Model Mathematics

\frac{d}{d time} (V) = (g_I {sI}^{3.0} yI + g_T xT) (V_I - V) + (g_K {xK}^{4.0} + g_P c {(Kp + c)}^{-1}) (V_K - V) + g_L (V_L - V)

g_I = 1 \frac{V_H_Na - V_H_K}{V_I - V_K}

g_T = 1 \frac{V_H_Na V_K - (V_I V_H_K)}{V_I - V_K}

Vs = 1 g_I V + 1 g_T

alpha_m = \frac{0.1 (50.0 - Vs)}{- (ⅇ^{\frac{50.0 - Vs}{10.0}})} beta_m = 4.0 ⅇ^{\frac{25.0 - Vs}{18.0}} sI = \frac{alpha_m}{alpha_m + beta_m}

alpha_h = 0.07 ⅇ^{\frac{25.0 - Vs}{20.0}} beta_h = \frac{1.0}{ⅇ^{\frac{55.0 - Vs}{10.0}} + 1.0} \frac{d}{d time} (yI) = \frac{ZI - yI}{tau_yI} ZI = \frac{alpha_h}{alpha_h + beta_h} tau_yI = \frac{12.5}{alpha_h + beta_h}

\frac{d}{d time} (xT) = \frac{sT - xT}{tau_xT} sT = \frac{1.0}{ⅇ^{0.15 (-50.0 - Vs)} + 1.0}

\frac{d}{d time} (c) = rho (K_c xT (V_Ca - V) - c)

alpha_n = \frac{0.01 (55.0 - Vs)}{ⅇ^{\frac{55.0 - Vs}{10.0}} - 1.0} beta_n = 0.125 ⅇ^{\frac{45.0 - Vs}{80.0}} \frac{d}{d time} (xK) = \frac{sK - xK}{tau_xK} sK = \frac{alpha_n}{alpha_n + beta_n} tau_xK = \frac{12.5}{alpha_n + beta_n}