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

这个项目是关于设计，分析和实现算法技术，用于解决放射外科，放射治疗和其他医疗应用中出现的几何问题。 放射外科手术是一种微创外科手术，使用一组聚焦的辐射束来破坏肿瘤。 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，该计划定义了最佳的放射束排列和时间设置，以摧毁靶肿瘤而不伤害周围的健康组织。 放射治疗计划的核心是一组非平凡的几何优化问题，本文试图研究放射治疗计划中的一些几何优化问题，如射束选择（包括射束探测及其许多变型）、手术导航和路由、球体填充、射束成形、图像分割、形状近似，这项跨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）中汲取各种技术。 此外，这项研究将提供丰富的问题和新的挑战，推动进一步发展的算法技术在这些理论领域。 计划中的研究包括一个重要的实验部分。 在计算医学的跨学科领域开展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.