Generated Code
The following is python code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 60
sizeStates = 33
sizeConstants = 79
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "time in component environment (second)"
legend_states[0] = "V in component membrane (millivolt)"
legend_constants[0] = "R in component membrane (joule_per_mole_kelvin)"
legend_constants[1] = "T in component membrane (kelvin)"
legend_constants[2] = "F in component membrane (coulomb_per_millimole)"
legend_constants[3] = "C_sc in component membrane (microF_per_cm2)"
legend_algebraic[23] = "i_Na in component fast_sodium_current (microA_per_microF)"
legend_algebraic[45] = "i_Ca in component L_type_Ca_current (microA_per_microF)"
legend_algebraic[48] = "i_Ca_K in component L_type_Ca_current (microA_per_microF)"
legend_algebraic[29] = "i_Kr in component rapid_activating_delayed_rectifiyer_K_current (microA_per_microF)"
legend_algebraic[31] = "i_Ks in component slow_activating_delayed_rectifiyer_K_current (microA_per_microF)"
legend_algebraic[32] = "i_to1 in component transient_outward_potassium_current (microA_per_microF)"
legend_algebraic[34] = "i_K1 in component time_independent_potassium_current (microA_per_microF)"
legend_algebraic[36] = "i_Kp in component plateau_potassium_current (microA_per_microF)"
legend_algebraic[37] = "i_NaCa in component Na_Ca_exchanger (microA_per_microF)"
legend_algebraic[39] = "i_NaK in component sodium_potassium_pump (microA_per_microF)"
legend_algebraic[40] = "i_p_Ca in component sarcolemmal_calcium_pump (microA_per_microF)"
legend_algebraic[42] = "i_Ca_b in component calcium_background_current (microA_per_microF)"
legend_algebraic[43] = "i_Na_b in component sodium_background_current (microA_per_microF)"
legend_algebraic[9] = "i_Stim in component membrane (microA_per_microF)"
legend_constants[4] = "stim_start in component membrane (second)"
legend_constants[5] = "stim_end in component membrane (second)"
legend_constants[6] = "stim_period in component membrane (second)"
legend_constants[7] = "stim_duration in component membrane (second)"
legend_constants[8] = "stim_amplitude in component membrane (microA_per_microF)"
legend_algebraic[19] = "E_Na in component fast_sodium_current (millivolt)"
legend_constants[9] = "g_Na in component fast_sodium_current (milliS_per_microF)"
legend_constants[10] = "Nao in component standard_ionic_concentrations (millimolar)"
legend_states[1] = "Nai in component intracellular_ion_concentrations (millimolar)"
legend_states[2] = "m in component fast_sodium_current_m_gate (dimensionless)"
legend_states[3] = "h in component fast_sodium_current_h_gate (dimensionless)"
legend_states[4] = "j in component fast_sodium_current_j_gate (dimensionless)"
legend_algebraic[10] = "alpha_m in component fast_sodium_current_m_gate (per_second)"
legend_algebraic[20] = "beta_m in component fast_sodium_current_m_gate (per_second)"
legend_algebraic[0] = "E0_m in component fast_sodium_current_m_gate (millivolt)"
legend_algebraic[1] = "alpha_h in component fast_sodium_current_h_gate (per_second)"
legend_algebraic[11] = "beta_h in component fast_sodium_current_h_gate (per_second)"
legend_algebraic[2] = "alpha_j in component fast_sodium_current_j_gate (per_second)"
legend_algebraic[12] = "beta_j in component fast_sodium_current_j_gate (per_second)"
legend_algebraic[26] = "E_K in component rapid_activating_delayed_rectifiyer_K_current (millivolt)"
legend_constants[11] = "g_Kr in component rapid_activating_delayed_rectifiyer_K_current (milliS_per_microF)"
legend_constants[77] = "f_Ko in component rapid_activating_delayed_rectifiyer_K_current (dimensionless)"
legend_algebraic[28] = "R_V in component rapid_activating_delayed_rectifiyer_K_current (dimensionless)"
legend_constants[12] = "Ko in component standard_ionic_concentrations (millimolar)"
legend_states[5] = "Ki in component intracellular_ion_concentrations (millimolar)"
legend_states[6] = "X_kr in component rapid_activating_delayed_rectifiyer_K_current_X_kr_gate (dimensionless)"
legend_algebraic[3] = "K12 in component rapid_activating_delayed_rectifiyer_K_current_X_kr_gate (dimensionless)"
legend_algebraic[13] = "K21 in component rapid_activating_delayed_rectifiyer_K_current_X_kr_gate (dimensionless)"
legend_algebraic[21] = "X_kr_inf in component rapid_activating_delayed_rectifiyer_K_current_X_kr_gate (dimensionless)"
legend_algebraic[24] = "tau_X_kr in component rapid_activating_delayed_rectifiyer_K_current_X_kr_gate (second)"
legend_constants[13] = "tau_factor in component rapid_activating_delayed_rectifiyer_K_current_X_kr_gate (dimensionless)"
legend_constants[14] = "g_Ks in component slow_activating_delayed_rectifiyer_K_current (milliS_per_microF)"
legend_algebraic[30] = "E_Ks in component slow_activating_delayed_rectifiyer_K_current (millivolt)"
legend_states[7] = "X_ks in component slow_activating_delayed_rectifiyer_K_current_X_ks_gate (dimensionless)"
legend_algebraic[14] = "tau_X_ks in component slow_activating_delayed_rectifiyer_K_current_X_ks_gate (second)"
legend_algebraic[4] = "X_ks_infinity in component slow_activating_delayed_rectifiyer_K_current_X_ks_gate (dimensionless)"
legend_constants[15] = "g_to1 in component transient_outward_potassium_current (milliS_per_microF)"
legend_states[8] = "X_to1 in component transient_outward_potassium_current_X_to1_gate (dimensionless)"
legend_states[9] = "Y_to1 in component transient_outward_potassium_current_Y_to1_gate (dimensionless)"
legend_algebraic[5] = "alpha_X_to1 in component transient_outward_potassium_current_X_to1_gate (per_second)"
legend_algebraic[15] = "beta_X_to1 in component transient_outward_potassium_current_X_to1_gate (per_second)"
legend_algebraic[6] = "alpha_Y_to1 in component transient_outward_potassium_current_Y_to1_gate (per_second)"
legend_algebraic[16] = "beta_Y_to1 in component transient_outward_potassium_current_Y_to1_gate (per_second)"
legend_constants[16] = "g_K1 in component time_independent_potassium_current (milliS_per_microF)"
legend_constants[17] = "K_mK1 in component time_independent_potassium_current (millimolar)"
legend_algebraic[33] = "K1_infinity_V in component time_independent_potassium_current_K1_gate (dimensionless)"
legend_constants[18] = "g_Kp in component plateau_potassium_current (milliS_per_microF)"
legend_algebraic[35] = "Kp_V in component plateau_potassium_current_Kp_gate (dimensionless)"
legend_constants[19] = "K_mCa in component Na_Ca_exchanger (millimolar)"
legend_constants[20] = "K_mNa in component Na_Ca_exchanger (millimolar)"
legend_constants[21] = "K_NaCa in component Na_Ca_exchanger (microA_per_microF)"
legend_constants[22] = "K_sat in component Na_Ca_exchanger (dimensionless)"
legend_constants[23] = "eta in component Na_Ca_exchanger (dimensionless)"
legend_states[10] = "Cai in component intracellular_ion_concentrations (millimolar)"
legend_constants[24] = "Cao in component standard_ionic_concentrations (millimolar)"
legend_constants[25] = "I_NaK in component sodium_potassium_pump (microA_per_microF)"
legend_algebraic[38] = "f_NaK in component sodium_potassium_pump (dimensionless)"
legend_constants[26] = "K_mNai in component sodium_potassium_pump (millimolar)"
legend_constants[27] = "K_mKo in component sodium_potassium_pump (millimolar)"
legend_constants[78] = "sigma in component sodium_potassium_pump (dimensionless)"
legend_constants[28] = "K_mpCa in component sarcolemmal_calcium_pump (millimolar)"
legend_constants[29] = "I_pCa in component sarcolemmal_calcium_pump (microA_per_microF)"
legend_constants[30] = "g_Cab in component calcium_background_current (milliS_per_microF)"
legend_algebraic[41] = "E_Ca in component calcium_background_current (millivolt)"
legend_constants[31] = "g_Nab in component sodium_background_current (milliS_per_microF)"
legend_constants[32] = "P_Ca in component L_type_Ca_current (cm_per_second)"
legend_constants[33] = "P_K in component L_type_Ca_current (cm_per_second)"
legend_algebraic[46] = "p_prime_k in component L_type_Ca_current (cm_per_second)"
legend_constants[34] = "i_Ca_half in component L_type_Ca_current (microA_per_microF)"
legend_algebraic[44] = "i_Ca_max in component L_type_Ca_current (microA_per_microF)"
legend_states[11] = "O in component L_type_Ca_current (dimensionless)"
legend_states[12] = "O_Ca in component L_type_Ca_current (dimensionless)"
legend_algebraic[7] = "alpha in component L_type_Ca_current (per_second)"
legend_algebraic[17] = "beta in component L_type_Ca_current (per_second)"
legend_algebraic[27] = "gamma in component L_type_Ca_current (per_second)"
legend_algebraic[22] = "alpha_a in component L_type_Ca_current (per_second)"
legend_algebraic[25] = "beta_b in component L_type_Ca_current (per_second)"
legend_constants[35] = "a in component L_type_Ca_current (dimensionless)"
legend_constants[36] = "b in component L_type_Ca_current (dimensionless)"
legend_constants[37] = "g in component L_type_Ca_current (per_second)"
legend_constants[38] = "f in component L_type_Ca_current (per_second)"
legend_constants[39] = "gprime in component L_type_Ca_current (per_second)"
legend_constants[40] = "fprime in component L_type_Ca_current (per_second)"
legend_constants[41] = "omega in component L_type_Ca_current (per_second)"
legend_states[13] = "C0 in component L_type_Ca_current (dimensionless)"
legend_states[14] = "C1 in component L_type_Ca_current (dimensionless)"
legend_states[15] = "C2 in component L_type_Ca_current (dimensionless)"
legend_states[16] = "C3 in component L_type_Ca_current (dimensionless)"
legend_states[17] = "C4 in component L_type_Ca_current (dimensionless)"
legend_states[18] = "C_Ca0 in component L_type_Ca_current (dimensionless)"
legend_states[19] = "C_Ca1 in component L_type_Ca_current (dimensionless)"
legend_states[20] = "C_Ca2 in component L_type_Ca_current (dimensionless)"
legend_states[21] = "C_Ca3 in component L_type_Ca_current (dimensionless)"
legend_states[22] = "C_Ca4 in component L_type_Ca_current (dimensionless)"
legend_states[23] = "Ca_ss in component intracellular_ion_concentrations (millimolar)"
legend_states[24] = "y in component L_type_Ca_current_y_gate (dimensionless)"
legend_algebraic[8] = "y_infinity in component L_type_Ca_current_y_gate (dimensionless)"
legend_algebraic[18] = "tau_y in component L_type_Ca_current_y_gate (second)"
legend_algebraic[47] = "J_rel in component RyR_channel (millimolar_per_second)"
legend_constants[42] = "v1 in component RyR_channel (per_second)"
legend_constants[43] = "k_a_plus in component RyR_channel (millimolar4_per_second)"
legend_constants[44] = "k_a_minus in component RyR_channel (per_second)"
legend_constants[45] = "k_b_plus in component RyR_channel (millimolar3_per_second)"
legend_constants[46] = "k_b_minus in component RyR_channel (per_second)"
legend_constants[47] = "k_c_plus in component RyR_channel (per_second)"
legend_constants[48] = "k_c_minus in component RyR_channel (per_second)"
legend_states[25] = "P_O1 in component RyR_channel (dimensionless)"
legend_states[26] = "P_O2 in component RyR_channel (dimensionless)"
legend_states[27] = "P_C1 in component RyR_channel (dimensionless)"
legend_states[28] = "P_C2 in component RyR_channel (dimensionless)"
legend_constants[49] = "n in component RyR_channel (dimensionless)"
legend_constants[50] = "m in component RyR_channel (dimensionless)"
legend_states[29] = "Ca_JSR in component intracellular_ion_concentrations (millimolar)"
legend_algebraic[51] = "J_up in component SERCA2a_pump (millimolar_per_second)"
legend_constants[51] = "K_fb in component SERCA2a_pump (millimolar)"
legend_constants[52] = "K_rb in component SERCA2a_pump (millimolar)"
legend_algebraic[49] = "fb in component SERCA2a_pump (dimensionless)"
legend_algebraic[50] = "rb in component SERCA2a_pump (dimensionless)"
legend_constants[53] = "Vmaxf in component SERCA2a_pump (millimolar_per_second)"
legend_constants[54] = "Vmaxr in component SERCA2a_pump (millimolar_per_second)"
legend_constants[55] = "K_SR in component SERCA2a_pump (dimensionless)"
legend_constants[56] = "N_fb in component SERCA2a_pump (dimensionless)"
legend_constants[57] = "N_rb in component SERCA2a_pump (dimensionless)"
legend_states[30] = "Ca_NSR in component intracellular_ion_concentrations (millimolar)"
legend_algebraic[53] = "J_tr in component intracellular_Ca_fluxes (millimolar_per_second)"
legend_algebraic[52] = "J_xfer in component intracellular_Ca_fluxes (millimolar_per_second)"
legend_algebraic[58] = "J_trpn in component intracellular_Ca_fluxes (millimolar_per_second)"
legend_constants[58] = "tau_tr in component intracellular_Ca_fluxes (second)"
legend_constants[59] = "tau_xfer in component intracellular_Ca_fluxes (second)"
legend_states[31] = "HTRPNCa in component intracellular_Ca_fluxes (millimolar)"
legend_states[32] = "LTRPNCa in component intracellular_Ca_fluxes (millimolar)"
legend_algebraic[56] = "J_HTRPNCa in component intracellular_Ca_fluxes (millimolar_per_second)"
legend_algebraic[57] = "J_LTRPNCa in component intracellular_Ca_fluxes (millimolar_per_second)"
legend_constants[60] = "HTRPN_tot in component intracellular_Ca_fluxes (dimensionless)"
legend_constants[61] = "LTRPN_tot in component intracellular_Ca_fluxes (dimensionless)"
legend_constants[62] = "k_htrpn_plus in component intracellular_Ca_fluxes (per_millimolar_second)"
legend_constants[63] = "k_htrpn_minus in component intracellular_Ca_fluxes (per_second)"
legend_constants[64] = "k_ltrpn_plus in component intracellular_Ca_fluxes (per_millimolar_second)"
legend_constants[65] = "k_ltrpn_minus in component intracellular_Ca_fluxes (per_second)"
legend_constants[66] = "A_cap in component intracellular_ion_concentrations (cm2)"
legend_constants[67] = "V_myo in component intracellular_ion_concentrations (micro_litre)"
legend_constants[68] = "V_JSR in component intracellular_ion_concentrations (micro_litre)"
legend_constants[69] = "V_NSR in component intracellular_ion_concentrations (micro_litre)"
legend_constants[70] = "V_SS in component intracellular_ion_concentrations (micro_litre)"
legend_constants[71] = "K_mCMDN in component intracellular_ion_concentrations (millimolar)"
legend_constants[72] = "K_mEGTA in component intracellular_ion_concentrations (millimolar)"
legend_constants[73] = "K_mCSQN in component intracellular_ion_concentrations (millimolar)"
legend_constants[74] = "CMDN_tot in component intracellular_ion_concentrations (millimolar)"
legend_constants[75] = "EGTA_tot in component intracellular_ion_concentrations (millimolar)"
legend_constants[76] = "CSQN_tot in component intracellular_ion_concentrations (millimolar)"
legend_algebraic[59] = "beta_i in component intracellular_ion_concentrations (dimensionless)"
legend_algebraic[54] = "beta_SS in component intracellular_ion_concentrations (dimensionless)"
legend_algebraic[55] = "beta_JSR in component intracellular_ion_concentrations (dimensionless)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[2] = "d/dt m in component fast_sodium_current_m_gate (dimensionless)"
legend_rates[3] = "d/dt h in component fast_sodium_current_h_gate (dimensionless)"
legend_rates[4] = "d/dt j in component fast_sodium_current_j_gate (dimensionless)"
legend_rates[6] = "d/dt X_kr in component rapid_activating_delayed_rectifiyer_K_current_X_kr_gate (dimensionless)"
legend_rates[7] = "d/dt X_ks in component slow_activating_delayed_rectifiyer_K_current_X_ks_gate (dimensionless)"
legend_rates[8] = "d/dt X_to1 in component transient_outward_potassium_current_X_to1_gate (dimensionless)"
legend_rates[9] = "d/dt Y_to1 in component transient_outward_potassium_current_Y_to1_gate (dimensionless)"
legend_rates[13] = "d/dt C0 in component L_type_Ca_current (dimensionless)"
legend_rates[14] = "d/dt C1 in component L_type_Ca_current (dimensionless)"
legend_rates[15] = "d/dt C2 in component L_type_Ca_current (dimensionless)"
legend_rates[16] = "d/dt C3 in component L_type_Ca_current (dimensionless)"
legend_rates[17] = "d/dt C4 in component L_type_Ca_current (dimensionless)"
legend_rates[11] = "d/dt O in component L_type_Ca_current (dimensionless)"
legend_rates[18] = "d/dt C_Ca0 in component L_type_Ca_current (dimensionless)"
legend_rates[19] = "d/dt C_Ca1 in component L_type_Ca_current (dimensionless)"
legend_rates[20] = "d/dt C_Ca2 in component L_type_Ca_current (dimensionless)"
legend_rates[21] = "d/dt C_Ca3 in component L_type_Ca_current (dimensionless)"
legend_rates[22] = "d/dt C_Ca4 in component L_type_Ca_current (dimensionless)"
legend_rates[12] = "d/dt O_Ca in component L_type_Ca_current (dimensionless)"
legend_rates[24] = "d/dt y in component L_type_Ca_current_y_gate (dimensionless)"
legend_rates[27] = "d/dt P_C1 in component RyR_channel (dimensionless)"
legend_rates[25] = "d/dt P_O1 in component RyR_channel (dimensionless)"
legend_rates[26] = "d/dt P_O2 in component RyR_channel (dimensionless)"
legend_rates[28] = "d/dt P_C2 in component RyR_channel (dimensionless)"
legend_rates[31] = "d/dt HTRPNCa in component intracellular_Ca_fluxes (millimolar)"
legend_rates[32] = "d/dt LTRPNCa in component intracellular_Ca_fluxes (millimolar)"
legend_rates[10] = "d/dt Cai in component intracellular_ion_concentrations (millimolar)"
legend_rates[1] = "d/dt Nai in component intracellular_ion_concentrations (millimolar)"
legend_rates[5] = "d/dt Ki in component intracellular_ion_concentrations (millimolar)"
legend_rates[23] = "d/dt Ca_ss in component intracellular_ion_concentrations (millimolar)"
legend_rates[29] = "d/dt Ca_JSR in component intracellular_ion_concentrations (millimolar)"
legend_rates[30] = "d/dt Ca_NSR in component intracellular_ion_concentrations (millimolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -96.1638
constants[0] = 8.314472
constants[1] = 310
constants[2] = 96.4853415
constants[3] = 0.001
constants[4] = 0.1
constants[5] = 100000000
constants[6] = 1
constants[7] = 0.002
constants[8] = -21.1268
constants[9] = 12.8
constants[10] = 138
states[1] = 10
states[2] = 0.0328302
states[3] = 0.988354
states[4] = 0.99254
constants[11] = 0.0034
constants[12] = 4
states[5] = 157.8
states[6] = 0.51
constants[13] = 1
constants[14] = 0.0027134
states[7] = 0.264
constants[15] = 0.23815
states[8] = 2.63
states[9] = 0.99
constants[16] = 2.8
constants[17] = 13
constants[18] = 0.002216
constants[19] = 1.38
constants[20] = 87.5
constants[21] = 0.3
constants[22] = 0.2
constants[23] = 0.35
states[10] = 0.00008
constants[24] = 2
constants[25] = 0.693
constants[26] = 10
constants[27] = 1.5
constants[28] = 0.00005
constants[29] = 0.05
constants[30] = 0.0003842
constants[31] = 0.0031
constants[32] = 3.125e-4
constants[33] = 5.79e-7
constants[34] = -0.265
states[11] = 9.84546e-21
states[12] = 0
constants[35] = 2
constants[36] = 2
constants[37] = 2000
constants[38] = 300
constants[39] = 7000
constants[40] = 7
constants[41] = 10
states[13] = 0.997208
states[14] = 6.38897e-5
states[15] = 1.535e-9
states[16] = 1.63909e-14
states[17] = 6.56337e-20
states[18] = 0.00272826
states[19] = 6.99215e-7
states[20] = 6.71989e-11
states[21] = 2.87031e-15
states[22] = 4.59752e-20
states[23] = 0.00011
states[24] = 0.798
constants[42] = 1800
constants[43] = 1.215e13
constants[44] = 576
constants[45] = 4.05e9
constants[46] = 1930
constants[47] = 100
constants[48] = 0.8
states[25] = 0
states[26] = 0
states[27] = 0.47
states[28] = 0.53
constants[49] = 4
constants[50] = 3
states[29] = 0.257
constants[51] = 0.000168
constants[52] = 3.29
constants[53] = 0.0813
constants[54] = 0.318
constants[55] = 1
constants[56] = 1.2
constants[57] = 1
states[30] = 0.257
constants[58] = 0.0005747
constants[59] = 0.0267
states[31] = 0.98
states[32] = 0.078
constants[60] = 0.14
constants[61] = 0.07
constants[62] = 20000
constants[63] = 0.066
constants[64] = 40000
constants[65] = 40
constants[66] = 0.0001534
constants[67] = 0.00002584
constants[68] = 0.00000016
constants[69] = 0.0000021
constants[70] = 0.0000000012
constants[71] = 0.00238
constants[72] = 0.00015
constants[73] = 0.8
constants[74] = 0.05
constants[75] = 0
constants[76] = 15
constants[77] = power(constants[12]/4.00000, 1.0/2)
constants[78] = (1.00000/7.00000)*(exp(constants[10]/67.3000)-1.00000)
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[11] = constants[38]*states[17]-constants[37]*states[11]
rates[12] = constants[40]*states[22]-constants[39]*states[12]
rates[27] = -constants[43]*(power(states[23], constants[49]))*states[27]+constants[44]*states[25]
rates[25] = (constants[43]*(power(states[23], constants[49]))*states[27]-(constants[44]*states[25]+constants[45]*(power(states[23], constants[50]))*states[25]+constants[47]*states[25]))+constants[46]*states[26]+constants[48]*states[28]
rates[26] = constants[45]*(power(states[23], constants[50]))*states[25]-constants[46]*states[26]
rates[28] = constants[47]*states[25]-constants[48]*states[28]
algebraic[1] = custom_piecewise([less(states[0] , -40.0000), 135.000*exp((80.0000+states[0])/-6.80000) , True, 0.00000])
algebraic[11] = custom_piecewise([less(states[0] , -40.0000), 3560.00*exp(0.0790000*states[0])+310000.*exp(0.350000*states[0]) , True, 1000.00/(0.130000*(1.00000+exp((states[0]+10.6600)/-11.1000)))])
rates[3] = algebraic[1]*(1.00000-states[3])-algebraic[11]*states[3]
algebraic[2] = custom_piecewise([less(states[0] , -40.0000), (1000.00*-(127140.*exp(0.244400*states[0])+3.47400e-05*exp(-0.0439100*states[0]))*(states[0]+37.7800))/(1.00000+exp(0.311000*(states[0]+79.2300))) , True, 0.00000])
algebraic[12] = custom_piecewise([less(states[0] , -40.0000), (121.200*exp(-0.0105200*states[0]))/(1.00000+exp(-0.137800*(states[0]+40.1400))) , True, (300.000*exp(-2.53500e-07*states[0]))/(1.00000+exp(-0.100000*(states[0]+32.0000)))])
rates[4] = algebraic[2]*(1.00000-states[4])-algebraic[12]*states[4]
algebraic[14] = 0.00100000/((7.19000e-05*(states[0]-10.0000))/(1.00000-exp(-0.148000*(states[0]-10.0000)))+(0.000131000*(states[0]-10.0000))/(exp(0.0687000*(states[0]-10.0000))-1.00000))
algebraic[4] = 1.00000/(1.00000+exp(-(states[0]-24.7000)/13.6000))
rates[7] = (algebraic[4]-states[7])/algebraic[14]
algebraic[5] = 45.1600*exp(0.0357700*states[0])
algebraic[15] = 98.9000*exp(-0.0623700*states[0])
rates[8] = algebraic[5]*(1.00000-states[8])-algebraic[15]*states[8]
algebraic[6] = (5.41500*exp(-(states[0]+33.5000)/5.00000))/(1.00000+0.0513350*exp(-(states[0]+33.5000)/5.00000))
algebraic[16] = (5.41500*exp((states[0]+33.5000)/5.00000))/(1.00000+0.0513350*exp((states[0]+33.5000)/5.00000))
rates[9] = algebraic[6]*(1.00000-states[9])-algebraic[16]*states[9]
algebraic[8] = 0.800000/(1.00000+exp((states[0]+12.5000)/5.00000))+0.200000
algebraic[18] = (20.0000+600.000/(1.00000+exp((states[0]+20.0000)/9.50000)))/1000.00
rates[24] = (algebraic[8]-states[24])/algebraic[18]
algebraic[0] = states[0]+47.1300
algebraic[10] = custom_piecewise([less(fabs(algebraic[0]) , 1.00000e-05), 1000.00/(0.100000-0.00500000*algebraic[0]) , True, (320.000*algebraic[0])/(1.00000-exp(-0.100000*algebraic[0]))])
algebraic[20] = 80.0000*exp(-states[0]/11.0000)
rates[2] = custom_piecewise([greater_equal(states[0] , -90.0000), algebraic[10]*(1.00000-states[2])-algebraic[20]*states[2] , True, 0.00000])
algebraic[3] = exp(-5.49500+0.169100*states[0])
algebraic[13] = exp(-7.67700-0.0128000*states[0])
algebraic[21] = algebraic[3]/(algebraic[3]+algebraic[13])
algebraic[24] = 0.00100000/(algebraic[3]+algebraic[13])+constants[13]*0.0270000
rates[6] = (algebraic[21]-states[6])/algebraic[24]
algebraic[7] = 400.000*exp((states[0]+2.00000)/10.0000)
algebraic[17] = 50.0000*exp(-(states[0]+2.00000)/13.0000)
algebraic[27] = (103.750*states[23])/1.00000
rates[13] = (algebraic[17]*states[14]+constants[41]*states[18])-(4.00000*algebraic[7]+algebraic[27])*states[13]
rates[14] = (4.00000*algebraic[7]*states[13]+2.00000*algebraic[17]*states[15]+(constants[41]/constants[36])*states[19])-(algebraic[17]+3.00000*algebraic[7]+algebraic[27]*constants[35])*states[14]
rates[15] = (3.00000*algebraic[7]*states[14]+3.00000*algebraic[17]*states[16]+(constants[41]/(power(constants[36], 2.00000)))*states[20])-(algebraic[17]*2.00000+2.00000*algebraic[7]+algebraic[27]*(power(constants[35], 2.00000)))*states[15]
rates[16] = (2.00000*algebraic[7]*states[15]+4.00000*algebraic[17]*states[17]+(constants[41]/(power(constants[36], 3.00000)))*states[21])-(algebraic[17]*3.00000+algebraic[7]+algebraic[27]*(power(constants[35], 3.00000)))*states[16]
rates[17] = (algebraic[7]*states[16]+constants[37]*states[11]+(constants[41]/(power(constants[36], 4.00000)))*states[22])-(algebraic[17]*4.00000+constants[38]+algebraic[27]*(power(constants[35], 4.00000)))*states[17]
algebraic[22] = algebraic[7]*constants[35]
algebraic[25] = algebraic[17]/constants[36]
rates[18] = (algebraic[25]*states[19]+algebraic[27]*states[13])-(4.00000*algebraic[22]+constants[41])*states[18]
rates[19] = (4.00000*algebraic[22]*states[18]+2.00000*algebraic[25]*states[20]+algebraic[27]*constants[35]*states[14])-(algebraic[25]+3.00000*algebraic[22]+constants[41]/constants[36])*states[19]
rates[20] = (3.00000*algebraic[22]*states[19]+3.00000*algebraic[25]*states[21]+algebraic[27]*(power(constants[35], 2.00000))*states[15])-(algebraic[25]*2.00000+2.00000*algebraic[22]+constants[41]/(power(constants[36], 2.00000)))*states[20]
rates[21] = (2.00000*algebraic[22]*states[20]+4.00000*algebraic[25]*states[22]+algebraic[27]*(power(constants[35], 3.00000))*states[16])-(algebraic[25]*3.00000+algebraic[22]+constants[41]/(power(constants[36], 3.00000)))*states[21]
rates[22] = (algebraic[22]*states[21]+constants[39]*states[12]+algebraic[27]*(power(constants[35], 4.00000))*states[17])-(algebraic[25]*4.00000+constants[40]+constants[41]/(power(constants[36], 4.00000)))*states[22]
algebraic[19] = ((constants[0]*constants[1])/constants[2])*log(constants[10]/states[1])
algebraic[23] = constants[9]*(power(states[2], 3.00000))*states[3]*states[4]*(states[0]-algebraic[19])
algebraic[37] = ((constants[21]*5000.00)/((power(constants[20], 3.00000)+power(constants[10], 3.00000))*(constants[19]+constants[24])*(1.00000+constants[22]*exp(((constants[23]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1])))))*(exp((constants[23]*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[1], 3.00000))*constants[24]-exp(((constants[23]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[10], 3.00000))*states[10])
algebraic[38] = 1.00000/(1.00000+0.124500*exp((-0.100000*states[0]*constants[2])/(constants[0]*constants[1]))+0.0365000*constants[78]*exp((-states[0]*constants[2])/(constants[0]*constants[1])))
algebraic[39] = (((constants[25]*algebraic[38])/(1.00000+power(constants[26]/states[1], 1.50000)))*constants[12])/(constants[12]+constants[27])
algebraic[43] = constants[31]*(states[0]-algebraic[19])
rates[1] = (-0.00000*(algebraic[23]+algebraic[43]+algebraic[37]*3.00000+algebraic[39]*3.00000)*constants[66]*1.00000)/(constants[67]*constants[2])
algebraic[44] = ((((constants[32]/(1.00000*1.00000))*4.00000*states[0]*(power(constants[2], 2.00000))*1000.00)/(constants[0]*constants[1]))*(0.00100000*exp((2.00000*states[0]*constants[2])/(constants[0]*constants[1]))-0.341000*constants[24]))/(exp((2.00000*states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[45] = algebraic[44]*states[24]*(states[11]+states[12])
algebraic[46] = constants[33]/(1.00000+algebraic[44]/constants[34])
algebraic[48] = ((((algebraic[46]/(1.00000*1.00000))*states[24]*(states[11]+states[12])*states[0]*(power(constants[2], 2.00000)))/(constants[0]*constants[1]))*(states[5]*exp((states[0]*constants[2])/(constants[0]*constants[1]))-constants[12]))/(exp((states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[26] = ((constants[0]*constants[1])/constants[2])*log(constants[12]/states[5])
algebraic[28] = 1.00000/(1.00000+1.49450*exp(0.0446000*states[0]))
algebraic[29] = constants[11]*constants[77]*algebraic[28]*states[6]*(states[0]-algebraic[26])
algebraic[30] = ((constants[0]*constants[1])/constants[2])*log((constants[12]+0.0183300*constants[10])/(states[5]+0.0183300*states[1]))
algebraic[31] = constants[14]*(power(states[7], 2.00000))*(states[0]-algebraic[30])
algebraic[32] = constants[15]*states[8]*states[9]*(states[0]-algebraic[26])
algebraic[33] = 1.00000/(2.00000+exp(((1.50000*constants[2])/(constants[0]*constants[1]))*(states[0]-algebraic[26])))
algebraic[34] = ((constants[16]*algebraic[33]*constants[12])/(constants[12]+constants[17]))*(states[0]-algebraic[26])
algebraic[35] = 1.00000/(1.00000+exp((7.48800-states[0])/5.98000))
algebraic[36] = constants[18]*algebraic[35]*(states[0]-algebraic[26])
algebraic[40] = (constants[29]*states[10])/(constants[28]+states[10])
algebraic[41] = ((constants[0]*constants[1])/(2.00000*constants[2]))*log(constants[24]/states[10])
algebraic[42] = constants[30]*(states[0]-algebraic[41])
algebraic[9] = custom_piecewise([greater_equal(voi , constants[4]) & less_equal(voi , constants[5]) & less_equal((voi-constants[4])-floor((voi-constants[4])/constants[6])*constants[6] , constants[7]), constants[8] , True, 0.00000])
rates[0] = (-1.00000*1.00000*(algebraic[23]+algebraic[45]+algebraic[48]+algebraic[29]+algebraic[31]+algebraic[32]+algebraic[34]+algebraic[36]+algebraic[37]+algebraic[39]+algebraic[40]+algebraic[43]+algebraic[42]+algebraic[9]))/constants[3]
rates[5] = (-0.00000*(algebraic[48]+algebraic[29]+algebraic[31]+algebraic[34]+algebraic[36]+algebraic[32]+algebraic[39]*-2.00000)*constants[66]*1.00000)/(constants[67]*constants[2])
rates[31] = constants[62]*states[10]*(1.00000-states[31])-constants[63]*states[31]
algebraic[49] = power(states[10]/constants[51], constants[56])
algebraic[50] = power(states[30]/constants[52], constants[57])
algebraic[51] = (constants[55]*(constants[53]*algebraic[49]-constants[54]*algebraic[50]))/(1.00000+algebraic[49]+algebraic[50])
algebraic[53] = (states[30]-states[29])/constants[58]
rates[30] = (algebraic[51]*constants[67])/constants[69]-(algebraic[53]*constants[68])/constants[69]
algebraic[47] = constants[42]*(states[25]+states[26])*(states[29]-states[23])
algebraic[52] = (states[23]-states[10])/constants[59]
algebraic[54] = 1.00000/(1.00000+(constants[74]*constants[71])/(power(constants[71]+states[23], 2.00000))+(constants[75]*constants[72])/(power(constants[72]+states[23], 2.00000)))
rates[23] = algebraic[54]*(((algebraic[47]*constants[68])/constants[70]-(algebraic[52]*constants[67])/constants[70])-(algebraic[45]*constants[66]*1.00000)/(2.00000*constants[70]*constants[2]))
algebraic[55] = 1.00000/(1.00000+(constants[76]*constants[73])/(power(constants[73]+states[29], 2.00000)))
rates[29] = algebraic[55]*(algebraic[53]-algebraic[47])
rates[32] = constants[64]*states[10]*(1.00000-states[32])-constants[65]*states[32]
algebraic[56] = rates[31]
algebraic[57] = rates[32]
algebraic[58] = constants[60]*algebraic[56]+constants[61]*algebraic[57]
algebraic[59] = 1.00000/(1.00000+(constants[74]*constants[71])/(power(constants[71]+states[10], 2.00000))+(constants[75]*constants[72])/(power(constants[72]+states[10], 2.00000)))
rates[10] = algebraic[59]*((algebraic[52]-(algebraic[51]+algebraic[58]))+((2.00000*algebraic[37]-(algebraic[40]+algebraic[42]))*constants[66]*1.00000)/(2.00000*constants[67]*constants[2]))
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = custom_piecewise([less(states[0] , -40.0000), 135.000*exp((80.0000+states[0])/-6.80000) , True, 0.00000])
algebraic[11] = custom_piecewise([less(states[0] , -40.0000), 3560.00*exp(0.0790000*states[0])+310000.*exp(0.350000*states[0]) , True, 1000.00/(0.130000*(1.00000+exp((states[0]+10.6600)/-11.1000)))])
algebraic[2] = custom_piecewise([less(states[0] , -40.0000), (1000.00*-(127140.*exp(0.244400*states[0])+3.47400e-05*exp(-0.0439100*states[0]))*(states[0]+37.7800))/(1.00000+exp(0.311000*(states[0]+79.2300))) , True, 0.00000])
algebraic[12] = custom_piecewise([less(states[0] , -40.0000), (121.200*exp(-0.0105200*states[0]))/(1.00000+exp(-0.137800*(states[0]+40.1400))) , True, (300.000*exp(-2.53500e-07*states[0]))/(1.00000+exp(-0.100000*(states[0]+32.0000)))])
algebraic[14] = 0.00100000/((7.19000e-05*(states[0]-10.0000))/(1.00000-exp(-0.148000*(states[0]-10.0000)))+(0.000131000*(states[0]-10.0000))/(exp(0.0687000*(states[0]-10.0000))-1.00000))
algebraic[4] = 1.00000/(1.00000+exp(-(states[0]-24.7000)/13.6000))
algebraic[5] = 45.1600*exp(0.0357700*states[0])
algebraic[15] = 98.9000*exp(-0.0623700*states[0])
algebraic[6] = (5.41500*exp(-(states[0]+33.5000)/5.00000))/(1.00000+0.0513350*exp(-(states[0]+33.5000)/5.00000))
algebraic[16] = (5.41500*exp((states[0]+33.5000)/5.00000))/(1.00000+0.0513350*exp((states[0]+33.5000)/5.00000))
algebraic[8] = 0.800000/(1.00000+exp((states[0]+12.5000)/5.00000))+0.200000
algebraic[18] = (20.0000+600.000/(1.00000+exp((states[0]+20.0000)/9.50000)))/1000.00
algebraic[0] = states[0]+47.1300
algebraic[10] = custom_piecewise([less(fabs(algebraic[0]) , 1.00000e-05), 1000.00/(0.100000-0.00500000*algebraic[0]) , True, (320.000*algebraic[0])/(1.00000-exp(-0.100000*algebraic[0]))])
algebraic[20] = 80.0000*exp(-states[0]/11.0000)
algebraic[3] = exp(-5.49500+0.169100*states[0])
algebraic[13] = exp(-7.67700-0.0128000*states[0])
algebraic[21] = algebraic[3]/(algebraic[3]+algebraic[13])
algebraic[24] = 0.00100000/(algebraic[3]+algebraic[13])+constants[13]*0.0270000
algebraic[7] = 400.000*exp((states[0]+2.00000)/10.0000)
algebraic[17] = 50.0000*exp(-(states[0]+2.00000)/13.0000)
algebraic[27] = (103.750*states[23])/1.00000
algebraic[22] = algebraic[7]*constants[35]
algebraic[25] = algebraic[17]/constants[36]
algebraic[19] = ((constants[0]*constants[1])/constants[2])*log(constants[10]/states[1])
algebraic[23] = constants[9]*(power(states[2], 3.00000))*states[3]*states[4]*(states[0]-algebraic[19])
algebraic[37] = ((constants[21]*5000.00)/((power(constants[20], 3.00000)+power(constants[10], 3.00000))*(constants[19]+constants[24])*(1.00000+constants[22]*exp(((constants[23]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1])))))*(exp((constants[23]*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[1], 3.00000))*constants[24]-exp(((constants[23]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[10], 3.00000))*states[10])
algebraic[38] = 1.00000/(1.00000+0.124500*exp((-0.100000*states[0]*constants[2])/(constants[0]*constants[1]))+0.0365000*constants[78]*exp((-states[0]*constants[2])/(constants[0]*constants[1])))
algebraic[39] = (((constants[25]*algebraic[38])/(1.00000+power(constants[26]/states[1], 1.50000)))*constants[12])/(constants[12]+constants[27])
algebraic[43] = constants[31]*(states[0]-algebraic[19])
algebraic[44] = ((((constants[32]/(1.00000*1.00000))*4.00000*states[0]*(power(constants[2], 2.00000))*1000.00)/(constants[0]*constants[1]))*(0.00100000*exp((2.00000*states[0]*constants[2])/(constants[0]*constants[1]))-0.341000*constants[24]))/(exp((2.00000*states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[45] = algebraic[44]*states[24]*(states[11]+states[12])
algebraic[46] = constants[33]/(1.00000+algebraic[44]/constants[34])
algebraic[48] = ((((algebraic[46]/(1.00000*1.00000))*states[24]*(states[11]+states[12])*states[0]*(power(constants[2], 2.00000)))/(constants[0]*constants[1]))*(states[5]*exp((states[0]*constants[2])/(constants[0]*constants[1]))-constants[12]))/(exp((states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[26] = ((constants[0]*constants[1])/constants[2])*log(constants[12]/states[5])
algebraic[28] = 1.00000/(1.00000+1.49450*exp(0.0446000*states[0]))
algebraic[29] = constants[11]*constants[77]*algebraic[28]*states[6]*(states[0]-algebraic[26])
algebraic[30] = ((constants[0]*constants[1])/constants[2])*log((constants[12]+0.0183300*constants[10])/(states[5]+0.0183300*states[1]))
algebraic[31] = constants[14]*(power(states[7], 2.00000))*(states[0]-algebraic[30])
algebraic[32] = constants[15]*states[8]*states[9]*(states[0]-algebraic[26])
algebraic[33] = 1.00000/(2.00000+exp(((1.50000*constants[2])/(constants[0]*constants[1]))*(states[0]-algebraic[26])))
algebraic[34] = ((constants[16]*algebraic[33]*constants[12])/(constants[12]+constants[17]))*(states[0]-algebraic[26])
algebraic[35] = 1.00000/(1.00000+exp((7.48800-states[0])/5.98000))
algebraic[36] = constants[18]*algebraic[35]*(states[0]-algebraic[26])
algebraic[40] = (constants[29]*states[10])/(constants[28]+states[10])
algebraic[41] = ((constants[0]*constants[1])/(2.00000*constants[2]))*log(constants[24]/states[10])
algebraic[42] = constants[30]*(states[0]-algebraic[41])
algebraic[9] = custom_piecewise([greater_equal(voi , constants[4]) & less_equal(voi , constants[5]) & less_equal((voi-constants[4])-floor((voi-constants[4])/constants[6])*constants[6] , constants[7]), constants[8] , True, 0.00000])
algebraic[49] = power(states[10]/constants[51], constants[56])
algebraic[50] = power(states[30]/constants[52], constants[57])
algebraic[51] = (constants[55]*(constants[53]*algebraic[49]-constants[54]*algebraic[50]))/(1.00000+algebraic[49]+algebraic[50])
algebraic[53] = (states[30]-states[29])/constants[58]
algebraic[47] = constants[42]*(states[25]+states[26])*(states[29]-states[23])
algebraic[52] = (states[23]-states[10])/constants[59]
algebraic[54] = 1.00000/(1.00000+(constants[74]*constants[71])/(power(constants[71]+states[23], 2.00000))+(constants[75]*constants[72])/(power(constants[72]+states[23], 2.00000)))
algebraic[55] = 1.00000/(1.00000+(constants[76]*constants[73])/(power(constants[73]+states[29], 2.00000)))
algebraic[56] = rates[31]
algebraic[57] = rates[32]
algebraic[58] = constants[60]*algebraic[56]+constants[61]*algebraic[57]
algebraic[59] = 1.00000/(1.00000+(constants[74]*constants[71])/(power(constants[71]+states[10], 2.00000))+(constants[75]*constants[72])/(power(constants[72]+states[10], 2.00000)))
return algebraic
def custom_piecewise(cases):
"""Compute result of a piecewise function"""
return select(cases[0::2],cases[1::2])
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)