{d}{d t} (q_Ca_o) = v_CaB \frac{d}{d t} (q_mem) = I_mem_CaB V_mem = \frac{q_mem}{C_m}

mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) mu_Ca_o = R T \ln (K_Ca_o q_Ca_o) Af_CaB = mu_Ca_i + zCa F V_mem Ar_CaB = mu_Ca_o Am_CaB = zCa F V_mem v_CaB = \{\begin{matrix} kappa_CaB (ⅇ^{\frac{Af_CaB}{R T}} - (ⅇ^{\frac{Ar_CaB}{R T}})) if Am_CaB = 0 \\ \frac{\frac{kappa_CaB Am_CaB}{R T}}{ⅇ^{\frac{Am_CaB}{R T}} - 1} (ⅇ^{\frac{Af_CaB}{R T}} - (ⅇ^{\frac{Ar_CaB}{R T}})) otherwise \end{matrix} I_mem_CaB = (- zCa) F v_CaB