# Size of variable arrays: sizeAlgebraic = 2 sizeStates = 9 sizeConstants = 38 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_constants[0] = "BW in component main (kilogram)" legend_constants[1] = "Qcc in component main (litre_per_hr_kg)" legend_constants[2] = "Qliv in component main (dimensionless)" legend_constants[3] = "Qfat in component main (dimensionless)" legend_constants[4] = "Qbrain in component main (dimensionless)" legend_constants[5] = "Qslow in component main (dimensionless)" legend_constants[20] = "Qc in component main (litre_per_hr)" legend_constants[28] = "Ql in component main (litre_per_hr)" legend_constants[33] = "Qf in component main (litre_per_hr)" legend_constants[35] = "Qbr in component main (litre_per_hr)" legend_constants[36] = "Qs in component main (litre_per_hr)" legend_constants[37] = "Qr in component main (litre_per_hr)" legend_constants[6] = "Vblood in component main (dimensionless)" legend_constants[7] = "Vbrain in component main (dimensionless)" legend_constants[8] = "Vliver in component main (dimensionless)" legend_constants[21] = "Vfat in component main (dimensionless)" legend_constants[9] = "Vslow in component main (dimensionless)" legend_constants[29] = "Vrap in component main (dimensionless)" legend_constants[30] = "Vf in component main (litre)" legend_constants[22] = "Vs in component main (litre)" legend_constants[23] = "Vl in component main (litre)" legend_constants[34] = "Vr in component main (litre)" legend_constants[24] = "Vbr in component main (litre)" legend_constants[25] = "Vb in component main (litre)" legend_constants[31] = "Vven in component main (litre)" legend_constants[32] = "Vart in component main (litre)" legend_constants[10] = "Pfat_bl in component main (dimensionless)" legend_constants[11] = "Pslow_bl in component main (dimensionless)" legend_constants[12] = "Pliv_bl in component main (dimensionless)" legend_constants[13] = "Prapid_bl in component main (dimensionless)" legend_constants[14] = "Pbrain_bl in component main (dimensionless)" legend_constants[15] = "dose in component main (mg_per_kg)" legend_constants[16] = "F in component main (dimensionless)" legend_constants[26] = "D0 in component main (mg)" legend_constants[17] = "Ka in component main (per_hr)" legend_constants[18] = "Kfc in component main (per_hr)" legend_constants[27] = "KF in component main (per_hr_kg)" legend_voi = "t in component main (hr)" legend_states[0] = "A_fat in component main (mg)" legend_states[1] = "A_slow in component main (mg)" legend_states[2] = "A_liv in component main (mg)" legend_states[3] = "A_rapid in component main (mg)" legend_states[4] = "A_brain in component main (mg)" legend_constants[19] = "A_blood in component main (mg)" legend_states[5] = "A_stomach in component main (mg)" legend_states[6] = "A_ven in component main (mg)" legend_states[7] = "A_art in component main (mg)" legend_states[8] = "A_liv_CL in component main (mg)" legend_algebraic[0] = "C_art in component main (mg_per_litre)" legend_algebraic[1] = "C_brain in component main (mg_per_litre)" legend_rates[6] = "d/dt A_ven in component main (mg)" legend_rates[7] = "d/dt A_art in component main (mg)" legend_rates[0] = "d/dt A_fat in component main (mg)" legend_rates[1] = "d/dt A_slow in component main (mg)" legend_rates[4] = "d/dt A_brain in component main (mg)" legend_rates[3] = "d/dt A_rapid in component main (mg)" legend_rates[5] = "d/dt A_stomach in component main (mg)" legend_rates[2] = "d/dt A_liv in component main (mg)" legend_rates[8] = "d/dt A_liv_CL in component main (mg)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.1615 constants[1] = 14 constants[2] = 0.25 constants[3] = 0.09 constants[4] = 0.03 constants[5] = 0.278 constants[6] = 0.05 constants[7] = 0.0116 constants[8] = 0.04 constants[9] = 0.63 constants[10] = 186 constants[11] = 3.4 constants[12] = 6.1 constants[13] = 6.1 constants[14] = 3 constants[15] = 60 constants[16] = 0.8 constants[17] = 0.1 constants[18] = 6 states[0] = 0 states[1] = 0 states[2] = 0 states[3] = 0 states[4] = 0 constants[19] = 0 states[6] = 0 states[7] = 0 states[8] = 0 constants[20] = constants[1]*(power(constants[0], 0.740000)) constants[21] = 0.0100000*(20.0000*constants[0]+1.66400) constants[22] = constants[9]*constants[0] constants[23] = constants[8]*constants[0] constants[24] = constants[7]*constants[0] constants[25] = constants[6]*constants[0] constants[26] = constants[16]*constants[15]*constants[0] constants[27] = constants[18]/(power(constants[0], 0.300000)) constants[28] = constants[2]*constants[20] constants[29] = (((1.00000-constants[6])-constants[8])-constants[21])-constants[9] constants[30] = constants[21]*constants[0] constants[31] = 0.750000*constants[25] constants[32] = 0.250000*constants[25] constants[33] = constants[3]*constants[20] constants[34] = constants[29]*constants[0] constants[35] = constants[4]*constants[20] constants[36] = constants[5]*constants[20] constants[37] = (((constants[20]-constants[28])-constants[33])-constants[35])-constants[36] states[5] = constants[26] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[6] = ((constants[33]*states[0])/constants[30])/constants[10]+((constants[35]*states[4])/constants[24])/constants[14]+((constants[36]*states[1])/constants[22])/constants[11]+((constants[28]*states[2])/constants[23])/constants[12]+((constants[37]*states[3])/constants[34])/constants[13] rates[0] = constants[33]*(states[7]/constants[25]-(states[0]/constants[30])/constants[10]) rates[1] = constants[36]*(states[7]/constants[25]-(states[1]/constants[22])/constants[11]) rates[4] = constants[35]*(states[7]/constants[25]-(states[4]/constants[24])/constants[14]) rates[3] = constants[37]*(states[7]/constants[25]-(states[3]/constants[34])/constants[13]) rates[5] = -constants[17]*states[5] rates[2] = (constants[28]*(states[7]/constants[25]-(states[2]/constants[23])/constants[12])-((constants[27]*constants[23]*states[2])/constants[23])/constants[12])+constants[17]*states[5] rates[8] = ((constants[27]*constants[23]*states[2])/constants[23])/constants[12] rates[7] = rates[6]-(constants[20]*states[7])/constants[25] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[7]/constants[25] algebraic[1] = states[4]/constants[24] 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)