# Size of variable arrays: sizeAlgebraic = 7 sizeStates = 2 sizeConstants = 17 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] = "MDFLW in component angiotensin (L_per_minute)" legend_constants[15] = "ANGSCR in component instantaneous_angiotensin_formation (dimensionless)" legend_constants[14] = "MDFLW3 in component instantaneous_angiotensin_formation (L_per_minute)" legend_states[0] = "ANX1 in component time_delayed_angiotensin_formation (dimensionless)" legend_constants[1] = "ANXM in component parameter_values (dimensionless)" legend_constants[2] = "ANV in component parameter_values (minute)" legend_constants[16] = "ANX in component time_delayed_angiotensin_formation (dimensionless)" legend_algebraic[2] = "ANPR in component total_angiotensin_formation (dimensionless)" legend_constants[3] = "REK in component parameter_values (dimensionless)" legend_algebraic[0] = "ANPRT in component total_angiotensin_formation (dimensionless)" legend_algebraic[4] = "ANPR1 in component artificial_angiotensin_formation (dimensionless)" legend_constants[4] = "ANGKNS in component parameter_values (dimensionless)" legend_constants[5] = "ANGINF in component parameter_values (dimensionless)" legend_states[1] = "ANC in component angiotensin_concentration (dimensionless)" legend_constants[6] = "ANT in component parameter_values (minute)" legend_algebraic[1] = "ANM in component general_angiotensin_multiplier (dimensionless)" legend_constants[7] = "ANMUL in component parameter_values (dimensionless)" legend_constants[8] = "ANMLL in component parameter_values (dimensionless)" legend_constants[9] = "ANCSNS in component parameter_values (dimensionless)" legend_algebraic[5] = "ANU in component angiotensin_effect_on_circulation (dimensionless)" legend_constants[10] = "ANUM in component parameter_values (dimensionless)" legend_constants[11] = "ANULL in component parameter_values (dimensionless)" legend_algebraic[3] = "ANU1 in component angiotensin_effect_on_circulation (dimensionless)" legend_algebraic[6] = "ANUVN in component angiotensin_effect_on_venous_constriction (dimensionless)" legend_constants[12] = "ANUVM in component parameter_values (dimensionless)" legend_constants[13] = "Z12 in component parameter_values (dimensionless)" legend_rates[0] = "d/dt ANX1 in component time_delayed_angiotensin_formation (dimensionless)" legend_rates[1] = "d/dt ANC in component angiotensin_concentration (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 1.00051 states[0] = 0.0 constants[1] = 0 constants[2] = 5000 constants[3] = 1 constants[4] = 0 constants[5] = 0 states[1] = 0.859476 constants[6] = 12 constants[7] = 1.8 constants[8] = 0.7 constants[9] = 0.4 constants[10] = 6 constants[11] = 0.8 constants[12] = 0 constants[13] = 5 constants[14] = constants[0] constants[15] = custom_piecewise([greater(constants[14] , 1.00000), 1.00000/(1.00000+(constants[14]-1.00000)*72.0000) , True, 10.0000-9.00000/(1.00000+(1.00000-constants[14])*8.00000)]) constants[16] = (constants[15]-1.00000)*constants[1] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[16]-states[0])/constants[2] algebraic[0] = (constants[15]+states[0])*constants[3] algebraic[2] = custom_piecewise([less(algebraic[0] , 1.00000e-05), 1.00000e-05 , True, algebraic[0]]) algebraic[4] = custom_piecewise([greater(constants[4] , 0.00000), constants[4] , True, algebraic[2]+constants[5]]) rates[1] = (algebraic[4]-states[1])/constants[6] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (constants[15]+states[0])*constants[3] algebraic[2] = custom_piecewise([less(algebraic[0] , 1.00000e-05), 1.00000e-05 , True, algebraic[0]]) algebraic[4] = custom_piecewise([greater(constants[4] , 0.00000), constants[4] , True, algebraic[2]+constants[5]]) algebraic[1] = constants[7]-(constants[7]-1.00000)/(((constants[8]-1.00000)/(constants[8]-constants[7]))*(states[1]-1.00000)*constants[9]+1.00000) algebraic[3] = (algebraic[1]-1.00000)*constants[10]+1.00000 algebraic[5] = custom_piecewise([less(algebraic[3] , constants[11]), constants[11] , True, algebraic[3]]) algebraic[6] = (algebraic[5]-1.00000)*constants[12]+1.00000 return algebraic def custom_piecewise(cases): """Compute result of a piecewise function""" return select(cases[0::2],cases[1::2]) def gcd(A, B): """Greatest common divisor""" if (iterable(A) and iterable(B)): x = []; for (a,b) in zip(A,B): assert (int(a) == a) and (int(b) == b) a = int(a); b = int(b) while a: a,b = b % a, a x.append(b) return x else: while A: A,B = B % A, A return b 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)