Model Mathematics

I_Na_s = g_Na_s h (V_s - V_Na) {m_infinity}^{3} I_K_DR_s = g_K_DR_s (V_s - V_K) n^{2} I_Ca_T = g_Ca_T h_T (V_s - V_Ca) {m_T}^{2} I_K_Ca = \frac{g_K_Ca {Ca}^{4}}{{Ca}^{4} + {K_Ca}^{4}} (V_s - V_K) I_A = g_A b (V_s - V_K) a^{4} I_h = g_h m_h (V_s - V_h) \frac{d}{d time} (V_s) = \frac{1000.0 (I_APP - (I_Na_s + I_Ca_T + I_K_DR_s + I_K_Ca + I_A + I_h + \frac{g_c}{p} (V_s - V_D)))}{C_m} \frac{d}{d time} (Ca) = - (beta I_Ca_T + k_Ca Ca)

I_K_DR_D = g_K_DR_D (V_D - V_K) n^{2} phi_Na = \frac{{Na}^{3}}{{Na}^{3} + {K_p}^{3}} phi_Na_eq = \frac{{Na_eq}^{3}}{{Na_eq}^{3} + {K_p}^{3}} I_pump = R_pump (phi_Na - phi_Na_eq) I_L = g_L (V_D - V_L) I_NMDA = \frac{g_NMDA}{1 + \frac{Mg_o}{K_Mg} ⅇ^{\frac{- V_D}{q}}} (V_D - V_NMDA) I_Na_NMDA = \frac{g_Na_NMDA}{1 + \frac{Mg_o}{K_Mg} ⅇ^{\frac{- V_D}{q}}} (V_D - V_Na) I_D = I_NMDA + I_pump + I_L I_Ca_L = g_Ca_L (V_D - V_Ca) {m_L}^{2} \frac{d}{d time} (V_D) = \frac{- (1000.0 (I_Ca_L + I_K_DR_D + I_NMDA + I_pump + I_L + \frac{g_c}{1 - p} (V_D - V_s)))}{C_m} \frac{d}{d time} (Na) = alpha (- I_Na_NMDA - (I_pump 3))

m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V_s + 35)}{6.2}}} n_infinity = \frac{1}{1 + ⅇ^{\frac{- (V_s + 31)}{5.3}}} h_infinity = \frac{1}{1 + ⅇ^{\frac{V_s + 30}{8.3}}} m_T_infinity = \frac{1}{1 + ⅇ^{\frac{- (V_s + 55)}{7}}} h_T_infinity = \frac{1}{1 + ⅇ^{\frac{V_s + 81}{11}}} a_infinity = \frac{1}{1 + ⅇ^{\frac{- (V_s + 60)}{10}}} b_infinity = \frac{1}{1 + ⅇ^{\frac{V_s + 70}{5.7}}} m_h_infinity = \frac{1}{1 + ⅇ^{\frac{V_s + 80}{8}}} m_L_infinity = \frac{1}{1 + ⅇ^{\frac{- (V_D + 20)}{5.3}}} tau_h = 0.4 (1 + \frac{2}{1 + ⅇ^{\frac{V_s + 25}{5}}}) tau_n = \frac{0.8 (1 + \frac{2}{1 + ⅇ^{\frac{V_s + 25}{10}}})}{1 + ⅇ^{\frac{- (V_s + 70)}{10}}} tau_m_L = \frac{0.4}{5 ⅇ^{\frac{- (V_D + 11)}{8.3}} + \frac{\frac{- (V_D + 11)}{8.3}}{ⅇ^{\frac{- (V_D + 11)}{8.3}} - 1}} tau_m_T = 1 tau_h_T = 10 tau_a = 0.5 tau_b = 10 tau_m_h = 190 \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} \frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} \frac{d}{d time} (m_T) = \frac{m_T_infinity - m_T}{tau_m_T} \frac{d}{d time} (m_L) = \frac{m_L_infinity - m_L}{tau_m_L} \frac{d}{d time} (m_h) = \frac{m_h_infinity - m_h}{tau_m_h} \frac{d}{d time} (a) = \frac{a_infinity - a}{tau_a} \frac{d}{d time} (b) = \frac{b_infinity - b}{tau_b} \frac{d}{d time} (h_T) = \frac{h_T_infinity - h_T}{tau_h_T}