Model Mathematics

\frac{d}{d time} (V) = \frac{(- (i_Na + i_NaP + i_K + i_leak + i_T + i_N + i_P + i_SK + i_A + i_H)) + i_app}{C}

i_Na = g_Na m^{3} h (V - E_Na)

tau_h = \frac{3.5}{ⅇ^{\frac{V + theta_1}{sigma_1}} + ⅇ^{\frac{- (V + theta_1)}{sigma_2}}} + 1 h_infinity = \frac{1}{1 + ⅇ^{\frac{V + theta_h}{sigma_h}}} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

m_infinity = \frac{1}{1 + ⅇ^{\frac{V + theta_m}{- sigma_m}}} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

i_NaP = g_NaP m h (V - E_Na)

h_infinity = \frac{1}{1 + ⅇ^{\frac{V + theta_h}{sigma_h}}} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + theta_m)}{sigma_m}}} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

i_K = g_K n^{4} (V - E_K)

tau_n = \frac{2.5}{ⅇ^{\frac{V + theta_1}{sigma_1}} + ⅇ^{\frac{- (V + theta_1)}{sigma_2}}} + 0.01 n_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + theta_n)}{sigma_n}}} \frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n}

i_leak = g_leak (V - E_leak)

i_T = g_T m h (V - E_Ca)

tau_m = \frac{5}{ⅇ^{\frac{V + theta_1}{sigma_1}} + ⅇ^{\frac{- (V + theta_1)}{sigma_2}}} + 2 m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + theta_m)}{sigma_m}}} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

tau_h = \frac{20}{ⅇ^{\frac{V + theta_1}{sigma_1}} + ⅇ^{\frac{- (V + theta_1)}{sigma_1}}} + 1 h_infinity = \frac{1}{1 + ⅇ^{\frac{V + theta_h}{sigma_h}}} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

i_N = g_N m h (V - E_Ca)

m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + theta_m)}{sigma_m}}} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

h_infinity = \frac{1}{1 + ⅇ^{\frac{V + theta_h}{sigma_h}}} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

i_P = g_P m (V - E_Ca)

m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + theta_m)}{sigma_m}}} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

i_SK = g_SK z^{2} (V - E_K)

\frac{d}{d time} (Ca_conc) = \frac{1}{1000} K1 (i_T + i_N + i_P) - (K2 Ca_conc) z_infinity = \frac{1}{1 + {(\frac{0.003}{Ca_conc})}^{2}} \frac{d}{d time} (z) = \frac{z_infinity - z}{tau_z}

i_A = g_A m h (V - E_K)

tau_m = \frac{1}{ⅇ^{\frac{V + theta_1}{sigma_1}} + ⅇ^{\frac{- (V + theta_2)}{sigma_2}}} + 0.37 m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + theta_m)}{sigma_m}}} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

h_infinity = \frac{1}{1 + ⅇ^{\frac{V + theta_h}{sigma_h}}} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

i_H = g_H m (V - E_H)

tau_m = \frac{1}{ⅇ^{\frac{V + theta_1}{sigma_1}} + ⅇ^{\frac{- (V + theta_1)}{sigma_1}}} + 50 m_infinity = \frac{1}{1 + ⅇ^{\frac{V + theta_m}{sigma_m}}} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

i_app = \{\begin{matrix} i_stimAmplitude if time \geq i_stimStart \land time ≦ i_stimEnd \\ 0 otherwise \end{matrix}