Model Mathematics

FoRT = \frac{F}{R T}

RToF = \frac{R T}{F}

T_correction_Ca = {Q10Ca}^{\frac{T - T_exp}{10}}

T_correction_K = {Q10K}^{\frac{T - T_exp}{10}}

T_correction_Na = {Q10Na}^{\frac{T - T_exp}{10}}

T_correction_BK = 1.1 (T - T_exp)

\frac{d}{d time} (Vm_SM) = (-1.0) \frac{1.0}{Cm_SM} (I_Na_SM + I_Ltype_SM + I_LVA_SM + I_kr_SM + I_ka_SM + I_BK_SM + I_NSCC_SM + I_bk_SM + (-1.0) I_stim)

\frac{d}{d time} (Ca_i) = \frac{(-1) I_Ltype_SM + (-1) I_LVA_SM}{2.0 0.001 F Vol_SM} + (-1) J_CaSR_SM

stim_start = \{\begin{matrix} period 1.0 if time > period 1.0 \land time ≦ period 2.0 \\ period 2.0 if time > period 2.0 \land time ≦ period 3.0 \\ period 3.0 if time > period 3.0 \land time ≦ period 4.0 \\ period 4.0 if time > period 4.0 \land time ≦ period 5.0 \\ 0.0 otherwise \end{matrix}

local_time = time - (stim_start + t_ICCpeak)

I_stim = \{\begin{matrix} Gcouple delta_VICC if local_time < t_ICCpeak \\ Gcouple delta_VICC \frac{1.0}{1.0 + ⅇ^{\frac{local_time - 8000}{1000}}} if local_time \geq t_ICCpeak \land local_time ≦ t_ICCplateau \\ Gcouple V_decay \frac{1.0}{1.0 + ⅇ^{\frac{local_time - 8000}{150}}} if local_time > t_ICCplateau \land local_time < t_ICC_stimulus \\ 0.0 otherwise \end{matrix}

d_inf_Ltype_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 17}{-4.3}}}

tau_d_Ltype_SM = T_correction_Ca 0.47

\frac{d}{d time} (d_Ltype_SM) = \frac{d_inf_Ltype_SM - d_Ltype_SM}{tau_d_Ltype_SM}

f_inf_Ltype_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 43}{8.9}}}

tau_f_Ltype_SM = T_correction_Ca 86

\frac{d}{d time} (f_Ltype_SM) = \frac{f_inf_Ltype_SM - f_Ltype_SM}{tau_f_Ltype_SM}

f_ca_inf_Ltype_SM = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{Ca_i - 0.00008999 - 0.000214}{-0.0000131}}})

tau_f_ca_Ltype_SM = T_correction_Ca 2

\frac{d}{d time} (f_ca_Ltype_SM) = \frac{f_ca_inf_Ltype_SM - f_ca_Ltype_SM}{tau_f_ca_Ltype_SM}

E_Ca = 0.5 RToF \ln (\frac{Ca_o}{Ca_i})

I_Ltype_SM = G_max_Ltype f_Ltype_SM d_Ltype_SM f_ca_Ltype_SM (Vm_SM - E_Ca)

J_CaSR_SM = J_max_CaSR {(Ca_i 1.0)}^{1.34}

d_inf_LVA_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 27.5}{-10.9}}}

tau_d_LVA_SM = T_correction_Ca 3.0

\frac{d}{d time} (d_LVA_SM) = \frac{d_inf_LVA_SM - d_LVA_SM}{tau_d_LVA_SM}

f_inf_LVA_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 15.8}{7}}}

tau_f_LVA_SM = T_correction_Ca 7.58 ⅇ^{Vm_SM 0.00817}

\frac{d}{d time} (f_LVA_SM) = \frac{f_inf_LVA_SM - f_LVA_SM}{tau_f_LVA_SM}

E_Ca = 0.5 RToF \ln (\frac{Ca_o}{Ca_i})

I_LVA_SM = G_max_LVA f_LVA_SM d_LVA_SM (Vm_SM - E_Ca)

d_BK_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM}{-17} - (2.0 \ln (\frac{Ca_i}{0.001}))}}

E_K = RToF \ln (\frac{K_o}{K_i})

I_BK_SM = (G_max_BK + T_correction_BK) d_BK_SM (Vm_SM - E_K)

E_K = RToF \ln (\frac{K_o}{K_i})

I_bk_SM = G_max_bk (Vm_SM - E_K)

xr1_inf_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 27}{-5.0}}}

tau_xr1_SM = T_correction_K 80

\frac{d}{d time} (xr1_SM) = \frac{xr1_inf_SM - xr1_SM}{tau_xr1_SM}

xr2_inf_SM = 0.2 + \frac{0.8}{1.0 + ⅇ^{\frac{Vm_SM + 58}{10}}}

tau_xr2_SM = T_correction_K ((-707) + 1481 ⅇ^{\frac{Vm_SM + 36}{95}})

\frac{d}{d time} (xr2_SM) = \frac{xr2_inf_SM - xr2_SM}{tau_xr2_SM}

E_K = RToF \ln (\frac{K_o}{K_i})

I_kr_SM = G_max_kr_SM xr1_SM xr2_SM (Vm_SM - E_K)

m_inf_Na = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 47}{-4.8}}}

tau_m_Na = T_correction_Na (Vm_SM (-0.017) 1 + 0.440)

\frac{d}{d time} (m_Na_SM) = \frac{m_inf_Na - m_Na_SM}{tau_m_Na}

h_inf_Na = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 78}{3}}}

tau_h_Na = T_correction_Na (Vm_SM (-0.25) 1 + 5.50)

\frac{d}{d time} (h_Na_SM) = \frac{h_inf_Na - h_Na_SM}{tau_h_Na}

E_Na = RToF \ln (\frac{Na_o}{Na_i})

I_Na_SM = G_max_Na_SM h_Na_SM m_Na_SM (Vm_SM - E_Na)

xa1_inf_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 26.5}{-7.9}}}

tau_xa1_SM = T_correction_K (31.8 + 175 ⅇ^{(-0.5) {(\frac{Vm_SM + 44.4}{22.3})}^{2}})

\frac{d}{d time} (xa1_SM) = \frac{xa1_inf_SM - xa1_SM}{tau_xa1_SM}

xa2_inf_SM = 0.1 + \frac{0.9}{1.0 + ⅇ^{\frac{Vm_SM + 65}{6.2}}}

tau_xa2_SM = T_correction_K 90

\frac{d}{d time} (xa2_SM) = \frac{xa2_inf_SM - xa2_SM}{tau_xa2_SM}

E_K = RToF \ln (\frac{K_o}{K_i})

I_ka_SM = G_max_ka_SM xa1_SM xa2_SM (Vm_SM - E_K)

m_inf_NSCC_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 25.0}{-20}}}

tau_m_NSCC_SM = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_SM + 66}{-26}}} 150

\frac{d}{d time} (m_NSCC_SM) = \frac{m_inf_NSCC_SM - m_NSCC_SM}{tau_m_NSCC_SM}

f_ca_NSCC_SM = \frac{1.0}{1.0 + {(\frac{Ca_i}{0.0002})}^{-4.0}}

rach_NSCC_SM = \frac{1.0}{1.0 + \frac{0.01}{Ach}}

I_NSCC_SM = G_max_NSCC_SM m_NSCC_SM f_ca_NSCC_SM rach_NSCC_SM (Vm_SM - E_NSCC)