Tomek et al. 2019

Key: tomek2019development

A human-based ventricular model (ToR-Ord, endocardial, epicardial, midmyocardial) for simulations of electrophysiology and excitation-contraction coupling, from ionic to whole-organ dynamics, including the electrocardiogram. Validation based on substantial multiscale simulations supports the credibility of the ToR-ORd model under healthy and key disease conditions, as well as drug blockade. In addition, the process uncovers new theoretical insights into the biophysical properties of the L-type calcium current, which are critical for sodium and calcium dynamics. These insights enable the reformulation of L-type calcium current, as well as replacement of the hERG current model.

References

1. https://doi.org/10.7554/eLife.48890

Figure

Variables

0. V = -88.7638

1. CaMKt = 0.0111

2. Nai = 12.1025

3. Nass = 12.1029

4. Ki = 142.3002

5. Kss = 142.3002

6. Cass = 7.0305e-05

7. Cansr = 1.5211

8. Cajsr = 1.5214

9. Cai = 8.1583e-05

10. m = 0.00080572

11. h = 0.8286

12. j = 0.8284

13. hp = 0.6707

14. jp = 0.8281

15. mL = 0.0001629

16. hL = 0.5255

17. hLp = 0.2872

18. a = 0.00095098

19. iF = 0.9996

20. iS = 0.5936

21. ap = 0.00048454

22. iFp = 0.9996

23. iSp = 0.6538

24. d = 8.1084e-09

25. ff = 1.0

26. fs = 0.939

27. fcaf = 1.0

28. fcas = 0.9999

29. jca = 1.0

30. ffp = 1.0

31. fcafp = 1.0

32. nca_ss = 0.00066462

33. nca_i = 0.0012

34. C1 = 0.00070344

35. C2 = 0.00085109

36. C3 = 0.9981

37. I = 1.3289e-05

38. O = 0.00037585

39. xs1 = 0.248

40. xs2 = 0.00017707

41. Jrel_np = 1.6129e-22

42. Jrel_p = 1.2475e-20

Parameters

• diffusivity_V = 1.0

• CaMKo = 0.05

• KmCaM = 0.0015

• KmCaMK = 0.15

• aCaMK = 0.05

• bCaMK = 0.00068

• GpCa = 0.0005

• KmCap = 0.0005

• Acap = 0.00015335760000000003

• vjsr = 1.8237120000000002e-07

• vmyo = 2.583592000000001e-05

• vnsr = 2.0972688000000006e-06

• vss = 7.598800000000002e-07

• tauCa = 0.2

• tauK = 2.0

• tauNa = 2.0

• celltype = 0.0

• cao = 1.8

• ko = 5.0

• nao = 140.0

• F = 96485.0

• R = 8314.0

• T = 310.0

• zca = 2.0

• zk = 1.0

• zna = 1.0

• Jup_b = 1.0

• upScale = 1.0

• BSLmax = 1.124

• BSRmax = 0.047

• KmBSL = 0.0087

• KmBSR = 0.00087

• cli = 24.0

• csqnmax = 10.0

• kmcmdn = 0.00238

• kmcsqn = 0.8

• kmtrpn = 0.0005

• trpnmax = 0.07

• cmdnmax = 0.05

• ECl = -48.95253676506265

• PKNa = 0.01833

• fkatp = 0.0

• gkatp = 4.3195

• akik = 1.0

• bkik = 0.015384615384615385

• GNa = 11.7802

• thL = 200.0

• GNaL = 0.0279

• thLp = 600.0

• EKshift = 0.0

• Gto = 0.16

• Aff = 0.6

• ICaL_fractionSS = 0.8

• Kmn = 0.002

• k2n = 500.0

• offset = 0.0

• tjca = 75.0

• vShift = 0.0

• Afs = 0.4

• PCa = 8.3757e-05

• constA = 0.5238190247282047

• PCaK = 2.99347518e-08

• PCaNa = 1.0469625000000001e-07

• PCap = 9.213270000000001e-05

• gamma_cao = 0.6117017520062547

• gamma_ko = 0.8843718923169582

• gamma_nao = 0.8843718923169582

• PCaKp = 3.292822698000001e-08

• PCaNap = 1.1516587500000002e-07

• alpha_1 = 0.154375

• beta_1 = 0.1911

• GKr = 0.0321

• GKs = 0.0011

• GK1 = 0.6992

• INaCa_fractionSS = 0.35

• KmCaAct = 0.00015

• kcaon = 1500000.0

• kna1 = 15.0

• kna2 = 5.0

• kna3 = 88.12

• qca = 0.167

• qna = 0.5224

• wca = 60000.0

• wna = 60000.0

• wnaca = 5000.0

• Gncx = 0.0034

• k2_i = 5000.0

• k2_ss = 5000.0

• k5_i = 5000.0

• k5_ss = 5000.0

• h11_i = 0.9196480938416423

• h11_ss = 0.9196480938416423

• k1_i = 9501.466275659823

• k1_ss = 9501.466275659823

• H = 1e-07

• Khp = 1.698e-07

• Kki = 0.5

• Kko = 0.3582

• Kmgatp = 1.698e-07

• Knai0 = 9.073

• Knao0 = 27.78

• Knap = 224.0

• Kxkur = 292.0

• MgATP = 9.8

• delta = -0.155

• eP = 4.2

• k1p = 949.5

• k2m = 39.4

• k3m = 79300.0

• k3p = 1899.0

• k4m = 40.0

• Pnak = 15.4509

• a2 = 687.2

• a4 = 638.9999889283472

• b1 = 9.120000000000001

• GKb = 0.0189

• PNab = 1.9239e-09

• PCab = 5.9194e-08

• Fjunc = 1.0

• GClCa = 0.2843

• GClb = 0.00198

• KdClCa = 0.1

• Jrel_b = 1.5378

• bt = 4.75

• cajsr_half = 1.7

• a_rel = 2.375

• btp = 5.9375

• a_relp = 2.96875

Source code

OpenCL kernel

// CaMK
const Real CaMKb = CaMKo * (1.0 - CaMKt) / (1.0 + KmCaM / (Cass));
const Real CaMKa = CaMKb + CaMKt;
*_new_CaMKt = CaMKt + dt*(aCaMK * CaMKb * (CaMKb + CaMKt) - bCaMK * CaMKt);

// IpCa
const Real IpCa = GpCa * Cai / (KmCap + Cai);

// diff
const Real Jdiff = (Cass - Cai) / tauCa;
const Real JdiffK = (Kss - Ki) / tauK;
const Real JdiffNa = (Nass - Nai) / tauNa;

// trans_flux
const Real Jtr = (Cansr - Cajsr) / 60.0;

// SERCA
const Real Jleak = 0.0048825 * Cansr / 15.0;
const Real fJupp = 1.0 / (1.0 + KmCaMK / (CaMKa));
const Real Jupnp = upScale * 0.005425 * Cai / (Cai + 0.00092);
const Real Jupp = upScale * 2.75 * 0.005425 * Cai / (Cai + 0.00092 - 0.00017);
const Real Jup = Jup_b * ((1.0 - fJupp) * Jupnp + fJupp * Jupp - Jleak);

// membrane
const Real vffrt = V * F * F / (R * T);
const Real vfrt = V * F / (R * T);

// intracellular_ions
*_new_Cansr = Cansr + dt*(Jup - Jtr * vjsr / vnsr);
const Real Bcajsr = 1.0 / (1.0 + csqnmax * kmcsqn / (pow(kmcsqn + Cajsr, 2.0)));
const Real Bcass = 1.0 / (1.0 + BSRmax * KmBSR / (pow(KmBSR + Cass, 2.0)) + BSLmax * KmBSL / (pow(KmBSL + Cass, 2.0)));
const Real Bcai = 1.0 / (1.0 + cmdnmax * kmcmdn / (pow(kmcmdn + Cai, 2.0)) + trpnmax * kmtrpn / (pow(kmtrpn + Cai, 2.0)));

// reversal_potentials
const Real EK = R * T / (zk * F) * log(ko / (Ki));
const Real ENa = R * T / (zna * F) * log(nao / (Nai));
const Real EKs = R * T / (zk * F) * log((ko + PKNa * nao) / (Ki + PKNa * Nai));

// I_katp
const Real I_katp = fkatp * gkatp * akik * bkik * (V - EK);

// INa
const Real ah = ((V >= -40.0) ? 0.0 : 0.057 * exp(-(V + 80.0) / 6.8));
const Real aj = ((V >= -40.0) ? 0.0 : (-25428.0 * exp(0.2444 * V) - 6.948e-06 * exp(-0.04391 * V)) * (V + 37.78) / (1.0 + exp(0.311 * (V + 79.23))));
const Real bh = ((V >= -40.0) ? 0.77 / (0.13 * (1.0 + exp(-(V + 10.66) / 11.1))) : 2.7 * exp(0.079 * V) + 310000.0 * exp(0.3485 * V));
const Real bj = ((V >= -40.0) ? 0.6 * exp(0.057 * V) / (1.0 + exp(-0.1 * (V + 32.0))) : 0.02424 * exp(-0.01052 * V) / (1.0 + exp(-0.1378 * (V + 40.14))));
const Real fINap = 1.0 / (1.0 + KmCaMK / (CaMKa));
const Real hss = 1.0 / (pow(1.0 + exp((V + 71.55) / 7.43), 2.0));
const Real hssp = 1.0 / (pow(1.0 + exp((V + 77.55) / 7.43), 2.0));
const Real mss = 1.0 / (pow(1.0 + exp(-(V + 56.86) / 9.03), 2.0));
const Real tm = 0.1292 * exp(-pow((V + 45.79) / 15.54, 2.0)) + 0.06487 * exp(-pow((V - 4.823) / 51.12, 2.0));
const Real INa = GNa * (V - ENa) * pow(m, 3.0) * ((1.0 - fINap) * h * j + fINap * hp * jp);
const Real jss = hss;
const Real th = 1.0 / (ah + bh);
const Real tj = 1.0 / (aj + bj);
*_new_m = mss + (m - mss) * exp(-(dt / tm));
const Real tjp = 1.46 * tj;
*_new_h = hss + (h - hss) * exp(-(dt / th));
*_new_hp = hssp + (hp - hssp) * exp(-(dt / th));
*_new_j = jss + (j - jss) * exp(-(dt / tj));
*_new_jp = jss + (jp - jss) * exp(-(dt / tjp));

// INaL
const Real fINaLp = 1.0 / (1.0 + KmCaMK / (CaMKa));
const Real hLss = 1.0 / (1.0 + exp((V + 87.61) / 7.488));
const Real hLssp = 1.0 / (1.0 + exp((V + 93.81) / 7.488));
const Real mLss = 1.0 / (1.0 + exp(-(V + 42.85) / 5.264));
const Real tmL = 0.1292 * exp(-pow((V + 45.79) / 15.54, 2.0)) + 0.06487 * exp(-pow((V - 4.823) / 51.12, 2.0));
*_new_hL = hLss + (hL - hLss) * exp(-(dt / thL));
*_new_mL = mLss + (mL - mLss) * exp(-(dt / tmL));
const Real INaL = GNaL * (V - ENa) * mL * ((1.0 - fINaLp) * hL + fINaLp * hLp);
*_new_hLp = hLssp + (hLp - hLssp) * exp(-(dt / thLp));

// Ito
const Real fItop = 1.0 / (1.0 + KmCaMK / (CaMKa));
const Real AiF = 1.0 / (1.0 + exp((V + EKshift - 213.6) / 151.2));
const Real ass = 1.0 / (1.0 + exp(-(V + EKshift - 14.34) / 14.82));
const Real assp = 1.0 / (1.0 + exp(-(V + EKshift - 24.34) / 14.82));
const Real delta_epi = ((celltype == 1.0) ? 1.0 - 0.95 / (1.0 + exp((V + EKshift + 70.0) / 5.0)) : 1.0);
const Real dti_develop = 1.354 + 0.0001 / (exp((V + EKshift - 167.4) / 15.89) + exp(-(V + EKshift - 12.23) / 0.2154));
const Real dti_recover = 1.0 - 0.5 / (1.0 + exp((V + EKshift + 70.0) / 20.0));
const Real iss = 1.0 / (1.0 + exp((V + EKshift + 43.94) / 5.711));
const Real ta = 1.0515 / (1.0 / (1.2089 * (1.0 + exp(-(V + EKshift - 18.4099) / 29.3814))) + 3.5 / (1.0 + exp((V + EKshift + 100.0) / 29.3814)));
const Real tiF_b = 4.562 + 1.0 / (0.3933 * exp(-(V + EKshift + 100.0) / 100.0) + 0.08004 * exp((V + EKshift + 50.0) / 16.59));
const Real tiS_b = 23.62 + 1.0 / (0.001416 * exp(-(V + EKshift + 96.52) / 59.05) + 1.78e-08 * exp((V + EKshift + 114.1) / 8.079));
const Real AiS = 1.0 - AiF;
const Real tiF = tiF_b * delta_epi;
const Real tiS = tiS_b * delta_epi;
*_new_a = ass + (a - ass) * exp(-(dt / ta));
*_new_ap = assp + (ap - assp) * exp(-(dt / ta));
const Real i = AiF * iF + AiS * iS;
const Real ip = AiF * iFp + AiS * iSp;
const Real tiFp = dti_develop * dti_recover * tiF;
const Real tiSp = dti_develop * dti_recover * tiS;
*_new_iF = iss + (iF - iss) * exp(-(dt / tiF));
*_new_iS = iss + (iS - iss) * exp(-(dt / tiS));
const Real Ito = Gto * (V - EK) * ((1.0 - fItop) * a * i + fItop * ap * ip);
*_new_iFp = iss + (iFp - iss) * exp(-(dt / tiFp));
*_new_iSp = iss + (iSp - iss) * exp(-(dt / tiSp));

// ICaL
const Real Afcaf = 0.3 + 0.6 / (1.0 + exp((V - 10.0) / 10.0));
const Real Ii = 0.5 * (Nai + Ki + cli + 4.0 * Cai) / 1000.0;
const Real Iss = 0.5 * (Nass + Kss + cli + 4.0 * Cass) / 1000.0;
const Real dss = ((V >= 31.4978) ? 1.0 : 1.0763 * exp(-1.007 * exp(-0.0829 * V)));
const Real fICaLp = 1.0 / (1.0 + KmCaMK / (CaMKa));
const Real fss = 1.0 / (1.0 + exp((V + 19.58) / 3.696));
const Real jcass = 1.0 / (1.0 + exp((V + 18.08) / 2.7916));
const Real km2n = jca * 1.0;
const Real tfcaf = 7.0 + 1.0 / (0.04 * exp(-(V - 4.0) / 7.0) + 0.04 * exp((V - 4.0) / 7.0));
const Real tfcas = 100.0 + 1.0 / (0.00012 * exp(-V / 3.0) + 0.00012 * exp(V / 7.0));
const Real tff = 7.0 + 1.0 / (0.0045 * exp(-(V + 20.0) / 10.0) + 0.0045 * exp((V + 20.0) / 10.0));
const Real tfs = 1000.0 + 1.0 / (3.5e-05 * exp(-(V + 5.0) / 4.0) + 3.5e-05 * exp((V + 5.0) / 6.0));
const Real Afcas = 1.0 - Afcaf;
const Real anca_i = 1.0 / (k2n / (km2n) + pow(1.0 + Kmn / (Cai), 4.0));
const Real anca_ss = 1.0 / (k2n / (km2n) + pow(1.0 + Kmn / (Cass), 4.0));
const Real fcass = fss;
const Real td = offset + 0.6 + 1.0 / (exp(-0.05 * (V + vShift + 6.0)) + exp(0.09 * (V + vShift + 14.0)));
const Real tfcafp = 2.5 * tfcaf;
const Real tffp = 2.5 * tff;
*_new_ff = fss + (ff - fss) * exp(-(dt / tff));
*_new_fs = fss + (fs - fss) * exp(-(dt / tfs));
*_new_jca = jcass + (jca - jcass) * exp(-(dt / tjca));
const Real f = Aff * ff + Afs * fs;
const Real fca = Afcaf * fcaf + Afcas * fcas;
const Real fcap = Afcaf * fcafp + Afcas * fcas;
const Real fp = Aff * ffp + Afs * fs;
const Real gamma_cai = exp(-constA * 4.0 * (sqrt(Ii) / (1.0 + sqrt(Ii)) - 0.3 * Ii));
const Real gamma_cass = exp(-constA * 4.0 * (sqrt(Iss) / (1.0 + sqrt(Iss)) - 0.3 * Iss));
const Real gamma_ki = exp(-constA * (sqrt(Ii) / (1.0 + sqrt(Ii)) - 0.3 * Ii));
const Real gamma_kss = exp(-constA * (sqrt(Iss) / (1.0 + sqrt(Iss)) - 0.3 * Iss));
const Real gamma_nai = exp(-constA * (sqrt(Ii) / (1.0 + sqrt(Ii)) - 0.3 * Ii));
const Real gamma_nass = exp(-constA * (sqrt(Iss) / (1.0 + sqrt(Iss)) - 0.3 * Iss));
*_new_d = dss + (d - dss) * exp(-(dt / td));
*_new_fcaf = fcass + (fcaf - fcass) * exp(-(dt / tfcaf));
*_new_fcafp = fcass + (fcafp - fcass) * exp(-(dt / tfcafp));
*_new_fcas = fcass + (fcas - fcass) * exp(-(dt / tfcas));
*_new_ffp = fss + (ffp - fss) * exp(-(dt / tffp));
*_new_nca_i = nca_i + dt*(anca_i * k2n - nca_i * km2n);
*_new_nca_ss = nca_ss + dt*(anca_ss * k2n - nca_ss * km2n);
const Real PhiCaK_i = vffrt * safe_divide(gamma_ki * Ki * exp(vfrt) - gamma_ko * ko, exp(vfrt) - 1.0);
const Real PhiCaK_ss = vffrt * safe_divide(gamma_kss * Kss * exp(vfrt) - gamma_ko * ko, exp(vfrt) - 1.0);
const Real PhiCaL_i = 4.0 * vffrt * safe_divide(gamma_cai * Cai * exp(2.0 * vfrt) - gamma_cao * cao, exp(2.0 * vfrt) - 1.0);
const Real PhiCaL_ss = 4.0 * vffrt * safe_divide(gamma_cass * Cass * exp(2.0 * vfrt) - gamma_cao * cao, exp(2.0 * vfrt) - 1.0);
const Real PhiCaNa_i = vffrt * safe_divide(gamma_nai * Nai * exp(vfrt) - gamma_nao * nao, exp(vfrt) - 1.0);
const Real PhiCaNa_ss = vffrt * safe_divide(gamma_nass * Nass * exp(vfrt) - gamma_nao * nao, exp(vfrt) - 1.0);
const Real ICaK_i = (1.0 - ICaL_fractionSS) * ((1.0 - fICaLp) * PCaK * PhiCaK_i * d * (f * (1.0 - nca_i) + jca * fca * nca_i) + fICaLp * PCaKp * PhiCaK_i * d * (fp * (1.0 - nca_i) + jca * fcap * nca_i));
const Real ICaK_ss = ICaL_fractionSS * ((1.0 - fICaLp) * PCaK * PhiCaK_ss * d * (f * (1.0 - nca_ss) + jca * fca * nca_ss) + fICaLp * PCaKp * PhiCaK_ss * d * (fp * (1.0 - nca_ss) + jca * fcap * nca_ss));
const Real ICaL_i = (1.0 - ICaL_fractionSS) * ((1.0 - fICaLp) * PCa * PhiCaL_i * d * (f * (1.0 - nca_i) + jca * fca * nca_i) + fICaLp * PCap * PhiCaL_i * d * (fp * (1.0 - nca_i) + jca * fcap * nca_i));
const Real ICaL_ss = ICaL_fractionSS * ((1.0 - fICaLp) * PCa * PhiCaL_ss * d * (f * (1.0 - nca_ss) + jca * fca * nca_ss) + fICaLp * PCap * PhiCaL_ss * d * (fp * (1.0 - nca_ss) + jca * fcap * nca_ss));
const Real ICaNa_i = (1.0 - ICaL_fractionSS) * ((1.0 - fICaLp) * PCaNa * PhiCaNa_i * d * (f * (1.0 - nca_i) + jca * fca * nca_i) + fICaLp * PCaNap * PhiCaNa_i * d * (fp * (1.0 - nca_i) + jca * fcap * nca_i));
const Real ICaNa_ss = ICaL_fractionSS * ((1.0 - fICaLp) * PCaNa * PhiCaNa_ss * d * (f * (1.0 - nca_ss) + jca * fca * nca_ss) + fICaLp * PCaNap * PhiCaNa_ss * d * (fp * (1.0 - nca_ss) + jca * fcap * nca_ss));
const Real ICaK = ICaK_ss + ICaK_i;
const Real ICaL = ICaL_ss + ICaL_i;
const Real ICaNa = ICaNa_ss + ICaNa_i;

// IKr
const Real alpha = 0.1161 * exp(0.299 * vfrt);
const Real alpha_2 = 0.0578 * exp(0.971 * vfrt);
const Real alpha_C2ToI = 5.2e-05 * exp(1.525 * vfrt);
const Real alpha_i = 0.2533 * exp(0.5953 * vfrt);
const Real beta = 0.2442 * exp(-1.604 * vfrt);
const Real beta_2 = 0.000349 * exp(-1.062 * vfrt);
const Real beta_i = 0.06525 * exp(-0.8209 * vfrt);
const Real beta_ItoC2 = beta_2 * beta_i * alpha_C2ToI / (alpha_2 * alpha_i);
*_new_C2 = C2 + dt*(alpha * C3 + beta_1 * C1 - (beta + alpha_1) * C2);
*_new_C3 = C3 + dt*(beta * C2 - alpha * C3);
*_new_O = O + dt*(alpha_2 * C1 + beta_i * I - (beta_2 + alpha_i) * O);
const Real IKr = GKr * sqrt(ko / 5.0) * O * (V - EK);
*_new_C1 = C1 + dt*(alpha_1 * C2 + beta_2 * O + beta_ItoC2 * I - (beta_1 + alpha_2 + alpha_C2ToI) * C1);
*_new_I = I + dt*(alpha_C2ToI * C1 + alpha_i * O - (beta_ItoC2 + beta_i) * I);

// IKs
const Real KsCa = 1.0 + 0.6 / (1.0 + pow(3.8e-05 / (Cai), 1.4));
const Real txs1 = 817.3 + 1.0 / (0.0002326 * exp((V + 48.28) / 17.8) + 0.001292 * exp(-(V + 210.0) / 230.0));
const Real txs2 = 1.0 / (0.01 * exp((V - 50.0) / 20.0) + 0.0193 * exp(-(V + 66.54) / 31.0));
const Real xs1ss = 1.0 / (1.0 + exp(-(V + 11.6) / 8.932));
const Real xs2ss = xs1ss;
*_new_xs1 = xs1ss + (xs1 - xs1ss) * exp(-(dt / txs1));
const Real IKs = GKs * KsCa * xs1 * xs2 * (V - EKs);
*_new_xs2 = xs2ss + (xs2 - xs2ss) * exp(-(dt / txs2));

// IK1
const Real aK1 = 4.094 / (1.0 + exp(0.1217 * (V - EK - 49.934)));
const Real bK1 = (15.72 * exp(0.0674 * (V - EK - 3.257)) + exp(0.0618 * (V - EK - 594.31))) / (1.0 + exp(-0.1629 * (V - EK + 14.207)));
const Real K1ss = aK1 / (aK1 + bK1);
const Real IK1 = GK1 * sqrt(ko / 5.0) * K1ss * (V - EK);

// INaCa
const Real allo_i = 1.0 / (1.0 + pow(KmCaAct / (Cai), 2.0));
const Real allo_ss = 1.0 / (1.0 + pow(KmCaAct / (Cass), 2.0));
const Real h4_i = 1.0 + Nai / kna1 * (1.0 + Nai / kna2);
const Real h4_ss = 1.0 + Nass / kna1 * (1.0 + Nass / kna2);
const Real hca = exp(qca * vfrt);
const Real hna = exp(qna * vfrt);
const Real h1_i = 1.0 + Nai / kna3 * (1.0 + hna);
const Real h1_ss = 1.0 + Nass / kna3 * (1.0 + hna);
const Real h5_i = Nai * Nai / (h4_i * kna1 * kna2);
const Real h5_ss = Nass * Nass / (h4_ss * kna1 * kna2);
const Real h6_i = 1.0 / (h4_i);
const Real h6_ss = 1.0 / (h4_ss);
const Real h7_i = 1.0 + nao / kna3 * (1.0 + 1.0 / (hna));
const Real h7_ss = 1.0 + nao / kna3 * (1.0 + 1.0 / (hna));
const Real h2_i = Nai * hna / (kna3 * h1_i);
const Real h2_ss = Nass * hna / (kna3 * h1_ss);
const Real h3_i = 1.0 / (h1_i);
const Real h3_ss = 1.0 / (h1_ss);
const Real h8_i = nao / (kna3 * hna * h7_i);
const Real h8_ss = nao / (kna3 * hna * h7_ss);
const Real h9_i = 1.0 / (h7_i);
const Real h9_ss = 1.0 / (h7_ss);
const Real k6_i = h6_i * Cai * kcaon;
const Real k6_ss = h6_ss * Cass * kcaon;
const Real k3p_i = h9_i * wca;
const Real k3p_ss = h9_ss * wca;
const Real k3pp_i = h8_i * wnaca;
const Real k3pp_ss = h8_ss * wnaca;
const Real k4p_i = h3_i * wca / (hca);
const Real k4p_ss = h3_ss * wca / (hca);
const Real k4pp_i = h2_i * wnaca;
const Real k4pp_ss = h2_ss * wnaca;
const Real k7_i = h5_i * h2_i * wna;
const Real k7_ss = h5_ss * h2_ss * wna;
const Real k8_i = h8_i * h11_i * wna;
const Real k8_ss = h8_ss * h11_ss * wna;
const Real k3_i = k3p_i + k3pp_i;
const Real k3_ss = k3p_ss + k3pp_ss;
const Real k4_i = k4p_i + k4pp_i;
const Real k4_ss = k4p_ss + k4pp_ss;
const Real x1_i = k2_i * k4_i * (k7_i + k6_i) + k5_i * k7_i * (k2_i + k3_i);
const Real x1_ss = k2_ss * k4_ss * (k7_ss + k6_ss) + k5_ss * k7_ss * (k2_ss + k3_ss);
const Real x2_i = k1_i * k7_i * (k4_i + k5_i) + k4_i * k6_i * (k1_i + k8_i);
const Real x2_ss = k1_ss * k7_ss * (k4_ss + k5_ss) + k4_ss * k6_ss * (k1_ss + k8_ss);
const Real x3_i = k1_i * k3_i * (k7_i + k6_i) + k8_i * k6_i * (k2_i + k3_i);
const Real x3_ss = k1_ss * k3_ss * (k7_ss + k6_ss) + k8_ss * k6_ss * (k2_ss + k3_ss);
const Real x4_i = k2_i * k8_i * (k4_i + k5_i) + k3_i * k5_i * (k1_i + k8_i);
const Real x4_ss = k2_ss * k8_ss * (k4_ss + k5_ss) + k3_ss * k5_ss * (k1_ss + k8_ss);
const Real E1_i = x1_i / (x1_i + x2_i + x3_i + x4_i);
const Real E1_ss = x1_ss / (x1_ss + x2_ss + x3_ss + x4_ss);
const Real E2_i = x2_i / (x1_i + x2_i + x3_i + x4_i);
const Real E2_ss = x2_ss / (x1_ss + x2_ss + x3_ss + x4_ss);
const Real E3_i = x3_i / (x1_i + x2_i + x3_i + x4_i);
const Real E3_ss = x3_ss / (x1_ss + x2_ss + x3_ss + x4_ss);
const Real E4_i = x4_i / (x1_i + x2_i + x3_i + x4_i);
const Real E4_ss = x4_ss / (x1_ss + x2_ss + x3_ss + x4_ss);
const Real JncxCa_i = E2_i * k2_i - E1_i * k1_i;
const Real JncxCa_ss = E2_ss * k2_ss - E1_ss * k1_ss;
const Real JncxNa_i = 3.0 * (E4_i * k7_i - E1_i * k8_i) + E3_i * k4pp_i - E2_i * k3pp_i;
const Real JncxNa_ss = 3.0 * (E4_ss * k7_ss - E1_ss * k8_ss) + E3_ss * k4pp_ss - E2_ss * k3pp_ss;
const Real INaCa_i = (1.0 - INaCa_fractionSS) * Gncx * allo_i * (zna * JncxNa_i + zca * JncxCa_i);
const Real INaCa_ss = INaCa_fractionSS * Gncx * allo_ss * (zna * JncxNa_ss + zca * JncxCa_ss);

// INaK
const Real Knai = Knai0 * exp(delta * vfrt / 3.0);
const Real Knao = Knao0 * exp((1.0 - delta) * vfrt / 3.0);
const Real P = eP / (1.0 + H / Khp + Nai / Knap + Ki / Kxkur);
const Real a1 = k1p * pow(Nai / (Knai), 3.0) / (pow(1.0 + Nai / (Knai), 3.0) + pow(1.0 + Ki / Kki, 2.0) - 1.0);
const Real a3 = k3p * pow(ko / Kko, 2.0) / (pow(1.0 + nao / (Knao), 3.0) + pow(1.0 + ko / Kko, 2.0) - 1.0);
const Real b2 = k2m * pow(nao / (Knao), 3.0) / (pow(1.0 + nao / (Knao), 3.0) + pow(1.0 + ko / Kko, 2.0) - 1.0);
const Real b3 = k3m * P * H / (1.0 + MgATP / Kmgatp);
const Real b4 = k4m * pow(Ki / Kki, 2.0) / (pow(1.0 + Nai / (Knai), 3.0) + pow(1.0 + Ki / Kki, 2.0) - 1.0);
const Real x1 = a4 * a1 * a2 + b2 * b4 * b3 + a2 * b4 * b3 + b3 * a1 * a2;
const Real x2 = b2 * b1 * b4 + a1 * a2 * a3 + a3 * b1 * b4 + a2 * a3 * b4;
const Real x3 = a2 * a3 * a4 + b3 * b2 * b1 + b2 * b1 * a4 + a3 * a4 * b1;
const Real x4 = b4 * b3 * b2 + a3 * a4 * a1 + b2 * a4 * a1 + b3 * b2 * a1;
const Real E1 = x1 / (x1 + x2 + x3 + x4);
const Real E2 = x2 / (x1 + x2 + x3 + x4);
const Real E3 = x3 / (x1 + x2 + x3 + x4);
const Real E4 = x4 / (x1 + x2 + x3 + x4);
const Real JnakK = 2.0 * (E4 * b1 - E3 * a1);
const Real JnakNa = 3.0 * (E1 * a3 - E2 * b3);
const Real INaK = Pnak * (zna * JnakNa + zk * JnakK);

// IKb
const Real xkb = 1.0 / (1.0 + exp(-(V - 10.8968) / 23.9871));
const Real IKb = GKb * xkb * (V - EK);

// INab
const Real INab = PNab * vffrt * safe_divide(Nai * exp(vfrt) - nao, exp(vfrt) - 1.0);

// ICab
const Real ICab = PCab * 4.0 * vffrt * safe_divide(gamma_cai * Cai * exp(2.0 * vfrt) - gamma_cao * cao, exp(2.0 * vfrt) - 1.0);

// ICl
const Real IClCa_junc = Fjunc * GClCa / (1.0 + KdClCa / (Cass)) * (V - ECl);
const Real IClCa_sl = (1.0 - Fjunc) * GClCa / (1.0 + KdClCa / (Cai)) * (V - ECl);
const Real IClb = GClb * (V - ECl);
const Real IClCa = IClCa_junc + IClCa_sl;

// ryr
const Real fJrelp = 1.0 / (1.0 + KmCaMK / (CaMKa));
const Real Jrel = Jrel_b * ((1.0 - fJrelp) * Jrel_np + fJrelp * Jrel_p);
const Real tau_rel_b = bt / (1.0 + 0.0123 / (Cajsr));
const Real Jrel_inf_b = -a_rel * ICaL_ss / 1.0 / (1.0 + pow(cajsr_half / (Cajsr), 8.0));
const Real tau_rel = ((tau_rel_b < 0.001) ? 0.001 : tau_rel_b);
const Real tau_relp_b = btp / (1.0 + 0.0123 / (Cajsr));
const Real Jrel_inf = ((celltype == 2.0) ? Jrel_inf_b * 1.7 : Jrel_inf_b);
const Real Jrel_infp_b = -a_relp * ICaL_ss / 1.0 / (1.0 + pow(cajsr_half / (Cajsr), 8.0));
const Real tau_relp = ((tau_relp_b < 0.001) ? 0.001 : tau_relp_b);
*_new_Jrel_np = Jrel_inf + (Jrel_np - Jrel_inf) * exp(-(dt / tau_rel));
const Real Jrel_infp = ((celltype == 2.0) ? Jrel_infp_b * 1.7 : Jrel_infp_b);
*_new_Jrel_p = Jrel_infp + (Jrel_p - Jrel_infp) * exp(-(dt / tau_relp));

// *remaining*
*_new_V = V + dt*(-(INa + INaL + Ito + ICaL + ICaNa + ICaK + IKr + IKs + IK1 + INaCa_i + INaCa_ss + INaK + INab + IKb + IpCa + ICab + IClCa + IClb + I_katp) + _diffuse_V);
*_new_Cai = Cai + dt*(Bcai * (-(ICaL_i + IpCa + ICab - 2.0 * INaCa_i) * Acap / (2.0 * F * vmyo) - Jup * vnsr / vmyo + Jdiff * vss / vmyo));
*_new_Cajsr = Cajsr + dt*(Bcajsr * (Jtr - Jrel));
*_new_Cass = Cass + dt*(Bcass * (-(ICaL_ss - 2.0 * INaCa_ss) * Acap / (2.0 * F * vss) + Jrel * vjsr / vss - Jdiff));
*_new_Ki = Ki + dt*(-(Ito + IKr + IKs + IK1 + IKb + I_katp - 2.0 * INaK + ICaK_i) * Acap / (F * vmyo) + JdiffK * vss / vmyo);
*_new_Kss = Kss + dt*(-ICaK_ss * Acap / (F * vss) - JdiffK);
*_new_Nai = Nai + dt*(-(INa + INaL + 3.0 * INaCa_i + ICaNa_i + 3.0 * INaK + INab) * Acap / (F * vmyo) + JdiffNa * vss / vmyo);
*_new_Nass = Nass + dt*(-(ICaNa_ss + 3.0 * INaCa_ss) * Acap / (F * vss) - JdiffNa);

Additional metadata

keywords:
- excitable media
- electrophysiology
- heart
- human
- ventricle
initial conditions:
  endo:
    V: -88.7638
    CaMKt: 0.0111
    Nai: 12.1025
    Nass: 12.1029
    Ki: 142.3002
    Kss: 142.3002
    Cass: 7.0305e-05
    Cansr: 1.5211
    Cajsr: 1.5214
    Cai: 8.1583e-05
    m: 0.00080572
    h: 0.8286
    j: 0.8284
    hp: 0.6707
    jp: 0.8281
    mL: 0.0001629
    hL: 0.5255
    hLp: 0.2872
    a: 0.00095098
    iF: 0.9996
    iS: 0.5936
    ap: 0.00048454
    iFp: 0.9996
    iSp: 0.6538
    d: 8.1084e-09
    ff: 1.0
    fs: 0.939
    fcaf: 1.0
    fcas: 0.9999
    jca: 1.0
    ffp: 1.0
    fcafp: 1.0
    nca_ss: 0.00066462
    nca_i: 0.0012
    C1: 0.00070344
    C2: 0.00085109
    C3: 0.9981
    I: 1.3289e-05
    O: 0.00037585
    xs1: 0.248
    xs2: 0.00017707
    Jrel_np: 1.6129e-22
    Jrel_p: 1.2475e-20
  epi:
    V: -89.14
    CaMKt: 0.0129
    Nai: 12.8363
    Nass: 12.8366
    Ki: 142.6951
    Kss: 142.6951
    Cass: 5.7672e-05
    Cansr: 1.8119
    Cajsr: 1.8102
    Cai: 6.6309e-05
    m: 0.00074303
    h: 0.836
    j: 0.8359
    hp: 0.6828
    jp: 0.8357
    mL: 0.00015166
    hL: 0.5401
    hLp: 0.3034
    a: 0.00092716
    iF: 0.9996
    iS: 0.9996
    ap: 0.0004724
    iFp: 0.9996
    iSp: 0.9996
    d: 0.0
    ff: 1.0
    fs: 0.9485
    fcaf: 1.0
    fcas: 0.9999
    jca: 1.0
    ffp: 1.0
    fcafp: 1.0
    nca_ss: 0.00030853
    nca_i: 0.00053006
    C1: 0.00067941
    C2: 0.00082869
    C3: 0.9982
    I: 9.5416e-06
    O: 0.00027561
    xs1: 0.2309
    xs2: 0.00016975
    Jrel_np: 2.8189e-24
    Jrel_p: 0.0
  mid:
    V: -89.1704
    CaMKt: 0.0192
    Nai: 15.0038
    Nass: 15.0043
    Ki: 143.0403
    Kss: 143.0402
    Cass: 6.5781e-05
    Cansr: 1.9557
    Cajsr: 1.9593
    Cai: 8.166e-05
    m: 0.00073818
    h: 0.8365
    j: 0.8363
    hp: 0.6838
    jp: 0.8358
    mL: 0.00015079
    hL: 0.5327
    hLp: 0.2834
    a: 0.00092527
    iF: 0.9996
    iS: 0.5671
    ap: 0.00047143
    iFp: 0.9996
    iSp: 0.6261
    d: 0.0
    ff: 1.0
    fs: 0.92
    fcaf: 1.0
    fcas: 0.9998
    jca: 1.0
    ffp: 1.0
    fcafp: 1.0
    nca_ss: 0.00051399
    nca_i: 0.0012
    C1: 0.0006956
    C2: 0.00082672
    C3: 0.9979
    I: 1.8784e-05
    O: 0.00054206
    xs1: 0.2653
    xs2: 0.00016921
    Jrel_np: 0.0
    Jrel_p: 0.0
parameter sets:
  endo:
    CaMKo: 0.05
    KmCaM: 0.0015
    KmCaMK: 0.15
    aCaMK: 0.05
    bCaMK: 0.00068
    GpCa: 0.0005
    KmCap: 0.0005
    Acap: 0.00015335760000000003
    vjsr: 1.8237120000000002e-07
    vmyo: 2.583592000000001e-05
    vnsr: 2.0972688000000006e-06
    vss: 7.598800000000002e-07
    tauCa: 0.2
    tauK: 2.0
    tauNa: 2.0
    celltype: 0.0
    cao: 1.8
    ko: 5.0
    nao: 140.0
    F: 96485.0
    R: 8314.0
    T: 310.0
    zca: 2.0
    zk: 1.0
    zna: 1.0
    Jup_b: 1.0
    upScale: 1.0
    BSLmax: 1.124
    BSRmax: 0.047
    KmBSL: 0.0087
    KmBSR: 0.00087
    cli: 24.0
    csqnmax: 10.0
    kmcmdn: 0.00238
    kmcsqn: 0.8
    kmtrpn: 0.0005
    trpnmax: 0.07
    cmdnmax: 0.05
    ECl: -48.95253676506265
    PKNa: 0.01833
    fkatp: 0.0
    gkatp: 4.3195
    akik: 1.0
    bkik: 0.015384615384615385
    GNa: 11.7802
    thL: 200.0
    GNaL: 0.0279
    thLp: 600.0
    EKshift: 0.0
    Gto: 0.16
    Aff: 0.6
    ICaL_fractionSS: 0.8
    Kmn: 0.002
    k2n: 500.0
    offset: 0.0
    tjca: 75.0
    vShift: 0.0
    Afs: 0.4
    PCa: 8.3757e-05
    constA: 0.5238190247282047
    PCaK: 2.99347518e-08
    PCaNa: 1.0469625000000001e-07
    PCap: 9.213270000000001e-05
    gamma_cao: 0.6117017520062547
    gamma_ko: 0.8843718923169582
    gamma_nao: 0.8843718923169582
    PCaKp: 3.292822698000001e-08
    PCaNap: 1.1516587500000002e-07
    alpha_1: 0.154375
    beta_1: 0.1911
    GKr: 0.0321
    GKs: 0.0011
    GK1: 0.6992
    INaCa_fractionSS: 0.35
    KmCaAct: 0.00015
    kcaon: 1500000.0
    kna1: 15.0
    kna2: 5.0
    kna3: 88.12
    qca: 0.167
    qna: 0.5224
    wca: 60000.0
    wna: 60000.0
    wnaca: 5000.0
    Gncx: 0.0034
    k2_i: 5000.0
    k2_ss: 5000.0
    k5_i: 5000.0
    k5_ss: 5000.0
    h11_i: 0.9196480938416423
    h11_ss: 0.9196480938416423
    k1_i: 9501.466275659823
    k1_ss: 9501.466275659823
    H: 1.0e-07
    Khp: 1.698e-07
    Kki: 0.5
    Kko: 0.3582
    Kmgatp: 1.698e-07
    Knai0: 9.073
    Knao0: 27.78
    Knap: 224.0
    Kxkur: 292.0
    MgATP: 9.8
    delta: -0.155
    eP: 4.2
    k1p: 949.5
    k2m: 39.4
    k3m: 79300.0
    k3p: 1899.0
    k4m: 40.0
    Pnak: 15.4509
    a2: 687.2
    a4: 638.9999889283472
    b1: 9.120000000000001
    GKb: 0.0189
    PNab: 1.9239e-09
    PCab: 5.9194e-08
    Fjunc: 1.0
    GClCa: 0.2843
    GClb: 0.00198
    KdClCa: 0.1
    Jrel_b: 1.5378
    bt: 4.75
    cajsr_half: 1.7
    a_rel: 2.375
    btp: 5.9375
    a_relp: 2.96875
  epi:
    CaMKo: 0.05
    KmCaM: 0.0015
    KmCaMK: 0.15
    aCaMK: 0.05
    bCaMK: 0.00068
    GpCa: 0.0005
    KmCap: 0.0005
    Acap: 0.00015335760000000003
    vjsr: 1.8237120000000002e-07
    vmyo: 2.583592000000001e-05
    vnsr: 2.0972688000000006e-06
    vss: 7.598800000000002e-07
    tauCa: 0.2
    tauK: 2.0
    tauNa: 2.0
    celltype: 1.0
    cao: 1.8
    ko: 5.0
    nao: 140.0
    F: 96485.0
    R: 8314.0
    T: 310.0
    zca: 2.0
    zk: 1.0
    zna: 1.0
    Jup_b: 1.0
    upScale: 1.3
    BSLmax: 1.124
    BSRmax: 0.047
    KmBSL: 0.0087
    KmBSR: 0.00087
    cli: 24.0
    csqnmax: 10.0
    kmcmdn: 0.00238
    kmcsqn: 0.8
    kmtrpn: 0.0005
    trpnmax: 0.07
    cmdnmax: 0.065
    ECl: -48.95253676506265
    PKNa: 0.01833
    fkatp: 0.0
    gkatp: 4.3195
    akik: 1.0
    bkik: 0.015384615384615385
    GNa: 11.7802
    thL: 200.0
    GNaL: 0.01674
    thLp: 600.0
    EKshift: 0.0
    Gto: 0.32
    Aff: 0.6
    ICaL_fractionSS: 0.8
    Kmn: 0.002
    k2n: 500.0
    offset: 0.0
    tjca: 75.0
    vShift: 0.0
    Afs: 0.4
    PCa: 0.00010050840000000001
    constA: 0.5238190247282047
    PCaK: 3.5921702160000004e-08
    PCaNa: 1.2563550000000001e-07
    PCap: 0.00011055924000000001
    gamma_cao: 0.6117017520062547
    gamma_ko: 0.8843718923169582
    gamma_nao: 0.8843718923169582
    PCaKp: 3.951387237600001e-08
    PCaNap: 1.3819905000000003e-07
    alpha_1: 0.154375
    beta_1: 0.1911
    GKr: 0.041729999999999996
    GKs: 0.00154
    GK1: 0.83904
    INaCa_fractionSS: 0.35
    KmCaAct: 0.00015
    kcaon: 1500000.0
    kna1: 15.0
    kna2: 5.0
    kna3: 88.12
    qca: 0.167
    qna: 0.5224
    wca: 60000.0
    wna: 60000.0
    wnaca: 5000.0
    Gncx: 0.0037400000000000003
    k2_i: 5000.0
    k2_ss: 5000.0
    k5_i: 5000.0
    k5_ss: 5000.0
    h11_i: 0.9196480938416423
    h11_ss: 0.9196480938416423
    k1_i: 9501.466275659823
    k1_ss: 9501.466275659823
    H: 1.0e-07
    Khp: 1.698e-07
    Kki: 0.5
    Kko: 0.3582
    Kmgatp: 1.698e-07
    Knai0: 9.073
    Knao0: 27.78
    Knap: 224.0
    Kxkur: 292.0
    MgATP: 9.8
    delta: -0.155
    eP: 4.2
    k1p: 949.5
    k2m: 39.4
    k3m: 79300.0
    k3p: 1899.0
    k4m: 40.0
    Pnak: 13.90581
    a2: 687.2
    a4: 638.9999889283472
    b1: 9.120000000000001
    GKb: 0.01134
    PNab: 1.9239e-09
    PCab: 5.9194e-08
    Fjunc: 1.0
    GClCa: 0.2843
    GClb: 0.00198
    KdClCa: 0.1
    Jrel_b: 1.5378
    bt: 4.75
    cajsr_half: 1.7
    a_rel: 2.375
    btp: 5.9375
    a_relp: 2.96875
  mid:
    CaMKo: 0.05
    KmCaM: 0.0015
    KmCaMK: 0.15
    aCaMK: 0.05
    bCaMK: 0.00068
    GpCa: 0.0005
    KmCap: 0.0005
    Acap: 0.00015335760000000003
    vjsr: 1.8237120000000002e-07
    vmyo: 2.583592000000001e-05
    vnsr: 2.0972688000000006e-06
    vss: 7.598800000000002e-07
    tauCa: 0.2
    tauK: 2.0
    tauNa: 2.0
    celltype: 2.0
    cao: 1.8
    ko: 5.0
    nao: 140.0
    F: 96485.0
    R: 8314.0
    T: 310.0
    zca: 2.0
    zk: 1.0
    zna: 1.0
    Jup_b: 1.0
    upScale: 1.0
    BSLmax: 1.124
    BSRmax: 0.047
    KmBSL: 0.0087
    KmBSR: 0.00087
    cli: 24.0
    csqnmax: 10.0
    kmcmdn: 0.00238
    kmcsqn: 0.8
    kmtrpn: 0.0005
    trpnmax: 0.07
    cmdnmax: 0.05
    ECl: -48.95253676506265
    PKNa: 0.01833
    fkatp: 0.0
    gkatp: 4.3195
    akik: 1.0
    bkik: 0.015384615384615385
    GNa: 11.7802
    thL: 200.0
    GNaL: 0.0279
    thLp: 600.0
    EKshift: 0.0
    Gto: 0.32
    Aff: 0.6
    ICaL_fractionSS: 0.8
    Kmn: 0.002
    k2n: 500.0
    offset: 0.0
    tjca: 75.0
    vShift: 0.0
    Afs: 0.4
    PCa: 0.000167514
    constA: 0.5238190247282047
    PCaK: 5.98695036e-08
    PCaNa: 2.0939250000000001e-07
    PCap: 0.00018426540000000003
    gamma_cao: 0.6117017520062547
    gamma_ko: 0.8843718923169582
    gamma_nao: 0.8843718923169582
    PCaKp: 6.585645396000002e-08
    PCaNap: 2.3033175000000005e-07
    alpha_1: 0.154375
    beta_1: 0.1911
    GKr: 0.025679999999999998
    GKs: 0.0011
    GK1: 0.9089600000000001
    INaCa_fractionSS: 0.35
    KmCaAct: 0.00015
    kcaon: 1500000.0
    kna1: 15.0
    kna2: 5.0
    kna3: 88.12
    qca: 0.167
    qna: 0.5224
    wca: 60000.0
    wna: 60000.0
    wnaca: 5000.0
    Gncx: 0.0047599999999999995
    k2_i: 5000.0
    k2_ss: 5000.0
    k5_i: 5000.0
    k5_ss: 5000.0
    h11_i: 0.9196480938416423
    h11_ss: 0.9196480938416423
    k1_i: 9501.466275659823
    k1_ss: 9501.466275659823
    H: 1.0e-07
    Khp: 1.698e-07
    Kki: 0.5
    Kko: 0.3582
    Kmgatp: 1.698e-07
    Knai0: 9.073
    Knao0: 27.78
    Knap: 224.0
    Kxkur: 292.0
    MgATP: 9.8
    delta: -0.155
    eP: 4.2
    k1p: 949.5
    k2m: 39.4
    k3m: 79300.0
    k3p: 1899.0
    k4m: 40.0
    Pnak: 10.81563
    a2: 687.2
    a4: 638.9999889283472
    b1: 9.120000000000001
    GKb: 0.0189
    PNab: 1.9239e-09
    PCab: 5.9194e-08
    Fjunc: 1.0
    GClCa: 0.2843
    GClb: 0.00198
    KdClCa: 0.1
    Jrel_b: 1.5378
    bt: 4.75
    cajsr_half: 1.7
    a_rel: 2.375
    btp: 5.9375
    a_relp: 2.96875
extra parameters:
  L: 0.01
  rad: 0.0011
  Ageo: 7.667880000000002e-05
  vcell: 3.799400000000001e-05
  clo: 150.0
  zcl: -1.0
  cmdnmax_b: 0.05
  A_atp: 2.0
  K_atp: 0.25
  K_o_n: 5.0
  GNaL_b: 0.0279
  Gto_b: 0.16
  Io: 0.15109999999999998
  PCa_b: 8.3757e-05
  dielConstant: 74.0
  GKr_b: 0.0321
  GKs_b: 0.0011
  GK1_b: 0.6992
  Gncx_b: 0.0034
  kasymm: 12.5
  kcaoff: 5000.0
  h10_i: 284.1666666666667
  h10_ss: 284.1666666666667
  h12_i: 0.003519061583577712
  h12_ss: 0.003519061583577712
  MgADP: 0.05
  Pnak_b: 15.4509
  k1m: 182.4
  k2p: 687.2
  k4p: 639.0
  GKb_b: 0.0189
example discretisation:
  dt: 0.02
  dx: 0.98
  stimulus: 50.7
units:
  t: ms
  x: mm
  u: mV