Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 10
sizeStates = 5
sizeConstants = 43
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_s (second)"
legend_constants[0] = "Nai_rate in component Nai (mM_per_s)"
legend_states[0] = "Nai in component Nai (mM)"
legend_constants[1] = "t_ss in component Vstim_para (second)"
legend_constants[2] = "V_actHolding in component Vstim_para (mV)"
legend_constants[3] = "t_act in component Vstim_para (second)"
legend_constants[4] = "V_actTest in component Vstim_para (mV)"
legend_constants[5] = "Cai in component control_para (mM)"
legend_constants[6] = "inhPump in component control_para (dimensionless)"
legend_constants[7] = "K_Cahalf in component control_para (mV)"
legend_algebraic[2] = "V in component sPulse_protocol_s (mV)"
legend_algebraic[8] = "J_VOCC in component J_VOCC (mM_per_s)"
legend_constants[36] = "J_CaPump in component J_CaPump (mM_per_s)"
legend_algebraic[9] = "J_NaCa in component J_NaCa (mM_per_s)"
legend_algebraic[5] = "rho_vCa in component J_VOCC (dimensionless)"
legend_constants[37] = "K_1 in component K_1 (per_s)"
legend_algebraic[0] = "stress in component CB4HM (dimensionless)"
legend_algebraic[1] = "phosphorylation in component CB4HM (dimensionless)"
legend_constants[8] = "R in component constants (J_per_K_mol)"
legend_constants[9] = "F in component constants (C_per_mmol)"
legend_constants[10] = "T in component model_para (kelvin)"
legend_constants[11] = "Nao in component model_para (mM)"
legend_constants[12] = "Cao in component model_para (mM)"
legend_constants[13] = "V_cell in component model_para (fm3)"
legend_constants[14] = "V_Cahalf in component model_para (mV)"
legend_constants[15] = "g_mCa in component model_para (nS)"
legend_constants[16] = "V_pmax in component model_para (mM_per_s)"
legend_constants[17] = "n in component model_para (dimensionless)"
legend_constants[18] = "K_ph in component model_para (mM)"
legend_constants[19] = "K_NaCa in component model_para (mM)"
legend_constants[20] = "G_NaCa in component model_para (mM_per_s_mV)"
legend_constants[21] = "n_M in component model_para (dimensionless)"
legend_constants[22] = "Ca_halfMLCK in component model_para (mM)"
legend_constants[23] = "M_init in component initials (dimensionless)"
legend_constants[24] = "Mp_init in component initials (dimensionless)"
legend_constants[25] = "AM_init in component initials (dimensionless)"
legend_constants[26] = "AMp_init in component initials (dimensionless)"
legend_constants[27] = "K_7 in component model_para (per_s)"
legend_constants[28] = "K_2 in component model_para (per_s)"
legend_constants[29] = "K_3 in component model_para (per_s)"
legend_constants[30] = "Nai in component model_para (mM)"
legend_constants[31] = "K_Cahalf in component model_para (mV)"
legend_constants[32] = "inhPump in component model_para (dimensionless)"
legend_constants[33] = "Cai_init in component initials (mM)"
legend_constants[34] = "z_Ca in component E_Ca (dimensionless)"
legend_constants[38] = "E in component Nernst_potential (mV)"
legend_constants[35] = "z_Na in component E_Na (dimensionless)"
legend_algebraic[4] = "E in component Nernst_potential (mV)"
legend_algebraic[6] = "I in component Ionic_currents (pA)"
legend_algebraic[7] = "V_mNaCa in component J_NaCa (mV)"
legend_constants[39] = "K_4 in component CB4HM (per_s)"
legend_constants[40] = "K_5 in component CB4HM (per_s)"
legend_constants[41] = "K_6 in component CB4HM (per_s)"
legend_algebraic[3] = "norm in component CB4HM (dimensionless)"
legend_states[1] = "M in component CB4HM (dimensionless)"
legend_states[2] = "Mp in component CB4HM (dimensionless)"
legend_states[3] = "AM in component CB4HM (dimensionless)"
legend_states[4] = "AMp in component CB4HM (dimensionless)"
legend_rates[0] = "d/dt Nai in component Nai (mM)"
legend_rates[1] = "d/dt M in component CB4HM (dimensionless)"
legend_rates[2] = "d/dt Mp in component CB4HM (dimensionless)"
legend_rates[3] = "d/dt AM in component CB4HM (dimensionless)"
legend_rates[4] = "d/dt AMp in component CB4HM (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 1
states[0] = 1
constants[1] = 0
constants[2] = -50
constants[3] = 1
constants[4] = 0
constants[5] = 0.0001
constants[6] = 1
constants[7] = 11
constants[8] = 8.314
constants[9] = 96.48534
constants[10] = 310
constants[11] = 140
constants[12] = 2
constants[13] = 21
constants[14] = -27
constants[15] = 0.046842
constants[16] = 5.1449e-4
constants[17] = 1.9015
constants[18] = 0.6e-3
constants[19] = 7e-3
constants[20] = 5.7297e-5
constants[21] = 8.7613
constants[22] = 256.98e-6
constants[23] = 1
constants[24] = 0
constants[25] = 0
constants[26] = 0
constants[27] = 0.0378
constants[28] = 1.2387
constants[29] = 0.1419
constants[30] = 2.9836
constants[31] = 11
constants[32] = 1
constants[33] = 0.1e-6
constants[34] = 2
constants[35] = 1
constants[36] = (-constants[16]*(power(constants[5], constants[17])))/(power(constants[18], constants[17])+power(constants[5], constants[17]))
constants[37] = ((power(constants[5], constants[21]))/(power(constants[22], constants[21])+power(constants[5], constants[21])))*1.00000
constants[38] = ((constants[8]*constants[10])/(constants[34]*constants[9]))*log(constants[12]/constants[5])
constants[39] = constants[29]/4.00000
constants[40] = constants[28]
constants[42] = constants[0]
constants[41] = constants[37]
states[1] = constants[23]
states[2] = constants[24]
states[3] = constants[25]
states[4] = constants[26]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[0] = constants[42]
algebraic[3] = states[1]+states[2]+states[3]+states[4]
rates[1] = (-constants[37]*states[1])/algebraic[3]+(constants[28]*states[2])/algebraic[3]+(constants[27]*states[3])/algebraic[3]
rates[2] = ((constants[39]*states[4])/algebraic[3]+(constants[37]*states[1])/algebraic[3])-((constants[28]+constants[29])*states[2])/algebraic[3]
rates[3] = (constants[40]*states[4])/algebraic[3]-((constants[41]+constants[27])*states[3])/algebraic[3]
rates[4] = ((constants[29]*states[2])/algebraic[3]+(constants[41]*states[3])/algebraic[3])-((constants[39]+constants[40])*states[4])/algebraic[3]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[3] = states[1]+states[2]+states[3]+states[4]
algebraic[0] = states[4]+states[3]
algebraic[1] = states[4]+states[2]
algebraic[2] = custom_piecewise([less(voi , constants[1]), constants[2] , greater_equal(voi , constants[1]) & less(voi , constants[3]+constants[1]), constants[4] , True, constants[2]])
algebraic[4] = ((constants[8]*constants[10])/(constants[35]*constants[9]))*log(constants[11]/states[0])
algebraic[5] = 1.00000/(1.00000+exp((constants[14]-algebraic[2])/constants[7]))
algebraic[6] = constants[15]*algebraic[5]*(algebraic[2]-constants[38])
algebraic[7] = 3.00000*algebraic[4]-2.00000*constants[38]
algebraic[8] = -algebraic[6]/(2.00000*constants[13]*constants[9])
algebraic[9] = ((constants[20]*constants[5])/(constants[5]+constants[19]))*(algebraic[2]-algebraic[7])
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)