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 = 29
sizeStates = 9
sizeConstants = 46
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "t in component main (second)"
legend_constants[0] = "RT in component main (J_per_mol)"
legend_constants[1] = "F in component main (C_per_mol)"
legend_states[0] = "q_ac_W in component main (litre)"
legend_states[1] = "q_vc_W in component main (litre)"
legend_states[2] = "q_gi_W in component main (litre)"
legend_states[3] = "q_pt_W in component main (litre)"
legend_constants[2] = "q_giEpi_W in component main (litre)"
legend_constants[3] = "q_ptEpi_W in component main (litre)"
legend_algebraic[0] = "q_tot_W in component main (litre)"
legend_states[4] = "q_vc_Na in component main (mole)"
legend_states[5] = "q_gi_Na in component main (mole)"
legend_states[6] = "q_pt_Na in component main (mole)"
legend_states[7] = "q_giEpi_Na in component main (mole)"
legend_states[8] = "q_ptEpi_Na in component main (mole)"
legend_constants[4] = "q_vc_K in component main (mole)"
legend_constants[5] = "q_giEpi_K in component main (mole)"
legend_constants[6] = "q_ptEpi_K in component main (mole)"
legend_algebraic[1] = "q_tot_Na in component main (mole)"
legend_algebraic[2] = "c_vc_Na in component main (mol_per_L)"
legend_algebraic[13] = "c_gi_Na in component main (mol_per_L)"
legend_algebraic[18] = "c_pt_Na in component main (mol_per_L)"
legend_algebraic[3] = "c_giEpi_Na in component main (mol_per_L)"
legend_algebraic[4] = "c_ptEpi_Na in component main (mol_per_L)"
legend_algebraic[14] = "C_vc_Na in component main (mM)"
legend_algebraic[19] = "C_gi_Na in component main (mM)"
legend_algebraic[22] = "C_pt_Na in component main (mM)"
legend_algebraic[15] = "C_giEpi_Na in component main (mM)"
legend_algebraic[16] = "C_ptEpi_Na in component main (mM)"
legend_constants[7] = "v_lv_W in component main (L_per_s)"
legend_constants[8] = "v_in_W_base in component main (L_per_s)"
legend_algebraic[5] = "v_in_W in component main (L_per_s)"
legend_constants[42] = "v_out1_W in component main (L_per_s)"
legend_constants[43] = "v_out2_W in component main (L_per_s)"
legend_algebraic[23] = "v_gl_W in component main (L_per_s)"
legend_algebraic[26] = "v_gi_W in component main (L_per_s)"
legend_algebraic[28] = "v_pt_W in component main (L_per_s)"
legend_algebraic[20] = "v_cc_W in component main (L_per_s)"
legend_constants[9] = "v_in_Na_base in component main (mol_per_s)"
legend_algebraic[6] = "v_in_Na in component main (mol_per_s)"
legend_constants[44] = "v_out1_Na in component main (mol_per_s)"
legend_constants[45] = "v_out2_Na in component main (mol_per_s)"
legend_algebraic[7] = "v_gl_Na in component main (mol_per_s)"
legend_algebraic[8] = "v_gi_Na in component main (mol_per_s)"
legend_algebraic[9] = "v_pt_Na in component main (mol_per_s)"
legend_algebraic[10] = "v_giEpi_NKE in component main (mol_per_s)"
legend_algebraic[11] = "v_ptEpi_NKE in component main (mol_per_s)"
legend_algebraic[12] = "u_vc_W in component main (kPa)"
legend_algebraic[17] = "u_ac_W in component main (kPa)"
legend_algebraic[21] = "u_pt_W in component main (kPa)"
legend_algebraic[25] = "u_vc_osmotic in component main (kPa)"
legend_algebraic[24] = "u_gi_osmotic in component main (kPa)"
legend_algebraic[27] = "u_pt_osmotic in component main (kPa)"
legend_constants[10] = "u_giEpi_e in component main (J_per_C)"
legend_constants[11] = "u_ptEpi_e in component main (J_per_C)"
legend_constants[12] = "k_gi_W in component main (L_per_s_per_kPa)"
legend_constants[13] = "k_pt_W in component main (L_per_s_per_kPa)"
legend_constants[14] = "k_gl_W in component main (L_per_s_per_kPa)"
legend_constants[15] = "k_cc_W in component main (L_per_s_per_kPa)"
legend_constants[16] = "kK_gi_Na in component main (per_s)"
legend_constants[17] = "kK_pt_Na in component main (per_s)"
legend_constants[18] = "kK_gl_Na in component main (per_s)"
legend_constants[19] = "k_giEpi_NKE in component main (mol_per_s)"
legend_constants[20] = "k_ptEpi_NKE in component main (mol_per_s)"
legend_constants[21] = "K_Na in component main (L_per_mol)"
legend_constants[22] = "K_K in component main (L_per_mol)"
legend_constants[23] = "E_vc in component main (joule)"
legend_constants[24] = "E_ac in component main (joule)"
legend_constants[25] = "E_pt in component main (joule)"
legend_constants[26] = "U_ac_W in component main (litre)"
legend_constants[27] = "U_vc_W in component main (litre)"
legend_constants[28] = "U_pt_W in component main (litre)"
legend_constants[29] = "L_ac_W in component main (litre)"
legend_constants[30] = "L_vc_W in component main (litre)"
legend_constants[31] = "L_pt_W in component main (litre)"
legend_constants[32] = "water_intake in component main (L_per_s)"
legend_constants[33] = "water_intake_start in component main (second)"
legend_constants[34] = "water_intake_duration in component main (second)"
legend_constants[35] = "water_kidney_excretion in component main (dimensionless)"
legend_constants[36] = "water_gi_excretion in component main (dimensionless)"
legend_constants[37] = "Na_intake in component main (mol_per_s)"
legend_constants[38] = "Na_intake_start in component main (second)"
legend_constants[39] = "Na_intake_duration in component main (second)"
legend_constants[40] = "Na_gi_excretion in component main (dimensionless)"
legend_constants[41] = "Na_kidney_excretion in component main (dimensionless)"
legend_rates[2] = "d/dt q_gi_W in component main (litre)"
legend_rates[3] = "d/dt q_pt_W in component main (litre)"
legend_rates[1] = "d/dt q_vc_W in component main (litre)"
legend_rates[0] = "d/dt q_ac_W in component main (litre)"
legend_rates[5] = "d/dt q_gi_Na in component main (mole)"
legend_rates[7] = "d/dt q_giEpi_Na in component main (mole)"
legend_rates[6] = "d/dt q_pt_Na in component main (mole)"
legend_rates[8] = "d/dt q_ptEpi_Na in component main (mole)"
legend_rates[4] = "d/dt q_vc_Na in component main (mole)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 2.5e3
constants[1] = 0.965e5
states[0] = 1
states[1] = 2
states[2] = 1
states[3] = 0.1
constants[2] = 0.5
constants[3] = 0.5
states[4] = 0.84
states[5] = 0.1
states[6] = 0.01
states[7] = 0.012
states[8] = 0.012
constants[4] = 0.03
constants[5] = 0.012
constants[6] = 0.012
constants[7] = 0.1
constants[8] = 0
constants[9] = 1.16e-06
constants[10] = -0.040
constants[11] = -0.040
constants[12] = 1
constants[13] = 0
constants[14] = 1
constants[15] = 1
constants[16] = 1
constants[17] = 1
constants[18] = 1
constants[19] = 1e4
constants[20] = 1e5
constants[21] = 1
constants[22] = 1
constants[23] = 6e1
constants[24] = 6e1
constants[25] = 1
constants[26] = 0.5
constants[27] = 1.5
constants[28] = 0.1
constants[29] = 1.5
constants[30] = 2.5
constants[31] = 1
constants[32] = 0.01
constants[33] = 10
constants[34] = 5
constants[35] = 0.94
constants[36] = 0.06
constants[37] = 0.001
constants[38] = 10
constants[39] = 10
constants[40] = 0.07
constants[41] = 0.93
constants[42] = constants[36]*constants[8]
constants[43] = constants[35]*constants[8]
constants[44] = constants[40]*constants[9]
constants[45] = constants[41]*constants[9]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[3] = (constants[14]*((constants[24]*(states[0]-constants[26]))/(power(constants[29]-states[0], 2.00000))-(constants[25]*(states[3]-constants[28]))/(power(constants[31]-states[3], 2.00000)))-constants[0]*constants[13]*(states[4]/states[1]-states[6]/states[3]))-constants[43]
rates[1] = (constants[15]*((constants[24]*(states[0]-constants[26]))/(power(constants[29]-states[0], 2.00000))-(constants[23]*(states[1]-constants[27]))/(power(constants[30]-states[1], 2.00000)))+constants[0]*constants[12]*(states[4]/states[1]-states[5]/states[2])+constants[0]*constants[13]*(states[4]/states[1]-states[6]/states[3]))-constants[7]
rates[0] = ((constants[7]+(constants[15]*constants[23]*(states[1]-constants[27]))/(power(constants[30]-states[1], 2.00000)))-((constants[14]+constants[15])*constants[24]*(states[0]-constants[26]))/(power(constants[29]-states[0], 2.00000)))+(constants[14]*constants[25]*(states[3]-constants[28]))/(power(constants[31]-states[3], 2.00000))
rates[7] = constants[16]*(states[5]-states[7])-(3.00000*constants[19]*((power((constants[21]*states[7])/constants[2], 3.00000))*(power((constants[22]*constants[4])/states[1], 2.00000))-(power((constants[21]*states[4])/states[1], 3.00000))*(power((constants[22]*constants[5])/constants[2], 2.00000))*exp((2.00000*constants[1]*constants[10])/constants[0])))/((1.00000+power((constants[21]*states[7])/constants[2], 3.00000))*(1.00000+power((constants[21]*states[4])/states[1], 3.00000))*(1.00000+power((constants[22]*constants[4])/states[1], 2.00000))*(1.00000+power((constants[22]*constants[5])/constants[2], 2.00000)))
rates[6] = (constants[18]*(states[4]-states[6])-constants[17]*(states[6]-states[8]))-constants[45]
rates[8] = constants[17]*(states[6]-states[8])-(3.00000*constants[20]*((power((constants[21]*states[8])/constants[3], 3.00000))*(power((constants[22]*constants[4])/states[1], 2.00000))-(power((constants[21]*states[4])/states[1], 3.00000))*(power((constants[22]*constants[6])/constants[3], 2.00000))*exp((2.00000*constants[1]*constants[11])/constants[0])))/((1.00000+power((constants[21]*states[8])/constants[3], 3.00000))*(1.00000+power((constants[21]*states[4])/states[1], 3.00000))*(1.00000+power((constants[22]*constants[4])/states[1], 2.00000))*(1.00000+power((constants[22]*constants[6])/constants[3], 2.00000)))
rates[4] = ((3.00000*constants[19]*((power((constants[21]*states[7])/constants[2], 3.00000))*(power((constants[22]*constants[4])/states[1], 2.00000))-(power((constants[21]*states[4])/states[1], 3.00000))*(power((constants[22]*constants[5])/constants[2], 2.00000))*exp((2.00000*constants[1]*constants[10])/constants[0])))/((1.00000+power((constants[21]*states[7])/constants[2], 3.00000))*(1.00000+power((constants[21]*states[4])/states[1], 3.00000))*(1.00000+power((constants[22]*constants[4])/states[1], 2.00000))*(1.00000+power((constants[22]*constants[5])/constants[2], 2.00000)))+(3.00000*constants[20]*((power((constants[21]*states[8])/constants[3], 3.00000))*(power((constants[22]*constants[4])/states[1], 2.00000))-(power((constants[21]*states[4])/states[1], 3.00000))*(power((constants[22]*constants[6])/constants[3], 2.00000))*exp((2.00000*constants[1]*constants[11])/constants[0])))/((1.00000+power((constants[21]*states[8])/constants[3], 3.00000))*(1.00000+power((constants[21]*states[4])/states[1], 3.00000))*(1.00000+power((constants[22]*constants[4])/states[1], 2.00000))*(1.00000+power((constants[22]*constants[6])/constants[3], 2.00000))))-constants[18]*(states[4]-states[6])
algebraic[5] = custom_piecewise([greater(voi , constants[33]) & less(voi , constants[33]+constants[34]), constants[32] , True, 0.00000])
rates[2] = (algebraic[5]-constants[0]*constants[12]*(states[4]/states[1]-states[5]/states[2]))-constants[42]
algebraic[6] = custom_piecewise([greater(voi , constants[38]) & less(voi , constants[38]+constants[39]), constants[9]+constants[37] , True, constants[9]])
rates[5] = (algebraic[6]-constants[16]*(states[5]-states[7]))-constants[44]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[5] = custom_piecewise([greater(voi , constants[33]) & less(voi , constants[33]+constants[34]), constants[32] , True, 0.00000])
algebraic[6] = custom_piecewise([greater(voi , constants[38]) & less(voi , constants[38]+constants[39]), constants[9]+constants[37] , True, constants[9]])
algebraic[0] = states[0]+states[1]+states[2]+states[3]+constants[2]+constants[3]
algebraic[1] = states[4]+states[5]+states[6]+states[7]+states[8]
algebraic[2] = states[4]/states[1]
algebraic[3] = states[7]/constants[2]
algebraic[4] = states[8]/constants[3]
algebraic[7] = constants[18]*(states[4]-states[6])
algebraic[8] = constants[16]*(states[5]-states[7])
algebraic[9] = constants[17]*(states[6]-states[8])
algebraic[10] = (3.00000*constants[19]*((power((constants[21]*states[7])/constants[2], 3.00000))*(power((constants[22]*constants[4])/states[1], 2.00000))-(power((constants[21]*states[4])/states[1], 3.00000))*(power((constants[22]*constants[5])/constants[2], 2.00000))*exp((2.00000*constants[1]*constants[10])/constants[0])))/((1.00000+power((constants[21]*states[7])/constants[2], 3.00000))*(1.00000+power((constants[21]*states[4])/states[1], 3.00000))*(1.00000+power((constants[22]*constants[4])/states[1], 2.00000))*(1.00000+power((constants[22]*constants[5])/constants[2], 2.00000)))
algebraic[11] = (3.00000*constants[20]*((power((constants[21]*states[8])/constants[3], 3.00000))*(power((constants[22]*constants[4])/states[1], 2.00000))-(power((constants[21]*states[4])/states[1], 3.00000))*(power((constants[22]*constants[6])/constants[3], 2.00000))*exp((2.00000*constants[1]*constants[11])/constants[0])))/((1.00000+power((constants[21]*states[8])/constants[3], 3.00000))*(1.00000+power((constants[21]*states[4])/states[1], 3.00000))*(1.00000+power((constants[22]*constants[4])/states[1], 2.00000))*(1.00000+power((constants[22]*constants[6])/constants[3], 2.00000)))
algebraic[12] = (constants[23]*(states[1]-constants[27]))/(power(constants[30]-states[1], 2.00000))
algebraic[13] = states[5]/states[2]
algebraic[14] = 1000.00*algebraic[2]
algebraic[15] = 1000.00*algebraic[3]
algebraic[16] = 1000.00*algebraic[4]
algebraic[17] = (constants[24]*(states[0]-constants[26]))/(power(constants[29]-states[0], 2.00000))
algebraic[18] = states[6]/states[3]
algebraic[19] = 1000.00*algebraic[13]
algebraic[20] = constants[15]*(algebraic[17]-algebraic[12])
algebraic[21] = (constants[25]*(states[3]-constants[28]))/(power(constants[31]-states[3], 2.00000))
algebraic[22] = 1000.00*algebraic[18]
algebraic[23] = constants[14]*(algebraic[17]-algebraic[21])
algebraic[24] = constants[0]*algebraic[13]
algebraic[25] = constants[0]*algebraic[2]
algebraic[26] = constants[12]*(algebraic[25]-algebraic[24])
algebraic[27] = constants[0]*algebraic[18]
algebraic[28] = constants[13]*(algebraic[25]-algebraic[27])
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)