# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 1 sizeConstants = 25 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] = "Na_ext in component concentrations (mM)" legend_constants[0] = "Na_int in component concentrations (mM)" legend_constants[1] = "H_ext in component concentrations (mM)" legend_constants[2] = "H_int in component concentrations (mM)" legend_constants[3] = "NH4_ext in component concentrations (mM)" legend_constants[4] = "NH4_int in component concentrations (mM)" legend_algebraic[2] = "J_NHE3_Na in component NHE3 (mM_per_s)" legend_algebraic[3] = "J_NHE3_H in component NHE3 (mM_per_s)" legend_algebraic[4] = "J_NHE3_NH4 in component NHE3 (mM_per_s)" legend_constants[22] = "J_NHE3_Na_Max in component NHE3 (mM_per_s)" legend_algebraic[5] = "plot in component fluxes (dimensionless)" legend_constants[5] = "x_T in component NHE3 (mM)" legend_algebraic[1] = "sigma in component NHE3 (per_s)" legend_constants[20] = "P_Na in component NHE3 (per_s)" legend_constants[21] = "P_H in component NHE3 (per_s)" legend_constants[23] = "P_NH4 in component NHE3 (per_s)" legend_constants[6] = "P0_Na in component NHE3 (per_s)" legend_constants[7] = "P0_H in component NHE3 (per_s)" legend_constants[8] = "P0_NH4 in component NHE3 (per_s)" legend_constants[9] = "K_Na in component NHE3 (mM)" legend_constants[10] = "K_H in component NHE3 (mM)" legend_constants[11] = "K_NH4 in component NHE3 (mM)" legend_constants[12] = "K_I in component NHE3 (mM)" legend_constants[13] = "f_m in component NHE3 (dimensionless)" legend_constants[14] = "f_M in component NHE3 (dimensionless)" legend_algebraic[0] = "alpha_ext_Na in component NHE3 (dimensionless)" legend_constants[15] = "alpha_int_Na in component NHE3 (dimensionless)" legend_constants[16] = "beta_ext_H in component NHE3 (dimensionless)" legend_constants[17] = "beta_int_H in component NHE3 (dimensionless)" legend_constants[18] = "gamma_ext_NH4 in component NHE3 (dimensionless)" legend_constants[19] = "gamma_int_NH4 in component NHE3 (dimensionless)" legend_rates[0] = "d/dt Na_ext 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] = 1.0 constants[0] = 0.0 constants[1] = 2.51189e-4 constants[2] = 1.0e-3 constants[3] = 0.0 constants[4] = 0.0 constants[5] = 1.0 constants[6] = 1.6e-3 constants[7] = 0.48e-3 constants[8] = 1.6e-3 constants[9] = 30.0 constants[10] = 72e-6 constants[11] = 27.0 constants[12] = 1.0e-6 constants[13] = 0.0 constants[14] = 2.0 constants[15] = constants[0]/constants[9] constants[24] = 100.000 constants[16] = constants[1]/constants[10] constants[17] = constants[2]/constants[10] constants[18] = constants[3]/constants[11] constants[19] = constants[4]/constants[11] constants[20] = (constants[6]*(constants[14]*constants[2]+constants[13]*constants[12]))/(constants[2]+constants[12]) constants[21] = (constants[7]*(constants[14]*constants[2]+constants[13]*constants[12]))/(constants[2]+constants[12]) constants[22] = (constants[5]*constants[20]*constants[21])/(constants[20]+constants[21]) constants[23] = (constants[8]*(constants[14]*constants[2]+constants[13]*constants[12]))/(constants[2]+constants[12]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[24] 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[9] algebraic[1] = (1.00000+algebraic[0]+constants[16]+constants[18])*(constants[20]*constants[15]+constants[21]*constants[17]+constants[23]*constants[19])+(1.00000+constants[15]+constants[17]+constants[19])*(constants[20]*algebraic[0]+constants[21]*constants[16]+constants[23]*constants[18]) algebraic[2] = (constants[5]/algebraic[1])*(constants[20]*constants[21]*(constants[15]*constants[16]-algebraic[0]*constants[17])+constants[20]*constants[23]*(constants[15]*constants[18]-algebraic[0]*constants[19])) algebraic[3] = (constants[5]/algebraic[1])*(constants[20]*constants[21]*(algebraic[0]*constants[17]-constants[15]*constants[16])+constants[21]*constants[23]*(constants[17]*constants[18]-constants[16]*constants[19])) algebraic[4] = (constants[5]/algebraic[1])*(constants[20]*constants[23]*(algebraic[0]*constants[19]-constants[15]*constants[18])+constants[21]*constants[23]*(constants[16]*constants[19]-constants[18]*constants[17])) algebraic[5] = -states[0]/(algebraic[2]/constants[22]) 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)