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 = 31
sizeStates = 6
sizeConstants = 23
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "time in component environment (second)"
legend_constants[0] = "C_m in component environment (fF)"
legend_states[0] = "q_Ca_o in component environment (fmol)"
legend_states[1] = "q_Ca_i in component environment (fmol)"
legend_states[2] = "q_s00_TCC in component environment (fmol)"
legend_states[3] = "q_s10_TCC in component environment (fmol)"
legend_states[4] = "q_s01_TCC in component environment (fmol)"
legend_states[5] = "q_s11_TCC in component environment (fmol)"
legend_algebraic[2] = "q_mem in component environment (fC)"
legend_algebraic[1] = "V_mem in component environment (volt)"
legend_constants[1] = "R in component environment (J_per_K_per_mol)"
legend_constants[2] = "T in component environment (kelvin)"
legend_constants[3] = "F in component environment (C_per_mol)"
legend_algebraic[22] = "v_TCC in component TCC (fmol_per_sec)"
legend_algebraic[28] = "I_mem_TCC in component TCC (fA)"
legend_constants[22] = "I_stim in component environment (fA)"
legend_constants[4] = "stimPeriod in component environment (second)"
legend_constants[5] = "stimDuration in component environment (second)"
legend_algebraic[0] = "tPeriod in component environment (second)"
legend_constants[6] = "kappa_TCC in component TCC_parameters (fmol_per_sec)"
legend_constants[7] = "kappa_R1_TCC in component TCC_parameters (fmol_per_sec)"
legend_constants[8] = "kappa_R2_TCC in component TCC_parameters (fmol_per_sec)"
legend_constants[9] = "kappa_R3_TCC in component TCC_parameters (fmol_per_sec)"
legend_constants[10] = "kappa_R4_TCC in component TCC_parameters (fmol_per_sec)"
legend_constants[11] = "K_Ca_i in component TCC_parameters (per_fmol)"
legend_constants[12] = "K_Ca_o in component TCC_parameters (per_fmol)"
legend_constants[13] = "K_S00_TCC in component TCC_parameters (per_fmol)"
legend_constants[14] = "K_S10_TCC in component TCC_parameters (per_fmol)"
legend_constants[15] = "K_S01_TCC in component TCC_parameters (per_fmol)"
legend_constants[16] = "K_S11_TCC in component TCC_parameters (per_fmol)"
legend_constants[17] = "zCa in component TCC_parameters (dimensionless)"
legend_constants[18] = "z_df in component TCC_parameters (dimensionless)"
legend_constants[19] = "z_ff in component TCC_parameters (dimensionless)"
legend_constants[20] = "z_dr in component TCC_parameters (dimensionless)"
legend_constants[21] = "z_fr in component TCC_parameters (dimensionless)"
legend_algebraic[3] = "u_Ca_i in component TCC (J_per_mol)"
legend_algebraic[4] = "u_Ca_o in component TCC (J_per_mol)"
legend_algebraic[5] = "V_mem in component TCC (J_per_C)"
legend_algebraic[6] = "Am_TCC in component TCC (J_per_mol)"
legend_algebraic[20] = "Af_Ca in component TCC (J_per_mol)"
legend_algebraic[21] = "Ar_Ca in component TCC (J_per_mol)"
legend_algebraic[18] = "v_s00_TCC in component TCC (fmol_per_sec)"
legend_algebraic[29] = "v_s10_TCC in component TCC (fmol_per_sec)"
legend_algebraic[26] = "v_s01_TCC in component TCC (fmol_per_sec)"
legend_algebraic[30] = "v_s11_TCC in component TCC (fmol_per_sec)"
legend_algebraic[13] = "v_R1_TCC in component TCC (fmol_per_sec)"
legend_algebraic[25] = "v_R2_TCC in component TCC (fmol_per_sec)"
legend_algebraic[17] = "v_R3_TCC in component TCC (fmol_per_sec)"
legend_algebraic[27] = "v_R4_TCC in component TCC (fmol_per_sec)"
legend_algebraic[7] = "mu_s00_TCC in component TCC (J_per_mol)"
legend_algebraic[10] = "mu_s10_TCC in component TCC (J_per_mol)"
legend_algebraic[14] = "mu_s01_TCC in component TCC (J_per_mol)"
legend_algebraic[19] = "mu_s11_TCC in component TCC (J_per_mol)"
legend_algebraic[8] = "Af_R1_TCC in component TCC (J_per_mol)"
legend_algebraic[11] = "Ar_R1_TCC in component TCC (J_per_mol)"
legend_algebraic[15] = "Af_R2_TCC in component TCC (J_per_mol)"
legend_algebraic[23] = "Ar_R2_TCC in component TCC (J_per_mol)"
legend_algebraic[9] = "Af_R3_TCC in component TCC (J_per_mol)"
legend_algebraic[16] = "Ar_R3_TCC in component TCC (J_per_mol)"
legend_algebraic[12] = "Af_R4_TCC in component TCC (J_per_mol)"
legend_algebraic[24] = "Ar_R4_TCC in component TCC (J_per_mol)"
legend_rates[1] = "d/dt q_Ca_i in component environment (fmol)"
legend_rates[0] = "d/dt q_Ca_o in component environment (fmol)"
legend_rates[2] = "d/dt q_s00_TCC in component environment (fmol)"
legend_rates[3] = "d/dt q_s10_TCC in component environment (fmol)"
legend_rates[4] = "d/dt q_s01_TCC in component environment (fmol)"
legend_rates[5] = "d/dt q_s11_TCC in component environment (fmol)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 60000
states[0] = 0.04653
states[1] = 0.000001551
states[2] = 3.653271338425772e-07
states[3] = 1e-16
states[4] = 1e-16
states[5] = 1e-16
constants[1] = 8.31
constants[2] = 310
constants[3] = 96500
constants[4] = 1
constants[5] = 0.0001
constants[6] = 11414.6
constants[7] = 1266.14
constants[8] = 4.33488
constants[9] = 1.34962
constants[10] = 7.44777
constants[11] = 28.7976
constants[12] = 211.182
constants[13] = 2.10659
constants[14] = 0.381738
constants[15] = 615.294
constants[16] = 111.498
constants[17] = 2
constants[18] = 0.876568910405296
constants[19] = -0.576510778245838
constants[20] = -0.872117216889333
constants[21] = 1.73582739545622
constants[22] = 0.00000
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[1] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 0.400000), -0.0900000 , greater(voi , 1.10000) & less(voi , 2.10000), -0.0600000 , greater(voi , 2.20000) & less(voi , 3.10000), 0.0400000 , greater(voi , 3.50000), -0.0900000 , True, -0.0800000])
algebraic[2] = algebraic[1]*constants[0]
algebraic[5] = algebraic[2]/constants[0]
algebraic[7] = constants[1]*constants[2]*log(constants[13]*states[2])
algebraic[8] = algebraic[7]+constants[18]*constants[3]*algebraic[5]
algebraic[10] = constants[1]*constants[2]*log(constants[14]*states[3])
algebraic[11] = algebraic[10]+constants[20]*constants[3]*algebraic[5]
algebraic[13] = constants[7]*(exp(algebraic[8]/(constants[1]*constants[2]))-exp(algebraic[11]/(constants[1]*constants[2])))
algebraic[9] = algebraic[7]+constants[19]*constants[3]*algebraic[5]
algebraic[14] = constants[1]*constants[2]*log(constants[15]*states[4])
algebraic[16] = algebraic[14]+constants[21]*constants[3]*algebraic[5]
algebraic[17] = constants[9]*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[16]/(constants[1]*constants[2])))
algebraic[18] = -algebraic[13]-algebraic[17]
rates[2] = algebraic[18]
algebraic[6] = constants[17]*constants[3]*algebraic[5]
algebraic[3] = constants[1]*constants[2]*log(constants[11]*states[1])
algebraic[19] = constants[1]*constants[2]*log(constants[16]*states[5])
algebraic[20] = algebraic[19]+algebraic[3]+algebraic[6]
algebraic[4] = constants[1]*constants[2]*log(constants[12]*states[0])
algebraic[21] = algebraic[19]+algebraic[4]
algebraic[22] = custom_piecewise([equal(algebraic[6] , 0.00000), constants[6]*(exp(algebraic[20]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2]))) , True, (((constants[6]*algebraic[6])/(constants[1]*constants[2]))/(exp(algebraic[6]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[20]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2])))])
rates[1] = -algebraic[22]
rates[0] = algebraic[22]
algebraic[15] = algebraic[14]+constants[18]*constants[3]*algebraic[5]
algebraic[23] = algebraic[19]+constants[20]*constants[3]*algebraic[5]
algebraic[25] = constants[8]*(exp(algebraic[15]/(constants[1]*constants[2]))-exp(algebraic[23]/(constants[1]*constants[2])))
algebraic[26] = algebraic[17]-algebraic[25]
rates[4] = algebraic[26]
algebraic[12] = algebraic[10]+constants[19]*constants[3]*algebraic[5]
algebraic[24] = algebraic[19]+constants[21]*constants[3]*algebraic[5]
algebraic[27] = constants[10]*(exp(algebraic[12]/(constants[1]*constants[2]))-exp(algebraic[24]/(constants[1]*constants[2])))
algebraic[29] = algebraic[13]-algebraic[27]
rates[3] = algebraic[29]
algebraic[30] = algebraic[25]+algebraic[27]
rates[5] = algebraic[30]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 0.400000), -0.0900000 , greater(voi , 1.10000) & less(voi , 2.10000), -0.0600000 , greater(voi , 2.20000) & less(voi , 3.10000), 0.0400000 , greater(voi , 3.50000), -0.0900000 , True, -0.0800000])
algebraic[2] = algebraic[1]*constants[0]
algebraic[5] = algebraic[2]/constants[0]
algebraic[7] = constants[1]*constants[2]*log(constants[13]*states[2])
algebraic[8] = algebraic[7]+constants[18]*constants[3]*algebraic[5]
algebraic[10] = constants[1]*constants[2]*log(constants[14]*states[3])
algebraic[11] = algebraic[10]+constants[20]*constants[3]*algebraic[5]
algebraic[13] = constants[7]*(exp(algebraic[8]/(constants[1]*constants[2]))-exp(algebraic[11]/(constants[1]*constants[2])))
algebraic[9] = algebraic[7]+constants[19]*constants[3]*algebraic[5]
algebraic[14] = constants[1]*constants[2]*log(constants[15]*states[4])
algebraic[16] = algebraic[14]+constants[21]*constants[3]*algebraic[5]
algebraic[17] = constants[9]*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[16]/(constants[1]*constants[2])))
algebraic[18] = -algebraic[13]-algebraic[17]
algebraic[6] = constants[17]*constants[3]*algebraic[5]
algebraic[3] = constants[1]*constants[2]*log(constants[11]*states[1])
algebraic[19] = constants[1]*constants[2]*log(constants[16]*states[5])
algebraic[20] = algebraic[19]+algebraic[3]+algebraic[6]
algebraic[4] = constants[1]*constants[2]*log(constants[12]*states[0])
algebraic[21] = algebraic[19]+algebraic[4]
algebraic[22] = custom_piecewise([equal(algebraic[6] , 0.00000), constants[6]*(exp(algebraic[20]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2]))) , True, (((constants[6]*algebraic[6])/(constants[1]*constants[2]))/(exp(algebraic[6]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[20]/(constants[1]*constants[2]))-exp(algebraic[21]/(constants[1]*constants[2])))])
algebraic[15] = algebraic[14]+constants[18]*constants[3]*algebraic[5]
algebraic[23] = algebraic[19]+constants[20]*constants[3]*algebraic[5]
algebraic[25] = constants[8]*(exp(algebraic[15]/(constants[1]*constants[2]))-exp(algebraic[23]/(constants[1]*constants[2])))
algebraic[26] = algebraic[17]-algebraic[25]
algebraic[12] = algebraic[10]+constants[19]*constants[3]*algebraic[5]
algebraic[24] = algebraic[19]+constants[21]*constants[3]*algebraic[5]
algebraic[27] = constants[10]*(exp(algebraic[12]/(constants[1]*constants[2]))-exp(algebraic[24]/(constants[1]*constants[2])))
algebraic[29] = algebraic[13]-algebraic[27]
algebraic[30] = algebraic[25]+algebraic[27]
algebraic[0] = voi-floor(voi/constants[4])*constants[4]
algebraic[28] = constants[3]*(-constants[17]*algebraic[22]+algebraic[13]*(constants[20]-constants[18])+algebraic[25]*(constants[20]-constants[18])+algebraic[17]*(constants[21]-constants[19])+algebraic[27]*(constants[21]-constants[19]))
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)