# Size of variable arrays: sizeAlgebraic = 7 sizeStates = 5 sizeConstants = 42 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_constants[0] = "V_init in component Vstim_para (mV)" legend_constants[1] = "V_rate in component Vstim_para (mV_per_s)" legend_constants[2] = "Nai in component control_para (mM)" legend_constants[3] = "Cai in component control_para (mM)" legend_constants[4] = "inhPump in component control_para (dimensionless)" legend_constants[5] = "K_Cahalf in component control_para (mV)" legend_voi = "time in component time_s (second)" legend_states[0] = "V in component vramp_protocol_s (mV)" legend_algebraic[6] = "J_VOCC in component J_VOCC (mM_per_s)" legend_constants[36] = "J_CaPump in component J_CaPump (mM_per_s)" legend_algebraic[0] = "J_NaCa in component J_NaCa (mM_per_s)" legend_algebraic[3] = "rho_vCa in component J_VOCC (dimensionless)" legend_constants[37] = "K_1 in component K_1 (per_s)" legend_algebraic[1] = "stress in component CB4HM (dimensionless)" legend_algebraic[2] = "phosphorylation in component CB4HM (dimensionless)" legend_constants[6] = "R in component constants (J_per_K_mol)" legend_constants[7] = "F in component constants (C_per_mmol)" legend_constants[8] = "T in component model_para (kelvin)" legend_constants[9] = "Nao in component model_para (mM)" legend_constants[10] = "Cao in component model_para (mM)" legend_constants[11] = "V_cell in component model_para (fm3)" legend_constants[12] = "V_Cahalf in component model_para (mV)" legend_constants[13] = "g_mCa in component model_para (nS)" legend_constants[14] = "V_pmax in component model_para (mM_per_s)" legend_constants[15] = "n in component model_para (dimensionless)" legend_constants[16] = "K_ph in component model_para (mM)" legend_constants[17] = "K_NaCa in component model_para (mM)" legend_constants[18] = "G_NaCa in component model_para (mM_per_s_mV)" legend_constants[19] = "n_M in component model_para (dimensionless)" legend_constants[20] = "Ca_halfMLCK in component model_para (mM)" legend_constants[21] = "M_init in component initials (dimensionless)" legend_constants[22] = "Mp_init in component initials (dimensionless)" legend_constants[23] = "AM_init in component initials (dimensionless)" legend_constants[24] = "AMp_init in component initials (dimensionless)" legend_constants[25] = "K_7 in component model_para (per_s)" legend_constants[26] = "K_2 in component model_para (per_s)" legend_constants[27] = "K_3 in component model_para (per_s)" legend_constants[28] = "K_4 in component model_para (per_s)" legend_constants[29] = "K_5 in component model_para (per_s)" legend_constants[30] = "Nai in component model_para (mM)" legend_constants[31] = "K_Cahalf in component model_para (mV)" legend_constants[32] = "inhPump in component model_para (dimensionless)" legend_constants[33] = "Cai_init in component initials (mM)" legend_constants[34] = "z_Ca in component E_Ca (dimensionless)" legend_constants[39] = "E in component Nernst_potential (mV)" legend_constants[35] = "z_Na in component E_Na (dimensionless)" legend_constants[38] = "E in component Nernst_potential (mV)" legend_algebraic[5] = "I in component Ionic_currents (pA)" legend_constants[40] = "V_mNaCa in component J_NaCa (mV)" legend_algebraic[4] = "norm in component CB4HM (dimensionless)" legend_states[1] = "M in component CB4HM (dimensionless)" legend_states[2] = "Mp in component CB4HM (dimensionless)" legend_states[3] = "AM in component CB4HM (dimensionless)" legend_states[4] = "AMp in component CB4HM (dimensionless)" legend_rates[0] = "d/dt V in component vramp_protocol_s (mV)" legend_rates[1] = "d/dt M in component CB4HM (dimensionless)" legend_rates[2] = "d/dt Mp in component CB4HM (dimensionless)" legend_rates[3] = "d/dt AM in component CB4HM (dimensionless)" legend_rates[4] = "d/dt AMp in component CB4HM (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = -100 constants[1] = 1 constants[2] = 16.55 constants[3] = 0.0001 constants[4] = 1 constants[5] = 11 constants[6] = 8.314 constants[7] = 96.48534 constants[8] = 310 constants[9] = 140 constants[10] = 2 constants[11] = 21 constants[12] = -27 constants[13] = 0.046842 constants[14] = 5.1449e-4 constants[15] = 1.9015 constants[16] = 0.6e-3 constants[17] = 7e-3 constants[18] = 5.7297e-5 constants[19] = 8.7613 constants[20] = 256.98e-6 constants[21] = 1 constants[22] = 0 constants[23] = 0 constants[24] = 0 constants[25] = 0.0378 constants[26] = 1.2387 constants[27] = 0.1419 constants[28] = 0.035475 constants[29] = 1.2387 constants[30] = 2.9836 constants[31] = 11 constants[32] = 1 constants[33] = 0.1e-6 constants[34] = 2 constants[35] = 1 constants[36] = (-constants[14]*(power(constants[3], constants[15])))/(power(constants[16], constants[15])+power(constants[3], constants[15])) constants[37] = ((power(constants[3], constants[19]))/(power(constants[20], constants[19])+power(constants[3], constants[19])))*1.00000 constants[38] = ((constants[6]*constants[8])/(constants[35]*constants[7]))*log(constants[9]/constants[2]) constants[41] = constants[1] constants[39] = ((constants[6]*constants[8])/(constants[34]*constants[7]))*log(constants[10]/constants[3]) constants[40] = 3.00000*constants[38]-2.00000*constants[39] states[0] = constants[0] states[1] = constants[21] states[2] = constants[22] states[3] = constants[23] states[4] = constants[24] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[0] = constants[41] algebraic[4] = states[1]+states[2]+states[3]+states[4] rates[1] = (-constants[37]*states[1])/algebraic[4]+(constants[26]*states[2])/algebraic[4]+(constants[25]*states[3])/algebraic[4] rates[2] = ((constants[28]*states[4])/algebraic[4]+(constants[37]*states[1])/algebraic[4])-((constants[26]+constants[27])*states[2])/algebraic[4] rates[3] = (constants[29]*states[4])/algebraic[4]-((constants[37]+constants[25])*states[3])/algebraic[4] rates[4] = ((constants[27]*states[2])/algebraic[4]+(constants[37]*states[3])/algebraic[4])-((constants[28]+constants[29])*states[4])/algebraic[4] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[4] = states[1]+states[2]+states[3]+states[4] algebraic[0] = ((constants[18]*constants[3])/(constants[3]+constants[17]))*(states[0]-constants[40]) algebraic[1] = states[4]+states[3] algebraic[2] = states[4]+states[2] algebraic[3] = 1.00000/(1.00000+exp((constants[12]-states[0])/constants[5])) algebraic[5] = constants[13]*algebraic[3]*(states[0]-constants[39]) algebraic[6] = -algebraic[5]/(2.00000*constants[11]*constants[7]) 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)