# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 4 sizeConstants = 20 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[3] = "Ca_i in component intracellular_ion_concentrations (uM)" legend_algebraic[0] = "mtime in component intracellular_ion_concentrations (dimensionless)" legend_states[0] = "xb in component crossbridges (dimensionless)" legend_states[1] = "TRPN in component troponin (dimensionless)" legend_constants[0] = "k_xb in component crossbridges (per_ms)" legend_constants[1] = "nperm in component crossbridges (dimensionless)" legend_constants[2] = "perm50 in component crossbridges (dimensionless)" legend_algebraic[1] = "permtot in component crossbridges (dimensionless)" legend_constants[3] = "Ca_50ref in component troponin (uM)" legend_constants[4] = "beta_1 in component troponin (dimensionless)" legend_constants[5] = "k_off in component troponin (per_ms)" legend_constants[6] = "n_TRPN in component troponin (dimensionless)" legend_constants[16] = "lambda_m in component filament_overlap (dimensionless)" legend_constants[17] = "Ca_50 in component troponin (uM)" legend_constants[14] = "lambda in component Myofilaments (dimensionless)" legend_constants[15] = "dlambdadt in component Myofilaments (per_ms)" legend_constants[19] = "overlap in component filament_overlap (dimensionless)" legend_constants[7] = "beta_0 in component filament_overlap (dimensionless)" legend_constants[18] = "lambda_s in component filament_overlap (dimensionless)" legend_constants[8] = "T_ref in component isometric_tension (kPa)" legend_algebraic[2] = "T_0 in component isometric_tension (kPa)" legend_algebraic[4] = "Q in component dynamic_stiffness (dimensionless)" legend_constants[9] = "a in component dynamic_stiffness (dimensionless)" legend_states[2] = "Q_1 in component dynamic_stiffness (dimensionless)" legend_states[3] = "Q_2 in component dynamic_stiffness (dimensionless)" legend_constants[10] = "A_1 in component dynamic_stiffness (dimensionless)" legend_constants[11] = "A_2 in component dynamic_stiffness (dimensionless)" legend_constants[12] = "alpha_1 in component dynamic_stiffness (per_ms)" legend_constants[13] = "alpha_2 in component dynamic_stiffness (per_ms)" legend_algebraic[5] = "Tension in component dynamic_stiffness (kPa)" legend_rates[0] = "d/dt xb in component crossbridges (dimensionless)" legend_rates[1] = "d/dt TRPN in component troponin (dimensionless)" legend_rates[2] = "d/dt Q_1 in component dynamic_stiffness (dimensionless)" legend_rates[3] = "d/dt Q_2 in component dynamic_stiffness (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.00046 states[1] = 0.0752 constants[0] = 0.1 constants[1] = 5 constants[2] = 0.35 constants[3] = 0.8 constants[4] = -1.5 constants[5] = 0.1 constants[6] = 2 constants[7] = 1.65 constants[8] = 120 constants[9] = 0.35 states[2] = 0 states[3] = 0 constants[10] = -29 constants[11] = 116 constants[12] = 0.1 constants[13] = 0.5 constants[14] = 1.00000 constants[15] = 0.00000 constants[16] = custom_piecewise([greater(constants[14] , 1.20000), 1.20000 , True, constants[14]]) constants[17] = constants[3]*(1.00000+constants[4]*(constants[16]-1.00000)) constants[18] = custom_piecewise([greater_equal(constants[16] , 0.870000), 0.870000 , True, constants[16]]) constants[19] = 1.00000+constants[7]*((constants[16]+constants[18])-1.87000) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[2] = constants[10]*constants[15]-constants[12]*states[2] rates[3] = constants[11]*constants[15]-constants[13]*states[3] algebraic[1] = power(power(states[1]/constants[2], constants[1]), 1.0/2) rates[0] = constants[0]*(algebraic[1]*(1.00000-states[0])-(1.00000/algebraic[1])*states[0]) algebraic[0] = (voi-167.000*floor(voi/167.000))/1.00000 algebraic[3] = custom_piecewise([greater_equal(algebraic[0] , 1.17000) & less(algebraic[0] , 30.8400), 1.00000*1.85358e-05*(power(algebraic[0], 3.00000))+-0.00159034*(power(algebraic[0], 2.00000))+0.0436459*(power(algebraic[0], 1.00000))+0.167079 , greater_equal(algebraic[0] , 30.8400), ((1.00000*-5.74585e-08*(power(algebraic[0], 3.00000))+3.11222e-05*(power(algebraic[0], 2.00000)))-0.00661849*(power(algebraic[0], 1.00000)))+0.720442 , True, 0.216000]) rates[1] = constants[5]*((power(algebraic[3]/constants[17], constants[6]))*(1.00000-states[1])-states[1]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[1] = power(power(states[1]/constants[2], constants[1]), 1.0/2) algebraic[0] = (voi-167.000*floor(voi/167.000))/1.00000 algebraic[3] = custom_piecewise([greater_equal(algebraic[0] , 1.17000) & less(algebraic[0] , 30.8400), 1.00000*1.85358e-05*(power(algebraic[0], 3.00000))+-0.00159034*(power(algebraic[0], 2.00000))+0.0436459*(power(algebraic[0], 1.00000))+0.167079 , greater_equal(algebraic[0] , 30.8400), ((1.00000*-5.74585e-08*(power(algebraic[0], 3.00000))+3.11222e-05*(power(algebraic[0], 2.00000)))-0.00661849*(power(algebraic[0], 1.00000)))+0.720442 , True, 0.216000]) algebraic[2] = constants[8]*states[0]*constants[19] algebraic[4] = states[2]+states[3] algebraic[5] = custom_piecewise([less(algebraic[4] , 0.00000), (algebraic[2]*(constants[9]*algebraic[4]+1.00000))/(1.00000-algebraic[4]) , True, (algebraic[2]*(1.00000+(constants[9]+2.00000)*algebraic[4]))/(1.00000+algebraic[4])]) 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)