Geometric Problems in Radiosurgery, Radiation Therapy, and Other Medical Applications

这个项目是关于解决放射外科、放射治疗和其他医疗应用中出现的几何问题的算法技术的设计、分析和实现。放射外科是一种微创外科手术，它使用一组聚焦的辐射束来摧毁肿瘤。放射治疗和放射外科的一个关键步骤是制定一个治疗计划，确定最佳的辐射束布置和时间设置，以在不损害周围健康组织的情况下摧毁目标肿瘤。放射治疗计划的核心是一组实质上非平凡的几何优化问题。我们试图研究放射治疗计划中出现的一系列几何优化问题，如束流选择(包括束流探测及其多种变化)、手术导航和路径选择、球体填充、束流成形、图像分割、形状逼近和束源路径规划。这一交叉学科的研究将从计算几何和其他理论领域，如运筹学和组合优化，汲取不同的技术。此外，这项研究将提供丰富的问题来源和新的挑战，推动算法技术在这些理论领域的进一步发展。计划中的研究包括一个重要的实验部分。计算医学跨学科领域的课程开发和学生培训方面的教育活动也是该项目的一部分。

This project is on the design, analysis, and implementation of algorithmic techniques for solving geometric problems that arise in radiosurgery, radiation therapy, and other medical applications. Radiosurgery is a minimally invasive surgical procedure that uses a set of focused beams of radiation to destroy tumors. A key step in radiotherapy and radiosurgery is to develop a treatment plan that defines the best radiation beam arrangements and time settings to destroy the target tumor without harming the surrounding healthy tissues. At the core of radiation treatment planning is a set of substantially non-trivial geometric optimization problems.We seek to investigate a number of geometric optimization problems arising in radiation treatment planning, such as beam selection (including beam probing and its many variations), surgical navigation and routing, sphere packing, beam shaping, image segmentation, shape approximation, and beam source path planning.This interdisciplinary research will draw diverse techniques from computational geometry and other theoretical areas, such as operations research and combinatorial optimization. Furthermore, this research will provide a rich source of problems and new challenges that prod further development of algorithmic techniques in these theoretical areas. The planned research includes an important experimental component. Educational activities on course development and student training in the interdisciplinary area of computational medicine are also part of the project.