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 = 20
sizeConstants = 66
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_kilomole_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 (microF)"
legend_algebraic[28] = "i_K1 in component time_independent_potassium_current (nanoA)"
legend_algebraic[51] = "i_to in component transient_outward_current (nanoA)"
legend_algebraic[30] = "i_Kr in component rapid_delayed_rectifier_potassium_current (nanoA)"
legend_algebraic[32] = "i_Ks in component slow_delayed_rectifier_potassium_current (nanoA)"
legend_algebraic[42] = "i_Ca_L_K_cyt in component L_type_Ca_channel (nanoA)"
legend_algebraic[47] = "i_Ca_L_K_ds in component L_type_Ca_channel (nanoA)"
legend_algebraic[52] = "i_NaK in component sodium_potassium_pump (nanoA)"
legend_algebraic[33] = "i_Na in component fast_sodium_current (nanoA)"
legend_algebraic[35] = "i_b_Na in component sodium_background_current (nanoA)"
legend_algebraic[34] = "i_p_Na in component persistent_sodium_current (nanoA)"
legend_algebraic[43] = "i_Ca_L_Na_cyt in component L_type_Ca_channel (nanoA)"
legend_algebraic[48] = "i_Ca_L_Na_ds in component L_type_Ca_channel (nanoA)"
legend_algebraic[53] = "i_NaCa_cyt in component sodium_calcium_exchanger (nanoA)"
legend_algebraic[54] = "i_NaCa_ds in component sodium_calcium_exchanger (nanoA)"
legend_algebraic[41] = "i_Ca_L_Ca_cyt in component L_type_Ca_channel (nanoA)"
legend_algebraic[46] = "i_Ca_L_Ca_ds in component L_type_Ca_channel (nanoA)"
legend_algebraic[50] = "i_b_Ca in component calcium_background_current (nanoA)"
legend_algebraic[6] = "i_Stim in component membrane (nanoA)"
legend_constants[4] = "stim_duration in component membrane (second)"
legend_constants[5] = "stim_amplitude in component membrane (nanoA)"
legend_algebraic[15] = "E_Na in component reversal_potentials (millivolt)"
legend_algebraic[20] = "E_K in component reversal_potentials (millivolt)"
legend_algebraic[22] = "E_Ks in component reversal_potentials (millivolt)"
legend_algebraic[24] = "E_Ca in component reversal_potentials (millivolt)"
legend_algebraic[26] = "E_mh in component reversal_potentials (millivolt)"
legend_constants[6] = "P_kna in component reversal_potentials (dimensionless)"
legend_constants[7] = "K_o in component extracellular_potassium_concentration (millimolar)"
legend_constants[8] = "Na_o in component extracellular_sodium_concentration (millimolar)"
legend_states[1] = "K_i in component intracellular_potassium_concentration (millimolar)"
legend_states[2] = "Na_i in component intracellular_sodium_concentration (millimolar)"
legend_constants[9] = "Ca_o in component extracellular_calcium_concentration (millimolar)"
legend_states[3] = "Ca_i in component intracellular_calcium_concentration (millimolar)"
legend_constants[10] = "K_mk1 in component time_independent_potassium_current (millimolar)"
legend_constants[11] = "g_K1 in component time_independent_potassium_current (microS)"
legend_constants[12] = "g_Kr1 in component rapid_delayed_rectifier_potassium_current (microS)"
legend_constants[13] = "g_Kr2 in component rapid_delayed_rectifier_potassium_current (microS)"
legend_states[4] = "xr1 in component rapid_delayed_rectifier_potassium_current_xr1_gate (dimensionless)"
legend_states[5] = "xr2 in component rapid_delayed_rectifier_potassium_current_xr2_gate (dimensionless)"
legend_algebraic[0] = "alpha_xr1 in component rapid_delayed_rectifier_potassium_current_xr1_gate (per_second)"
legend_algebraic[9] = "beta_xr1 in component rapid_delayed_rectifier_potassium_current_xr1_gate (per_second)"
legend_algebraic[1] = "alpha_xr2 in component rapid_delayed_rectifier_potassium_current_xr2_gate (per_second)"
legend_algebraic[10] = "beta_xr2 in component rapid_delayed_rectifier_potassium_current_xr2_gate (per_second)"
legend_constants[14] = "g_Ks in component slow_delayed_rectifier_potassium_current (microS)"
legend_states[6] = "xs in component slow_delayed_rectifier_potassium_current_xs_gate (dimensionless)"
legend_algebraic[2] = "alpha_xs in component slow_delayed_rectifier_potassium_current_xs_gate (per_second)"
legend_algebraic[11] = "beta_xs in component slow_delayed_rectifier_potassium_current_xs_gate (per_second)"
legend_constants[15] = "g_Na in component fast_sodium_current (microS)"
legend_states[7] = "m in component fast_sodium_current_m_gate (dimensionless)"
legend_states[8] = "h in component fast_sodium_current_h_gate (dimensionless)"
legend_algebraic[12] = "alpha_m in component fast_sodium_current_m_gate (per_second)"
legend_algebraic[18] = "beta_m in component fast_sodium_current_m_gate (per_second)"
legend_constants[16] = "delta_m in component fast_sodium_current_m_gate (millivolt)"
legend_algebraic[3] = "E0_m in component fast_sodium_current_m_gate (millivolt)"
legend_algebraic[4] = "alpha_h in component fast_sodium_current_h_gate (per_second)"
legend_algebraic[13] = "beta_h in component fast_sodium_current_h_gate (per_second)"
legend_constants[17] = "shift_h in component fast_sodium_current_h_gate (millivolt)"
legend_constants[18] = "g_pna in component persistent_sodium_current (microS)"
legend_constants[19] = "g_bna in component sodium_background_current (microS)"
legend_algebraic[49] = "i_Ca_L in component L_type_Ca_channel (nanoA)"
legend_constants[20] = "P_Ca_L in component L_type_Ca_channel (nanoA_per_millimolar)"
legend_constants[21] = "P_CaK in component L_type_Ca_channel (dimensionless)"
legend_constants[22] = "P_CaNa in component L_type_Ca_channel (dimensionless)"
legend_states[9] = "Ca_ds in component intracellular_calcium_concentration (millimolar)"
legend_states[10] = "d in component L_type_Ca_channel_d_gate (dimensionless)"
legend_algebraic[40] = "CaChoncyt in component L_type_Ca_channel_f_gate (dimensionless)"
legend_algebraic[45] = "CaChonds in component L_type_Ca_channel_f_gate (dimensionless)"
legend_constants[23] = "KCaChoff in component L_type_Ca_channel (millimolar)"
legend_constants[24] = "Kmdsinact in component L_type_Ca_channel (millimolar)"
legend_constants[25] = "FrICa in component L_type_Ca_channel (dimensionless)"
legend_algebraic[14] = "alpha_d in component L_type_Ca_channel_d_gate (per_second)"
legend_algebraic[19] = "beta_d in component L_type_Ca_channel_d_gate (per_second)"
legend_algebraic[5] = "E0_d in component L_type_Ca_channel_d_gate (millivolt)"
legend_constants[26] = "speed_d in component L_type_Ca_channel_d_gate (dimensionless)"
legend_states[11] = "f in component L_type_Ca_channel_f_gate (dimensionless)"
legend_algebraic[39] = "CaChoffcyt in component L_type_Ca_channel_f_gate (dimensionless)"
legend_algebraic[44] = "CaChoffds in component L_type_Ca_channel_f_gate (dimensionless)"
legend_algebraic[37] = "alpha_f in component L_type_Ca_channel_f_gate (per_second)"
legend_algebraic[38] = "beta_f in component L_type_Ca_channel_f_gate (per_second)"
legend_constants[27] = "speed_f in component L_type_Ca_channel_f_gate (dimensionless)"
legend_constants[28] = "delta_f in component L_type_Ca_channel_f_gate (millivolt)"
legend_algebraic[36] = "E0_f in component L_type_Ca_channel_f_gate (millivolt)"
legend_constants[29] = "g_bca in component calcium_background_current (microS)"
legend_constants[30] = "g_to in component transient_outward_current (microS)"
legend_constants[31] = "g_tos in component transient_outward_current (dimensionless)"
legend_states[12] = "s in component transient_outward_current_s_gate (dimensionless)"
legend_states[13] = "r in component transient_outward_current_r_gate (dimensionless)"
legend_algebraic[7] = "alpha_s in component transient_outward_current_s_gate (per_second)"
legend_algebraic[16] = "beta_s in component transient_outward_current_s_gate (per_second)"
legend_constants[32] = "i_NaK_max in component sodium_potassium_pump (nanoA)"
legend_constants[33] = "K_mK in component sodium_potassium_pump (millimolar)"
legend_constants[34] = "K_mNa in component sodium_potassium_pump (millimolar)"
legend_algebraic[55] = "i_NaCa in component sodium_calcium_exchanger (nanoA)"
legend_constants[35] = "k_NaCa in component sodium_calcium_exchanger (nanoA)"
legend_constants[36] = "n_NaCa in component sodium_calcium_exchanger (dimensionless)"
legend_constants[37] = "d_NaCa in component sodium_calcium_exchanger (dimensionless)"
legend_constants[38] = "gamma in component sodium_calcium_exchanger (dimensionless)"
legend_constants[39] = "FRiNaCa in component sodium_calcium_exchanger (dimensionless)"
legend_algebraic[57] = "i_up in component sarcoplasmic_reticulum_calcium_pump (millimolar_per_second)"
legend_constants[63] = "K_1 in component sarcoplasmic_reticulum_calcium_pump (dimensionless)"
legend_algebraic[56] = "K_2 in component sarcoplasmic_reticulum_calcium_pump (millimolar)"
legend_constants[40] = "K_cyca in component sarcoplasmic_reticulum_calcium_pump (millimolar)"
legend_constants[41] = "K_xcs in component sarcoplasmic_reticulum_calcium_pump (dimensionless)"
legend_constants[42] = "K_srca in component sarcoplasmic_reticulum_calcium_pump (millimolar)"
legend_constants[43] = "alpha_up in component sarcoplasmic_reticulum_calcium_pump (millimolar_per_second)"
legend_constants[44] = "beta_up in component sarcoplasmic_reticulum_calcium_pump (millimolar_per_second)"
legend_states[14] = "Ca_up in component intracellular_calcium_concentration (millimolar)"
legend_algebraic[58] = "i_trans in component calcium_translocation (millimolar_per_second)"
legend_states[15] = "Ca_rel in component intracellular_calcium_concentration (millimolar)"
legend_algebraic[59] = "i_rel in component calcium_release (millimolar_per_second)"
legend_algebraic[8] = "VoltDep in component calcium_release (dimensionless)"
legend_algebraic[23] = "RegBindSite in component calcium_release (dimensionless)"
legend_algebraic[17] = "CaiReg in component calcium_release (dimensionless)"
legend_algebraic[21] = "CadsReg in component calcium_release (dimensionless)"
legend_algebraic[25] = "ActRate in component calcium_release (per_second)"
legend_algebraic[27] = "InactRate in component calcium_release (per_second)"
legend_constants[45] = "K_leak_rate in component calcium_release (per_second)"
legend_constants[46] = "K_m_rel in component calcium_release (per_second)"
legend_constants[47] = "K_m_Ca_cyt in component calcium_release (millimolar)"
legend_constants[48] = "K_m_Ca_ds in component calcium_release (millimolar)"
legend_algebraic[31] = "PrecFrac in component calcium_release (dimensionless)"
legend_states[16] = "ActFrac in component calcium_release (dimensionless)"
legend_states[17] = "ProdFrac in component calcium_release (dimensionless)"
legend_algebraic[29] = "SpeedRel in component calcium_release (dimensionless)"
legend_constants[65] = "V_i in component intracellular_calcium_concentration (micrometre3)"
legend_states[18] = "Ca_Calmod in component intracellular_calcium_concentration (millimolar)"
legend_states[19] = "Ca_Trop in component intracellular_calcium_concentration (millimolar)"
legend_constants[49] = "Calmod in component intracellular_calcium_concentration (millimolar)"
legend_constants[50] = "Trop in component intracellular_calcium_concentration (millimolar)"
legend_constants[51] = "alpha_Calmod in component intracellular_calcium_concentration (per_millimolar_second)"
legend_constants[52] = "beta_Calmod in component intracellular_calcium_concentration (per_second)"
legend_constants[53] = "alpha_Trop in component intracellular_calcium_concentration (per_millimolar_second)"
legend_constants[54] = "beta_Trop in component intracellular_calcium_concentration (per_second)"
legend_constants[55] = "radius in component intracellular_calcium_concentration (micrometre)"
legend_constants[56] = "length in component intracellular_calcium_concentration (micrometre)"
legend_constants[62] = "V_Cell in component intracellular_calcium_concentration (micrometre3)"
legend_constants[64] = "V_i_ratio in component intracellular_calcium_concentration (dimensionless)"
legend_constants[57] = "V_ds_ratio in component intracellular_calcium_concentration (dimensionless)"
legend_constants[58] = "V_rel_ratio in component intracellular_calcium_concentration (dimensionless)"
legend_constants[59] = "V_e_ratio in component intracellular_calcium_concentration (dimensionless)"
legend_constants[60] = "V_up_ratio in component intracellular_calcium_concentration (dimensionless)"
legend_constants[61] = "Kdecay in component intracellular_calcium_concentration (per_second)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[4] = "d/dt xr1 in component rapid_delayed_rectifier_potassium_current_xr1_gate (dimensionless)"
legend_rates[5] = "d/dt xr2 in component rapid_delayed_rectifier_potassium_current_xr2_gate (dimensionless)"
legend_rates[6] = "d/dt xs in component slow_delayed_rectifier_potassium_current_xs_gate (dimensionless)"
legend_rates[7] = "d/dt m in component fast_sodium_current_m_gate (dimensionless)"
legend_rates[8] = "d/dt h in component fast_sodium_current_h_gate (dimensionless)"
legend_rates[10] = "d/dt d in component L_type_Ca_channel_d_gate (dimensionless)"
legend_rates[11] = "d/dt f in component L_type_Ca_channel_f_gate (dimensionless)"
legend_rates[12] = "d/dt s in component transient_outward_current_s_gate (dimensionless)"
legend_rates[13] = "d/dt r in component transient_outward_current_r_gate (dimensionless)"
legend_rates[16] = "d/dt ActFrac in component calcium_release (dimensionless)"
legend_rates[17] = "d/dt ProdFrac in component calcium_release (dimensionless)"
legend_rates[2] = "d/dt Na_i in component intracellular_sodium_concentration (millimolar)"
legend_rates[1] = "d/dt K_i in component intracellular_potassium_concentration (millimolar)"
legend_rates[3] = "d/dt Ca_i in component intracellular_calcium_concentration (millimolar)"
legend_rates[18] = "d/dt Ca_Calmod in component intracellular_calcium_concentration (millimolar)"
legend_rates[19] = "d/dt Ca_Trop in component intracellular_calcium_concentration (millimolar)"
legend_rates[9] = "d/dt Ca_ds in component intracellular_calcium_concentration (millimolar)"
legend_rates[14] = "d/dt Ca_up in component intracellular_calcium_concentration (millimolar)"
legend_rates[15] = "d/dt Ca_rel in component intracellular_calcium_concentration (millimolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -92.8915042
constants[0] = 8314.472
constants[1] = 310
constants[2] = 96485.3415
constants[3] = 9.5e-5
constants[4] = 0.002
constants[5] = -6
constants[6] = 0.03
constants[7] = 4
constants[8] = 140
states[1] = 136.1745362
states[2] = 7.6713487
constants[9] = 2
states[3] = 1.49e-5
constants[10] = 10
constants[11] = 0.5
constants[12] = 0.0028
constants[13] = 0.0017
states[4] = 1.02e-5
states[5] = 2e-7
constants[14] = 0.0016
states[6] = 0.0006469
constants[15] = 0.5
states[7] = 0.0016111
states[8] = 0.9944559
constants[16] = 1e-5
constants[17] = 0
constants[18] = 0.0027
constants[19] = 0.0006
constants[20] = 1
constants[21] = 0.002
constants[22] = 0.01
states[9] = 2.7e-6
states[10] = 0
constants[23] = 0.01
constants[24] = 0.001
constants[25] = 0.7
constants[26] = 3
states[11] = 0
constants[27] = 0.3
constants[28] = 0.0001
constants[29] = 0.00025
constants[30] = 0.005
constants[31] = 0
states[12] = 0.9948645
states[13] = 0
constants[32] = 0.7
constants[33] = 1
constants[34] = 40
constants[35] = 0.0005
constants[36] = 3
constants[37] = 0
constants[38] = 0.2
constants[39] = 0.001
constants[40] = 0.0003
constants[41] = 0.4
constants[42] = 0.5
constants[43] = 0.4
constants[44] = 0.03
states[14] = 0.36963
states[15] = 0.6460487
constants[45] = 0.05
constants[46] = 250
constants[47] = 0.0005
constants[48] = 0.01
states[16] = 0.0049039
states[17] = 0.6950649
states[18] = 0.0005841
states[19] = 0.0003732
constants[49] = 0.02
constants[50] = 0.05
constants[51] = 100000
constants[52] = 50
constants[53] = 100000
constants[54] = 200
constants[55] = 12
constants[56] = 74
constants[57] = 0.1
constants[58] = 0.1
constants[59] = 0.4
constants[60] = 0.01
constants[61] = 10
constants[62] = (3.14159*(power(constants[55]/1000.00, 2.00000))*constants[56])/1000.00
constants[63] = (constants[40]*constants[41])/constants[42]
constants[64] = ((1.00000-constants[59])-constants[60])-constants[58]
constants[65] = constants[62]*constants[64]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[13] = 333.000*(1.00000/(1.00000+exp(-(states[0]+4.00000)/5.00000))-states[13])
algebraic[0] = 50.0000/(1.00000+exp(-(states[0]-5.00000)/9.00000))
algebraic[9] = 0.0500000*exp(-(states[0]-20.0000)/15.0000)
rates[4] = algebraic[0]*(1.00000-states[4])-algebraic[9]*states[4]
algebraic[1] = 50.0000/(1.00000+exp(-(states[0]-5.00000)/9.00000))
algebraic[10] = 0.400000*exp(-(power((states[0]+30.0000)/30.0000, 3.00000)))
rates[5] = algebraic[1]*(1.00000-states[5])-algebraic[10]*states[5]
algebraic[2] = 14.0000/(1.00000+exp(-(states[0]-40.0000)/9.00000))
algebraic[11] = 1.00000*exp(-states[0]/45.0000)
rates[6] = algebraic[2]*(1.00000-states[6])-algebraic[11]*states[6]
algebraic[4] = 20.0000*exp(-0.125000*((states[0]+75.0000)-constants[17]))
algebraic[13] = 2000.00/(1.00000+320.000*exp(-0.100000*((states[0]+75.0000)-constants[17])))
rates[8] = algebraic[4]*(1.00000-states[8])-algebraic[13]*states[8]
algebraic[7] = 0.0330000*exp(-states[0]/17.0000)
algebraic[16] = 33.0000/(1.00000+exp(-0.125000*(states[0]+10.0000)))
rates[12] = algebraic[7]*(1.00000-states[12])-algebraic[16]*states[12]
algebraic[3] = states[0]+41.0000
algebraic[12] = custom_piecewise([less(fabs(algebraic[3]) , constants[16]), 2000.00 , True, (200.000*algebraic[3])/(1.00000-exp(-0.100000*algebraic[3]))])
algebraic[18] = 8000.00*exp(-0.0560000*(states[0]+66.0000))
rates[7] = algebraic[12]*(1.00000-states[7])-algebraic[18]*states[7]
algebraic[5] = (states[0]+24.0000)-5.00000
algebraic[14] = custom_piecewise([less(fabs(algebraic[5]) , 0.000100000), 120.000 , True, (30.0000*algebraic[5])/(1.00000-exp(-algebraic[5]/4.00000))])
algebraic[19] = custom_piecewise([less(fabs(algebraic[5]) , 0.000100000), 120.000 , True, (12.0000*algebraic[5])/(exp(algebraic[5]/10.0000)-1.00000)])
rates[10] = constants[26]*(algebraic[14]*(1.00000-states[10])-algebraic[19]*states[10])
algebraic[17] = states[3]/(states[3]+constants[47])
algebraic[21] = states[9]/(states[9]+constants[48])
algebraic[23] = algebraic[17]+(1.00000-algebraic[17])*algebraic[21]
algebraic[27] = 60.0000+500.000*(power(algebraic[23], 2.00000))
algebraic[29] = custom_piecewise([less(states[0] , -50.0000), 5.00000 , True, 1.00000])
rates[17] = states[16]*algebraic[29]*algebraic[27]-algebraic[29]*1.00000*states[17]
algebraic[8] = exp(0.0800000*(states[0]-40.0000))
algebraic[25] = 0.00000*algebraic[8]+90.0000*(power(algebraic[23], 2.00000))
algebraic[31] = (1.00000-states[16])-states[17]
rates[16] = algebraic[31]*algebraic[29]*algebraic[25]-states[16]*algebraic[29]*algebraic[27]
algebraic[39] = states[3]/(constants[23]+states[3])
algebraic[36] = states[0]+34.0000
algebraic[37] = custom_piecewise([less(fabs(algebraic[36]) , constants[28]), 25.0000 , True, (6.25000*algebraic[36])/(exp(algebraic[36]/4.00000)-1.00000)])
algebraic[38] = 12.0000/(1.00000+exp((-1.00000*(states[0]+34.0000))/4.00000))
rates[11] = (120.000*(1.00000-states[11])*algebraic[39]+(1.00000-states[11])*(1.00000-algebraic[39]))*constants[27]*algebraic[38]-algebraic[37]*states[11]
algebraic[44] = states[9]/(constants[24]+states[9])
algebraic[45] = (1.00000-states[11])*(1.00000-algebraic[44])
algebraic[46] = (((constants[25]*4.00000*constants[20]*states[10]*algebraic[45]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2]*2.00000)/(constants[0]*constants[1]))))*(states[3]*exp((100.000*constants[2])/(constants[0]*constants[1]))-constants[9]*exp((-(states[0]-50.0000)*constants[2]*2.00000)/(constants[0]*constants[1])))
rates[9] = (-1.00000*algebraic[46])/(2.00000*1.00000*constants[57]*constants[65]*constants[2])-states[9]*constants[61]
algebraic[20] = ((constants[0]*constants[1])/constants[2])*log(constants[7]/states[1])
algebraic[28] = (((constants[11]*constants[7])/(constants[7]+constants[10]))*(states[0]-algebraic[20]))/(1.00000+exp((((states[0]-algebraic[20])-10.0000)*constants[2]*1.25000)/(constants[0]*constants[1])))
algebraic[51] = constants[30]*(constants[31]+states[12]*(1.00000-constants[31]))*states[13]*(states[0]-algebraic[20])
algebraic[30] = (((constants[12]*states[4]+constants[13]*states[5])*1.00000)/(1.00000+exp((states[0]+9.00000)/22.4000)))*(states[0]-algebraic[20])
algebraic[22] = ((constants[0]*constants[1])/constants[2])*log((constants[7]+constants[6]*constants[8])/(states[1]+constants[6]*states[2]))
algebraic[32] = constants[14]*(power(states[6], 2.00000))*(states[0]-algebraic[22])
algebraic[40] = (1.00000-states[11])*(1.00000-algebraic[39])
algebraic[42] = ((((1.00000-constants[25])*constants[21]*constants[20]*states[10]*algebraic[40]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))))*(states[1]*exp((50.0000*constants[2])/(constants[0]*constants[1]))-constants[7]*exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1])))
algebraic[47] = (((constants[25]*constants[21]*constants[20]*states[10]*algebraic[45]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))))*(states[1]*exp((50.0000*constants[2])/(constants[0]*constants[1]))-constants[7]*exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1])))
algebraic[52] = (((constants[32]*constants[7])/(constants[33]+constants[7]))*states[2])/(constants[34]+states[2])
rates[1] = (-1.00000/(1.00000*constants[65]*constants[2]))*((algebraic[28]+algebraic[30]+algebraic[32]+algebraic[42]+algebraic[47]+algebraic[51])-2.00000*algebraic[52])
algebraic[26] = ((constants[0]*constants[1])/constants[2])*log((constants[8]+0.120000*constants[7])/(states[2]+0.120000*states[1]))
algebraic[33] = constants[15]*(power(states[7], 3.00000))*states[8]*(states[0]-algebraic[26])
algebraic[15] = ((constants[0]*constants[1])/constants[2])*log(constants[8]/states[2])
algebraic[35] = constants[19]*(states[0]-algebraic[15])
algebraic[34] = ((constants[18]*1.00000)/(1.00000+exp(-(states[0]+52.0000)/8.00000)))*(states[0]-algebraic[15])
algebraic[43] = ((((1.00000-constants[25])*constants[22]*constants[20]*states[10]*algebraic[40]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))))*(states[2]*exp((50.0000*constants[2])/(constants[0]*constants[1]))-constants[8]*exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1])))
algebraic[48] = (((constants[25]*constants[22]*constants[20]*states[10]*algebraic[45]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))))*(states[2]*exp((50.0000*constants[2])/(constants[0]*constants[1]))-constants[8]*exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1])))
algebraic[53] = ((1.00000-constants[39])*constants[35]*(exp((constants[38]*(constants[36]-2.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[2], constants[36]))*constants[9]-exp(((constants[38]-1.00000)*(constants[36]-2.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[8], constants[36]))*states[3]))/((1.00000+constants[37]*(states[3]*(power(constants[8], constants[36]))+constants[9]*(power(states[2], constants[36]))))*(1.00000+states[3]/0.00690000))
rates[2] = (-1.00000/(1.00000*constants[65]*constants[2]))*(algebraic[33]+algebraic[34]+algebraic[35]+3.00000*algebraic[52]+3.00000*algebraic[53]+algebraic[43]+algebraic[48])
algebraic[54] = (constants[39]*constants[35]*(exp((constants[38]*(constants[36]-2.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[2], constants[36]))*constants[9]-exp(((constants[38]-1.00000)*(constants[36]-2.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[8], constants[36]))*states[9]))/((1.00000+constants[37]*(states[9]*(power(constants[8], constants[36]))+constants[9]*(power(states[2], constants[36]))))*(1.00000+states[9]/0.00690000))
algebraic[41] = ((((1.00000-constants[25])*4.00000*constants[20]*states[10]*algebraic[40]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2]*2.00000)/(constants[0]*constants[1]))))*(states[3]*exp((100.000*constants[2])/(constants[0]*constants[1]))-constants[9]*exp((-(states[0]-50.0000)*constants[2]*2.00000)/(constants[0]*constants[1])))
algebraic[24] = ((0.500000*constants[0]*constants[1])/constants[2])*log(constants[9]/states[3])
algebraic[50] = constants[29]*(states[0]-algebraic[24])
algebraic[6] = custom_piecewise([greater_equal(voi , 0.0500000) & less_equal(voi , 0.0500000+constants[4]), constants[5] , True, 0.00000])
rates[0] = (-1.00000/constants[3])*(algebraic[6]+algebraic[28]+algebraic[51]+algebraic[30]+algebraic[32]+algebraic[52]+algebraic[33]+algebraic[35]+algebraic[34]+algebraic[43]+algebraic[48]+algebraic[53]+algebraic[54]+algebraic[41]+algebraic[46]+algebraic[42]+algebraic[47]+algebraic[50])
algebraic[56] = states[3]+states[14]*constants[63]+constants[40]*constants[41]+constants[40]
algebraic[57] = (states[3]/algebraic[56])*constants[43]-((states[14]*constants[63])/algebraic[56])*constants[44]
algebraic[58] = 50.0000*(states[14]-states[15])
rates[14] = (constants[64]/constants[60])*algebraic[57]-algebraic[58]
rates[18] = constants[51]*states[3]*(constants[49]-states[18])-constants[52]*states[18]
algebraic[59] = ((power(states[16]/(states[16]+0.250000), 2.00000))*constants[46]+constants[45])*states[15]
rates[15] = (constants[60]/constants[58])*algebraic[58]-algebraic[59]
rates[19] = constants[53]*states[3]*(constants[50]-states[19])-constants[54]*states[19]
rates[3] = ((((-1.00000/(2.00000*1.00000*constants[65]*constants[2]))*(((algebraic[41]+algebraic[50])-2.00000*algebraic[53])-2.00000*algebraic[54])+states[9]*constants[57]*constants[61]+(algebraic[59]*constants[58])/constants[64])-rates[18])-rates[19])-algebraic[57]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = 50.0000/(1.00000+exp(-(states[0]-5.00000)/9.00000))
algebraic[9] = 0.0500000*exp(-(states[0]-20.0000)/15.0000)
algebraic[1] = 50.0000/(1.00000+exp(-(states[0]-5.00000)/9.00000))
algebraic[10] = 0.400000*exp(-(power((states[0]+30.0000)/30.0000, 3.00000)))
algebraic[2] = 14.0000/(1.00000+exp(-(states[0]-40.0000)/9.00000))
algebraic[11] = 1.00000*exp(-states[0]/45.0000)
algebraic[4] = 20.0000*exp(-0.125000*((states[0]+75.0000)-constants[17]))
algebraic[13] = 2000.00/(1.00000+320.000*exp(-0.100000*((states[0]+75.0000)-constants[17])))
algebraic[7] = 0.0330000*exp(-states[0]/17.0000)
algebraic[16] = 33.0000/(1.00000+exp(-0.125000*(states[0]+10.0000)))
algebraic[3] = states[0]+41.0000
algebraic[12] = custom_piecewise([less(fabs(algebraic[3]) , constants[16]), 2000.00 , True, (200.000*algebraic[3])/(1.00000-exp(-0.100000*algebraic[3]))])
algebraic[18] = 8000.00*exp(-0.0560000*(states[0]+66.0000))
algebraic[5] = (states[0]+24.0000)-5.00000
algebraic[14] = custom_piecewise([less(fabs(algebraic[5]) , 0.000100000), 120.000 , True, (30.0000*algebraic[5])/(1.00000-exp(-algebraic[5]/4.00000))])
algebraic[19] = custom_piecewise([less(fabs(algebraic[5]) , 0.000100000), 120.000 , True, (12.0000*algebraic[5])/(exp(algebraic[5]/10.0000)-1.00000)])
algebraic[17] = states[3]/(states[3]+constants[47])
algebraic[21] = states[9]/(states[9]+constants[48])
algebraic[23] = algebraic[17]+(1.00000-algebraic[17])*algebraic[21]
algebraic[27] = 60.0000+500.000*(power(algebraic[23], 2.00000))
algebraic[29] = custom_piecewise([less(states[0] , -50.0000), 5.00000 , True, 1.00000])
algebraic[8] = exp(0.0800000*(states[0]-40.0000))
algebraic[25] = 0.00000*algebraic[8]+90.0000*(power(algebraic[23], 2.00000))
algebraic[31] = (1.00000-states[16])-states[17]
algebraic[39] = states[3]/(constants[23]+states[3])
algebraic[36] = states[0]+34.0000
algebraic[37] = custom_piecewise([less(fabs(algebraic[36]) , constants[28]), 25.0000 , True, (6.25000*algebraic[36])/(exp(algebraic[36]/4.00000)-1.00000)])
algebraic[38] = 12.0000/(1.00000+exp((-1.00000*(states[0]+34.0000))/4.00000))
algebraic[44] = states[9]/(constants[24]+states[9])
algebraic[45] = (1.00000-states[11])*(1.00000-algebraic[44])
algebraic[46] = (((constants[25]*4.00000*constants[20]*states[10]*algebraic[45]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2]*2.00000)/(constants[0]*constants[1]))))*(states[3]*exp((100.000*constants[2])/(constants[0]*constants[1]))-constants[9]*exp((-(states[0]-50.0000)*constants[2]*2.00000)/(constants[0]*constants[1])))
algebraic[20] = ((constants[0]*constants[1])/constants[2])*log(constants[7]/states[1])
algebraic[28] = (((constants[11]*constants[7])/(constants[7]+constants[10]))*(states[0]-algebraic[20]))/(1.00000+exp((((states[0]-algebraic[20])-10.0000)*constants[2]*1.25000)/(constants[0]*constants[1])))
algebraic[51] = constants[30]*(constants[31]+states[12]*(1.00000-constants[31]))*states[13]*(states[0]-algebraic[20])
algebraic[30] = (((constants[12]*states[4]+constants[13]*states[5])*1.00000)/(1.00000+exp((states[0]+9.00000)/22.4000)))*(states[0]-algebraic[20])
algebraic[22] = ((constants[0]*constants[1])/constants[2])*log((constants[7]+constants[6]*constants[8])/(states[1]+constants[6]*states[2]))
algebraic[32] = constants[14]*(power(states[6], 2.00000))*(states[0]-algebraic[22])
algebraic[40] = (1.00000-states[11])*(1.00000-algebraic[39])
algebraic[42] = ((((1.00000-constants[25])*constants[21]*constants[20]*states[10]*algebraic[40]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))))*(states[1]*exp((50.0000*constants[2])/(constants[0]*constants[1]))-constants[7]*exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1])))
algebraic[47] = (((constants[25]*constants[21]*constants[20]*states[10]*algebraic[45]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))))*(states[1]*exp((50.0000*constants[2])/(constants[0]*constants[1]))-constants[7]*exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1])))
algebraic[52] = (((constants[32]*constants[7])/(constants[33]+constants[7]))*states[2])/(constants[34]+states[2])
algebraic[26] = ((constants[0]*constants[1])/constants[2])*log((constants[8]+0.120000*constants[7])/(states[2]+0.120000*states[1]))
algebraic[33] = constants[15]*(power(states[7], 3.00000))*states[8]*(states[0]-algebraic[26])
algebraic[15] = ((constants[0]*constants[1])/constants[2])*log(constants[8]/states[2])
algebraic[35] = constants[19]*(states[0]-algebraic[15])
algebraic[34] = ((constants[18]*1.00000)/(1.00000+exp(-(states[0]+52.0000)/8.00000)))*(states[0]-algebraic[15])
algebraic[43] = ((((1.00000-constants[25])*constants[22]*constants[20]*states[10]*algebraic[40]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))))*(states[2]*exp((50.0000*constants[2])/(constants[0]*constants[1]))-constants[8]*exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1])))
algebraic[48] = (((constants[25]*constants[22]*constants[20]*states[10]*algebraic[45]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))))*(states[2]*exp((50.0000*constants[2])/(constants[0]*constants[1]))-constants[8]*exp((-(states[0]-50.0000)*constants[2])/(constants[0]*constants[1])))
algebraic[53] = ((1.00000-constants[39])*constants[35]*(exp((constants[38]*(constants[36]-2.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[2], constants[36]))*constants[9]-exp(((constants[38]-1.00000)*(constants[36]-2.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[8], constants[36]))*states[3]))/((1.00000+constants[37]*(states[3]*(power(constants[8], constants[36]))+constants[9]*(power(states[2], constants[36]))))*(1.00000+states[3]/0.00690000))
algebraic[54] = (constants[39]*constants[35]*(exp((constants[38]*(constants[36]-2.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[2], constants[36]))*constants[9]-exp(((constants[38]-1.00000)*(constants[36]-2.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[8], constants[36]))*states[9]))/((1.00000+constants[37]*(states[9]*(power(constants[8], constants[36]))+constants[9]*(power(states[2], constants[36]))))*(1.00000+states[9]/0.00690000))
algebraic[41] = ((((1.00000-constants[25])*4.00000*constants[20]*states[10]*algebraic[40]*(states[0]-50.0000)*constants[2])/(constants[0]*constants[1]))/(1.00000-exp((-(states[0]-50.0000)*constants[2]*2.00000)/(constants[0]*constants[1]))))*(states[3]*exp((100.000*constants[2])/(constants[0]*constants[1]))-constants[9]*exp((-(states[0]-50.0000)*constants[2]*2.00000)/(constants[0]*constants[1])))
algebraic[24] = ((0.500000*constants[0]*constants[1])/constants[2])*log(constants[9]/states[3])
algebraic[50] = constants[29]*(states[0]-algebraic[24])
algebraic[6] = custom_piecewise([greater_equal(voi , 0.0500000) & less_equal(voi , 0.0500000+constants[4]), constants[5] , True, 0.00000])
algebraic[56] = states[3]+states[14]*constants[63]+constants[40]*constants[41]+constants[40]
algebraic[57] = (states[3]/algebraic[56])*constants[43]-((states[14]*constants[63])/algebraic[56])*constants[44]
algebraic[58] = 50.0000*(states[14]-states[15])
algebraic[59] = ((power(states[16]/(states[16]+0.250000), 2.00000))*constants[46]+constants[45])*states[15]
algebraic[49] = algebraic[41]+algebraic[42]+algebraic[43]+algebraic[46]+algebraic[47]+algebraic[48]
algebraic[55] = algebraic[53]+algebraic[54]
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)