A computational solution of the inverse problem in radiation-therapy treatment planning

doi:10.1016/0096-3003(88)90064-1

Applied Mathematics and Computation

Volume 25, Issue 1, January 1988, Pages 57-87

https://doi.org/10.1016/0096-3003(88)90064-1 Get rights and content

Abstract

Radiation therapy concerns the delivery of the proper dose of radiation to a tumor volume without causing irreparable damage to healthy tissue and critical organs. The forward problem refers to calculating the dose distribution that would be delivered to a measured patient cross-section when the radiation field generated by the beam sources is specified. The inverse problem refers to calculating the radiation field that will provide a specified dose distribution in the patient. The forward and inverse problems of radiation-therapy treatment planning are first formulated in their continuous versions, and the point is made that, in this field of application, the inverse problem calls for the inversion of an operator for which no analytic closed-form mathematical representation exists. To attack the inverse problem under such circumstances, a discretized model is set up in which both patient section and radiation field are finely discretized. This leads to a linear feasibility problem, which is solved by a relaxation method. The paper includes full details of this new approach, with discussion of technical aspects such as dose apportionment, software development, and experimental results. Consequences and limitations as well as a precise comparison with other methodologies are also discussed.

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^☆: A preliminary report on this research was presented at the Eighth International Conference on the Use of Computers in Radiation Therapy, 9-12 July 1984, Toronto, Canada [24].

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A computational solution of the inverse problem in radiation-therapy treatment planning☆

Abstract

Comput. Prog. Biomed.

Rad. Onc. Biol. Phys.

Internat. J. Rad. Onc. Biol. Phys.

J. Comput. Appl. Math.

Computational methods in beam therapy planning

Comput. Prog. Biomed.

The equivalent tissue-air ratio method for making absorbed dose calculations in a heterogeneous medium

Radiology

Computer generated isodose curves for high energy x-ray machines

Amer. J. Roentgen. Rad. Therapy and Nucl. Med.

Scatter-air ratios

Phys. in Med. and Biol.

Limitations of two-dimensional treatment planning programs

Med. Phys.

The relaxation method for linear inequalities

Canad. J. Math.

The relaxation method for linear inequalities

Canad. J. Math.

Row-action methods for huge and sparse systems and their applications

SIAM Rev.