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# Size of variable arrays:
sizeAlgebraic = 16
sizeStates = 8
sizeConstants = 37
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 Environmental (second)"
    legend_constants[0] = "S in component Parameters (hertz)"
    legend_constants[1] = "Zeta in component Parameters (dimensionless)"
    legend_constants[2] = "R0 in component Parameters (mm)"
    legend_constants[3] = "Cwall in component Parameters (mm_per_mmHg)"
    legend_constants[4] = "Kne in component Parameters (mmHg_per_mm)"
    legend_constants[5] = "K1 in component Parameters (mmHg_per_mm)"
    legend_constants[6] = "K2 in component Parameters (mmHg_per_mm)"
    legend_constants[7] = "K3 in component Parameters (mmHg_per_mm)"
    legend_constants[8] = "Bwall in component Parameters (mmHg_s_per_sq_mm)"
    legend_constants[9] = "B1 in component Parameters (mmHg_s_per_mm)"
    legend_constants[10] = "B2 in component Parameters (mmHg_s_per_mm)"
    legend_constants[11] = "B3 in component Parameters (mmHg_s_per_mm)"
    legend_constants[12] = "Tsmax in component Parameters (AU)"
    legend_constants[13] = "Tpmax in component Parameters (AU)"
    legend_constants[14] = "Tsmin in component Parameters (AU)"
    legend_constants[15] = "Tpmin in component Parameters (AU)"
    legend_constants[16] = "Gcns in component Parameters (dimensionless)"
    legend_constants[17] = "Gs in component Parameters (per_Hertz)"
    legend_constants[18] = "Gp in component Parameters (per_Hertz)"
    legend_constants[19] = "tau_nor in component Parameters (second)"
    legend_constants[20] = "tau_ach in component Parameters (second)"
    legend_constants[21] = "tau_HR_nor in component Parameters (second)"
    legend_constants[22] = "tau_HR_ach in component Parameters (second)"
    legend_constants[23] = "HRo in component Parameters (Beats_per_min)"
    legend_constants[24] = "HRmax in component Parameters (Beats_per_min)"
    legend_constants[25] = "HRmin in component Parameters (Beats_per_min)"
    legend_constants[26] = "Beta in component Parameters (dimensionless)"
    legend_constants[27] = "delta_th in component Parameters (dimensionless)"
    legend_constants[28] = "q_nor in component Parameters (per_s)"
    legend_constants[29] = "q_ach in component Parameters (per_s)"
    legend_constants[30] = "K_nor in component Parameters (AU)"
    legend_constants[31] = "K_ach in component Parameters (AU)"
    legend_constants[32] = "Gamma in component Parameters (dimensionless)"
    legend_algebraic[10] = "alpha_cns in component Nervous_System (hertz)"
    legend_algebraic[8] = "n in component Nervous_System (hertz)"
    legend_algebraic[6] = "Delta in component Coupling_Dynamics (dimensionless)"
    legend_constants[33] = "alpha_s0 in component Nervous_System (hertz)"
    legend_constants[34] = "alpha_p0 in component Nervous_System (hertz)"
    legend_states[0] = "A in component Aortic_Wall (mm_sq)"
    legend_algebraic[0] = "P in component Aortic_Wall (mmHg)"
    legend_algebraic[1] = "R in component Aortic_Wall (mm)"
    legend_states[1] = "Eps_1 in component Coupling_Dynamics (dimensionless)"
    legend_states[2] = "Eps_2 in component Coupling_Dynamics (dimensionless)"
    legend_states[3] = "Eps_3 in component Coupling_Dynamics (dimensionless)"
    legend_algebraic[4] = "Eps_wall in component Coupling_Dynamics (dimensionless)"
    legend_algebraic[12] = "Ts in component PNS_tones (AU)"
    legend_algebraic[13] = "Tp in component PNS_tones (AU)"
    legend_states[4] = "c_nor in component Norepinephrine (AU)"
    legend_states[5] = "C_ach in component Acetylcholine (AU)"
    legend_algebraic[2] = "delta_HR_ss in component Heart_Response_Nor (Beats_per_min)"
    legend_constants[35] = "delta_HR_smax in component Heart_Response_Nor (Beats_per_min)"
    legend_states[6] = "delta_HR_s in component Heart_Response_Nor (Beats_per_min)"
    legend_algebraic[3] = "delta_HR_ps in component HR_ach (Beats_per_min)"
    legend_constants[36] = "delta_HR_pmax in component HR_ach (Beats_per_min)"
    legend_algebraic[5] = "delta_HR_pfast in component HR_ach (Beats_per_min)"
    legend_states[7] = "delta_HR_pslow in component HR_ach (Beats_per_min)"
    legend_algebraic[7] = "delta_HR_p in component HR_ach (Beats_per_min)"
    legend_algebraic[14] = "HR in component HR_Combined (Beats_per_min)"
    legend_algebraic[11] = "HR_p in component HR_Combined (Beats_per_min)"
    legend_algebraic[9] = "HR_s in component HR_Combined (Beats_per_min)"
    legend_algebraic[15] = "Period in component HR_Combined (Sec_per_Beat)"
    legend_rates[0] = "d/dt A in component Aortic_Wall (mm_sq)"
    legend_rates[1] = "d/dt Eps_1 in component Coupling_Dynamics (dimensionless)"
    legend_rates[2] = "d/dt Eps_2 in component Coupling_Dynamics (dimensionless)"
    legend_rates[3] = "d/dt Eps_3 in component Coupling_Dynamics (dimensionless)"
    legend_rates[4] = "d/dt c_nor in component Norepinephrine (AU)"
    legend_rates[5] = "d/dt C_ach in component Acetylcholine (AU)"
    legend_rates[6] = "d/dt delta_HR_s in component Heart_Response_Nor (Beats_per_min)"
    legend_rates[7] = "d/dt delta_HR_pslow in component HR_ach (Beats_per_min)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 480
    constants[1] = 1
    constants[2] = 1.6
    constants[3] = 0.006
    constants[4] = 1
    constants[5] = 1.5
    constants[6] = 3.75
    constants[7] = 1.05
    constants[8] = 1
    constants[9] = 1
    constants[10] = 10
    constants[11] = 206.973
    constants[12] = 4.12
    constants[13] = 4.994
    constants[14] = 0.5
    constants[15] = 1.6
    constants[16] = 1
    constants[17] = 0.178
    constants[18] = 0.492
    constants[19] = 9.1
    constants[20] = 0.2
    constants[21] = 2.1
    constants[22] = 2.5
    constants[23] = 282.648
    constants[24] = 483.218
    constants[25] = 226.238
    constants[26] = 0.175
    constants[27] = 0
    constants[28] = 0.1099
    constants[29] = 5
    constants[30] = 1.12
    constants[31] = 0.65
    constants[32] = 0.75
    constants[33] = 58.6
    constants[34] = 76.019
    states[0] = 15.20531
    states[1] = 0.2042
    states[2] = 0.183
    states[3] = 0.161
    states[4] = 1.441
    states[5] = 1.0
    states[6] = 0
    states[7] = 0
    constants[35] = constants[24]-constants[23]
    constants[36] = constants[23]-constants[25]
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = 100.000+10.0000*sin(5.00000*voi)
    rates[0] = (-(power(states[0]/ pi, 1.0/2)-constants[2])/constants[3]+algebraic[0])/constants[8]
    algebraic[2] = (constants[35]*(power(states[4], 2.00000)))/(power(constants[30], 2.00000)+power(states[4], 2.00000))
    rates[6] = (-states[6]+algebraic[2])/constants[21]
    algebraic[3] = (constants[36]*(power(states[5], 2.00000)))/(power(constants[31], 2.00000)+power(states[5], 2.00000))
    rates[7] = (-states[7]+(1.00000-constants[32])*algebraic[3])/constants[22]
    algebraic[1] = power(states[0]/ pi, 0.500000)
    algebraic[4] = (algebraic[1]-constants[2])/constants[2]
    algebraic = rootfind_0(voi, constants, states, algebraic)
    algebraic[6] = algebraic[4]-states[1]
    algebraic[8] = constants[0]*(algebraic[6]-constants[1]*constants[27])
    algebraic[10] = constants[16]*algebraic[8]
    algebraic[12] = constants[14]+(constants[12]-constants[14])/(exp(constants[17]*(algebraic[10]-constants[33]))+1.00000)
    rates[4] = -(states[4]/constants[19])+constants[28]*algebraic[12]
    algebraic[13] = constants[15]+(constants[13]-constants[15])/(exp(-constants[18]*(algebraic[10]-constants[34]))+1.00000)
    rates[5] = -(states[5]/constants[20])+constants[29]*algebraic[13]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = 100.000+10.0000*sin(5.00000*voi)
    algebraic[2] = (constants[35]*(power(states[4], 2.00000)))/(power(constants[30], 2.00000)+power(states[4], 2.00000))
    algebraic[3] = (constants[36]*(power(states[5], 2.00000)))/(power(constants[31], 2.00000)+power(states[5], 2.00000))
    algebraic[1] = power(states[0]/ pi, 0.500000)
    algebraic[4] = (algebraic[1]-constants[2])/constants[2]
    algebraic = rootfind_0(voi, constants, states, algebraic)
    algebraic[6] = algebraic[4]-states[1]
    algebraic[8] = constants[0]*(algebraic[6]-constants[1]*constants[27])
    algebraic[10] = constants[16]*algebraic[8]
    algebraic[12] = constants[14]+(constants[12]-constants[14])/(exp(constants[17]*(algebraic[10]-constants[33]))+1.00000)
    algebraic[13] = constants[15]+(constants[13]-constants[15])/(exp(-constants[18]*(algebraic[10]-constants[34]))+1.00000)
    algebraic[5] = constants[32]*algebraic[3]
    algebraic[7] = algebraic[5]+states[7]
    algebraic[9] = constants[23]+states[6]
    algebraic[11] = constants[23]-algebraic[7]
    algebraic[14] = algebraic[11]+((algebraic[9]-constants[23])*(algebraic[11]-constants[26]*constants[25]))/(constants[23]-constants[26]*constants[25])
    algebraic[15] = 60.0000/algebraic[14]
    return algebraic

initialGuess0 = None
def rootfind_0(voi, constants, states, algebraic):
    """Calculate values of algebraic variables for DAE"""
    from scipy.optimize import fsolve
    global initialGuess0
    if (initialGuess0 == None): initialGuess0 = ones(3)*0.1
    if not iterable(voi):
        soln = fsolve(residualSN_0, initialGuess0, args=(algebraic, voi, constants, states), xtol=1E-6, warning=False)
        initialGuess0 = soln
        rates[1] = soln[0]
        rates[2] = soln[1]
        rates[3] = soln[2]
    else:
        for (i,t) in enumerate(voi):
            soln = fsolve(residualSN_0, initialGuess0, args=(algebraic[:,i], voi[i], constants, states[:,i]), xtol=1E-6, warning=False)
            initialGuess0 = soln
            rates[1][i] = soln[0]
            rates[2][i] = soln[1]
            rates[3][i] = soln[2]
    return algebraic

def residualSN_0(algebraicCandidate, algebraic, voi, constants, states):
    resid = array([0.0] * 3)
    rates[1] = algebraicCandidate[0]
    rates[2] = algebraicCandidate[1]
    rates[3] = algebraicCandidate[2]
    resid[0] = (rates[1]-((constants[4]*(algebraic[4]-states[1])-constants[5]*(states[1]-states[2]))/constants[9]+rates[2]))
    resid[1] = (rates[2]-((constants[5]*(states[1]-states[2])-constants[6]*(states[2]-states[3]))+constants[9]*rates[1]+constants[10]*rates[3])/(constants[9]+constants[10]))
    resid[2] = (rates[3]-((constants[6]*(states[2]-states[3])-constants[7]*states[3])+constants[10]*rates[2])/(constants[10]+constants[11]))
    return resid

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)
Source
Derived from workspace Bugenhagen 2010 at changeset cac8b4a154b4.
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This work is licensed under a Creative Commons Attribution 3.0 Unported License.