# Size of variable arrays: sizeAlgebraic = 8 sizeStates = 1 sizeConstants = 10 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] = "BFM in component muscle_O2_delivery (L_per_minute)" legend_constants[1] = "OVA in component muscle_O2_delivery (mL_per_L)" legend_constants[2] = "HM in component muscle_O2_delivery (dimensionless)" legend_constants[3] = "AOM in component muscle_O2_delivery (dimensionless)" legend_constants[9] = "O2ARTM in component M_O2_blood_supply (mL_per_minute)" legend_algebraic[4] = "RMO in component delivery_of_O2_to_M_tissues (mL_per_minute)" legend_algebraic[5] = "PVO in component M_venous_O2_content (mmHg)" legend_constants[4] = "EXC in component parameter_values (dimensionless)" legend_constants[5] = "EXCXP2 in component parameter_values (dimensionless)" legend_algebraic[6] = "OVS in component M_venous_O2_content (dimensionless)" legend_algebraic[1] = "PMO in component pressure_of_O2_in_M_tissue_cells (mmHg)" legend_algebraic[3] = "MMO in component metabolic_O2_consumption_by_M_tissue (mL_per_minute)" legend_algebraic[2] = "P2O in component metabolic_O2_consumption_by_M_tissue (mmHg)" legend_constants[6] = "OMM in component parameter_values (mL_per_minute)" legend_constants[7] = "PM5 in component parameter_values (per_mmHg)" legend_algebraic[0] = "QOM in component volume_of_O2_in_M_tissue (mL)" legend_algebraic[7] = "DO2M in component volume_of_O2_in_M_tissue (mL_per_minute)" legend_states[0] = "QOM1 in component volume_of_O2_in_M_tissue (mL)" legend_constants[8] = "PK2 in component parameter_values (mmHg_per_mL)" legend_rates[0] = "d/dt QOM1 in component volume_of_O2_in_M_tissue (mL)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.989949 constants[1] = 204.497 constants[2] = 40.0381 constants[3] = 1.00002 constants[4] = 1 constants[5] = 0.17 constants[6] = 57.1 constants[7] = 30 states[0] = 48.0839 constants[8] = 0.79167 constants[9] = constants[1]*constants[0] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = custom_piecewise([less(states[0] , 0.000100000), 0.000100000 , True, states[0]]) algebraic[1] = constants[8]*algebraic[0] rootfind_0(voi, constants, rates, states, algebraic) algebraic[2] = custom_piecewise([greater(algebraic[1] , 38.0000), 38.0000 , True, algebraic[1]]) algebraic[3] = constants[3]*constants[6]*constants[4]*(1.00000-(power(38.0001-algebraic[2], 3.00000))/54872.0) algebraic[7] = algebraic[4]-algebraic[3] rates[0] = algebraic[7] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = custom_piecewise([less(states[0] , 0.000100000), 0.000100000 , True, states[0]]) algebraic[1] = constants[8]*algebraic[0] algebraic[2] = custom_piecewise([greater(algebraic[1] , 38.0000), 38.0000 , True, algebraic[1]]) algebraic[3] = constants[3]*constants[6]*constants[4]*(1.00000-(power(38.0001-algebraic[2], 3.00000))/54872.0) algebraic[7] = algebraic[4]-algebraic[3] 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(3)*0.1 if not iterable(voi): soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, rates, states), xtol=1E-6) initialGuess0 = soln algebraic[4] = soln[0] algebraic[5] = soln[1] algebraic[6] = soln[2] 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[4][i] = soln[0] algebraic[5][i] = soln[1] algebraic[6][i] = soln[2] def residualSN_0(algebraicCandidate, algebraic, voi, constants, rates, states): resid = array([0.0] * 3) algebraic[4] = algebraicCandidate[0] algebraic[5] = algebraicCandidate[1] algebraic[6] = algebraicCandidate[2] resid[0] = (algebraic[6]-(constants[9]-algebraic[4])/(constants[2]*5.25000*constants[0])) resid[1] = (algebraic[5]-57.1400*algebraic[6]*(power(constants[4], constants[5]))) resid[2] = (algebraic[4]-(algebraic[5]-algebraic[1])*constants[7]*constants[0]) 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)