Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 12
sizeStates = 5
sizeConstants = 31
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 interface (ms)"
legend_constants[0] = "Cm in component interface (uFpmmsq)"
legend_constants[1] = "Am in component interface (pmm)"
legend_algebraic[0] = "Istim in component interface (uApmmcu)"
legend_states[0] = "Vm in component membrane (mV)"
legend_states[1] = "Vt in component Ttubular_current_Vt_var (mV)"
legend_states[2] = "m in component sodium_current_m_gate (dimensionless)"
legend_states[3] = "h in component sodium_current_h_gate (dimensionless)"
legend_states[4] = "n in component potassium_current_n_gate (dimensionless)"
legend_algebraic[4] = "INa in component sodium_current (uApmmsq)"
legend_algebraic[9] = "IK in component potassium_current (uApmmsq)"
legend_algebraic[10] = "IL in component leak_current (uApmmsq)"
legend_algebraic[11] = "IT in component Ttubular_current (uApmmsq)"
legend_algebraic[5] = "IStimC in component interface (uApmmcu)"
legend_constants[30] = "AmC in component interface (pmm)"
legend_constants[2] = "IstimStart in component interface (ms)"
legend_constants[3] = "IstimEnd in component interface (ms)"
legend_constants[4] = "IstimAmplitude in component interface (uApmmcu)"
legend_constants[5] = "IstimPeriod in component interface (ms)"
legend_constants[6] = "IstimPulseDuration in component interface (ms)"
legend_constants[7] = "gNa_max in component sodium_current (mSpmmsq)"
legend_constants[8] = "ENa in component sodium_current (mV)"
legend_algebraic[1] = "alpha_m in component sodium_current_m_gate (pms)"
legend_algebraic[6] = "beta_m in component sodium_current_m_gate (pms)"
legend_constants[9] = "alpha_m_max in component sodium_current_m_gate (pms)"
legend_constants[10] = "beta_m_max in component sodium_current_m_gate (pms)"
legend_constants[11] = "Em in component sodium_current_m_gate (mV)"
legend_constants[12] = "v_alpha_m in component sodium_current_m_gate (dimensionless)"
legend_constants[13] = "v_beta_m in component sodium_current_m_gate (mV)"
legend_algebraic[2] = "alpha_h in component sodium_current_h_gate (pms)"
legend_algebraic[7] = "beta_h in component sodium_current_h_gate (pms)"
legend_constants[14] = "alpha_h_max in component sodium_current_h_gate (pms)"
legend_constants[15] = "beta_h_max in component sodium_current_h_gate (pms)"
legend_constants[16] = "Eh in component sodium_current_h_gate (mV)"
legend_constants[17] = "v_alpha_h in component sodium_current_h_gate (mV)"
legend_constants[18] = "v_beta_h in component sodium_current_h_gate (mV)"
legend_constants[19] = "gK_max in component potassium_current (mSpmmsq)"
legend_constants[20] = "EK in component potassium_current (mV)"
legend_algebraic[3] = "alpha_n in component potassium_current_n_gate (pms)"
legend_algebraic[8] = "beta_n in component potassium_current_n_gate (pms)"
legend_constants[21] = "alpha_n_max in component potassium_current_n_gate (pms)"
legend_constants[22] = "beta_n_max in component potassium_current_n_gate (pms)"
legend_constants[23] = "En in component potassium_current_n_gate (mV)"
legend_constants[24] = "v_alpha_n in component potassium_current_n_gate (dimensionless)"
legend_constants[25] = "v_beta_n in component potassium_current_n_gate (mV)"
legend_constants[26] = "EL in component leak_current (mV)"
legend_constants[27] = "gL_max in component leak_current (mSpmmsq)"
legend_constants[28] = "Rs in component Ttubular_current (mmsqpmS)"
legend_constants[29] = "Ct in component Ttubular_current_Vt_var (uFpmmsq)"
legend_rates[0] = "d/dt Vm in component membrane (mV)"
legend_rates[2] = "d/dt m in component sodium_current_m_gate (dimensionless)"
legend_rates[3] = "d/dt h in component sodium_current_h_gate (dimensionless)"
legend_rates[4] = "d/dt n in component potassium_current_n_gate (dimensionless)"
legend_rates[1] = "d/dt Vt in component Ttubular_current_Vt_var (mV)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 0.009
constants[1] = 200.0
states[0] = -95.0
states[1] = -95.0
states[2] = 0.0
states[3] = 1.0
states[4] = 0.0
constants[2] = 10
constants[3] = 50000
constants[4] = 0.5
constants[5] = 1000
constants[6] = 1
constants[7] = 1.8
constants[8] = 50.0
constants[9] = 0.208
constants[10] = 2.081
constants[11] = -42.0
constants[12] = 10.0
constants[13] = 18.0
constants[14] = 0.0156
constants[15] = 3.382
constants[16] = -41.0
constants[17] = 14.7
constants[18] = 7.6
constants[19] = 0.415
constants[20] = -70.0
constants[21] = 0.0229
constants[22] = 0.09616
constants[23] = -40.0
constants[24] = 7.0
constants[25] = 40.0
constants[26] = -95.0
constants[27] = 0.0024
constants[28] = 15.0
constants[29] = 0.04
constants[30] = constants[1]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[1] = (states[0]-states[1])/(constants[28]*constants[29])
algebraic[1] = (constants[9]*(states[0]-constants[11]))/(1.00000-exp((constants[11]-states[0])/constants[12]))
algebraic[6] = constants[10]*exp((constants[11]-states[0])/constants[13])
rates[2] = algebraic[1]*(1.00000-states[2])-algebraic[6]*states[2]
algebraic[2] = constants[14]*exp((constants[16]-states[0])/constants[17])
algebraic[7] = constants[15]/(1.00000+exp((constants[16]-states[0])/constants[18]))
rates[3] = algebraic[2]*(1.00000-states[3])-algebraic[7]*states[3]
algebraic[3] = (constants[21]*(states[0]-constants[23]))/(1.00000-exp((constants[23]-states[0])/constants[24]))
algebraic[8] = constants[22]*exp((constants[23]-states[0])/constants[25])
rates[4] = algebraic[3]*(1.00000-states[4])-algebraic[8]*states[4]
algebraic[0] = custom_piecewise([greater_equal(voi , constants[2]) & less_equal(voi , constants[3]) & less_equal((voi-constants[2])-floor((voi-constants[2])/constants[5])*constants[5] , constants[6]), constants[4] , True, 0.00000])
algebraic[4] = constants[7]*states[2]*states[2]*states[2]*states[3]*(states[0]-constants[8])
algebraic[9] = constants[19]*states[4]*states[4]*states[4]*states[4]*(states[0]-constants[20])
algebraic[10] = constants[27]*(states[0]-constants[26])
algebraic[11] = (states[0]-states[1])/constants[28]
rates[0] = (algebraic[0]-(algebraic[4]+algebraic[9]+algebraic[10]+algebraic[11]))/constants[0]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = (constants[9]*(states[0]-constants[11]))/(1.00000-exp((constants[11]-states[0])/constants[12]))
algebraic[6] = constants[10]*exp((constants[11]-states[0])/constants[13])
algebraic[2] = constants[14]*exp((constants[16]-states[0])/constants[17])
algebraic[7] = constants[15]/(1.00000+exp((constants[16]-states[0])/constants[18]))
algebraic[3] = (constants[21]*(states[0]-constants[23]))/(1.00000-exp((constants[23]-states[0])/constants[24]))
algebraic[8] = constants[22]*exp((constants[23]-states[0])/constants[25])
algebraic[0] = custom_piecewise([greater_equal(voi , constants[2]) & less_equal(voi , constants[3]) & less_equal((voi-constants[2])-floor((voi-constants[2])/constants[5])*constants[5] , constants[6]), constants[4] , True, 0.00000])
algebraic[4] = constants[7]*states[2]*states[2]*states[2]*states[3]*(states[0]-constants[8])
algebraic[9] = constants[19]*states[4]*states[4]*states[4]*states[4]*(states[0]-constants[20])
algebraic[10] = constants[27]*(states[0]-constants[26])
algebraic[11] = (states[0]-states[1])/constants[28]
algebraic[5] = algebraic[0]
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)