# Size of variable arrays: sizeAlgebraic = 12 sizeStates = 1 sizeConstants = 11 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 (minute)" legend_constants[0] = "VP in component red_cells_and_viscosity (litre)" legend_states[0] = "VRC in component RBC_volume (litre)" legend_algebraic[2] = "HM in component hematocrit_fraction (dimensionless)" legend_algebraic[1] = "HM1 in component hematocrit_fraction (dimensionless)" legend_algebraic[0] = "VB in component hematocrit_fraction (litre)" legend_algebraic[3] = "VIE in component viscosity_due_to_RBCs (dimensionless)" legend_constants[1] = "HMK in component parameter_values (dimensionless)" legend_constants[2] = "HKM in component parameter_values (dimensionless)" legend_algebraic[5] = "VIM in component blood_viscosity (dimensionless)" legend_algebraic[4] = "VIB in component blood_viscosity (dimensionless)" legend_algebraic[8] = "HM7 in component oxygen_stimulation (mmHg)" legend_constants[3] = "PO2AMB in component parameter_values (mmHg)" legend_constants[4] = "HM6 in component parameter_values (mmHg)" legend_constants[9] = "PO2AM1 in component oxygen_stimulation (mmHg)" legend_algebraic[6] = "HM3 in component oxygen_stimulation (mmHg)" legend_constants[10] = "HM4 in component oxygen_stimulation (mmHg)" legend_algebraic[7] = "HM5 in component oxygen_stimulation (mmHg)" legend_algebraic[9] = "RC1 in component RBC_production (L_per_minute)" legend_constants[5] = "HM8 in component parameter_values (L_per_minute_per_mmHg)" legend_constants[6] = "REK in component parameter_values (dimensionless)" legend_algebraic[10] = "RC2 in component RBC_destruction (L_per_minute)" legend_constants[7] = "RKC in component parameter_values (per_minute)" legend_constants[8] = "TRRBC in component parameter_values (L_per_minute)" legend_algebraic[11] = "RCD in component RBC_volume (L_per_minute)" legend_rates[0] = "d/dt VRC in component RBC_volume (litre)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 3.00449 states[0] = 2.00439 constants[1] = 90 constants[2] = 0.53333 constants[3] = 150 constants[4] = 1850 constants[5] = 4.714e-08 constants[6] = 1 constants[7] = 5.8e-06 constants[8] = 0 constants[9] = custom_piecewise([greater(constants[3] , 80.0000), 80.0000 , True, constants[3]]) constants[10] = constants[3]-40.0000 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[0]+states[0] algebraic[1] = states[0]/algebraic[0] algebraic[2] = 100.000*algebraic[1] algebraic[6] = (constants[9]-40.0000)*algebraic[2] algebraic[7] = custom_piecewise([less(algebraic[6]+constants[10] , 0.00000), 0.00000 , True, algebraic[6]+constants[10]]) algebraic[8] = constants[4]-algebraic[7] algebraic[9] = custom_piecewise([less(algebraic[8]*constants[5]*constants[6]+5.00000e-06 , 0.00000), 0.00000 , True, algebraic[8]*constants[5]*constants[6]+5.00000e-06]) algebraic[3] = algebraic[2]/((constants[1]-algebraic[2])*constants[2]) algebraic[4] = algebraic[3]+1.50000 algebraic[5] = 0.333300*algebraic[4] algebraic[10] = states[0]*constants[7]*algebraic[5] algebraic[11] = (algebraic[9]-algebraic[10])+constants[8] rates[0] = algebraic[11] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[0]+states[0] algebraic[1] = states[0]/algebraic[0] algebraic[2] = 100.000*algebraic[1] algebraic[6] = (constants[9]-40.0000)*algebraic[2] algebraic[7] = custom_piecewise([less(algebraic[6]+constants[10] , 0.00000), 0.00000 , True, algebraic[6]+constants[10]]) algebraic[8] = constants[4]-algebraic[7] algebraic[9] = custom_piecewise([less(algebraic[8]*constants[5]*constants[6]+5.00000e-06 , 0.00000), 0.00000 , True, algebraic[8]*constants[5]*constants[6]+5.00000e-06]) algebraic[3] = algebraic[2]/((constants[1]-algebraic[2])*constants[2]) algebraic[4] = algebraic[3]+1.50000 algebraic[5] = 0.333300*algebraic[4] algebraic[10] = states[0]*constants[7]*algebraic[5] algebraic[11] = (algebraic[9]-algebraic[10])+constants[8] 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)