Model Mathematics

\frac{d}{d time} (V) = \frac{i_app - (i_Na + i_Ca_L + i_Ca_T + i_K_dr + i_M + i_ir + i_d)}{Cm}

i_Na = g_Na O (V - V_Na) O = A^{3}

\frac{d}{d time} (A) = alpha D + k1_A_- (beta A + k1 A)

\frac{d}{d time} (A_) = alpha a D_+ k1 A - (\frac{beta}{a} A_+ k1_A_)

\frac{d}{d time} (D) = beta A + k2_D_- (alpha D + k2 D)

\frac{d}{d time} (D_) = \frac{beta}{a} A_+ k2 D - (alpha a D_+ k2_D_)

alpha = \frac{10}{1 + ⅇ^{\frac{- (V + 6)}{10}}} beta = \frac{10}{1 + ⅇ^{\frac{V + 54.4}{4.6}}} a = \sqrt{\frac{k1 k2_}{k1_k2}}

i_Ca_L = g_Ca_L m^{2} (V - V_Ca)

\frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m} m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V - Vh)}{12}}} tau_m = \frac{5}{ⅇ^{\frac{V + 15}{25}} + ⅇ^{\frac{- (V + 15)}{25}}}

i_Ca_T = g_Ca_T m^{2} h (V - V_Ca)

\frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m} m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V - 56.1)}{10}}} tau_m = \frac{7}{ⅇ^{\frac{V + 50}{9}} + ⅇ^{\frac{- (V + 50)}{9}}} + 0.8

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1}{1 + ⅇ^{\frac{V + 86.4}{4.7}}}

i_K_dr = g_K_dr n^{4} h (V - V_K)

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + 25)}{15}}} tau_n = \frac{15}{ⅇ^{\frac{V + 30}{15}} + ⅇ^{\frac{- (V + 30)}{15}}} + 1

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{0.7}{1 + ⅇ^{\frac{- (V + 35)}{10}}} + 0.3

i_M = g_M n (V - V_K)

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + 37)}{4}}} tau_n = \frac{80}{ⅇ^{\frac{V + 30}{15}} + ⅇ^{\frac{- (V + 30)}{15}}}

i_ir = g_ir n_infinity (V - V_K)

n_infinity = \frac{0.8 1}{1 + ⅇ^{\frac{V + 80}{12}}} + 0.2

i_d = g_d (V - V_Ca)