Model Mathematics

\frac{d}{d time} (V) = \frac{- (i_sp + i_Na + i_K + i_l + i_Ca + i_SK + i_ex)}{Cm}

i_sp = G (V - E_rev) \frac{d}{d time} (G) = L \frac{1}{tau1} - (D \frac{1}{tau2})

i_Na = g_Na m^{3.0} h (V - E_Na)

alpha_m = \frac{0.109 (V + 38.0)}{1.0 - (ⅇ^{\frac{- (V + 38.0)}{5.0}})} beta_m = \frac{0.0744 (V + 38.0)}{ⅇ^{\frac{V + 38.0}{5.0}} - 1.0} \frac{d}{d time} (m) = alpha_m (1.0 - m) - (beta_m m)

alpha_h = 0.0192 ⅇ^{\frac{- (55.0 + V)}{15.0}} beta_h = \frac{2.48}{1.0 + ⅇ^{\frac{17.0 - V}{21.0}}} \frac{d}{d time} (h) = alpha_h (1.0 - h) - (beta_h h)

i_K = g_K n^{4.0} (V - E_K)

alpha_n = \frac{0.012 (V + 45.0)}{1.0 - (ⅇ^{\frac{- (45.0 + V)}{5.0}})} beta_n = 0.204 ⅇ^{\frac{- (V + 50.0)}{40.0}} \frac{d}{d time} (n) = alpha_n (1.0 - n) - (beta_n n)

i_l = g_l (V - E_l)

i_Ca = PCa m^{2.0} h ghk ghk = \frac{V {(2.0 F)}^{2.0}}{R T} \frac{Cao - (Ca0 ⅇ^{\frac{2.0 V F}{R T}})}{1.0 - (ⅇ^{\frac{2.0 V F}{R T}})}

alpha_m = \frac{5.0}{1.0 + ⅇ^{(-0.075) (V - 5.0)}} beta_m = \frac{0.05 (2.0 - V)}{1.0 - (ⅇ^{\frac{V - 2.0}{8.0}})} \frac{d}{d time} (m) = alpha_m (1.0 - m) - (beta_m m)

h = Ff ⅇ^{\frac{- time}{tau_f}} + Fm ⅇ^{\frac{- time}{tau_m}} + Fs ⅇ^{\frac{- time}{tau_s}} + Fr

i_SK = g_SK m^{2.0} (V - E_K)

m_infinity = \frac{Car}{1.0 + Car} tau_m = \frac{1.0}{beta_k (1.0 + Car)} Car = {(\frac{Ca0}{Cac})}^{n_SK} \frac{d}{d time} (m) = \frac{- (m - m_infinity)}{tau_m}

Cai = CaBu k2b - (Cai Bu k1b) Bu = CaBu k2b - (Cai Bu k1b) CaBu = Cai Bu k1b - (CaBu k2b) kfc = \frac{DCa Ai2}{delta_r vol_i} kbc = \frac{DCa Ai2}{delta_r vol_i}

i_ex = Vmax \frac{Ca0}{Kex + Ca0} - (Vmax \frac{Ca_rest}{Kex + Ca_rest})

k1f = a1 \frac{Ca0}{b1 + Ca0} k1b = a2 k2 = a3 {Ca0}^{3.0} B = A k1f - (B k1b + B k2) C = B k2 SR = k2 B

Dy = Dyi2 kbd - (Dy kfd) kfd = \frac{Ddy Ai2}{delta_r vol_i} kbd = \frac{Ddy Ai2}{delta_r vol_i} CaDy = Dy Cai k1d - (CaDy k2d) FDy = (1.0 - F0) FCaDy + F0

\frac{d}{d time} (Ca0) = kbc Ca1 + k2b CaBu + k2d CaDy - (\frac{(i_Ca + i_ex) A0}{2.0 F vol0} + kfc Ca0 + k1b Bu Ca0 + k1d Dy Ca0)

delta_r = \frac{diameter}{2.0 (Nc - 1.0)}