Model Mathematics

i_Na = g_Na P_open (V - E_Na)

P_open = O1 + O2

\frac{d}{d time} (C0) = beta C1 + cf C0I - ((cn + 4 alpha) C0)

\frac{d}{d time} (C1) = 2 beta C2 + 4 alpha C0 + \frac{cf}{a} C1I - ((beta + 3 alpha + cn a) C1)

\frac{d}{d time} (C2) = 3 beta C3 + 3 alpha C1 + \frac{cf}{a^{2}} C2I - ((2 beta + 2 alpha + cn a^{2}) C2)

\frac{d}{d time} (C3) = 4 beta C4 + 2 alpha C2 + \frac{cf}{a^{3}} C3I - ((3 beta + alpha + cn a^{3}) C3)

\frac{d}{d time} (C4) = delta O1 + v O2 + alpha C3 + \frac{cf}{a^{4}} C4I - ((4 beta + gamma + eta + cn a^{4}) C4)

\frac{d}{d time} (O1) = gamma C4 + omega O2 + of I - ((delta + epsilon + on) O1)

\frac{d}{d time} (O2) = epsilon O1 + eta C4 - ((v + omega) O2)

\frac{d}{d time} (C0I) = \frac{beta}{a} C1I + cn C0 - ((cf + 4 alpha a) C0I)

\frac{d}{d time} (C1I) = \frac{2 beta}{a} C2I + 4 alpha a C0I + cn a C1 - ((\frac{beta}{a} + 3 alpha a + \frac{cf}{a}) C1I)

\frac{d}{d time} (C2I) = \frac{3 beta}{a} C3I + 3 alpha a C1I + cn a^{2} C2 - ((\frac{2 beta}{a} + 2 alpha a + \frac{cf}{a^{2}}) C2I)

\frac{d}{d time} (C3I) = \frac{4 beta}{a} C4I + 2 alpha a C2I + cn a^{3} C3 - ((\frac{3 beta}{a} + alpha a + \frac{cf}{a^{3}}) C3I)

\frac{d}{d time} (C4I) = delta_delta I + alpha a C3I + cn a^{4} C4 - ((\frac{4 beta}{a} + gamma_gamma + \frac{cf}{a^{4}}) C4I)

\frac{d}{d time} (I) = gamma_gamma C4I + on O1 - ((delta_delta + of) I)

alpha = \frac{k T}{h} ⅇ^{\frac{- delta_H_alpha}{R T} + \frac{delta_S_alpha}{R} + \frac{z_alpha F V}{R T}}

beta = \frac{k T}{h} ⅇ^{\frac{- delta_H_beta}{R T} + \frac{delta_S_beta}{R} + \frac{z_beta F V}{R T}}

gamma = \frac{k T}{h} ⅇ^{\frac{- delta_H_gamma}{R T} + \frac{delta_S_gamma}{R} + \frac{z_gamma F V}{R T}}

delta = \frac{k T}{h} ⅇ^{\frac{- delta_H_delta}{R T} + \frac{delta_S_delta}{R} + \frac{z_delta F V}{R T}}

on = \frac{k T}{h} ⅇ^{\frac{- delta_H_on}{R T} + \frac{delta_S_on}{R} + \frac{z_on F V}{R T}}

of = \frac{k T}{h} ⅇ^{\frac{- delta_H_of}{R T} + \frac{delta_S_of}{R} + \frac{z_of F V}{R T}}

gamma_gamma = \frac{k T}{h} ⅇ^{\frac{- delta_H_gamma_gamma}{R T} + \frac{delta_S_gamma_gamma}{R} + \frac{z_gamma_gamma F V}{R T}}

delta_delta = \frac{k T}{h} ⅇ^{\frac{- delta_H_delta_delta}{R T} + \frac{delta_S_delta_delta}{R} + \frac{z_delta_delta F V}{R T}}

epsilon = \frac{k T}{h} ⅇ^{\frac{- delta_H_epsilon}{R T} + \frac{delta_S_epsilon}{R} + \frac{z_epsilon F V}{R T}}

omega = \frac{k T}{h} ⅇ^{\frac{- delta_H_omega}{R T} + \frac{delta_S_omega}{R} + \frac{z_omega F V}{R T}}

eta = \frac{k T}{h} ⅇ^{\frac{- delta_H_eta}{R T} + \frac{delta_S_eta}{R} + \frac{z_eta F V}{R T}}

v = \frac{k T}{h} ⅇ^{\frac{- delta_H_v}{R T} + \frac{delta_S_v}{R} + \frac{z_v F V}{R T}}

cn = \frac{k T}{h} ⅇ^{\frac{- delta_H_cn}{R T} + \frac{delta_S_cn}{R} + \frac{z_cn F V}{R T}}

cf = \frac{k T}{h} ⅇ^{\frac{- delta_H_cf}{R T} + \frac{delta_S_cf}{R} + \frac{z_cf F V}{R T}}