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 = 73
sizeStates = 19
sizeConstants = 53
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 (picoF)"
legend_constants[4] = "V_c in component membrane (micrometre3)"
legend_algebraic[47] = "i_K1 in component inward_rectifier_potassium_current (picoA_per_picoF)"
legend_algebraic[54] = "i_to in component transient_outward_current (picoA_per_picoF)"
legend_algebraic[48] = "i_Kr in component rapid_time_dependent_potassium_current (picoA_per_picoF)"
legend_algebraic[49] = "i_Ks in component slow_time_dependent_potassium_current (picoA_per_picoF)"
legend_algebraic[52] = "i_CaL in component L_type_Ca_current (picoA_per_picoF)"
legend_algebraic[55] = "i_NaK in component sodium_potassium_pump_current (picoA_per_picoF)"
legend_algebraic[50] = "i_Na in component fast_sodium_current (picoA_per_picoF)"
legend_algebraic[51] = "i_b_Na in component sodium_background_current (picoA_per_picoF)"
legend_algebraic[56] = "i_NaCa in component sodium_calcium_exchanger_current (picoA_per_picoF)"
legend_algebraic[53] = "i_b_Ca in component calcium_background_current (picoA_per_picoF)"
legend_algebraic[58] = "i_p_K in component potassium_pump_current (picoA_per_picoF)"
legend_algebraic[57] = "i_p_Ca in component calcium_pump_current (picoA_per_picoF)"
legend_algebraic[12] = "i_Stim in component membrane (picoA_per_picoF)"
legend_constants[5] = "stim_start in component membrane (millisecond)"
legend_constants[6] = "stim_period in component membrane (millisecond)"
legend_constants[7] = "stim_duration in component membrane (millisecond)"
legend_constants[8] = "stim_amplitude in component membrane (picoA_per_picoF)"
legend_algebraic[25] = "E_Na in component reversal_potentials (millivolt)"
legend_algebraic[33] = "E_K in component reversal_potentials (millivolt)"
legend_algebraic[41] = "E_Ks in component reversal_potentials (millivolt)"
legend_algebraic[43] = "E_Ca in component reversal_potentials (millivolt)"
legend_constants[9] = "P_kna in component reversal_potentials (dimensionless)"
legend_constants[10] = "K_o in component potassium_dynamics (millimolar)"
legend_constants[11] = "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[12] = "Ca_o in component calcium_dynamics (millimolar)"
legend_states[3] = "Ca_i in component calcium_dynamics (millimolar)"
legend_constants[13] = "g_K1 in component inward_rectifier_potassium_current (nanoS_per_picoF)"
legend_algebraic[46] = "xK1_inf in component inward_rectifier_potassium_current (dimensionless)"
legend_algebraic[44] = "alpha_K1 in component inward_rectifier_potassium_current (dimensionless)"
legend_algebraic[45] = "beta_K1 in component inward_rectifier_potassium_current (dimensionless)"
legend_constants[14] = "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[0] = "xr1_inf in component rapid_time_dependent_potassium_current_Xr1_gate (dimensionless)"
legend_algebraic[13] = "alpha_xr1 in component rapid_time_dependent_potassium_current_Xr1_gate (dimensionless)"
legend_algebraic[26] = "beta_xr1 in component rapid_time_dependent_potassium_current_Xr1_gate (dimensionless)"
legend_algebraic[34] = "tau_xr1 in component rapid_time_dependent_potassium_current_Xr1_gate (millisecond)"
legend_algebraic[1] = "xr2_inf in component rapid_time_dependent_potassium_current_Xr2_gate (dimensionless)"
legend_algebraic[14] = "alpha_xr2 in component rapid_time_dependent_potassium_current_Xr2_gate (dimensionless)"
legend_algebraic[27] = "beta_xr2 in component rapid_time_dependent_potassium_current_Xr2_gate (dimensionless)"
legend_algebraic[35] = "tau_xr2 in component rapid_time_dependent_potassium_current_Xr2_gate (millisecond)"
legend_constants[15] = "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[2] = "xs_inf in component slow_time_dependent_potassium_current_Xs_gate (dimensionless)"
legend_algebraic[15] = "alpha_xs in component slow_time_dependent_potassium_current_Xs_gate (dimensionless)"
legend_algebraic[28] = "beta_xs in component slow_time_dependent_potassium_current_Xs_gate (dimensionless)"
legend_algebraic[36] = "tau_xs in component slow_time_dependent_potassium_current_Xs_gate (millisecond)"
legend_constants[16] = "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[3] = "m_inf in component fast_sodium_current_m_gate (dimensionless)"
legend_algebraic[16] = "alpha_m in component fast_sodium_current_m_gate (dimensionless)"
legend_algebraic[29] = "beta_m in component fast_sodium_current_m_gate (dimensionless)"
legend_algebraic[37] = "tau_m in component fast_sodium_current_m_gate (millisecond)"
legend_algebraic[4] = "h_inf in component fast_sodium_current_h_gate (dimensionless)"
legend_algebraic[17] = "alpha_h in component fast_sodium_current_h_gate (per_millisecond)"
legend_algebraic[30] = "beta_h in component fast_sodium_current_h_gate (per_millisecond)"
legend_algebraic[38] = "tau_h in component fast_sodium_current_h_gate (millisecond)"
legend_algebraic[5] = "j_inf in component fast_sodium_current_j_gate (dimensionless)"
legend_algebraic[18] = "alpha_j in component fast_sodium_current_j_gate (per_millisecond)"
legend_algebraic[31] = "beta_j in component fast_sodium_current_j_gate (per_millisecond)"
legend_algebraic[39] = "tau_j in component fast_sodium_current_j_gate (millisecond)"
legend_constants[17] = "g_bna in component sodium_background_current (nanoS_per_picoF)"
legend_constants[18] = "g_CaL in component L_type_Ca_current (litre_per_farad_second)"
legend_states[10] = "Ca_ss in component calcium_dynamics (millimolar)"
legend_states[11] = "d in component L_type_Ca_current_d_gate (dimensionless)"
legend_states[12] = "f in component L_type_Ca_current_f_gate (dimensionless)"
legend_states[13] = "f2 in component L_type_Ca_current_f2_gate (dimensionless)"
legend_states[14] = "fCass in component L_type_Ca_current_fCass_gate (dimensionless)"
legend_algebraic[6] = "d_inf in component L_type_Ca_current_d_gate (dimensionless)"
legend_algebraic[19] = "alpha_d in component L_type_Ca_current_d_gate (dimensionless)"
legend_algebraic[32] = "beta_d in component L_type_Ca_current_d_gate (dimensionless)"
legend_algebraic[40] = "gamma_d in component L_type_Ca_current_d_gate (millisecond)"
legend_algebraic[42] = "tau_d in component L_type_Ca_current_d_gate (millisecond)"
legend_algebraic[7] = "f_inf in component L_type_Ca_current_f_gate (dimensionless)"
legend_algebraic[20] = "tau_f in component L_type_Ca_current_f_gate (millisecond)"
legend_algebraic[8] = "f2_inf in component L_type_Ca_current_f2_gate (dimensionless)"
legend_algebraic[21] = "tau_f2 in component L_type_Ca_current_f2_gate (millisecond)"
legend_algebraic[9] = "fCass_inf in component L_type_Ca_current_fCass_gate (dimensionless)"
legend_algebraic[22] = "tau_fCass in component L_type_Ca_current_fCass_gate (millisecond)"
legend_constants[19] = "g_bca in component calcium_background_current (nanoS_per_picoF)"
legend_constants[20] = "g_to in component transient_outward_current (nanoS_per_picoF)"
legend_states[15] = "s in component transient_outward_current_s_gate (dimensionless)"
legend_states[16] = "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 (millisecond)"
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[21] = "P_NaK in component sodium_potassium_pump_current (picoA_per_picoF)"
legend_constants[22] = "K_mk in component sodium_potassium_pump_current (millimolar)"
legend_constants[23] = "K_mNa in component sodium_potassium_pump_current (millimolar)"
legend_constants[24] = "K_NaCa in component sodium_calcium_exchanger_current (picoA_per_picoF)"
legend_constants[25] = "K_sat in component sodium_calcium_exchanger_current (dimensionless)"
legend_constants[26] = "alpha in component sodium_calcium_exchanger_current (dimensionless)"
legend_constants[27] = "gamma in component sodium_calcium_exchanger_current (dimensionless)"
legend_constants[28] = "Km_Ca in component sodium_calcium_exchanger_current (millimolar)"
legend_constants[29] = "Km_Nai in component sodium_calcium_exchanger_current (millimolar)"
legend_constants[30] = "g_pCa in component calcium_pump_current (picoA_per_picoF)"
legend_constants[31] = "K_pCa in component calcium_pump_current (millimolar)"
legend_constants[32] = "g_pK in component potassium_pump_current (nanoS_per_picoF)"
legend_states[17] = "Ca_SR in component calcium_dynamics (millimolar)"
legend_algebraic[68] = "i_rel in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[59] = "i_up in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[60] = "i_leak in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[61] = "i_xfer in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[67] = "O in component calcium_dynamics (dimensionless)"
legend_states[18] = "R_prime in component calcium_dynamics (dimensionless)"
legend_algebraic[64] = "k1 in component calcium_dynamics (per_millimolar2_per_millisecond)"
legend_algebraic[65] = "k2 in component calcium_dynamics (per_millimolar_per_millisecond)"
legend_constants[33] = "k1_prime in component calcium_dynamics (per_millimolar2_per_millisecond)"
legend_constants[34] = "k2_prime in component calcium_dynamics (per_millimolar_per_millisecond)"
legend_constants[35] = "k3 in component calcium_dynamics (per_millisecond)"
legend_constants[36] = "k4 in component calcium_dynamics (per_millisecond)"
legend_constants[37] = "EC in component calcium_dynamics (millimolar)"
legend_constants[38] = "max_sr in component calcium_dynamics (dimensionless)"
legend_constants[39] = "min_sr in component calcium_dynamics (dimensionless)"
legend_algebraic[62] = "kcasr in component calcium_dynamics (dimensionless)"
legend_constants[40] = "V_rel in component calcium_dynamics (per_millisecond)"
legend_constants[41] = "V_xfer in component calcium_dynamics (per_millisecond)"
legend_constants[42] = "K_up in component calcium_dynamics (millimolar)"
legend_constants[43] = "V_leak in component calcium_dynamics (per_millisecond)"
legend_constants[44] = "Vmax_up in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[63] = "ddt_Ca_i_total in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[69] = "ddt_Ca_sr_total in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[70] = "ddt_Ca_ss_total in component calcium_dynamics (millimolar_per_millisecond)"
legend_algebraic[66] = "f_JCa_i_free in component calcium_dynamics (dimensionless)"
legend_algebraic[71] = "f_JCa_sr_free in component calcium_dynamics (dimensionless)"
legend_algebraic[72] = "f_JCa_ss_free in component calcium_dynamics (dimensionless)"
legend_constants[45] = "Buf_c in component calcium_dynamics (millimolar)"
legend_constants[46] = "K_buf_c in component calcium_dynamics (millimolar)"
legend_constants[47] = "Buf_sr in component calcium_dynamics (millimolar)"
legend_constants[48] = "K_buf_sr in component calcium_dynamics (millimolar)"
legend_constants[49] = "Buf_ss in component calcium_dynamics (millimolar)"
legend_constants[50] = "K_buf_ss in component calcium_dynamics (millimolar)"
legend_constants[51] = "V_sr in component calcium_dynamics (micrometre3)"
legend_constants[52] = "V_ss in component calcium_dynamics (micrometre3)"
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[11] = "d/dt d in component L_type_Ca_current_d_gate (dimensionless)"
legend_rates[12] = "d/dt f in component L_type_Ca_current_f_gate (dimensionless)"
legend_rates[13] = "d/dt f2 in component L_type_Ca_current_f2_gate (dimensionless)"
legend_rates[14] = "d/dt fCass in component L_type_Ca_current_fCass_gate (dimensionless)"
legend_rates[15] = "d/dt s in component transient_outward_current_s_gate (dimensionless)"
legend_rates[16] = "d/dt r in component transient_outward_current_r_gate (dimensionless)"
legend_rates[18] = "d/dt R_prime in component calcium_dynamics (dimensionless)"
legend_rates[3] = "d/dt Ca_i in component calcium_dynamics (millimolar)"
legend_rates[17] = "d/dt Ca_SR in component calcium_dynamics (millimolar)"
legend_rates[10] = "d/dt Ca_ss 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] = -86.709
constants[0] = 8.314
constants[1] = 310
constants[2] = 96.485
constants[3] = 185
constants[4] = 16404
constants[5] = 10
constants[6] = 1000
constants[7] = 1
constants[8] = -52
constants[9] = 0.03
constants[10] = 5.4
constants[11] = 140
states[1] = 138.4
states[2] = 10.355
constants[12] = 2
states[3] = 0.00013
constants[13] = 5.405
constants[14] = 0.153
states[4] = 0.00448
states[5] = 0.476
constants[15] = 0.392
states[6] = 0.0087
constants[16] = 14.838
states[7] = 0.00155
states[8] = 0.7573
states[9] = 0.7225
constants[17] = 0.00029
constants[18] = 0.0398
states[10] = 0.00036
states[11] = 3.164e-5
states[12] = 0.8009
states[13] = 0.9778
states[14] = 0.9953
constants[19] = 0.000592
constants[20] = 0.073
states[15] = 0.3212
states[16] = 2.235e-8
constants[21] = 2.724
constants[22] = 1
constants[23] = 40
constants[24] = 1000
constants[25] = 0.1
constants[26] = 2.5
constants[27] = 0.35
constants[28] = 1.38
constants[29] = 87.5
constants[30] = 0.1238
constants[31] = 0.0005
constants[32] = 0.0146
states[17] = 3.715
states[18] = 0.9068
constants[33] = 0.15
constants[34] = 0.045
constants[35] = 0.06
constants[36] = 0.005
constants[37] = 1.5
constants[38] = 2.5
constants[39] = 1
constants[40] = 0.102
constants[41] = 0.0038
constants[42] = 0.00025
constants[43] = 0.00036
constants[44] = 0.006375
constants[45] = 0.2
constants[46] = 0.001
constants[47] = 10
constants[48] = 0.3
constants[49] = 0.4
constants[50] = 0.00025
constants[51] = 1094
constants[52] = 54.68
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[7] = 1.00000/(1.00000+exp((states[0]+20.0000)/7.00000))
algebraic[20] = 1102.50*exp(-(power(states[0]+27.0000, 2.00000))/225.000)+200.000/(1.00000+exp((13.0000-states[0])/10.0000))+180.000/(1.00000+exp((states[0]+30.0000)/10.0000))+20.0000
rates[12] = (algebraic[7]-states[12])/algebraic[20]
algebraic[8] = 0.670000/(1.00000+exp((states[0]+35.0000)/7.00000))+0.330000
algebraic[21] = 562.000*exp(-(power(states[0]+27.0000, 2.00000))/240.000)+31.0000/(1.00000+exp((25.0000-states[0])/10.0000))+80.0000/(1.00000+exp((states[0]+30.0000)/10.0000))
rates[13] = (algebraic[8]-states[13])/algebraic[21]
algebraic[9] = 0.600000/(1.00000+power(states[10]/0.0500000, 2.00000))+0.400000
algebraic[22] = 80.0000/(1.00000+power(states[10]/0.0500000, 2.00000))+2.00000
rates[14] = (algebraic[9]-states[14])/algebraic[22]
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[15] = (algebraic[10]-states[15])/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[16] = (algebraic[11]-states[16])/algebraic[24]
algebraic[0] = 1.00000/(1.00000+exp((-26.0000-states[0])/7.00000))
algebraic[13] = 450.000/(1.00000+exp((-45.0000-states[0])/10.0000))
algebraic[26] = 6.00000/(1.00000+exp((states[0]+30.0000)/11.5000))
algebraic[34] = 1.00000*algebraic[13]*algebraic[26]
rates[4] = (algebraic[0]-states[4])/algebraic[34]
algebraic[1] = 1.00000/(1.00000+exp((states[0]+88.0000)/24.0000))
algebraic[14] = 3.00000/(1.00000+exp((-60.0000-states[0])/20.0000))
algebraic[27] = 1.12000/(1.00000+exp((states[0]-60.0000)/20.0000))
algebraic[35] = 1.00000*algebraic[14]*algebraic[27]
rates[5] = (algebraic[1]-states[5])/algebraic[35]
algebraic[2] = 1.00000/(1.00000+exp((-5.00000-states[0])/14.0000))
algebraic[15] = 1400.00/(power(1.00000+exp((5.00000-states[0])/6.00000), 1.0/2))
algebraic[28] = 1.00000/(1.00000+exp((states[0]-35.0000)/15.0000))
algebraic[36] = 1.00000*algebraic[15]*algebraic[28]+80.0000
rates[6] = (algebraic[2]-states[6])/algebraic[36]
algebraic[3] = 1.00000/(power(1.00000+exp((-56.8600-states[0])/9.03000), 2.00000))
algebraic[16] = 1.00000/(1.00000+exp((-60.0000-states[0])/5.00000))
algebraic[29] = 0.100000/(1.00000+exp((states[0]+35.0000)/5.00000))+0.100000/(1.00000+exp((states[0]-50.0000)/200.000))
algebraic[37] = 1.00000*algebraic[16]*algebraic[29]
rates[7] = (algebraic[3]-states[7])/algebraic[37]
algebraic[4] = 1.00000/(power(1.00000+exp((states[0]+71.5500)/7.43000), 2.00000))
algebraic[17] = custom_piecewise([less(states[0] , -40.0000), 0.0570000*exp(-(states[0]+80.0000)/6.80000) , True, 0.00000])
algebraic[30] = 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[38] = 1.00000/(algebraic[17]+algebraic[30])
rates[8] = (algebraic[4]-states[8])/algebraic[38]
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), (((-25428.0*exp(0.244400*states[0])-6.94800e-06*exp(-0.0439100*states[0]))*(states[0]+37.7800))/1.00000)/(1.00000+exp(0.311000*(states[0]+79.2300))) , True, 0.00000])
algebraic[31] = 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[39] = 1.00000/(algebraic[18]+algebraic[31])
rates[9] = (algebraic[5]-states[9])/algebraic[39]
algebraic[6] = 1.00000/(1.00000+exp((-8.00000-states[0])/7.50000))
algebraic[19] = 1.40000/(1.00000+exp((-35.0000-states[0])/13.0000))+0.250000
algebraic[32] = 1.40000/(1.00000+exp((states[0]+5.00000)/5.00000))
algebraic[40] = 1.00000/(1.00000+exp((50.0000-states[0])/20.0000))
algebraic[42] = 1.00000*algebraic[19]*algebraic[32]+algebraic[40]
rates[11] = (algebraic[6]-states[11])/algebraic[42]
algebraic[55] = ((((constants[21]*constants[10])/(constants[10]+constants[22]))*states[2])/(states[2]+constants[23]))/(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[25] = ((constants[0]*constants[1])/constants[2])*log(constants[11]/states[2])
algebraic[50] = constants[16]*(power(states[7], 3.00000))*states[8]*states[9]*(states[0]-algebraic[25])
algebraic[51] = constants[17]*(states[0]-algebraic[25])
algebraic[56] = (constants[24]*(exp((constants[27]*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[2], 3.00000))*constants[12]-exp(((constants[27]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[11], 3.00000))*states[3]*constants[26]))/((power(constants[29], 3.00000)+power(constants[11], 3.00000))*(constants[28]+constants[12])*(1.00000+constants[25]*exp(((constants[27]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))))
rates[2] = (-(algebraic[50]+algebraic[51]+3.00000*algebraic[55]+3.00000*algebraic[56])/(constants[4]*constants[2]))*constants[3]
algebraic[33] = ((constants[0]*constants[1])/constants[2])*log(constants[10]/states[1])
algebraic[44] = 0.100000/(1.00000+exp(0.0600000*((states[0]-algebraic[33])-200.000)))
algebraic[45] = (3.00000*exp(0.000200000*((states[0]-algebraic[33])+100.000))+exp(0.100000*((states[0]-algebraic[33])-10.0000)))/(1.00000+exp(-0.500000*(states[0]-algebraic[33])))
algebraic[46] = algebraic[44]/(algebraic[44]+algebraic[45])
algebraic[47] = constants[13]*algebraic[46]*(power(constants[10]/5.40000, 1.0/2))*(states[0]-algebraic[33])
algebraic[54] = constants[20]*states[16]*states[15]*(states[0]-algebraic[33])
algebraic[48] = constants[14]*(power(constants[10]/5.40000, 1.0/2))*states[4]*states[5]*(states[0]-algebraic[33])
algebraic[41] = ((constants[0]*constants[1])/constants[2])*log((constants[10]+constants[9]*constants[11])/(states[1]+constants[9]*states[2]))
algebraic[49] = constants[15]*(power(states[6], 2.00000))*(states[0]-algebraic[41])
algebraic[52] = (((constants[18]*states[11]*states[12]*states[13]*states[14]*4.00000*(states[0]-15.0000)*(power(constants[2], 2.00000)))/(constants[0]*constants[1]))*(0.250000*states[10]*exp((2.00000*(states[0]-15.0000)*constants[2])/(constants[0]*constants[1]))-constants[12]))/(exp((2.00000*(states[0]-15.0000)*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[43] = ((0.500000*constants[0]*constants[1])/constants[2])*log(constants[12]/states[3])
algebraic[53] = constants[19]*(states[0]-algebraic[43])
algebraic[58] = (constants[32]*(states[0]-algebraic[33]))/(1.00000+exp((25.0000-states[0])/5.98000))
algebraic[57] = (constants[30]*states[3])/(states[3]+constants[31])
algebraic[12] = custom_piecewise([greater_equal(voi-floor(voi/constants[6])*constants[6] , constants[5]) & less_equal(voi-floor(voi/constants[6])*constants[6] , constants[5]+constants[7]), constants[8] , True, 0.00000])
rates[0] = -(algebraic[47]+algebraic[54]+algebraic[48]+algebraic[49]+algebraic[52]+algebraic[55]+algebraic[50]+algebraic[51]+algebraic[56]+algebraic[53]+algebraic[58]+algebraic[57]+algebraic[12])
rates[1] = (-((algebraic[47]+algebraic[54]+algebraic[48]+algebraic[49]+algebraic[58]+algebraic[12])-2.00000*algebraic[55])/(constants[4]*constants[2]))*constants[3]
algebraic[62] = constants[38]-(constants[38]-constants[39])/(1.00000+power(constants[37]/states[17], 2.00000))
algebraic[65] = constants[34]*algebraic[62]
rates[18] = -algebraic[65]*states[10]*states[18]+constants[36]*(1.00000-states[18])
algebraic[59] = constants[44]/(1.00000+(power(constants[42], 2.00000))/(power(states[3], 2.00000)))
algebraic[60] = constants[43]*(states[17]-states[3])
algebraic[61] = constants[41]*(states[10]-states[3])
algebraic[63] = (-((algebraic[53]+algebraic[57])-2.00000*algebraic[56])*constants[3])/(2.00000*constants[4]*constants[2])+((algebraic[60]-algebraic[59])*constants[51])/constants[4]+algebraic[61]
algebraic[66] = 1.00000/(1.00000+(constants[45]*constants[46])/(power(states[3]+constants[46], 2.00000)))
rates[3] = algebraic[63]*algebraic[66]
algebraic[64] = constants[33]/algebraic[62]
algebraic[67] = (algebraic[64]*(power(states[10], 2.00000))*states[18])/(constants[35]+algebraic[64]*(power(states[10], 2.00000)))
algebraic[68] = constants[40]*algebraic[67]*(states[17]-states[10])
algebraic[69] = algebraic[59]-(algebraic[68]+algebraic[60])
algebraic[71] = 1.00000/(1.00000+(constants[47]*constants[48])/(power(states[17]+constants[48], 2.00000)))
rates[17] = algebraic[69]*algebraic[71]
algebraic[70] = ((-algebraic[52]*constants[3])/(2.00000*constants[52]*constants[2])+(algebraic[68]*constants[51])/constants[52])-(algebraic[61]*constants[4])/constants[52]
algebraic[72] = 1.00000/(1.00000+(constants[49]*constants[50])/(power(states[10]+constants[50], 2.00000)))
rates[10] = algebraic[70]*algebraic[72]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[7] = 1.00000/(1.00000+exp((states[0]+20.0000)/7.00000))
algebraic[20] = 1102.50*exp(-(power(states[0]+27.0000, 2.00000))/225.000)+200.000/(1.00000+exp((13.0000-states[0])/10.0000))+180.000/(1.00000+exp((states[0]+30.0000)/10.0000))+20.0000
algebraic[8] = 0.670000/(1.00000+exp((states[0]+35.0000)/7.00000))+0.330000
algebraic[21] = 562.000*exp(-(power(states[0]+27.0000, 2.00000))/240.000)+31.0000/(1.00000+exp((25.0000-states[0])/10.0000))+80.0000/(1.00000+exp((states[0]+30.0000)/10.0000))
algebraic[9] = 0.600000/(1.00000+power(states[10]/0.0500000, 2.00000))+0.400000
algebraic[22] = 80.0000/(1.00000+power(states[10]/0.0500000, 2.00000))+2.00000
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[0] = 1.00000/(1.00000+exp((-26.0000-states[0])/7.00000))
algebraic[13] = 450.000/(1.00000+exp((-45.0000-states[0])/10.0000))
algebraic[26] = 6.00000/(1.00000+exp((states[0]+30.0000)/11.5000))
algebraic[34] = 1.00000*algebraic[13]*algebraic[26]
algebraic[1] = 1.00000/(1.00000+exp((states[0]+88.0000)/24.0000))
algebraic[14] = 3.00000/(1.00000+exp((-60.0000-states[0])/20.0000))
algebraic[27] = 1.12000/(1.00000+exp((states[0]-60.0000)/20.0000))
algebraic[35] = 1.00000*algebraic[14]*algebraic[27]
algebraic[2] = 1.00000/(1.00000+exp((-5.00000-states[0])/14.0000))
algebraic[15] = 1400.00/(power(1.00000+exp((5.00000-states[0])/6.00000), 1.0/2))
algebraic[28] = 1.00000/(1.00000+exp((states[0]-35.0000)/15.0000))
algebraic[36] = 1.00000*algebraic[15]*algebraic[28]+80.0000
algebraic[3] = 1.00000/(power(1.00000+exp((-56.8600-states[0])/9.03000), 2.00000))
algebraic[16] = 1.00000/(1.00000+exp((-60.0000-states[0])/5.00000))
algebraic[29] = 0.100000/(1.00000+exp((states[0]+35.0000)/5.00000))+0.100000/(1.00000+exp((states[0]-50.0000)/200.000))
algebraic[37] = 1.00000*algebraic[16]*algebraic[29]
algebraic[4] = 1.00000/(power(1.00000+exp((states[0]+71.5500)/7.43000), 2.00000))
algebraic[17] = custom_piecewise([less(states[0] , -40.0000), 0.0570000*exp(-(states[0]+80.0000)/6.80000) , True, 0.00000])
algebraic[30] = 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[38] = 1.00000/(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), (((-25428.0*exp(0.244400*states[0])-6.94800e-06*exp(-0.0439100*states[0]))*(states[0]+37.7800))/1.00000)/(1.00000+exp(0.311000*(states[0]+79.2300))) , True, 0.00000])
algebraic[31] = 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[39] = 1.00000/(algebraic[18]+algebraic[31])
algebraic[6] = 1.00000/(1.00000+exp((-8.00000-states[0])/7.50000))
algebraic[19] = 1.40000/(1.00000+exp((-35.0000-states[0])/13.0000))+0.250000
algebraic[32] = 1.40000/(1.00000+exp((states[0]+5.00000)/5.00000))
algebraic[40] = 1.00000/(1.00000+exp((50.0000-states[0])/20.0000))
algebraic[42] = 1.00000*algebraic[19]*algebraic[32]+algebraic[40]
algebraic[55] = ((((constants[21]*constants[10])/(constants[10]+constants[22]))*states[2])/(states[2]+constants[23]))/(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[25] = ((constants[0]*constants[1])/constants[2])*log(constants[11]/states[2])
algebraic[50] = constants[16]*(power(states[7], 3.00000))*states[8]*states[9]*(states[0]-algebraic[25])
algebraic[51] = constants[17]*(states[0]-algebraic[25])
algebraic[56] = (constants[24]*(exp((constants[27]*states[0]*constants[2])/(constants[0]*constants[1]))*(power(states[2], 3.00000))*constants[12]-exp(((constants[27]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))*(power(constants[11], 3.00000))*states[3]*constants[26]))/((power(constants[29], 3.00000)+power(constants[11], 3.00000))*(constants[28]+constants[12])*(1.00000+constants[25]*exp(((constants[27]-1.00000)*states[0]*constants[2])/(constants[0]*constants[1]))))
algebraic[33] = ((constants[0]*constants[1])/constants[2])*log(constants[10]/states[1])
algebraic[44] = 0.100000/(1.00000+exp(0.0600000*((states[0]-algebraic[33])-200.000)))
algebraic[45] = (3.00000*exp(0.000200000*((states[0]-algebraic[33])+100.000))+exp(0.100000*((states[0]-algebraic[33])-10.0000)))/(1.00000+exp(-0.500000*(states[0]-algebraic[33])))
algebraic[46] = algebraic[44]/(algebraic[44]+algebraic[45])
algebraic[47] = constants[13]*algebraic[46]*(power(constants[10]/5.40000, 1.0/2))*(states[0]-algebraic[33])
algebraic[54] = constants[20]*states[16]*states[15]*(states[0]-algebraic[33])
algebraic[48] = constants[14]*(power(constants[10]/5.40000, 1.0/2))*states[4]*states[5]*(states[0]-algebraic[33])
algebraic[41] = ((constants[0]*constants[1])/constants[2])*log((constants[10]+constants[9]*constants[11])/(states[1]+constants[9]*states[2]))
algebraic[49] = constants[15]*(power(states[6], 2.00000))*(states[0]-algebraic[41])
algebraic[52] = (((constants[18]*states[11]*states[12]*states[13]*states[14]*4.00000*(states[0]-15.0000)*(power(constants[2], 2.00000)))/(constants[0]*constants[1]))*(0.250000*states[10]*exp((2.00000*(states[0]-15.0000)*constants[2])/(constants[0]*constants[1]))-constants[12]))/(exp((2.00000*(states[0]-15.0000)*constants[2])/(constants[0]*constants[1]))-1.00000)
algebraic[43] = ((0.500000*constants[0]*constants[1])/constants[2])*log(constants[12]/states[3])
algebraic[53] = constants[19]*(states[0]-algebraic[43])
algebraic[58] = (constants[32]*(states[0]-algebraic[33]))/(1.00000+exp((25.0000-states[0])/5.98000))
algebraic[57] = (constants[30]*states[3])/(states[3]+constants[31])
algebraic[12] = custom_piecewise([greater_equal(voi-floor(voi/constants[6])*constants[6] , constants[5]) & less_equal(voi-floor(voi/constants[6])*constants[6] , constants[5]+constants[7]), constants[8] , True, 0.00000])
algebraic[62] = constants[38]-(constants[38]-constants[39])/(1.00000+power(constants[37]/states[17], 2.00000))
algebraic[65] = constants[34]*algebraic[62]
algebraic[59] = constants[44]/(1.00000+(power(constants[42], 2.00000))/(power(states[3], 2.00000)))
algebraic[60] = constants[43]*(states[17]-states[3])
algebraic[61] = constants[41]*(states[10]-states[3])
algebraic[63] = (-((algebraic[53]+algebraic[57])-2.00000*algebraic[56])*constants[3])/(2.00000*constants[4]*constants[2])+((algebraic[60]-algebraic[59])*constants[51])/constants[4]+algebraic[61]
algebraic[66] = 1.00000/(1.00000+(constants[45]*constants[46])/(power(states[3]+constants[46], 2.00000)))
algebraic[64] = constants[33]/algebraic[62]
algebraic[67] = (algebraic[64]*(power(states[10], 2.00000))*states[18])/(constants[35]+algebraic[64]*(power(states[10], 2.00000)))
algebraic[68] = constants[40]*algebraic[67]*(states[17]-states[10])
algebraic[69] = algebraic[59]-(algebraic[68]+algebraic[60])
algebraic[71] = 1.00000/(1.00000+(constants[47]*constants[48])/(power(states[17]+constants[48], 2.00000)))
algebraic[70] = ((-algebraic[52]*constants[3])/(2.00000*constants[52]*constants[2])+(algebraic[68]*constants[51])/constants[52])-(algebraic[61]*constants[4])/constants[52]
algebraic[72] = 1.00000/(1.00000+(constants[49]*constants[50])/(power(states[10]+constants[50], 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)