# 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)