[en] The extended track interaction model (ETIM) describes heavy charged particle (HCP) thermoluminescence (TL) fluence response, taking into account both supralinearity and saturation effects. The supralinearity is very sensitive to the 'track escape' parameter, defined by N_e/N_w, where N_e represents the number of electrons which escape the parent track during heating, and N_w is the number of electrons which recombine within the parent track to produce a TL photon. In this study a first attempt is carried out to theoretically model track segment-escape parameters as a function of particle type and energy using trapping center (TC), luminescent centers (LCs) and competitive center (CC) occupation probabilities calculated from track segment radial dose distributions and optical absorption (OA) dose response. A Monte Carlo approach is employed which samples the point of creation of charge carriers according to the TC occupation probability densities and then estimates N_w by sampling the chord length to the track exterior and calculating the probability of capture by an activated LC within the track volume. Charge carriers which escape the irradiated track volume contribute to Ne. Values of N_e/N_w consistent with recent experimental estimates can be generated using physically reasonable values for the LC and CC cross-sections