Mathematical cancer therapy planning in deep regional hyperthermia
Mathematical cancer therapy planning in deep regional hyperthermia
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DOI：
10.1017/s0962492912000049
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发表时间：
2012-01-01
期刊：
影响因子：
14.2
通讯作者：
Weiser, Martin
中科院分区：
文献类型：
--
作者：
Deuflhard, Peter;Schiela, Anton;Weiser, Martin
本文调查了计算医学中一个典型的具有挑战性的问题所需的数学：深部区域热疗中的癌症治疗计划。在多年与诊所的密切合作过程中，医疗问题引发了许多微妙的数学问题，其中一些在项目开始时尚未解决。数值算法的效率，即，计算速度和监测的可靠性，在医疗中起着决定性的作用。现成的软件已被证明不足以满足医学的要求。相反，新的数学理论以及新的数值算法必须发展。为了使我们的算法在临床环境中有用，新的可视化软件，必须设计和实施"虚拟实验室"，包括对各个虚拟患者进行三维几何处理。此外，在用数值算法解决这些问题之前，必须进行仔细的数学建模。最后，参数识别和约束优化的偏微分方程进行了新的分析，并实现了对个别病人的几何形状。我们的新技术对个体患者治疗的特异性和改进的热疗施加器的构造产生了影响。
This paper surveys the mathematics required for a typically challenging problem from computational medicine: cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem has given rise to many subtle mathematical problems, some of which were unsolved when the project started. Efficiency of numerical algorithms, i.e., computational speed and monitored reliability, plays a decisive role in the medical treatment. Off-the-shelf software had turned out to be insufficient to meet the requirements of medicine. Instead, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, i.e., a 'virtual lab', including three-dimensional geometry processing of individual virtual patients, had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analysed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the treatment of individual patients and on the construction of an improved hyperthermia applicator.