# Size of variable arrays: sizeAlgebraic = 13 sizeStates = 2 sizeConstants = 41 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 (minute)" legend_constants[0] = "PA in component autonomics (mmHg)" legend_constants[1] = "PO2ART in component autonomics (mmHg)" legend_constants[2] = "PLA in component autonomics (mmHg)" legend_constants[3] = "PRA in component autonomics (mmHg)" legend_constants[4] = "PPA in component autonomics (mmHg)" legend_constants[31] = "PA1 in component pressure_driving_autonomic_receptors (mmHg)" legend_constants[5] = "CRRFLX in component parameter_values (mmHg)" legend_constants[6] = "EXE in component parameter_values (mmHg)" legend_constants[32] = "AUC in component chemoreceptors_effect_of_PA (dimensionless)" legend_constants[7] = "AUC1 in component parameter_values (dimensionless)" legend_constants[37] = "AUC3 in component chemoreceptors_effect_of_art_PO2 (dimensionless)" legend_constants[8] = "O2CHMO in component parameter_values (per_mmHg)" legend_constants[34] = "AUC2 in component chemoreceptors_effect_of_art_PO2 (dimensionless)" legend_algebraic[0] = "AU6C in component arterial_baroreceptor_reflex (dimensionless)" legend_constants[9] = "AUX in component parameter_values (dimensionless)" legend_constants[10] = "AUK in component parameter_values (per_minute)" legend_constants[11] = "BAROTC in component parameter_values (minute)" legend_constants[33] = "AUB in component arterial_baroreceptor_reflex (dimensionless)" legend_constants[35] = "A1B in component arterial_baroreceptor_reflex (dimensionless)" legend_constants[36] = "AU6A in component arterial_baroreceptor_reflex (dimensionless)" legend_constants[12] = "AU4 in component arterial_baroreceptor_reflex (dimensionless)" legend_states[0] = "AU6 in component arterial_baroreceptor_reflex (dimensionless)" legend_constants[38] = "AUN in component CNS_ischemic_reflex (dimensionless)" legend_constants[13] = "AUN1 in component parameter_values (dimensionless)" legend_constants[39] = "AULP in component autonomic_response_to_vasculature_pressure (dimensionless)" legend_constants[14] = "AULPM in component parameter_values (dimensionless)" legend_constants[40] = "AUEX in component autonomic_response_to_exercise (dimensionless)" legend_constants[15] = "EXC in component parameter_values (dimensionless)" legend_constants[16] = "EXCXP in component parameter_values (dimensionless)" legend_algebraic[4] = "AUTTL in component total_autonomic_stimulation (dimensionless)" legend_algebraic[2] = "AUTTL1 in component total_autonomic_stimulation (dimensionless)" legend_constants[17] = "EXCML in component parameter_values (dimensionless)" legend_algebraic[3] = "AU in component actual_autonomic_stimulation (dimensionless)" legend_constants[18] = "AUDMP in component parameter_values (minute)" legend_constants[19] = "AUMAX in component parameter_values (dimensionless)" legend_constants[20] = "AUMIN in component parameter_values (dimensionless)" legend_constants[21] = "AUSLP in component parameter_values (dimensionless)" legend_algebraic[7] = "DAU in component actual_autonomic_stimulation (per_minute)" legend_states[1] = "AU1 in component actual_autonomic_stimulation (dimensionless)" legend_algebraic[1] = "AUT in component actual_autonomic_stimulation (dimensionless)" legend_algebraic[5] = "VVR in component autonomic_drive_on_target_organs_and_tissues (litre)" legend_algebraic[8] = "AUH in component autonomic_drive_on_target_organs_and_tissues (dimensionless)" legend_algebraic[9] = "AUR in component autonomic_drive_on_target_organs_and_tissues (dimensionless)" legend_algebraic[10] = "AOM in component autonomic_drive_on_target_organs_and_tissues (dimensionless)" legend_algebraic[11] = "AUM in component autonomic_drive_on_target_organs_and_tissues (dimensionless)" legend_algebraic[12] = "AVE in component autonomic_drive_on_target_organs_and_tissues (dimensionless)" legend_constants[22] = "VV9 in component parameter_values (litre)" legend_constants[23] = "AUL in component parameter_values (litre)" legend_constants[24] = "AUV in component parameter_values (dimensionless)" legend_constants[25] = "AUS in component parameter_values (dimensionless)" legend_constants[26] = "O2A in component parameter_values (dimensionless)" legend_constants[27] = "AUM1 in component parameter_values (dimensionless)" legend_constants[28] = "AUM2 in component parameter_values (dimensionless)" legend_constants[29] = "AUY in component parameter_values (dimensionless)" legend_algebraic[6] = "AUO in component autonomic_drive_on_target_organs_and_tissues (dimensionless)" legend_constants[30] = "MDMP in component parameter_values (dimensionless)" legend_rates[0] = "d/dt AU6 in component arterial_baroreceptor_reflex (dimensionless)" legend_rates[1] = "d/dt AU1 in component actual_autonomic_stimulation (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 103.525 constants[1] = 97.0439 constants[2] = 2 constants[3] = 0.00852183 constants[4] = 15.6376 constants[5] = 0 constants[6] = 0 constants[7] = 0.3 constants[8] = 0.01 constants[9] = 1 constants[10] = 0.004 constants[11] = 0.16 constants[12] = -0.060024 states[0] = 1.00132 constants[13] = 0.5 constants[14] = 0 constants[15] = 1 constants[16] = 1.0 constants[17] = 0.01 constants[18] = 0.3 constants[19] = 5.0 constants[20] = 0.4 constants[21] = 1.5 states[1] = 1.00007 constants[22] = 2.51 constants[23] = 1.5 constants[24] = 0.55 constants[25] = 1 constants[26] = 0.1 constants[27] = 3 constants[28] = 1 constants[29] = 0 constants[30] = 0 constants[31] = custom_piecewise([greater(constants[5] , 1.00000e-07), constants[5] , True, constants[0]-constants[6]]) constants[32] = custom_piecewise([less(constants[31] , 80.0000) & greater_equal(constants[31] , 40.0000), 0.00500000*(80.0000-constants[31])*constants[7] , less(constants[31] , 40.0000), 0.200000*constants[7] , True, 0.00000]) constants[33] = custom_piecewise([less(constants[31] , 160.000) & greater_equal(constants[31] , 80.0000), 0.0166670*(160.000-constants[31]) , less(constants[31] , 80.0000), 1.33360 , True, 0.00000]) constants[34] = custom_piecewise([less(constants[1] , 80.0000) & greater_equal(constants[1] , 40.0000), constants[8]*(80.0000-constants[1]) , less(constants[1] , 40.0000), constants[8]*40.0000 , True, 0.00000]) constants[35] = (constants[33]-1.00000)*constants[9]+1.00000 constants[36] = constants[35]-constants[12] constants[37] = constants[32]+constants[34] constants[38] = custom_piecewise([less(constants[31] , 40.0000), 0.0400000*(40.0000-constants[31])*constants[13] , True, 0.00000]) constants[39] = (15.0000/(constants[2]+constants[3]+constants[4])-1.00000)*constants[14]+1.00000 constants[40] = power(constants[15], constants[16]) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = (constants[36]-states[0])/constants[11] algebraic[0] = states[0] algebraic[2] = (constants[40]*constants[39]*(constants[37]+algebraic[0]+constants[38])-1.00000)*constants[17]+1.00000 algebraic[4] = custom_piecewise([less(algebraic[2] , 0.00000), 0.00000 , True, algebraic[2]]) algebraic[7] = (algebraic[4]-states[1])/constants[18] rates[1] = algebraic[7] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[0] algebraic[2] = (constants[40]*constants[39]*(constants[37]+algebraic[0]+constants[38])-1.00000)*constants[17]+1.00000 algebraic[4] = custom_piecewise([less(algebraic[2] , 0.00000), 0.00000 , True, algebraic[2]]) algebraic[7] = (algebraic[4]-states[1])/constants[18] algebraic[1] = constants[19]-(constants[19]-1.00000)/exp(constants[21]*(states[1]-1.00000)) algebraic[3] = custom_piecewise([less(algebraic[1] , constants[20]), constants[20] , True, algebraic[1]]) algebraic[5] = (constants[22]-algebraic[3]*constants[23])+constants[23] algebraic[6] = algebraic[3]-1.00000 algebraic[8] = algebraic[6]*constants[24]+1.00000 algebraic[9] = algebraic[6]*constants[25]+1.00000 algebraic[10] = algebraic[6]*constants[26]+1.00000 algebraic[11] = power(algebraic[6]*constants[27]+1.00000, constants[28]) algebraic[12] = algebraic[6]*constants[29]+1.00000 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)