The unified interaction model (UNIM) was developed to simulate thermoluminescence (TL) linear/supralinear dose-response and the dependence of the supralinearity on ionisation density, i.e. particle type and energy. Before the development of the UNIM, this behaviour had eluded all types of TL modelling including conduction band/valence band (CB/VB) kinetic models. The dependence of the supralinearity on photon energy was explained in the UNIM as due to the increasing role of geminate (localised recombination) with decreasing photon/electron energy. Recently, the Ben Gurion University group has incorporated the concept of trapping centre/luminescent centre (TC/LC) spatially correlated complexes and localised/delocalised recombination into the CB/VB kinetic modelling of the LiF:Mg,Ti system. Track structure considerations are used to describe the relative population of the TC/LC complexes by an electron-hole or by an electron-only as a function of both photon/electron energy and dose. The latter dependence was not included in the original UNIM formulation, a significant over-simplification that is herein corrected. The modified version, the M-UNIM, is then applied to the simulation of the linear/supralinear dose-response characteristics of composite peak 5 in the TL glow curve of LiF:Mg,Ti at two representative average photon/electron energies of 500 and 8 keV.