# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 1 sizeConstants = 22 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 (second)" legend_states[0] = "C_ext_Na in component Concentrations (mM)" legend_constants[0] = "C_ext_H in component Concentrations (mM)" legend_constants[1] = "C_ext_NH4 in component Concentrations (mM)" legend_constants[2] = "C_int_Na in component Concentrations (mM)" legend_constants[3] = "C_int_H in component Concentrations (mM)" legend_constants[4] = "C_int_NH4 in component Concentrations (mM)" legend_constants[5] = "XTxP0_NHE3_Na in component NHE3_Parameters (nmol_per_s_per_cm2)" legend_constants[6] = "XTxP0_NHE3_H in component NHE3_Parameters (nmol_per_s_per_cm2)" legend_constants[7] = "XTxP0_NHE3_NH4 in component NHE3_Parameters (nmol_per_s_per_cm2)" legend_constants[8] = "K_NHE3_Na in component NHE3_Parameters (mM)" legend_constants[9] = "K_NHE3_H in component NHE3_Parameters (mM)" legend_constants[10] = "K_NHE3_NH4 in component NHE3_Parameters (mM)" legend_constants[16] = "XTxP_NHE3_Na in component NHE3 (nmol_per_s_per_cm2)" legend_constants[17] = "XTxP_NHE3_H in component NHE3 (nmol_per_s_per_cm2)" legend_constants[18] = "XTxP_NHE3_NH4 in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[0] = "alpha_ext_Na in component NHE3 (dimensionless)" legend_constants[11] = "beta_ext_H in component NHE3 (dimensionless)" legend_constants[12] = "gamma_ext_NH4 in component NHE3 (dimensionless)" legend_constants[13] = "alpha_int_Na in component NHE3 (dimensionless)" legend_constants[14] = "beta_int_H in component NHE3 (dimensionless)" legend_constants[15] = "gamma_int_NH4 in component NHE3 (dimensionless)" legend_algebraic[1] = "sum_NHE3 in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[2] = "J_NHE3_Na in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[3] = "J_NHE3_H in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[4] = "J_NHE3_NH4 in component NHE3 (nmol_per_s_per_cm2)" legend_constants[19] = "J_NHE3_Na_Max in component NHE3 (nmol_per_s_per_cm2)" legend_constants[20] = "K_Na in component NHE3 (dimensionless)" legend_algebraic[5] = "plot in component NHE3 (mM)" legend_rates[0] = "d/dt C_ext_Na in component Concentrations (mM)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 1 constants[0] = 3.1623e-5 constants[1] = 0 constants[2] = 0 constants[3] = 1e-3 constants[4] = 0 constants[5] = 1.6e-3 constants[6] = 0.48e-3 constants[7] = 1.6e-3 constants[8] = 30 constants[9] = 72e-6 constants[10] = 0.027e3 constants[11] = constants[0]/constants[9] constants[21] = 100.000 constants[12] = constants[1]/constants[10] constants[13] = constants[2]/constants[8] constants[14] = constants[3]/constants[9] constants[15] = constants[4]/constants[10] constants[16] = (constants[5]*2.00000*constants[3])/(constants[3]+1.00000e-06) constants[17] = (constants[6]*2.00000*constants[3])/(constants[3]+1.00000e-06) constants[18] = (constants[7]*2.00000*constants[3])/(constants[3]+1.00000e-06) constants[19] = (constants[16]*constants[17])/(constants[16]+constants[17]) constants[20] = (constants[14]+2.00000*constants[14]*constants[11]+constants[11])/(constants[14]+((1.00000+constants[14])*constants[16])/constants[17]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[21] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[0]/constants[8] algebraic[1] = (1.00000+algebraic[0]+constants[11]+constants[12])*(constants[16]*constants[13]+constants[17]*constants[14]+constants[18]*constants[15])+(1.00000+constants[13]+constants[14]+constants[15])*(constants[16]*algebraic[0]+constants[17]*constants[11]+constants[18]*constants[12]) algebraic[2] = ((constants[16]*constants[17])/algebraic[1])*(algebraic[0]*constants[14]-constants[13]*constants[11])+((constants[16]*constants[18])/algebraic[1])*(algebraic[0]*constants[15]-constants[13]*constants[12]) algebraic[3] = ((constants[16]*constants[17])/algebraic[1])*(constants[13]*constants[11]-algebraic[0]*constants[14])+((constants[17]*constants[18])/algebraic[1])*(constants[11]*constants[15]-constants[14]*constants[12]) algebraic[4] = ((constants[16]*constants[18])/algebraic[1])*(constants[13]*constants[12]-algebraic[0]*constants[15])+((constants[17]*constants[18])/algebraic[1])*(constants[12]*constants[14]-constants[11]*constants[15]) algebraic[5] = states[0]/(algebraic[2]/constants[19]) 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)