Model Mathematics

\frac{d}{d time} (V) = \frac{(- (i_NaP + i_Na + i_K + i_L + i_tonic_e + i_syn_e)) + i_app}{C}

i_Na = g_Na {m_infinity}^{3.0} (1.0 - n) (V - E_Na)

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

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

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

i_NaP = g_NaP m_infinity h (V - E_Na)

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_h}{sigma_h}}} tau_h = \frac{tau_h_max}{\cosh (\frac{V - theta_h}{2.0 sigma_h})}

i_L = g_L (V - E_L)

i_tonic_e = g_tonic_e (V - E_syn_e)

i_syn_e = sum_g_syn_e_s (V - E_syn_e) s_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}