Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 8
sizeStates = 6
sizeConstants = 21
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 (min)"
legend_constants[0] = "Vp in component environment (l)"
legend_constants[1] = "Vi in component environment (l)"
legend_constants[2] = "Vg in component environment (l)"
legend_constants[3] = "E in component environment (l_per_min)"
legend_states[0] = "Ip in component plasma_insulin (mU)"
legend_algebraic[0] = "Ip_conc in component plasma_insulin (mU_per_l)"
legend_constants[4] = "tp in component plasma_insulin (min)"
legend_algebraic[1] = "f1_G in component plasma_insulin (mU_per_min)"
legend_constants[5] = "Rm in component plasma_insulin (mU_per_min)"
legend_constants[6] = "C1 in component plasma_insulin (mg_per_l)"
legend_constants[7] = "a1 in component plasma_insulin (mg_per_l)"
legend_states[1] = "Ii in component intercellular_insulin (mU)"
legend_states[2] = "G in component glucose (mg)"
legend_algebraic[2] = "Ii_conc in component intercellular_insulin (mU_per_l)"
legend_constants[8] = "ti in component intercellular_insulin (min)"
legend_algebraic[3] = "G_conc in component glucose (mg_per_dl)"
legend_constants[9] = "Gin in component glucose (mg_per_min)"
legend_algebraic[4] = "f2_G in component glucose (mg_per_min)"
legend_algebraic[5] = "f3_G in component glucose (dimensionless)"
legend_algebraic[6] = "f4_Ii in component glucose (mg_per_min)"
legend_algebraic[7] = "f5_x3 in component glucose (mg_per_min)"
legend_constants[10] = "C2 in component glucose (mg_per_l)"
legend_constants[11] = "C3 in component glucose (mg_per_l)"
legend_constants[12] = "C4 in component glucose (mU_per_l)"
legend_constants[13] = "C5 in component glucose (mU_per_l)"
legend_constants[14] = "U0 in component glucose (mg_per_min)"
legend_constants[15] = "Um in component glucose (mg_per_min)"
legend_constants[16] = "Ub in component glucose (mg_per_min)"
legend_constants[17] = "beta in component glucose (dimensionless)"
legend_constants[18] = "Rg in component glucose (mg_per_min)"
legend_constants[19] = "alpha in component glucose (l_per_mU)"
legend_states[3] = "x3 in component delay (min)"
legend_constants[20] = "td in component delay (min)"
legend_states[4] = "x1 in component delay (min)"
legend_states[5] = "x2 in component delay (min)"
legend_rates[0] = "d/dt Ip in component plasma_insulin (mU)"
legend_rates[1] = "d/dt Ii in component intercellular_insulin (mU)"
legend_rates[2] = "d/dt G in component glucose (mg)"
legend_rates[4] = "d/dt x1 in component delay (min)"
legend_rates[5] = "d/dt x2 in component delay (min)"
legend_rates[3] = "d/dt x3 in component delay (min)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 3
constants[1] = 11
constants[2] = 10
constants[3] = 0.2
states[0] = 93.36441699
constants[4] = 6
constants[5] = 210
constants[6] = 2000
constants[7] = 300
states[1] = 243.2865183
states[2] = 12342.61665
constants[8] = 100
constants[9] = 216
constants[10] = 144
constants[11] = 1000
constants[12] = 80
constants[13] = 26
constants[14] = 40
constants[15] = 940
constants[16] = 72
constants[17] = 1.77
constants[18] = 180
constants[19] = 0.29
states[3] = 104.5878705
constants[20] = 36
states[4] = 110.420253
states[5] = 112.7601171
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[1] = constants[3]*(states[0]/constants[0]-states[1]/constants[1])-states[1]/constants[8]
rates[4] = (3.00000/constants[20])*(states[0]/1.00000-states[4])
rates[5] = (3.00000/constants[20])*(states[4]-states[5])
rates[3] = (3.00000/constants[20])*(states[5]-states[3])
algebraic[1] = constants[5]/(1.00000+exp((constants[6]-states[2]/constants[2])/constants[7]))
rates[0] = algebraic[1]-(constants[3]*(states[0]/constants[0]-states[1]/constants[1])+states[0]/constants[4])
algebraic[4] = constants[16]*(1.00000-exp(-states[2]/(constants[10]*constants[2])))
algebraic[5] = states[2]/(constants[11]*constants[2])
algebraic[6] = constants[14]+(constants[15]-constants[14])/(1.00000+exp(-constants[17]*log((states[1]/constants[12])*(1.00000/constants[1]+1.00000/(constants[3]*constants[8])))))
algebraic[7] = constants[18]/(1.00000+exp(constants[19]*((states[3]*1.00000)/constants[0]-constants[13])))
rates[2] = constants[9]+algebraic[7]+-(algebraic[4]+algebraic[5]*algebraic[6])
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = constants[5]/(1.00000+exp((constants[6]-states[2]/constants[2])/constants[7]))
algebraic[4] = constants[16]*(1.00000-exp(-states[2]/(constants[10]*constants[2])))
algebraic[5] = states[2]/(constants[11]*constants[2])
algebraic[6] = constants[14]+(constants[15]-constants[14])/(1.00000+exp(-constants[17]*log((states[1]/constants[12])*(1.00000/constants[1]+1.00000/(constants[3]*constants[8])))))
algebraic[7] = constants[18]/(1.00000+exp(constants[19]*((states[3]*1.00000)/constants[0]-constants[13])))
algebraic[0] = states[0]/constants[0]
algebraic[2] = states[1]/constants[1]
algebraic[3] = states[2]/(constants[2]*10.0000)
return algebraic
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)