Model Mathematics

\frac{d}{d time} (q_Ca_i) = (- v_R_TRPNCa) n_CaTRPN + v_Ca_stim \frac{d}{d time} (q_TRPN) = - v_R_TRPNCa \frac{d}{d time} (q_Ca_TRPN) = v_R_TRPNCa \frac{d}{d time} (q_B_XB) = - v_R_BU \frac{d}{d time} (q_U_XB) = (v_R_BU - v_R_UW) + v_R_SU \frac{d}{d time} (q_W_XB) = v_R_UW - v_R_WS \frac{d}{d time} (q_S_XB) = v_R_WS - v_R_SU

tPeriod = time - (⌊ \frac{time}{stimPeriod} ⌋ stimPeriod) v_Ca_stim = \{\begin{matrix} 1 80 if tPeriod \geq 0.3 \land tPeriod ≦ 0.3 + stimDuration \\ 0.0 otherwise \end{matrix}

dSL = \{\begin{matrix} 1 V_max if time < 0.06 \\ (- 1) V_max if time > 0.5 \land time < 0.56 \\ 0 V_max otherwise \end{matrix}

mu_TRPN = R T \ln (K_TRPN q_TRPN) mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) mu_Ca_TRPN = R T \ln (K_Ca_TRPN q_Ca_TRPN) mu_B_XB = R T \ln (K_B_XB q_B_XB) mu_U_XB = R T \ln (K_U_XB q_U_XB) mu_W_XB = R T \ln (K_W_XB q_W_XB) mu_S_XB = R T \ln (K_S_XB q_S_XB) v_R_TRPNCa = kappa_R_TRPNCa (ⅇ^{\frac{n_CaTRPN mu_Ca_i + mu_TRPN}{R T}} - (ⅇ^{\frac{mu_Ca_TRPN}{R T}})) v_R_BU = kappa_R_BU (ⅇ^{\frac{mu_B_XB + n_Tm mu_Ca_TRPN}{R T}} - (ⅇ^{\frac{mu_U_XB + n_Tm mu_Ca_TRPN}{R T}})) v_R_UW = kappa_R_UW (ⅇ^{\frac{mu_U_XB}{R T}} - (ⅇ^{\frac{mu_W_XB}{R T}})) v_R_WS = kappa_R_WS (ⅇ^{\frac{mu_W_XB}{R T}} - (ⅇ^{\frac{mu_S_XB}{R T}})) v_R_SU = kappa_R_SU (ⅇ^{\frac{mu_S_XB}{R T}} - (ⅇ^{\frac{mu_U_XB}{R T}}))

A_w = \frac{A_eff r_s}{(1 - r_s) r_w + r_s} A_s = A_w c_w = \frac{phi k_uw (1 - r_w)}{r_w} c_s = \frac{phi k_ws (1 - r_s) r_w}{r_s}

v_2 = dSL v_1 = nu_1 nu_2 = (- A_w) v_2 nu_3 = c_w G_w v_4 = nu_4 nu_5 = (- A_s) v_2 nu_6 = c_s G_s \frac{d}{d time} (G_w) = v_1 \frac{d}{d time} (SL) = v_2 \frac{d}{d time} (G_s) = v_4 nu_1 = - nu_2 - nu_3 nu_4 = - nu_5 - nu_6

F_T_S = \frac{T_ref}{SL_0 q_MS r_s} q_S_XB (G_s + SL_0) F_T_W = \frac{T_ref}{SL_0 q_MS r_s} q_W_XB G_w T_active = F_T_S + F_T_W

C_s = SL - SL_0 - C_d

eta = \{\begin{matrix} eta_l if C_s > 0 \\ eta_s otherwise \end{matrix} \frac{d}{d time} (C_d) = v_Cdd v_Cdd = \frac{k C_s}{eta} nu_k = \frac{k}{eta} C_d nu_f = \frac{k}{eta} (SL - SL_0) nu_d = (- nu_k) + nu_f

F_1 = alpha (ⅇ^{\frac{b SL}{SL_0}} - 1) F_d = \frac{alpha eta}{SL_0} v_Cdd T_passive = F_1 + F_d

T_total = T_active + T_passive