Model Mathematics

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Component: strain_control

Component: environment

Component: cell_geom

rho = \frac{A_cap}{V_myo}

Component: membrane

Cm = \frac{CmF}{A_cap} \frac{d}{d time} (V) = \frac{- (I_H + I_Cl + i_Na + I_CaL + i_t + i_ss + i_f + i_K1 + I_Cab + I_SAC_Na + i_B_K + i_B_Na + I_Ko + I_SAC_K + i_NaK + I_NaCa + I_pCa + i_Stim)}{Cm}

Component: I_stimulus

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

Component: SAC_current

gamma_SLSAC = \{\begin{matrix} (ExtensionRatio - 1) 10 if SAC_on = 1 \\ 0 otherwise \end{matrix} r = \frac{- (E_R + 85)}{E_R - 65} I_SAC_Na = \frac{g_SAC gamma_SLSAC (V - E_Na)}{A_cap} r I_SAC_K = \frac{g_SAC gamma_SLSAC (V - E_K)}{A_cap} I_SAC = I_SAC_K + I_SAC_Na

Component: KSA_current

gamma_SLKO = \{\begin{matrix} 0.7 + (ExtensionRatio - 1) 3 if SAC_on = 1 \\ 0.7 otherwise \end{matrix} I_Ko = \frac{\frac{g_Ko}{1 + ⅇ^{\frac{- (10 + V)}{45}}} (V - E_K) gamma_SLKO}{A_cap}

Component: sodium_current

g_Na_endo = 1.33 g_Na E_Na = \frac{R T}{F} \ln (\frac{Na_o}{Na_i}) i_Na = \frac{g_Na_endo m^{3} h j (V - E_Na)}{A_cap}

Component: sodium_current_m_gate

m_infinity = \frac{1}{1 + ⅇ^{\frac{V + 45}{- 6.5}}} tau_m = \frac{0.00136e3}{\frac{0.32 (V + 47.13)}{1 - (ⅇ^{(- 0.1) (V + 47.13)})} + 0.08 ⅇ^{\frac{- V}{11}}} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

Component: sodium_current_h_gate

h_infinity = \frac{1}{1 + ⅇ^{\frac{V + 76.1}{6.07}}} tau_h = \{\begin{matrix} 0.0004537e3 (1 + ⅇ^{\frac{- (V + 10.66)}{11.1}}) if V \geq - 40 \\ \frac{0.00349e3}{0.135 ⅇ^{\frac{- (V + 80)}{6.8}} + 3.56 ⅇ^{0.079 V} + 310000 ⅇ^{0.35 V}} otherwise \end{matrix} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

Component: sodium_current_j_gate

j_infinity = \frac{1}{1 + ⅇ^{\frac{V + 76.1}{6.07}}} tau_j = \{\begin{matrix} \frac{0.01163e3 (1 + ⅇ^{(- 0.1) (V + 32)})}{ⅇ^{(- 0.0000002535) V}} if V \geq - 40 \\ \frac{0.00349e3}{\frac{V + 37.78}{1 + ⅇ^{0.311 (V + 79.23)}} ((- 127140) ⅇ^{0.2444 V} - (0.00003474 ⅇ^{(- 0.04391) V})) + \frac{0.1212 ⅇ^{(- 0.01052) V}}{1 + ⅇ^{(- 0.1378) (V + 40.14)}}} otherwise \end{matrix} \frac{d}{d time} (j) = \frac{j_infinity - j}{tau_j}

Component: Ca_independent_transient_outward_K_current

g_t_endo = 0.4647 g_t E_K = \frac{R T}{F} \ln (\frac{K_o}{K_i}) i_t = \frac{g_t_endo r (a_endo s + b_endo s_slow) (V - E_K)}{A_cap}

Component: Ca_independent_transient_outward_K_current_r_gate

r_infinity = \frac{1}{1 + ⅇ^{\frac{V + 10.6}{- 11.42}}} tau_r = \frac{1e3}{45.16 ⅇ^{0.03577 (V + 50)} + 98.9 ⅇ^{(- 0.1) (V + 38)}} \frac{d}{d time} (r) = \frac{r_infinity - r}{tau_r}

Component: Ca_independent_transient_outward_K_current_s_gate

s_infinity = \frac{1}{1 + ⅇ^{\frac{V + 45.3}{6.8841}}} tau_s_endo = 0.55e3 ⅇ^{- ({(\frac{V + 70}{25})}^{2})} + 0.049e3 \frac{d}{d time} (s) = \frac{s_infinity - s}{tau_s_endo}

Component: Ca_independent_transient_outward_K_current_s_slow_gate

s_slow_infinity = \frac{1}{1 + ⅇ^{\frac{V + 45.3}{6.8841}}} tau_s_slow_endo = 3.3e3 ⅇ^{- ({(\frac{V + 70}{30})}^{2})} + 0.049e3 \frac{d}{d time} (s_slow) = \frac{s_slow_infinity - s_slow}{tau_s_slow_endo}

Component: steady_state_outward_K_current

i_ss = \frac{g_ss r_ss s_ss (V - E_K)}{A_cap}

Component: steady_state_outward_K_current_r_ss_gate

r_ss_infinity = \frac{1}{1 + ⅇ^{\frac{V + 11.5}{- 11.82}}} tau_r_ss = \frac{10e3}{45.16 ⅇ^{0.03577 (V + 50)} + 98.9 ⅇ^{(- 0.1) (V + 38)}} \frac{d}{d time} (r_ss) = \frac{r_ss_infinity - r_ss}{tau_r_ss}

Component: steady_state_outward_K_current_s_ss_gate

s_ss_infinity = \frac{1}{1 + ⅇ^{\frac{V + 87.5}{10.3}}} tau_s_ss = 2.1e3 \frac{d}{d time} (s_ss) = \frac{s_ss_infinity - s_ss}{tau_s_ss}

Component: inward_rectifier

i_K1 = \frac{\frac{(\frac{48e-3}{ⅇ^{\frac{V + 37}{25}} + ⅇ^{\frac{V + 37}{- 25}}} + (10e-3)) 0.001}{1 + ⅇ^{\frac{V - (E_K + 76.77)}{- 17}}} + \frac{g_K1 (V - (E_K + 1.73))}{(1 + ⅇ^{\frac{1.613 F (V - (E_K + 1.73))}{R T}}) (1 + ⅇ^{\frac{K_o - 0.9988}{- 0.124}})}}{A_cap}

Component: hyperpolarisation_activated_current

f_K = 1 - f_Na i_f_Na = \frac{g_f y f_Na (V - E_Na)}{A_cap} i_f_K = \frac{g_f y f_K (V - E_K)}{A_cap} i_f = i_f_Na + i_f_K

Component: hyperpolarisation_activated_current_y_gate

y_infinity = \frac{1}{1 + ⅇ^{\frac{V + 138.6}{10.48}}} tau_y = \frac{1e3}{0.11885 ⅇ^{\frac{V + 80}{28.37}} + 0.5623 ⅇ^{\frac{V + 80}{- 14.19}}} \frac{d}{d time} (y) = \frac{y_infinity - y}{tau_y}

Component: background_currents

i_B_Na = \frac{scale_Na g_B_Na (V - E_Na)}{A_cap} i_B_K = \frac{scale_K g_B_K (V - E_K)}{A_cap}

Component: sodium_potassium_pump

p_nai = \frac{1}{1 + {(\frac{K_m_Na}{Na_i})}^{4}} sigma = \frac{ⅇ^{\frac{Na_o}{67.3}} - 1}{7} p_v = \frac{1}{1 + 0.1245 ⅇ^{\frac{(- 0.1) V F}{R T}} + 0.0365 sigma ⅇ^{\frac{(- V) F}{R T}}} i_NaK = \frac{\frac{i_NaK_max}{A_cap} p_v K_o}{K_o + K_m_K} p_nai

Component: J_CO2

jco2 = V_myo rho Pco2 (CO2e - CO2i)

Component: comp_v_nhe_exchanger

gamma_NHE = \{\begin{matrix} 1 - (2.804 (ExtensionRatio - 1)) if pH_on = 1 \\ 1 otherwise \end{matrix} K_Hs = K_Hi gamma_NHE km2 = \frac{kp1 kp2}{km1} Be = 10^{- pH_e} 1e3 Bi = 10^{- pH_i} 1e3 ap1 = \frac{KB Ae kp1}{KA KB + KB Ae + Ae Be + KA Be} am1 = \frac{KB Ai km1}{KA KB + KB Ai + Ai Bi + KA Bi} ap2 = \frac{KA Bi kp2}{KA KB + KB Ai + Ai Bi + KA Bi} am2 = \frac{KA Be km2}{KA KB + KB Ae + Ae Be + KA Be} reg = \frac{{Bi}^{n_Hi}}{{Bi}^{n_Hi} + {K_Hs}^{n_Hi}} flux_nhe = \frac{reg (ap1 ap2 - (am1 am2))}{ap1 + ap2 + am1 + am2} v_nhe = flux_nhe V_myo Q_10Scaler

Component: comp_v_che_exchanger

km2 = \frac{kp2 km1}{kp1} OHe = 1000 10^{(- 14) + pH_e} OHi = 1000 10^{(- 14) + pH_i} a = 1 + \frac{K_OH}{OHe} + \frac{K_OH Cle}{OHe K_Cl} b = 1 + \frac{K_Cl}{Cle} + \frac{K_Cl OHe}{Cle K_OH} c = 1 + \frac{K_Cl}{Cli} + \frac{K_Cl OHi}{Cli K_OH} d = 1 + \frac{K_OH}{OHi} + \frac{K_OH Cli}{OHi K_Cl} s1 = \frac{1}{a + \frac{d (kp1 + \frac{kp2 a}{b})}{km1 + \frac{km2 d}{c}}} s6 = \frac{1}{d + \frac{a (km1 + \frac{km2 d}{c})}{kp1 + \frac{kp2 a}{b}}} v_che = \frac{V_myo (km1 s6 - (kp1 s1))}{60 1000} Q_10Scaler

Component: comp_v_nbc

km2 = \frac{kp2 km1}{kp1} a = 1 + \frac{Nae}{K_Na} + \frac{Nae HCO3e}{K_Na K_HCO3} b = 1 + \frac{K_HCO3}{HCO3e} + \frac{K_Na K_HCO3}{HCO3e Nae} c = 1 + \frac{K_HCO3}{HCO3i} + \frac{K_Na K_HCO3}{HCO3i Nai} d = 1 + \frac{Nai}{K_Na} + \frac{Nai HCO3i}{K_Na K_HCO3} He = 1000 10^{- pH_e} Hi = 1000 10^{- pH_i} s1 = \frac{1}{a + \frac{d (kp1 + \frac{kp2 a}{b})}{km1 + \frac{km2 d}{c}}} s6 = \frac{1}{d + \frac{a (km1 + \frac{km2 d}{c})}{kp1 + \frac{kp2 a}{b}}} reg = \frac{{Hi}^{n_Hi}}{{Hi}^{n_Hi} + {K_Hi}^{n_Hi}} (1 - (\frac{{He}^{n_He}}{{He}^{n_He} + {K_He}^{n_He}})) v_nbc = \frac{V_myo reg (km1 s6 - (kp1 s1))}{60 1000} Q_10Scaler

Component: comp_v_ae

gamma_AE = \{\begin{matrix} 1 + 2.5 (ExtensionRatio - 1) if pH_on = 1 \\ 1 otherwise \end{matrix} K_Hs = K_Hi gamma_AE km2 = \frac{kp2 km1}{kp1} He = 1000 10^{- pH_e} Hi = 1000 10^{- pH_i} a = 1 + \frac{K_HCO3}{HCO3e} + \frac{K_HCO3 Cle}{HCO3e K_Cl} b = 1 + \frac{K_Cl}{Cle} + \frac{K_Cl HCO3e}{Cle K_HCO3} c = 1 + \frac{K_Cl}{Cli} + \frac{K_Cl HCO3i}{Cli K_HCO3} d = 1 + \frac{K_HCO3}{HCO3i} + \frac{K_HCO3 Cli}{HCO3i K_Cl} s1 = \frac{1}{a + \frac{d (kp1 + \frac{kp2 a}{b})}{km1 + \frac{km2 d}{c}}} s6 = \frac{1}{d + \frac{a (km1 + \frac{km2 d}{c})}{kp1 + \frac{kp2 a}{b}}} reg = \frac{\frac{{K_Hs}^{n_Hi}}{{Hi}^{n_Hi} + {K_Hs}^{n_Hi}} {He}^{n_He}}{{He}^{n_He} + {K_He}^{n_He}} v_ae = \frac{V_myo reg (km1 s6 - (kp1 s1))}{60 1000} Q_10Scaler

Component: intracellular_ion_concentrations

E_Cl = \frac{R T}{F} \ln (\frac{Cli}{Cle}) I_Cl = g_Cl (V - E_Cl) H_o = 1000 10^{- pH_e} H_i = 1000 10^{- pH_i} E_H = \frac{R T}{F} \ln (\frac{H_o}{H_i}) I_H = g_H (V - E_H) K_Nak = \frac{i_NaK (- 2) A_cap}{V_myo F} K_flux = \frac{(- (I_SAC_K + i_ss + I_Ko + i_t + i_K1 + i_f_K + i_NaK (- 2) + i_B_K)) A_cap}{V_myo F} nai_flux = \frac{(- (i_B_Na + I_SAC_Na + i_Na + I_NaCa 3 + i_NaK 3 + i_f_Na)) A_cap}{V_myo F} nai_total = nai_flux + nai_NHE + nai_NBC nai_NHE = \frac{v_nhe}{V_myo} nai_NBC = \frac{v_nbc}{V_myo} nai_Nak = \frac{i_NaK 3 A_cap}{V_myo F} nai_NaCa = \frac{I_NaCa 3 A_cap}{V_myo F} nai_na = \frac{i_Na A_cap}{V_myo F} nai_bg = \frac{i_f_Na A_cap}{V_myo F} beta_intr = \ln 10 (10^{- pH_i} + \frac{10^{pH_i + pKa_ib1} ib1}{{(10^{pH_i} + 10^{pKa_ib1})}^{2}} + \frac{10^{pH_i + pKa_ib2} ib2}{{(10^{pH_i} + 10^{pKa_ib2})}^{2}}) CO2e = PP_co2e CO_2sol P_atm HCO3e = \frac{\frac{kf_co2hyd}{kr_co2hyd} CO2e}{10^{- pH_e} 1e3} v_co2hyd = (V_myo + V_SR) (kf_co2hyd CO2i - (kr_co2hyd HCO3i 10^{- pH_i} 1e3)) \frac{d}{d time} (HCO3i) = \frac{v_co2hyd}{V_myo + V_SR} + \frac{v_nbc - v_ae}{V_myo} \frac{d}{d time} (CO2i) = (\frac{jco2}{V_myo} - (\frac{v_co2hyd}{V_myo + V_SR})) + J_CO2 \frac{d}{d time} (pH_i) = \frac{1}{- beta_intr} (\frac{(- v_nhe) + v_che}{V_myo} + \frac{v_co2hyd}{V_myo + V_SR} - (\frac{I_H A_cap}{V_myo F})) \frac{d}{d time} (Na_i) = \frac{(- (i_B_Na + I_SAC_Na + i_Na + I_NaCa 3 + i_NaK 3 + i_f_Na)) A_cap}{V_myo F} + \frac{v_nhe + v_nbc}{V_myo} \frac{d}{d time} (K_i) = \frac{(- ((i_Stim + I_SAC_K + i_ss + I_Ko + i_t + i_K1 + i_f_K - (2 i_NaK)) + i_B_K)) A_cap}{V_myo F} \frac{d}{d time} (Cli) = \frac{I_Cl A_cap}{V_myo F} + \frac{pH_scale (v_che + v_ae)}{V_myo}

Component: standard_ionic_concentrations

Component: SL_pump

I_pCa = \frac{\frac{g_pCa Ca_i}{K_mpCa + Ca_i} 2 V_myo F}{A_cap}

Component: Cab

E_Ca = \frac{\log_{10} (\frac{Ca_e}{Ca_i})}{delta} I_Cab = \frac{g_Cab (V - E_Ca) 2 V_myo F}{A_cap}

Component: I_Ca_L

I_CaL = \frac{(- J_LC) 2 V_myo F}{A_cap}

Component: NCX

edv = ⅇ^{delta 0.5 V eta} edv2 = ⅇ^{delta 0.5 V (eta - 1)} Nai3 = {Na_i}^{3} Nae3 = {Na_e}^{3} I_NaCa = \frac{\frac{\frac{g_NCX}{(Nae3 + {K_mNa}^{3}) (Ca_e + K_mCa)} (edv Nai3 Ca_e - (edv2 Nae3 Ca_i))}{1 + k_sat edv2} V_myo F}{A_cap}

Component: SERCA

I_SERCA = \frac{g_SERCA {Ca_i}^{2}}{{K_SERCA}^{2} + {Ca_i}^{2}}

Component: ionic_concentrations

Ca_b = B_TRPN - TRPN J_SR = (- J_RY) + I_SERCA - (g_SRl (Ca_SR - Ca_i)) \frac{d}{d time} (Ca_SR) = \frac{V_myo}{V_SR} J_SR \frac{d}{d time} (Ca_i) = \frac{1}{1 + \frac{B_CMDN K_CMDN}{(Ca_i + K_CMDN) (Ca_i + K_CMDN)}} ((J_TPRN - J_SR) + \frac{(2 I_NaCa - I_pCa - I_Cab - I_CaL) A_cap}{2 V_myo F}) \frac{d}{d time} (TRPN) = J_TPRN

Component: Ca_conductances

Component: Ca_voltage

dV = delta V expmdV = ⅇ^{- dV} expVL = ⅇ^{\frac{V - V_L0}{delta_VL}}

Component: C_ij

C_cc = Ca_i C_co = \frac{Ca_i + \frac{J_R}{g_D} Ca_SR}{1 + \frac{J_R}{g_D}} C_oc = \{\begin{matrix} \frac{Ca_i + \frac{\frac{J_L}{g_D} Ca_e dV expmdV}{1 - expmdV}}{1 + \frac{\frac{J_L}{g_D} dV}{1 - expmdV}} if | dV | > 0.000000001 \\ \frac{Ca_i + \frac{J_L}{g_D} Ca_e}{1 + \frac{J_L}{g_D}} otherwise \end{matrix} C_oo = \{\begin{matrix} \frac{Ca_i + \frac{J_R}{g_D} Ca_SR + \frac{\frac{J_L}{g_D} Ca_e dV expmdV}{1 - expmdV}}{1 + \frac{J_R}{g_D} + \frac{\frac{J_L}{g_D} dV}{1 - expmdV}} if | dV | > 0.000000001 \\ \frac{Ca_i + \frac{J_R}{g_D} Ca_SR + \frac{J_L}{g_D} Ca_e}{1 + \frac{J_R}{g_D} + \frac{J_L}{g_D}} otherwise \end{matrix}

Component: J_ij

J_Rco = \frac{J_R (Ca_SR - Ca_i)}{1 + \frac{J_R}{g_D}} J_Roo = \{\begin{matrix} \frac{J_R ((Ca_SR - Ca_i) + \frac{\frac{J_L}{g_D} dV}{1 - expmdV} (Ca_SR - (Ca_e expmdV)))}{1 + \frac{J_R}{g_D} + \frac{\frac{J_L}{g_D} dV}{1 - expmdV}} if | dV | > 0.00001 \\ \frac{J_R ((Ca_SR - Ca_i) + \frac{\frac{J_L}{g_D} 0.00001}{1 - (ⅇ^{- 0.00001})} (Ca_SR - (Ca_e ⅇ^{- 0.00001})))}{1 + \frac{J_R}{g_D} + \frac{\frac{J_L}{g_D} 0.00001}{1 - (ⅇ^{- 0.00001})}} otherwise \end{matrix} J_Loc = \{\begin{matrix} \frac{\frac{J_L dV}{1 - expmdV} (Ca_e expmdV - Ca_i)}{1 + \frac{\frac{J_L}{g_D} dV}{1 - expmdV}} if | dV | > 0.00001 \\ \frac{\frac{J_L 0.00001}{1 - (ⅇ^{- 0.00001})} (Ca_e ⅇ^{- 0.00001} - Ca_i)}{1 + \frac{\frac{J_L}{g_D} 0.00001}{1 - (ⅇ^{- 0.00001})}} otherwise \end{matrix} J_Loo = \{\begin{matrix} \frac{\frac{J_L dV}{1 - expmdV} ((Ca_e expmdV - Ca_i) + \frac{J_R}{g_D} (Ca_e expmdV - Ca_SR))}{1 + \frac{J_R}{g_D} + \frac{\frac{J_L}{g_D} dV}{1 - expmdV}} if | dV | > 0.00001 \\ \frac{\frac{J_L 0.00001}{1 - (ⅇ^{- 0.00001})} ((Ca_e ⅇ^{- 0.00001} - Ca_i) + \frac{J_R}{g_D} (Ca_e ⅇ^{- 0.00001} - Ca_SR))}{1 + \frac{J_R}{g_D} + \frac{\frac{J_L}{g_D} 0.00001}{1 - (ⅇ^{- 0.00001})}} otherwise \end{matrix}

Component: Ca_tau

t_R = 1.17 t_L

Component: epsilon

epsilon_pco = \frac{\frac{\frac{1}{tau_L} C_co}{K_L} (expVL + a)}{expVL + 1} epsilon_pcc = \frac{\frac{\frac{1}{tau_L} Ca_i}{K_L} (expVL + a)}{expVL + 1} epsilon_m = \frac{\frac{1}{tau_L} b (expVL + a)}{b expVL + a}

Component: alpha

alpha_p = \frac{expVL}{t_L (expVL + 1)} alpha_m = \frac{phi_L}{t_L}

Component: RyR_param

gamma_NO = \{\begin{matrix} 1 + 22.41 (ExtensionRatio - 1) if NO_on = 1 \\ 1 otherwise \end{matrix} phi_R = phi_R_base gamma_NO

Component: beta

beta_poc = \frac{\frac{1}{t_R} {C_oc}^{2}}{{C_oc}^{2} + {K_RyR}^{2}} beta_pcc = \frac{\frac{1}{t_R} {Ca_i}^{2}}{{Ca_i}^{2} + {K_RyR}^{2}} beta_m = \frac{phi_R}{t_R}

Component: mu_ij

mu_poc = \frac{\frac{1}{tau_R} ({C_oc}^{2} + c {K_RyR}^{2})}{{C_oc}^{2} + {K_RyR}^{2}} mu_pcc = \frac{\frac{1}{tau_R} ({Ca_i}^{2} + c {K_RyR}^{2})}{{Ca_i}^{2} + {K_RyR}^{2}} mu_moc = \frac{\frac{theta_R}{tau_R} d ({C_oc}^{2} + c {K_RyR}^{2})}{d {C_oc}^{2} + c {K_RyR}^{2}} mu_mcc = \frac{\frac{theta_R}{tau_R} d ({Ca_i}^{2} + c {K_RyR}^{2})}{d {Ca_i}^{2} + c {K_RyR}^{2}}

Component: y_ij

denom = (alpha_p + alpha_m) ((beta_m + beta_poc + alpha_m) (beta_m + beta_pcc) + alpha_p (beta_m + beta_poc)) y_oc = \frac{alpha_p beta_m (alpha_p + alpha_m + beta_m + beta_pcc)}{denom} y_co = \frac{alpha_m (beta_pcc (alpha_m + beta_m + beta_poc) + beta_poc alpha_p)}{denom} y_oo = \frac{alpha_p (beta_poc (alpha_p + beta_m + beta_pcc) + beta_pcc alpha_m)}{denom} y_cc = \frac{alpha_m beta_m (alpha_m + alpha_p + beta_m + beta_poc)}{denom}

Component: r_i

r_1 = y_oc mu_poc + y_cc mu_pcc r_2 = \frac{alpha_p mu_moc + alpha_m mu_mcc}{alpha_p + alpha_m} r_3 = \frac{beta_m mu_pcc}{beta_m + beta_pcc} r_4 = mu_mcc r_5 = y_co epsilon_pco + y_cc epsilon_pcc r_6 = epsilon_m r_7 = \frac{alpha_m epsilon_pcc}{alpha_p + alpha_m} r_8 = epsilon_m

Component: z_i

z_4 = 1 - z_1 - z_2 - z_3 \frac{d}{d time} (z_1) = (- (r_1 + r_5)) z_1 + r_2 z_2 + r_6 z_3 \frac{d}{d time} (z_2) = (r_1 z_1 - ((r_2 + r_7) z_2)) + r_8 z_4 \frac{d}{d time} (z_3) = (r_5 z_1 - ((r_6 + r_3) z_3)) + r_4 z_4

Component: J_values

J_R1 = y_oo J_Roo + J_Rco y_co J_R3 = \frac{J_Rco beta_pcc}{beta_m + beta_pcc} J_L1 = J_Loo y_oo + J_Loc y_oc J_L2 = \frac{J_Loc alpha_p}{alpha_p + alpha_m}

Component: L_flux

J_LC = \frac{(z_1 J_L1 + z_2 J_L2) N}{V_myo}

Component: R_flux

J_RY = \frac{(z_1 J_R1 + z_3 J_R3) N}{V_myo}

Component: troponin

betaCab = \{\begin{matrix} k_off (1 - (\frac{Tension}{gamma_trpn T_ref})) if 1 - (\frac{Tension}{gamma_trpn T_ref}) > 0.1 \\ k_off 0.1 otherwise \end{matrix} J_TPRN = (B_TRPN - TRPN) betaCab - (Ca_i TRPN k_on)

Component: Myofilaments

lambda_prev = ExtensionRatio dExtensionRatiodt = 0 lamda = \{\begin{matrix} ExtensionRatio if ExtensionRatio > 0.8 \land ExtensionRatio ≦ 1.15 \\ 1.15 if ExtensionRatio > 1.15 \\ 0.8 otherwise \end{matrix}

Component: thinfilaments

Component: tropomyosin

K_2 = \frac{alpha_r2 {z_p}^{n_Rel}}{{z_p}^{n_Rel} + {K_z}^{n_Rel}} (1 - (\frac{n_Rel {K_z}^{n_Rel}}{{z_p}^{n_Rel} + {K_z}^{n_Rel}})) K_1 = \frac{alpha_r2 {z_p}^{n_Rel - 1} n_Rel {K_z}^{n_Rel}}{{({z_p}^{n_Rel} + {K_z}^{n_Rel})}^{2}} z_max = \frac{\frac{alpha_0}{{(\frac{Ca_TRPN_50}{TRPN_tot})}^{n_Hill}} - K_2}{alpha_r1 + K_1 + \frac{alpha_0}{{(\frac{Ca_TRPN_50}{TRPN_tot})}^{n_Hill}}} Ca_50 = Ca_50ref (1 + beta_1 (lamda - 1)) Ca_TRPN_50 = \frac{Ca_50 TRPN_tot}{Ca_50 + \frac{k_off}{k_on} (1 - (\frac{(1 + beta_0 (lamda - 1)) 0.5}{gamma_trpn}))} alpha_Tm = alpha_0 {(\frac{Ca_b}{Ca_TRPN_50})}^{n_Hill} beta_Tm = alpha_r1 + \frac{alpha_r2 z^{n_Rel - 1}}{z^{n_Rel} + {K_z}^{n_Rel}} \frac{d}{d time} (z) = alpha_Tm (1 - z) - (beta_Tm z)

Component: filament_overlap

overlap = 1 + beta_0 (lamda - 1)

Component: length_independent_tension

T_Base = \frac{T_ref z}{z_max}

Component: isometric_tension

T_0 = T_Base overlap

Component: Cross_Bridges

Q = Q_1 + Q_2 + Q_3 Tension = \{\begin{matrix} \frac{T_0 (a Q + 1)}{1 - Q} if Q < 0 \\ \frac{T_0 (1 + (a + 2) Q)}{1 + Q} otherwise \end{matrix} \frac{d}{d time} (Q_1) = A_1 dExtensionRatiodt - (alpha_1 Q_1) \frac{d}{d time} (Q_2) = A_2 dExtensionRatiodt - (alpha_2 Q_2) \frac{d}{d time} (Q_3) = A_3 dExtensionRatiodt - (alpha_3 Q_3)

Model Mathematics

Component: strain_control

Component: environment

Component: cell_geom

Component: membrane

Component: I_stimulus

Component: SAC_current

Component: KSA_current

Component: sodium_current

Component: sodium_current_m_gate

Component: sodium_current_h_gate

Component: sodium_current_j_gate

Component: Ca_independent_transient_outward_K_current

Component: Ca_independent_transient_outward_K_current_r_gate

Component: Ca_independent_transient_outward_K_current_s_gate

Component: Ca_independent_transient_outward_K_current_s_slow_gate

Component: steady_state_outward_K_current

Component: steady_state_outward_K_current_r_ss_gate

Component: steady_state_outward_K_current_s_ss_gate

Component: inward_rectifier

Component: hyperpolarisation_activated_current

Component: hyperpolarisation_activated_current_y_gate

Component: background_currents

Component: sodium_potassium_pump

Component: J_CO2

Component: comp_v_nhe_exchanger

Component: comp_v_che_exchanger

Component: comp_v_nbc

Component: comp_v_ae

Component: intracellular_ion_concentrations

Component: standard_ionic_concentrations

Component: SL_pump

Component: Cab

Component: I_Ca_L

Component: NCX

Component: SERCA

Component: ionic_concentrations

Component: Ca_conductances

Component: Ca_voltage

Component: C_ij

Component: J_ij

Component: Ca_tau

Component: epsilon

Component: alpha

Component: RyR_param

Component: beta

Component: mu_ij

Component: y_ij

Component: r_i

Component: z_i

Component: J_values

Component: L_flux

Component: R_flux

Component: troponin

Component: Myofilaments

Component: thinfilaments

Component: tropomyosin

Component: filament_overlap

Component: length_independent_tension

Component: isometric_tension

Component: Cross_Bridges

Component: Calcium_Handling

Component: Calcium_membrane

Component: pH_regulation