## Biomathematical Problems in Optimization of Cancer RadiotherapyBiomathematical Problems in Optimization of Cancer Radiotherapy provides insight into the role of cell population heterogeneity in the optimal control of fractionated irradiation of tumors. The book emphasizes the mathematical modeling aspect of the problem and presents the state of the art in the stochastic description of irradiated cell survival. Some of the results are of general theoretical interest and can be applied to other areas of optimal control methodology. Detailed explanations of all mathematical statements are provided throughout the text. The book is excellent for biomathematicians, radiotherapists, oncologists, health physicists, and other researchers and students interested in the topic. |

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### Contents

Introduction | 1 |

Chapter | 3 |

Tumors | 31 |

3 | 55 |

Optimal Fractionation Problem | 81 |

Irradiation Scheme | 101 |

Conclusion | 113 |

Appendix 2 | 119 |

Subject Index | 129 |

### Common terms and phrases

3T3 cells assumed Biomathematics branching process cancer cell death cell population cell proliferation clonogens surviving considered corresponding critical number damage repair defined distribution function dose fractions dose-effect efficiency endophytic equations experimental Figure Formula 2.1 fractionated irradiation function F gamma distribution given hazard function hit and target inactivation irradiated cell survival irradiation schemes Kaplan-Meier estimate lethal lesions LICH cells Lipschitz Markov mean number mesE misrepair multihit multihit-one target model neoplastic neoplastic cells Ni(t normal and neoplastic number of clonogens number of hits number of lesions obtained optimal control optimal fractionation parametric estimates Poisson distribution Poisson statistics potentially lethal problem radiation damage radiation dose radiation-induced radiobiological radiobiology radiosensitivity distributions random variable regimen repair processes reparon response function Section stochastic stochastic differential equations stochastic process survival function survival probability theorem total dose treatment Tucker tumor cure two-fraction unrepaired upper bound Variant Yakovlev