Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T10:03:09.686Z Has data issue: false hasContentIssue false
  • English
  • Français

On a boundary-value problem posed by cancer therapy with neutron beams

Published online by Cambridge University Press:  17 February 2009

Nassar H. S. Haidar
Nassar H. S. Haidar
Affiliation:
Departments of Mathematics and Physics, American University of Beirut, Beirut, Lebanon, email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper contains a detailed formulation of advanced tumor therapy with neutron beams as a mixed boundary initial value problem for multigroup neutron diffusion in a composite 3D multiregional system. By applying a vector-matrix composite region finite-integral transformation we derive the principal operational solution to this problem as the group-regional neutron flux distribution inside the tumor 3D subregions. The principal solution is then converted into expressions of various order approximation, which may be directly programmed on a computer.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 1 , July 1997 , pp. 46 - 60
Copyright
Copyright © Australian Mathematical Society 1997

References

[1] Bers, L., John, F. and Schechter, M., Partial differential equations, Lectures in Applied Mathematics (AMS, Rhode Island, 1964).Google Scholar
[2] Birattari, C., Bonardi, M., Ferrari, A., Milanesi, L. and Silari, M., “Biomedical applications of cyclotrons and review of commercially available models”, J. Med. Eng. Technol. 11 (1987) 166–176.CrossRefGoogle ScholarPubMed
[3] Ford, F., “Little LINACS fight cancer”, Beam Line 23 (1993) 6–13.Google Scholar
[4] Hahn, P. F. and Sheppard, C. W., “The therapeutic use of radioactive elements in malignancy”, Ann. Int. Med. 28 (1948) 598–607.Google ScholarPubMed
[5] Haidar, N. H. S., “Breeder reactor eigenproblems and finite Sturm-Liouville transforms”, Atomkernenergie/Kerntechnik 68 (1981) 278–281.Google Scholar
[6] Haidar, N. H. S., “Operational analysis of multiregional nuclear reactor kinetics”, IMA J. Appl. Math. 30 (1983) 247–267.CrossRefGoogle Scholar
[7] Haidar, N. H. S., “Eigenfunctions for a class of parametric Sturm-Liouville problems with an eigenvalue continuum”, J. Math. Anal. Appl. 161 (1991) 20–27.CrossRefGoogle Scholar
[8] Haidar, N. H. S., “A phenomenological model for radioactive poisoning by a human body”, Rev. de Bio-Math. 30 (1992) 21–47.Google Scholar
[9] Henry, A. F., Nuclear reactor analysis (MIT Press, Massachusetts, 1975).Google Scholar
[10] Jongen, Y., “Intense accelerator based neutron sources and their applications”, Symposium on policy and promotion of nuclear technology based on small accelerators used in industry, health, environment and other applications, held at IAEA headquarters, Vienna (1994), unpublished.Google Scholar
[11] Ölçer, N. Y., “A general class of unsteady heat flow problems in a finite composite hollow circular cylinder”, Q. Appl. Math. 26 (1968) 355–371.CrossRefGoogle Scholar
[12] Webb, S., The physics of three dimensional radiation therapy (IOP, Bristol, 1993).CrossRefGoogle Scholar