# Size of variable arrays: sizeAlgebraic = 9 sizeStates = 16 sizeConstants = 14 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 (day)" legend_states[0] = "B0 in component B0 (cells_per_GC)" legend_constants[0] = "pr in component kinetic_parameters (dimensionless)" legend_constants[1] = "mu in component kinetic_parameters (first_order_rate_constant)" legend_constants[2] = "rho in component kinetic_parameters (first_order_rate_constant)" legend_constants[3] = "delta_B in component kinetic_parameters (first_order_rate_constant)" legend_algebraic[0] = "CT_star in component CT_star (cells_per_GC)" legend_states[1] = "B1 in component B1 (cells_per_GC)" legend_algebraic[4] = "alpha_B in component alpha_B (dimensionless)" legend_states[2] = "B2 in component B2 (cells_per_GC)" legend_states[3] = "B3 in component B3 (cells_per_GC)" legend_states[4] = "B4 in component B4 (cells_per_GC)" legend_states[5] = "B5 in component B5 (cells_per_GC)" legend_states[6] = "B6 in component B6 (cells_per_GC)" legend_states[7] = "B7 in component B7 (cells_per_GC)" legend_states[8] = "B8 in component B8 (cells_per_GC)" legend_states[9] = "B9 in component B9 (cells_per_GC)" legend_states[10] = "B10 in component B10 (cells_per_GC)" legend_algebraic[1] = "B_sum in component centroblasts_sum (cells_per_GC)" legend_states[11] = "C in component C (cells_per_GC)" legend_constants[4] = "d in component C (first_order_rate_constant)" legend_states[12] = "C_star in component C_star (cells_per_GC)" legend_algebraic[2] = "CA in component CA (cells_per_GC)" legend_algebraic[5] = "C_starsum in component centrocytes_sum (cells_per_GC)" legend_states[13] = "M in component M (cells_per_GC)" legend_states[14] = "A in component A (cells_per_GC)" legend_constants[5] = "z in component A (first_order_rate_constant)" legend_constants[6] = "u in component A (dimensionless)" legend_algebraic[3] = "log_A in component A (dimensionless)" legend_states[15] = "T in component T (cells_per_GC)" legend_constants[7] = "p in component T (first_order_rate_constant)" legend_constants[8] = "sigma in component T (first_order_rate_constant)" legend_constants[9] = "delta_T in component T (first_order_rate_constant)" legend_algebraic[6] = "alpha_T in component alpha_T (dimensionless)" legend_constants[10] = "SA in component CA (dimensionless)" legend_constants[11] = "ST in component CT_star (dimensionless)" legend_constants[12] = "KB in component alpha_B (dimensionless)" legend_constants[13] = "KT in component alpha_T (dimensionless)" legend_algebraic[7] = "total in component total (cells_per_GC)" legend_algebraic[8] = "log_total in component total (dimensionless)" legend_rates[0] = "d/dt B0 in component B0 (cells_per_GC)" legend_rates[1] = "d/dt B1 in component B1 (cells_per_GC)" legend_rates[2] = "d/dt B2 in component B2 (cells_per_GC)" legend_rates[3] = "d/dt B3 in component B3 (cells_per_GC)" legend_rates[4] = "d/dt B4 in component B4 (cells_per_GC)" legend_rates[5] = "d/dt B5 in component B5 (cells_per_GC)" legend_rates[6] = "d/dt B6 in component B6 (cells_per_GC)" legend_rates[7] = "d/dt B7 in component B7 (cells_per_GC)" legend_rates[8] = "d/dt B8 in component B8 (cells_per_GC)" legend_rates[9] = "d/dt B9 in component B9 (cells_per_GC)" legend_rates[10] = "d/dt B10 in component B10 (cells_per_GC)" legend_rates[11] = "d/dt C in component C (cells_per_GC)" legend_rates[12] = "d/dt C_star in component C_star (cells_per_GC)" legend_rates[13] = "d/dt M in component M (cells_per_GC)" legend_rates[14] = "d/dt A in component A (cells_per_GC)" legend_rates[15] = "d/dt T in component T (cells_per_GC)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 3 constants[0] = 0.15 constants[1] = 3 constants[2] = 4 constants[3] = 0.8 states[1] = 0 states[2] = 0 states[3] = 0 states[4] = 0 states[5] = 0 states[6] = 0 states[7] = 0 states[8] = 0 states[9] = 0 states[10] = 0 states[11] = 0 constants[4] = 2 states[12] = 0 states[13] = 0 states[14] = 500 constants[5] = 0.02 constants[6] = 0.15 states[15] = 0 constants[7] = 2 constants[8] = 5 constants[9] = 0.8 constants[10] = 500 constants[11] = 50 constants[12] = 1e4 constants[13] = 100 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[11] = constants[4]*constants[2]*states[10]*1.00000-constants[1]*states[11] algebraic[0] = (states[12]*states[15])/(constants[11]*1.00000+states[12]) rates[0] = constants[0]*constants[1]*algebraic[0]-(constants[2]*states[0]+constants[3]*states[0]) algebraic[2] = (states[11]*states[14])/(constants[10]*1.00000+states[14]) rates[12] = constants[1]*algebraic[2]-constants[1]*states[12] rates[13] = (1.00000-constants[0])*constants[1]*algebraic[0] rates[14] = -constants[5]*states[14]-constants[6]*algebraic[2]*1.00000 algebraic[1] = states[1]+states[1]+states[3]+states[4]+states[5]+states[6]+states[6]+states[7]+states[8]+states[9]+states[10] algebraic[4] = constants[12]/(constants[12]+algebraic[1]/1.00000) rates[1] = constants[2]*(1.00000+algebraic[4])*states[0]-(constants[2]*states[1]+constants[3]*states[1]) rates[2] = constants[2]*(1.00000+algebraic[4])*states[1]-(constants[2]*states[2]+constants[3]*states[2]) rates[3] = constants[2]*(1.00000+algebraic[4])*states[2]-(constants[2]*states[3]+constants[3]*states[3]) rates[4] = constants[2]*(1.00000+algebraic[4])*states[3]-(constants[2]*states[4]+constants[3]*states[4]) rates[5] = constants[2]*(1.00000+algebraic[4])*states[4]-(constants[2]*states[5]+constants[3]*states[5]) rates[6] = constants[2]*(1.00000+algebraic[4])*states[5]-(constants[2]*states[6]+constants[3]*states[6]) rates[7] = constants[2]*(1.00000+algebraic[4])*states[6]-(constants[2]*states[7]+constants[3]*states[7]) rates[8] = constants[2]*(1.00000+algebraic[4])*states[7]-(constants[2]*states[8]+constants[3]*states[8]) rates[9] = constants[2]*(1.00000+algebraic[4])*states[8]-(constants[2]*states[9]+constants[3]*states[9]) rates[10] = constants[2]*(1.00000+algebraic[4])*states[9]-(constants[2]*states[10]+constants[3]*states[10]) algebraic[6] = constants[13]/(constants[13]+states[15]/1.00000) rates[15] = (constants[8]*1.00000+constants[7]*algebraic[6]*algebraic[0])-constants[9]*states[15] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (states[12]*states[15])/(constants[11]*1.00000+states[12]) algebraic[2] = (states[11]*states[14])/(constants[10]*1.00000+states[14]) algebraic[1] = states[1]+states[1]+states[3]+states[4]+states[5]+states[6]+states[6]+states[7]+states[8]+states[9]+states[10] algebraic[4] = constants[12]/(constants[12]+algebraic[1]/1.00000) algebraic[6] = constants[13]/(constants[13]+states[15]/1.00000) algebraic[3] = log(states[14]/1.00000, 10) algebraic[5] = states[11]+states[12] algebraic[7] = algebraic[1]+algebraic[5] algebraic[8] = log(algebraic[7]/1.00000+1.00000e-12, 10) return algebraic 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)