Generated Code
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The raw code is available.
# Size of variable arrays: sizeAlgebraic = 18 sizeStates = 8 sizeConstants = 10 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 (ms)" legend_states[0] = "V in component membrane (mV)" legend_constants[0] = "C in component membrane (uF_per_mm2)" legend_algebraic[0] = "i_Na in component sodium_current (uA_per_mm2)" legend_algebraic[14] = "i_s in component slow_inward_current (uA_per_mm2)" legend_algebraic[15] = "i_x1 in component time_dependent_outward_current (uA_per_mm2)" legend_algebraic[16] = "i_K1 in component time_independent_outward_current (uA_per_mm2)" legend_algebraic[17] = "Istim in component stimulus_protocol (uA_per_mm2)" legend_constants[1] = "g_Na in component sodium_current (mS_per_mm2)" legend_constants[2] = "E_Na in component sodium_current (mV)" legend_constants[3] = "g_Nac in component sodium_current (mS_per_mm2)" legend_states[1] = "m in component sodium_current_m_gate (dimensionless)" legend_states[2] = "h in component sodium_current_h_gate (dimensionless)" legend_states[3] = "j in component sodium_current_j_gate (dimensionless)" legend_algebraic[1] = "alpha_m in component sodium_current_m_gate (per_ms)" legend_algebraic[8] = "beta_m in component sodium_current_m_gate (per_ms)" legend_algebraic[2] = "alpha_h in component sodium_current_h_gate (per_ms)" legend_algebraic[9] = "beta_h in component sodium_current_h_gate (per_ms)" legend_algebraic[3] = "alpha_j in component sodium_current_j_gate (per_ms)" legend_algebraic[10] = "beta_j in component sodium_current_j_gate (per_ms)" legend_constants[4] = "g_s in component slow_inward_current (mS_per_mm2)" legend_algebraic[7] = "E_s in component slow_inward_current (mV)" legend_states[4] = "Cai in component slow_inward_current (concentration_units)" legend_states[5] = "d in component slow_inward_current_d_gate (dimensionless)" legend_states[6] = "f in component slow_inward_current_f_gate (dimensionless)" legend_algebraic[4] = "alpha_d in component slow_inward_current_d_gate (per_ms)" legend_algebraic[11] = "beta_d in component slow_inward_current_d_gate (per_ms)" legend_algebraic[5] = "alpha_f in component slow_inward_current_f_gate (per_ms)" legend_algebraic[12] = "beta_f in component slow_inward_current_f_gate (per_ms)" legend_states[7] = "x1 in component time_dependent_outward_current_x1_gate (dimensionless)" legend_algebraic[6] = "alpha_x1 in component time_dependent_outward_current_x1_gate (per_ms)" legend_algebraic[13] = "beta_x1 in component time_dependent_outward_current_x1_gate (per_ms)" legend_constants[5] = "IstimStart in component stimulus_protocol (ms)" legend_constants[6] = "IstimEnd in component stimulus_protocol (ms)" legend_constants[7] = "IstimAmplitude in component stimulus_protocol (uA_per_mm2)" legend_constants[8] = "IstimPeriod in component stimulus_protocol (ms)" legend_constants[9] = "IstimPulseDuration in component stimulus_protocol (ms)" legend_rates[0] = "d/dt V in component membrane (mV)" legend_rates[1] = "d/dt m in component sodium_current_m_gate (dimensionless)" legend_rates[2] = "d/dt h in component sodium_current_h_gate (dimensionless)" legend_rates[3] = "d/dt j in component sodium_current_j_gate (dimensionless)" legend_rates[4] = "d/dt Cai in component slow_inward_current (concentration_units)" legend_rates[5] = "d/dt d in component slow_inward_current_d_gate (dimensionless)" legend_rates[6] = "d/dt f in component slow_inward_current_f_gate (dimensionless)" legend_rates[7] = "d/dt x1 in component time_dependent_outward_current_x1_gate (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = -84.624 constants[0] = 0.01 constants[1] = 4e-2 constants[2] = 50 constants[3] = 3e-5 states[1] = 0.011 states[2] = 0.988 states[3] = 0.975 constants[4] = 9e-4 states[4] = 1e-4 states[5] = 0.003 states[6] = 0.994 states[7] = 0.0001 constants[5] = 10 constants[6] = 50000 constants[7] = 0.5 constants[8] = 1000 constants[9] = 1 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[1] = (-1.00000*(states[0]+47.0000))/(exp(-0.100000*(states[0]+47.0000))-1.00000) algebraic[8] = 40.0000*exp(-0.0560000*(states[0]+72.0000)) rates[1] = algebraic[1]*(1.00000-states[1])-algebraic[8]*states[1] algebraic[2] = 0.126000*exp(-0.250000*(states[0]+77.0000)) algebraic[9] = 1.70000/(exp(-0.0820000*(states[0]+22.5000))+1.00000) rates[2] = algebraic[2]*(1.00000-states[2])-algebraic[9]*states[2] algebraic[3] = (0.0550000*exp(-0.250000*(states[0]+78.0000)))/(exp(-0.200000*(states[0]+78.0000))+1.00000) algebraic[10] = 0.300000/(exp(-0.100000*(states[0]+32.0000))+1.00000) rates[3] = algebraic[3]*(1.00000-states[3])-algebraic[10]*states[3] algebraic[4] = (0.0950000*exp(-(states[0]-5.00000)/100.000))/(1.00000+exp(-(states[0]-5.00000)/13.8900)) algebraic[11] = (0.0700000*exp(-(states[0]+44.0000)/59.0000))/(1.00000+exp((states[0]+44.0000)/20.0000)) rates[5] = algebraic[4]*(1.00000-states[5])-algebraic[11]*states[5] algebraic[5] = (0.0120000*exp(-(states[0]+28.0000)/125.000))/(1.00000+exp((states[0]+28.0000)/6.67000)) algebraic[12] = (0.00650000*exp(-(states[0]+30.0000)/50.0000))/(1.00000+exp(-(states[0]+30.0000)/5.00000)) rates[6] = algebraic[5]*(1.00000-states[6])-algebraic[12]*states[6] algebraic[6] = (0.000500000*exp((states[0]+50.0000)/12.1000))/(1.00000+exp((states[0]+50.0000)/17.5000)) algebraic[13] = (0.00130000*exp(-(states[0]+20.0000)/16.6700))/(1.00000+exp(-(states[0]+20.0000)/25.0000)) rates[7] = algebraic[6]*(1.00000-states[7])-algebraic[13]*states[7] algebraic[7] = -82.3000-13.0287*log(states[4]*0.00100000) algebraic[14] = constants[4]*states[5]*states[6]*(states[0]-algebraic[7]) rates[4] = (-0.0100000*algebraic[14])/1.00000+0.0700000*(0.000100000-states[4]) algebraic[0] = (constants[1]*(power(states[1], 3.00000))*states[2]*states[3]+constants[3])*(states[0]-constants[2]) algebraic[15] = (states[7]*0.00800000*(exp(0.0400000*(states[0]+77.0000))-1.00000))/exp(0.0400000*(states[0]+35.0000)) algebraic[16] = 0.00350000*((4.00000*(exp(0.0400000*(states[0]+85.0000))-1.00000))/(exp(0.0800000*(states[0]+53.0000))+exp(0.0400000*(states[0]+53.0000)))+(0.200000*(states[0]+23.0000))/(1.00000-exp(-0.0400000*(states[0]+23.0000)))) algebraic[17] = custom_piecewise([greater_equal(voi , constants[5]) & less_equal(voi , constants[6]) & less_equal((voi-constants[5])-floor((voi-constants[5])/constants[8])*constants[8] , constants[9]), constants[7] , True, 0.00000]) rates[0] = (algebraic[17]-(algebraic[0]+algebraic[14]+algebraic[15]+algebraic[16]))/constants[0] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[1] = (-1.00000*(states[0]+47.0000))/(exp(-0.100000*(states[0]+47.0000))-1.00000) algebraic[8] = 40.0000*exp(-0.0560000*(states[0]+72.0000)) algebraic[2] = 0.126000*exp(-0.250000*(states[0]+77.0000)) algebraic[9] = 1.70000/(exp(-0.0820000*(states[0]+22.5000))+1.00000) algebraic[3] = (0.0550000*exp(-0.250000*(states[0]+78.0000)))/(exp(-0.200000*(states[0]+78.0000))+1.00000) algebraic[10] = 0.300000/(exp(-0.100000*(states[0]+32.0000))+1.00000) algebraic[4] = (0.0950000*exp(-(states[0]-5.00000)/100.000))/(1.00000+exp(-(states[0]-5.00000)/13.8900)) algebraic[11] = (0.0700000*exp(-(states[0]+44.0000)/59.0000))/(1.00000+exp((states[0]+44.0000)/20.0000)) algebraic[5] = (0.0120000*exp(-(states[0]+28.0000)/125.000))/(1.00000+exp((states[0]+28.0000)/6.67000)) algebraic[12] = (0.00650000*exp(-(states[0]+30.0000)/50.0000))/(1.00000+exp(-(states[0]+30.0000)/5.00000)) algebraic[6] = (0.000500000*exp((states[0]+50.0000)/12.1000))/(1.00000+exp((states[0]+50.0000)/17.5000)) algebraic[13] = (0.00130000*exp(-(states[0]+20.0000)/16.6700))/(1.00000+exp(-(states[0]+20.0000)/25.0000)) algebraic[7] = -82.3000-13.0287*log(states[4]*0.00100000) algebraic[14] = constants[4]*states[5]*states[6]*(states[0]-algebraic[7]) algebraic[0] = (constants[1]*(power(states[1], 3.00000))*states[2]*states[3]+constants[3])*(states[0]-constants[2]) algebraic[15] = (states[7]*0.00800000*(exp(0.0400000*(states[0]+77.0000))-1.00000))/exp(0.0400000*(states[0]+35.0000)) algebraic[16] = 0.00350000*((4.00000*(exp(0.0400000*(states[0]+85.0000))-1.00000))/(exp(0.0800000*(states[0]+53.0000))+exp(0.0400000*(states[0]+53.0000)))+(0.200000*(states[0]+23.0000))/(1.00000-exp(-0.0400000*(states[0]+23.0000)))) algebraic[17] = custom_piecewise([greater_equal(voi , constants[5]) & less_equal(voi , constants[6]) & less_equal((voi-constants[5])-floor((voi-constants[5])/constants[8])*constants[8] , constants[9]), constants[7] , True, 0.00000]) 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)