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 = 34
sizeStates = 14
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 Time (time_units)"
legend_constants[0] = "Ach in component Neural_input (millimolar)"
legend_constants[1] = "Gcouple in component Gap_junction (conductance_units)"
legend_constants[2] = "T in component Environment (Temperature_units)"
legend_constants[3] = "T_exp in component Environment (Temperature_units)"
legend_constants[4] = "F in component Environment (F_units)"
legend_constants[5] = "R in component Environment (R_units)"
legend_constants[6] = "Q10Ca in component Environment (dimensionless)"
legend_constants[7] = "Q10K in component Environment (dimensionless)"
legend_constants[8] = "Q10Na in component Environment (dimensionless)"
legend_constants[9] = "Ca_o in component Environment (millimolar)"
legend_constants[10] = "Na_o in component Environment (millimolar)"
legend_constants[11] = "K_o in component Environment (millimolar)"
legend_constants[12] = "Cl_o in component Environment (millimolar)"
legend_constants[33] = "T_correction_Na in component Environment (dimensionless)"
legend_constants[34] = "T_correction_K in component Environment (dimensionless)"
legend_constants[35] = "T_correction_Ca in component Environment (dimensionless)"
legend_constants[36] = "T_correction_BK in component Environment (conductance_units)"
legend_constants[37] = "FoRT in component Environment (Inverse_Voltage_units)"
legend_constants[38] = "RToF in component Environment (voltage_units)"
legend_constants[13] = "Cm_SM in component SM_Membrane (capacitance_units)"
legend_constants[14] = "Vol_SM in component SM_Membrane (volume_units)"
legend_states[0] = "Vm_SM in component SM_Membrane (voltage_units)"
legend_states[1] = "Ca_i in component SM_Membrane (millimolar)"
legend_constants[15] = "Na_i in component SM_Membrane (millimolar)"
legend_constants[16] = "K_i in component SM_Membrane (millimolar)"
legend_algebraic[30] = "I_Na_SM in component I_Na_SM (current_units)"
legend_algebraic[22] = "I_Ltype_SM in component I_Ltype_SM (current_units)"
legend_algebraic[25] = "I_LVA_SM in component I_LVA_SM (current_units)"
legend_algebraic[29] = "I_kr_SM in component I_kr_SM (current_units)"
legend_algebraic[31] = "I_ka_SM in component I_ka_SM (current_units)"
legend_algebraic[27] = "I_BK_SM in component I_BK_SM (current_units)"
legend_algebraic[33] = "I_NSCC_SM in component I_NSCC_SM (current_units)"
legend_algebraic[28] = "I_bk_SM in component I_bk_SM (current_units)"
legend_algebraic[23] = "J_CaSR_SM in component J_CaSR_SM (millimolar_per_millisecond)"
legend_algebraic[20] = "I_stim in component I_stim (current_units)"
legend_algebraic[13] = "local_time in component I_stim (time_units)"
legend_constants[17] = "period in component I_stim (time_units)"
legend_algebraic[0] = "stim_start in component I_stim (time_units)"
legend_constants[18] = "delta_VICC in component I_stim (voltage_units)"
legend_constants[19] = "t_ICCpeak in component I_stim (time_units)"
legend_constants[20] = "t_ICCplateau in component I_stim (time_units)"
legend_constants[21] = "t_ICC_stimulus in component I_stim (time_units)"
legend_constants[22] = "V_decay in component I_stim (voltage_units)"
legend_algebraic[1] = "d_inf_Ltype_SM in component d_Ltype_SM (dimensionless)"
legend_constants[40] = "tau_d_Ltype_SM in component d_Ltype_SM (time_units)"
legend_states[2] = "d_Ltype_SM in component d_Ltype_SM (dimensionless)"
legend_algebraic[2] = "f_inf_Ltype_SM in component f_Ltype_SM (dimensionless)"
legend_constants[41] = "tau_f_Ltype_SM in component f_Ltype_SM (time_units)"
legend_states[3] = "f_Ltype_SM in component f_Ltype_SM (dimensionless)"
legend_algebraic[3] = "f_ca_inf_Ltype_SM in component f_ca_Ltype_SM (dimensionless)"
legend_constants[42] = "tau_f_ca_Ltype_SM in component f_ca_Ltype_SM (time_units)"
legend_states[4] = "f_ca_Ltype_SM in component f_ca_Ltype_SM (dimensionless)"
legend_algebraic[21] = "E_Ca in component I_Ltype_SM (voltage_units)"
legend_constants[23] = "G_max_Ltype in component I_Ltype_SM (conductance_units)"
legend_constants[24] = "J_max_CaSR in component J_CaSR_SM (millimolar_per_millisecond)"
legend_algebraic[4] = "d_inf_LVA_SM in component d_LVA_SM (dimensionless)"
legend_constants[43] = "tau_d_LVA_SM in component d_LVA_SM (time_units)"
legend_states[5] = "d_LVA_SM in component d_LVA_SM (dimensionless)"
legend_algebraic[5] = "f_inf_LVA_SM in component f_LVA_SM (dimensionless)"
legend_algebraic[14] = "tau_f_LVA_SM in component f_LVA_SM (time_units)"
legend_states[6] = "f_LVA_SM in component f_LVA_SM (dimensionless)"
legend_algebraic[24] = "E_Ca in component I_LVA_SM (voltage_units)"
legend_constants[25] = "G_max_LVA in component I_LVA_SM (conductance_units)"
legend_algebraic[26] = "d_BK_SM in component d_BK_SM (dimensionless)"
legend_constants[44] = "E_K in component I_BK_SM (voltage_units)"
legend_constants[26] = "G_max_BK in component I_BK_SM (conductance_units)"
legend_constants[45] = "E_K in component I_bk_SM (voltage_units)"
legend_constants[27] = "G_max_bk in component I_bk_SM (conductance_units)"
legend_algebraic[6] = "xr1_inf_SM in component xr1_SM (dimensionless)"
legend_constants[46] = "tau_xr1_SM in component xr1_SM (time_units)"
legend_states[7] = "xr1_SM in component xr1_SM (dimensionless)"
legend_algebraic[7] = "xr2_inf_SM in component xr2_SM (dimensionless)"
legend_algebraic[15] = "tau_xr2_SM in component xr2_SM (time_units)"
legend_states[8] = "xr2_SM in component xr2_SM (dimensionless)"
legend_constants[47] = "E_K in component I_kr_SM (voltage_units)"
legend_constants[28] = "G_max_kr_SM in component I_kr_SM (conductance_units)"
legend_algebraic[8] = "m_inf_Na in component m_Na_SM (dimensionless)"
legend_algebraic[16] = "tau_m_Na in component m_Na_SM (time_units)"
legend_states[9] = "m_Na_SM in component m_Na_SM (dimensionless)"
legend_algebraic[9] = "h_inf_Na in component h_Na_SM (dimensionless)"
legend_algebraic[17] = "tau_h_Na in component h_Na_SM (time_units)"
legend_states[10] = "h_Na_SM in component h_Na_SM (dimensionless)"
legend_constants[48] = "E_Na in component I_Na_SM (voltage_units)"
legend_constants[29] = "G_max_Na_SM in component I_Na_SM (conductance_units)"
legend_algebraic[10] = "xa1_inf_SM in component xa1_SM (dimensionless)"
legend_algebraic[18] = "tau_xa1_SM in component xa1_SM (time_units)"
legend_states[11] = "xa1_SM in component xa1_SM (dimensionless)"
legend_algebraic[11] = "xa2_inf_SM in component xa2_SM (dimensionless)"
legend_constants[49] = "tau_xa2_SM in component xa2_SM (time_units)"
legend_states[12] = "xa2_SM in component xa2_SM (dimensionless)"
legend_constants[50] = "E_K in component I_ka_SM (voltage_units)"
legend_constants[30] = "G_max_ka_SM in component I_ka_SM (conductance_units)"
legend_algebraic[12] = "m_inf_NSCC_SM in component m_NSCC_SM (dimensionless)"
legend_algebraic[19] = "tau_m_NSCC_SM in component m_NSCC_SM (time_units)"
legend_states[13] = "m_NSCC_SM in component m_NSCC_SM (dimensionless)"
legend_constants[31] = "E_NSCC in component I_NSCC_SM (voltage_units)"
legend_constants[32] = "G_max_NSCC_SM in component I_NSCC_SM (conductance_units)"
legend_algebraic[32] = "f_ca_NSCC_SM in component I_NSCC_SM (dimensionless)"
legend_constants[39] = "rach_NSCC_SM in component I_NSCC_SM (dimensionless)"
legend_rates[0] = "d/dt Vm_SM in component SM_Membrane (voltage_units)"
legend_rates[1] = "d/dt Ca_i in component SM_Membrane (millimolar)"
legend_rates[2] = "d/dt d_Ltype_SM in component d_Ltype_SM (dimensionless)"
legend_rates[3] = "d/dt f_Ltype_SM in component f_Ltype_SM (dimensionless)"
legend_rates[4] = "d/dt f_ca_Ltype_SM in component f_ca_Ltype_SM (dimensionless)"
legend_rates[5] = "d/dt d_LVA_SM in component d_LVA_SM (dimensionless)"
legend_rates[6] = "d/dt f_LVA_SM in component f_LVA_SM (dimensionless)"
legend_rates[7] = "d/dt xr1_SM in component xr1_SM (dimensionless)"
legend_rates[8] = "d/dt xr2_SM in component xr2_SM (dimensionless)"
legend_rates[9] = "d/dt m_Na_SM in component m_Na_SM (dimensionless)"
legend_rates[10] = "d/dt h_Na_SM in component h_Na_SM (dimensionless)"
legend_rates[11] = "d/dt xa1_SM in component xa1_SM (dimensionless)"
legend_rates[12] = "d/dt xa2_SM in component xa2_SM (dimensionless)"
legend_rates[13] = "d/dt m_NSCC_SM in component m_NSCC_SM (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 0.00001
constants[1] = 1.3
constants[2] = 310
constants[3] = 297
constants[4] = 96486
constants[5] = 8314.4
constants[6] = 2.1
constants[7] = 1.365
constants[8] = 2.45
constants[9] = 2.5
constants[10] = 137
constants[11] = 5.9
constants[12] = 134
constants[13] = 77
constants[14] = 3500
states[0] = -69.75
states[1] = 0.00008
constants[15] = 10
constants[16] = 164
constants[17] = 20000
constants[18] = 59
constants[19] = 98
constants[20] = 7582
constants[21] = 10000
constants[22] = 37.25
states[2] = 0.0
states[3] = 0.95
states[4] = 1.0
constants[23] = 65
constants[24] = 0.31705
states[5] = 0.02
states[6] = 0.99
constants[25] = 0.18
constants[26] = 45.7
constants[27] = 0.0144
states[7] = 0.0
states[8] = 0.82
constants[28] = 35
states[9] = 0.005
states[10] = 0.05787
constants[29] = 3
states[11] = 0.00414
states[12] = 0.72
constants[30] = 9
states[13] = 0.0
constants[31] = -28
constants[32] = 50
constants[33] = power(constants[8], (constants[2]-constants[3])/10.0000)
constants[34] = power(constants[7], (constants[2]-constants[3])/10.0000)
constants[35] = power(constants[6], (constants[2]-constants[3])/10.0000)
constants[36] = 1.10000*(constants[2]-constants[3])
constants[37] = constants[4]/(constants[5]*constants[2])
constants[38] = (constants[5]*constants[2])/constants[4]
constants[39] = 1.00000/(1.00000+0.0100000/constants[0])
constants[40] = constants[35]*0.470000
constants[41] = constants[35]*86.0000
constants[42] = constants[35]*2.00000
constants[43] = constants[35]*3.00000
constants[44] = constants[38]*log(constants[11]/constants[16])
constants[45] = constants[38]*log(constants[11]/constants[16])
constants[46] = constants[34]*80.0000
constants[47] = constants[38]*log(constants[11]/constants[16])
constants[48] = constants[38]*log(constants[10]/constants[15])
constants[49] = constants[34]*90.0000
constants[50] = constants[38]*log(constants[11]/constants[16])
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[1] = 1.00000/(1.00000+exp((states[0]+17.0000)/-4.30000))
rates[2] = (algebraic[1]-states[2])/constants[40]
algebraic[2] = 1.00000/(1.00000+exp((states[0]+43.0000)/8.90000))
rates[3] = (algebraic[2]-states[3])/constants[41]
algebraic[3] = 1.00000-1.00000/(1.00000+exp(((states[1]-8.99900e-05)-0.000214000)/-1.31000e-05))
rates[4] = (algebraic[3]-states[4])/constants[42]
algebraic[4] = 1.00000/(1.00000+exp((states[0]+27.5000)/-10.9000))
rates[5] = (algebraic[4]-states[5])/constants[43]
algebraic[6] = 1.00000/(1.00000+exp((states[0]+27.0000)/-5.00000))
rates[7] = (algebraic[6]-states[7])/constants[46]
algebraic[11] = 0.100000+0.900000/(1.00000+exp((states[0]+65.0000)/6.20000))
rates[12] = (algebraic[11]-states[12])/constants[49]
algebraic[5] = 1.00000/(1.00000+exp((states[0]+15.8000)/7.00000))
algebraic[14] = constants[35]*(7.58000*exp(states[0]*0.00817000))
rates[6] = (algebraic[5]-states[6])/algebraic[14]
algebraic[7] = 0.200000+0.800000/(1.00000+exp((states[0]+58.0000)/10.0000))
algebraic[15] = constants[34]*(-707.000+1481.00*exp((states[0]+36.0000)/95.0000))
rates[8] = (algebraic[7]-states[8])/algebraic[15]
algebraic[8] = 1.00000/(1.00000+exp((states[0]+47.0000)/-4.80000))
algebraic[16] = constants[33]*(states[0]*-0.0170000*1.00000+0.440000)
rates[9] = (algebraic[8]-states[9])/algebraic[16]
algebraic[9] = 1.00000/(1.00000+exp((states[0]+78.0000)/3.00000))
algebraic[17] = constants[33]*(states[0]*-0.250000*1.00000+5.50000)
rates[10] = (algebraic[9]-states[10])/algebraic[17]
algebraic[10] = 1.00000/(1.00000+exp((states[0]+26.5000)/-7.90000))
algebraic[18] = constants[34]*(31.8000+175.000*exp(-0.500000*(power((states[0]+44.4000)/22.3000, 2.00000))))
rates[11] = (algebraic[10]-states[11])/algebraic[18]
algebraic[12] = 1.00000/(1.00000+exp((states[0]+25.0000)/-20.0000))
algebraic[19] = (1.00000/(1.00000+exp((states[0]+66.0000)/-26.0000)))*150.000
rates[13] = (algebraic[12]-states[13])/algebraic[19]
algebraic[21] = 0.500000*constants[38]*log(constants[9]/states[1])
algebraic[22] = constants[23]*(states[3]*states[2]*states[4])*(states[0]-algebraic[21])
algebraic[24] = 0.500000*constants[38]*log(constants[9]/states[1])
algebraic[25] = constants[25]*(states[6]*states[5])*(states[0]-algebraic[24])
algebraic[23] = constants[24]*(power(states[1]*1.00000, 1.34000))
rates[1] = (-1.00000*algebraic[22]+-1.00000*algebraic[25])/(2.00000*0.00100000*constants[4]*constants[14])+-1.00000*algebraic[23]
algebraic[30] = constants[29]*(states[10]*states[9])*(states[0]-constants[48])
algebraic[29] = constants[28]*(states[7]*states[8])*(states[0]-constants[47])
algebraic[31] = constants[30]*(states[11]*states[12])*(states[0]-constants[50])
algebraic[26] = 1.00000/(1.00000+exp(states[0]/-17.0000-2.00000*log(states[1]/0.00100000)))
algebraic[27] = (constants[26]+constants[36])*algebraic[26]*(states[0]-constants[44])
algebraic[32] = 1.00000/(1.00000+power(states[1]/0.000200000, -4.00000))
algebraic[33] = constants[32]*states[13]*algebraic[32]*constants[39]*(states[0]-constants[31])
algebraic[28] = constants[27]*(states[0]-constants[45])
algebraic[0] = custom_piecewise([greater(voi , constants[17]*1.00000) & less_equal(voi , constants[17]*2.00000), constants[17]*1.00000 , greater(voi , constants[17]*2.00000) & less_equal(voi , constants[17]*3.00000), constants[17]*2.00000 , greater(voi , constants[17]*3.00000) & less_equal(voi , constants[17]*4.00000), constants[17]*3.00000 , greater(voi , constants[17]*4.00000) & less_equal(voi , constants[17]*5.00000), constants[17]*4.00000 , True, 0.00000])
algebraic[13] = voi-(algebraic[0]+constants[19])
algebraic[20] = custom_piecewise([less(algebraic[13] , constants[19]), constants[1]*constants[18] , greater_equal(algebraic[13] , constants[19]) & less_equal(algebraic[13] , constants[20]), constants[1]*constants[18]*(1.00000/(1.00000+exp((algebraic[13]-8000.00)/1000.00))) , greater(algebraic[13] , constants[20]) & less(algebraic[13] , constants[21]), constants[1]*constants[22]*(1.00000/(1.00000+exp((algebraic[13]-8000.00)/150.000))) , True, 0.00000])
rates[0] = -1.00000*(1.00000/constants[13])*(algebraic[30]+algebraic[22]+algebraic[25]+algebraic[29]+algebraic[31]+algebraic[27]+algebraic[33]+algebraic[28]+-1.00000*algebraic[20])
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = 1.00000/(1.00000+exp((states[0]+17.0000)/-4.30000))
algebraic[2] = 1.00000/(1.00000+exp((states[0]+43.0000)/8.90000))
algebraic[3] = 1.00000-1.00000/(1.00000+exp(((states[1]-8.99900e-05)-0.000214000)/-1.31000e-05))
algebraic[4] = 1.00000/(1.00000+exp((states[0]+27.5000)/-10.9000))
algebraic[6] = 1.00000/(1.00000+exp((states[0]+27.0000)/-5.00000))
algebraic[11] = 0.100000+0.900000/(1.00000+exp((states[0]+65.0000)/6.20000))
algebraic[5] = 1.00000/(1.00000+exp((states[0]+15.8000)/7.00000))
algebraic[14] = constants[35]*(7.58000*exp(states[0]*0.00817000))
algebraic[7] = 0.200000+0.800000/(1.00000+exp((states[0]+58.0000)/10.0000))
algebraic[15] = constants[34]*(-707.000+1481.00*exp((states[0]+36.0000)/95.0000))
algebraic[8] = 1.00000/(1.00000+exp((states[0]+47.0000)/-4.80000))
algebraic[16] = constants[33]*(states[0]*-0.0170000*1.00000+0.440000)
algebraic[9] = 1.00000/(1.00000+exp((states[0]+78.0000)/3.00000))
algebraic[17] = constants[33]*(states[0]*-0.250000*1.00000+5.50000)
algebraic[10] = 1.00000/(1.00000+exp((states[0]+26.5000)/-7.90000))
algebraic[18] = constants[34]*(31.8000+175.000*exp(-0.500000*(power((states[0]+44.4000)/22.3000, 2.00000))))
algebraic[12] = 1.00000/(1.00000+exp((states[0]+25.0000)/-20.0000))
algebraic[19] = (1.00000/(1.00000+exp((states[0]+66.0000)/-26.0000)))*150.000
algebraic[21] = 0.500000*constants[38]*log(constants[9]/states[1])
algebraic[22] = constants[23]*(states[3]*states[2]*states[4])*(states[0]-algebraic[21])
algebraic[24] = 0.500000*constants[38]*log(constants[9]/states[1])
algebraic[25] = constants[25]*(states[6]*states[5])*(states[0]-algebraic[24])
algebraic[23] = constants[24]*(power(states[1]*1.00000, 1.34000))
algebraic[30] = constants[29]*(states[10]*states[9])*(states[0]-constants[48])
algebraic[29] = constants[28]*(states[7]*states[8])*(states[0]-constants[47])
algebraic[31] = constants[30]*(states[11]*states[12])*(states[0]-constants[50])
algebraic[26] = 1.00000/(1.00000+exp(states[0]/-17.0000-2.00000*log(states[1]/0.00100000)))
algebraic[27] = (constants[26]+constants[36])*algebraic[26]*(states[0]-constants[44])
algebraic[32] = 1.00000/(1.00000+power(states[1]/0.000200000, -4.00000))
algebraic[33] = constants[32]*states[13]*algebraic[32]*constants[39]*(states[0]-constants[31])
algebraic[28] = constants[27]*(states[0]-constants[45])
algebraic[0] = custom_piecewise([greater(voi , constants[17]*1.00000) & less_equal(voi , constants[17]*2.00000), constants[17]*1.00000 , greater(voi , constants[17]*2.00000) & less_equal(voi , constants[17]*3.00000), constants[17]*2.00000 , greater(voi , constants[17]*3.00000) & less_equal(voi , constants[17]*4.00000), constants[17]*3.00000 , greater(voi , constants[17]*4.00000) & less_equal(voi , constants[17]*5.00000), constants[17]*4.00000 , True, 0.00000])
algebraic[13] = voi-(algebraic[0]+constants[19])
algebraic[20] = custom_piecewise([less(algebraic[13] , constants[19]), constants[1]*constants[18] , greater_equal(algebraic[13] , constants[19]) & less_equal(algebraic[13] , constants[20]), constants[1]*constants[18]*(1.00000/(1.00000+exp((algebraic[13]-8000.00)/1000.00))) , greater(algebraic[13] , constants[20]) & less(algebraic[13] , constants[21]), constants[1]*constants[22]*(1.00000/(1.00000+exp((algebraic[13]-8000.00)/150.000))) , True, 0.00000])
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)