# Size of variable arrays: sizeAlgebraic = 9 sizeStates = 1 sizeConstants = 6 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] = "BFN in component non_muscle_O2_delivery (L_per_minute)" legend_constants[1] = "OVA in component non_muscle_O2_delivery (mL_per_L)" legend_constants[2] = "HM in component non_muscle_O2_delivery (dimensionless)" legend_constants[3] = "AOM in component non_muscle_O2_delivery (dimensionless)" legend_constants[5] = "O2ARTN in component NM_O2_blood_supply (mL_per_minute)" legend_algebraic[4] = "DOB in component delivery_of_O2_to_NM_tissues (mL_per_minute)" legend_algebraic[5] = "POV in component NM_venous_O2_content (mmHg)" legend_algebraic[6] = "OSV in component NM_venous_O2_content (dimensionless)" legend_algebraic[1] = "POT in component pressure_of_O2_in_NM_tissue_cells (mmHg)" legend_algebraic[3] = "MO2 in component O2_consumption_by_NM_tissue (mL_per_minute)" legend_constants[4] = "O2M in component parameter_values (mL_per_minute)" legend_algebraic[2] = "P1O in component O2_consumption_by_NM_tissue (mmHg)" legend_algebraic[0] = "QO2 in component volume_of_O2_in_NM_tissue (mL)" legend_algebraic[8] = "DO2N in component volume_of_O2_in_NM_tissue (mL_per_minute)" legend_algebraic[7] = "DO2N1 in component volume_of_O2_in_NM_tissue (mL_per_minute)" legend_states[0] = "QO2T in component volume_of_O2_in_NM_tissue (mL)" legend_rates[0] = "d/dt QO2T in component volume_of_O2_in_NM_tissue (mL)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 2.79521 constants[1] = 204.497 constants[2] = 40.0381 constants[3] = 1.00002 constants[4] = 164 states[0] = 72.2362 constants[5] = 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] , 0.00000), 0.00000 , True, states[0]]) algebraic[1] = algebraic[0]*0.486110 rootfind_0(voi, constants, rates, states, algebraic) algebraic[2] = custom_piecewise([greater(algebraic[1] , 35.0000), 35.0000 , True, algebraic[1]]) algebraic[3] = constants[3]*constants[4]*(1.00000-(power(35.0001-algebraic[2], 3.00000))/42875.0) algebraic[7] = algebraic[4]-algebraic[3] algebraic[8] = custom_piecewise([less(algebraic[0] , 6.00000) & less(algebraic[7] , 0.00000), algebraic[7]*0.100000 , True, algebraic[7]]) rates[0] = algebraic[8] 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] , 0.00000), 0.00000 , True, states[0]]) algebraic[1] = algebraic[0]*0.486110 algebraic[2] = custom_piecewise([greater(algebraic[1] , 35.0000), 35.0000 , True, algebraic[1]]) algebraic[3] = constants[3]*constants[4]*(1.00000-(power(35.0001-algebraic[2], 3.00000))/42875.0) algebraic[7] = algebraic[4]-algebraic[3] algebraic[8] = custom_piecewise([less(algebraic[0] , 6.00000) & less(algebraic[7] , 0.00000), algebraic[7]*0.100000 , True, algebraic[7]]) 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[5]-algebraic[4])/(constants[2]*5.25000*constants[0])) resid[1] = (algebraic[5]-algebraic[6]*57.1400) resid[2] = (algebraic[4]-(algebraic[5]-algebraic[1])*12.8570*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)