The forward problem of radiation therapy treatment planning (RTTP)--commonly called dose calculation--involves the use of empirical look-up tables and complex formulae. In order to represent it with a closed-form mathematical formula several simplifying assumptions need to be made on the model. Even then transform inversion is not readily available.

The fully discretized approach to RTTP [1, 2] allows us to maintain the forward calculations in their utmost accurate form and use special-purpose iterative mathematical optimization algorithms for the inversion. Some of these algorithms are either parallelizable or parallel already in their mathematical formulations, [3].

The ray-intensities solution obtained in such a way needs to be appropriately translated to treatment machine parameters. We review this approach, point out some of its weaknesses and compare it with other solution methods of the inverse problem in RTTP.

1. Y. Censor, M.D. Altschuler, and W.D. Powlis, ``On the use of Cimmino's simultaneous projections method for computing a solution of the inverse problem in radiation therapy treatment planning", Inverse Problems, 4:607-623, 1988.
2. W.D. Powlis, M.D. Altschuler, Y. Censor, and E.L. Buhle, Jr., ``Semi- automatic radiotherapy treatment planning with a mathematical model to satisfy treatment goals", International Journal Radiation Oncology Biology Physics, 16:271-276, 1989.
3. Y. Censor and S.A. Zenios, Parallel Optimization : Theory, Algorithms, and Applications, A volume in the series: Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 1997.

Back to Workshop Schedule

1996-1997 Mathematics in High Performance Computing