# Size of variable arrays: sizeAlgebraic = 18 sizeStates = 4 sizeConstants = 14 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_int in component concentrations (mM)" legend_states[1] = "HCO3_ext in component concentrations (mM)" legend_states[2] = "Cl_int in component concentrations (mM)" legend_states[3] = "Cl_ext in component concentrations (mM)" legend_algebraic[12] = "J_AE1_HCO3 in component AE1 (mM_per_s)" legend_algebraic[17] = "J_AE1_Cl in component AE1 (mM_per_s)" legend_algebraic[13] = "J_HCO3_influx in component AE1 (mM_per_s)" legend_algebraic[14] = "J_Cl_influx in component AE1 (mM_per_s)" legend_constants[0] = "K_HCO3_ext in component AE1 (mM)" legend_constants[1] = "K_HCO3_int in component AE1 (mM)" legend_constants[2] = "K_Cl_ext in component AE1 (mM)" legend_constants[3] = "K_Cl_int in component AE1 (mM)" legend_constants[4] = "P_HCO3_ext in component AE1 (per_s)" legend_constants[5] = "P_HCO3_int in component AE1 (per_s)" legend_constants[6] = "P_Cl_ext in component AE1 (per_s)" legend_constants[7] = "P_Cl_int in component AE1 (per_s)" legend_algebraic[1] = "beta_ext in component AE1 (dimensionless)" legend_algebraic[8] = "beta_int in component AE1 (dimensionless)" legend_algebraic[9] = "gamma_ext in component AE1 (dimensionless)" legend_algebraic[10] = "gamma_int in component AE1 (dimensionless)" legend_algebraic[11] = "sigma in component AE1 (per_s)" legend_constants[8] = "x_Tmax in component AE1 (mM)" legend_constants[9] = "K_I in component AE1 (mM)" legend_algebraic[0] = "x_T in component AE1 (mM)" legend_algebraic[15] = "x_ext in component AE1 (mM)" legend_algebraic[16] = "x_int in component AE1 (mM)" legend_algebraic[2] = "Jo_bm in component AE1 (mM_per_s)" legend_algebraic[3] = "Ji_bm in component AE1 (mM_per_s)" legend_algebraic[4] = "Js_bm in component AE1 (mM_per_s)" legend_algebraic[5] = "Jo_cm in component AE1 (mM_per_s)" legend_algebraic[6] = "Ji_cm in component AE1 (mM_per_s)" legend_algebraic[7] = "Js_cm in component AE1 (mM_per_s)" legend_rates[0] = "d/dt HCO3_int in component concentrations (mM)" legend_rates[1] = "d/dt HCO3_ext in component concentrations (mM)" legend_rates[2] = "d/dt Cl_int in component concentrations (mM)" legend_rates[3] = "d/dt Cl_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 states[1] = 1.0 states[2] = 0.0 states[3] = 0.0 constants[0] = 198 constants[1] = 198 constants[2] = 50 constants[3] = 50 constants[4] = 1247 constants[5] = 135 constants[6] = 562 constants[7] = 61 constants[8] = 1 constants[9] = 172 constants[10] = 1.00000 constants[11] = 1.00000 constants[12] = 0.00000 constants[13] = 0.00000 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[10] rates[1] = constants[11] rates[2] = constants[12] rates[3] = constants[13] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[8]/(1.00000+states[0]/constants[9]) algebraic[1] = states[1]/constants[0] algebraic[2] = power((1.00000/algebraic[0])*(1.00000/constants[4]+1.00000/constants[5]+constants[1]/(constants[5]*states[0])), -1.00000) algebraic[3] = power((1.00000/algebraic[0])*(1.00000/constants[4]+1.00000/constants[5]+constants[0]/(constants[4]*states[1])), -1.00000) algebraic[4] = power((1.00000/algebraic[0])*(1.00000/constants[4]+1.00000/constants[5]), -1.00000) algebraic[5] = power((1.00000/algebraic[0])*(1.00000/constants[6]+1.00000/constants[7]+constants[3]/(constants[7]*states[2])), -1.00000) algebraic[6] = power((1.00000/algebraic[0])*(1.00000/constants[6]+1.00000/constants[7]+constants[2]/(constants[6]*states[3])), -1.00000) algebraic[7] = power((1.00000/algebraic[0])*(1.00000/constants[6]+1.00000/constants[7]), -1.00000) algebraic[8] = states[0]/constants[1] algebraic[9] = states[3]/constants[2] algebraic[10] = states[2]/constants[3] algebraic[11] = (1.00000+algebraic[1]+algebraic[9])*(constants[5]*algebraic[8]+constants[7]*algebraic[10])+(1.00000+algebraic[8]+algebraic[10])*(constants[4]*algebraic[1]+constants[6]*algebraic[9]) algebraic[12] = (algebraic[0]/algebraic[11])*(constants[5]*algebraic[8]*constants[6]*algebraic[9]-constants[4]*algebraic[1]*constants[7]*algebraic[10]) algebraic[13] = (algebraic[0]/algebraic[11])*constants[4]*algebraic[1]*(constants[5]*algebraic[8]+constants[7]*algebraic[10]) algebraic[14] = (algebraic[0]/algebraic[11])*constants[6]*algebraic[9]*(constants[5]*algebraic[8]+constants[7]*algebraic[10]) algebraic[15] = (algebraic[0]*(constants[5]*algebraic[8]+constants[7]*algebraic[10]))/algebraic[11] algebraic[16] = (algebraic[0]*(constants[4]*algebraic[1]+constants[6]*algebraic[9]))/algebraic[11] algebraic[17] = -algebraic[12] 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)