An additive separation of variables 3D solution to a dynamical BVP for neutron cancer therapy
by Nassar H.S. Haidar
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 9, No. 2, 2019

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.

Online publication date: Thu, 04-Jul-2019

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