Model Mathematics

\frac{d}{d t} (q_K_i) = - v_Kr \frac{d}{d t} (q_K_o) = v_Kr \frac{d}{d t} (q_mem) = I_mem_Kr + I_stim

tPeriod = t - (⌊ \frac{t}{stimPeriod} ⌋ stimPeriod) I_stim = \{\begin{matrix} \frac{0 0.075 C_m}{stimDuration} if tPeriod \geq 0.3 \land tPeriod ≦ 0.3 + stimDuration \\ 0.0 otherwise \end{matrix}

i_Kr = \frac{1 e -9 F}{C_m} v_Kr q_mem = Vmem C_m

Am_Kr = zK F V_mem u_K_i = R T \ln (K_K_i q_K_i) u_K_o = R T \ln (K_K_o q_K_o) Af_Kr = mu_Sd + u_K_i + Am_Kr Ar_Kr = mu_Sd + u_K_o v_Kr = \{\begin{matrix} 1 kappa_Kr (ⅇ^{\frac{Af_Kr}{R T}} - (ⅇ^{\frac{Ar_Kr}{R T}})) if Am_Kr = 0 \\ \frac{\frac{1 kappa_Kr Am_Kr}{R T}}{ⅇ^{\frac{Am_Kr}{R T}} - 1} (ⅇ^{\frac{Af_Kr}{R T}} - (ⅇ^{\frac{Ar_Kr}{R T}})) otherwise \end{matrix} V_mem = \frac{q_mem}{C_m} I_mem_Kr = F ((- zK) v_Kr + v_x10 (z_xr1_r - z_xr1_f) + v_x11 (z_xr1_r - z_xr1_r) + v_x20 (z_xr2_r - z_xr2_f) + v_x21 (z_xr2_r - z_xr2_f))

Af_x10 = mu_Sa + z_xr1_f F V_mem Ar_x10 = mu_Sb + z_xr1_r F V_mem Af_x11 = mu_Sc + z_xr1_f F V_mem Ar_x11 = mu_Sd + z_xr1_r F V_mem Af_x20 = mu_Sa + z_xr2_f F V_mem Ar_x20 = mu_Sc + z_xr2_r F V_mem Af_x21 = mu_Sb + z_xr2_f F V_mem Ar_x21 = mu_Sd + z_xr2_r F V_mem v_x10 = kappa_xr10 (ⅇ^{\frac{Af_x10}{R T}} - (ⅇ^{\frac{Ar_x10}{R T}})) v_x11 = kappa_xr11 (ⅇ^{\frac{Af_x11}{R T}} - (ⅇ^{\frac{Ar_x11}{R T}})) v_x20 = kappa_xr20 (ⅇ^{\frac{Af_x20}{R T}} - (ⅇ^{\frac{Ar_x20}{R T}})) v_x21 = kappa_xr21 (ⅇ^{\frac{Af_x21}{R T}} - (ⅇ^{\frac{Ar_x21}{R T}})) v_Sa = - v_x10 - v_x20 v_Sb = v_x10 - v_x21 v_Sc = v_x20 - v_x11 v_Sd = v_x11 + v_x21 mu_Sa = R T \ln (K_Sa_Kr q_Sa) mu_Sb = R T \ln (K_Sb_Kr q_Sb) mu_Sc = R T \ln (K_Sc_Kr q_Sc) mu_Sd = R T \ln (K_Sd_Kr q_Sd) \frac{d}{d t} (q_Sa) = v_Sa \frac{d}{d t} (q_Sb) = v_Sb \frac{d}{d t} (q_Sc) = v_Sc \frac{d}{d t} (q_Sd) = v_Sd