ITR/AP(CCR): Investigation of Computational Optimization in Brachytherapy Cancer Treatment

近距离癌症治疗中的计算优化研究该项目汇集了计算优化和医学方面的研究人员，以解决近距离癌症治疗计划的基本问题。该项目涉及四个研究途径：1)基于混合整数规划（MIP）技术设计现实和实用的数学模型，以描述近距离放射治疗的物理规划，其中包括确定植入肿瘤内/附近的放射源的“最佳”配置。2)通过构造冲突超图对MIP模型的多面体结构进行理论研究。相关的多面体影响将被利用来开发和实施分离算法，以协助解决过程。3)开发新的计算工具，旨在从这类问题以及其他应用中解决困难的密集MIP实例。计算方法包括矩阵约简技术、惩罚分支策略、集中分支（以变量集代替变量二分法关注成本降低和多分支）以及从超图结构生成强切割面。4)将数学模型和计算引擎集成为手术室使用的专家规划系统。该研究的成功将通过超图构造得到与整数规划相关的重要理论成果；它将导致解决密集MIP实例的计算进步，这一特征与大多数工业应用相当不同，但通常出现在医疗诊断和治疗计划问题中；它将提高以最好的方式治疗病人的能力。此外，由此产生的治疗计划系统将作为一种研究工具，推动对近距离治疗的前沿理解，开启进行临床研究的可能性，这些研究需要在短时间内制定公正的计划。教育推广包括为工程和医学领域的本科生和研究生开发与该项目相关的教材。该项目还将培养2名博士生进行涉及优化、算法设计和癌症治疗的多学科研究。博士研究将侧重于理论和计算优化，特别是与本项目相关的问题。本科生和少数族裔学生将通过本科课程和定期的医学预科和少数族裔学生指导参与研究经验。该研究项目的一部分也将在“癌症生物学和生物技术”课程的信息和生物技术讲座中传播，该课程最近由佐治亚理工学院的一组跨学科教师研究人员开发，重点是多方面的方法来推进癌症技术。这项强调工程技术在医学/肿瘤学研究中的应用的新的教育努力将包括在可能的小组讨论和高中学生的招聘中。

Investigations of Computational Optimization in Brachytherapy CancerTreatmentThis project brings together researchers in computational optimization and medicine to address the fundamental problem of treatment planning for brachytherapy treatment of cancer. The project involves four avenues of investigation: 1) Design of realistic and practical mathematical models based on mixed integer programming (MIP) technology to describe the physical planning of brachytherapy, which involves the determination of an``optimal'' configuration of radioactive sources to be implanted in/near the tumor. 2) Theoretical investigation of the underlying polyhedral structure of the MIP models via the construction of conflict hypergraphs. Associated polyhedral implications will be exploited to develop and implement separation algorithms to assist in the solution process. 3) Develop new computational tools aimed at solving the difficult dense MIP instances from this class of problems, as well as from other applications. Computational approaches include matrix reductiontechniques, penalty branching strategies, aggregate branching which focuses on reduced-cost and multiple branches with sets of variables instead of variable dichotomy, and generation of strong cutting planes from hypergraphic structures. 4) Integration of the mathematical models and computational engine into an expert planning system for use in the operating room.The success of the research will lead to important theoretical results related to integer programming through the hypergrahic constructs; it will lead to computational advances for solving dense MIP instances, a characteristic rather different from most industrial applications, but arising commonly in medical diagnosis and treatment planning problems; and it will improve the ability to treat patients in the best possibleway. Furthermore, the resulting treatment planning system will serve as a research tool to push the frontier of understanding for brachytherapy treatment, opening up the possibility of conducting clinicalinvestigations which require unbiased plans to be produced within a short time frame.Educational outreach involves developing teaching materials relatedto the project for undergraduate and graduate students in engineering and in the medical domain. It also involves training of 2 Ph.D. students inthis multidisciplinary research involving optimization, algorithmic design and cancer treatment. The Ph.D. research will focus on theoretical and computational optimization, and in particular, on issues related to the project herein. Undergraduates and minorities will be involved in the research experience through undergraduate courses and regular premed and minority student mentoring. Part of the research project will also be disseminated in the lectures on information and biotechnology in the course ``Cancer Biology and Biotechnology'', developed recently by a group of interdisciplinary faculty researchers at Georgia Tech with a focus on multi-faceted approaches for advancing cancer technology. Mention of this new educational effort highlighting applications of engineering technology in medical/oncological research will be included in possible paneldiscussions and in the recruitment of high school students.