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On the optimal control of cancer radiotherapy for non-homogeneous cell populations. (English) Zbl 0767.60011
Summary: 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 distribution for normal and tumor tissues is demonstrated.

##### MSC:
 60E05 Probability distributions: general theory 62P10 Applications of statistics to biology and medical sciences; meta analysis
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