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 = 68
sizeStates = 17
sizeConstants = 47
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 (millisecond)"
legend_states[0] = "V in component membrane (millivolt)"
legend_constants[0] = "R in component membrane (joule_per_mole_kelvin)"
legend_constants[1] = "T in component membrane (kelvin)"
legend_constants[2] = "F in component membrane (coulomb_per_millimole)"
legend_constants[3] = "Cm in component membrane (microF_per_cm2)"
legend_constants[4] = "V_c in component membrane (micrometre3)"
legend_algebraic[49] = "i_K1 in component inward_rectifier_potassium_current (picoA_per_picoF)"
legend_algebraic[56] = "i_to in component transient_outward_current (picoA_per_picoF)"
legend_algebraic[50] = "i_Kr in component rapid_time_dependent_potassium_current (picoA_per_picoF)"
legend_algebraic[51] = "i_Ks in component slow_time_dependent_potassium_current (picoA_per_picoF)"
legend_algebraic[54] = "i_CaL in component L_type_Ca_current (picoA_per_picoF)"
legend_algebraic[57] = "i_NaK in component sodium_potassium_pump_current (picoA_per_picoF)"
legend_algebraic[52] = "i_Na in component fast_sodium_current (picoA_per_picoF)"
legend_algebraic[53] = "i_b_Na in component sodium_background_current (picoA_per_picoF)"
legend_algebraic[58] = "i_NaCa in component sodium_calcium_exchanger_current (picoA_per_picoF)"
legend_algebraic[55] = "i_b_Ca in component calcium_background_current (picoA_per_picoF)"
legend_algebraic[60] = "i_p_K in component potassium_pump_current (picoA_per_picoF)"
legend_algebraic[59] = "i_p_Ca in component calcium_pump_current (picoA_per_picoF)"
legend_algebraic[64] = "i_Stim in component membrane (picoA_per_picoF)"
legend_algebraic[62] = "Istim in component stimulus_protocol (picoA_per_picoF)"
legend_algebraic[0] = "E_Na in component reversal_potentials (millivolt)"
legend_algebraic[13] = "E_K in component reversal_potentials (millivolt)"
legend_algebraic[26] = "E_Ks in component reversal_potentials (millivolt)"
legend_algebraic[35] = "E_Ca in component reversal_potentials (millivolt)"
legend_constants[5] = "P_kna in component reversal_potentials (nanoA_per_millimolar)"
legend_constants[6] = "K_o in component potassium_dynamics (millimolar)"
legend_constants[7] = "Na_o in component sodium_dynamics (millimolar)"
legend_states[1] = "K_i in component potassium_dynamics (millimolar)"
legend_states[2] = "Na_i in component sodium_dynamics (millimolar)"
legend_constants[8] = "Ca_o in component calcium_dynamics (millimolar)"
legend_states[3] = "Ca_i in component calcium_dynamics (millimolar)"
legend_constants[9] = "g_K1 in component inward_rectifier_potassium_current (nanoS_per_picoF)"
legend_algebraic[48] = "xK1_inf in component inward_rectifier_potassium_current (dimensionless)"
legend_algebraic[44] = "alpha_K1 in component inward_rectifier_potassium_current (dimensionless)"
legend_algebraic[47] = "beta_K1 in component inward_rectifier_potassium_current (dimensionless)"
legend_constants[10] = "g_Kr in component rapid_time_dependent_potassium_current (nanoS_per_picoF)"
legend_states[4] = "Xr1 in component rapid_time_dependent_potassium_current_Xr1_gate (dimensionless)"
legend_states[5] = "Xr2 in component rapid_time_dependent_potassium_current_Xr2_gate (dimensionless)"
legend_algebraic[1] = "xr1_inf in component rapid_time_dependent_potassium_current_Xr1_gate (dimensionless)"
legend_algebraic[14] = "alpha_xr1 in component rapid_time_dependent_potassium_current_Xr1_gate (per_millisecond)"
legend_algebraic[27] = "beta_xr1 in component rapid_time_dependent_potassium_current_Xr1_gate (per_millisecond)"
legend_algebraic[36] = "tau_xr1 in component rapid_time_dependent_potassium_current_Xr1_gate (millisecond)"
legend_algebraic[2] = "xr2_inf in component rapid_time_dependent_potassium_current_Xr2_gate (dimensionless)"
legend_algebraic[15] = "alpha_xr2 in component rapid_time_dependent_potassium_current_Xr2_gate (per_millisecond)"
legend_algebraic[28] = "beta_xr2 in component rapid_time_dependent_potassium_current_Xr2_gate (per_millisecond)"
legend_algebraic[37] = "tau_xr2 in component rapid_time_dependent_potassium_current_Xr2_gate (millisecond)"
legend_constants[11] = "g_Ks in component slow_time_dependent_potassium_current (nanoS_per_picoF)"
legend_states[6] = "Xs in component slow_time_dependent_potassium_current_Xs_gate (dimensionless)"
legend_algebraic[3] = "xs_inf in component slow_time_dependent_potassium_current_Xs_gate (dimensionless)"
legend_algebraic[16] = "alpha_xs in component slow_time_dependent_potassium_current_Xs_gate (per_millisecond)"
legend_algebraic[29] = "beta_xs in component slow_time_dependent_potassium_current_Xs_gate (per_millisecond)"
legend_algebraic[38] = "tau_xs in component slow_time_dependent_potassium_current_Xs_gate (millisecond)"
legend_constants[12] = "g_Na in component fast_sodium_current (nanoS_per_picoF)"
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_states[9] = "j in component fast_sodium_current_j_gate (dimensionless)"
legend_algebraic[4] = "m_inf in component fast_sodium_current_m_gate (dimensionless)"
legend_algebraic[17] = "alpha_m in component fast_sodium_current_m_gate (per_millisecond)"
legend_algebraic[30] = "beta_m in component fast_sodium_current_m_gate (per_millisecond)"
legend_algebraic[39] = "tau_m in component fast_sodium_current_m_gate (millisecond)"
legend_algebraic[5] = "h_inf in component fast_sodium_current_h_gate (dimensionless)"
legend_algebraic[18] = "alpha_h in component fast_sodium_current_h_gate (per_millisecond)"
legend_algebraic[31] = "beta_h in component fast_sodium_current_h_gate (per_millisecond)"
legend_algebraic[40] = "tau_h in component fast_sodium_current_h_gate (millisecond)"
legend_algebraic[6] = "j_inf in component fast_sodium_current_j_gate (dimensionless)"
legend_algebraic[19] = "alpha_j in component fast_sodium_current_j_gate (per_millisecond)"
legend_algebraic[32] = "beta_j in component fast_sodium_current_j_gate (per_millisecond)"
legend_algebraic[41] = "tau_j in component fast_sodium_current_j_gate (millisecond)"
legend_constants[13] = "g_bna in component sodium_background_current (nanoS_per_picoF)"
legend_constants[14] = "g_CaL in component L_type_Ca_current (nanoS_per_picoF)"
legend_states[10] = "d in component L_type_Ca_current_d_gate (dimensionless)"
legend_states[11] = "f in component L_type_Ca_current_f_gate (dimensionless)"
legend_states[12] = "fCa in component L_type_Ca_current_fCa_gate (dimensionless)"
legend_algebraic[7] = "d_inf in component L_type_Ca_current_d_gate (dimensionless)"
legend_algebraic[20] = "alpha_d in component L_type_Ca_current_d_gate (per_millisecond)"
legend_algebraic[33] = "beta_d in component L_type_Ca_current_d_gate (per_millisecond)"
legend_algebraic[42] = "gamma_d in component L_type_Ca_current_d_gate (per_millisecond)"
legend_algebraic[45] = "tau_d in component L_type_Ca_current_d_gate (millisecond)"
legend_algebraic[8] = "f_inf in component L_type_Ca_current_f_gate (dimensionless)"
legend_algebraic[21] = "tau_f in component L_type_Ca_current_f_gate (millisecond)"
legend_algebraic[9] = "alpha_fCa in component L_type_Ca_current_fCa_gate (dimensionless)"
legend_algebraic[22] = "beta_fCa in component L_type_Ca_current_fCa_gate (dimensionless)"
legend_algebraic[34] = "gama_fCa in component L_type_Ca_current_fCa_gate (dimensionless)"
legend_algebraic[43] = "fCa_inf in component L_type_Ca_current_fCa_gate (dimensionless)"
legend_constants[46] = "tau_fCa in component L_type_Ca_current_fCa_gate (millisecond)"
legend_algebraic[46] = "d_fCa in component L_type_Ca_current_fCa_gate (dimensionless)"
legend_constants[15] = "g_bca in component calcium_background_current (nanoS_per_picoF)"
legend_constants[16] = "g_to in component transient_outward_current (nanoS_per_picoF)"
legend_states[13] = "s in component transient_outward_current_s_gate (dimensionless)"
legend_states[14] = "r in component transient_outward_current_r_gate (dimensionless)"
legend_algebraic[10] = "s_inf in component transient_outward_current_s_gate (dimensionless)"
legend_algebraic[23] = "tau_s in component transient_outward_current_s_gate (dimensionless)"
legend_algebraic[11] = "r_inf in component transient_outward_current_r_gate (dimensionless)"
legend_algebraic[24] = "tau_r in component transient_outward_current_r_gate (millisecond)"
legend_constants[17] = "P_NaK in component sodium_potassium_pump_current (picoA_per_picoF)"
legend_constants[18] = "K_mk in component sodium_potassium_pump_current (millimolar)"
legend_constants[19] = "K_mNa in component sodium_potassium_pump_current (millimolar)"
legend_constants[20] = "K_NaCa in component sodium_calcium_exchanger_current (picoA_per_picoF)"
legend_constants[21] = "K_sat in component sodium_calcium_exchanger_current (dimensionless)"
legend_constants[22] = "alpha in component sodium_calcium_exchanger_current (dimensionless)"
legend_constants[23] = "gamma in component sodium_calcium_exchanger_current (dimensionless)"
legend_constants[24] = "Km_Ca in component sodium_calcium_exchanger_current (millimolar)"
legend_constants[25] = "Km_Nai in component sodium_calcium_exchanger_current (millimolar)"
legend_constants[26] = "g_pCa in component calcium_pump_current (nanoS_per_picoF)"
legend_constants[27] = "K_pCa in component calcium_pump_current (millimolar)"
legend_constants[28] = "g_pK in component potassium_pump_current (nanoS_per_picoF)"
legend_states[15] = "Ca_SR in component calcium_dynamics (millimolar)"
legend_algebraic[61] = "i_rel in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[63] = "i_up in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[65] = "i_leak in component calcium_dynamics (millimolar_per_millisecond)"
legend_states[16] = "g in component calcium_dynamics (dimensionless)"
legend_constants[29] = "tau_g in component calcium_dynamics (millisecond)"
legend_algebraic[12] = "g_inf in component calcium_dynamics (dimensionless)"
legend_constants[30] = "a_rel in component calcium_dynamics (millimolar_per_millisecond)"
legend_constants[31] = "b_rel in component calcium_dynamics (millimolar)"
legend_constants[32] = "c_rel in component calcium_dynamics (millimolar_per_millisecond)"
legend_constants[33] = "K_up in component calcium_dynamics (millimolar)"
legend_constants[34] = "V_leak in component calcium_dynamics (per_millisecond)"
legend_constants[35] = "Vmax_up in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[66] = "Ca_i_bufc in component calcium_dynamics (millimolar)"
legend_algebraic[67] = "Ca_sr_bufsr in component calcium_dynamics (millimolar)"
legend_constants[36] = "Buf_c in component calcium_dynamics (millimolar)"
legend_constants[37] = "K_buf_c in component calcium_dynamics (millimolar)"
legend_constants[38] = "Buf_sr in component calcium_dynamics (millimolar)"
legend_constants[39] = "K_buf_sr in component calcium_dynamics (millimolar)"
legend_constants[40] = "V_sr in component calcium_dynamics (micrometre3)"
legend_algebraic[25] = "d_g in component calcium_dynamics (dimensionless)"
legend_constants[41] = "IstimStart in component stimulus_protocol (millisecond)"
legend_constants[42] = "IstimEnd in component stimulus_protocol (millisecond)"
legend_constants[43] = "IstimAmplitude in component stimulus_protocol (picoA_per_picoF)"
legend_constants[44] = "IstimPeriod in component stimulus_protocol (millisecond)"
legend_constants[45] = "IstimPulseDuration in component stimulus_protocol (millisecond)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[4] = "d/dt Xr1 in component rapid_time_dependent_potassium_current_Xr1_gate (dimensionless)"
legend_rates[5] = "d/dt Xr2 in component rapid_time_dependent_potassium_current_Xr2_gate (dimensionless)"
legend_rates[6] = "d/dt Xs in component slow_time_dependent_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[9] = "d/dt j in component fast_sodium_current_j_gate (dimensionless)"
legend_rates[10] = "d/dt d in component L_type_Ca_current_d_gate (dimensionless)"
legend_rates[11] = "d/dt f in component L_type_Ca_current_f_gate (dimensionless)"
legend_rates[12] = "d/dt fCa in component L_type_Ca_current_fCa_gate (dimensionless)"
legend_rates[13] = "d/dt s in component transient_outward_current_s_gate (dimensionless)"
legend_rates[14] = "d/dt r in component transient_outward_current_r_gate (dimensionless)"
legend_rates[16] = "d/dt g in component calcium_dynamics (dimensionless)"
legend_rates[3] = "d/dt Ca_i in component calcium_dynamics (millimolar)"
legend_rates[15] = "d/dt Ca_SR in component calcium_dynamics (millimolar)"
legend_rates[2] = "d/dt Na_i in component sodium_dynamics (millimolar)"
legend_rates[1] = "d/dt K_i in component potassium_dynamics (millimolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -86.2
constants[0] = 8314.472
constants[1] = 310
constants[2] = 96485.3415
constants[3] = 0.185
constants[4] = 0.016404
constants[5] = 0.03
constants[6] = 5.4
constants[7] = 140
states[1] = 138.3
states[2] = 11.6
constants[8] = 2
states[3] = 0.0002
constants[9] = 5.405
constants[10] = 0.096
states[4] = 0
states[5] = 1
constants[11] = 0.245
states[6] = 0
constants[12] = 14.838
states[7] = 0
states[8] = 0.75
states[9] = 0.75
constants[13] = 0.00029
constants[14] = 0.000175
states[10] = 0
states[11] = 1
states[12] = 1
constants[15] = 0.000592
constants[16] = 0.073
states[13] = 1
states[14] = 0
constants[17] = 1.362
constants[18] = 1
constants[19] = 40
constants[20] = 1000
constants[21] = 0.1
constants[22] = 2.5
constants[23] = 0.35
constants[24] = 1.38
constants[25] = 87.5
constants[26] = 0.825
constants[27] = 0.0005
constants[28] = 0.0146
states[15] = 0.2
states[16] = 1
constants[29] = 2
constants[30] = 0.016464
constants[31] = 0.25
constants[32] = 0.008232
constants[33] = 0.00025
constants[34] = 8e-5
constants[35] = 0.000425
constants[36] = 0.15
constants[37] = 0.001
constants[38] = 10
constants[39] = 0.3
constants[40] = 0.001094
constants[41] = 100
constants[42] = 50000
constants[43] = -52
constants[44] = 1000
constants[45] = 1
constants[46] = 2.00000
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[8] = 1.00000/(1.00000+exp((states[0]+20.0000)/7.00000))
algebraic[21] = 1125.00*exp(-(power(states[0]+27.0000, 2.00000))/240.000)+80.0000+165.000/(1.00000+exp((25.0000-states[0])/10.0000))
rates[11] = (algebraic[8]-states[11])/algebraic[21]
algebraic[10] = 1.00000/(1.00000+exp((states[0]+28.0000)/5.00000))
algebraic[23] = 1000.00*exp(-(power(states[0]+67.0000, 2.00000))/1000.00)+8.00000
rates[13] = (algebraic[10]-states[13])/algebraic[23]
algebraic[11] = 1.00000/(1.00000+exp((20.0000-states[0])/6.00000))
algebraic[24] = 9.50000*exp(-(power(states[0]+40.0000, 2.00000))/1800.00)+0.800000
rates[14] = (algebraic[11]-states[14])/algebraic[24]
algebraic[12] = custom_piecewise([less(states[3] , 0.000350000), 1.00000/(1.00000+power(states[3]/0.000350000, 6.00000)) , True, 1.00000/(1.00000+power(states[3]/0.000350000, 16.0000))])
algebraic[25] = (algebraic[12]-states[16])/constants[29]
rates[16] = custom_piecewise([greater(0.0100000*algebraic[25] , 0.00000) & greater(states[0] , -60.0000), 0.00000 , True, algebraic[25]])
algebraic[1] = 1.00000/(1.00000+exp((-26.0000-states[0])/7.00000))
algebraic[14] = 450.000/(1.00000+exp((-45.0000-states[0])/10.0000))
algebraic[27] = 6.00000/(1.00000+exp((states[0]+30.0000)/11.5000))
algebraic[36] = algebraic[14]*algebraic[27]
rates[4] = (algebraic[1]-states[4])/algebraic[36]
algebraic[2] = 1.00000/(1.00000+exp((states[0]+88.0000)/24.0000))
algebraic[15] = 3.00000/(1.00000+exp((-60.0000-states[0])/20.0000))
algebraic[28] = 1.12000/(1.00000+exp((states[0]-60.0000)/20.0000))
algebraic[37] = algebraic[15]*algebraic[28]
rates[5] = (algebraic[2]-states[5])/algebraic[37]
algebraic[3] = 1.00000/(1.00000+exp((-5.00000-states[0])/14.0000))
algebraic[16] = 1100.00/(power(1.00000+exp((-10.0000-states[0])/6.00000), 1.0/2))
algebraic[29] = 1.00000/(1.00000+exp((states[0]-60.0000)/20.0000))
algebraic[38] = algebraic[16]*algebraic[29]
rates[6] = (algebraic[3]-states[6])/algebraic[38]
algebraic[4] = 1.00000/(power(1.00000+exp((-56.8600-states[0])/9.03000), 2.00000))
algebraic[17] = 1.00000/(1.00000+exp((-60.0000-states[0])/5.00000))
algebraic[30] = 0.100000/(1.00000+exp((states[0]+35.0000)/5.00000))+0.100000/(1.00000+exp((states[0]-50.0000)/200.000))
algebraic[39] = algebraic[17]*algebraic[30]
rates[7] = (algebraic[4]-states[7])/algebraic[39]
algebraic[5] = 1.00000/(power(1.00000+exp((states[0]+71.5500)/7.43000), 2.00000))
algebraic[18] = custom_piecewise([less(states[0] , -40.0000), 0.0570000*exp(-(states[0]+80.0000)/6.80000) , True, 0.00000])
algebraic[31] = custom_piecewise([less(states[0] , -40.0000), 2.70000*exp(0.0790000*states[0])+310000.*exp(0.348500*states[0]) , True, 0.770000/(0.130000*(1.00000+exp((states[0]+10.6600)/-11.1000)))])
algebraic[40] = 1.00000/(algebraic[18]+algebraic[31])
rates[8] = (algebraic[5]-states[8])/algebraic[40]
algebraic[6] = 1.00000/(power(1.00000+exp((states[0]+71.5500)/7.43000), 2.00000))
algebraic[19] = custom_piecewise([less(states[0] , -40.0000), ((-25428.0*exp(0.244400*states[0])-6.94800e-06*exp(-0.0439100*states[0]))*(states[0]+37.7800))/(1.00000+exp(0.311000*(states[0]+79.2300))) , True, 0.00000])
algebraic[32] = custom_piecewise([less(states[0] , -40.0000), (0.0242400*exp(-0.0105200*states[0]))/(1.00000+exp(-0.137800*(states[0]+40.1400))) , True, (0.600000*exp(0.0570000*states[0]))/(1.00000+exp(-0.100000*(states[0]+32.0000)))])
algebraic[41] = 1.00000/(algebraic[19]+algebraic[32])
rates[9] = (algebraic[6]-states[9])/algebraic[41]
algebraic[7] = 1.00000/(1.00000+exp((-5.00000-states[0])/7.50000))
algebraic[20] = 1.40000/(1.00000+exp((-35.0000-states[0])/13.0000))+0.250000
algebraic[33] = 1.40000/(1.00000+exp((states[0]+5.00000)/5.00000))
algebraic[42] = 1.00000/(1.00000+exp((50.0000-states[0])/20.0000))
algebraic[45] = algebraic[20]*algebraic[33]+algebraic[42]
rates[10] = (algebraic[7]-states[10])/algebraic[45]
algebraic[9] = 1.00000/(1.00000+power(states[3]/0.000325000, 8.00000))
algebraic[22] = 0.100000/(1.00000+exp((states[3]-0.000500000)/0.000100000))
algebraic[34] = 0.200000/(1.00000+exp((states[3]-0.000750000)/0.000800000))
algebraic[43] = (algebraic[9]+algebraic[22]+algebraic[34]+0.230000)/1.46000
algebraic[46] = (algebraic[43]-states[12])/constants[46]
rates[12] = custom_piecewise([greater(0.0100000*algebraic[46] , 0.00000) & greater(states[0] , -60.0000), 0.00000 , True, algebraic[46]])
algebraic[57] = ((((constants[17]*constants[6])/(constants[6]+constants[18]))*states[2])/(states[2]+constants[19]))/(1.00000+0.124500*exp((-0.100000*states[0]*constants[2])/(constants[0]*constants[1]))+0.0353000*exp((-states[0]*constants[2])/(constants[0]*constants[1])))
algebraic[0] = ((constants[0]*constants[1])/constants[2])*log(constants[7]/states[2])
algebraic[52] = constants[12]*(power(states[7], 3.00000))*states[8]*states[9]*(states[0]-algebraic[0])
algebraic[53] = constants[13]*(states[0]-algebraic[0])
algebraic[58] = (constants[20]*(exp((constants[23]*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[2], 3.00000))*constants[8]-exp(((constants[23]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[7], 3.00000))*states[3]*constants[22]))/((power(constants[25], 3.00000)+power(constants[7], 3.00000))*(constants[24]+constants[8])*(1.00000+constants[21]*exp(((constants[23]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))))
rates[2] = (-(algebraic[52]+algebraic[53]+3.00000*algebraic[57]+3.00000*algebraic[58])/(constants[4]*constants[2]))*constants[3]
algebraic[13] = ((constants[0]*constants[1])/constants[2])*log(constants[6]/states[1])
algebraic[44] = 0.100000/(1.00000+exp(0.0600000*((states[0]-algebraic[13])-200.000)))
algebraic[47] = (3.00000*exp(0.000200000*((states[0]-algebraic[13])+100.000))+exp(0.100000*((states[0]-algebraic[13])-10.0000)))/(1.00000+exp(-0.500000*(states[0]-algebraic[13])))
algebraic[48] = algebraic[44]/(algebraic[44]+algebraic[47])
algebraic[49] = constants[9]*algebraic[48]*(states[0]-algebraic[13])
algebraic[56] = constants[16]*states[14]*states[13]*(states[0]-algebraic[13])
algebraic[50] = constants[10]*(power(constants[6]/5.40000, 1.0/2))*states[4]*states[5]*(states[0]-algebraic[13])
algebraic[26] = ((constants[0]*constants[1])/constants[2])*log((constants[6]+constants[5]*constants[7])/(states[1]+constants[5]*states[2]))
algebraic[51] = constants[11]*(power(states[6], 2.00000))*(states[0]-algebraic[26])
algebraic[54] = (((constants[14]*states[10]*states[11]*states[12]*4.00000*states[0]*(power(constants[2], 2.00000)))/(constants[0]*constants[1]))*(states[3]*exp((2.00000*states[0]*constants[2])/(constants[0]*constants[1]))-0.341000*constants[8]))/(exp((2.00000*states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[35] = ((0.500000*constants[0]*constants[1])/constants[2])*log(constants[8]/states[3])
algebraic[55] = constants[15]*(states[0]-algebraic[35])
algebraic[60] = (constants[28]*(states[0]-algebraic[13]))/(1.00000+exp((25.0000-states[0])/5.98000))
algebraic[59] = (constants[26]*states[3])/(states[3]+constants[27])
algebraic[62] = custom_piecewise([greater_equal(voi , constants[41]) & less_equal(voi , constants[42]) & less_equal((voi-constants[41])-floor((voi-constants[41])/constants[44])*constants[44] , constants[45]), constants[43] , True, 0.00000])
algebraic[64] = algebraic[62]
rates[0] = (-1.00000/1.00000)*(algebraic[49]+algebraic[56]+algebraic[50]+algebraic[51]+algebraic[54]+algebraic[57]+algebraic[52]+algebraic[53]+algebraic[58]+algebraic[55]+algebraic[60]+algebraic[59]+algebraic[64])
rates[1] = (-((algebraic[49]+algebraic[56]+algebraic[50]+algebraic[51]+algebraic[60]+algebraic[64])-2.00000*algebraic[57])/(constants[4]*constants[2]))*constants[3]
algebraic[61] = ((constants[30]*(power(states[15], 2.00000)))/(power(constants[31], 2.00000)+power(states[15], 2.00000))+constants[32])*states[10]*states[16]
algebraic[63] = constants[35]/(1.00000+(power(constants[33], 2.00000))/(power(states[3], 2.00000)))
algebraic[65] = constants[34]*(states[15]-states[3])
algebraic[66] = 1.00000/(1.00000+(constants[36]*constants[37])/(power(states[3]+constants[37], 2.00000)))
rates[3] = algebraic[66]*(((algebraic[65]-algebraic[63])+algebraic[61])-(((algebraic[54]+algebraic[55]+algebraic[59])-2.00000*algebraic[58])/(2.00000*constants[4]*constants[2]))*constants[3])
algebraic[67] = 1.00000/(1.00000+(constants[38]*constants[39])/(power(states[15]+constants[39], 2.00000)))
rates[15] = ((algebraic[67]*constants[4])/constants[40])*(algebraic[63]-(algebraic[61]+algebraic[65]))
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[8] = 1.00000/(1.00000+exp((states[0]+20.0000)/7.00000))
algebraic[21] = 1125.00*exp(-(power(states[0]+27.0000, 2.00000))/240.000)+80.0000+165.000/(1.00000+exp((25.0000-states[0])/10.0000))
algebraic[10] = 1.00000/(1.00000+exp((states[0]+28.0000)/5.00000))
algebraic[23] = 1000.00*exp(-(power(states[0]+67.0000, 2.00000))/1000.00)+8.00000
algebraic[11] = 1.00000/(1.00000+exp((20.0000-states[0])/6.00000))
algebraic[24] = 9.50000*exp(-(power(states[0]+40.0000, 2.00000))/1800.00)+0.800000
algebraic[12] = custom_piecewise([less(states[3] , 0.000350000), 1.00000/(1.00000+power(states[3]/0.000350000, 6.00000)) , True, 1.00000/(1.00000+power(states[3]/0.000350000, 16.0000))])
algebraic[25] = (algebraic[12]-states[16])/constants[29]
algebraic[1] = 1.00000/(1.00000+exp((-26.0000-states[0])/7.00000))
algebraic[14] = 450.000/(1.00000+exp((-45.0000-states[0])/10.0000))
algebraic[27] = 6.00000/(1.00000+exp((states[0]+30.0000)/11.5000))
algebraic[36] = algebraic[14]*algebraic[27]
algebraic[2] = 1.00000/(1.00000+exp((states[0]+88.0000)/24.0000))
algebraic[15] = 3.00000/(1.00000+exp((-60.0000-states[0])/20.0000))
algebraic[28] = 1.12000/(1.00000+exp((states[0]-60.0000)/20.0000))
algebraic[37] = algebraic[15]*algebraic[28]
algebraic[3] = 1.00000/(1.00000+exp((-5.00000-states[0])/14.0000))
algebraic[16] = 1100.00/(power(1.00000+exp((-10.0000-states[0])/6.00000), 1.0/2))
algebraic[29] = 1.00000/(1.00000+exp((states[0]-60.0000)/20.0000))
algebraic[38] = algebraic[16]*algebraic[29]
algebraic[4] = 1.00000/(power(1.00000+exp((-56.8600-states[0])/9.03000), 2.00000))
algebraic[17] = 1.00000/(1.00000+exp((-60.0000-states[0])/5.00000))
algebraic[30] = 0.100000/(1.00000+exp((states[0]+35.0000)/5.00000))+0.100000/(1.00000+exp((states[0]-50.0000)/200.000))
algebraic[39] = algebraic[17]*algebraic[30]
algebraic[5] = 1.00000/(power(1.00000+exp((states[0]+71.5500)/7.43000), 2.00000))
algebraic[18] = custom_piecewise([less(states[0] , -40.0000), 0.0570000*exp(-(states[0]+80.0000)/6.80000) , True, 0.00000])
algebraic[31] = custom_piecewise([less(states[0] , -40.0000), 2.70000*exp(0.0790000*states[0])+310000.*exp(0.348500*states[0]) , True, 0.770000/(0.130000*(1.00000+exp((states[0]+10.6600)/-11.1000)))])
algebraic[40] = 1.00000/(algebraic[18]+algebraic[31])
algebraic[6] = 1.00000/(power(1.00000+exp((states[0]+71.5500)/7.43000), 2.00000))
algebraic[19] = custom_piecewise([less(states[0] , -40.0000), ((-25428.0*exp(0.244400*states[0])-6.94800e-06*exp(-0.0439100*states[0]))*(states[0]+37.7800))/(1.00000+exp(0.311000*(states[0]+79.2300))) , True, 0.00000])
algebraic[32] = custom_piecewise([less(states[0] , -40.0000), (0.0242400*exp(-0.0105200*states[0]))/(1.00000+exp(-0.137800*(states[0]+40.1400))) , True, (0.600000*exp(0.0570000*states[0]))/(1.00000+exp(-0.100000*(states[0]+32.0000)))])
algebraic[41] = 1.00000/(algebraic[19]+algebraic[32])
algebraic[7] = 1.00000/(1.00000+exp((-5.00000-states[0])/7.50000))
algebraic[20] = 1.40000/(1.00000+exp((-35.0000-states[0])/13.0000))+0.250000
algebraic[33] = 1.40000/(1.00000+exp((states[0]+5.00000)/5.00000))
algebraic[42] = 1.00000/(1.00000+exp((50.0000-states[0])/20.0000))
algebraic[45] = algebraic[20]*algebraic[33]+algebraic[42]
algebraic[9] = 1.00000/(1.00000+power(states[3]/0.000325000, 8.00000))
algebraic[22] = 0.100000/(1.00000+exp((states[3]-0.000500000)/0.000100000))
algebraic[34] = 0.200000/(1.00000+exp((states[3]-0.000750000)/0.000800000))
algebraic[43] = (algebraic[9]+algebraic[22]+algebraic[34]+0.230000)/1.46000
algebraic[46] = (algebraic[43]-states[12])/constants[46]
algebraic[57] = ((((constants[17]*constants[6])/(constants[6]+constants[18]))*states[2])/(states[2]+constants[19]))/(1.00000+0.124500*exp((-0.100000*states[0]*constants[2])/(constants[0]*constants[1]))+0.0353000*exp((-states[0]*constants[2])/(constants[0]*constants[1])))
algebraic[0] = ((constants[0]*constants[1])/constants[2])*log(constants[7]/states[2])
algebraic[52] = constants[12]*(power(states[7], 3.00000))*states[8]*states[9]*(states[0]-algebraic[0])
algebraic[53] = constants[13]*(states[0]-algebraic[0])
algebraic[58] = (constants[20]*(exp((constants[23]*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[2], 3.00000))*constants[8]-exp(((constants[23]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[7], 3.00000))*states[3]*constants[22]))/((power(constants[25], 3.00000)+power(constants[7], 3.00000))*(constants[24]+constants[8])*(1.00000+constants[21]*exp(((constants[23]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))))
algebraic[13] = ((constants[0]*constants[1])/constants[2])*log(constants[6]/states[1])
algebraic[44] = 0.100000/(1.00000+exp(0.0600000*((states[0]-algebraic[13])-200.000)))
algebraic[47] = (3.00000*exp(0.000200000*((states[0]-algebraic[13])+100.000))+exp(0.100000*((states[0]-algebraic[13])-10.0000)))/(1.00000+exp(-0.500000*(states[0]-algebraic[13])))
algebraic[48] = algebraic[44]/(algebraic[44]+algebraic[47])
algebraic[49] = constants[9]*algebraic[48]*(states[0]-algebraic[13])
algebraic[56] = constants[16]*states[14]*states[13]*(states[0]-algebraic[13])
algebraic[50] = constants[10]*(power(constants[6]/5.40000, 1.0/2))*states[4]*states[5]*(states[0]-algebraic[13])
algebraic[26] = ((constants[0]*constants[1])/constants[2])*log((constants[6]+constants[5]*constants[7])/(states[1]+constants[5]*states[2]))
algebraic[51] = constants[11]*(power(states[6], 2.00000))*(states[0]-algebraic[26])
algebraic[54] = (((constants[14]*states[10]*states[11]*states[12]*4.00000*states[0]*(power(constants[2], 2.00000)))/(constants[0]*constants[1]))*(states[3]*exp((2.00000*states[0]*constants[2])/(constants[0]*constants[1]))-0.341000*constants[8]))/(exp((2.00000*states[0]*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[35] = ((0.500000*constants[0]*constants[1])/constants[2])*log(constants[8]/states[3])
algebraic[55] = constants[15]*(states[0]-algebraic[35])
algebraic[60] = (constants[28]*(states[0]-algebraic[13]))/(1.00000+exp((25.0000-states[0])/5.98000))
algebraic[59] = (constants[26]*states[3])/(states[3]+constants[27])
algebraic[62] = custom_piecewise([greater_equal(voi , constants[41]) & less_equal(voi , constants[42]) & less_equal((voi-constants[41])-floor((voi-constants[41])/constants[44])*constants[44] , constants[45]), constants[43] , True, 0.00000])
algebraic[64] = algebraic[62]
algebraic[61] = ((constants[30]*(power(states[15], 2.00000)))/(power(constants[31], 2.00000)+power(states[15], 2.00000))+constants[32])*states[10]*states[16]
algebraic[63] = constants[35]/(1.00000+(power(constants[33], 2.00000))/(power(states[3], 2.00000)))
algebraic[65] = constants[34]*(states[15]-states[3])
algebraic[66] = 1.00000/(1.00000+(constants[36]*constants[37])/(power(states[3]+constants[37], 2.00000)))
algebraic[67] = 1.00000/(1.00000+(constants[38]*constants[39])/(power(states[15]+constants[39], 2.00000)))
return algebraic
def custom_piecewise(cases):
"""Compute result of a piecewise function"""
return select(cases[0::2],cases[1::2])
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)