# Size of variable arrays: sizeAlgebraic = 8 sizeStates = 4 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] = "AMK in component electrolytes (dimensionless)" legend_constants[1] = "TVD in component electrolytes (L_per_minute)" legend_constants[2] = "NOD in component electrolytes (monovalent_mEq_per_minute)" legend_constants[3] = "STH in component electrolytes (dimensionless)" legend_constants[4] = "KOD in component electrolytes (monovalent_mEq_per_minute)" legend_constants[5] = "VUD in component electrolytes (L_per_minute)" legend_algebraic[3] = "VEC in component extracellular_fluid_volume (litre)" legend_algebraic[4] = "CNA in component extracellular_Na_concentration (monovalent_mEq_per_litre)" legend_constants[6] = "NID in component parameter_values (monovalent_mEq_per_minute)" legend_constants[7] = "TRPL in component parameter_values (L_per_minute)" legend_constants[11] = "NED in component extracellular_Na_concentration (monovalent_mEq_per_minute)" legend_states[0] = "NAE in component extracellular_Na_concentration (monovalent_mEq)" legend_constants[12] = "AMK1 in component aldosterone_effect_on_cellular_K_distribution (dimensionless)" legend_constants[8] = "ALCLK in component parameter_values (dimensionless)" legend_algebraic[5] = "CKE in component extracellular_K_concentration (monovalent_mEq_per_litre)" legend_algebraic[0] = "KE in component extracellular_K_concentration (monovalent_mEq)" legend_states[1] = "KTOT in component extracellular_K_concentration (monovalent_mEq)" legend_constants[9] = "KID in component parameter_values (monovalent_mEq_per_minute)" legend_constants[13] = "KTOTD in component extracellular_K_concentration (monovalent_mEq_per_minute)" legend_states[2] = "VIC in component intracellular_fluid_volume (litre)" legend_algebraic[2] = "CKI in component intracellular_K_concentration (monovalent_mEq_per_litre)" legend_algebraic[1] = "KI in component intracellular_K_concentration (monovalent_mEq)" legend_algebraic[7] = "VID in component intracellular_fluid_volume (L_per_minute)" legend_constants[10] = "VIDML in component parameter_values (litre2_per_monovalent_mEq_per_minute)" legend_algebraic[6] = "CCD in component intracellular_fluid_volume (monovalent_mEq_per_litre)" legend_states[3] = "VTW in component total_body_water (litre)" legend_rates[0] = "d/dt NAE in component extracellular_Na_concentration (monovalent_mEq)" legend_rates[1] = "d/dt KTOT in component extracellular_K_concentration (monovalent_mEq)" legend_rates[2] = "d/dt VIC in component intracellular_fluid_volume (litre)" legend_rates[3] = "d/dt VTW in component total_body_water (litre)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 1.037 constants[1] = 0.000980838 constants[2] = 0.0959449 constants[3] = 0.977181 constants[4] = 0.0804374 constants[5] = 0.000989 constants[6] = 0.1 constants[7] = 0 states[0] = 2109.91 constants[8] = 0.3 states[1] = 3622.54 constants[9] = 0.08 states[2] = 25.0404 constants[10] = 0.01 states[3] = 39.8952 constants[11] = (constants[6]*constants[3]-constants[2])+constants[7]*142.000 constants[12] = (constants[0]-1.00000)*constants[8]+1.00000 constants[13] = constants[9]-constants[4] constants[14] = constants[1]-constants[5] constants[15] = constants[11] constants[16] = constants[13] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[3] = constants[14] rates[0] = constants[15] rates[1] = constants[16] algebraic[3] = states[3]-states[2] algebraic[4] = states[0]/algebraic[3] algebraic[0] = (states[1]-3000.00)/(constants[12]*9.33330) algebraic[1] = states[1]-algebraic[0] algebraic[2] = algebraic[1]/states[2] algebraic[6] = algebraic[2]-algebraic[4] algebraic[7] = algebraic[6]*constants[10] rates[2] = algebraic[7] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[3] = states[3]-states[2] algebraic[4] = states[0]/algebraic[3] algebraic[0] = (states[1]-3000.00)/(constants[12]*9.33330) algebraic[1] = states[1]-algebraic[0] algebraic[2] = algebraic[1]/states[2] algebraic[6] = algebraic[2]-algebraic[4] algebraic[7] = algebraic[6]*constants[10] algebraic[5] = algebraic[0]/algebraic[3] return algebraic 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)