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 = 69
sizeStates = 22
sizeConstants = 63
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 Time (time_units)"
legend_constants[0] = "T in component Environment (Temperature_units)"
legend_constants[1] = "F in component Environment (F_units)"
legend_constants[2] = "R in component Environment (R_units)"
legend_constants[3] = "Ca_o in component Environment (millimolar)"
legend_constants[4] = "Na_o in component Environment (millimolar)"
legend_constants[5] = "K_o in component Environment (millimolar)"
legend_constants[57] = "FoRT in component Environment (inverse_voltage_units)"
legend_constants[58] = "RToF in component Environment (voltage_units)"
legend_constants[6] = "Cm in component membrane (capacitance_units)"
legend_states[0] = "Vm in component membrane (voltage_units)"
legend_states[1] = "Ca_i_peripheral in component membrane (millimolar)"
legend_states[2] = "Ca_i_bulk in component membrane (millimolar)"
legend_states[3] = "Ca_sr in component membrane (millimolar)"
legend_states[4] = "Na_i in component membrane (millimolar)"
legend_states[5] = "K_i in component membrane (millimolar)"
legend_algebraic[43] = "i_k1 in component i_k1 (current_units)"
legend_algebraic[33] = "i_to_fast in component i_to_fast (current_units)"
legend_algebraic[36] = "i_to_sustained in component i_to_sustained (current_units)"
legend_algebraic[46] = "i_kr in component i_kr (current_units)"
legend_algebraic[48] = "i_ks in component i_ks (current_units)"
legend_algebraic[54] = "i_kb in component i_kb (current_units)"
legend_algebraic[52] = "i_nak in component i_nak (current_units)"
legend_algebraic[31] = "i_cal in component i_cal (current_units)"
legend_algebraic[25] = "i_cat in component i_cat (current_units)"
legend_algebraic[38] = "i_na_fast in component i_na_fast (current_units)"
legend_algebraic[40] = "i_na_late in component i_na_late (current_units)"
legend_algebraic[59] = "i_pmca in component i_pmca (current_units)"
legend_algebraic[58] = "i_cab in component i_cab (current_units)"
legend_algebraic[66] = "i_f_na in component i_f_na (current_units)"
legend_algebraic[62] = "i_f_k in component i_f_k (current_units)"
legend_algebraic[49] = "i_naca in component i_naca (current_units)"
legend_algebraic[56] = "i_nab in component i_nab (current_units)"
legend_algebraic[0] = "i_stim in component membrane (current_units)"
legend_algebraic[61] = "i_rel_per in component i_rel_per (current_units)"
legend_algebraic[63] = "i_serca_per in component i_serca_per (current_units)"
legend_algebraic[65] = "i_serca_bulk in component i_serca_bulk (current_units)"
legend_algebraic[68] = "i_diff in component i_diff (current_units)"
legend_algebraic[67] = "i_leak in component i_leak (current_units)"
legend_constants[60] = "peripheral_volume in component membrane (volume_units)"
legend_constants[59] = "bulk_volume in component membrane (volume_units)"
legend_constants[62] = "diffusable_volume in component membrane (volume_units)"
legend_constants[61] = "sr_volume in component membrane (volume_units)"
legend_constants[7] = "cell_volume in component membrane (volume_units)"
legend_constants[8] = "bulk_fraction in component membrane (dimensionless)"
legend_constants[9] = "periphery_fraction in component membrane (dimensionless)"
legend_constants[10] = "sr_fraction in component membrane (dimensionless)"
legend_constants[11] = "stim_start in component membrane (time_units)"
legend_constants[12] = "stim_end in component membrane (time_units)"
legend_constants[13] = "stim_period in component membrane (time_units)"
legend_constants[14] = "stim_duration in component membrane (time_units)"
legend_constants[15] = "stim_amplitude in component membrane (current_units)"
legend_algebraic[1] = "x_inf_Ttype in component x_Ttype (dimensionless)"
legend_constants[16] = "tau_x_Ttype in component x_Ttype (time_units)"
legend_states[6] = "x_Ttype in component x_Ttype (dimensionless)"
legend_algebraic[2] = "y_inf_Ttype in component y_Ttype (dimensionless)"
legend_algebraic[17] = "tau_y_Ttype in component y_Ttype (time_units)"
legend_states[7] = "y_Ttype in component y_Ttype (dimensionless)"
legend_algebraic[16] = "E_Ca in component i_cat (voltage_units)"
legend_constants[17] = "G_max_Ttype in component i_cat (conductance_units)"
legend_algebraic[3] = "x_inf_Ltype in component x_Ltype (dimensionless)"
legend_constants[18] = "tau_x_Ltype in component x_Ltype (time_units)"
legend_states[8] = "x_Ltype in component x_Ltype (dimensionless)"
legend_algebraic[4] = "y_inf_Ltype in component y_Ltype (dimensionless)"
legend_algebraic[18] = "tau_y_Ltype in component y_Ltype (time_units)"
legend_states[9] = "y_Ltype in component y_Ltype (dimensionless)"
legend_algebraic[5] = "y_ca_inf_Ltype in component y_ca_Ltype (dimensionless)"
legend_algebraic[19] = "tau_y_ca_Ltype in component y_ca_Ltype (time_units)"
legend_states[10] = "y_ca_Ltype in component y_ca_Ltype (dimensionless)"
legend_algebraic[28] = "E_Ca in component i_cal (voltage_units)"
legend_constants[19] = "G_max_Ltype in component i_cal (conductance_units)"
legend_algebraic[6] = "x_inf_to_fast in component x_to_fast (dimensionless)"
legend_constants[20] = "tau_x_to_fast in component x_to_fast (time_units)"
legend_states[11] = "x_to_fast in component x_to_fast (dimensionless)"
legend_algebraic[7] = "y_inf_to_fast in component y_to_fast (dimensionless)"
legend_constants[21] = "tau_y_to_fast in component y_to_fast (time_units)"
legend_states[12] = "y_to_fast in component y_to_fast (dimensionless)"
legend_algebraic[32] = "E_k in component i_to_fast (voltage_units)"
legend_constants[22] = "G_max_to_fast in component i_to_fast (conductance_units)"
legend_algebraic[34] = "x_to_sustained in component x_to_sustained (dimensionless)"
legend_algebraic[35] = "E_k in component i_to_sustained (voltage_units)"
legend_constants[23] = "G_max_to_sustained in component i_to_sustained (conductance_units)"
legend_algebraic[8] = "x_inf_na_fast in component x_na_fast (dimensionless)"
legend_constants[24] = "tau_x_na_fast in component x_na_fast (time_units)"
legend_states[13] = "x_na_fast in component x_na_fast (dimensionless)"
legend_algebraic[9] = "y_inf_na_fast in component y_na_fast (dimensionless)"
legend_constants[25] = "tau_y_na_fast in component y_na_fast (time_units)"
legend_states[14] = "y_na_fast in component y_na_fast (dimensionless)"
legend_algebraic[37] = "E_na in component i_na_fast (voltage_units)"
legend_constants[26] = "G_max_na_fast in component i_na_fast (conductance_units)"
legend_algebraic[10] = "x_inf_na_late in component x_na_late (dimensionless)"
legend_constants[27] = "tau_x_na_late in component x_na_late (time_units)"
legend_states[15] = "x_na_late in component x_na_late (dimensionless)"
legend_algebraic[11] = "y_inf_na_late in component y_na_late (dimensionless)"
legend_algebraic[20] = "tau_y_na_late in component y_na_late (time_units)"
legend_states[16] = "y_na_late in component y_na_late (dimensionless)"
legend_algebraic[39] = "E_na in component i_na_late (voltage_units)"
legend_constants[28] = "G_max_na_late in component i_na_late (conductance_units)"
legend_algebraic[41] = "x_k1 in component x_k1 (dimensionless)"
legend_algebraic[42] = "E_k in component i_k1 (voltage_units)"
legend_constants[29] = "G_max_k1 in component i_k1 (conductance_units)"
legend_algebraic[44] = "x_kr in component x_kr (dimensionless)"
legend_algebraic[12] = "y_inf_kr in component y_kr (dimensionless)"
legend_algebraic[29] = "tau_y_kr in component y_kr (time_units)"
legend_states[17] = "y_kr in component y_kr (dimensionless)"
legend_algebraic[21] = "ykrv1 in component y_kr (rate_constants_units)"
legend_algebraic[26] = "ykrv2 in component y_kr (rate_constants_units)"
legend_algebraic[45] = "E_k in component i_kr (voltage_units)"
legend_constants[30] = "G_max_kr in component i_kr (conductance_units)"
legend_algebraic[13] = "x_inf_ks in component x_ks (dimensionless)"
legend_algebraic[22] = "tau_x_ks in component x_ks (time_units)"
legend_states[18] = "x_ks in component x_ks (dimensionless)"
legend_algebraic[27] = "y_inf_ks in component y_ks (dimensionless)"
legend_algebraic[30] = "tau_y_ks in component y_ks (time_units)"
legend_states[19] = "y_ks in component y_ks (dimensionless)"
legend_algebraic[47] = "E_k in component i_ks (voltage_units)"
legend_constants[31] = "G_max_ks in component i_ks (conductance_units)"
legend_constants[32] = "n_NaCa in component i_naca (dimensionless)"
legend_constants[33] = "g_NaCa in component i_naca (current_units)"
legend_constants[34] = "d_NaCa in component i_naca (dimensionless)"
legend_constants[35] = "gamma in component i_naca (dimensionless)"
legend_algebraic[50] = "x_nak in component x_nak (dimensionless)"
legend_algebraic[51] = "y_nak in component y_nak (dimensionless)"
legend_constants[36] = "g_nak in component i_nak (current_units)"
legend_algebraic[53] = "E_k in component i_kb (voltage_units)"
legend_constants[37] = "G_max_kb in component i_kb (conductance_units)"
legend_algebraic[55] = "E_na in component i_nab (voltage_units)"
legend_constants[38] = "G_max_nab in component i_nab (conductance_units)"
legend_algebraic[57] = "E_ca in component i_cab (voltage_units)"
legend_constants[39] = "G_max_cab in component i_cab (conductance_units)"
legend_constants[40] = "PMCA_max in component i_pmca (current_units)"
legend_constants[41] = "Kpmca in component i_pmca (millimolar)"
legend_constants[42] = "Hpmca in component i_pmca (dimensionless)"
legend_constants[43] = "G_f_k in component i_f_k (conductance_units)"
legend_algebraic[60] = "E_k in component i_f_k (voltage_units)"
legend_states[20] = "y_gate_f_k in component y_gate_f_k (dimensionless)"
legend_constants[44] = "G_f_na in component i_f_na (conductance_units)"
legend_algebraic[64] = "E_na in component i_f_na (voltage_units)"
legend_states[21] = "y_gate_f_na in component y_gate_f_na (dimensionless)"
legend_algebraic[14] = "y_inf_f_gate in component y_gate_f_k (dimensionless)"
legend_algebraic[23] = "tau_y_f_gate in component y_gate_f_k (time_units)"
legend_algebraic[15] = "y_inf_f_gate in component y_gate_f_na (dimensionless)"
legend_algebraic[24] = "tau_y_f_gate in component y_gate_f_na (time_units)"
legend_constants[45] = "REL_max in component i_rel_per (current_per_millimolar_units)"
legend_constants[46] = "Krel in component i_rel_per (millimolar)"
legend_constants[47] = "SERCA_max in component i_serca_per (current_units)"
legend_constants[48] = "Kmf in component i_serca_per (millimolar)"
legend_constants[49] = "Kmr in component i_serca_per (millimolar)"
legend_constants[50] = "H in component i_serca_per (dimensionless)"
legend_constants[51] = "SERCA_max in component i_serca_bulk (current_units)"
legend_constants[52] = "Kmf in component i_serca_bulk (millimolar)"
legend_constants[53] = "Kmr in component i_serca_bulk (millimolar)"
legend_constants[54] = "H in component i_serca_bulk (dimensionless)"
legend_constants[55] = "LEAK_max in component i_leak (current_per_millimolar_units)"
legend_constants[56] = "DIFF_max in component i_diff (current_per_millimolar_units)"
legend_rates[0] = "d/dt Vm in component membrane (voltage_units)"
legend_rates[1] = "d/dt Ca_i_peripheral in component membrane (millimolar)"
legend_rates[2] = "d/dt Ca_i_bulk in component membrane (millimolar)"
legend_rates[3] = "d/dt Ca_sr in component membrane (millimolar)"
legend_rates[5] = "d/dt K_i in component membrane (millimolar)"
legend_rates[4] = "d/dt Na_i in component membrane (millimolar)"
legend_rates[6] = "d/dt x_Ttype in component x_Ttype (dimensionless)"
legend_rates[7] = "d/dt y_Ttype in component y_Ttype (dimensionless)"
legend_rates[8] = "d/dt x_Ltype in component x_Ltype (dimensionless)"
legend_rates[9] = "d/dt y_Ltype in component y_Ltype (dimensionless)"
legend_rates[10] = "d/dt y_ca_Ltype in component y_ca_Ltype (dimensionless)"
legend_rates[11] = "d/dt x_to_fast in component x_to_fast (dimensionless)"
legend_rates[12] = "d/dt y_to_fast in component y_to_fast (dimensionless)"
legend_rates[13] = "d/dt x_na_fast in component x_na_fast (dimensionless)"
legend_rates[14] = "d/dt y_na_fast in component y_na_fast (dimensionless)"
legend_rates[15] = "d/dt x_na_late in component x_na_late (dimensionless)"
legend_rates[16] = "d/dt y_na_late in component y_na_late (dimensionless)"
legend_rates[17] = "d/dt y_kr in component y_kr (dimensionless)"
legend_rates[18] = "d/dt x_ks in component x_ks (dimensionless)"
legend_rates[19] = "d/dt y_ks in component y_ks (dimensionless)"
legend_rates[20] = "d/dt y_gate_f_k in component y_gate_f_k (dimensionless)"
legend_rates[21] = "d/dt y_gate_f_na in component y_gate_f_na (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 310.0
constants[1] = 96485.3415
constants[2] = 8314.472
constants[3] = 2.0
constants[4] = 140
constants[5] = 5.4
constants[6] = 69.0
states[0] = -88.34
states[1] = 0.00001
states[2] = 0.000032
states[3] = 0.17
states[4] = 6.7
states[5] = 140
constants[7] = 13266.5
constants[8] = 0.6
constants[9] = 0.2
constants[10] = 0.06
constants[11] = 700
constants[12] = 9000000
constants[13] = 500
constants[14] = 0.5
constants[15] = -4320.0
constants[16] = 1.0
states[6] = 0.001337
states[7] = 0.01
constants[17] = 0.9
constants[18] = 0.7
states[8] = 0.000003
states[9] = 0.1
states[10] = 0.7
constants[19] = 5.4
constants[20] = 5.0
states[11] = 0.0
constants[21] = 350.0
states[12] = 0.7
constants[22] = 10.0
constants[23] = 3.0
constants[24] = 0.005
states[13] = 0.000007
constants[25] = 2.0
states[14] = 0.978861
constants[26] = 1140.0
constants[27] = 15.0
states[15] = 0.000012
states[16] = 0.864489
constants[28] = 2.0
constants[29] = 20.0
states[17] = 0.25
constants[30] = 1.5
states[18] = 1.0
states[19] = 0.0
constants[31] = 3.0
constants[32] = 3
constants[33] = 0.001
constants[34] = 0.001
constants[35] = 0.5
constants[36] = 442.2
constants[37] = 0.01
constants[38] = 0.01
constants[39] = 0.0001
constants[40] = 5.0
constants[41] = 0.0001
constants[42] = 1.5
constants[43] = 0.188709677
states[20] = 0.011099
constants[44] = 0.045290323
states[21] = 0.011099
constants[45] = 2500.0
constants[46] = 0.001
constants[47] = 120.0
constants[48] = 0.000246
constants[49] = 1.7
constants[50] = 1.6
constants[51] = 120.0
constants[52] = 0.000246
constants[53] = 1.7
constants[54] = 1.6
constants[55] = 10.0
constants[56] = 5000.0
constants[57] = constants[1]/(constants[2]*constants[0])
constants[58] = (constants[2]*constants[0])/constants[1]
constants[59] = constants[8]*constants[7]
constants[60] = constants[9]*constants[7]
constants[61] = constants[10]*constants[7]
constants[62] = (constants[8]+constants[9])*constants[7]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[1] = 1.00000/(1.00000+exp((states[0]+47.8000)/-5.50000))
rates[6] = (algebraic[1]-states[6])/constants[16]
algebraic[3] = 1.00000/(1.00000+exp((states[0]+14.6000)/-5.50000))
rates[8] = (algebraic[3]-states[8])/constants[18]
algebraic[6] = 1.00000/(1.00000+exp((states[0]+-7.00000)/-9.00000))
rates[11] = (algebraic[6]-states[11])/constants[20]
algebraic[7] = 1.00000/(1.00000+exp((states[0]+27.5000)/8.00000))
rates[12] = (algebraic[7]-states[12])/constants[21]
algebraic[8] = 1.00000/(1.00000+exp((states[0]+25.0000)/-5.00000))
rates[13] = (algebraic[8]-states[13])/constants[24]
algebraic[9] = 1.00000/(1.00000+exp((states[0]+69.0000)/3.96000))
rates[14] = (algebraic[9]-states[14])/constants[25]
algebraic[10] = 1.00000/(1.00000+exp((states[0]+30.0000)/-5.00000))
rates[15] = (algebraic[10]-states[15])/constants[27]
algebraic[2] = 1.00000/(1.00000+exp((states[0]+67.9000)/3.87000))
algebraic[17] = 1.42271*exp(-0.0511900*states[0])
rates[7] = (algebraic[2]-states[7])/algebraic[17]
algebraic[4] = 1.00000/(1.00000+exp((states[0]+31.0000)/5.54000))
algebraic[18] = 25.1000/(0.0400000+0.700000*exp(-1.00000*(power(0.0280000*(states[0]+14.5000), 2.00000))))
rates[9] = (algebraic[4]-states[9])/algebraic[18]
algebraic[5] = 0.400000+0.600000/(1.00000+power(states[1]/0.000100000, 2.00000))
algebraic[19] = 2.00000+80.0000/(1.00000+power(states[1]/0.000100000, 2.00000))
rates[10] = (algebraic[5]-states[10])/algebraic[19]
algebraic[11] = 0.100000+0.900000/(1.00000+exp((states[0]+75.6000)/6.30000))
algebraic[20] = 120.000+1.00000*exp((states[0]+100.000)/25.0000)
rates[16] = (algebraic[11]-states[16])/algebraic[20]
algebraic[13] = 1.00000/(1.00000+exp((states[0]-1.50000)/-16.7000))
algebraic[22] = custom_piecewise([less(fabs(states[0]+30.0000) , 0.0145000), 417.946 , True, 1.00000/((7.19000e-05*(states[0]+30.0000))/(1.00000-exp(-0.148000*(states[0]+30.0000)))+(0.000131000*(states[0]+30.0000))/(exp(0.0687000*(states[0]+30.0000))-1.00000))])
rates[18] = (algebraic[13]-states[18])/algebraic[22]
algebraic[14] = 1.00000/(1.00000+exp((states[0]+109.000)/10.0000))
algebraic[23] = 6000.00/(exp(-1.00000*(2.90000+0.0400000*states[0]))+exp(1.00000*(3.60000+0.110000*states[0])))
rates[20] = (algebraic[14]-states[20])/algebraic[23]
algebraic[15] = 1.00000/(1.00000+exp((states[0]+109.000)/10.0000))
algebraic[24] = 6000.00/(exp(-1.00000*(2.90000+0.0400000*states[0]))+exp(1.00000*(3.60000+0.110000*states[0])))
rates[21] = (algebraic[15]-states[21])/algebraic[24]
algebraic[12] = 1.00000/(1.00000+exp((states[0]+50.0000)/-7.50000))
algebraic[21] = custom_piecewise([greater(fabs(states[0]+7.00000) , 0.00100000), (0.00138000*1.00000*(states[0]+7.00000))/(1.00000-exp(-0.123000*(states[0]+7.00000))) , True, 0.00138000/0.123000])
algebraic[26] = custom_piecewise([greater(fabs(states[0]+10.0000) , 0.00100000), (6.10000e-05*1.00000*(states[0]+10.0000))/(exp(0.145000*(states[0]+10.0000))-1.00000) , True, 0.000610000/0.145000])
algebraic[29] = 1.00000/(algebraic[21]+algebraic[26])
rates[17] = (algebraic[12]-states[17])/algebraic[29]
algebraic[27] = algebraic[13]
algebraic[30] = 4.00000*algebraic[22]
rates[19] = (algebraic[27]-states[19])/algebraic[30]
algebraic[41] = 1.00000/(1.00000+exp((92.0000+states[0])/10.0000))
algebraic[42] = constants[58]*log(constants[5]/states[5])
algebraic[43] = constants[29]*(power(constants[5]/5.40000, 0.800000))*algebraic[41]*(states[0]-algebraic[42])
algebraic[32] = constants[58]*log(constants[5]/states[5])
algebraic[33] = constants[22]*states[11]*states[12]*(states[0]-algebraic[32])
algebraic[34] = 1.00000/(1.00000+exp((5.00000-states[0])/17.0000))
algebraic[35] = constants[58]*log(constants[5]/states[5])
algebraic[36] = constants[23]*algebraic[34]*(states[0]-algebraic[35])
algebraic[44] = 1.00000/(1.00000+exp((33.0000+states[0])/22.4000))
algebraic[45] = constants[58]*log(constants[5]/states[5])
algebraic[46] = constants[30]*(power(constants[5]/5.40000, 1.00000))*algebraic[44]*states[17]*(states[0]-algebraic[45])
algebraic[47] = constants[58]*log(constants[5]/states[5])
algebraic[48] = constants[31]*states[18]*states[19]*(states[0]-algebraic[47])
algebraic[53] = constants[58]*log(constants[5]/states[5])
algebraic[54] = constants[37]*(states[0]-algebraic[53])
algebraic[50] = 1.00000/(1.00000+exp((states[0]+80.0000)/-45.0000))
algebraic[51] = 1.00000/(1.00000+exp((states[0]+0.00000)/125.000))
algebraic[52] = constants[36]*algebraic[50]*algebraic[51]*(1.00000/(1.00000+power(1.90000/constants[5], 1.45000)))*(1.00000/(1.00000+power(31.9800/states[4], 1.00000)))
algebraic[60] = constants[58]*log(constants[5]/states[5])
algebraic[62] = constants[43]*states[20]*(states[0]-algebraic[60])
algebraic[0] = custom_piecewise([greater_equal(voi , constants[11]) & less_equal(voi , constants[12]) & less_equal((voi-constants[11])-floor((voi-constants[11])/constants[13])*constants[13] , constants[14]), constants[15] , True, 0.00000])
rates[5] = ((-1.00000*algebraic[33]+-1.00000*algebraic[36]+-1.00000*algebraic[46]+-1.00000*algebraic[48]+-1.00000*algebraic[43]+-1.00000*algebraic[54]+-1.00000*algebraic[62]+-1.00000*algebraic[0]+2.00000*algebraic[52])*1000.00)/(constants[1]*constants[62])
algebraic[28] = 0.500000*constants[58]*log(constants[3]/states[1])
algebraic[31] = constants[19]*states[8]*states[9]*states[10]*(states[0]-algebraic[28])
algebraic[16] = 0.500000*constants[58]*log(constants[3]/states[1])
algebraic[25] = constants[17]*states[6]*states[7]*(states[0]-algebraic[16])
algebraic[37] = constants[58]*log(constants[4]/states[4])
algebraic[38] = constants[26]*states[13]*states[14]*(states[0]-algebraic[37])
algebraic[39] = constants[58]*log(constants[4]/states[4])
algebraic[40] = constants[28]*states[15]*states[16]*(states[0]-algebraic[39])
algebraic[59] = constants[40]*(1.00000/(1.00000+power(constants[41]/states[1], constants[42])))
algebraic[57] = 0.500000*constants[58]*log(constants[3]/states[1])
algebraic[58] = constants[39]*(states[0]-algebraic[57])
algebraic[64] = constants[58]*log(constants[4]/states[4])
algebraic[66] = constants[44]*states[21]*(states[0]-algebraic[64])
algebraic[49] = (512.009*constants[33]*(exp((constants[35]*(constants[32]-2.00000)*states[0])/constants[58])*(power(states[4], constants[32]))*constants[3]-states[1]*exp(((constants[35]-1.00000)*(constants[32]-2.00000)*states[0])/constants[58])*(power(constants[4], constants[32]))))/((1.00000+constants[34]*(states[1]*(power(constants[4], constants[32]))+constants[3]*(power(states[4], constants[32]))))*(1.00000+states[1]/0.00690000))
algebraic[55] = constants[58]*log(constants[4]/states[4])
algebraic[56] = constants[38]*(states[0]-algebraic[55])
rates[0] = ((-1.00000*1.00000)/constants[6])*(algebraic[43]+algebraic[33]+algebraic[36]+algebraic[46]+algebraic[48]+algebraic[54]+algebraic[52]+algebraic[31]+algebraic[25]+algebraic[38]+algebraic[40]+algebraic[59]+algebraic[58]+algebraic[66]+algebraic[62]+algebraic[49]+algebraic[56]+algebraic[0])
algebraic[61] = constants[45]*(states[3]/(1.00000+power(constants[46]/states[1], 2.00000)))
algebraic[63] = constants[47]*((power(states[1]/constants[48], constants[50])-power(states[3]/constants[49], constants[50]))/(1.00000+power(states[1]/constants[48], constants[50])+power(states[3]/constants[49], constants[50])))
algebraic[65] = constants[51]*((power(states[2]/constants[52], constants[54])-power(states[3]/constants[53], constants[54]))/(1.00000+power(states[2]/constants[52], constants[54])+power(states[3]/constants[53], constants[54])))
algebraic[67] = constants[55]*(states[3]-states[2])
rates[3] = ((-1.00000*algebraic[61]+-1.00000*algebraic[67]+algebraic[65]+algebraic[63])*1000.00)/(2.00000*constants[1]*constants[61])
rates[4] = ((-1.00000*algebraic[38]+-1.00000*algebraic[40]+-3.00000*algebraic[52]+-3.00000*algebraic[49]+-1.00000*algebraic[66]+-1.00000*algebraic[56])*1000.00)/(constants[1]*constants[62])
algebraic[68] = constants[56]*(states[1]-states[2])
rates[1] = ((-1.00000*algebraic[31]+-1.00000*algebraic[25]+-1.00000*algebraic[58]+1.00000*algebraic[61]+-1.00000*algebraic[63]+-1.00000*algebraic[68]+2.00000*algebraic[49]+-1.00000*algebraic[59])*1000.00)/(2.00000*constants[1]*constants[60])
rates[2] = ((-1.00000*algebraic[65]+algebraic[68]+algebraic[67])*1000.00)/(2.00000*constants[1]*constants[59])
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = 1.00000/(1.00000+exp((states[0]+47.8000)/-5.50000))
algebraic[3] = 1.00000/(1.00000+exp((states[0]+14.6000)/-5.50000))
algebraic[6] = 1.00000/(1.00000+exp((states[0]+-7.00000)/-9.00000))
algebraic[7] = 1.00000/(1.00000+exp((states[0]+27.5000)/8.00000))
algebraic[8] = 1.00000/(1.00000+exp((states[0]+25.0000)/-5.00000))
algebraic[9] = 1.00000/(1.00000+exp((states[0]+69.0000)/3.96000))
algebraic[10] = 1.00000/(1.00000+exp((states[0]+30.0000)/-5.00000))
algebraic[2] = 1.00000/(1.00000+exp((states[0]+67.9000)/3.87000))
algebraic[17] = 1.42271*exp(-0.0511900*states[0])
algebraic[4] = 1.00000/(1.00000+exp((states[0]+31.0000)/5.54000))
algebraic[18] = 25.1000/(0.0400000+0.700000*exp(-1.00000*(power(0.0280000*(states[0]+14.5000), 2.00000))))
algebraic[5] = 0.400000+0.600000/(1.00000+power(states[1]/0.000100000, 2.00000))
algebraic[19] = 2.00000+80.0000/(1.00000+power(states[1]/0.000100000, 2.00000))
algebraic[11] = 0.100000+0.900000/(1.00000+exp((states[0]+75.6000)/6.30000))
algebraic[20] = 120.000+1.00000*exp((states[0]+100.000)/25.0000)
algebraic[13] = 1.00000/(1.00000+exp((states[0]-1.50000)/-16.7000))
algebraic[22] = custom_piecewise([less(fabs(states[0]+30.0000) , 0.0145000), 417.946 , True, 1.00000/((7.19000e-05*(states[0]+30.0000))/(1.00000-exp(-0.148000*(states[0]+30.0000)))+(0.000131000*(states[0]+30.0000))/(exp(0.0687000*(states[0]+30.0000))-1.00000))])
algebraic[14] = 1.00000/(1.00000+exp((states[0]+109.000)/10.0000))
algebraic[23] = 6000.00/(exp(-1.00000*(2.90000+0.0400000*states[0]))+exp(1.00000*(3.60000+0.110000*states[0])))
algebraic[15] = 1.00000/(1.00000+exp((states[0]+109.000)/10.0000))
algebraic[24] = 6000.00/(exp(-1.00000*(2.90000+0.0400000*states[0]))+exp(1.00000*(3.60000+0.110000*states[0])))
algebraic[12] = 1.00000/(1.00000+exp((states[0]+50.0000)/-7.50000))
algebraic[21] = custom_piecewise([greater(fabs(states[0]+7.00000) , 0.00100000), (0.00138000*1.00000*(states[0]+7.00000))/(1.00000-exp(-0.123000*(states[0]+7.00000))) , True, 0.00138000/0.123000])
algebraic[26] = custom_piecewise([greater(fabs(states[0]+10.0000) , 0.00100000), (6.10000e-05*1.00000*(states[0]+10.0000))/(exp(0.145000*(states[0]+10.0000))-1.00000) , True, 0.000610000/0.145000])
algebraic[29] = 1.00000/(algebraic[21]+algebraic[26])
algebraic[27] = algebraic[13]
algebraic[30] = 4.00000*algebraic[22]
algebraic[41] = 1.00000/(1.00000+exp((92.0000+states[0])/10.0000))
algebraic[42] = constants[58]*log(constants[5]/states[5])
algebraic[43] = constants[29]*(power(constants[5]/5.40000, 0.800000))*algebraic[41]*(states[0]-algebraic[42])
algebraic[32] = constants[58]*log(constants[5]/states[5])
algebraic[33] = constants[22]*states[11]*states[12]*(states[0]-algebraic[32])
algebraic[34] = 1.00000/(1.00000+exp((5.00000-states[0])/17.0000))
algebraic[35] = constants[58]*log(constants[5]/states[5])
algebraic[36] = constants[23]*algebraic[34]*(states[0]-algebraic[35])
algebraic[44] = 1.00000/(1.00000+exp((33.0000+states[0])/22.4000))
algebraic[45] = constants[58]*log(constants[5]/states[5])
algebraic[46] = constants[30]*(power(constants[5]/5.40000, 1.00000))*algebraic[44]*states[17]*(states[0]-algebraic[45])
algebraic[47] = constants[58]*log(constants[5]/states[5])
algebraic[48] = constants[31]*states[18]*states[19]*(states[0]-algebraic[47])
algebraic[53] = constants[58]*log(constants[5]/states[5])
algebraic[54] = constants[37]*(states[0]-algebraic[53])
algebraic[50] = 1.00000/(1.00000+exp((states[0]+80.0000)/-45.0000))
algebraic[51] = 1.00000/(1.00000+exp((states[0]+0.00000)/125.000))
algebraic[52] = constants[36]*algebraic[50]*algebraic[51]*(1.00000/(1.00000+power(1.90000/constants[5], 1.45000)))*(1.00000/(1.00000+power(31.9800/states[4], 1.00000)))
algebraic[60] = constants[58]*log(constants[5]/states[5])
algebraic[62] = constants[43]*states[20]*(states[0]-algebraic[60])
algebraic[0] = custom_piecewise([greater_equal(voi , constants[11]) & less_equal(voi , constants[12]) & less_equal((voi-constants[11])-floor((voi-constants[11])/constants[13])*constants[13] , constants[14]), constants[15] , True, 0.00000])
algebraic[28] = 0.500000*constants[58]*log(constants[3]/states[1])
algebraic[31] = constants[19]*states[8]*states[9]*states[10]*(states[0]-algebraic[28])
algebraic[16] = 0.500000*constants[58]*log(constants[3]/states[1])
algebraic[25] = constants[17]*states[6]*states[7]*(states[0]-algebraic[16])
algebraic[37] = constants[58]*log(constants[4]/states[4])
algebraic[38] = constants[26]*states[13]*states[14]*(states[0]-algebraic[37])
algebraic[39] = constants[58]*log(constants[4]/states[4])
algebraic[40] = constants[28]*states[15]*states[16]*(states[0]-algebraic[39])
algebraic[59] = constants[40]*(1.00000/(1.00000+power(constants[41]/states[1], constants[42])))
algebraic[57] = 0.500000*constants[58]*log(constants[3]/states[1])
algebraic[58] = constants[39]*(states[0]-algebraic[57])
algebraic[64] = constants[58]*log(constants[4]/states[4])
algebraic[66] = constants[44]*states[21]*(states[0]-algebraic[64])
algebraic[49] = (512.009*constants[33]*(exp((constants[35]*(constants[32]-2.00000)*states[0])/constants[58])*(power(states[4], constants[32]))*constants[3]-states[1]*exp(((constants[35]-1.00000)*(constants[32]-2.00000)*states[0])/constants[58])*(power(constants[4], constants[32]))))/((1.00000+constants[34]*(states[1]*(power(constants[4], constants[32]))+constants[3]*(power(states[4], constants[32]))))*(1.00000+states[1]/0.00690000))
algebraic[55] = constants[58]*log(constants[4]/states[4])
algebraic[56] = constants[38]*(states[0]-algebraic[55])
algebraic[61] = constants[45]*(states[3]/(1.00000+power(constants[46]/states[1], 2.00000)))
algebraic[63] = constants[47]*((power(states[1]/constants[48], constants[50])-power(states[3]/constants[49], constants[50]))/(1.00000+power(states[1]/constants[48], constants[50])+power(states[3]/constants[49], constants[50])))
algebraic[65] = constants[51]*((power(states[2]/constants[52], constants[54])-power(states[3]/constants[53], constants[54]))/(1.00000+power(states[2]/constants[52], constants[54])+power(states[3]/constants[53], constants[54])))
algebraic[67] = constants[55]*(states[3]-states[2])
algebraic[68] = constants[56]*(states[1]-states[2])
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)