Title: An additive separation of variables 3D solution to a dynamical BVP for neutron cancer therapy
Authors: Nassar H.S. Haidar
Addresses: CRAMS: Center for Research in Applied Mathematics and Statistics, AUL, Cola St., Beirut, Lebanon
Abstract: We study the boundary-value problem (BVP) for irradiation of a right parallelepipedal cancerous region in a (B/Gd) neutron cancer therapy (NCT) composite- region setup by three mutually orthogonal, time-modulated, one-speed neutron beams. The technique of composite region coupling by a neutron source at a common boundary of different regions is demonstrated to allow for an additive separation of variables (ASOV) regional neutron-density 3D wave solution to the posing four-regional BVP. The beams, which may have different pulse shapes, have different modulation frequencies and variable relative time delays. The obtained analytical solution is intended to facilitate future work on optimisation towards improving the therapeutic quality of the associated setup.
Keywords: accelerator based modulated neutron sources; four-regional boundary-value problems; ASOV; additive separation of variables; one-speed neutron diffusion; neutron-density 3D wave; dynamical NCT; Laplace transforms; three mutually orthogonal neutron beams.
International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.2, pp.140 - 163
Received: 22 Aug 2017
Accepted: 23 Nov 2017
Published online: 27 Jun 2019 *