# Size of variable arrays: sizeAlgebraic = 19 sizeStates = 7 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_constants[0] = "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_Na_o in component environment (fmol)" legend_states[3] = "q_Na_i in component environment (fmol)" legend_states[4] = "q_x0_funny in component environment (fmol)" legend_states[5] = "q_x1_funny in component environment (fmol)" legend_states[6] = "q_mem in component environment (fC)" legend_constants[1] = "R in component environment (J_per_K_per_mol)" legend_constants[2] = "T in component environment (kelvin)" legend_constants[3] = "F in component environment (C_per_mol)" legend_algebraic[13] = "v_funny_K in component funny (fmol_per_sec)" legend_algebraic[14] = "v_funny_Na in component funny (fmol_per_sec)" legend_algebraic[18] = "I_mem_funny in component funny (fA)" legend_constants[4] = "kappa_funny_Na in component funny_parameters (fmol_per_sec)" legend_constants[5] = "kappa_funny_K in component funny_parameters (fmol_per_sec)" legend_constants[6] = "kappa_R_xf in component funny_parameters (fmol_per_sec)" legend_constants[7] = "K_Na_i in component funny_parameters (per_fmol)" legend_constants[8] = "K_Na_o in component funny_parameters (per_fmol)" legend_constants[9] = "K_K_i in component funny_parameters (per_fmol)" legend_constants[10] = "K_K_o in component funny_parameters (per_fmol)" legend_constants[11] = "K_x0_funny in component funny_parameters (per_fmol)" legend_constants[12] = "K_x1_funny in component funny_parameters (per_fmol)" legend_constants[13] = "zNa in component funny_parameters (dimensionless)" legend_constants[14] = "zK in component funny_parameters (dimensionless)" legend_constants[15] = "z_xff in component funny_parameters (dimensionless)" legend_constants[16] = "z_xfr in component funny_parameters (dimensionless)" legend_algebraic[0] = "mu_K_i in component funny (J_per_mol)" legend_algebraic[1] = "mu_K_o in component funny (J_per_mol)" legend_algebraic[2] = "mu_Na_i in component funny (J_per_mol)" legend_algebraic[3] = "mu_Na_o in component funny (J_per_mol)" legend_algebraic[4] = "V_mem in component funny (J_per_C)" legend_algebraic[6] = "Am_Na in component funny (J_per_mol)" legend_algebraic[5] = "Am_K in component funny (J_per_mol)" legend_algebraic[9] = "Af_K in component funny (J_per_mol)" legend_algebraic[10] = "Ar_K in component funny (J_per_mol)" legend_algebraic[11] = "Af_Na in component funny (J_per_mol)" legend_algebraic[12] = "Ar_Na in component funny (J_per_mol)" legend_algebraic[7] = "mu_x0_funny in component funny (J_per_mol)" legend_algebraic[8] = "mu_x1_funny in component funny (J_per_mol)" legend_algebraic[15] = "Af_R_xf in component funny (J_per_mol)" legend_algebraic[16] = "Ar_R_xf in component funny (J_per_mol)" legend_algebraic[17] = "v_xf in component funny (fmol_per_sec)" legend_rates[1] = "d/dt q_K_i in component environment (fmol)" legend_rates[0] = "d/dt q_K_o in component environment (fmol)" legend_rates[3] = "d/dt q_Na_i in component environment (fmol)" legend_rates[2] = "d/dt q_Na_o in component environment (fmol)" legend_rates[6] = "d/dt q_mem in component environment (fC)" legend_rates[4] = "d/dt q_x0_funny in component environment (fmol)" legend_rates[5] = "d/dt q_x1_funny 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] = 153400 states[0] = 27.9828 states[1] = 5510 states[2] = 9.3276 states[3] = 0.00456 states[4] = 5.4799070E-06 states[5] = 5.4799070E-06 states[6] = -8.5e4 constants[1] = 8.31 constants[2] = 310 constants[3] = 96500 constants[4] = 45.0247 constants[5] = 91.4974 constants[6] = 0.188833 constants[7] = 1.80864 constants[8] = 13.2633 constants[9] = 2.57828 constants[10] = 18.9074 constants[11] = 0.00306604 constants[12] = 61.5887 constants[13] = 1 constants[14] = 1 constants[15] = -1.8309039 constants[16] = 0.787348905 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[4] = states[6]/constants[0] algebraic[5] = constants[14]*constants[3]*algebraic[4] algebraic[0] = constants[1]*constants[2]*log(constants[9]*states[1]) algebraic[8] = constants[1]*constants[2]*log(constants[12]*states[5]) algebraic[9] = algebraic[8]+algebraic[0]+algebraic[5] algebraic[1] = constants[1]*constants[2]*log(constants[10]*states[0]) algebraic[10] = algebraic[8]+algebraic[1] algebraic[13] = custom_piecewise([equal(algebraic[5] , 0.00000), 1.00000*constants[5]*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[10]/(constants[1]*constants[2]))) , True, (((1.00000*constants[5]*algebraic[5])/(constants[1]*constants[2]))/(exp(algebraic[5]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[10]/(constants[1]*constants[2])))]) rates[1] = -algebraic[13] rates[0] = algebraic[13] algebraic[6] = constants[13]*constants[3]*algebraic[4] algebraic[2] = constants[1]*constants[2]*log(constants[7]*states[3]) algebraic[11] = algebraic[8]+algebraic[2]+algebraic[6] algebraic[3] = constants[1]*constants[2]*log(constants[8]*states[2]) algebraic[12] = algebraic[8]+algebraic[3] algebraic[14] = custom_piecewise([equal(algebraic[6] , 0.00000), 1.00000*constants[4]*(exp(algebraic[11]/(constants[1]*constants[2]))-exp(algebraic[12]/(constants[1]*constants[2]))) , True, (((1.00000*constants[4]*algebraic[6])/(constants[1]*constants[2]))/(exp(algebraic[6]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[11]/(constants[1]*constants[2]))-exp(algebraic[12]/(constants[1]*constants[2])))]) rates[3] = -algebraic[14] rates[2] = algebraic[14] algebraic[7] = constants[1]*constants[2]*log(constants[11]*states[4]) algebraic[15] = algebraic[7]+constants[15]*constants[3]*algebraic[4] algebraic[16] = algebraic[8]+constants[16]*constants[3]*algebraic[4] algebraic[17] = constants[6]*(exp(algebraic[15]/(constants[1]*constants[2]))-exp(algebraic[16]/(constants[1]*constants[2]))) rates[4] = -algebraic[17] rates[5] = algebraic[17] algebraic[18] = constants[3]*((-constants[14]*algebraic[13]+constants[13]*algebraic[14]+constants[16]*algebraic[17])-constants[15]*algebraic[17]) rates[6] = algebraic[18] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[4] = states[6]/constants[0] algebraic[5] = constants[14]*constants[3]*algebraic[4] algebraic[0] = constants[1]*constants[2]*log(constants[9]*states[1]) algebraic[8] = constants[1]*constants[2]*log(constants[12]*states[5]) algebraic[9] = algebraic[8]+algebraic[0]+algebraic[5] algebraic[1] = constants[1]*constants[2]*log(constants[10]*states[0]) algebraic[10] = algebraic[8]+algebraic[1] algebraic[13] = custom_piecewise([equal(algebraic[5] , 0.00000), 1.00000*constants[5]*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[10]/(constants[1]*constants[2]))) , True, (((1.00000*constants[5]*algebraic[5])/(constants[1]*constants[2]))/(exp(algebraic[5]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[9]/(constants[1]*constants[2]))-exp(algebraic[10]/(constants[1]*constants[2])))]) algebraic[6] = constants[13]*constants[3]*algebraic[4] algebraic[2] = constants[1]*constants[2]*log(constants[7]*states[3]) algebraic[11] = algebraic[8]+algebraic[2]+algebraic[6] algebraic[3] = constants[1]*constants[2]*log(constants[8]*states[2]) algebraic[12] = algebraic[8]+algebraic[3] algebraic[14] = custom_piecewise([equal(algebraic[6] , 0.00000), 1.00000*constants[4]*(exp(algebraic[11]/(constants[1]*constants[2]))-exp(algebraic[12]/(constants[1]*constants[2]))) , True, (((1.00000*constants[4]*algebraic[6])/(constants[1]*constants[2]))/(exp(algebraic[6]/(constants[1]*constants[2]))-1.00000))*(exp(algebraic[11]/(constants[1]*constants[2]))-exp(algebraic[12]/(constants[1]*constants[2])))]) algebraic[7] = constants[1]*constants[2]*log(constants[11]*states[4]) algebraic[15] = algebraic[7]+constants[15]*constants[3]*algebraic[4] algebraic[16] = algebraic[8]+constants[16]*constants[3]*algebraic[4] algebraic[17] = constants[6]*(exp(algebraic[15]/(constants[1]*constants[2]))-exp(algebraic[16]/(constants[1]*constants[2]))) algebraic[18] = constants[3]*((-constants[14]*algebraic[13]+constants[13]*algebraic[14]+constants[16]*algebraic[17])-constants[15]*algebraic[17]) 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)