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 = 70
sizeStates = 30
sizeConstants = 51
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[0] = "Q_tot in component membrane (millivolt)"
legend_algebraic[37] = "i_Na in component sodium_current (picoA)"
legend_algebraic[41] = "i_Ca_L in component L_type_Ca_channel (picoA)"
legend_algebraic[44] = "i_t in component Ca_independent_transient_outward_K_current (picoA)"
legend_algebraic[45] = "i_Kur in component ultra_rapid_K_current (picoA)"
legend_algebraic[46] = "i_K1 in component inward_rectifier (picoA)"
legend_algebraic[49] = "i_Kr in component delayed_rectifier_K_currents (picoA)"
legend_algebraic[47] = "i_Ks in component delayed_rectifier_K_currents (picoA)"
legend_algebraic[50] = "i_B_Na in component background_currents (picoA)"
legend_algebraic[52] = "i_B_Ca in component background_currents (picoA)"
legend_algebraic[54] = "i_NaK in component sodium_potassium_pump (picoA)"
legend_algebraic[55] = "i_CaP in component sarcolemmal_calcium_pump_current (picoA)"
legend_algebraic[56] = "i_NaCa in component Na_Ca_ion_exchanger_current (picoA)"
legend_algebraic[57] = "i_KACh in component ACh_dependent_K_current (picoA)"
legend_algebraic[59] = "I in component membrane (pA_per_nF)"
legend_algebraic[24] = "i_Stim in component membrane (pA_per_nF)"
legend_constants[4] = "stim_offset in component membrane (second)"
legend_constants[5] = "stim_period in component membrane (second)"
legend_constants[6] = "stim_duration in component membrane (second)"
legend_constants[7] = "stim_amplitude in component membrane (pA_per_nF)"
legend_algebraic[1] = "past in component membrane (second)"
legend_algebraic[35] = "E_Na in component sodium_current (millivolt)"
legend_constants[8] = "P_Na in component sodium_current (nanolitre_per_second)"
legend_states[1] = "Na_c in component cleft_space_ion_concentrations (millimolar)"
legend_states[2] = "Na_i in component intracellular_ion_concentrations (millimolar)"
legend_states[3] = "m in component sodium_current_m_gate (dimensionless)"
legend_states[4] = "h1 in component sodium_current_h1_gate (dimensionless)"
legend_states[5] = "h2 in component sodium_current_h2_gate (dimensionless)"
legend_algebraic[14] = "m_infinity in component sodium_current_m_gate (dimensionless)"
legend_algebraic[2] = "m_factor in component sodium_current_m_gate (dimensionless)"
legend_algebraic[26] = "tau_m in component sodium_current_m_gate (second)"
legend_algebraic[3] = "h_infinity in component sodium_current_h1_gate (dimensionless)"
legend_algebraic[15] = "h_factor in component sodium_current_h1_gate (dimensionless)"
legend_algebraic[27] = "tau_h1 in component sodium_current_h1_gate (second)"
legend_algebraic[28] = "tau_h2 in component sodium_current_h2_gate (second)"
legend_constants[9] = "g_Ca_L in component L_type_Ca_channel (nanoS)"
legend_constants[10] = "E_Ca_app in component L_type_Ca_channel (millivolt)"
legend_algebraic[39] = "f_Ca in component L_type_Ca_channel (dimensionless)"
legend_constants[11] = "k_Ca in component L_type_Ca_channel (millimolar)"
legend_states[6] = "Ca_d in component intracellular_ion_concentrations (millimolar)"
legend_states[7] = "d_L in component L_type_Ca_channel_d_L_gate (dimensionless)"
legend_states[8] = "f_L1 in component L_type_Ca_channel_f_L1_gate (dimensionless)"
legend_states[9] = "f_L2 in component L_type_Ca_channel_f_L2_gate (dimensionless)"
legend_algebraic[4] = "d_L_infinity in component L_type_Ca_channel_d_L_gate (dimensionless)"
legend_algebraic[16] = "d_L_factor in component L_type_Ca_channel_d_L_gate (dimensionless)"
legend_algebraic[29] = "tau_d_L in component L_type_Ca_channel_d_L_gate (second)"
legend_algebraic[5] = "f_L_infinity in component L_type_Ca_channel_f_L1_gate (dimensionless)"
legend_algebraic[17] = "f_L_factor in component L_type_Ca_channel_f_L1_gate (millivolt)"
legend_algebraic[30] = "tau_f_L1 in component L_type_Ca_channel_f_L1_gate (second)"
legend_algebraic[31] = "tau_f_L2 in component L_type_Ca_channel_f_L2_gate (second)"
legend_algebraic[43] = "E_K in component Ca_independent_transient_outward_K_current (millivolt)"
legend_constants[12] = "g_t in component Ca_independent_transient_outward_K_current (nanoS)"
legend_states[10] = "K_c in component cleft_space_ion_concentrations (millimolar)"
legend_states[11] = "K_i in component intracellular_ion_concentrations (millimolar)"
legend_states[12] = "r in component Ca_independent_transient_outward_K_current_r_gate (dimensionless)"
legend_states[13] = "s in component Ca_independent_transient_outward_K_current_s_gate (dimensionless)"
legend_algebraic[18] = "tau_r in component Ca_independent_transient_outward_K_current_r_gate (second)"
legend_algebraic[6] = "r_infinity in component Ca_independent_transient_outward_K_current_r_gate (dimensionless)"
legend_algebraic[32] = "tau_s in component Ca_independent_transient_outward_K_current_s_gate (second)"
legend_algebraic[7] = "s_infinity in component Ca_independent_transient_outward_K_current_s_gate (dimensionless)"
legend_algebraic[19] = "s_factor in component Ca_independent_transient_outward_K_current_s_gate (dimensionless)"
legend_constants[13] = "g_kur in component ultra_rapid_K_current (nanoS)"
legend_states[14] = "a_ur in component ultra_rapid_K_current_aur_gate (dimensionless)"
legend_states[15] = "i_ur in component ultra_rapid_K_current_iur_gate (dimensionless)"
legend_algebraic[8] = "a_ur_infinity in component ultra_rapid_K_current_aur_gate (dimensionless)"
legend_algebraic[20] = "tau_a_ur in component ultra_rapid_K_current_aur_gate (second)"
legend_algebraic[9] = "i_ur_infinity in component ultra_rapid_K_current_iur_gate (dimensionless)"
legend_algebraic[21] = "tau_i_ur in component ultra_rapid_K_current_iur_gate (second)"
legend_constants[14] = "g_K1 in component inward_rectifier (nanoS)"
legend_constants[15] = "g_Ks in component delayed_rectifier_K_currents (nanoS)"
legend_constants[16] = "g_Kr in component delayed_rectifier_K_currents (nanoS)"
legend_states[16] = "n in component delayed_rectifier_K_currents_n_gate (dimensionless)"
legend_states[17] = "pa in component delayed_rectifier_K_currents_pa_gate (dimensionless)"
legend_algebraic[48] = "pip in component delayed_rectifier_K_currents_pi_gate (dimensionless)"
legend_algebraic[33] = "tau_n in component delayed_rectifier_K_currents_n_gate (second)"
legend_algebraic[10] = "n_infinity in component delayed_rectifier_K_currents_n_gate (dimensionless)"
legend_algebraic[22] = "n_factor in component delayed_rectifier_K_currents_n_gate (dimensionless)"
legend_algebraic[34] = "tau_pa in component delayed_rectifier_K_currents_pa_gate (second)"
legend_algebraic[23] = "pa_factor in component delayed_rectifier_K_currents_pa_gate (dimensionless)"
legend_algebraic[11] = "p_a_infinity in component delayed_rectifier_K_currents_pa_gate (dimensionless)"
legend_constants[17] = "g_B_Na in component background_currents (nanoS)"
legend_constants[18] = "g_B_Ca in component background_currents (nanoS)"
legend_algebraic[51] = "E_Ca in component background_currents (millivolt)"
legend_states[18] = "Ca_c in component cleft_space_ion_concentrations (millimolar)"
legend_states[19] = "Ca_i in component intracellular_ion_concentrations (millimolar)"
legend_constants[19] = "K_NaK_K in component sodium_potassium_pump (millimolar)"
legend_constants[20] = "i_NaK_max in component sodium_potassium_pump (picoA)"
legend_constants[21] = "pow_K_NaK_Na_15 in component sodium_potassium_pump (millimolar15)"
legend_algebraic[53] = "pow_Na_i_15 in component sodium_potassium_pump (millimolar15)"
legend_constants[22] = "i_CaP_max in component sarcolemmal_calcium_pump_current (picoA)"
legend_constants[23] = "k_CaP in component sarcolemmal_calcium_pump_current (millimolar)"
legend_constants[24] = "K_NaCa in component Na_Ca_ion_exchanger_current (picoA_per_millimolar_4)"
legend_constants[25] = "d_NaCa in component Na_Ca_ion_exchanger_current (per_millimolar_4)"
legend_constants[26] = "gamma_Na in component Na_Ca_ion_exchanger_current (dimensionless)"
legend_constants[27] = "ACh in component ACh_dependent_K_current (millimolar)"
legend_constants[28] = "phi_Na_en in component intracellular_ion_concentrations (picoA)"
legend_constants[29] = "Vol_i in component intracellular_ion_concentrations (nanolitre)"
legend_constants[30] = "Vol_d in component intracellular_ion_concentrations (nanolitre)"
legend_algebraic[58] = "i_di in component intracellular_ion_concentrations (picoA)"
legend_constants[31] = "tau_di in component intracellular_ion_concentrations (second)"
legend_algebraic[67] = "i_up in component Ca_handling_by_the_SR (picoA)"
legend_algebraic[66] = "i_rel in component Ca_handling_by_the_SR (picoA)"
legend_algebraic[63] = "J_O in component intracellular_Ca_buffering (per_second)"
legend_states[20] = "O_C in component intracellular_Ca_buffering (dimensionless)"
legend_states[21] = "O_TC in component intracellular_Ca_buffering (dimensionless)"
legend_states[22] = "O_TMgC in component intracellular_Ca_buffering (dimensionless)"
legend_states[23] = "O_TMgMg in component intracellular_Ca_buffering (dimensionless)"
legend_states[24] = "O in component intracellular_Ca_buffering (dimensionless)"
legend_algebraic[60] = "J_O_C in component intracellular_Ca_buffering (per_second)"
legend_algebraic[61] = "J_O_TC in component intracellular_Ca_buffering (per_second)"
legend_algebraic[62] = "J_O_TMgC in component intracellular_Ca_buffering (per_second)"
legend_algebraic[12] = "J_O_TMgMg in component intracellular_Ca_buffering (per_second)"
legend_constants[32] = "Mg_i in component intracellular_Ca_buffering (millimolar)"
legend_constants[33] = "Vol_c in component cleft_space_ion_concentrations (nanolitre)"
legend_constants[34] = "tau_Na in component cleft_space_ion_concentrations (second)"
legend_constants[35] = "tau_K in component cleft_space_ion_concentrations (second)"
legend_constants[36] = "tau_Ca in component cleft_space_ion_concentrations (second)"
legend_constants[37] = "Na_b in component cleft_space_ion_concentrations (millimolar)"
legend_constants[38] = "Ca_b in component cleft_space_ion_concentrations (millimolar)"
legend_constants[39] = "K_b in component cleft_space_ion_concentrations (millimolar)"
legend_algebraic[68] = "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[25] = "Ca_rel in component Ca_handling_by_the_SR (millimolar)"
legend_states[26] = "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[40] = "r_act in component Ca_handling_by_the_SR (per_second)"
legend_algebraic[42] = "r_inact in component Ca_handling_by_the_SR (per_second)"
legend_constants[47] = "r_recov in component Ca_handling_by_the_SR (per_second)"
legend_algebraic[13] = "r_Ca_d_term in component Ca_handling_by_the_SR (dimensionless)"
legend_algebraic[25] = "r_Ca_i_term in component Ca_handling_by_the_SR (dimensionless)"
legend_algebraic[36] = "r_Ca_d_factor in component Ca_handling_by_the_SR (dimensionless)"
legend_algebraic[38] = "r_Ca_i_factor in component Ca_handling_by_the_SR (dimensionless)"
legend_algebraic[64] = "i_rel_f2 in component Ca_handling_by_the_SR (dimensionless)"
legend_algebraic[65] = "i_rel_factor in component Ca_handling_by_the_SR (dimensionless)"
legend_states[27] = "O_Calse in component Ca_handling_by_the_SR (dimensionless)"
legend_algebraic[69] = "J_O_Calse in component Ca_handling_by_the_SR (per_second)"
legend_states[28] = "F1 in component Ca_handling_by_the_SR (dimensionless)"
legend_states[29] = "F2 in component Ca_handling_by_the_SR (dimensionless)"
legend_constants[48] = "tau_tr in component Ca_handling_by_the_SR (second)"
legend_constants[49] = "k_rel_i in component Ca_handling_by_the_SR (millimolar)"
legend_constants[50] = "k_rel_d in component Ca_handling_by_the_SR (millimolar)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[3] = "d/dt m in component sodium_current_m_gate (dimensionless)"
legend_rates[4] = "d/dt h1 in component sodium_current_h1_gate (dimensionless)"
legend_rates[5] = "d/dt h2 in component sodium_current_h2_gate (dimensionless)"
legend_rates[7] = "d/dt d_L in component L_type_Ca_channel_d_L_gate (dimensionless)"
legend_rates[8] = "d/dt f_L1 in component L_type_Ca_channel_f_L1_gate (dimensionless)"
legend_rates[9] = "d/dt f_L2 in component L_type_Ca_channel_f_L2_gate (dimensionless)"
legend_rates[12] = "d/dt r in component Ca_independent_transient_outward_K_current_r_gate (dimensionless)"
legend_rates[13] = "d/dt s in component Ca_independent_transient_outward_K_current_s_gate (dimensionless)"
legend_rates[14] = "d/dt a_ur in component ultra_rapid_K_current_aur_gate (dimensionless)"
legend_rates[15] = "d/dt i_ur in component ultra_rapid_K_current_iur_gate (dimensionless)"
legend_rates[16] = "d/dt n in component delayed_rectifier_K_currents_n_gate (dimensionless)"
legend_rates[17] = "d/dt pa in component delayed_rectifier_K_currents_pa_gate (dimensionless)"
legend_rates[11] = "d/dt K_i in component intracellular_ion_concentrations (millimolar)"
legend_rates[2] = "d/dt Na_i in component intracellular_ion_concentrations (millimolar)"
legend_rates[19] = "d/dt Ca_i in component intracellular_ion_concentrations (millimolar)"
legend_rates[6] = "d/dt Ca_d in component intracellular_ion_concentrations (millimolar)"
legend_rates[20] = "d/dt O_C in component intracellular_Ca_buffering (dimensionless)"
legend_rates[21] = "d/dt O_TC in component intracellular_Ca_buffering (dimensionless)"
legend_rates[22] = "d/dt O_TMgC in component intracellular_Ca_buffering (dimensionless)"
legend_rates[23] = "d/dt O_TMgMg in component intracellular_Ca_buffering (dimensionless)"
legend_rates[24] = "d/dt O in component intracellular_Ca_buffering (dimensionless)"
legend_rates[18] = "d/dt Ca_c in component cleft_space_ion_concentrations (millimolar)"
legend_rates[10] = "d/dt K_c in component cleft_space_ion_concentrations (millimolar)"
legend_rates[1] = "d/dt Na_c in component cleft_space_ion_concentrations (millimolar)"
legend_rates[28] = "d/dt F1 in component Ca_handling_by_the_SR (dimensionless)"
legend_rates[29] = "d/dt F2 in component Ca_handling_by_the_SR (dimensionless)"
legend_rates[27] = "d/dt O_Calse in component Ca_handling_by_the_SR (dimensionless)"
legend_rates[26] = "d/dt Ca_up in component Ca_handling_by_the_SR (millimolar)"
legend_rates[25] = "d/dt Ca_rel in component Ca_handling_by_the_SR (millimolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -74.031982
constants[0] = 8314
constants[1] = 306.15
constants[2] = 96487
constants[3] = 50
constants[4] = 0
constants[5] = 1
constants[6] = 0.006
constants[7] = -15
constants[8] = 0.0018
states[1] = 130.022096
states[2] = 8.516766
states[3] = 0.003289
states[4] = 0.877202
states[5] = 0.873881
constants[9] = 6.75
constants[10] = 60
constants[11] = 0.025
states[6] = 7.1e-5
states[7] = 0.000014
states[8] = 0.998597
states[9] = 0.998586
constants[12] = 8.25
states[10] = 5.560224
states[11] = 129.485991
states[12] = 0.001089
states[13] = 0.948597
constants[13] = 2.25
states[14] = 0.000367
states[15] = 0.96729
constants[14] = 3.1
constants[15] = 1
constants[16] = 0.5
states[16] = 0.004374
states[17] = 0.000053
constants[17] = 0.060599
constants[18] = 0.078681
states[18] = 1.815768
states[19] = 6.5e-5
constants[19] = 1
constants[20] = 68.55
constants[21] = 36.4829
constants[22] = 4
constants[23] = 0.0002
constants[24] = 0.0374842
constants[25] = 0.0003
constants[26] = 0.45
constants[27] = 1e-24
constants[28] = 0
constants[29] = 0.005884
constants[30] = 0.00011768
constants[31] = 0.01
states[20] = 0.026766
states[21] = 0.012922
states[22] = 0.190369
states[23] = 0.714463
states[24] = 1.38222
constants[32] = 2.5
constants[33] = 0.000800224
constants[34] = 14.3
constants[35] = 10
constants[36] = 24.7
constants[37] = 130
constants[38] = 1.8
constants[39] = 5.4
constants[40] = 2800
constants[41] = 0.0003
constants[42] = 0.5
constants[43] = 0.4
constants[44] = 200000
states[25] = 0.632613
states[26] = 0.649195
constants[45] = 0.0003969
constants[46] = 0.0000441
constants[47] = 0.815
states[27] = 0.431547
states[28] = 0.470055
states[29] = 0.002814
constants[48] = 0.01
constants[49] = 0.0003
constants[50] = 0.003
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[12] = 2000.00*constants[32]*((1.00000-states[22])-states[23])-666.000*states[23]
rates[23] = algebraic[12]
algebraic[18] = 0.00350000*exp(((-states[0]*states[0])/30.0000)/30.0000)+0.00150000
algebraic[6] = 1.00000/(1.00000+exp((states[0]-1.00000)/-11.0000))
rates[12] = (algebraic[6]-states[12])/algebraic[18]
algebraic[8] = 1.00000/(1.00000+exp(-(states[0]+6.00000)/8.60000))
algebraic[20] = 0.00900000/(1.00000+exp((states[0]+5.00000)/12.0000))+0.000500000
rates[14] = (algebraic[8]-states[14])/algebraic[20]
algebraic[9] = 1.00000/(1.00000+exp((states[0]+7.50000)/10.0000))
algebraic[21] = 0.590000/(1.00000+exp((states[0]+60.0000)/10.0000))+3.05000
rates[15] = (algebraic[9]-states[15])/algebraic[21]
algebraic[14] = 1.00000/(1.00000+exp((states[0]+27.1200)/-8.21000))
algebraic[2] = (states[0]+25.5700)/28.8000
algebraic[26] = 4.20000e-05*exp(-algebraic[2]*algebraic[2])+2.40000e-05
rates[3] = (algebraic[14]-states[3])/algebraic[26]
algebraic[3] = 1.00000/(1.00000+exp((states[0]+63.6000)/5.30000))
algebraic[15] = 1.00000/(1.00000+exp((states[0]+35.1000)/3.20000))
algebraic[27] = 0.0300000*algebraic[15]+0.000300000
rates[4] = (algebraic[3]-states[4])/algebraic[27]
algebraic[28] = 0.120000*algebraic[15]+0.00300000
rates[5] = (algebraic[3]-states[5])/algebraic[28]
algebraic[4] = 1.00000/(1.00000+exp((states[0]+9.00000)/-5.80000))
algebraic[16] = (states[0]+35.0000)/30.0000
algebraic[29] = 0.00270000*exp(-algebraic[16]*algebraic[16])+0.00200000
rates[7] = (algebraic[4]-states[7])/algebraic[29]
algebraic[5] = 1.00000/(1.00000+exp((states[0]+27.4000)/7.10000))
algebraic[17] = states[0]+40.0000
algebraic[30] = 0.161000*exp(((-algebraic[17]*algebraic[17])/14.4000)/14.4000)+0.0100000
rates[8] = (algebraic[5]-states[8])/algebraic[30]
algebraic[31] = 1.33230*exp(((-algebraic[17]*algebraic[17])/14.2000)/14.2000)+0.0626000
rates[9] = (algebraic[5]-states[9])/algebraic[31]
algebraic[19] = (states[0]+52.4500)/15.8827
algebraic[32] = 0.0256350*exp(-algebraic[19]*algebraic[19])+0.0141400
algebraic[7] = 1.00000/(1.00000+exp((states[0]+40.5000)/11.5000))
rates[13] = (algebraic[7]-states[13])/algebraic[32]
algebraic[22] = (states[0]-20.0000)/20.0000
algebraic[33] = 0.700000+0.400000*exp(-algebraic[22]*algebraic[22])
algebraic[10] = 1.00000/(1.00000+exp((states[0]-19.9000)/-12.7000))
rates[16] = (algebraic[10]-states[16])/algebraic[33]
algebraic[23] = (states[0]+20.1376)/22.1996
algebraic[34] = 0.0311800+0.217180*exp(-algebraic[23]*algebraic[23])
algebraic[11] = 1.00000/(1.00000+exp((states[0]+15.0000)/-6.00000))
rates[17] = (algebraic[11]-states[17])/algebraic[34]
algebraic[13] = states[6]/(states[6]+constants[50])
algebraic[36] = algebraic[13]*algebraic[13]*algebraic[13]*algebraic[13]
algebraic[25] = states[19]/(states[19]+constants[49])
algebraic[38] = algebraic[25]*algebraic[25]*algebraic[25]*algebraic[25]
algebraic[40] = 203.800*(algebraic[38]+algebraic[36])
rates[28] = constants[47]*((1.00000-states[28])-states[29])-algebraic[40]*states[28]
algebraic[42] = 33.9600+339.600*algebraic[38]
rates[29] = algebraic[40]*states[28]-algebraic[42]*states[29]
algebraic[43] = ((constants[0]*constants[1])/constants[2])*log(states[10]/states[11])
algebraic[44] = constants[12]*states[12]*states[13]*(states[0]-algebraic[43])
algebraic[45] = constants[13]*states[14]*states[15]*(states[0]-algebraic[43])
algebraic[46] = (constants[14]*(power(states[10]/1.00000, 0.445700))*(states[0]-algebraic[43]))/(1.00000+exp((1.50000*((states[0]-algebraic[43])+3.60000)*constants[2])/(constants[0]*constants[1])))
algebraic[48] = 1.00000/(1.00000+exp((states[0]+55.0000)/24.0000))
algebraic[49] = constants[16]*states[17]*algebraic[48]*(states[0]-algebraic[43])
algebraic[47] = constants[15]*states[16]*(states[0]-algebraic[43])
algebraic[53] = power(states[2], 1.50000)
algebraic[54] = (((((constants[20]*states[10])/(states[10]+constants[19]))*algebraic[53])/(algebraic[53]+constants[21]))*(states[0]+150.000))/(states[0]+200.000)
algebraic[1] = floor(voi/constants[5])*constants[5]
algebraic[24] = custom_piecewise([greater_equal(voi-algebraic[1] , constants[4]) & less_equal(voi-algebraic[1] , constants[4]+constants[6]), constants[7] , True, 0.00000])
rates[11] = -(((algebraic[44]+algebraic[45]+algebraic[46]+algebraic[47]+algebraic[49])-2.00000*algebraic[54])+algebraic[24]*constants[3])/(constants[29]*constants[2])
rates[10] = (constants[39]-states[10])/constants[35]+((algebraic[44]+algebraic[45]+algebraic[46]+algebraic[47]+algebraic[49])-2.00000*algebraic[54])/(constants[33]*constants[2])
algebraic[35] = ((constants[0]*constants[1])/constants[2])*log(states[1]/states[2])
algebraic[37] = (((constants[8]*states[3]*states[3]*states[3]*(0.900000*states[4]+0.100000*states[5])*states[1]*states[0]*constants[2]*constants[2])/(constants[0]*constants[1]))*(exp(((states[0]-algebraic[35])*constants[2])/(constants[0]*constants[1]))-1.00000))/(exp((states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[50] = constants[17]*(states[0]-algebraic[35])
algebraic[56] = (constants[24]*(states[2]*states[2]*states[2]*states[18]*exp((constants[2]*states[0]*constants[26])/(constants[0]*constants[1]))-states[1]*states[1]*states[1]*states[19]*exp(((constants[26]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))))/(1.00000+constants[25]*(states[1]*states[1]*states[1]*states[19]+states[2]*states[2]*states[2]*states[18]))
rates[2] = -(algebraic[37]+algebraic[50]+3.00000*algebraic[56]+3.00000*algebraic[54]+constants[28])/(constants[29]*constants[2])
algebraic[39] = states[6]/(states[6]+constants[11])
algebraic[41] = constants[9]*states[7]*(algebraic[39]*states[8]+(1.00000-algebraic[39])*states[9])*(states[0]-constants[10])
algebraic[51] = ((constants[0]*constants[1])/(2.00000*constants[2]))*log(states[18]/states[19])
algebraic[52] = constants[18]*(states[0]-algebraic[51])
algebraic[55] = (constants[22]*states[19])/(states[19]+constants[23])
rates[18] = (constants[38]-states[18])/constants[36]+((algebraic[41]+algebraic[52]+algebraic[55])-2.00000*algebraic[56])/(2.00000*constants[33]*constants[2])
rates[1] = (constants[37]-states[1])/constants[34]+(algebraic[37]+algebraic[50]+3.00000*algebraic[56]+3.00000*algebraic[54]+constants[28])/(constants[33]*constants[2])
algebraic[58] = ((states[6]-states[19])*2.00000*constants[30]*constants[2])/constants[31]
rates[6] = -(algebraic[41]+algebraic[58])/(2.00000*constants[30]*constants[2])
algebraic[57] = (10.0000/(1.00000+(9.13652*(power(1.00000, 0.477811)))/(power(constants[27], 0.477811))))*(0.0517000+0.451600/(1.00000+exp((states[0]+59.5300)/17.1800)))*(states[0]-algebraic[43])*constants[3]
algebraic[59] = (algebraic[37]+algebraic[41]+algebraic[44]+algebraic[45]+algebraic[46]+algebraic[49]+algebraic[47]+algebraic[50]+algebraic[52]+algebraic[54]+algebraic[55]+algebraic[56]+algebraic[57])/constants[3]+algebraic[24]
rates[0] = -algebraic[59]*1000.00
algebraic[60] = 200000.*states[19]*(1.00000-states[20])-476.000*states[20]
rates[20] = algebraic[60]
algebraic[61] = 78400.0*states[19]*(1.00000-states[21])-392.000*states[21]
rates[21] = algebraic[61]
algebraic[62] = 200000.*states[19]*((1.00000-states[22])-states[23])-6.60000*states[22]
rates[22] = algebraic[62]
algebraic[63] = 0.0800000*algebraic[61]+0.160000*algebraic[62]+0.0450000*algebraic[60]
rates[24] = algebraic[63]
algebraic[67] = (constants[40]*(states[19]/constants[41]-(constants[43]*constants[43]*states[26])/constants[42]))/((states[19]+constants[41])/constants[41]+(constants[43]*(states[26]+constants[42]))/constants[42])
algebraic[64] = states[29]/(states[29]+0.250000)
algebraic[65] = algebraic[64]*algebraic[64]
algebraic[66] = constants[44]*algebraic[65]*(states[25]-states[19])
rates[19] = -((algebraic[52]+algebraic[55]+algebraic[67])-(algebraic[58]+algebraic[66]+2.00000*algebraic[56]))/(2.00000*constants[29]*constants[2])-1.00000*algebraic[63]
algebraic[68] = ((states[26]-states[25])*2.00000*constants[46]*constants[2])/constants[48]
rates[26] = (algebraic[67]-algebraic[68])/(2.00000*constants[45]*constants[2])
algebraic[69] = 480.000*states[25]*(1.00000-states[27])-400.000*states[27]
rates[27] = algebraic[69]
rates[25] = (algebraic[68]-algebraic[66])/(2.00000*constants[46]*constants[2])-31.0000*algebraic[69]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[12] = 2000.00*constants[32]*((1.00000-states[22])-states[23])-666.000*states[23]
algebraic[18] = 0.00350000*exp(((-states[0]*states[0])/30.0000)/30.0000)+0.00150000
algebraic[6] = 1.00000/(1.00000+exp((states[0]-1.00000)/-11.0000))
algebraic[8] = 1.00000/(1.00000+exp(-(states[0]+6.00000)/8.60000))
algebraic[20] = 0.00900000/(1.00000+exp((states[0]+5.00000)/12.0000))+0.000500000
algebraic[9] = 1.00000/(1.00000+exp((states[0]+7.50000)/10.0000))
algebraic[21] = 0.590000/(1.00000+exp((states[0]+60.0000)/10.0000))+3.05000
algebraic[14] = 1.00000/(1.00000+exp((states[0]+27.1200)/-8.21000))
algebraic[2] = (states[0]+25.5700)/28.8000
algebraic[26] = 4.20000e-05*exp(-algebraic[2]*algebraic[2])+2.40000e-05
algebraic[3] = 1.00000/(1.00000+exp((states[0]+63.6000)/5.30000))
algebraic[15] = 1.00000/(1.00000+exp((states[0]+35.1000)/3.20000))
algebraic[27] = 0.0300000*algebraic[15]+0.000300000
algebraic[28] = 0.120000*algebraic[15]+0.00300000
algebraic[4] = 1.00000/(1.00000+exp((states[0]+9.00000)/-5.80000))
algebraic[16] = (states[0]+35.0000)/30.0000
algebraic[29] = 0.00270000*exp(-algebraic[16]*algebraic[16])+0.00200000
algebraic[5] = 1.00000/(1.00000+exp((states[0]+27.4000)/7.10000))
algebraic[17] = states[0]+40.0000
algebraic[30] = 0.161000*exp(((-algebraic[17]*algebraic[17])/14.4000)/14.4000)+0.0100000
algebraic[31] = 1.33230*exp(((-algebraic[17]*algebraic[17])/14.2000)/14.2000)+0.0626000
algebraic[19] = (states[0]+52.4500)/15.8827
algebraic[32] = 0.0256350*exp(-algebraic[19]*algebraic[19])+0.0141400
algebraic[7] = 1.00000/(1.00000+exp((states[0]+40.5000)/11.5000))
algebraic[22] = (states[0]-20.0000)/20.0000
algebraic[33] = 0.700000+0.400000*exp(-algebraic[22]*algebraic[22])
algebraic[10] = 1.00000/(1.00000+exp((states[0]-19.9000)/-12.7000))
algebraic[23] = (states[0]+20.1376)/22.1996
algebraic[34] = 0.0311800+0.217180*exp(-algebraic[23]*algebraic[23])
algebraic[11] = 1.00000/(1.00000+exp((states[0]+15.0000)/-6.00000))
algebraic[13] = states[6]/(states[6]+constants[50])
algebraic[36] = algebraic[13]*algebraic[13]*algebraic[13]*algebraic[13]
algebraic[25] = states[19]/(states[19]+constants[49])
algebraic[38] = algebraic[25]*algebraic[25]*algebraic[25]*algebraic[25]
algebraic[40] = 203.800*(algebraic[38]+algebraic[36])
algebraic[42] = 33.9600+339.600*algebraic[38]
algebraic[43] = ((constants[0]*constants[1])/constants[2])*log(states[10]/states[11])
algebraic[44] = constants[12]*states[12]*states[13]*(states[0]-algebraic[43])
algebraic[45] = constants[13]*states[14]*states[15]*(states[0]-algebraic[43])
algebraic[46] = (constants[14]*(power(states[10]/1.00000, 0.445700))*(states[0]-algebraic[43]))/(1.00000+exp((1.50000*((states[0]-algebraic[43])+3.60000)*constants[2])/(constants[0]*constants[1])))
algebraic[48] = 1.00000/(1.00000+exp((states[0]+55.0000)/24.0000))
algebraic[49] = constants[16]*states[17]*algebraic[48]*(states[0]-algebraic[43])
algebraic[47] = constants[15]*states[16]*(states[0]-algebraic[43])
algebraic[53] = power(states[2], 1.50000)
algebraic[54] = (((((constants[20]*states[10])/(states[10]+constants[19]))*algebraic[53])/(algebraic[53]+constants[21]))*(states[0]+150.000))/(states[0]+200.000)
algebraic[1] = floor(voi/constants[5])*constants[5]
algebraic[24] = custom_piecewise([greater_equal(voi-algebraic[1] , constants[4]) & less_equal(voi-algebraic[1] , constants[4]+constants[6]), constants[7] , True, 0.00000])
algebraic[35] = ((constants[0]*constants[1])/constants[2])*log(states[1]/states[2])
algebraic[37] = (((constants[8]*states[3]*states[3]*states[3]*(0.900000*states[4]+0.100000*states[5])*states[1]*states[0]*constants[2]*constants[2])/(constants[0]*constants[1]))*(exp(((states[0]-algebraic[35])*constants[2])/(constants[0]*constants[1]))-1.00000))/(exp((states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[50] = constants[17]*(states[0]-algebraic[35])
algebraic[56] = (constants[24]*(states[2]*states[2]*states[2]*states[18]*exp((constants[2]*states[0]*constants[26])/(constants[0]*constants[1]))-states[1]*states[1]*states[1]*states[19]*exp(((constants[26]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))))/(1.00000+constants[25]*(states[1]*states[1]*states[1]*states[19]+states[2]*states[2]*states[2]*states[18]))
algebraic[39] = states[6]/(states[6]+constants[11])
algebraic[41] = constants[9]*states[7]*(algebraic[39]*states[8]+(1.00000-algebraic[39])*states[9])*(states[0]-constants[10])
algebraic[51] = ((constants[0]*constants[1])/(2.00000*constants[2]))*log(states[18]/states[19])
algebraic[52] = constants[18]*(states[0]-algebraic[51])
algebraic[55] = (constants[22]*states[19])/(states[19]+constants[23])
algebraic[58] = ((states[6]-states[19])*2.00000*constants[30]*constants[2])/constants[31]
algebraic[57] = (10.0000/(1.00000+(9.13652*(power(1.00000, 0.477811)))/(power(constants[27], 0.477811))))*(0.0517000+0.451600/(1.00000+exp((states[0]+59.5300)/17.1800)))*(states[0]-algebraic[43])*constants[3]
algebraic[59] = (algebraic[37]+algebraic[41]+algebraic[44]+algebraic[45]+algebraic[46]+algebraic[49]+algebraic[47]+algebraic[50]+algebraic[52]+algebraic[54]+algebraic[55]+algebraic[56]+algebraic[57])/constants[3]+algebraic[24]
algebraic[60] = 200000.*states[19]*(1.00000-states[20])-476.000*states[20]
algebraic[61] = 78400.0*states[19]*(1.00000-states[21])-392.000*states[21]
algebraic[62] = 200000.*states[19]*((1.00000-states[22])-states[23])-6.60000*states[22]
algebraic[63] = 0.0800000*algebraic[61]+0.160000*algebraic[62]+0.0450000*algebraic[60]
algebraic[67] = (constants[40]*(states[19]/constants[41]-(constants[43]*constants[43]*states[26])/constants[42]))/((states[19]+constants[41])/constants[41]+(constants[43]*(states[26]+constants[42]))/constants[42])
algebraic[64] = states[29]/(states[29]+0.250000)
algebraic[65] = algebraic[64]*algebraic[64]
algebraic[66] = constants[44]*algebraic[65]*(states[25]-states[19])
algebraic[68] = ((states[26]-states[25])*2.00000*constants[46]*constants[2])/constants[48]
algebraic[69] = 480.000*states[25]*(1.00000-states[27])-400.000*states[27]
algebraic[0] = 0.0500000*states[0]
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)