An additive separation of variables 3D solution to a dynamical BVP for neutron cancer therapy

Nassar H.S. Haidar

doi:10.1504/ijdsde.2019.100563

An additive separation of variables 3D solution to a dynamical BVP for neutron cancer therapy

International Journal of Dynamical Systems and Differential Equations ◽

10.1504/ijdsde.2019.100563 ◽

2019 ◽

Vol 9 (2) ◽

pp. 140 ◽

Cited By ~ 1

Author(s):

Nassar H.S. Haidar

Keyword(s):

Cancer Therapy ◽

Separation Of Variables

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A Resonated and Synchrophased Three Beams Neutron Cancer Therapy Installation

Journal of Nuclear Engineering and Radiation Science ◽

10.1115/1.4045395 ◽

2020 ◽

Vol 6 (3) ◽

Author(s):

Nassar H. S. Haidar

Keyword(s):

Cancer Therapy ◽

Time Delays ◽

Optimization Problem ◽

Separation Of Variables ◽

Neutron Density ◽

Common Boundary ◽

Utility Index ◽

Composite Region ◽

3D Problem ◽

Regional Boundary

Abstract The technique of composite region coupling by a neutron source at a common boundary of different regions that has been introduced in 2019 has allowed for an additive separation of variables neutron-density 3D wave analytical solution to the posing four-regional boundary value problem (BVP) of neutron cancer therapy (NCT). The three employable mutually orthogonal neutron beams, which may have different pulse shapes, have distinct modulation frequencies ω,ϖ, and ŵ and distinct relative time delays ε and ε̂. By employing this solution, we demonstrate in this paper how the therapeutic utility index and the ballistic index for this kind of dynamical NCT form a nonlinear optimization problem. Both of these indices are demonstrated to be remarkably periodically discontinuous in ε or ε̂, even in the neighborhood of the respective ε∗ or ε̂∗. As an extension of a result obtained also in 2019, for a certain lower-dimensional setup, a Pareto optimal control vector ω∗=(ω∗,ϖ∗,ε∗,ŵ∗,ε̂∗) is identified for this 3D problem. The existence of this vector paves the way toward what we call a “resonated and synchrophased three beams neutron cancer therapy (RASP-3BNCT) installation.”

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