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

Part of: Distribution theory - Probability Applications

Published online by Cambridge University Press:  01 July 2016

L. G. Hanin ,
S. T. Rachev  and
A. Yu. Yakovlev
L. G. Hanin*
Affiliation:
Technion-Israel Institute of Technology
S. T. Rachev*
Affiliation:
University of California at Santa Barbara
A. Yu. Yakovlev*
Affiliation:
St Petersburg Technical University
*
∗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.
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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.

Keywords

TUMOR IRRADIATIONEFFICIENCY FUNCTIONALPRECISE UPPER BOUND OVER A SET OF FUNCTIONSPROBABILITY METRICSOPTIMAL FRACTIONATIONSTABILITY PROPERTIES

MSC classification

Primary: 60E05: Distributions
Secondary: 62P10: Applications to biology and medical sciences
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 1 , March 1993 , pp. 1 - 23
Copyright
Copyright © Applied Probability Trust 1993 

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