Model Mathematics

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

Istim = \{\begin{matrix} IstimAmplitude if time \geq IstimStart \land time ≦ IstimEnd \land time - IstimStart - (⌊ \frac{time - IstimStart}{IstimPeriod} ⌋ IstimPeriod) ≦ IstimPulseDuration \\ 0 otherwise \end{matrix}

i_Na = 120.0 {x_infinity}^{3.0} (1.0 - n) (V - 120.0) x_infinity = \frac{alpha_x}{alpha_x + beta_x} alpha_x = \frac{0.2 (V + 40)}{1 - (ⅇ^{\frac{- (V + 40)}{10}})} beta_x = 8 ⅇ^{- (V + \frac{65}{18})}

i_K = 36.0 n^{4.0} (V + 77.0)

\frac{d}{d time} (n) = alpha_n (1.0 - n) - (beta_n n) alpha_n = \frac{0.02 (V + 55.0)}{1.0 - (ⅇ^{\frac{- (V + 55.0)}{10.0}})} beta_n = 0.25 ⅇ^{\frac{- (V + 65.0)}{80.0}}

i_leak = 0.3 (V + 54.0)

\frac{d}{d time} (R) = kr_plus Ca (1.0 - R) - (kr_minus R) T = T_R

Ca_open = \frac{sigma}{2.0 Dc r π} sigma = (-5.182) i_V i_V = g_Ca P \frac{2.0 F V}{R T} \frac{Ca_ex}{1.0 - (ⅇ^{\frac{2.0 F V}{R T}})} Ca = O Ca_open + 0.1

alpha = 0.45 ⅇ^{\frac{V}{22.0}} alpha_= \frac{alpha}{8.0} beta = 0.015 ⅇ^{\frac{- V}{14.0}} beta_= beta 8.0 \frac{d}{d time} (a) = ka_plus T (1.0 - a) - (ka_minus a) kG_plus = \frac{3.0 a}{680.0 + 320.0 a} T = t

\frac{d}{d time} (C1) = beta C2 + kG_minus C_G1 - (C1 (4 alpha + kG_plus))

\frac{d}{d time} (C2) = 4 alpha C1 + 2 beta C3 + kG2_minus C_G2 - (C2 (beta + 3 alpha + kG_plus))

\frac{d}{d time} (C3) = 3 alpha C2 + 3 beta C4 + kG3_minus C_G3 - (C3 (2 beta + 2 alpha + kG_plus))

\frac{d}{d time} (C4) = 2 alpha C3 + 4 beta O - (C4 (3 beta + alpha))

O = 1 - C1 - C2 - C3 - C4 - C_G1 - C_G2 - C_G3

\frac{d}{d time} (C_G1) = beta_C_G2 + kG_plus C1 - (C_G1 (4 alpha_+ kG_minus))

\frac{d}{d time} (C_G2) = 4 alpha_C_G1 + 2 beta_C_G3 + kG_plus C2 - (C_G2 (beta_+ 3 alpha_+ kG2_minus))

\frac{d}{d time} (C_G3) = 3 alpha_C_G2 + kG_plus C3 - (C_G3 (2 beta_+ kG3_minus))