diff --git a/c/ohara-cipa-v1-2017.mmt b/c/ohara-cipa-v1-2017.mmt index 27e6328..09156f9 100644 --- a/c/ohara-cipa-v1-2017.mmt +++ b/c/ohara-cipa-v1-2017.mmt @@ -1,30 +1,37 @@ [[model]] -name: li-2017 -version: 20240307 +name: dutta-2017 +version: 20240814 mmt_authors: Michael Clerx display_name: O'Hara-CiPA-v1, 2017 desc: """ - The 2017 "CiPA v1" update [1] of the O'Hara et al. model of the human - ventricular AP [2]. + The 2017 "CiPA v1" update [1, 2, 3] of the O'Hara et al. model of the human + ventricular AP [4]. - This Myokit implementation was based on CellML code [3], published by Chang - et al. [4]. The authors checked the CellML output (after converting to - Chaste using PyCML) against derivatives calculated with the original code - published by the FDA [5]. + This Myokit implementation was based on CellML code [5], published by Chang + et al. [3]. The CellML authors checked the CellML output (after converting + to Chaste using PyCML) against derivatives calculated with the original + code published by the FDA [6]. - The model differs from the original O'Hara model [2] in the following + The model differs from the original O'Hara model [4] in the following aspects: - - The IKr formulation was replaced entirely, as described in [1,4]. + - The IKr formulation was replaced entirely, as described in [2, 3]. - Conductances for INaL, ICaL, IKs, and IK1 were rescaled, as described - in [6]. + in [1]. - This implementation includes a further two corrections to INaK, as - documented at - https://docs.google.com/document/d/111fqNzQGvGAjB_PrkvejEhzqwROrR6czz_OBz7Ep-iM + This Myokit implementation includes a further two corrections to INaK, as + documented in [7]. Compared to the CellML [5], it uses a simpler fix for + discontinuities in the phiCaL parameters, and it has a more readable + notation for the IKr model. References: - [1] Li, Z., Dutta, S., Sheng, J., Tran, P. N., Wu, W., Chang, K., Mdluli, + [1] Dutta, S., Chang, K. C., Beattie, K. A., Sheng, J., Tran, P. N., Wu, + W. W., Wu, M., Strauss, D. G., Colatsky, T., & Li, Z. (2017). + Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk + Assessment. Frontiers in Physiology, 8, 616. + https://doi.org/10.3389/fphys.2017.00616 + + [2] Li, Z., Dutta, S., Sheng, J., Tran, P. N., Wu, W., Chang, K., Mdluli, T., Strauss, D. G., & Colatsky, T. (2017). Improving the In Silico Assessment of Proarrhythmia Risk by Combining hERG (Human Ether-a-go-go-Related Gene) Channel-Drug Binding Kinetics and @@ -32,28 +39,24 @@ desc: """ Electrophysiology, 10(2), e004628. https://doi.org/10.1161/CIRCEP.116.004628 - [2] O'Hara, T., Virág, L., Varró, A., & Rudy, Y. (2011). Simulation of the - Undiseased Human Cardiac Ventricular Action Potential: Model - Formulation and Experimental Validation. PLOS Computational Biology, - 7(5), e1002061. - https://doi.org/10.1371/journal.pcbi.1002061 - - [3] https://models.cellml.org/e/4e8/ohara_rudy_cipa_v1_2017.cellml/view - - [4] Chang, K. C., Dutta, S., Mirams, G. R., Beattie, K. A., Sheng, J., + [3] Chang, K. C., Dutta, S., Mirams, G. R., Beattie, K. A., Sheng, J., Tran, P. N., Wu, M., Wu, W. W., Colatsky, T., Strauss, D. G., & Li, Z. (2017). Uncertainty quantification reveals the importance of data variability and experimental design considerations for in silico proarrhythmia risk assessment. Frontiers in physiology, 8, 917. https://doi.org/10.3389/fphys.2017.00917 - [5] https://github.com/FDA/CiPA/blob/master/AP_simulation/models/newordherg_qNet.c + [4] O'Hara, T., Virág, L., Varró, A., & Rudy, Y. (2011). Simulation of the + Undiseased Human Cardiac Ventricular Action Potential: Model + Formulation and Experimental Validation. PLOS Computational Biology, + 7(5), e1002061. + https://doi.org/10.1371/journal.pcbi.1002061 + + [5] https://models.cellml.org/e/4e8/ohara_rudy_cipa_v1_2017.cellml/view - [6] Dutta, S., Chang, K. C., Beattie, K. A., Sheng, J., Tran, P. N., Wu, - W. W., Wu, M., Strauss, D. G., Colatsky, T., & Li, Z. (2017). - Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk - Assessment. Frontiers in Physiology, 8, 616. - https://doi.org/10.3389/fphys.2017.00616 + [6] https://github.com/FDA/CiPA/blob/master/AP_simulation/models/newordherg_qNet.c + + [7] https://docs.google.com/document/d/111fqNzQGvGAjB_PrkvejEhzqwROrR6czz_OBz7Ep-iM """ # Initial values @@ -99,7 +102,6 @@ ikr.IO = 5.67622999999999969e-5 ikr.IObound = 0 ikr.Obound = 0 ikr.Cbound = 0 -ikr.D = 0 iks.x1 = 2.70775802499999996e-1 iks.x2 = 1.92850342599999990e-4 ik1.x = 9.96759759399999945e-1 @@ -118,7 +120,7 @@ pace = 0 bind pace # # Membrane potential -# Page 5 of the supplement to [2] +# Page 5 of the supplement to [4] # [membrane] dot(V) = -(i_ion + stimulus.i_stim) @@ -137,7 +139,7 @@ i_ion = ( # # Stimulus current -# Page 5 of the supplement to [2] +# Page 5 of the supplement to [4] # [stimulus] i_stim = engine.pace * amplitude @@ -147,7 +149,7 @@ amplitude = -80 [A/F] # # Cell geometry -# Page 6 of the supplement to [2] +# Page 6 of the supplement to [4] # [cell] mode = 1 @@ -182,7 +184,7 @@ vss = 0.02 * vcell # # Physical constants -# Page 2 of the appendix to [2] +# Page 2 of the appendix to [4] # [phys] R = 8314 [J/kmol/K] : Gas constant @@ -200,7 +202,7 @@ FFRT = F * FRT # # Extracellular concentrations -# Page 5 of the supplement to [2] +# Page 5 of the supplement to [4] # [extra] Na_o = 140 [mM] : Extracellular Na+ concentration @@ -212,7 +214,7 @@ K_o = 5.4 [mM] : Extracellular K+ concentration # # Reversal potentials -# Page 6 of the supplement to [2] +# Page 6 of the supplement to [4] # [rev] ENa = phys.RTF * log(extra.Na_o / sodium.Na_i) @@ -229,7 +231,7 @@ EKs = phys.RTF * log((extra.K_o + PNaK * extra.Na_o) / (potassium.K_i + PNaK * s # # INa: Fast sodium current -# Page 6 of the supplement to [2] +# Page 6 of the supplement to [4] # # The fast sodium current is modelled using a Hodgkin-Huxley type formulation # including activation (m), slow and fast components of inactivation (h) and @@ -296,7 +298,7 @@ INa = gNa * (V - rev.ENa) * m^3 * ((1 - camk.f) * h * j + camk.f * hp * jp) # # INaL: Late component of the sodium current -# Page 7 of the supplement to [2] +# Page 7 of the supplement to [4] # [inal] use membrane.V @@ -328,7 +330,7 @@ INaL = fNaL * gNaL * (V - rev.ENa) * m * ((1 - camk.f) * h + camk.f * hp) # # Ito: Transient outward potassium current -# page 8 of the supplement to [2] +# page 8 of the supplement to [4] # [ito] use membrane.V @@ -392,7 +394,7 @@ Ito = fto * gto * (V - rev.EK) * ((1 - camk.f) * a * i + camk.f * ap * ip) # ICaL: L-type calcium current # ICaNa: Sodium current through the L-type calcium channel # ICaK: Potassium current through the L-type calcium channel -# Page 9 of the supplement to [2] +# Page 9 of the supplement to [4] # # The ICaL channel is modeled using activation, inactivation (fast and slow), # Ca-dependent inactivation (fast and slow) and recovery from Ca-dependent @@ -407,6 +409,8 @@ use calcium.Ca_ss, potassium.K_ss, sodium.Na_ss vf = V * phys.FRT vff = V * phys.FFRT in [C/mol] +evf = exp(vf) +evf2 = exp(2 * vf) # Activation sd = 1 / (1 + exp((V + 3.94 [mV]) / -4.23 [mV])) desc: Steady-state value for activation gate of ICaL @@ -483,11 +487,17 @@ dot(nca) = anca * k2n - nca * km2n in [1/ms] anca = 1 / (k2n / km2n + (1 + Kmn / Ca_ss)^4) # Total currents through L-type calcium channels -PhiCaL = if(vf == 0, 1 [C/mol] * 4 * (Ca_ss - 0.341 * Ca_o), 4 * vff * (Ca_ss * exp(2 * vf) - 0.341 * Ca_o) / (exp(2 * vf) - 1)) +PhiCaL = if(abs(vf) < 1e-6, + 2 * phys.F * (Ca_ss - 0.341 * Ca_o), + 4 * vff * (Ca_ss * evf2 - 0.341 * Ca_o) / (evf2 - 1)) in [mC/L] -PhiCaNa = if(vf == 0, 1 [C/mol] * 1 * (0.75 * Na_ss - 0.75 * Na_o), 1 * vff * (0.75 * Na_ss * exp(1 * vf) - 0.75 * Na_o) / (exp(1 * vf) - 1)) +PhiCaNa = if(abs(vf) < 1e-6, + 0.75 * phys.F * (Na_ss - Na_o), + 0.75 * vff * (Na_ss * evf - Na_o) / (evf - 1)) in [mC/L] -PhiCaK = if(vf == 0, 1 [C/mol] * 1 * (0.75 * K_ss - 0.75 * K_o), 1 * vff * (0.75 * K_ss * exp(1 * vf) - 0.75 * K_o) / (exp(1 * vf) - 1)) +PhiCaK = if(abs(vf) < 1e-6, + 0.75 * phys.F * (K_ss - K_o), + 0.75 * vff * (K_ss * evf - K_o) / (evf - 1)) in [mC/L] PCa_base = 0.0001 [L/ms/F] in [L/ms/F] @@ -527,69 +537,44 @@ ICaL_total = ICaL + ICaK + ICaNa # [ikr] use membrane.V -A1 = 0.0264 [mS/uF] - in [mS/uF] -A11 = 0.0007868 [mS/uF] - in [mS/uF] -A2 = 4.986e-6 [mS/uF] - in [mS/uF] -A21 = 5.455e-6 [mS/uF] - in [mS/uF] -A3 = 0.001214 [mS/uF] - in [mS/uF] -A31 = 0.005509 [mS/uF] - in [mS/uF] -A4 = 1.854e-5 [mS/uF] - in [mS/uF] -A41 = 0.001416 [mS/uF] - in [mS/uF] -A51 = 0.4492 [mS/uF] - in [mS/uF] -A52 = 0.3181 [mS/uF] - in [mS/uF] -A53 = 0.149 [mS/uF] - in [mS/uF] -A61 = 0.01241 [mS/uF] - in [mS/uF] -A62 = 0.3226 [mS/uF] - in [mS/uF] -A63 = 0.008978 [mS/uF] - in [mS/uF] -B1 = 4.631e-5 [1/mV] - in [1/mV] -B11 = 1.535e-8 [1/mV] - in [1/mV] -B2 = -0.004226 [1/mV] - in [1/mV] -B21 = -0.1688 [1/mV] - in [1/mV] -B3 = 0.008516 [1/mV] - in [1/mV] -B31 = 7.771e-9 [1/mV] - in [1/mV] -B4 = -0.04641 [1/mV] - in [1/mV] -B41 = -0.02877 [1/mV] - in [1/mV] -B51 = 0.008595 [1/mV] - in [1/mV] -B52 = 3.613e-8 [1/mV] - in [1/mV] -B53 = 0.004668 [1/mV] - in [1/mV] -B61 = 0.1725 [1/mV] - in [1/mV] -B62 = -6.57499999999999990e-4 [1/mV] - in [1/mV] -B63 = -0.02215 [1/mV] - in [1/mV] +# Rate parameters +a1 = 0.0264 [1/ms] in [1/ms] +a2 = 4.986e-6 [1/ms] in [1/ms] +a3 = 0.001214 [1/ms] in [1/ms] +a4 = 1.854e-5 [1/ms] in [1/ms] +a11 = 0.0007868 [1/ms] in [1/ms] +a21 = 5.455e-6 [1/ms] in [1/ms] +a31 = 0.005509 [1/ms] in [1/ms] +a41 = 0.001416 [1/ms] in [1/ms] +a51 = 0.4492 [1/ms] in [1/ms] +a52 = 0.3181 [1/ms] in [1/ms] +a53 = 0.149 [1/ms] in [1/ms] +a61 = 0.01241 [1/ms] in [1/ms] +a62 = 0.3226 [1/ms] in [1/ms] +a63 = 0.008978 [1/ms] in [1/ms] +b1 = 4.631e-5 [1/mV] in [1/mV] +b2 = -0.004226 [1/mV] in [1/mV] +b3 = 0.008516 [1/mV] in [1/mV] +b4 = -0.04641 [1/mV] in [1/mV] +b11 = 1.535e-8 [1/mV] in [1/mV] +b21 = -0.1688 [1/mV] in [1/mV] +b31 = 7.771e-9 [1/mV] in [1/mV] +b41 = -0.02877 [1/mV] in [1/mV] +b51 = 0.008595 [1/mV] in [1/mV] +b52 = 3.613e-8 [1/mV] in [1/mV] +b53 = 0.004668 [1/mV] in [1/mV] +b61 = 0.1725 [1/mV] in [1/mV] +b62 = -6.575e-4 [1/mV] in [1/mV] +b63 = -0.02215 [1/mV] in [1/mV] +# Temperature parameters +Temp = 37 q1 = 4.843 -q11 = 4.942 q2 = 4.23 -q21 = 4.156 q3 = 4.962 -q31 = 4.22 q4 = 3.769 +q11 = 4.942 +q21 = 4.156 +q31 = 4.22 q41 = 1.459 q51 = 5 q52 = 4.663 @@ -597,26 +582,64 @@ q53 = 2.412 q61 = 5.568 q62 = 5 q63 = 5.682 -Kt = 0 [mS/uF] - in [mS/uF] -Ku = 0 [mS/uF] - in [mS/uF] -Temp = 37 -Vhalf = 1 [mV] - in [mV] +# Drug binding parameters +Kt = 0 [1/ms] in [1/ms] +Ku = 0 [1/ms] in [1/ms] +Vhalf = 1 [mV] in [mV] halfmax = 1 n = 1 Kmax = 0 -dot(C1) = -(A1 * exp(B1 * V) * C1 * exp((Temp - 20) * log(q1) / 10) - A2 * exp(B2 * V) * C2 * exp((Temp - 20) * log(q2) / 10)) - (A51 * exp(B51 * V) * C1 * exp((Temp - 20) * log(q51) / 10) - A61 * exp(B61 * V) * IC1 * exp((Temp - 20) * log(q61) / 10)) -dot(C2) = A1 * exp(B1 * V) * C1 * exp((Temp - 20) * log(q1) / 10) - A2 * exp(B2 * V) * C2 * exp((Temp - 20) * log(q2) / 10) - (A31 * exp(B31 * V) * C2 * exp((Temp - 20) * log(q31) / 10) - A41 * exp(B41 * V) * O * exp((Temp - 20) * log(q41) / 10)) - (A52 * exp(B52 * V) * C2 * exp((Temp - 20) * log(q52) / 10) - A62 * exp(B62 * V) * IC2 * exp((Temp - 20) * log(q62) / 10)) -dot(D) = 0 [1/ms] -dot(IC1) = -(A11 * exp(B11 * V) * IC1 * exp((Temp - 20) * log(q11) / 10) - A21 * exp(B21 * V) * IC2 * exp((Temp - 20) * log(q21) / 10)) + A51 * exp(B51 * V) * C1 * exp((Temp - 20) * log(q51) / 10) - A61 * exp(B61 * V) * IC1 * exp((Temp - 20) * log(q61) / 10) -dot(IC2) = A11 * exp(B11 * V) * IC1 * exp((Temp - 20) * log(q11) / 10) - A21 * exp(B21 * V) * IC2 * exp((Temp - 20) * log(q21) / 10) - (A3 * exp(B3 * V) * IC2 * exp((Temp - 20) * log(q3) / 10) - A4 * exp(B4 * V) * IO * exp((Temp - 20) * log(q4) / 10)) + A52 * exp(B52 * V) * C2 * exp((Temp - 20) * log(q52) / 10) - A62 * exp(B62 * V) * IC2 * exp((Temp - 20) * log(q62) / 10) -dot(IO) = A3 * exp(B3 * V) * IC2 * exp((Temp - 20) * log(q3) / 10) - A4 * exp(B4 * V) * IO * exp((Temp - 20) * log(q4) / 10) + A53 * exp(B53 * V) * O * exp((Temp - 20) * log(q53) / 10) - A63 * exp(B63 * V) * IO * exp((Temp - 20) * log(q63) / 10) - (Kmax * Ku * exp(n * log(D)) / (exp(n * log(D)) + halfmax) * IO - Ku * A53 * exp(B53 * V) * exp((Temp - 20) * log(q53) / 10) / (A63 * exp(B63 * V) * exp((Temp - 20) * log(q63) / 10)) * IObound) -dot(O) = A31 * exp(B31 * V) * C2 * exp((Temp - 20) * log(q31) / 10) - A41 * exp(B41 * V) * O * exp((Temp - 20) * log(q41) / 10) - (A53 * exp(B53 * V) * O * exp((Temp - 20) * log(q53) / 10) - A63 * exp(B63 * V) * IO * exp((Temp - 20) * log(q63) / 10)) - (Kmax * Ku * exp(n * log(D)) / (exp(n * log(D)) + halfmax) * O - Ku * Obound) -dot(Cbound) = -(Kt / (1 + exp(-(V - Vhalf) / 6.789 [mV])) * Cbound - Kt * Obound) - (Kt / (1 + exp(-(V - Vhalf) / 6.789 [mV])) * Cbound - Kt * IObound) -dot(IObound) = Kmax * Ku * exp(n * log(D)) / (exp(n * log(D)) + halfmax) * IO - Ku * A53 * exp(B53 * V) * exp((Temp - 20) * log(q53) / 10) / (A63 * exp(B63 * V) * exp((Temp - 20) * log(q63) / 10)) * IObound + Kt / (1 + exp(-(V - Vhalf) / 6.789 [mV])) * Cbound - Kt * IObound -dot(Obound) = Kmax * Ku * exp(n * log(D)) / (exp(n * log(D)) + halfmax) * O - Ku * Obound + Kt / (1 + exp(-(V - Vhalf) / 6.789 [mV])) * Cbound - Kt * Obound +D = 0 [mM] + in [mM] + desc: Drug concentration +# Rates +k1 = a1 * exp(b1 * V) * exp((Temp - 20) * log(q1) / 10) + in [1/ms] +k2 = a2 * exp(b2 * V) * exp((Temp - 20) * log(q2) / 10) + in [1/ms] +k3 = a3 * exp(b3 * V) * exp((Temp - 20) * log(q3) / 10) + in [1/ms] +k4 = a4 * exp(b4 * V) * exp((Temp - 20) * log(q4) / 10) + in [1/ms] +k10 = a63 * exp(b63 * V) * exp((Temp - 20) * log(q63) / 10) + in [1/ms] +k11 = a11 * exp(b11 * V) * exp((Temp - 20) * log(q11) / 10) + in [1/ms] +k21 = a21 * exp(b21 * V) * exp((Temp - 20) * log(q21) / 10) + in [1/ms] +k31 = a31 * exp(b31 * V) * exp((Temp - 20) * log(q31) / 10) + in [1/ms] +k41 = a41 * exp(b41 * V) * exp((Temp - 20) * log(q41) / 10) + in [1/ms] +k51 = a51 * exp(b51 * V) * exp((Temp - 20) * log(q51) / 10) + in [1/ms] +k52 = a52 * exp(b52 * V) * exp((Temp - 20) * log(q52) / 10) + in [1/ms] +k53 = a53 * exp(b53 * V) * exp((Temp - 20) * log(q53) / 10) + in [1/ms] +k61 = a61 * exp(b61 * V) * exp((Temp - 20) * log(q61) / 10) + in [1/ms] +k62 = a62 * exp(b62 * V) * exp((Temp - 20) * log(q62) / 10) + in [1/ms] +k63 = a63 * exp(b63 * V) * exp((Temp - 20) * log(q63) / 10) + in [1/ms] +r1 = if(D == 0 [mM], 0 [1/ms], Kmax * Ku * exp(n * log(D / 1 [mM])) / (exp(n * log(D / 1 [mM])) + halfmax)) + in [1/ms] +r2 = Ku * k53 / k63 + in [1/ms] +r3 = Kt / (1 + exp(-(V - Vhalf) / 6.789 [mV])) + in [1/ms] +# States +dot(C2) = (k1 * C1 - k2 * C2) - (k31 * C2 - k41 * O) - (k52 * C2 - k62 * IC2) +dot(C1) = -(k1 * C1 - k2 * C2) - (k51 * C1 - k61 * IC1) +dot(O) = (k31 * C2 - k41 * O) - (k53 * O - k10 * IO) - (r1 * O - Ku * Obound) +dot(IC2) = (k11 * IC1 - k21 * IC2) - (k3 * IC2 - k4 * IO) + (k52 * C2 - k62 * IC2) +dot(IC1) = -(k11 * IC1 - k21 * IC2) + (k51 * C1 - k61 * IC1) +dot(IO) = (k3 * IC2 - k4 * IO) + (k53 * O - k63 * IO) - (r1 * IO - r2 * IObound) +dot(Obound) = (r1 * O - Ku * Obound) + (r3 * Cbound - Kt * Obound) +dot(IObound) = (r1 * IO - r2 * IObound) + (r3 * Cbound - Kt * IObound) +dot(Cbound) = -(r3 * Cbound - Kt * Obound) - (r3 * Cbound - Kt * IObound) +# Current fKr = piecewise(cell.mode == 0, 1, cell.mode == 1, 1.3, 0.8) gKr = 4.65854545454545618e-2 [mS/uF] in [mS/uF] @@ -625,7 +648,7 @@ IKr = fKr * gKr * sqrt(extra.K_o / 5.4 [mM]) * O * (V - rev.EK) # # IKs: Slow delayed rectifier potassium current -# Page 11 of the supplement to [2] +# Page 11 of the supplement to [4] # # Modelled with two activation gates # @@ -653,7 +676,7 @@ IKs = fKs * gKs * KsCa * x1 * x2 * (V - rev.EKs) # # IK1: Inward rectifier potassium current -# Page 12 of the supplement to [2] +# Page 12 of the supplement to [4] # # Modelled with an activation channel and an instantaneous inactivation channel # @@ -679,7 +702,7 @@ IK1 = fK1 * gK1 * sqrt(K_o / 1 [mM]) * r * x * (V - rev.EK) # # INaCa: Sodium/calcium exchange current -# Page 12 of the supplement to [2] +# Page 12 of the supplement to [4] # [inaca] use membrane.V @@ -774,7 +797,7 @@ INaCa_total = INaCa + inacass.INaCa_ss # # INaCa_ss: Sodium/calcium exchanger current into the L-type subspace -# Page 12 of the supplement to [2] +# Page 12 of the supplement to [4] # [inacass] use membrane.V @@ -843,10 +866,9 @@ INaCa_ss = 0.2 * inaca.fNaCa * inaca.gNaCa * allo * (JncxNa + 2 * JncxCa) # # INaK: Sodium/potassium ATPase current # Based on Smith & Crampin 2004 https://doi.org/10.1016/j.pbiomolbio.2004.01.010 -# The formulation below was corrected from the O'Hara implementation, see -# https://docs.google.com/document/d/111fqNzQGvGAjB_PrkvejEhzqwROrR6czz_OBz7Ep-iM +# The formulation below was corrected from the O'Hara implementation, see [7]. # -# Page 14 of the supplement to [2] +# Page 14 of the supplement to [4] # [inak] use membrane.V @@ -940,7 +962,7 @@ INaK = fNaK * PNaK * (JnakNa + JnakK) # # IKb: Background potassium current -# Page 15 of the supplement to [2] +# Page 15 of the supplement to [4] # [ikb] use membrane.V @@ -954,7 +976,7 @@ IKb = fKb * gKb * xkb * (V - rev.EK) # # INab: Background sodium current -# Page 15 of the supplement to [2] +# Page 15 of the supplement to [4] # [inab] use membrane.V @@ -967,7 +989,7 @@ INab = PNab * V * phys.FFRT * (sodium.Na_i * evf - extra.Na_o) / (evf - 1) # # ICab: Background calcium current -# Page 15 of the supplement to [2] +# Page 15 of the supplement to [4] # [icab] use membrane.V @@ -980,7 +1002,7 @@ ICab = PCab * 4 * V * phys.FFRT * (calcium.Ca_i * evf2 - 0.341 * extra.Ca_o) / ( # # IpCa: Sarcolemmal calcium pump current -# Page 15 of the supplement to [2] +# Page 15 of the supplement to [4] # [ipca] GpCa = 0.0005 [A/F] @@ -991,7 +1013,7 @@ IpCa = GpCa * calcium.Ca_i / (0.0005 [mM] + calcium.Ca_i) # # Jrel: SR Calcium release flux via ryanodine receptor -# Page 17 of the supplement to [2] +# Page 17 of the supplement to [4] # [ryr] use calcium.Ca_jsr @@ -1029,7 +1051,7 @@ Jrel = (1 - camk.f) * Jrelnp + camk.f * Jrelp # # Jup: Calcium uptake via SERCA pump -# Page 17 of the supplement to [2] +# Page 17 of the supplement to [4] # [serca] use calcium.Ca_i, calcium.Ca_jsr, calcium.Ca_nsr @@ -1049,7 +1071,7 @@ Jtr = (Ca_nsr - Ca_jsr) / 100 [ms] # # Diffusion fluxes -# Page 16 of the supplement to [2] +# Page 16 of the supplement to [4] # [diff] JdiffNa = (sodium.Na_ss - sodium.Na_i) / 2 [ms] @@ -1061,7 +1083,7 @@ Jdiff = (calcium.Ca_ss - calcium.Ca_i) / 0.2 [ms] # # Intracellular sodium concentrations -# Page 18 of the supplement to [2] +# Page 18 of the supplement to [4] # [sodium] use cell.AFC, cell.vss, cell.vmyo @@ -1077,7 +1099,7 @@ dot(Na_ss) = -INa_ss_tot * AFC / vss - diff.JdiffNa # # Intracellular potassium concentrations -# Page 18 of the supplement to [2] +# Page 18 of the supplement to [4] # [potassium] use cell.AFC, cell.vss, cell.vmyo @@ -1101,7 +1123,7 @@ dot(K_ss) = -IK_ss_tot * AFC / vss - diff.JdiffK # # Intracellular calcium concentrations and buffers -# Page 18 of the supplement to [2] +# Page 18 of the supplement to [4] # [calcium] use cell.AFC, cell.vmyo, cell.vnsr, cell.vjsr, cell.vss @@ -1149,7 +1171,7 @@ dot(Ca_nsr) = serca.Jup - serca.Jtr * vjsr / vnsr # # Active CaMKII subunits. -# Equations given on page 16 of the supplement to [2]. +# Equations given on page 16 of the supplement to [4]. # Described in more detail in Hund et al. 2004. # [camk]