Model Mathematics

\frac{d}{d time} (V) = \frac{- (i_Na + i_K + i_Leak)}{Cm}

g_Na = m^{3} h g_Na_max i_Na = (g_Na + 140) (V - E_Na)

alpha_m = \frac{100 (- V - 48)}{ⅇ^{\frac{- V - 48}{15}} - 1} beta_m = \frac{120 (V + 8)}{ⅇ^{\frac{V + 8}{5}} - 1} \frac{d}{d time} (m) = alpha_m (1 - m) - (beta_m m)

alpha_h = 170 ⅇ^{\frac{- V - 90}{20}} beta_h = \frac{1000}{1 + ⅇ^{\frac{- V - 42}{10}}} \frac{d}{d time} (h) = alpha_h (1 - h) - (beta_h h)

i_K = (g_K1 + g_K2) (V + 100) g_K1 = 1200 ⅇ^{\frac{- V - 90}{50}} + 15 ⅇ^{\frac{V + 90}{60}} g_K2 = 1200 n^{4}

alpha_n = \frac{0.1 (- V - 50)}{ⅇ^{\frac{- V - 50}{10}} - 1} beta_n = 2 ⅇ^{\frac{- V - 90}{80}} \frac{d}{d time} (n) = alpha_n (1 - n) - (beta_n n)

i_Leak = g_L (V - E_L)