Generated Code
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# Size of variable arrays: sizeAlgebraic = 17 sizeStates = 5 sizeConstants = 25 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] = "Ca_i in component intracellular_ion_concentrations (mM)" legend_algebraic[0] = "Ca_b in component intracellular_ion_concentrations (mM)" legend_states[0] = "TRPN in component intracellular_ion_concentrations (mM)" legend_constants[0] = "Ca_TRPN_Max in component troponin (mM)" legend_algebraic[16] = "J_TRPN in component troponin (mM_per_ms)" legend_states[1] = "z in component tropomyosin (dimensionless)" legend_algebraic[9] = "z_max in component tropomyosin (dimensionless)" legend_constants[1] = "k_on in component troponin (per_mM_per_ms)" legend_constants[2] = "k_Ref_off in component troponin (per_ms)" legend_constants[3] = "gamma_trpn in component troponin (dimensionless)" legend_constants[4] = "alpha_0 in component tropomyosin (per_ms)" legend_constants[5] = "alpha_r1 in component tropomyosin (per_ms)" legend_constants[6] = "alpha_r2 in component tropomyosin (per_ms)" legend_constants[7] = "n_Rel in component tropomyosin (dimensionless)" legend_constants[8] = "K_z in component tropomyosin (dimensionless)" legend_constants[9] = "n_Hill in component tropomyosin (dimensionless)" legend_constants[10] = "Ca_50ref in component tropomyosin (mM)" legend_constants[11] = "z_p in component tropomyosin (dimensionless)" legend_constants[12] = "beta_1 in component tropomyosin (dimensionless)" legend_algebraic[6] = "Ca_50 in component tropomyosin (mM)" legend_algebraic[7] = "Ca_TRPN_50 in component tropomyosin (mM)" legend_constants[22] = "K_2 in component tropomyosin (per_ms)" legend_constants[24] = "K_1 in component tropomyosin (per_ms)" legend_algebraic[8] = "alpha_Tm in component tropomyosin (per_ms)" legend_algebraic[2] = "beta_Tm in component tropomyosin (per_ms)" legend_constants[13] = "beta_0 in component filament_overlap (dimensionless)" legend_algebraic[4] = "lambda in component Myofilaments (dimensionless)" legend_algebraic[15] = "k_off in component troponin (per_ms)" legend_algebraic[14] = "Tension in component Cross_Bridges (N_per_mm2)" legend_constants[14] = "T_ref in component length_independent_tension (N_per_mm2)" legend_algebraic[3] = "ExtensionRatio in component Myofilaments (dimensionless)" legend_constants[23] = "dExtensionRatiodt in component Myofilaments (per_ms)" legend_algebraic[5] = "lambda_prev in component Myofilaments (dimensionless)" legend_algebraic[10] = "overlap in component filament_overlap (dimensionless)" legend_algebraic[11] = "T_Base in component length_independent_tension (N_per_mm2)" legend_algebraic[12] = "T_0 in component isometric_tension (N_per_mm2)" legend_algebraic[13] = "Q in component Cross_Bridges (dimensionless)" legend_constants[15] = "a in component Cross_Bridges (dimensionless)" legend_states[2] = "Q_1 in component Cross_Bridges (dimensionless)" legend_states[3] = "Q_2 in component Cross_Bridges (dimensionless)" legend_states[4] = "Q_3 in component Cross_Bridges (dimensionless)" legend_constants[16] = "A_1 in component Cross_Bridges (dimensionless)" legend_constants[17] = "A_2 in component Cross_Bridges (dimensionless)" legend_constants[18] = "A_3 in component Cross_Bridges (dimensionless)" legend_constants[19] = "alpha_1 in component Cross_Bridges (per_ms)" legend_constants[20] = "alpha_2 in component Cross_Bridges (per_ms)" legend_constants[21] = "alpha_3 in component Cross_Bridges (per_ms)" legend_rates[0] = "d/dt TRPN in component intracellular_ion_concentrations (mM)" legend_rates[1] = "d/dt z in component tropomyosin (dimensionless)" legend_rates[2] = "d/dt Q_1 in component Cross_Bridges (dimensionless)" legend_rates[3] = "d/dt Q_2 in component Cross_Bridges (dimensionless)" legend_rates[4] = "d/dt Q_3 in component Cross_Bridges (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.067593139865 constants[0] = 70e-3 states[1] = 0.014417937837 constants[1] = 100 constants[2] = 0.2 constants[3] = 2 constants[4] = 8e-3 constants[5] = 2e-3 constants[6] = 1.75e-3 constants[7] = 3 constants[8] = 0.15 constants[9] = 3 constants[10] = 1.05e-3 constants[11] = 0.85 constants[12] = -4 constants[13] = 4.9 constants[14] = 56.2 constants[15] = 0.35 states[2] = 0 states[3] = 0 states[4] = 0 constants[16] = -29 constants[17] = 138 constants[18] = 129 constants[19] = 0.03 constants[20] = 0.13 constants[21] = 0.625 constants[22] = ((constants[6]*(power(constants[11], constants[7])))/(power(constants[11], constants[7])+power(constants[8], constants[7])))*(1.00000-(constants[7]*(power(constants[8], constants[7])))/(power(constants[11], constants[7])+power(constants[8], constants[7]))) constants[23] = 0.00000 constants[24] = (constants[6]*(power(constants[11], constants[7]-1.00000))*constants[7]*(power(constants[8], constants[7])))/(power(power(constants[11], constants[7])+power(constants[8], constants[7]), 2.00000)) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[2] = constants[16]*constants[23]-constants[19]*states[2] rates[3] = constants[17]*constants[23]-constants[20]*states[3] rates[4] = constants[18]*constants[23]-constants[21]*states[4] algebraic[0] = constants[0]-states[0] algebraic[3] = custom_piecewise([greater(voi , 1000.00), 1.00000 , True, 1.00000]) algebraic[4] = custom_piecewise([greater(algebraic[3] , 0.800000) & less_equal(algebraic[3] , 1.15000), algebraic[3] , greater(algebraic[3] , 1.15000), 1.15000 , True, 0.800000]) algebraic[6] = constants[10]*(1.00000+constants[12]*(algebraic[4]-1.00000)) algebraic[7] = (algebraic[6]*constants[0])/(algebraic[6]+(constants[2]/constants[1])*(1.00000-((1.00000+constants[13]*(algebraic[4]-1.00000))*0.500000)/constants[3])) algebraic[8] = constants[4]*(power(algebraic[0]/algebraic[7], constants[9])) algebraic[2] = constants[5]+(constants[6]*(power(states[1], constants[7]-1.00000)))/(power(states[1], constants[7])+power(constants[8], constants[7])) rates[1] = algebraic[8]*(1.00000-states[1])-algebraic[2]*states[1] algebraic[1] = custom_piecewise([less(voi , 1.00000), 1000.00*1.84330e-07 , greater_equal(voi , 10.0000) & less(voi , 15.0000), 1000.00*(((1.05500*(power(voi/1000.00, 3.00000))-0.0350700*(power(voi/1000.00, 2.00000)))+(0.000399200*voi)/1000.00)-1.35600e-06) , greater_equal(voi , 15.0000) & less(voi , 55.0000), 1000.00*(((0.0140000*(power(voi/1000.00, 3.00000))-0.00255500*(power(voi/1000.00, 2.00000)))+(0.000149400*voi)/1000.00)-1.42800e-06) , greater_equal(voi , 55.0000) & less(voi , 250.000), 1000.00*(((1.73900e-05*(power(voi/1000.00, 3.00000))-3.20900e-06*(power(voi/1000.00, 2.00000)))-(5.68900e-06*voi)/1000.00)+1.71900e-06) , greater_equal(voi , 250.000) & less(voi , 490.000), 1000.00*((((0.000132100*(power(voi/1000.00, 4.00000))-0.000219700*(power(voi/1000.00, 3.00000)))+0.000137400*(power(voi/1000.00, 2.00000)))-(3.89500e-05*voi)/1000.00)+4.44100e-06) , True, 1000.00*1.21480e-07]) algebraic[10] = 1.00000+constants[13]*(algebraic[4]-1.00000) algebraic[9] = (constants[4]/(power(algebraic[7]/constants[0], constants[9]))-constants[22])/(constants[5]+constants[24]+constants[4]/(power(algebraic[7]/constants[0], constants[9]))) algebraic[11] = (constants[14]*states[1])/algebraic[9] algebraic[12] = algebraic[11]*algebraic[10] algebraic[13] = states[2]+states[3]+states[4] algebraic[14] = custom_piecewise([less(algebraic[13] , 0.00000), (algebraic[12]*(constants[15]*algebraic[13]+1.00000))/(1.00000-algebraic[13]) , True, (algebraic[12]*(1.00000+(constants[15]+2.00000)*algebraic[13]))/(1.00000+algebraic[13])]) algebraic[15] = custom_piecewise([greater(1.00000-algebraic[14]/(constants[3]*constants[14]) , 0.100000), constants[2]*(1.00000-algebraic[14]/(constants[3]*constants[14])) , True, constants[2]*0.100000]) algebraic[16] = (constants[0]-states[0])*algebraic[15]-algebraic[1]*states[0]*constants[1] rates[0] = algebraic[16] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[0]-states[0] algebraic[3] = custom_piecewise([greater(voi , 1000.00), 1.00000 , True, 1.00000]) algebraic[4] = custom_piecewise([greater(algebraic[3] , 0.800000) & less_equal(algebraic[3] , 1.15000), algebraic[3] , greater(algebraic[3] , 1.15000), 1.15000 , True, 0.800000]) algebraic[6] = constants[10]*(1.00000+constants[12]*(algebraic[4]-1.00000)) algebraic[7] = (algebraic[6]*constants[0])/(algebraic[6]+(constants[2]/constants[1])*(1.00000-((1.00000+constants[13]*(algebraic[4]-1.00000))*0.500000)/constants[3])) algebraic[8] = constants[4]*(power(algebraic[0]/algebraic[7], constants[9])) algebraic[2] = constants[5]+(constants[6]*(power(states[1], constants[7]-1.00000)))/(power(states[1], constants[7])+power(constants[8], constants[7])) algebraic[1] = custom_piecewise([less(voi , 1.00000), 1000.00*1.84330e-07 , greater_equal(voi , 10.0000) & less(voi , 15.0000), 1000.00*(((1.05500*(power(voi/1000.00, 3.00000))-0.0350700*(power(voi/1000.00, 2.00000)))+(0.000399200*voi)/1000.00)-1.35600e-06) , greater_equal(voi , 15.0000) & less(voi , 55.0000), 1000.00*(((0.0140000*(power(voi/1000.00, 3.00000))-0.00255500*(power(voi/1000.00, 2.00000)))+(0.000149400*voi)/1000.00)-1.42800e-06) , greater_equal(voi , 55.0000) & less(voi , 250.000), 1000.00*(((1.73900e-05*(power(voi/1000.00, 3.00000))-3.20900e-06*(power(voi/1000.00, 2.00000)))-(5.68900e-06*voi)/1000.00)+1.71900e-06) , greater_equal(voi , 250.000) & less(voi , 490.000), 1000.00*((((0.000132100*(power(voi/1000.00, 4.00000))-0.000219700*(power(voi/1000.00, 3.00000)))+0.000137400*(power(voi/1000.00, 2.00000)))-(3.89500e-05*voi)/1000.00)+4.44100e-06) , True, 1000.00*1.21480e-07]) algebraic[10] = 1.00000+constants[13]*(algebraic[4]-1.00000) algebraic[9] = (constants[4]/(power(algebraic[7]/constants[0], constants[9]))-constants[22])/(constants[5]+constants[24]+constants[4]/(power(algebraic[7]/constants[0], constants[9]))) algebraic[11] = (constants[14]*states[1])/algebraic[9] algebraic[12] = algebraic[11]*algebraic[10] algebraic[13] = states[2]+states[3]+states[4] algebraic[14] = custom_piecewise([less(algebraic[13] , 0.00000), (algebraic[12]*(constants[15]*algebraic[13]+1.00000))/(1.00000-algebraic[13]) , True, (algebraic[12]*(1.00000+(constants[15]+2.00000)*algebraic[13]))/(1.00000+algebraic[13])]) algebraic[15] = custom_piecewise([greater(1.00000-algebraic[14]/(constants[3]*constants[14]) , 0.100000), constants[2]*(1.00000-algebraic[14]/(constants[3]*constants[14])) , True, constants[2]*0.100000]) algebraic[16] = (constants[0]-states[0])*algebraic[15]-algebraic[1]*states[0]*constants[1] algebraic[5] = algebraic[3] 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)