A line of the Boron Neutron Capture Therapy (BNCT) research program aimed at the treatment of brain tumors, carried on at the Nuclear Departments of Pisa and Genova Universities (DIMNP and DITEC), is being focused on a new, H3(d,n)4He (D–T), accelerator-based neutron source concept, developed at Lawrence Berkeley National Laboratory (LBNL). Simple and compact accelerator designs, using mixed D+ T+ ion beam with relatively low energy, ∼100 keV, have been developed which, in turn, can generate high neutron yields. New approaches have thus been started to design an epithermal neutron irradiation facility able to selectively slow the 14.1 MeV D–T neutrons down to the epithermal (1 eV–10 KeV) energy range. New neutron spectrum shifter and filtering materials, as well as different facility layout approaches have been tested. Possible beam shaping assembly models have also been designed. The research demonstrates that a D–T neutron source could be successfully implemented to provide a ∼1×109 n/cm2 s epithermal neutron flux, in spite of its hard spectrum, although a generator device, able to yield ∼1014 n/s is, at present, not yet available. The latest Monte Carlo simulation of an accelerator-based facility, which relies on a single or multiple rf driven DT fusion neutron generator, is presented.