# Size of variable arrays: sizeAlgebraic = 15 sizeStates = 1 sizeConstants = 18 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_constants[0] = "C_ext_Na in component Concentrations (mM)" legend_constants[1] = "C_ext_H in component Concentrations (mM)" legend_constants[2] = "C_ext_NH4 in component Concentrations (mM)" legend_constants[3] = "C_int_Na in component Concentrations (mM)" legend_algebraic[0] = "C_int_H in component Concentrations (mM)" legend_constants[4] = "C_int_NH4 in component Concentrations (mM)" legend_states[0] = "pH_int in component Concentrations (dimensionless)" 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_algebraic[2] = "XTxP_NHE3_Na in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[3] = "XTxP_NHE3_H in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[4] = "XTxP_NHE3_NH4 in component NHE3 (nmol_per_s_per_cm2)" legend_constants[11] = "alpha_ext_Na in component NHE3 (dimensionless)" legend_constants[12] = "beta_ext_H in component NHE3 (dimensionless)" legend_constants[13] = "gamma_ext_NH4 in component NHE3 (dimensionless)" legend_constants[14] = "alpha_int_Na in component NHE3 (dimensionless)" legend_algebraic[1] = "beta_int_H in component NHE3 (dimensionless)" legend_constants[15] = "gamma_int_NH4 in component NHE3 (dimensionless)" legend_algebraic[5] = "sum_NHE3 in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[6] = "J_NHE3_Na in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[7] = "J_NHE3_H in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[8] = "J_NHE3_NH4 in component NHE3 (nmol_per_s_per_cm2)" legend_constants[16] = "J_NHE3_Na_Max in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[10] = "plot in component NHE3 (dimensionless)" legend_algebraic[11] = "J_NHE3_Na2 in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[12] = "J_NHE3_H2 in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[13] = "J_NHE3_NH42 in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[9] = "sum0_NHE3 in component NHE3 (nmol_per_s_per_cm2)" legend_algebraic[14] = "plot2 in component NHE3 (dimensionless)" legend_rates[0] = "d/dt pH_int in component Concentrations (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 1 constants[1] = 5.4954e-5 constants[2] = 0 constants[3] = 0 constants[4] = 0 states[0] = 4 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[8] constants[17] = 5.00000 constants[12] = constants[1]/constants[9] constants[13] = constants[2]/constants[10] constants[14] = constants[3]/constants[8] constants[15] = constants[4]/constants[10] constants[16] = (constants[5]*constants[6])/(constants[5]+constants[6]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[17] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = 1000.00*(power(10.0000, -states[0])) algebraic[1] = algebraic[0]/constants[9] algebraic[2] = (constants[5]*2.00000*algebraic[0])/(algebraic[0]+0.00100000) algebraic[3] = (constants[6]*2.00000*algebraic[0])/(algebraic[0]+0.00100000) algebraic[4] = (constants[7]*2.00000*algebraic[0])/(algebraic[0]+0.00100000) algebraic[5] = (1.00000+constants[11]+constants[12]+constants[13])*(algebraic[2]*constants[14]+algebraic[3]*algebraic[1]+algebraic[4]*constants[15])+(1.00000+constants[14]+algebraic[1]+constants[15])*(algebraic[2]*constants[11]+algebraic[3]*constants[12]+algebraic[4]*constants[13]) algebraic[6] = ((algebraic[2]*algebraic[3])/algebraic[5])*(constants[11]*algebraic[1]-constants[14]*constants[12])+((algebraic[2]*algebraic[4])/algebraic[5])*(constants[11]*constants[15]-constants[14]*constants[13]) algebraic[7] = ((algebraic[2]*algebraic[3])/algebraic[5])*(constants[14]*constants[12]-constants[11]*algebraic[1])+((algebraic[3]*algebraic[4])/algebraic[5])*(constants[12]*constants[15]-algebraic[1]*constants[13]) algebraic[8] = ((algebraic[2]*algebraic[4])/algebraic[5])*(constants[14]*constants[13]-constants[11]*constants[15])+((algebraic[3]*algebraic[4])/algebraic[5])*(constants[13]*algebraic[1]-constants[12]*constants[15]) algebraic[9] = (1.00000+constants[11]+constants[12]+constants[13])*(constants[5]*constants[14]+constants[6]*algebraic[1]+constants[7]*constants[15])+(1.00000+constants[14]+algebraic[1]+constants[15])*(constants[5]*constants[11]+constants[6]*constants[12]+constants[7]*constants[13]) algebraic[10] = algebraic[6]/constants[16] algebraic[11] = ((constants[5]*constants[6])/algebraic[9])*(constants[11]*algebraic[1]-constants[14]*constants[12])+((constants[5]*constants[7])/algebraic[5])*(constants[11]*constants[15]-constants[14]*constants[13]) algebraic[12] = ((constants[5]*constants[6])/algebraic[9])*(constants[14]*constants[12]-constants[11]*algebraic[1])+((constants[6]*constants[7])/algebraic[5])*(constants[12]*constants[15]-algebraic[1]*constants[13]) algebraic[13] = ((constants[5]*constants[7])/algebraic[9])*(constants[14]*constants[13]-constants[11]*constants[15])+((constants[6]*constants[7])/algebraic[5])*(constants[13]*algebraic[1]-constants[12]*constants[15]) algebraic[14] = algebraic[11]/constants[16] 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)