Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 21
sizeStates = 6
sizeConstants = 40
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] = "R_mt in component heart_parameters (kPa_second_per_liter)"
legend_constants[1] = "R_av in component heart_parameters (kPa_second_per_liter)"
legend_constants[2] = "R_tc in component heart_parameters (kPa_second_per_liter)"
legend_constants[3] = "R_pv in component heart_parameters (kPa_second_per_liter)"
legend_constants[4] = "R_pul in component heart_parameters (kPa_second_per_liter)"
legend_constants[5] = "R_sys in component heart_parameters (kPa_second_per_liter)"
legend_constants[6] = "HR in component heart_parameters (dimensionless)"
legend_constants[7] = "V_tot in component heart_parameters (liter)"
legend_constants[8] = "P_pl in component heart_parameters (kPa)"
legend_algebraic[1] = "e_t in component driver_function (dimensionless)"
legend_constants[9] = "A in component driver_function (dimensionless)"
legend_constants[10] = "B in component driver_function (dimensionless)"
legend_constants[11] = "C in component driver_function (dimensionless)"
legend_algebraic[0] = "tau in component driver_function (second)"
legend_constants[12] = "period in component driver_function (dimensionless)"
legend_algebraic[2] = "V_pcd in component pericardium (liter)"
legend_algebraic[3] = "P_pcd in component pericardium (kPa)"
legend_algebraic[4] = "P_peri in component pericardium (kPa)"
legend_states[0] = "V_lv in component left_ventricle (liter)"
legend_states[1] = "V_rv in component right_ventricle (liter)"
legend_constants[13] = "P_0_pcd in component pericardium (kPa)"
legend_constants[14] = "V_0_pcd in component pericardium (liter)"
legend_constants[15] = "lambda_pcd in component pericardium (per_liter)"
legend_algebraic[9] = "V_lvf in component left_ventricle (liter)"
legend_algebraic[10] = "P_lvf in component left_ventricle (kPa)"
legend_algebraic[18] = "P_lv in component left_ventricle (kPa)"
legend_algebraic[11] = "V_spt in component septum (liter)"
legend_algebraic[12] = "P_es_lvf in component lvf_calculator (kPa)"
legend_algebraic[13] = "P_ed_lvf in component lvf_calculator (kPa)"
legend_algebraic[6] = "P_pu in component pulmonary_vein (kPa)"
legend_algebraic[7] = "P_ao in component aorta (kPa)"
legend_constants[16] = "E_es_lvf in component lvf_calculator (kPa_per_liter)"
legend_constants[17] = "V_d_lvf in component lvf_calculator (liter)"
legend_constants[18] = "P_0_lvf in component lvf_calculator (kPa)"
legend_constants[19] = "lambda_lvf in component lvf_calculator (per_liter)"
legend_constants[20] = "V_0_lvf in component lvf_calculator (liter)"
legend_algebraic[14] = "V_rvf in component right_ventricle (liter)"
legend_algebraic[15] = "P_rvf in component right_ventricle (kPa)"
legend_algebraic[19] = "P_rv in component right_ventricle (kPa)"
legend_algebraic[16] = "P_es_rvf in component rvf_calculator (kPa)"
legend_algebraic[17] = "P_ed_rvf in component rvf_calculator (kPa)"
legend_algebraic[5] = "P_pa in component pulmonary_artery (kPa)"
legend_algebraic[8] = "P_vc in component vena_cava (kPa)"
legend_constants[21] = "E_es_rvf in component rvf_calculator (kPa_per_liter)"
legend_constants[22] = "V_d_rvf in component rvf_calculator (liter)"
legend_constants[23] = "P_0_rvf in component rvf_calculator (kPa)"
legend_constants[24] = "lambda_rvf in component rvf_calculator (per_liter)"
legend_constants[25] = "V_0_rvf in component rvf_calculator (liter)"
legend_algebraic[20] = "P_sept in component septum (kPa)"
legend_constants[26] = "E_es_spt in component septum (kPa_per_liter)"
legend_constants[27] = "V_d_spt in component septum (liter)"
legend_constants[28] = "P_0_spt in component septum (kPa)"
legend_constants[29] = "lambda_spt in component septum (per_liter)"
legend_constants[30] = "V_0_spt in component septum (liter)"
legend_constants[31] = "one in component septum (dimensionless)"
legend_constants[32] = "E_es_pa in component pulmonary_artery (kPa_per_liter)"
legend_states[2] = "V_pa in component pulmonary_artery (liter)"
legend_constants[33] = "V_d_pa in component pulmonary_artery (liter)"
legend_constants[34] = "E_es_pu in component pulmonary_vein (kPa_per_liter)"
legend_states[3] = "V_pu in component pulmonary_vein (liter)"
legend_constants[35] = "V_d_pu in component pulmonary_vein (liter)"
legend_constants[36] = "E_es_ao in component aorta (kPa_per_liter)"
legend_states[4] = "V_ao in component aorta (liter)"
legend_constants[37] = "V_d_ao in component aorta (liter)"
legend_constants[38] = "E_es_vc in component vena_cava (kPa_per_liter)"
legend_states[5] = "V_vc in component vena_cava (liter)"
legend_constants[39] = "V_d_vc in component vena_cava (liter)"
legend_rates[0] = "d/dt V_lv in component left_ventricle (liter)"
legend_rates[1] = "d/dt V_rv in component right_ventricle (liter)"
legend_rates[2] = "d/dt V_pa in component pulmonary_artery (liter)"
legend_rates[3] = "d/dt V_pu in component pulmonary_vein (liter)"
legend_rates[4] = "d/dt V_ao in component aorta (liter)"
legend_rates[5] = "d/dt V_vc in component vena_cava (liter)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 0.06
constants[1] = 1.4
constants[2] = 0.18
constants[3] = 0.48
constants[4] = 19
constants[5] = 140
constants[6] = 80
constants[7] = 5.5
constants[8] = -0.533289474
constants[9] = 1
constants[10] = 80
constants[11] = 0.27
constants[12] = 0.405
states[0] = 0.005
states[1] = 0.005
constants[13] = 0.067
constants[14] = 0.2
constants[15] = 30
constants[16] = 454
constants[17] = 0.005
constants[18] = 0.17
constants[19] = 15
constants[20] = 0.005
constants[21] = 87
constants[22] = 0.005
constants[23] = 0.16
constants[24] = 15
constants[25] = 0.005
constants[26] = 6500
constants[27] = 0.002
constants[28] = 0.148
constants[29] = 435
constants[30] = 0.002
constants[31] = 1
constants[32] = 45
states[2] = 0.16
constants[33] = 0.16
constants[34] = 0.8
states[3] = 0.2
constants[35] = 0.2
constants[36] = 94
states[4] = 0.8
constants[37] = 0.8
constants[38] = 1.5
states[5] = 2.83
constants[39] = 2.83
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[2] = states[0]+states[1]
algebraic[3] = constants[13]*(exp(constants[15]*(algebraic[2]-constants[14]))-1.00000)
algebraic[4] = algebraic[3]+constants[8]
algebraic[0] = voi % constants[12]
algebraic[1] = constants[9]*exp(-constants[10]*(power((algebraic[0]*constants[6])/60.0000-constants[11], 2.00000)))
rootfind_0(voi, constants, rates, states, algebraic)
algebraic[18] = algebraic[10]+algebraic[4]
algebraic[6] = constants[34]*(states[3]-constants[35])
algebraic[7] = constants[36]*(states[4]-constants[37])
rates[0] = custom_piecewise([less(algebraic[6]-algebraic[18] , 0.00000) & less(algebraic[18]-algebraic[7] , 0.00000), 0.00000 , less(algebraic[6]-algebraic[18] , 0.00000), -(algebraic[18]-algebraic[7])/constants[1] , less(algebraic[18]-algebraic[7] , 0.00000), (algebraic[6]-algebraic[18])/constants[0] , True, (algebraic[6]-algebraic[18])/constants[0]-(algebraic[18]-algebraic[7])/constants[1]])
algebraic[5] = constants[32]*(states[2]-constants[33])
rates[3] = custom_piecewise([less(algebraic[5]-algebraic[6] , 0.00000) & less(algebraic[6]-algebraic[18] , 0.00000), 0.00000 , less(algebraic[5]-algebraic[6] , 0.00000), -(algebraic[6]-algebraic[18])/constants[0] , less(algebraic[6]-algebraic[18] , 0.00000), (algebraic[5]-algebraic[6])/constants[4] , True, (algebraic[5]-algebraic[6])/constants[4]-(algebraic[6]-algebraic[18])/constants[0]])
algebraic[8] = constants[38]*(states[5]-constants[39])
rates[4] = custom_piecewise([less(algebraic[18]-algebraic[7] , 0.00000) & less(algebraic[7]-algebraic[8] , 0.00000), 0.00000 , less(algebraic[18]-algebraic[7] , 0.00000), -(algebraic[7]-algebraic[8])/constants[5] , less(algebraic[7]-algebraic[8] , 0.00000), (algebraic[18]-algebraic[7])/constants[1] , True, (algebraic[18]-algebraic[7])/constants[1]-(algebraic[7]-algebraic[8])/constants[5]])
algebraic[19] = algebraic[15]+algebraic[4]
rates[1] = custom_piecewise([less(algebraic[8]-algebraic[19] , 0.00000) & less(algebraic[19]-algebraic[5] , 0.00000), 0.00000 , less(algebraic[8]-algebraic[19] , 0.00000), -(algebraic[19]-algebraic[5])/constants[3] , less(algebraic[19]-algebraic[5] , 0.00000), (algebraic[8]-algebraic[19])/constants[2] , True, (algebraic[8]-algebraic[19])/constants[2]-(algebraic[19]-algebraic[5])/constants[3]])
rates[2] = custom_piecewise([less(algebraic[19]-algebraic[5] , 0.00000) & less(algebraic[5]-algebraic[6] , 0.00000), 0.00000 , less(algebraic[19]-algebraic[5] , 0.00000), -(algebraic[5]-algebraic[6])/constants[4] , less(algebraic[5]-algebraic[6] , 0.00000), (algebraic[19]-algebraic[5])/constants[3] , True, (algebraic[19]-algebraic[5])/constants[3]-(algebraic[5]-algebraic[6])/constants[4]])
rates[5] = custom_piecewise([less(algebraic[7]-algebraic[8] , 0.00000) & less(algebraic[8]-algebraic[19] , 0.00000), 0.00000 , less(algebraic[7]-algebraic[8] , 0.00000), -(algebraic[8]-algebraic[19])/constants[2] , less(algebraic[8]-algebraic[19] , 0.00000), (algebraic[7]-algebraic[8])/constants[5] , True, (algebraic[7]-algebraic[8])/constants[5]-(algebraic[8]-algebraic[19])/constants[2]])
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[2] = states[0]+states[1]
algebraic[3] = constants[13]*(exp(constants[15]*(algebraic[2]-constants[14]))-1.00000)
algebraic[4] = algebraic[3]+constants[8]
algebraic[0] = voi % constants[12]
algebraic[1] = constants[9]*exp(-constants[10]*(power((algebraic[0]*constants[6])/60.0000-constants[11], 2.00000)))
algebraic[18] = algebraic[10]+algebraic[4]
algebraic[6] = constants[34]*(states[3]-constants[35])
algebraic[7] = constants[36]*(states[4]-constants[37])
algebraic[5] = constants[32]*(states[2]-constants[33])
algebraic[8] = constants[38]*(states[5]-constants[39])
algebraic[19] = algebraic[15]+algebraic[4]
algebraic[20] = algebraic[18]-algebraic[19]
return algebraic
initialGuess0 = None
def rootfind_0(voi, constants, rates, states, algebraic):
"""Calculate values of algebraic variables for DAE"""
from scipy.optimize import fsolve
global initialGuess0
if initialGuess0 is None: initialGuess0 = ones(9)*0.1
if not iterable(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6)
initialGuess0 = soln
algebraic[9] = soln[0]
algebraic[10] = soln[1]
algebraic[11] = soln[2]
algebraic[12] = soln[3]
algebraic[13] = soln[4]
algebraic[14] = soln[5]
algebraic[15] = soln[6]
algebraic[16] = soln[7]
algebraic[17] = soln[8]
else:
for (i,t) in enumerate(voi):
soln = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, rates[:i], states[:,i]), xtol=1E-6)
initialGuess0 = soln
algebraic[9][i] = soln[0]
algebraic[10][i] = soln[1]
algebraic[11][i] = soln[2]
algebraic[12][i] = soln[3]
algebraic[13][i] = soln[4]
algebraic[14][i] = soln[5]
algebraic[15][i] = soln[6]
algebraic[16][i] = soln[7]
algebraic[17][i] = soln[8]
def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states):
resid = array([0.0] * 9)
algebraic[9] = algebraicCandidate[0]
algebraic[10] = algebraicCandidate[1]
algebraic[11] = algebraicCandidate[2]
algebraic[12] = algebraicCandidate[3]
algebraic[13] = algebraicCandidate[4]
algebraic[14] = algebraicCandidate[5]
algebraic[15] = algebraicCandidate[6]
algebraic[16] = algebraicCandidate[7]
algebraic[17] = algebraicCandidate[8]
resid[0] = (algebraic[9]-(states[0]-algebraic[11]))
resid[1] = (algebraic[10]-(algebraic[1]*algebraic[12]+(1.00000-algebraic[1])*algebraic[13]))
resid[2] = (algebraic[12]-constants[16]*(algebraic[9]-constants[17]))
resid[3] = (algebraic[13]-constants[18]*(exp(constants[19]*(algebraic[9]-constants[20]))-1.00000))
resid[4] = (algebraic[14]-(states[1]+algebraic[11]))
resid[5] = (algebraic[15]-(algebraic[1]*algebraic[16]+(1.00000-algebraic[1])*algebraic[17]))
resid[6] = (algebraic[16]-constants[21]*(algebraic[14]-constants[22]))
resid[7] = (algebraic[17]-constants[23]*(exp(constants[24]*(algebraic[14]-constants[25]))-1.00000))
resid[8] = (algebraic[10]-((algebraic[1]*constants[26]*(algebraic[11]-constants[27])+(constants[31]-algebraic[1])*constants[28]*(exp(constants[29]*(algebraic[11]-constants[30]))-constants[31]))-algebraic[15]))
return resid
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)