Model Mathematics

\frac{d}{d time} (V1) = \frac{- (i_NaP + i_K + i_L1 + i_synE1 + i_synI1)}{C}

\frac{d}{d time} (V2) = \frac{- (i_AD2 + i_L2 + i_synE2 + i_synI2)}{C}

\frac{d}{d time} (V3) = \frac{- (i_AD3 + i_L3 + i_synE3 + i_synI3)}{C}

\frac{d}{d time} (V4) = \frac{- (i_AD4 + i_L4 + i_synE4 + i_synI4)}{C}

i_NaP = g_NaP m h \frac{1}{1000} (V1 - E_Na)

m = \frac{1}{1 + ⅇ^{\frac{- (V1 + 40)}{6}}}

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1}{1 + ⅇ^{\frac{V1 + 48}{6}}} tau_h = \frac{tau_h_max}{\cosh (\frac{V1 + 48}{12})}

i_K = g_K m^{4} \frac{1}{1000} (V1 - E_K)

m = \frac{1}{1 + ⅇ^{\frac{- (V1 + 29)}{4}}}

i_AD2 = g_AD m \frac{1}{1000} (V2 - E_K)

\frac{d}{d time} (m) = \frac{k_AD2 f2_V2 - m}{tau_AD2}

i_AD3 = g_AD m \frac{1}{1000} (V3 - E_K)

\frac{d}{d time} (m) = \frac{k_AD3 f3_V3 - m}{tau_AD3}

i_AD4 = g_AD m \frac{1}{1000} (V4 - E_K)

\frac{d}{d time} (m) = \frac{k_AD4 f4_V4 - m}{tau_AD4}

i_L1 = g_L \frac{1}{1000} (V1 - E_L)

i_L2 = g_L \frac{1}{1000} (V2 - E_L)

i_L3 = g_L \frac{1}{1000} (V3 - E_L)

i_L4 = g_L \frac{1}{1000} (V4 - E_L)

i_synE1 = g_synE \frac{1}{1000} (V1 - E_synE) (c11 d1 + c21 d2 + c31 d3)

i_synE2 = g_synE \frac{1}{1000} (V2 - E_synE) (a12 f1_V1 + c12 d1 + c22 d2 + c32 d3)

i_synE3 = g_synE \frac{1}{1000} (V3 - E_synE) (c13 d1 + c23 d2 + c33 d3)

i_synE4 = g_synE \frac{1}{1000} (V4 - E_synE) (c14 d1 + c24 d2 + c34 d3)

i_synI1 = g_synI \frac{1}{1000} (V1 - E_synI) (b21 f2_V2 + b31 f3_V3 + b41 f4_V4)

i_synI2 = g_synI \frac{1}{1000} (V2 - E_synI) (b32 f3_V3 + b42 f4_V4)

i_synI3 = g_synI \frac{1}{1000} (V3 - E_synI) (b23 f2_V2 + b43 f4_V4)

i_synI4 = g_synI \frac{1}{1000} (V4 - E_synI) (b24 f2_V2 + b34 f3_V3)

f1_V1 = \frac{1}{1 + ⅇ^{\frac{- (V1 - V_half)}{k_V1}}} f2_V2 = \frac{1}{1 + ⅇ^{\frac{- (V2 - V_half)}{k_V2}}} f3_V3 = \frac{1}{1 + ⅇ^{\frac{- (V3 - V_half)}{k_V3}}} f4_V4 = \frac{1}{1 + ⅇ^{\frac{- (V4 - V_half)}{k_V4}}}