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 = 78
sizeStates = 28
sizeConstants = 52
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 (millijoule_per_mole_kelvin)"
legend_constants[1] = "T in component membrane (kelvin)"
legend_constants[2] = "F in component membrane (coulomb_per_mole)"
legend_constants[3] = "Cm in component membrane (nanoF)"
legend_algebraic[30] = "i_Na in component sodium_current (picoA)"
legend_algebraic[52] = "i_Ca_L in component L_type_Ca_channel (picoA)"
legend_algebraic[57] = "i_Ca_T in component T_type_Ca_channel (picoA)"
legend_algebraic[61] = "i_to in component Ca_independent_transient_outward_K_current (picoA)"
legend_algebraic[64] = "i_K1 in component inward_rectifier (picoA)"
legend_algebraic[63] = "i_Kr in component delayed_rectifier_K_current (picoA)"
legend_algebraic[62] = "i_Ks in component delayed_rectifier_K_current (picoA)"
legend_algebraic[66] = "i_B_Na in component background_currents (picoA)"
legend_algebraic[67] = "i_B_Ca in component background_currents (picoA)"
legend_algebraic[68] = "i_B_Cl in component background_currents (picoA)"
legend_algebraic[69] = "i_p in component sodium_potassium_pump (picoA)"
legend_algebraic[70] = "i_CaP in component sarcolemmal_calcium_pump_current (picoA)"
legend_algebraic[71] = "i_NaCa in component Na_Ca_ion_exchanger_current (picoA)"
legend_algebraic[0] = "i_Stim in component membrane (picoA)"
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 (picoA)"
legend_algebraic[15] = "E_Na in component sodium_current (millivolt)"
legend_constants[9] = "P_Na in component sodium_current (nanolitre_per_second)"
legend_constants[10] = "Na_c in component cleft_space_ion_concentrations (millimolar)"
legend_states[1] = "Na_i in component intracellular_ion_concentrations (millimolar)"
legend_states[2] = "m in component sodium_current_m_gate (dimensionless)"
legend_states[3] = "h1 in component sodium_current_h1_gate (dimensionless)"
legend_states[4] = "h2 in component sodium_current_h2_gate (dimensionless)"
legend_algebraic[1] = "E0_m in component sodium_current_m_gate (millivolt)"
legend_algebraic[16] = "alpha_m in component sodium_current_m_gate (per_second)"
legend_algebraic[31] = "beta_m in component sodium_current_m_gate (per_second)"
legend_algebraic[2] = "alpha_h in component sodium_current_h1_gate (per_second)"
legend_algebraic[17] = "beta_h in component sodium_current_h1_gate (per_second)"
legend_algebraic[32] = "h_infinity in component sodium_current_h1_gate (dimensionless)"
legend_algebraic[42] = "tau_h1 in component sodium_current_h1_gate (second)"
legend_algebraic[43] = "tau_h2 in component sodium_current_h2_gate (second)"
legend_constants[11] = "g_Ca_L in component L_type_Ca_channel (nanoS)"
legend_constants[12] = "E_Ca_app in component L_type_Ca_channel (millivolt)"
legend_algebraic[41] = "d_prime in component L_type_Ca_channel (dimensionless)"
legend_states[5] = "d_L in component L_type_Ca_channel_d_L_gate (dimensionless)"
legend_states[6] = "f_L in component L_type_Ca_channel_f_L_gate (dimensionless)"
legend_algebraic[3] = "E0_alpha_d_L in component L_type_Ca_channel_d_L_gate (millivolt)"
legend_algebraic[18] = "E0_beta_d_L in component L_type_Ca_channel_d_L_gate (millivolt)"
legend_algebraic[33] = "alpha_d_L in component L_type_Ca_channel_d_L_gate (per_second)"
legend_algebraic[44] = "beta_d_L in component L_type_Ca_channel_d_L_gate (per_second)"
legend_algebraic[53] = "d_L_infinity in component L_type_Ca_channel_d_L_gate (dimensionless)"
legend_algebraic[58] = "tau_d_L in component L_type_Ca_channel_d_L_gate (second)"
legend_algebraic[4] = "E0_f_L in component L_type_Ca_channel_f_L_gate (millivolt)"
legend_algebraic[19] = "alpha_f_L in component L_type_Ca_channel_f_L_gate (per_second)"
legend_algebraic[34] = "beta_f_L in component L_type_Ca_channel_f_L_gate (per_second)"
legend_algebraic[45] = "f_L_infinity in component L_type_Ca_channel_f_L_gate (dimensionless)"
legend_algebraic[54] = "x_f in component L_type_Ca_channel_f_L_gate (dimensionless)"
legend_algebraic[59] = "tau_f_L in component L_type_Ca_channel_f_L_gate (second)"
legend_constants[13] = "g_Ca_T in component T_type_Ca_channel (nanoS)"
legend_constants[14] = "E_Ca_T in component T_type_Ca_channel (millivolt)"
legend_states[7] = "d_T in component T_type_Ca_channel_d_T_gate (dimensionless)"
legend_states[8] = "f_T in component T_type_Ca_channel_f_T_gate (dimensionless)"
legend_algebraic[5] = "E0_d_T in component T_type_Ca_channel_d_T_gate (millivolt)"
legend_algebraic[20] = "alpha_d_T in component T_type_Ca_channel_d_T_gate (per_second)"
legend_algebraic[35] = "beta_d_T in component T_type_Ca_channel_d_T_gate (per_second)"
legend_algebraic[46] = "d_T_infinity in component T_type_Ca_channel_d_T_gate (dimensionless)"
legend_algebraic[55] = "tau_d_T in component T_type_Ca_channel_d_T_gate (second)"
legend_algebraic[6] = "E0_f_T in component T_type_Ca_channel_f_T_gate (millivolt)"
legend_algebraic[21] = "alpha_f_T in component T_type_Ca_channel_f_T_gate (per_second)"
legend_algebraic[36] = "beta_f_T in component T_type_Ca_channel_f_T_gate (per_second)"
legend_algebraic[47] = "f_T_infinity in component T_type_Ca_channel_f_T_gate (dimensionless)"
legend_algebraic[56] = "tau_f_T in component T_type_Ca_channel_f_T_gate (second)"
legend_algebraic[60] = "E_K in component Ca_independent_transient_outward_K_current (millivolt)"
legend_constants[15] = "g_to in component Ca_independent_transient_outward_K_current (nanoS)"
legend_constants[16] = "K_c in component cleft_space_ion_concentrations (millimolar)"
legend_states[9] = "K_i in component intracellular_ion_concentrations (millimolar)"
legend_states[10] = "r in component Ca_independent_transient_outward_K_current_r_gate (dimensionless)"
legend_states[11] = "s1 in component Ca_independent_transient_outward_K_current_s1_gate (dimensionless)"
legend_states[12] = "s2 in component Ca_independent_transient_outward_K_current_s2_gate (dimensionless)"
legend_states[13] = "s3 in component Ca_independent_transient_outward_K_current_s3_gate (dimensionless)"
legend_algebraic[7] = "alpha_r in component Ca_independent_transient_outward_K_current_r_gate (per_second)"
legend_algebraic[22] = "beta_r in component Ca_independent_transient_outward_K_current_r_gate (per_second)"
legend_algebraic[48] = "tau_r in component Ca_independent_transient_outward_K_current_r_gate (second)"
legend_algebraic[37] = "r_infinity in component Ca_independent_transient_outward_K_current_r_gate (dimensionless)"
legend_algebraic[23] = "tau_s1 in component Ca_independent_transient_outward_K_current_s1_gate (second)"
legend_algebraic[8] = "s1_infinity in component Ca_independent_transient_outward_K_current_s1_gate (dimensionless)"
legend_algebraic[24] = "tau_s2 in component Ca_independent_transient_outward_K_current_s2_gate (second)"
legend_algebraic[9] = "s2_infinity in component Ca_independent_transient_outward_K_current_s2_gate (dimensionless)"
legend_algebraic[25] = "tau_s3 in component Ca_independent_transient_outward_K_current_s3_gate (second)"
legend_algebraic[10] = "s3_infinity in component Ca_independent_transient_outward_K_current_s3_gate (dimensionless)"
legend_constants[17] = "g_Ks in component delayed_rectifier_K_current (nanoS)"
legend_constants[18] = "g_Kr in component delayed_rectifier_K_current (nanoS)"
legend_states[14] = "z in component delayed_rectifier_K_current_z_gate (dimensionless)"
legend_states[15] = "p_a in component delayed_rectifier_K_current_pa_gate (dimensionless)"
legend_states[16] = "p_i in component delayed_rectifier_K_current_pi_gate (dimensionless)"
legend_algebraic[11] = "alpha_z in component delayed_rectifier_K_current_z_gate (per_second)"
legend_algebraic[26] = "beta_z in component delayed_rectifier_K_current_z_gate (per_second)"
legend_algebraic[49] = "tau_z in component delayed_rectifier_K_current_z_gate (second)"
legend_algebraic[38] = "z_infinity in component delayed_rectifier_K_current_z_gate (dimensionless)"
legend_algebraic[12] = "alpha_p_a in component delayed_rectifier_K_current_pa_gate (per_second)"
legend_algebraic[27] = "beta_p_a in component delayed_rectifier_K_current_pa_gate (per_second)"
legend_algebraic[50] = "tau_p_a in component delayed_rectifier_K_current_pa_gate (second)"
legend_algebraic[39] = "p_a_infinity in component delayed_rectifier_K_current_pa_gate (dimensionless)"
legend_algebraic[13] = "alpha_p_i in component delayed_rectifier_K_current_pi_gate (per_second)"
legend_algebraic[28] = "beta_p_i in component delayed_rectifier_K_current_pi_gate (per_second)"
legend_algebraic[51] = "tau_p_i in component delayed_rectifier_K_current_pi_gate (second)"
legend_algebraic[40] = "p_i_infinity in component delayed_rectifier_K_current_pi_gate (dimensionless)"
legend_constants[19] = "g_K1 in component inward_rectifier (nanoS)"
legend_constants[20] = "KmK1 in component inward_rectifier (millimolar)"
legend_constants[21] = "steepK1 in component inward_rectifier (dimensionless)"
legend_constants[22] = "shiftK1 in component inward_rectifier (millivolt)"
legend_constants[23] = "g_B_Na in component background_currents (nanoS)"
legend_constants[24] = "g_B_Ca in component background_currents (nanoS)"
legend_constants[25] = "g_B_Cl in component background_currents (nanoS)"
legend_algebraic[65] = "E_Ca in component background_currents (millivolt)"
legend_constants[50] = "E_Cl in component background_currents (millivolt)"
legend_constants[51] = "E_B_Cl in component background_currents (millivolt)"
legend_constants[26] = "Ca_c in component cleft_space_ion_concentrations (millimolar)"
legend_states[17] = "Ca_i in component intracellular_ion_concentrations (millimolar)"
legend_constants[27] = "Cl_c in component cleft_space_ion_concentrations (millimolar)"
legend_constants[28] = "Cl_i in component intracellular_ion_concentrations (millimolar)"
legend_constants[29] = "k_NaK_K in component sodium_potassium_pump (millimolar)"
legend_constants[30] = "k_NaK_Na in component sodium_potassium_pump (millimolar)"
legend_constants[31] = "i_NaK_max in component sodium_potassium_pump (picoA)"
legend_constants[32] = "i_CaP_max in component sarcolemmal_calcium_pump_current (picoA)"
legend_constants[33] = "k_CaP in component sarcolemmal_calcium_pump_current (millimolar)"
legend_constants[34] = "k_NaCa in component Na_Ca_ion_exchanger_current (picoA_per_millimolar_4)"
legend_constants[35] = "d_NaCa in component Na_Ca_ion_exchanger_current (per_millimolar_4)"
legend_constants[36] = "gamma in component Na_Ca_ion_exchanger_current (dimensionless)"
legend_constants[37] = "Vol_i in component intracellular_ion_concentrations (nanolitre)"
legend_constants[38] = "Vol_Ca in component intracellular_ion_concentrations (nanolitre)"
legend_algebraic[75] = "i_up in component Ca_handling_by_the_SR (picoA)"
legend_algebraic[77] = "i_rel in component Ca_handling_by_the_SR (picoA)"
legend_algebraic[72] = "dOCdt in component intracellular_Ca_buffering (per_second)"
legend_algebraic[73] = "dOTCdt in component intracellular_Ca_buffering (per_second)"
legend_algebraic[74] = "dOTMgCdt in component intracellular_Ca_buffering (per_second)"
legend_states[18] = "O_C in component intracellular_Ca_buffering (dimensionless)"
legend_states[19] = "O_TC in component intracellular_Ca_buffering (dimensionless)"
legend_states[20] = "O_TMgC in component intracellular_Ca_buffering (dimensionless)"
legend_states[21] = "O_TMgMg in component intracellular_Ca_buffering (dimensionless)"
legend_constants[39] = "Mg_i in component intracellular_Ca_buffering (millimolar)"
legend_algebraic[76] = "i_tr in component Ca_handling_by_the_SR (picoA)"
legend_constants[40] = "I_up_max in component Ca_handling_by_the_SR (picoA)"
legend_constants[41] = "k_cyca in component Ca_handling_by_the_SR (millimolar)"
legend_constants[42] = "k_srca in component Ca_handling_by_the_SR (millimolar)"
legend_constants[43] = "k_xcs in component Ca_handling_by_the_SR (dimensionless)"
legend_constants[44] = "alpha_rel in component Ca_handling_by_the_SR (picoA_per_millimolar)"
legend_states[22] = "Ca_rel in component Ca_handling_by_the_SR (millimolar)"
legend_states[23] = "Ca_up in component Ca_handling_by_the_SR (millimolar)"
legend_constants[45] = "Vol_up in component Ca_handling_by_the_SR (nanolitre)"
legend_constants[46] = "Vol_rel in component Ca_handling_by_the_SR (nanolitre)"
legend_algebraic[14] = "r_act in component Ca_handling_by_the_SR (per_second)"
legend_algebraic[29] = "r_inact in component Ca_handling_by_the_SR (per_second)"
legend_states[24] = "O_Calse in component Ca_handling_by_the_SR (dimensionless)"
legend_states[25] = "F1 in component Ca_handling_by_the_SR (dimensionless)"
legend_states[26] = "F2 in component Ca_handling_by_the_SR (dimensionless)"
legend_states[27] = "F3 in component Ca_handling_by_the_SR (dimensionless)"
legend_constants[47] = "tau_tr in component Ca_handling_by_the_SR (second)"
legend_constants[48] = "k_rel in component Ca_handling_by_the_SR (millimolar)"
legend_constants[49] = "k_F3 in component Ca_handling_by_the_SR (per_second)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[2] = "d/dt m in component sodium_current_m_gate (dimensionless)"
legend_rates[3] = "d/dt h1 in component sodium_current_h1_gate (dimensionless)"
legend_rates[4] = "d/dt h2 in component sodium_current_h2_gate (dimensionless)"
legend_rates[5] = "d/dt d_L in component L_type_Ca_channel_d_L_gate (dimensionless)"
legend_rates[6] = "d/dt f_L in component L_type_Ca_channel_f_L_gate (dimensionless)"
legend_rates[7] = "d/dt d_T in component T_type_Ca_channel_d_T_gate (dimensionless)"
legend_rates[8] = "d/dt f_T in component T_type_Ca_channel_f_T_gate (dimensionless)"
legend_rates[10] = "d/dt r in component Ca_independent_transient_outward_K_current_r_gate (dimensionless)"
legend_rates[11] = "d/dt s1 in component Ca_independent_transient_outward_K_current_s1_gate (dimensionless)"
legend_rates[12] = "d/dt s2 in component Ca_independent_transient_outward_K_current_s2_gate (dimensionless)"
legend_rates[13] = "d/dt s3 in component Ca_independent_transient_outward_K_current_s3_gate (dimensionless)"
legend_rates[14] = "d/dt z in component delayed_rectifier_K_current_z_gate (dimensionless)"
legend_rates[15] = "d/dt p_a in component delayed_rectifier_K_current_pa_gate (dimensionless)"
legend_rates[16] = "d/dt p_i in component delayed_rectifier_K_current_pi_gate (dimensionless)"
legend_rates[1] = "d/dt Na_i in component intracellular_ion_concentrations (millimolar)"
legend_rates[9] = "d/dt K_i in component intracellular_ion_concentrations (millimolar)"
legend_rates[17] = "d/dt Ca_i in component intracellular_ion_concentrations (millimolar)"
legend_rates[18] = "d/dt O_C in component intracellular_Ca_buffering (dimensionless)"
legend_rates[19] = "d/dt O_TC in component intracellular_Ca_buffering (dimensionless)"
legend_rates[20] = "d/dt O_TMgC in component intracellular_Ca_buffering (dimensionless)"
legend_rates[21] = "d/dt O_TMgMg in component intracellular_Ca_buffering (dimensionless)"
legend_rates[24] = "d/dt O_Calse in component Ca_handling_by_the_SR (dimensionless)"
legend_rates[22] = "d/dt Ca_rel in component Ca_handling_by_the_SR (millimolar)"
legend_rates[23] = "d/dt Ca_up in component Ca_handling_by_the_SR (millimolar)"
legend_rates[25] = "d/dt F1 in component Ca_handling_by_the_SR (dimensionless)"
legend_rates[26] = "d/dt F2 in component Ca_handling_by_the_SR (dimensionless)"
legend_rates[27] = "d/dt F3 in component Ca_handling_by_the_SR (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -69.83663
constants[0] = 8314.472
constants[1] = 308
constants[2] = 96485.3415
constants[3] = 0.00005
constants[4] = 0.1
constants[5] = 100000
constants[6] = 1
constants[7] = 0.0008
constants[8] = -2
constants[9] = 0.0000014
constants[10] = 140
states[1] = 8.4
states[2] = 0.01309
states[3] = 0.706
states[4] = 0.61493
constants[11] = 0.004
constants[12] = 60
states[5] = 3e-5
states[6] = 0.99981
constants[13] = 0.006
constants[14] = 38
states[7] = 4.6e-4
states[8] = 0.30752
constants[15] = 0.050002
constants[16] = 5
states[9] = 100
states[10] = 6e-5
states[11] = 0.5753
states[12] = 0.39871
states[13] = 0.57363
constants[17] = 0.0025
constants[18] = 0.0035
states[14] = 0.02032
states[15] = 1.6e-4
states[16] = 0.76898
constants[19] = 0.005088
constants[20] = 0.59
constants[21] = 1.393
constants[22] = -3.6
constants[23] = 6.4e-5
constants[24] = 3.1e-5
constants[25] = 1.2e-4
constants[26] = 2.5
states[17] = 7.305e-5
constants[27] = 132
constants[28] = 30
constants[29] = 1
constants[30] = 11
constants[31] = 0.06441
constants[32] = 0.009509
constants[33] = 2e-4
constants[34] = 2e-5
constants[35] = 3e-4
constants[36] = 0.45
constants[37] = 1.26e-5
constants[38] = 5.884e-6
states[18] = 0.02981
states[19] = 0.01442
states[20] = 0.23532
states[21] = 0.67476
constants[39] = 2.5
constants[40] = 2.8
constants[41] = 0.0003
constants[42] = 0.5
constants[43] = 0.4
constants[44] = 200
states[22] = 0.59984
states[23] = 0.64913
constants[45] = 3.969e-7
constants[46] = 4.41e-8
states[24] = 0.41837
states[25] = 0.21603
states[26] = 0.00205
states[27] = 0.68492
constants[47] = 0.01
constants[48] = 0.0003
constants[49] = 0.815
constants[50] = ((constants[0]*constants[1])/constants[2])*log(constants[28]/constants[27])
constants[51] = constants[50]-0.490000*(constants[50]+30.5900)
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[21] = 2000.00*constants[39]*((1.00000-states[20])-states[21])-666.000*states[21]
algebraic[14] = 203.800*exp(0.0800000*(states[0]-40.0000))+203.800*(power(states[17]/(states[17]+constants[48]), 4.00000))
rates[25] = constants[49]*states[27]-algebraic[14]*states[25]
algebraic[23] = 0.546600/(1.00000+exp((states[0]+32.8000)/0.100000))+0.0204000
algebraic[8] = 1.00000/(1.00000+exp((states[0]+28.2900)/7.06000))
rates[11] = (algebraic[8]-states[11])/algebraic[23]
algebraic[24] = 5.75000/(1.00000+exp((states[0]+32.8000)/0.100000))+0.450000/(1.00000+exp((states[0]-13.5400)/-13.9700))
algebraic[9] = 1.00000/(1.00000+exp((states[0]+28.2900)/7.06000))
rates[12] = (algebraic[9]-states[12])/algebraic[24]
algebraic[25] = 7.50000/(1.00000+exp((states[0]+23.0000)/0.500000))+0.500000
algebraic[10] = (1.00000/(1.00000+exp((states[0]+50.6700)/27.3800))+0.666000)/1.66600
rates[13] = (algebraic[10]-states[13])/algebraic[25]
algebraic[29] = 33.9600+339.600*(power(states[17]/(states[17]+constants[48]), 4.00000))
rates[26] = algebraic[14]*states[25]-algebraic[29]*states[26]
rates[27] = states[26]*algebraic[29]-constants[49]*states[27]
algebraic[1] = states[0]+44.4000
algebraic[16] = (-460.000*algebraic[1])/(exp(algebraic[1]/-12.6730)-1.00000)
algebraic[31] = 18400.0*exp(algebraic[1]/-12.6730)
rates[2] = algebraic[16]*(1.00000-states[2])-algebraic[31]*states[2]
algebraic[2] = 44.9000*exp((states[0]+66.9000)/-5.57000)
algebraic[17] = 1491.00/(1.00000+323.300*exp((states[0]+94.6000)/-12.9000))
algebraic[32] = algebraic[2]/(algebraic[2]+algebraic[17])
algebraic[42] = 0.0300000/(1.00000+exp((states[0]+40.0000)/6.00000))+0.000350000
rates[3] = (algebraic[32]-states[3])/algebraic[42]
algebraic[43] = 0.120000/(1.00000+exp((states[0]+60.0000)/2.00000))+0.00295000
rates[4] = (algebraic[32]-states[4])/algebraic[43]
algebraic[7] = 386.600*exp(states[0]/12.0000)
algebraic[22] = 8.01100*exp(states[0]/-7.20000)
algebraic[48] = 1.00000/(algebraic[7]+algebraic[22])+0.000400000
algebraic[37] = 1.00000/(1.00000+exp((states[0]+15.0000)/-5.63300))
rates[10] = (algebraic[37]-states[10])/algebraic[48]
algebraic[11] = 1.66000*exp(states[0]/69.4520)
algebraic[26] = 0.300000*exp(states[0]/-21.8260)
algebraic[49] = 1.00000/(algebraic[11]+algebraic[26])+0.0600000
algebraic[38] = 1.00000/(1.00000+exp((states[0]-0.900000)/-13.8000))
rates[14] = (algebraic[38]-states[14])/algebraic[49]
algebraic[12] = 9.00000*exp(states[0]/25.3710)
algebraic[27] = 1.30000*exp(states[0]/-13.0260)
algebraic[50] = 1.00000/(algebraic[12]+algebraic[27])
algebraic[39] = 1.00000/(1.00000+exp((states[0]+5.10000)/-7.40000))
rates[15] = (algebraic[39]-states[15])/algebraic[50]
algebraic[13] = 100.000*exp(states[0]/-54.6450)
algebraic[28] = 656.000*exp(states[0]/106.157)
algebraic[51] = 1.00000/(algebraic[13]+algebraic[28])
algebraic[40] = 1.00000/(1.00000+exp((states[0]+47.3921)/18.6603))
rates[16] = (algebraic[40]-states[16])/algebraic[51]
algebraic[5] = states[0]+23.0000
algebraic[46] = 1.00000/(1.00000+exp(algebraic[5]/-6.10000))
algebraic[20] = 674.173*exp(algebraic[5]/30.0000)
algebraic[35] = 674.173*exp(algebraic[5]/-30.0000)
algebraic[55] = 1.00000/(algebraic[20]+algebraic[35])
rates[7] = (algebraic[46]-states[7])/algebraic[55]
algebraic[6] = states[0]+75.0000
algebraic[21] = 9.63700*exp(algebraic[6]/-83.3330)
algebraic[36] = 9.63700*exp(algebraic[6]/15.3850)
algebraic[47] = algebraic[21]/(algebraic[21]+algebraic[36])
algebraic[56] = 1.00000/(algebraic[21]+algebraic[36])
rates[8] = (algebraic[47]-states[8])/algebraic[56]
algebraic[53] = 1.00000/(1.00000+exp((states[0]+0.950000)/-6.60000))
algebraic[3] = states[0]+35.0000
algebraic[33] = (-16.7200*algebraic[3])/(exp(algebraic[3]/-2.50000)-1.00000)+(-50.0000*states[0])/(exp(states[0]/-4.80800)-1.00000)
algebraic[18] = states[0]-5.00000
algebraic[44] = (4.48000*algebraic[18])/(exp(algebraic[18]/2.50000)-1.00000)
algebraic[58] = 1.00000/(algebraic[33]+algebraic[44])
rates[5] = (algebraic[53]-states[5])/algebraic[58]
algebraic[4] = states[0]+28.0000
algebraic[19] = (8.49000*algebraic[4])/(exp(algebraic[4]/4.00000)-1.00000)
algebraic[34] = 67.9220/(1.00000+exp(algebraic[4]/-4.00000))
algebraic[45] = algebraic[19]/(algebraic[19]+algebraic[34])
algebraic[54] = (states[0]+37.4270)/20.2130
algebraic[59] = 0.211000*exp(-algebraic[54]*algebraic[54])+0.0150000
rates[6] = (algebraic[45]-states[6])/algebraic[59]
algebraic[60] = ((constants[0]*constants[1])/constants[2])*log(constants[16]/states[9])
algebraic[61] = constants[15]*states[10]*(0.590000*(power(states[11], 3.00000))+0.410000*(power(states[12], 3.00000)))*(0.600000*(power(states[13], 6.00000))+0.400000)*(states[0]-algebraic[60])
algebraic[64] = (constants[19]*(states[0]-algebraic[60])*(power(constants[16]/(constants[16]+constants[20]), 3.00000))*1.00000)/(1.00000+exp((constants[21]*constants[2]*((states[0]-algebraic[60])-constants[22]))/(constants[0]*constants[1])))
algebraic[63] = constants[18]*states[15]*states[16]*(states[0]-algebraic[60])
algebraic[62] = constants[17]*states[14]*(states[0]-algebraic[60])
algebraic[69] = (((((constants[31]*constants[16])/(constants[16]+constants[29]))*(power(states[1], 1.50000)))/(power(states[1], 1.50000)+power(constants[30], 1.50000)))*1.60000)/(1.50000+exp((states[0]+60.0000)/-40.0000))
rates[9] = -((algebraic[61]+algebraic[64]+algebraic[63]+algebraic[62])-2.00000*algebraic[69])/(constants[37]*constants[2])
algebraic[15] = ((constants[0]*constants[1])/constants[2])*log(constants[10]/states[1])
algebraic[30] = (((constants[9]*(power(states[2], 3.00000))*(0.635000*states[3]+0.365000*states[4])*constants[10]*states[0]*(power(constants[2], 2.00000)))/(constants[0]*constants[1]))*(exp(((states[0]-algebraic[15])*constants[2])/(constants[0]*constants[1]))-1.00000))/(exp((states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[41] = 1.00000/(1.00000+exp((states[0]-33.0000)/-12.0000))
algebraic[52] = constants[11]*states[5]*states[6]*algebraic[41]*(states[0]-constants[12])
algebraic[57] = constants[13]*states[7]*states[8]*(states[0]-constants[14])
algebraic[66] = constants[23]*(states[0]-algebraic[15])
algebraic[65] = ((constants[0]*constants[1])/(2.00000*constants[2]))*log(constants[26]/states[17])
algebraic[67] = constants[24]*(states[0]-algebraic[65])
algebraic[68] = constants[25]*(states[0]-constants[51])*(1.00000+exp((states[0]-(constants[50]+36.9500))/74.5140))
algebraic[70] = (constants[32]*states[17])/(states[17]+constants[33])
algebraic[71] = (constants[34]*((power(states[1], 3.00000))*constants[26]*exp((constants[36]*constants[2]*states[0])/(constants[0]*constants[1]))-(power(constants[10], 3.00000))*states[17]*exp(((constants[36]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))))/(1.00000+constants[35]*((power(constants[10], 3.00000))*states[17]+(power(states[1], 3.00000))*constants[26])*(1.00000+states[17]/0.00690000))
algebraic[0] = 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/constants[3])*(algebraic[63]+algebraic[62]+algebraic[30]+algebraic[52]+algebraic[57]+algebraic[61]+algebraic[64]+algebraic[66]+algebraic[67]+algebraic[68]+algebraic[69]+algebraic[70]+algebraic[71]+algebraic[0])
rates[1] = -(algebraic[30]+algebraic[66]+3.00000*algebraic[69]+3.00000*algebraic[71])/(constants[37]*constants[2])
algebraic[72] = 200000.*states[17]*(1.00000-states[18])-476.000*states[18]
rates[18] = algebraic[72]
algebraic[73] = 78400.0*states[17]*(1.00000-states[19])-392.000*states[19]
rates[19] = algebraic[73]
rates[24] = 480.000*states[22]*(1.00000-states[24])-400.000*states[24]
algebraic[74] = 200000.*states[17]*((1.00000-states[20])-states[21])-6.60000*states[20]
rates[20] = algebraic[74]
algebraic[75] = (constants[40]*(states[17]/constants[41]-((power(constants[43], 2.00000))*states[23])/constants[42]))/((states[17]+constants[41])/constants[41]+(constants[43]*(states[23]+constants[42]))/constants[42])
algebraic[76] = ((states[23]-states[22])*2.00000*constants[2]*constants[46])/constants[47]
rates[23] = (algebraic[75]-algebraic[76])/(2.00000*constants[45]*constants[2])
algebraic[77] = constants[44]*(power(states[26]/(states[26]+0.250000), 2.00000))*(states[22]-states[17])
rates[17] = -((((algebraic[52]+algebraic[57]+algebraic[67]+algebraic[70])-2.00000*algebraic[71])+algebraic[75])-algebraic[77])/(2.00000*constants[38]*constants[2])-(0.0800000*algebraic[73]+0.160000*algebraic[74]+0.0450000*algebraic[72])
rates[22] = (algebraic[76]-algebraic[77])/(2.00000*constants[46]*constants[2])-31.0000*rates[24]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[14] = 203.800*exp(0.0800000*(states[0]-40.0000))+203.800*(power(states[17]/(states[17]+constants[48]), 4.00000))
algebraic[23] = 0.546600/(1.00000+exp((states[0]+32.8000)/0.100000))+0.0204000
algebraic[8] = 1.00000/(1.00000+exp((states[0]+28.2900)/7.06000))
algebraic[24] = 5.75000/(1.00000+exp((states[0]+32.8000)/0.100000))+0.450000/(1.00000+exp((states[0]-13.5400)/-13.9700))
algebraic[9] = 1.00000/(1.00000+exp((states[0]+28.2900)/7.06000))
algebraic[25] = 7.50000/(1.00000+exp((states[0]+23.0000)/0.500000))+0.500000
algebraic[10] = (1.00000/(1.00000+exp((states[0]+50.6700)/27.3800))+0.666000)/1.66600
algebraic[29] = 33.9600+339.600*(power(states[17]/(states[17]+constants[48]), 4.00000))
algebraic[1] = states[0]+44.4000
algebraic[16] = (-460.000*algebraic[1])/(exp(algebraic[1]/-12.6730)-1.00000)
algebraic[31] = 18400.0*exp(algebraic[1]/-12.6730)
algebraic[2] = 44.9000*exp((states[0]+66.9000)/-5.57000)
algebraic[17] = 1491.00/(1.00000+323.300*exp((states[0]+94.6000)/-12.9000))
algebraic[32] = algebraic[2]/(algebraic[2]+algebraic[17])
algebraic[42] = 0.0300000/(1.00000+exp((states[0]+40.0000)/6.00000))+0.000350000
algebraic[43] = 0.120000/(1.00000+exp((states[0]+60.0000)/2.00000))+0.00295000
algebraic[7] = 386.600*exp(states[0]/12.0000)
algebraic[22] = 8.01100*exp(states[0]/-7.20000)
algebraic[48] = 1.00000/(algebraic[7]+algebraic[22])+0.000400000
algebraic[37] = 1.00000/(1.00000+exp((states[0]+15.0000)/-5.63300))
algebraic[11] = 1.66000*exp(states[0]/69.4520)
algebraic[26] = 0.300000*exp(states[0]/-21.8260)
algebraic[49] = 1.00000/(algebraic[11]+algebraic[26])+0.0600000
algebraic[38] = 1.00000/(1.00000+exp((states[0]-0.900000)/-13.8000))
algebraic[12] = 9.00000*exp(states[0]/25.3710)
algebraic[27] = 1.30000*exp(states[0]/-13.0260)
algebraic[50] = 1.00000/(algebraic[12]+algebraic[27])
algebraic[39] = 1.00000/(1.00000+exp((states[0]+5.10000)/-7.40000))
algebraic[13] = 100.000*exp(states[0]/-54.6450)
algebraic[28] = 656.000*exp(states[0]/106.157)
algebraic[51] = 1.00000/(algebraic[13]+algebraic[28])
algebraic[40] = 1.00000/(1.00000+exp((states[0]+47.3921)/18.6603))
algebraic[5] = states[0]+23.0000
algebraic[46] = 1.00000/(1.00000+exp(algebraic[5]/-6.10000))
algebraic[20] = 674.173*exp(algebraic[5]/30.0000)
algebraic[35] = 674.173*exp(algebraic[5]/-30.0000)
algebraic[55] = 1.00000/(algebraic[20]+algebraic[35])
algebraic[6] = states[0]+75.0000
algebraic[21] = 9.63700*exp(algebraic[6]/-83.3330)
algebraic[36] = 9.63700*exp(algebraic[6]/15.3850)
algebraic[47] = algebraic[21]/(algebraic[21]+algebraic[36])
algebraic[56] = 1.00000/(algebraic[21]+algebraic[36])
algebraic[53] = 1.00000/(1.00000+exp((states[0]+0.950000)/-6.60000))
algebraic[3] = states[0]+35.0000
algebraic[33] = (-16.7200*algebraic[3])/(exp(algebraic[3]/-2.50000)-1.00000)+(-50.0000*states[0])/(exp(states[0]/-4.80800)-1.00000)
algebraic[18] = states[0]-5.00000
algebraic[44] = (4.48000*algebraic[18])/(exp(algebraic[18]/2.50000)-1.00000)
algebraic[58] = 1.00000/(algebraic[33]+algebraic[44])
algebraic[4] = states[0]+28.0000
algebraic[19] = (8.49000*algebraic[4])/(exp(algebraic[4]/4.00000)-1.00000)
algebraic[34] = 67.9220/(1.00000+exp(algebraic[4]/-4.00000))
algebraic[45] = algebraic[19]/(algebraic[19]+algebraic[34])
algebraic[54] = (states[0]+37.4270)/20.2130
algebraic[59] = 0.211000*exp(-algebraic[54]*algebraic[54])+0.0150000
algebraic[60] = ((constants[0]*constants[1])/constants[2])*log(constants[16]/states[9])
algebraic[61] = constants[15]*states[10]*(0.590000*(power(states[11], 3.00000))+0.410000*(power(states[12], 3.00000)))*(0.600000*(power(states[13], 6.00000))+0.400000)*(states[0]-algebraic[60])
algebraic[64] = (constants[19]*(states[0]-algebraic[60])*(power(constants[16]/(constants[16]+constants[20]), 3.00000))*1.00000)/(1.00000+exp((constants[21]*constants[2]*((states[0]-algebraic[60])-constants[22]))/(constants[0]*constants[1])))
algebraic[63] = constants[18]*states[15]*states[16]*(states[0]-algebraic[60])
algebraic[62] = constants[17]*states[14]*(states[0]-algebraic[60])
algebraic[69] = (((((constants[31]*constants[16])/(constants[16]+constants[29]))*(power(states[1], 1.50000)))/(power(states[1], 1.50000)+power(constants[30], 1.50000)))*1.60000)/(1.50000+exp((states[0]+60.0000)/-40.0000))
algebraic[15] = ((constants[0]*constants[1])/constants[2])*log(constants[10]/states[1])
algebraic[30] = (((constants[9]*(power(states[2], 3.00000))*(0.635000*states[3]+0.365000*states[4])*constants[10]*states[0]*(power(constants[2], 2.00000)))/(constants[0]*constants[1]))*(exp(((states[0]-algebraic[15])*constants[2])/(constants[0]*constants[1]))-1.00000))/(exp((states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[41] = 1.00000/(1.00000+exp((states[0]-33.0000)/-12.0000))
algebraic[52] = constants[11]*states[5]*states[6]*algebraic[41]*(states[0]-constants[12])
algebraic[57] = constants[13]*states[7]*states[8]*(states[0]-constants[14])
algebraic[66] = constants[23]*(states[0]-algebraic[15])
algebraic[65] = ((constants[0]*constants[1])/(2.00000*constants[2]))*log(constants[26]/states[17])
algebraic[67] = constants[24]*(states[0]-algebraic[65])
algebraic[68] = constants[25]*(states[0]-constants[51])*(1.00000+exp((states[0]-(constants[50]+36.9500))/74.5140))
algebraic[70] = (constants[32]*states[17])/(states[17]+constants[33])
algebraic[71] = (constants[34]*((power(states[1], 3.00000))*constants[26]*exp((constants[36]*constants[2]*states[0])/(constants[0]*constants[1]))-(power(constants[10], 3.00000))*states[17]*exp(((constants[36]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))))/(1.00000+constants[35]*((power(constants[10], 3.00000))*states[17]+(power(states[1], 3.00000))*constants[26])*(1.00000+states[17]/0.00690000))
algebraic[0] = 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[72] = 200000.*states[17]*(1.00000-states[18])-476.000*states[18]
algebraic[73] = 78400.0*states[17]*(1.00000-states[19])-392.000*states[19]
algebraic[74] = 200000.*states[17]*((1.00000-states[20])-states[21])-6.60000*states[20]
algebraic[75] = (constants[40]*(states[17]/constants[41]-((power(constants[43], 2.00000))*states[23])/constants[42]))/((states[17]+constants[41])/constants[41]+(constants[43]*(states[23]+constants[42]))/constants[42])
algebraic[76] = ((states[23]-states[22])*2.00000*constants[2]*constants[46])/constants[47]
algebraic[77] = constants[44]*(power(states[26]/(states[26]+0.250000), 2.00000))*(states[22]-states[17])
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)