Model Mathematics

\frac{d}{d time} (V) = \frac{- (i_K_dr + i_K_Ca + i_K_ATP + i_fast + i_Ca + i_NS + i_NaL)}{Cm}

i_fast = g_fast {m_infinity}^{3} h (V - V_fast)

m_infinity = \frac{1}{1 + ⅇ^{\frac{Vm - V}{Sm}}}

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1}{1 + ⅇ^{\frac{Vh - V}{Sh}}} tau_h = \frac{1}{lamda_h (ⅇ^{\frac{Vh - V}{2 Sh}} + ⅇ^{\frac{V - Vh}{2 Sh}})}

i_Ca = \frac{\frac{P_Ca d f_infinity 2 F V}{R T} (Ca_o - (Ca_i ⅇ^{\frac{2 F V}{R T}}))}{1 - (ⅇ^{\frac{2 F V}{R T}})}

\frac{d}{d time} (d) = \frac{d_infinity - d}{tau_d} d_infinity = \frac{1}{1 + ⅇ^{\frac{Vd - V}{Sd}}} tau_d = \frac{1}{lamda_d (ⅇ^{\frac{Vd - V}{2 Sd}} + ⅇ^{\frac{V - Vd}{2 Sd}})}

f_infinity = \frac{K_Ca}{K_Ca + Ca_i}

i_NS = \frac{g_NS {K_NS}^{2}}{{K_NS}^{2} + {Ca_lum}^{2}} (\frac{V - VNS}{1 - (ⅇ^{0.1 (VNS - V)})} - 10)

i_K_dr = g_K_dr n^{4} (V - V_K)

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1}{1 + ⅇ^{\frac{Vn - V}{Sn}}} tau_n = \frac{1}{lamda_n (ⅇ^{\frac{Vn - V}{2 Sn}} + ⅇ^{\frac{V - Vn}{2 Sn}})}

i_K_Ca = \frac{g_K_Ca {Ca_i}^{3}}{{K_Ca}^{3} + {Ca_i}^{3}} (V - V_K)

i_K_ATP = g_K_ATP (V - V_K)

i_NaL = g_NaL (V - V_Na)

\frac{d}{d time} (Ca_i) = k_rel (Ca_lum - Ca_i) - (omega i_Ca + k_Ca Ca_i + k_pump Ca_i) \frac{d}{d time} (Ca_lum) = (- k_rel) (Ca_lum - Ca_i) + k_pump Ca_i