Generated Code

# Size of variable arrays:
sizeAlgebraic = 8
sizeStates = 3
sizeConstants = 22
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_algebraic[1] = "Istim in component stimulus_protocol (per_ms)"
    legend_constants[0] = "IstimStart in component stimulus_protocol (ms)"
    legend_constants[1] = "IstimEnd in component stimulus_protocol (ms)"
    legend_constants[2] = "IstimAmplitude in component stimulus_protocol (per_ms)"
    legend_constants[3] = "IstimPeriod in component stimulus_protocol (ms)"
    legend_constants[4] = "IstimPulseDuration in component stimulus_protocol (ms)"
    legend_states[0] = "u in component membrane (dimensionless)"
    legend_constants[5] = "Cm in component membrane (uF_per_cm2)"
    legend_algebraic[0] = "Vm in component membrane (mV)"
    legend_constants[6] = "V_0 in component membrane (mV)"
    legend_constants[7] = "V_fi in component membrane (mV)"
    legend_algebraic[3] = "J_fi in component fast_inward_current (per_ms)"
    legend_algebraic[5] = "J_so in component slow_outward_current (per_ms)"
    legend_algebraic[7] = "J_si in component slow_inward_current (per_ms)"
    legend_algebraic[2] = "p in component p (dimensionless)"
    legend_constants[8] = "u_c in component p (dimensionless)"
    legend_algebraic[4] = "q in component q (dimensionless)"
    legend_constants[9] = "u_v in component q (dimensionless)"
    legend_constants[21] = "tau_d in component fast_inward_current (ms)"
    legend_constants[10] = "g_fi_max in component fast_inward_current (mS_per_cm2)"
    legend_states[1] = "v in component fast_inward_current_v_gate (dimensionless)"
    legend_algebraic[6] = "tau_v_minus in component fast_inward_current_v_gate (ms)"
    legend_constants[11] = "tau_v1_minus in component fast_inward_current_v_gate (ms)"
    legend_constants[12] = "tau_v2_minus in component fast_inward_current_v_gate (ms)"
    legend_constants[13] = "tau_v_plus in component fast_inward_current_v_gate (ms)"
    legend_constants[14] = "tau_0 in component slow_outward_current (ms)"
    legend_constants[15] = "tau_r in component slow_outward_current (ms)"
    legend_constants[16] = "tau_si in component slow_inward_current (ms)"
    legend_constants[17] = "u_csi in component slow_inward_current (dimensionless)"
    legend_constants[18] = "k in component slow_inward_current (dimensionless)"
    legend_states[2] = "w in component slow_inward_current_w_gate (dimensionless)"
    legend_constants[19] = "tau_w_minus in component slow_inward_current_w_gate (ms)"
    legend_constants[20] = "tau_w_plus in component slow_inward_current_w_gate (ms)"
    legend_rates[0] = "d/dt u in component membrane (dimensionless)"
    legend_rates[1] = "d/dt v in component fast_inward_current_v_gate (dimensionless)"
    legend_rates[2] = "d/dt w in component slow_inward_current_w_gate (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 100
    constants[1] = 50000
    constants[2] = -0.2
    constants[3] = 1000
    constants[4] = 1
    states[0] = 0
    constants[5] = 1
    constants[6] = -85
    constants[7] = 15
    constants[8] = 0.13
    constants[9] = 0
    constants[10] = 5.8
    states[1] = 1
    constants[11] = 18.2
    constants[12] = 18.2
    constants[13] = 10
    constants[14] = 12.5
    constants[15] = 130
    constants[16] = 127
    constants[17] = 0.85
    constants[18] = 10
    states[2] = 1
    constants[19] = 80
    constants[20] = 1020
    constants[21] = constants[5]/constants[10]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[2] = custom_piecewise([less(states[0] , constants[8]), 0.00000 , True, 1.00000])
    rates[2] = ((1.00000-algebraic[2])*(1.00000-states[2]))/constants[19]-(algebraic[2]*states[2])/constants[20]
    algebraic[4] = custom_piecewise([less(states[0] , constants[9]), 0.00000 , True, 1.00000])
    algebraic[6] = algebraic[4]*constants[11]+(1.00000-algebraic[4])*constants[12]
    rates[1] = ((1.00000-algebraic[2])*(1.00000-states[1]))/algebraic[6]-(algebraic[2]*states[1])/constants[13]
    algebraic[1] = custom_piecewise([greater_equal(voi , constants[0]) & less_equal(voi , constants[1]) & less_equal((voi-constants[0])-floor((voi-constants[0])/constants[3])*constants[3] , constants[4]), constants[2] , True, 0.00000])
    algebraic[3] = (-states[1]*algebraic[2]*(1.00000-states[0])*(states[0]-constants[8]))/constants[21]
    algebraic[5] = (states[0]*(1.00000-algebraic[2]))/constants[14]+algebraic[2]/constants[15]
    algebraic[7] = (-states[2]*(1.00000+tanh(constants[18]*(states[0]-constants[17]))))/(2.00000*constants[16])
    rates[0] = -(algebraic[3]+algebraic[5]+algebraic[7]+algebraic[1])
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[2] = custom_piecewise([less(states[0] , constants[8]), 0.00000 , True, 1.00000])
    algebraic[4] = custom_piecewise([less(states[0] , constants[9]), 0.00000 , True, 1.00000])
    algebraic[6] = algebraic[4]*constants[11]+(1.00000-algebraic[4])*constants[12]
    algebraic[1] = custom_piecewise([greater_equal(voi , constants[0]) & less_equal(voi , constants[1]) & less_equal((voi-constants[0])-floor((voi-constants[0])/constants[3])*constants[3] , constants[4]), constants[2] , True, 0.00000])
    algebraic[3] = (-states[1]*algebraic[2]*(1.00000-states[0])*(states[0]-constants[8]))/constants[21]
    algebraic[5] = (states[0]*(1.00000-algebraic[2]))/constants[14]+algebraic[2]/constants[15]
    algebraic[7] = (-states[2]*(1.00000+tanh(constants[18]*(states[0]-constants[17]))))/(2.00000*constants[16])
    algebraic[0] = constants[6]+states[0]*(constants[7]-constants[6])
    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)