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myokit.load_model('stewart-2009.mmt') +mt = myokit.load_model('tentusscher-2006-lhopital.mmt') + +# Create a protocol +p = myokit.pacing.blocktrain(period=1000, duration=2) + +# Set up a simulation +s = myokit.FiberTissueSimulation( + mf, + mt, + p, + ncells_fiber=(32, 2), + ncells_tissue=(32, 32), + nx_paced=5, + g_fiber=(3, 1), + g_tissue=(3, 1), + g_fiber_tissue=3, +) +s.set_step_size(0.0005) + +# Debugging? Then log all variables +if debug: + logf = logt = myokit.LOG_STATE + myokit.LOG_BOUND +else: + logf = ['engine.time', 'membrane.V', 'calcium.Ca_i'] + logt = ['engine.time', 'membrane.V', 'calcium.Cai'] + +# Run (using a progress printer to see how far we got) +pr = myokit.ProgressPrinter() +df, dt = s.run(50, logf=logf, logt=logt, log_interval=0.5, progress=pr) +if debug: + print('Sim OK!') + sys.exit(1) + +# Convert the dictionary logs to structured 2d arrays +bf = df.block2d() +bt = dt.block2d() + +# Create a combined data block +# First define a map that indicates equivalent variables. Format: +# new_name : (modelf name, modelt name, padding value) +varmap = { + 'V' : ('membrane.V', 'membrane.V', -100), + 'Cai': ('calcium.Ca_i', 'calcium.Cai', 0), +} +b = myokit.DataBlock2d.combine(bf, bt, map2d=varmap, pos1=(0, 15)) + +# Store the data block +fname = 'combined.zip' +print(f'Storing in {fname}') +b.save(fname) + +print('Done!') +print('View with: python3 -m myokit block combined.zip') + diff --git a/ft-example/stewart-2009.mmt b/ft-example/stewart-2009.mmt new file mode 100644 index 0000000..fa18924 --- /dev/null +++ b/ft-example/stewart-2009.mmt @@ -0,0 +1,577 @@ +[[model]] +name: stewart-2009 +display_name: Stewart et al., 2009 +version: 20211027 +mmt_authors: Michael Clerx +desc: """ + Model of the human Purinkje action potential by Stewart et al. [1], based + on the ventricular endocardial model by Ten Tusscher et al. [2]. + + This implementation was created from the CellML code made available with + the original publication [2]. Several "cosmetic" changes were made without + affecting the equations, which were tested against the CellML from PMR and + matched to within rounding error precision. + - The state variables were ordered as in the publication + - The components were ordered as in the publication, and were annotated + with links to the relevant document section. + In addition, incorrect units in F, R, Cm, gCaL, Vc, Vss, and Vsr were + corrected. + + [1] Mathematical model of the electrical action potential of Purkinje fibre + cells. + Philip Stewart, Oleg V. Aslanidi, Denis Noble, Penelope J. Noble, Mark + R. Boyett, and Henggui Zhang, 2009 + Philosophical Transactions of the Royal Society, 367, 2225-2255. + https://doi.org/10.1098/rsta.2008.0283 + + [2] Alternans and spiral breakup in a human ventricular tissue model. + K.H.W.J. ten Tusscher, A.V. Panfilov, Sep 2006, + American Journal of Physiology, Heart and Circulatory Physiology, + 291 3, H1088-1100. + https://doi.org/10.1152/ajpheart.00109.2006 + + [3] https://models.physiomeproject.org/exposure/38cf8387b0707f0ef6947f009710aeb5 + Retrieved on 2021-10-27 + + An extract from the CellML file's meta data follows below: + --------------------------------------------------------------------------- + Penny Noble + DPAG, University of Oxford + + Model Status + This CellML ersion of the model has been checked in COR and OpenCell. The + units are consistent and the model runs to recreate the published results. + + Model Structure + In the paper described here, Philip Stewart and colleagues present a + details of their newly developed model for the human Purkinje cell + including validation against experimental data. Ionic mechanisms underlying + the heterogeneity between the Purkinje fibre and ventricular action + potentials in humans and other species were analysed. The newly developed + Purkinje fibre cell model adds a new member to the family of human cardiac + cell models developed previously for the sino-atrial node, atrial and + ventricular cells, which can be incorporated into an anatomical model of + human heart with details of its electrophysiological heterogeneity and + anatomical complexity. + """ +# Initial values +membrane.V = -7.12864384994752527e+01 +calcium.Ca_i = 1.02363913704157998e-04 +calcium.Ca_SR = 3.14149868138687083e+00 +calcium.Ca_ss = 3.81250245527617196e-04 +sodium.Na_i = 8.80505373054986329e+00 +potassium.K_i = 1.36773426842998674e+02 +ina.m = 2.83293473203283658e-02 +ina.h = 2.51110676365191021e-01 +ina.j = 2.65680422809985550e-01 +ikr.Xr1 = 1.34628009070351228e-02 +ikr.Xr2 = 3.32697379577155727e-01 +iks.Xs = 8.40127007165385360e-03 +ito.r = 8.84290083740064937e-04 +ito.s = 9.68749754333663282e-01 +ical.d = 2.16290842830038621e-04 +ical.f1 = 9.68969771502977917e-01 +ical.f2 = 9.96328488888527430e-01 +ical.fCass = 9.99935288766206076e-01 +if.y = 3.84052487230444398e-02 +irel.R_prime = 9.84086493577585375e-01 + +# +# Simulation variables +# +[engine] +time = 0 [ms] + in [ms] + bind time +pace = 0 + bind pace + +# +# Membrane potential +# +[membrane] +dot(V) = -(i_ion + i_stim + i_diff) + in [mV] + label membrane_potential +i_ion = sodium.INa_tot + potassium.IK_tot + calcium.ICa_tot + in [A/F] +i_diff = 0 [A/F] + in [A/F] + bind diffusion_current +i_stim = engine.pace * amplitude + in [A/F] +amplitude = -30 [A/F] + in [A/F] + +# +# (a) Inward rectifier current, IK1 +# Appendix page 2242 +# +[ik1] +use membrane.V +inf = 1 / (1 + exp(0.1 [1/mV] * (V + 75.44 [mV]))) +g_K1 = 0.065 [mS/uF] + in [mS/uF] +i_K1 = g_K1 * inf * (V - 8 [mV] - nernst.E_K) + in [A/F] + +# +# (b) Transient outward current, ITo +# Appendix page 2242 +# +[ito] +use membrane.V +dot(r) = (r_inf - r) / tau_r + r_inf = 1 / (1 + exp((20 [mV] - V) / 13 [mV])) + tau_r = 10.45 [ms] * exp(-(V + 40 [mV])^2 / 1800 [mV^2]) + 7.3 [ms] + in [ms] +dot(s) = (s_inf - s) / tau_s + s_inf = 1 / (1 + exp((V + 27 [mV]) / 13 [mV])) + tau_s = 85 [ms] * exp(-(V + 25 [mV])^2 / 320 [mV^2]) + 5 [ms] / (1 + exp((V - 40 [mV]) / 5 [mV])) + 42 [ms] + in [ms] +g_to = 0.08184 [mS/uF] + in [mS/uF] +i_to = g_to * r * s * (V - nernst.E_K) + in [A/F] + +# +# (c) Sustained current, Isus +# Appendix page 2243 +# +[isus] +use membrane.V +a = 1 / (1 + exp((5 [mV] - V) / 17 [mV])) +g_sus = 0.0227 [mS/uF] + in [mS/uF] +i_sus = g_sus * a * (V - nernst.E_K) + in [A/F] + +# +# (d) Hyperpolarization-activated current, If +# Appendix page 2243 +# Described in detail on page 2229 +# +[if] +use membrane.V +dot(y) = (y_inf - y) / tau_y + alpha_y = 1 [1/ms] * exp(-2.9 - 0.04 [1/mV] * V) + in [1/ms] + beta_y = 1 [1/ms] * exp(3.6 + 0.11 [1/mV] * V) + in [1/ms] + tau_y = 4000 / (alpha_y + beta_y) + in [ms] + y_inf = 1 / (1 + exp((V + 80.6 [mV]) / 6.8 [mV])) +g_f_K = 0.0234346 [mS/uF] + in [mS/uF] +g_f_Na = 0.0145654 [mS/uF] + in [mS/uF] +i_f_K = y * g_f_K * (V - nernst.E_K) + in [A/F] +i_f_Na = y * g_f_Na * (V - nernst.E_Na) + in [A/F] +i_f = i_f_Na + i_f_K + in [A/F] + +# +# (e) Fast sodium current, INa +# Appendix page 2243 +# +[ina] +use membrane.V +dot(m) = (inf - m) / tau + alpha = 1 / (1 + exp((-60 [mV] - V) / 5 [mV])) + beta = 0.1 / (1 + exp((V + 35 [mV]) / 5 [mV])) + 0.1 / (1 + exp((V - 50 [mV]) / 200 [mV])) + tau = 1 [ms] * alpha * beta + in [ms] + inf = 1 / (1 + exp((-56.86 [mV] - V) / 9.03 [mV]))^2 +dot(h) = (inf - h) / tau + alpha = if(V < -40 [mV], 0.057 [1/ms] * exp(-(V + 80 [mV]) / 6.8 [mV]), 0 [1/ms]) + in [1/ms] + beta = if(V < -40 [mV], + 2.7 [1/ms] * exp(0.079 [1/mV] * V) + 310000 [1/ms] * exp(0.3485 [1/mV] * V), + 0.77 [1/ms] / (0.13 * (1 + exp((V + 10.66 [mV]) / -11.1 [mV])))) + in [1/ms] + tau = 1 / (alpha + beta) + in [ms] + inf = 1 / (1 + exp((V + 71.55 [mV]) / 7.43 [mV]))^2 +dot(j) = (inf - j) / tau + alpha = if(V < -40 [mV], + (-25428 [1/ms] * exp(0.2444 [1/mV] * V) - 6.948e-6 [1/ms] * exp(-0.04391 [1/mV] * V)) * (V + 37.78 [mV]) / 1 [mV] / (1 + exp(0.311 [1/mV] * (V + 79.23 [mV]))), + 0 [1/ms]) + in [1/ms] + beta = if(V < -40 [mV], + 0.02424 [1/ms] * exp(-0.01052 [1/mV] * V) / (1 + exp(-0.1378 [1/mV] * (V + 40.14 [mV]))), + 0.6 [1/ms] * exp(0.057 [1/mV] * V) / (1 + exp(-0.1 [1/mV] * (V + 32 [mV])))) + in [1/ms] + tau = 1 / (alpha + beta) + in [ms] + inf = 1 / (1 + exp((V + 71.55 [mV]) / 7.43 [mV]))^2 +g_Na = 130.5744 [mS/uF] + in [mS/uF] +i_Na = g_Na * m^3 * h * j * (V - nernst.E_Na) + in [A/F] + +# +# (f) L-type calcium current, ICaL +# Appendix page 2244 +# +[ical] +use membrane.V +use phys.FRT, phys.FFRT +use calcium.Ca_ss, extra.Ca_o +dot(d) = (d_inf - d) / tau_d + alpha_d = 1.4 / (1 + exp((-35 [mV] - V) / 13 [mV])) + 0.25 + beta_d = 1.4 / (1 + exp((V + 5 [mV]) / 5 [mV])) + gamma_d = 1 [ms] / (1 + exp((50 [mV] - V) / 20 [mV])) + in [ms] + tau_d = 1 [ms] * alpha_d * beta_d + gamma_d + in [ms] + d_inf = 1 / (1 + exp((-8 [mV] - V) / 7.5 [mV])) +dot(f1) = (f_inf - f1) / tau_f + f_inf = 1 / (1 + exp((V + 20 [mV]) / 7 [mV])) + tau_f = 1102.5 [ms] * exp(-(V + 27 [mV])^2 / 225 [mV^2]) + 200 [ms] / (1 + exp((13 [mV] - V) / 10 [mV])) + 180 [ms] / (1 + exp((V + 30 [mV]) / 10 [mV])) + 20 [ms] + in [ms] +dot(f2) = (f2_inf - f2) / tau_f2 + f2_inf = 0.67 / (1 + exp((V + 35 [mV]) / 7 [mV])) + 0.33 + tau_f2 = 562 [ms] * exp(-(V + 27 [mV])^2 / 240 [mV^2]) + 31 [ms] / (1 + exp((25 [mV] - V) / 10 [mV])) + 80 [ms] / (1 + exp((V + 30 [mV]) / 10 [mV])) + in [ms] +dot(fCass) = (fCass_inf - fCass) / tau_fCass + fCass_inf = 0.6 / (1 + (calcium.Ca_ss / 0.05 [mM])^2) + 0.4 + tau_fCass = 80 [ms] / (1 + (calcium.Ca_ss / 0.05 [mM])^2) + 2 [ms] + in [ms] +g_CaL = 0.0398 [L/F/s] + in [L/F/s] +i_CaL = if(abs(V - 15 [mV]) < 1e-6 [mV], a * (b - Ca_o) / (2 * FRT), numer / denom) + in [A/F] + a = g_CaL * d * f1 * f2 * fCass * 4 * FFRT + in [1/mM/ms] + b = 0.25 * Ca_ss + in [mM] + numer = a * (V - 15 [mV]) * (b * exp((V - 15 [mV]) * 2 * FRT) - Ca_o) + in [A/F] + denom = (exp(2 * (V - 15 [mV]) * FRT) - 1) + +# +# (g) Slow delayed rectifier current, IKs +# Appendix page 2245 +# Also called the "slow time-dependent potassium current" +# +[iks] +use membrane.V +dot(Xs) = (inf - Xs) / tau + alpha = 1400 / sqrt(1 + exp((5 [mV] - V) / 6 [mV])) + beta = 1 / (1 + exp((V - 35 [mV]) / 15 [mV])) + tau = 1 [ms] * alpha * beta + 80 [ms] + in [ms] + inf = 1 / (1 + exp((-5 [mV] - V) / 14 [mV])) +g_Ks = 0.2352 [mS/uF] + in [mS/uF] +i_Ks = g_Ks * Xs^2 * (V - nernst.E_Ks) + in [A/F] + +# +# (h) Rapid delayed rectifier current, IKr +# Appendix page 2246 +# Also called the "rapid time-dependent potassium current" +# +[ikr] +use membrane.V +dot(Xr1) = (xr1_inf - Xr1) / tau_xr1 + alpha_xr1 = 450 / (1 + exp((-45 [mV] - V) / 10 [mV])) + beta_xr1 = 6 / (1 + exp((V + 30 [mV]) / 11.5 [mV])) + tau_xr1 = 1 [ms] * alpha_xr1 * beta_xr1 + in [ms] + xr1_inf = 1 / (1 + exp((-26 [mV] - V) / 7 [mV])) +dot(Xr2) = (xr2_inf - Xr2) / tau_xr2 + alpha_xr2 = 3 / (1 + exp((-60 [mV] - V) / 20 [mV])) + beta_xr2 = 1.12 / (1 + exp((V - 60 [mV]) / 20 [mV])) + tau_xr2 = 1 [ms] * alpha_xr2 * beta_xr2 + in [ms] + xr2_inf = 1 / (1 + exp((V + 88 [mV]) / 24 [mV])) +g_Kr = 0.0918 [mS/uF] + in [mS/uF] +i_Kr = g_Kr * sqrt(extra.K_o / 5.4 [mM]) * Xr1 * Xr2 * (V - nernst.E_K) + in [A/F] + +# +# (i) Na/Ca exchange current, INaCa +# Appendix page 2246 +# +[inaca] +use membrane.V, phys.FRT +use extra.Na_o, extra.Ca_o +use sodium.Na_i, calcium.Ca_i +alpha = 2.5 +gamma = 0.35 +K_sat = 0.1 +K_NaCa = 1000 [A/F] + in [A/F] +Km_Nai = 87.5 [mM] + in [mM] +Km_Ca = 1.38 [mM] + in [mM] +i_NaCa = K_NaCa * (exp(gamma * V * FRT) * Na_i^3 * Ca_o - exp((gamma - 1) * V * FRT) * Na_o^3 * Ca_i * alpha) / ((Na_o^3 + Km_Nai^3) * (Km_Ca + Ca_o) * (1 + K_sat * exp((gamma - 1) * V * FRT))) + in [A/F] + +# +# (j) Na/K pump current, INaK +# Appendix page 2247 +# +[inak] +use membrane.V, phys.FRT +use extra.K_o, sodium.Na_i +K_mNa = 40 [mM] + in [mM] +K_mk = 1 [mM] + in [mM] +P_NaK = 2.724 [A/F] + in [A/F] +i_NaK = P_NaK * K_o / (K_o + K_mk) * Na_i / (Na_i + K_mNa) / (1 + 0.1245 * exp(-0.1 * V * FRT) + 0.0353 * exp(-V * FRT)) + in [A/F] + +# +# (j) Calcium pump current, IpCa +# Appendix page 2247 +# +[ipca] +K_pCa = 0.0005 [mM] + in [mM] +g_pCa = 0.1238 [A/F] + in [A/F] +i_p_Ca = g_pCa * calcium.Ca_i / (calcium.Ca_i + K_pCa) + in [A/F] + +# +# (j) Potassium pump current, IpK +# Appendix page 2247 +# +[ipk] +use membrane.V +g_pK = 0.0146 [mS/uF] + in [mS/uF] +i_p_K = g_pK * (V - nernst.E_K) / (1 + exp((25 [mV] - V) / 5.98 [mV])) + in [A/F] + +# +# (k) Sodium background current, IbNa +# Appendix page 2247 +# +[ibna] +g_bna = 0.00029 [mS/uF] + in [mS/uF] +i_b_Na = g_bna * (membrane.V - nernst.E_Na) + in [A/F] + +# +# (k) Calcium background current, IbCa +# Appendix page 2247 +# +[ibca] +g_bca = 0.000592 [mS/uF] + in [mS/uF] +i_b_Ca = g_bca * (membrane.V - nernst.E_Ca) + in [A/F] + +# +# (l) Calcium uptake into the SR (SERCA) +# +[iup] +use calcium.Ca_i +Vmax_up = 0.006375 [mM/ms] + in [mM/ms] +K_up = 0.00025 [mM] + in [mM] +i_up = Vmax_up / (1 + K_up^2 / Ca_i^2) + in [mM/ms] + +# +# (l) Calcium release from the SR (RyR) +# +[irel] +use calcium.Ca_ss, calcium.Ca_SR +k1_prime = 0.15 [1/mM^2/ms] + in [1/mM^2/ms] +k2_prime = 0.045 [1/mM/ms] + in [1/mM/ms] +kcasr = max_sr - (max_sr - min_sr) / (1 + (EC / Ca_SR)^2) + max_sr = 2.5 + min_sr = 1 + EC = 1.5 [mM] + in [mM] +k1 = k1_prime / kcasr + in [1/mM^2/ms] +k2 = k2_prime * kcasr + in [1/mM/ms] +k3 = 0.06 [1/ms] + in [1/ms] +k4 = 0.005 [1/ms] + in [1/ms] +dot(R_prime) = -k2 * Ca_ss * R_prime + k4 * (1 - R_prime) +O = k1 * Ca_ss^2 * R_prime / (k3 + k1 * Ca_ss^2) +V_rel = 0.102 [mS/uF] + in [mS/uF] +i_rel = V_rel * O * (Ca_SR - Ca_ss) + in [mM/ms] + +# +# (l) Calcium leak from SR +# +[ileak] +use calcium.Ca_SR, calcium.Ca_i +V_leak = 0.00036 [mS/uF] + in [mS/uF] +i_leak = V_leak * (Ca_SR - Ca_i) + in [mM/ms] + +# +# (l) Diffusion from SS to Bulk +# +[ixfer] +use calcium.Ca_i, calcium.Ca_ss +V_xfer = 0.0038 [mS/uF] + in [mS/uF] +i_xfer = V_xfer * (Ca_ss - Ca_i) + in [mM/ms] + +# +# (l) Calcium dynamics +# Appendix page 2247 +# +[calcium] +use membrane.V +use cell.V_c, cell.V_sr, cell.V_ss, cell.Cm +use ileak.i_leak, iup.i_up, irel.i_rel, ixfer.i_xfer +# Buffering constants +Buf_c = 0.2 [mM] + in [mM] +Buf_ss = 0.4 [mM] + in [mM] +Buf_sr = 10 [mM] + in [mM] +K_buf_c = 0.001 [mM] + in [mM] +K_buf_ss = 0.00025 [mM] + in [mM] +K_buf_sr = 0.3 [mM] + in [mM] +# Buffered concentrations +Ca_i_bufc = 1 / (1 + Buf_c * K_buf_c / (Ca_i + K_buf_c)^2) +Ca_ss_bufss = 1 / (1 + Buf_ss * K_buf_ss / (Ca_ss + K_buf_ss)^2) +Ca_sr_bufsr = 1 / (1 + Buf_sr * K_buf_sr / (Ca_SR + K_buf_sr)^2) +# Free calcium in cytosol, SS, and SR +dot(Ca_i) = Ca_i_bufc * ((i_leak - i_up) * V_sr / V_c + i_xfer - ICa_cyt * Cm / (2 * V_c * phys.F)) + in [mM] +dot(Ca_ss) = Ca_ss_bufss * (-ical.i_CaL * Cm / (2 * V_ss * phys.F) + i_rel * V_sr / V_ss - i_xfer * V_c / V_ss) + in [mM] +dot(Ca_SR) = Ca_sr_bufsr * (i_up - (i_rel + i_leak)) + in [mM] +# Total calcium currents +ICa_cyt = ibca.i_b_Ca + ipca.i_p_Ca - 2 * inaca.i_NaCa + in [A/F] +ICa_tot = ICa_cyt + ical.i_CaL + in [A/F] + +# +# (m) Sodium dynamics +# Appendix page 2248 +# +[sodium] +INa_tot = ina.i_Na + ibna.i_b_Na + if.i_f_Na + 3 * inak.i_NaK + 3 * inaca.i_NaCa + in [A/F] +dot(Na_i) = -INa_tot / (cell.V_c * phys.F) * cell.Cm + in [mM] + +# +# (m) Potassium dynamics +# Appendix page 2248 +# +[potassium] +IK_tot = ik1.i_K1 + ito.i_to + if.i_f_K + isus.i_sus + ikr.i_Kr + iks.i_Ks + ipk.i_p_K - 2 * inak.i_NaK + in [A/F] +dot(K_i) = -IK_tot / (cell.V_c * phys.F) * cell.Cm # cell.Cm is not in the appendix! + in [mM] + +# +# Physical constants +# +[phys] +R = 8.314472 [J/mol/K] + in [J/mol/K] +T = 310 [K] + in [K] +F = 9.64853414999999950e+01 [C/mmol] + in [C/mmol] +RTF = R * T / F + in [mV] +FRT = F / R / T + in [1/mV] +FFRT = F * FRT + in [C/mmol/mV] + +# +# Cell geometry +# +[cell] +Cm = 185 [pF] + in [pF] + desc: Cell capacitance +V_c = 16404 [um^3] + in [um^3] + desc: Bulk cytoplasm volume +V_ss = 54.68 [um^3] + in [um^3] + desc: Dyadic (junctional) subspace volume +V_sr = 1094 [um^3] + in [um^3] + desc: Sarcoplasmic reticulum volume + +# +# Extracellular concentrations +# +[extra] +K_o = 5.4 [mM] + in [mM] +Na_o = 140 [mM] + in [mM] +Ca_o = 2 [mM] + in [mM] + +# +# Reversal potentials +# +[nernst] +use extra.K_o, extra.Na_o, extra.Ca_o +use potassium.K_i, sodium.Na_i, calcium.Ca_i +E_Ca = 0.5 * phys.RTF * log(Ca_o / Ca_i) + in [mV] +E_K = phys.RTF * log(K_o / K_i) + in [mV] +E_Ks = phys.RTF * log((K_o + P_kna * Na_o) / (K_i + P_kna * Na_i)) + in [mV] +E_Na = phys.RTF * log(Na_o / Na_i) + in [mV] +P_kna = 0.03 + +[[protocol]] +# Level Start Length Period Multiplier +1 100 0.5 1000 0 + +[[script]] +import matplotlib.pyplot as plt +import myokit + +# Get model and protocol, create simulation +m = get_model() +#p = get_protocol() +s = myokit.Simulation(m) + +# Run simulation +d = s.run(3000) + +# Display the result +plt.figure() +plt.xlabel('Time (ms)') +plt.ylabel('Membrane potential (mV)') +plt.plot(d['engine.time'], d['membrane.V']) +plt.show() + diff --git a/ft-example/tentusscher-2006-lhopital.mmt b/ft-example/tentusscher-2006-lhopital.mmt new file mode 100644 index 0000000..276c39f --- /dev/null +++ b/ft-example/tentusscher-2006-lhopital.mmt @@ -0,0 +1,618 @@ +[[model]] +name: tentusscher-2006-lhopital +version: 20220502 +mmt_authors: Michael Clerx +desc: """ + Human ventricular myocyte model by ten Tusscher et al., 2006. + + The model contains a switch for endo, epi and mid-myocardial modes. + + References: + + [1] The CellML versions of the model (http://models.cellml.org) + [2] Alternans and spiral breakup in a human ventricular tissue model, + ten Tusscher, Panfilov (2006) AJPHeart + [3] A model for human ventricular tissue, + ten Tusscher, Noble, Noble, Panfilov (2003) AJPHeart + + Adapted from CellML (October 2020 version). The original CellML model meta + data follows below. + + --------------------------------------------------------------------------- + + Alternans and spiral breakup in a human ventricular tissue model + + Penny Noble + Oxford University Cardiac Electrophysiology Group + + Model Status + + This is the EPICARDIAL CELL VARIANT of the model. This model was created by + Penny Noble of Oxford University and is known to read in COR and PCEnv. A + stimulus protocol has been added that allows the model to simulate multiple + action potentials at 1Hz. + + Model Structure + + ABSTRACT: Ventricular fibrillation (VF) is one of the main causes of death + in the Western world. According to one hypothesis, the chaotic excitation + dynamics during VF are the result of dynamical instabilities in action + potential duration (APD) the occurrence of which requires that the slope of + the APD restitution curve exceeds 1. Other factors such as electrotonic + coupling and cardiac memory also determine whether these instabilities can + develop. In this paper we study the conditions for alternans and spiral + breakup in human cardiac tissue. Therefore, we develop a new version of our + human ventricular cell model, which is based on recent experimental + measurements of human APD restitution and includes a more extensive + description of intracellular calcium dynamics. We apply this model to study + the conditions for electrical instability in single cells, for reentrant + waves in a ring of cells, and for reentry in two-dimensional sheets of + ventricular tissue. We show that an important determinant for the onset of + instability is the recovery dynamics of the fast sodium current. Slower + sodium current recovery leads to longer periods of spiral wave rotation and + more gradual conduction velocity restitution, both of which suppress + restitution-mediated instability. As a result, maximum restitution slopes + considerably exceeding 1 (up to 1.5) may be necessary for electrical + instability to occur. Although slopes necessary for the onset of + instabilities found in our study exceed 1, they are within the range of + experimentally measured slopes. Therefore, we conclude that steep APD + restitution-mediated instability is a potential mechanism for VF in the + human heart. + + The original paper reference is cited below: + + Alternans and spiral breakup in a human ventricular tissue model, K.H.W.J. + ten Tusscher, A.V. Panfilov, Sep 2006, + American Journal of Physiology, Heart and Circulatory Physiology , 291 3, + H1088-1100. PubMed ID: 16565318 + """ +# Initial values (ordered as in the original code) +membrane.V = -85.23 +calcium.Cai = 0.000126 +calcium.CaSR = 3.64 +calcium.CaSS = 0.00036 +sodium.Nai = 8.604 +potassium.Ki = 136.89 +ina.m = 0.00172 +ina.h = 0.7444 +ina.j = 0.7045 +ikr.xr1 = 0.00621 +ikr.xr2 = 0.4712 +iks.xs = 0.0095 +ito.r = 2.42e-8 +ito.s = 0.999998 +ical.d = 3.373e-5 +ical.f = 0.7888 +ical.f2 = 0.9755 +ical.fCaSS = 0.9953 +jrel.R_prime = 0.9073 + +# +# Simulator variables +# +[engine] +time = 0 [ms] + in [ms] + bind time +pace = 0 + bind pace + +# +# Membrane potential +# +# Appendix to [3] +# +[membrane] +use stimulus.i_stim +dot(V) = -(i_ion + i_stim + i_diff) + in [mV] + label membrane_potential +i_ion = (+ ina.INa + + ik1.IK1 + + ikr.IKr + + iks.IKs + + ito.Ito + + ical.ICaL + + inak.INaK + + inaca.INaCa + + ipca.IpCa + + ipk.IpK + + icab.ICab + + inab.INab + ) + in [A/F] +i_diff = 0 [A/F] + in [A/F] + bind diffusion_current + +# +# Stimulus current +# +# Appendix to [3] +# +[stimulus] +i_stim = engine.pace * amplitude + in [A/F] +amplitude = -52 [A/F] + in [A/F] + +# +# Cell parameters +# +[cell] +type = 1 + desc: The type of cell: endocardial = 0, epicardial = 1, mid-myocardial = 2 +Vc = 16404 [um^3] + in [um^3] + desc: Bulk cytoplasm volume +Vss = 54.68 [um^3] + in [um^3] + desc: Dyadic (junctional) subspace volume +Vsr = 1094 [um^3] + in [um^3] + desc: Sarcoplasmic reticulum volume +Cm = 185 [pF] + in [pF] + desc: Cell capacitance + +# +# Physical constants +# +# Appendix to [3] +# +[phys] +F = 96.485 [C/mmol] + in [C/mmol] +R = 8.314 [J/mol/K] + in [J/mol/K] +T = 310 [K] + in [K] +RTF = R * T / F + in [mV] +FRT = F / (R * T) + in [1/mV] +FFRT = F * FRT + in [C/mmol/mV] + +# +# Fast sodium current +# +# Appendix to [3] +# +[ina] +use membrane.V, nernst.ENa +INa = gNa * m ^ 3 * h * j * (V - ENa) + in [A/F] +gNa = 14.838 [mS/uF] + in [mS/uF] +dot(m) = (inf - m) / tau + inf = 1 / (1 + exp((-56.86 [mV] - V) / 9.03 [mV])) ^ 2 + tau = 1 [ms] * alpha * beta + in [ms] + alpha = 1 / (1 + exp((-60 [mV] - V) / 5 [mV])) + beta = 0.1 / (1 + exp((V + 35 [mV]) / 5 [mV])) + 0.1 / (1 + exp((V - 50 [mV]) / 200 [mV])) +dot(h) = (inf - h) / tau + inf = 1 / (1 + exp((V + 71.55 [mV]) / 7.43 [mV])) ^ 2 + tau = 1 / (alpha + beta) + in [ms] + alpha = if(V < -40 [mV], + 0.057 [mS/uF] * exp(-(V + 80 [mV]) / 6.8 [mV]), + 0 [mS/uF]) + in [1/ms] + beta = if(V < -40 [mV], + 2.7 [mS/uF] * exp(0.079 [1/mV] * V) + 310000 [mS/uF] * exp(0.3485 [1/mV] * V), + 0.77 [mS/uF] / (0.13 * (1 + exp((V + 10.66 [mV]) / -11.1 [mV])))) + in [1/ms] +dot(j) = (inf - j) / tau + inf = 1 / (1 + exp((V + 71.55 [mV]) / 7.43 [mV])) ^ 2 + tau = 1 / (alpha + beta) + in [ms] + alpha = if(V < -40 [mV], + (-25428 [mS/uF] * exp(0.2444 [1/mV] * V) - 6.948e-6 [mS/uF] * exp(-0.04391 [1/mV] * V)) * (V + 37.78 [mV]) / 1 [mV] / (1 + exp(0.311 [1/mV] * (V + 79.23 [mV]))), + 0 [mS/uF]) + in [1/ms] + beta = if(V < -40 [mV], + 0.02424 [mS/uF] * exp(-0.01052 [1/mV] * V) / (1 + exp(-0.1378 [1/mV] * (V + 40.14 [mV]))), + 0.6 [mS/uF] * exp(0.057 [1/mV] * V) / (1 + exp(-0.1 [1/mV] * (V + 32 [mV])))) + in [1/ms] + +# +# Inward rectifier potassium current +# +# Appendix to [3] +# +[ik1] +use membrane.V, nernst.EK +IK1 = gK1 * inf * (V - EK) + in [A/F] +gK1 = 5.405 [mS/uF] * sqrt(extra.Ko / 5.4 [mM]) + in [mS/uF] +inf = alpha / (alpha + beta) + alpha = 0.1 [1/ms] / (1 + exp(0.06 [1/mV] * (V - EK - 200 [mV]))) + in [1/ms] + beta = (3 [1/ms] * exp(0.0002 [1/mV] * (V - EK + 100 [mV])) + 1 [1/ms] * exp(0.1 [1/mV] * (V - EK - 10 [mV]))) / (1 + exp(-0.5 [1/mV] * (V - EK))) + in [1/ms] + +# +# Rapid time-dependent potassium current +# +# Appendix to [3] +# +[ikr] +use membrane.V, nernst.EK +IKr = gKr * xr1 * xr2 * (V - EK) + in [A/F] +gKr = 0.153 [mS/uF] * sqrt(extra.Ko / 5.4 [mM]) + in [mS/uF] +dot(xr1) = (inf - xr1) / tau + inf = 1 / (1 + exp((-26 [mV] - V) / 7 [mV])) + tau = 1 [ms] * alpha * beta + in [ms] + alpha = 450 / (1 + exp((-45 [mV] - V) / 10 [mV])) + beta = 6 / (1 + exp((V + 30 [mV]) / 11.5 [mV])) +dot(xr2) = (inf - xr2) / tau + inf = 1 / (1 + exp((V + 88 [mV]) / 24 [mV])) + tau = 1 [ms] * alpha * beta + in [ms] + alpha = 3 / (1 + exp((-60 [mV] - V) / 20 [mV])) + beta = 1.12 / (1 + exp((V - 60 [mV]) / 20 [mV])) + +# +# Slow time-dependent potassium current +# +# Appendix to [2] +# +[iks] +use membrane.V, nernst.EKs +IKs = gKs * xs ^ 2 * (V - EKs) + in [A/F] +gKs = if(cell.type != 2, + 0.392 [mS/uF], # Endo and epicardial + 0.098 [mS/uF] # Mid-myocardial + ) + in [mS/uF] +dot(xs) = (inf - xs) / tau + inf = 1 / (1 + exp((-5 [mV] - V) / 14 [mV])) + tau = 1 [ms] * alpha * beta + 80 [ms] + in [ms] + alpha = 1400 / sqrt(1 + exp((5 [mV] - V) / 6 [mV])) + beta = 1 / (1 + exp((V - 35 [mV]) / 15 [mV])) + +# +# Transient outward current +# +# Appendix to [2] +# +[ito] +use membrane.V, nernst.EK +Ito = gto * r * s * (V - EK) + in [A/F] +gto = if(cell.type == 0, + 0.073 [mS/uF], # Endocardial + 0.294 [mS/uF] # Epicardial and mid-myocardial + ) + in [mS/uF] +dot(r) = (inf - r) / tau + inf = 1 / (1 + exp((20 [mV] - V) / 6 [mV])) + tau = 9.5 [ms] * exp(-(V + 40 [mV]) ^ 2 / 1800 [mV^2]) + 0.8 [ms] + in [ms] +dot(s) = (inf - s) / tau + inf = if(cell.type == 0, + 1 / (1 + exp((V + 28 [mV]) / 5 [mV])), # Endocardial + 1 / (1 + exp((V + 20 [mV]) / 5 [mV])) # Epicardial and mid-myocardial + ) + tau = if(cell.type == 0, + # Endocardial: + 1000 [ms] * exp(-(V + 67 [mV]) ^ 2 / 1000 [mV^2]) + 8 [ms], + # Epicardial and mid-myocardial: + 85 [ms] * exp(-(V + 45 [mV]) ^ 2 / 320 [mV^2]) + 5 [ms] / (1 + exp((V - 20 [mV]) / 5 [mV])) + 3 [ms] + ) + in [ms] + +# +# L-type calcium current +# +# Appendix to [2] +# +[ical] +use membrane.V +use phys.FRT, phys.FFRT +use extra.Cao, calcium.Cai, calcium.CaSS +ICaL = gCaL * d * f * f2 * fCaSS * 4 * FFRT * if(abs(V - 15) < 1e-5, + (0.25 * CaSS - Cao) / (2 * FRT), + (V - 15 [mV]) * (0.25 * CaSS * exp(2 * (V - 15 [mV]) * FRT) - Cao) / (exp(2 * (V - 15 [mV]) * FRT) - 1)) + in [A/F] +gCaL = 0.0398 [L/F/s] + in [L/F/s] +dot(d) = (inf - d) / tau + inf = 1 / (1 + exp((-8 [mV] - V) / 7.5 [mV])) + tau = 1 [ms] * (alpha * beta + gamma) + in [ms] + alpha = 1.4 / (1 + exp((-35 [mV] - V) / 13 [mV])) + 0.25 + beta = 1.4 / (1 + exp((V + 5 [mV]) / 5 [mV])) + gamma = 1 / (1 + exp((50 [mV] - V) / 20 [mV])) +dot(f) = (inf - f) / tau + inf = 1 / (1 + exp((V + 20 [mV]) / 7 [mV])) + tau = 1102.5 [ms] * exp(-(V + 27 [mV]) ^ 2 / 225 [mV^2]) + 200 [ms] / (1 + exp((13 [mV] - V) / 10 [mV])) + 180 [ms] / (1 + exp((V + 30 [mV]) / 10 [mV])) + 20 [ms] + in [ms] +dot(f2) = (inf - f2) / tau + inf = 0.67 / (1 + exp((V + 35 [mV]) / 7 [mV])) + 0.33 + tau = 562 [ms] * exp(-(V + 27 [mV]) ^ 2 / 240 [mV^2]) + 31 [ms] / (1 + exp((25 [mV] - V) / 10 [mV])) + 80 [ms] / (1 + exp((V + 30 [mV]) / 10 [mV])) + in [ms] +dot(fCaSS) = (inf - fCaSS) / tau + inf = 0.6 / (1 + (CaSS / 0.05 [mM]) ^ 2) + 0.4 + tau = 80 [ms] / (1 + (CaSS / 0.05 [mM]) ^ 2) + 2 [ms] + in [ms] + +# +# Sodium-potassium pump +# +# Appendix to [3] +# +[inak] +use membrane.V, phys.FRT +use extra.Ko, sodium.Nai +INaK = P_NaK * Ko / (Ko + K_mk) * Nai / (Nai + K_mNa) / (1 + 0.1245 * exp(-0.1 * V * FRT) + 0.0353 * exp(-V * FRT)) + in [A/F] +P_NaK = 2.724 [A/F] + in [A/F] +K_mNa = 40 [mM] + in [mM] +K_mk = 1 [mM] + in [mM] + +# +# Sodium-calcium exchanger +# +# Appendix to [3] +# +[inaca] +use membrane.V, phys.FRT +use extra.Nao, extra.Cao +use sodium.Nai, calcium.Cai +INaCa = (K_NaCa + * (exp(gamma * V * FRT) * Nai ^ 3 * Cao - exp((gamma - 1) * V * FRT) * Nao ^ 3 * Cai * alpha) + / ((Km_Nai ^ 3 + Nao ^ 3) * (Km_Ca + Cao) * (1 + K_sat * exp((gamma - 1) * V * FRT)))) + in [A/F] +K_NaCa = 1000 [A/F] + in [A/F] +Km_Ca = 1.38 [mM] + in [mM] +Km_Nai = 87.5 [mM] + in [mM] +K_sat = 0.1 +alpha = 2.5 +gamma = 0.35 + +# +# Calcium pump +# +# Appendix to [3] +# +[ipca] +use calcium.Cai +IpCa = gpCa * Cai / (Cai + KpCa) + in [A/F] +gpCa = 0.1238 [A/F] + in [A/F] +KpCa = 0.0005 [mM] + in [mM] + +# +# Potassium pump +# +# Appendix to [3] +# +[ipk] +use membrane.V, nernst.EK +IpK = gpK * (V - EK) / (1 + exp((25 [mV] - V) / 5.98 [mV])) + in [A/F] +gpK = 0.0146 [mS/uF] + in [mS/uF] + +# +# Background calcium current +# +# Appendix to [3] +# +[icab] +use membrane.V, nernst.ECa +ICab = gCab * (V - ECa) + in [A/F] +gCab = 0.000592 [mS/uF] + in [mS/uF] + +# +# Background sodium current +# +# Appendix to [3] +# +[inab] +use membrane.V, nernst.ENa +INab = gNab * (V - ENa) + in [A/F] +gNab = 0.00029 [mS/uF] + in [mS/uF] + +# +# External concentrations +# +# Appendix to [3] +# +[extra] +Cao = 2 [mM] + in [mM] +Nao = 140 [mM] + in [mM] +Ko = 5.4 [mM] + in [mM] + +# +# Nernst/Reversal potentials +# +# Appendix to [3] +# +[nernst] +use extra.Cao, calcium.Cai +use extra.Nao, sodium.Nai +use extra.Ko, potassium.Ki +use phys.RTF +ECa = RTF * log(Cao / Cai) * 0.5 + in [mV] +ENa = RTF * log(Nao / Nai) + in [mV] +EK = RTF * log(Ko / Ki) + in [mV] +EKs = RTF * log((Ko + P_kna * Nao) / (Ki + P_kna * Nai)) + in [mV] +P_kna = 0.03 + +# +# Calcium release from the SR (RyR) +# +[jrel] +use membrane.V +use calcium.CaSS, calcium.CaSR +Jrel = Vrel * O * (CaSR - CaSS) + in [mM/ms] +Vrel = 0.102 [mS/uF] + in [mS/uF] +O = k1 * CaSS ^ 2 * R_prime / (k3 + k1 * CaSS ^ 2) +kcasr = max_sr - (max_sr - min_sr) / (1 + (EC / CaSR) ^ 2) + max_sr = 2.5 + min_sr = 1 + EC = 1.5 [mM] + in [mM] +k1 = k1_prime / kcasr + in [1/mM^2/ms] +k1_prime = 0.15 [1/mM^2/ms] + in [1/mM^2/ms] +k2 = k2_prime * kcasr + in [1/mM/ms] +k2_prime = 0.045 [1/mM/ms] + in [1/mM/ms] +k3 = 0.06 [mS/uF] + in [mS/uF] +k4 = 0.005 [mS/uF] + in [mS/uF] +dot(R_prime) = -k2 * CaSS * R_prime + k4 * (1 - R_prime) + +# +# Leak from the SR +# +[jleak] +use calcium.Cai, calcium.CaSR +Jleak = Vleak * (CaSR - Cai) + in [mM/ms] +Vleak = 0.00036 [mS/uF] + in [mS/uF] + +# +# Calcium uptake into the SR (SERCA) +# +[jup] +use calcium.Cai +Jup = Vmax_up / (1 + K_up ^ 2 / Cai ^ 2) + in [mM/ms] +Vmax_up = 0.006375 [mM/ms] + in [mM/ms] +K_up = 0.00025 [mM] + in [mM] + +# +# Diffusion from SS to Bulk +# +[jxfer] +use calcium.Cai, calcium.CaSS +Jxfer = Vxfer * (CaSS - Cai) + in [mM/ms] +Vxfer = 0.0038 [mS/uF] + in [mS/uF] + +# +# Calcium dynamics +# +# Appendix to [2] +# +[calcium] +use jup.Jup, jrel.Jrel, jleak.Jleak, jxfer.Jxfer +use phys.F, cell.Cm, cell.Vc, cell.Vss, cell.Vsr +# Free calcium in cytosol, SS, and SR +dot(Cai) = ddt_Cai_total * f_JCai_free + in [mM] +dot(CaSS) = ddt_CaSS_total * f_JCaSS_free + in [mM] +dot(CaSR) = ddt_CaSR_total * f_JCaSR_free + in [mM] +# Derivative of total calcium concentrations (free + buffered) +ddt_Cai_total = -(icab.ICab + ipca.IpCa - 2 * inaca.INaCa) * Cm / (2 * Vc * F) + (Jleak - Jup) * Vsr / Vc + Jxfer + in [mM/ms] +ddt_CaSS_total = -ical.ICaL * Cm / (2 * Vss * F) + Jrel * Vsr / Vss - Jxfer * Vc / Vss + in [mM/ms] +ddt_CaSR_total = Jup - (Jrel + Jleak) + in [mM/ms] +# Conversion factors from d/dt total to d/dt free +f_JCai_free = 1 / (1 + Buf_c * K_buf_c / (Cai + K_buf_c) ^ 2) +f_JCaSS_free = 1 / (1 + Buf_SS * K_buf_SS / (CaSS + K_buf_SS) ^ 2) +f_JCaSR_free = 1 / (1 + Buf_SR * K_buf_SR / (CaSR + K_buf_SR) ^ 2) +# Buffering: Ca_buffered = Ca_i * Buf_c / (Ca_i + K_bufc) +Buf_c = 0.2 [mM] + in [mM] +Buf_SS = 0.4 [mM] + in [mM] +Buf_SR = 10 [mM] + in [mM] +K_buf_c = 0.001 [mM] + in [mM] +K_buf_SS = 0.00025 [mM] + in [mM] +K_buf_SR = 0.3 [mM] + in [mM] + +# +# Sodium dynamics +# +# Appendix to [3] +# +[sodium] +use phys.F, cell.Cm, cell.Vc +dot(Nai) = -INa_total * Cm / (Vc * F) + in [mM] +INa_total = ina.INa + inab.INab + 3 * inak.INaK + 3 * inaca.INaCa + in [A/F] + +# +# Potassium dynamics +# +# Appendix to [3] +# +[potassium] +use phys.F, cell.Cm, cell.Vc +dot(Ki) = -IK_total * Cm / (Vc * F) + in [mM] +IK_total = ik1.IK1 + ito.Ito + ikr.IKr + iks.IKs + ipk.IpK + stimulus.i_stim - 2 * inak.INaK + in [A/F] + +[[protocol]] +# Level Start Length Period Multiplier +1.0 10.0 1.0 1000.0 0 + +[[script]] +import matplotlib.pyplot as plt +import myokit + +# Get model and protocol, create simulation +m = get_model() +p = get_protocol() +s = myokit.Simulation(m, p) + +# Run simulation +d = s.run(1000) + +# Display the results +plt.figure() +plt.xlabel('Time (ms)') +plt.ylabel('Membrane potential (mV)') +plt.plot(d.time(), d['membrane.V']) +plt.show() + From 0cebbfda8de97ef0c7e762708299ccef39f748f6 Mon Sep 17 00:00:00 2001 From: Michael Clerx Date: Wed, 4 May 2022 08:25:44 +0100 Subject: [PATCH 2/2] Removed ft sim result --- ft-example/.gitignore | 1 + ft-example/combined.zip | Bin 421475 -> 0 bytes 2 files changed, 1 insertion(+) create mode 100644 ft-example/.gitignore delete mode 100644 ft-example/combined.zip diff --git a/ft-example/.gitignore b/ft-example/.gitignore new file mode 100644 index 0000000..7f47fdc --- /dev/null +++ b/ft-example/.gitignore @@ -0,0 +1 @@ +combined.zip diff --git a/ft-example/combined.zip b/ft-example/combined.zip deleted file mode 100644 index 9641c9c1d294b02f970500ab908993d019262dea..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 421475 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