# Size of variable arrays: sizeAlgebraic = 15 sizeStates = 1 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 (second)" legend_states[0] = "HCO3_i in component Concentrations (mM)" legend_constants[0] = "HCO3_e in component Concentrations (mM)" legend_constants[1] = "Cl_i in component Concentrations (mM)" legend_constants[2] = "Cl_e in component Concentrations (mM)" legend_constants[3] = "x_Tmax in component Concentrations (nmol_per_cm2)" legend_algebraic[0] = "x_T in component Concentrations (nmol_per_cm2)" legend_constants[4] = "K_I in component AE1_rate_constants (mM)" legend_constants[5] = "Kc_p in component AE1_rate_constants (mM)" legend_constants[6] = "Kc_pp in component AE1_rate_constants (mM)" legend_constants[7] = "Kb_p in component AE1_rate_constants (mM)" legend_constants[8] = "Kb_pp in component AE1_rate_constants (mM)" legend_constants[9] = "Pc_p in component AE1_rate_constants (per_s)" legend_constants[10] = "Pc_pp in component AE1_rate_constants (per_s)" legend_constants[11] = "Pb_p in component AE1_rate_constants (per_s)" legend_constants[12] = "Pb_pp in component AE1_rate_constants (per_s)" legend_constants[13] = "beta_p in component AE1 (dimensionless)" legend_algebraic[1] = "beta_pp in component AE1 (dimensionless)" legend_constants[14] = "gamma_p in component AE1 (dimensionless)" legend_constants[15] = "gamma_pp in component AE1 (dimensionless)" legend_algebraic[8] = "sigma in component AE1 (per_s)" legend_algebraic[9] = "x_p in component AE1 (nmol_per_cm2)" legend_algebraic[10] = "x_pp in component AE1 (nmol_per_cm2)" legend_algebraic[11] = "J_HCO3 in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[14] = "J_Cl in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[12] = "Jb_influx in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[13] = "Jc_influx in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[2] = "Jo_bm in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[3] = "Ji_bm in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[4] = "Js_bm in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[5] = "Jo_cm in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[6] = "Ji_cm in component AE1 (nmol_per_s_per_cm2)" legend_algebraic[7] = "Js_cm in component AE1 (nmol_per_s_per_cm2)" legend_rates[0] = "d/dt HCO3_i 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] = 0 constants[0] = 26 constants[1] = 29 constants[2] = 114 constants[3] = 1 constants[4] = 172 constants[5] = 50 constants[6] = 50 constants[7] = 198 constants[8] = 198 constants[9] = 562 constants[10] = 61 constants[11] = 1247 constants[12] = 135 constants[13] = constants[0]/constants[7] constants[16] = 60.0000 constants[14] = constants[2]/constants[5] constants[15] = constants[1]/constants[6] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[16] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[3]/(1.00000+states[0]/constants[4]) algebraic[1] = states[0]/constants[8] algebraic[2] = power((1.00000/algebraic[0])*(1.00000/constants[11]+1.00000/constants[12]+constants[8]/(constants[12]*states[0])), -1.00000) algebraic[3] = power((1.00000/algebraic[0])*(1.00000/constants[11]+1.00000/constants[12]+constants[7]/(constants[11]*constants[0])), -1.00000) algebraic[4] = power((1.00000/algebraic[0])*(1.00000/constants[11]+1.00000/constants[12]), -1.00000) algebraic[5] = power((1.00000/algebraic[0])*(1.00000/constants[9]+1.00000/constants[10]+constants[6]/(constants[10]*constants[1])), -1.00000) algebraic[6] = power((1.00000/algebraic[0])*(1.00000/constants[9]+1.00000/constants[10]+constants[5]/(constants[9]*constants[2])), -1.00000) algebraic[7] = power((1.00000/algebraic[0])*(1.00000/constants[9]+1.00000/constants[10]), -1.00000) algebraic[8] = (1.00000+constants[13]+constants[14])*(constants[12]*algebraic[1]+constants[10]*constants[15])+(1.00000+algebraic[1]+constants[15])*(constants[11]*constants[13]+constants[9]*constants[14]) algebraic[9] = (algebraic[0]*(constants[12]*algebraic[1]+constants[10]*constants[15]))/algebraic[8] algebraic[10] = (algebraic[0]*(constants[11]*constants[13]+constants[9]*constants[14]))/algebraic[8] algebraic[11] = (algebraic[0]/algebraic[8])*(constants[12]*algebraic[1]*constants[9]*constants[14]-constants[11]*constants[13]*constants[10]*constants[15]) algebraic[12] = (algebraic[0]/algebraic[8])*constants[11]*constants[13]*(constants[12]*algebraic[1]+constants[10]*constants[15]) algebraic[13] = (algebraic[0]/algebraic[8])*constants[9]*constants[14]*(constants[12]*algebraic[1]+constants[10]*constants[15]) algebraic[14] = -algebraic[11] 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)