# Size of variable arrays: sizeAlgebraic = 13 sizeStates = 4 sizeConstants = 29 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_states[0] = "P_Open in component kinetics (dimensionless)" legend_states[1] = "P_Closed in component kinetics (dimensionless)" legend_states[2] = "P_I1 in component kinetics (dimensionless)" legend_states[3] = "P_I2 in component kinetics (dimensionless)" legend_voi = "time in component environment (ms)" legend_algebraic[2] = "current in component stimulus_protocol (nA_per_nF)" legend_algebraic[3] = "voltage_out in component environment (mV)" legend_algebraic[4] = "transmembranevoltage in component environment (mV)" legend_algebraic[1] = "pressure in component environment (mmHg)" legend_algebraic[0] = "stretch in component stimulus_protocol (dimensionless)" legend_constants[0] = "pressure_stim_offset in component environment (ms)" legend_constants[1] = "pressure_stim_period in component environment (ms)" legend_constants[2] = "pressure_stim_duration in component environment (ms)" legend_constants[3] = "pressure_stim_amplitude in component environment (dimensionless)" legend_constants[4] = "current_stim_offset in component environment (ms)" legend_constants[5] = "current_stim_period in component environment (ms)" legend_constants[6] = "current_stim_duration in component environment (ms)" legend_constants[7] = "current_stim_amplitude in component environment (nA_per_nF)" legend_constants[8] = "current_stim_end in component environment (ms)" legend_constants[9] = "current_N_period_total in component environment (dimensionless)" legend_constants[10] = "current_N_period_applied in component environment (dimensionless)" legend_constants[11] = "r1 in component kinetics (per_ms)" legend_constants[12] = "r3 in component kinetics (per_ms)" legend_constants[13] = "r4 in component kinetics (per_ms)" legend_constants[14] = "r5 in component kinetics (per_ms)" legend_constants[15] = "r6 in component kinetics (per_ms)" legend_constants[16] = "r7 in component kinetics (per_ms)" legend_constants[17] = "r8 in component kinetics (per_ms)" legend_constants[18] = "ce1 in component kinetics (dimensionless)" legend_constants[19] = "ce3 in component kinetics (dimensionless)" legend_constants[20] = "ce4 in component kinetics (dimensionless)" legend_constants[21] = "cm4 in component kinetics (dimensionless)" legend_constants[22] = "ce5 in component kinetics (dimensionless)" legend_constants[23] = "ce6 in component kinetics (dimensionless)" legend_constants[24] = "ce7 in component kinetics (dimensionless)" legend_constants[25] = "ce8 in component kinetics (dimensionless)" legend_constants[26] = "r2 in component kinetics (per_ms)" legend_constants[27] = "ce2 in component kinetics (dimensionless)" legend_constants[28] = "cm2 in component kinetics (dimensionless)" legend_algebraic[5] = "p_O_I1 in component kinetics (per_ms)" legend_algebraic[6] = "p_I1_O in component kinetics (per_ms)" legend_algebraic[7] = "p_I1_C in component kinetics (per_ms)" legend_algebraic[8] = "p_C_I1 in component kinetics (per_ms)" legend_algebraic[9] = "p_C_O in component kinetics (per_ms)" legend_algebraic[10] = "p_O_C in component kinetics (per_ms)" legend_algebraic[11] = "p_I2_O in component kinetics (per_ms)" legend_algebraic[12] = "p_O_I2 in component kinetics (per_ms)" legend_rates[0] = "d/dt P_Open in component kinetics (dimensionless)" legend_rates[1] = "d/dt P_Closed in component kinetics (dimensionless)" legend_rates[2] = "d/dt P_I1 in component kinetics (dimensionless)" legend_rates[3] = "d/dt P_I2 in component kinetics (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.0 states[1] = 0.3 states[2] = 0.1 states[3] = 0.6 constants[0] = 100 constants[1] = 2000 constants[2] = 5 constants[3] = 1.1 constants[4] = 100 constants[5] = 1000 constants[6] = 500 constants[7] = 80 constants[8] = 999999999999999 constants[9] = 1 constants[10] = 1 constants[11] = 0.02634342 constants[12] = 0.0008000712 constants[13] = 0.008945307 constants[14] = 1.3529515e-5 constants[15] = 6.206403e-5 constants[16] = 6.603723e-6 constants[17] = 0.00079357607 constants[18] = -2.3753126 constants[19] = -5.6010337 constants[20] = 0.70629007 constants[21] = -12.101605 constants[22] = 6.46389 constants[23] = -1.2173947 constants[24] = 8.739162 constants[25] = -3.364573 constants[26] = (constants[11]*constants[12]*constants[14])/(constants[13]*constants[15]) constants[27] = ((constants[18]+constants[19]+constants[22])-constants[20])-constants[23] constants[28] = -constants[21] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[2] = custom_piecewise([greater_equal(voi , constants[4]) & less(voi , constants[8]) & less_equal( voi-constants[4] % constants[5] , constants[6]) & less( voi-constants[4] % constants[9]*constants[5] , constants[10]*constants[5]), constants[7] , True, 0.00000]) algebraic[3] = (algebraic[2]/1.00000)*1.00000 algebraic[5] = constants[11]*exp((constants[18]*algebraic[3])/140.000) algebraic[0] = custom_piecewise([greater_equal(voi , constants[0]) & less_equal( voi-constants[0] % constants[1] , constants[2]), constants[3] , True, 1.00000]) algebraic[1] = 350.000*amax(vstack(0.00000, algebraic[0]-1.00000),0) algebraic[6] = constants[26]*exp((constants[27]*algebraic[3])/140.000+(constants[28]*algebraic[1])/70.0000) algebraic[7] = constants[12]*exp((constants[19]*algebraic[3])/140.000) algebraic[8] = constants[13]*exp((constants[20]*algebraic[3])/140.000+(constants[21]*algebraic[1])/70.0000) rates[2] = -(algebraic[6]+algebraic[7])*states[2]+algebraic[8]*states[1]+algebraic[5]*states[0] algebraic[9] = constants[14]*exp((constants[22]*algebraic[3])/140.000) algebraic[10] = constants[15]*exp((constants[23]*algebraic[3])/140.000) rates[1] = -(algebraic[8]+algebraic[9])*states[1]+algebraic[10]*states[0]+algebraic[7]*states[2] algebraic[11] = constants[16]*exp((((constants[24]*algebraic[3])/140.000)*algebraic[1])/70.0000) algebraic[12] = constants[17]*exp((constants[25]*algebraic[3])/140.000) rates[0] = -(algebraic[5]+algebraic[12]+algebraic[10])*states[0]+algebraic[9]*states[1]+algebraic[6]*states[2]+algebraic[11]*states[3] rates[3] = -algebraic[11]*states[3]+algebraic[12]*states[0] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[2] = custom_piecewise([greater_equal(voi , constants[4]) & less(voi , constants[8]) & less_equal( voi-constants[4] % constants[5] , constants[6]) & less( voi-constants[4] % constants[9]*constants[5] , constants[10]*constants[5]), constants[7] , True, 0.00000]) algebraic[3] = (algebraic[2]/1.00000)*1.00000 algebraic[5] = constants[11]*exp((constants[18]*algebraic[3])/140.000) algebraic[0] = custom_piecewise([greater_equal(voi , constants[0]) & less_equal( voi-constants[0] % constants[1] , constants[2]), constants[3] , True, 1.00000]) algebraic[1] = 350.000*amax(vstack(0.00000, algebraic[0]-1.00000),0) algebraic[6] = constants[26]*exp((constants[27]*algebraic[3])/140.000+(constants[28]*algebraic[1])/70.0000) algebraic[7] = constants[12]*exp((constants[19]*algebraic[3])/140.000) algebraic[8] = constants[13]*exp((constants[20]*algebraic[3])/140.000+(constants[21]*algebraic[1])/70.0000) algebraic[9] = constants[14]*exp((constants[22]*algebraic[3])/140.000) algebraic[10] = constants[15]*exp((constants[23]*algebraic[3])/140.000) algebraic[11] = constants[16]*exp((((constants[24]*algebraic[3])/140.000)*algebraic[1])/70.0000) algebraic[12] = constants[17]*exp((constants[25]*algebraic[3])/140.000) algebraic[4] = (algebraic[3]-5.00000)*states[0] 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)