# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 1 sizeConstants = 21 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] = "ANM in component aldosterone (dimensionless)" legend_constants[1] = "CKE in component aldosterone (monovalent_mEq_per_litre)" legend_constants[15] = "ANMAL in component angiotensin_control_of_aldosterone_secretion (dimensionless)" legend_constants[2] = "ANMALD in component parameter_values (dimensionless)" legend_constants[16] = "OSMAL in component osmotic_control_of_aldosterone_secretion (dimensionless)" legend_constants[20] = "AMR1 in component aldosterone_secretion (dimensionless)" legend_constants[3] = "AMKMUL in component parameter_values (dimensionless)" legend_constants[4] = "ALDINF in component parameter_values (dimensionless)" legend_constants[5] = "ALDKNS in component parameter_values (dimensionless)" legend_constants[17] = "AMRBSC in component aldosterone_secretion (dimensionless)" legend_constants[18] = "AMRT in component aldosterone_secretion (dimensionless)" legend_constants[19] = "AMR in component aldosterone_secretion (dimensionless)" legend_states[0] = "AMC in component aldosterone_concentration (dimensionless)" legend_constants[6] = "AMT in component parameter_values (minute)" legend_algebraic[1] = "AM in component general_aldosterone_multiplier (dimensionless)" legend_constants[7] = "AM1UL in component parameter_values (dimensionless)" legend_constants[8] = "AM1LL in component parameter_values (dimensionless)" legend_constants[9] = "AMCSNS in component parameter_values (dimensionless)" legend_constants[10] = "ALDMM in component parameter_values (dimensionless)" legend_algebraic[0] = "AM1 in component general_aldosterone_multiplier (dimensionless)" legend_algebraic[4] = "AMK in component aldosterone_effect_on_cell_membrane_K_transport (dimensionless)" legend_constants[11] = "AMKM in component parameter_values (dimensionless)" legend_algebraic[2] = "AMKT in component aldosterone_effect_on_cell_membrane_K_transport (dimensionless)" legend_algebraic[5] = "AMNA in component aldosterone_effect_on_cell_membrane_Na_transport (dimensionless)" legend_constants[12] = "AMNAM in component parameter_values (dimensionless)" legend_constants[13] = "AMNAUL in component parameter_values (dimensionless)" legend_constants[14] = "AMNALL in component parameter_values (dimensionless)" legend_algebraic[3] = "AMNAT in component aldosterone_effect_on_cell_membrane_Na_transport (dimensionless)" legend_rates[0] = "d/dt AMC in component aldosterone_concentration (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.987545 constants[1] = 4.44092 constants[2] = 2.5 constants[3] = 12 constants[4] = 0 constants[5] = 0 states[0] = 1.0 constants[6] = 60 constants[7] = 5 constants[8] = 0 constants[9] = 0.65 constants[10] = 2.5 constants[11] = 0.5 constants[12] = 0.8 constants[13] = 15 constants[14] = 0.04 constants[15] = (constants[0]-1.00000)*constants[2]+1.00000 constants[16] = (constants[1]-3.30000)/1.00000 constants[17] = constants[15]*0.909000*constants[16] constants[18] = (constants[17]-1.00000)*constants[3]+1.00000 constants[19] = custom_piecewise([less(constants[18] , 0.00000), 0.00000 , True, constants[18]]) constants[20] = custom_piecewise([greater(constants[5] , 0.00000), constants[5] , True, constants[19]+constants[4]]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[20]-states[0])/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[7]-(constants[7]-1.00000)/(((constants[8]-1.00000)/(constants[8]-constants[7]))*(states[0]-1.00000)*constants[9]+1.00000) algebraic[1] = (algebraic[0]-1.00000)*constants[10]+1.00000 algebraic[2] = (algebraic[1]-1.00000)*constants[11]+1.00000 algebraic[3] = (algebraic[1]-1.00000)*constants[12]+1.00000 algebraic[4] = custom_piecewise([less(algebraic[2] , 0.200000), 0.200000 , True, algebraic[2]]) algebraic[5] = custom_piecewise([less(algebraic[3] , constants[14]), constants[14] , greater(algebraic[3] , constants[13]), constants[13] , True, algebraic[3]]) 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)