# Size of variable arrays: sizeAlgebraic = 15 sizeStates = 5 sizeConstants = 13 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "t in component environment (second)" legend_constants[0] = "R in component environment (J_per_K_per_mol)" legend_constants[1] = "T in component environment (kelvin)" legend_constants[2] = "F in component environment (C_per_mol)" legend_constants[3] = "C_m in component environment (fF)" legend_states[0] = "q_K_o in component environment (fmol)" legend_states[1] = "q_K_i in component environment (fmol)" legend_states[2] = "q_C_Kp in component environment (fmol)" legend_states[3] = "q_O_Kp in component environment (fmol)" legend_algebraic[11] = "v_Kp in component Kp (fmol_per_sec)" legend_states[4] = "q_mem in component environment (fC)" legend_algebraic[13] = "I_mem_Kp in component Kp (fA)" legend_constants[4] = "K_C_Kp in component Kp_parameters (per_fmol)" legend_constants[5] = "K_K_o in component Kp_parameters (per_fmol)" legend_constants[6] = "K_K_i in component Kp_parameters (per_fmol)" legend_constants[7] = "K_O_Kp in component Kp_parameters (per_fmol)" legend_constants[8] = "kappa_Kp in component Kp_parameters (fmol_per_sec)" legend_constants[9] = "kappa_gKp in component Kp_parameters (fmol_per_sec)" legend_constants[10] = "zK in component Kp_parameters (dimensionless)" legend_constants[11] = "z_f_Kp in component Kp_parameters (dimensionless)" legend_constants[12] = "z_r_Kp in component Kp_parameters (dimensionless)" legend_algebraic[2] = "mu_K_o in component Kp (J_per_mol)" legend_algebraic[3] = "mu_K_i in component Kp (J_per_mol)" legend_algebraic[1] = "mu_C_Kp in component Kp (J_per_mol)" legend_algebraic[4] = "mu_O_Kp in component Kp (J_per_mol)" legend_algebraic[7] = "Am_Kp in component Kp (J_per_mol)" legend_algebraic[5] = "Af_Kp in component Kp (J_per_mol)" legend_algebraic[8] = "Ar_Kp in component Kp (J_per_mol)" legend_algebraic[6] = "Af_gKp in component Kp (J_per_mol)" legend_algebraic[9] = "Ar_gKp in component Kp (J_per_mol)" legend_algebraic[10] = "v_gKp in component Kp (fmol_per_sec)" legend_algebraic[12] = "v_C_Kp in component Kp (fmol_per_sec)" legend_algebraic[14] = "v_O_Kp in component Kp (fmol_per_sec)" legend_algebraic[0] = "V_mem in component Kp (volt)" legend_rates[0] = "d/dt q_K_o in component environment (fmol)" legend_rates[1] = "d/dt q_K_i in component environment (fmol)" legend_rates[4] = "d/dt q_mem in component environment (fC)" legend_rates[2] = "d/dt q_C_Kp in component environment (fmol)" legend_rates[3] = "d/dt q_O_Kp in component environment (fmol)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 8.314 constants[1] = 310 constants[2] = 96485 constants[3] = 153400 states[0] = 27.9828 states[1] = 5510 states[2] = 1.3813E-07 states[3] = 3.45317E-08 states[4] = -13039 constants[4] = 41.6265 constants[5] = 0.059344 constants[6] = 0.0080926 constants[7] = 145.607 constants[8] = 252.3419 constants[9] = 24.0195 constants[10] = 1 constants[11] = 0 constants[12] = -4.4669 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = states[4]/constants[3] algebraic[7] = constants[10]*constants[2]*algebraic[0] algebraic[3] = constants[0]*constants[1]*log(constants[6]*states[1]) algebraic[4] = constants[0]*constants[1]*log(constants[7]*states[3]) algebraic[5] = algebraic[3]+constants[10]*constants[2]*algebraic[0]+algebraic[4] algebraic[2] = constants[0]*constants[1]*log(constants[5]*states[0]) algebraic[8] = algebraic[2]+algebraic[4] algebraic[11] = custom_piecewise([equal(algebraic[7] , 0.00000), constants[8]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1]))) , True, (((constants[8]*algebraic[7])/(constants[0]*constants[1]))/(exp(algebraic[7]/(constants[0]*constants[1]))-1.00000))*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1])))]) rates[0] = algebraic[11] rates[1] = -algebraic[11] algebraic[6] = constants[0]*constants[1]*log(constants[4]*states[2])+constants[11]*constants[2]*algebraic[0] algebraic[9] = constants[0]*constants[1]*log(constants[7]*states[3])+constants[12]*constants[2]*algebraic[0] algebraic[10] = constants[9]*(exp(algebraic[6]/(constants[0]*constants[1]))-exp(algebraic[9]/(constants[0]*constants[1]))) algebraic[12] = -algebraic[10] rates[2] = algebraic[12] algebraic[13] = constants[2]*((-constants[10]*algebraic[11]+constants[12]*algebraic[10])-constants[11]*algebraic[10]) rates[4] = algebraic[13] algebraic[14] = algebraic[10]-(algebraic[11]-algebraic[11]) rates[3] = algebraic[14] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[4]/constants[3] algebraic[7] = constants[10]*constants[2]*algebraic[0] algebraic[3] = constants[0]*constants[1]*log(constants[6]*states[1]) algebraic[4] = constants[0]*constants[1]*log(constants[7]*states[3]) algebraic[5] = algebraic[3]+constants[10]*constants[2]*algebraic[0]+algebraic[4] algebraic[2] = constants[0]*constants[1]*log(constants[5]*states[0]) algebraic[8] = algebraic[2]+algebraic[4] algebraic[11] = custom_piecewise([equal(algebraic[7] , 0.00000), constants[8]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1]))) , True, (((constants[8]*algebraic[7])/(constants[0]*constants[1]))/(exp(algebraic[7]/(constants[0]*constants[1]))-1.00000))*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1])))]) algebraic[6] = constants[0]*constants[1]*log(constants[4]*states[2])+constants[11]*constants[2]*algebraic[0] algebraic[9] = constants[0]*constants[1]*log(constants[7]*states[3])+constants[12]*constants[2]*algebraic[0] algebraic[10] = constants[9]*(exp(algebraic[6]/(constants[0]*constants[1]))-exp(algebraic[9]/(constants[0]*constants[1]))) algebraic[12] = -algebraic[10] algebraic[13] = constants[2]*((-constants[10]*algebraic[11]+constants[12]*algebraic[10])-constants[11]*algebraic[10]) algebraic[14] = algebraic[10]-(algebraic[11]-algebraic[11]) algebraic[1] = constants[0]*constants[1]*log(constants[4]*states[2]) return algebraic def custom_piecewise(cases): """Compute result of a piecewise function""" return select(cases[0::2],cases[1::2]) 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)