Model Mathematics

i_Stim = \{\begin{matrix} 20 if time \geq 10 \land time ≦ 10.5 \\ 0 otherwise \end{matrix} \frac{d}{d time} (V) = \frac{- ((- i_Stim) + i_Na + i_K + i_L)}{Cm}

E_Na = E_R + 115 i_Na = g_Na m^{3} h (V - E_Na)

alpha_m = \frac{(- 0.1) (V + 50)}{ⅇ^{\frac{- (V + 50)}{10}} - 1} beta_m = 4 ⅇ^{\frac{- (V + 75)}{18}} \frac{d}{d time} (m) = alpha_m (1 - m) - (beta_m m)

alpha_h = 0.07 ⅇ^{\frac{- (V + 75)}{20}} beta_h = \frac{1}{ⅇ^{\frac{- (V + 45)}{10}} + 1} \frac{d}{d time} (h) = alpha_h (1 - h) - (beta_h h)

E_K = E_R - 12 i_K = g_K n^{4} (V - E_K)

alpha_n = \frac{(- 0.01) (V + 65)}{ⅇ^{\frac{- (V + 65)}{10}} - 1} beta_n = 0.125 ⅇ^{\frac{V + 75}{80}} \frac{d}{d time} (n) = alpha_n (1 - n) - (beta_n n)

E_L = E_R + 10.613 i_L = g_L (V - E_L)