Model Mathematics

Vm = \{\begin{matrix} 1e-7 if | VmReal | < 1e-7 \\ VmReal otherwise \end{matrix} \frac{d}{d time} (VmReal) = \frac{- (I_Kir + I_Shkr + I_b - I_stim)}{Cm}

I_Kir = GKir OKir \sqrt{Ko (1e-3)} (Vm - EK) OKir = \frac{1}{aKir + ⅇ^{\frac{bKir (Vm - EK) F}{R T}}} EK = \frac{R T}{F} \ln (\frac{Ko}{Ki})

I_Shkr = \frac{\frac{PShkr OShkr Vm F^{2}}{R T} (Ki - (Ko ⅇ^{\frac{(- Vm) F}{R T}}))}{1 - (ⅇ^{\frac{(- Vm) F}{R T}})} C0Shkr = \{\begin{matrix} 0 if C0ShkrReal < 0 \\ 1 if C0ShkrReal > 1 \\ C0ShkrReal otherwise \end{matrix} C1Shkr = \{\begin{matrix} 0 if C1ShkrReal < 0 \\ 1 if C1ShkrReal > 1 \\ C1ShkrReal otherwise \end{matrix} C2Shkr = \{\begin{matrix} 0 if C2ShkrReal < 0 \\ 1 if C2ShkrReal > 1 \\ C2ShkrReal otherwise \end{matrix} C3Shkr = \{\begin{matrix} 0 if C3ShkrReal < 0 \\ 1 if C3ShkrReal > 1 \\ C3ShkrReal otherwise \end{matrix} C4Shkr = \{\begin{matrix} 0 if C4ShkrReal < 0 \\ 1 if C4ShkrReal > 1 \\ C4ShkrReal otherwise \end{matrix} OShkr = \{\begin{matrix} 0 if OShkrReal < 0 \\ 1 if OShkrReal > 1 \\ OShkrReal otherwise \end{matrix} kv = kv0 ⅇ^{\frac{Vm zv F}{R T}} k_v = k_v0 ⅇ^{\frac{Vm z_v F}{R T}} \frac{d}{d time} (C0ShkrReal) = k_v C1Shkr - (4 kv C0Shkr) \frac{d}{d time} (C1ShkrReal) = 2 k_v C2Shkr + 4 kv C0Shkr - ((3 kv + k_v) C1Shkr) \frac{d}{d time} (C2ShkrReal) = 3 k_v C3Shkr + 3 kv C1Shkr - ((2 kv + 2 k_v) C2Shkr) \frac{d}{d time} (C3ShkrReal) = 4 k_v C4Shkr + 2 kv C2Shkr - ((kv + 3 k_v) C3Shkr) \frac{d}{d time} (C4ShkrReal) = k_o OShkr + kv C3Shkr - ((ko + 4 k_v) C4Shkr) \frac{d}{d time} (OShkrReal) = ko C4Shkr - (k_o OShkr)

I_b = Gb (Vm - Eb)

I_stim = \{\begin{matrix} stim_amplitude if time \geq stim_start \land time ≦ stim_end \land time - stim_start - (⌊ \frac{time - stim_start}{stim_period} ⌋ stim_period) ≦ stim_duration \\ 0 otherwise \end{matrix}