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On the optimal control of cancer radiotherapy for non-homogeneous cell populations

  • L. G. Hanin (a1), S. T. Rachev (a2) and A. Yu. Yakovlev (a3)

Abstract

Optimization problems in cancer radiation therapy are considered, with the efficiency functional defined as the difference between expected survival probabilities for normal and neoplastic tissues. Precise upper bounds of the efficiency functional over natural classes of cellular response functions are found. The ‘Lipschitz' upper bound gives rise to a new family of probability metrics. In the framework of the ‘m hit-one target' model of irradiated cell survival the problem of optimal fractionation of the given total dose into n fractions is treated. For m = 1, n arbitrary, and n = 1, 2, m arbitrary, complete solution is obtained. In other cases an approximation procedure is constructed. Stability of extremal values and upper bounds of the efficiency functional with respect to perturbation of radiosensitivity distributions for normal and tumor tissues is demonstrated.

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Postal address: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel.
∗∗ Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA.
∗∗∗ Postal address: Department of Applied Mathematics, St Petersburg Technical University, Polytechnicheskaya, St Petersburg 195251, Russia.

References

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[12] Turner, M. M. (1975) Some classes of hit-target models. Math. Biosci. 23, 219235.
[13] Yakovlev, A. Yu and Zorin, A. V. (1988) Computer Simulation in Cell Radiobiology. Lecture Notes in Biomathematics 74, Springer-Verlag.

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On the optimal control of cancer radiotherapy for non-homogeneous cell populations

  • L. G. Hanin (a1), S. T. Rachev (a2) and A. Yu. Yakovlev (a3)

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