CAREER: Efficient Geometric Techniques for Problems Arising in Cardiovascular Intervention Procedures

本课题的研究处于计算几何与心血管疾病相关外科手术的交叉领域。长期以来，心血管疾病（如血管狭窄和堵塞）一直是美国人死亡的主要原因。治疗此类疾病的主要方法是以微创的方式进行介入手术，如血管造影术、血管成形术、冠脉支架植入等。该项目的研究重点是开发有效的算法和技术来解决这些介入过程中出现的一系列重要几何问题。目标几何问题包括成像几何确定、高维最大内切球、k集对应、投影曲线水平、曲线和点集聚类以及最小能量路径。针对这些问题的新算法不仅为这些介入过程中的关键问题提供了更有效的解决方案，而且还具有在许多其他应用中使用的潜力。计算几何技术在医学问题上的应用在智力上是深刻的，可以导致计算几何和医学的进步。本研究的一个重要目标是将软件中实现的算法传播到应用领域。在这样做的过程中，它将有助于将计算机科学和医学界结合在一起。

The research of this project is at the interface between computational geometry and surgery related to cardiovascular diseases. Cardiovascular diseases (such as vessel narrowing and blockage) have been major causes of death in the United States for a long time. The primary method for dealing with such diseases is to conduct interventional procedures, such as angiography, angioplasty, and coronary stent implant, in a minimally invasive manner. The research focus of this project is on developing efficient algorithms and techniques for solving a set of important geometric problems arising in these interventional procedures.The target geometric problems include imaging geometry determination, high dimensional maximum inscribed sphere, k-set correspondence, projective curve-level, curve and point-set clustering, and minimum energy paths. New algorithms for these problems not only provide more efficient solutions to key problems in these interventional procedures, but also have the potential to be used in many other applications. The application of computational geometry techniques to medical problems is intellectually deep and can result in advances in both computational geometry and medicine. An important goal of this research is dissemination of implemented algorithms in software to application domains. In doing this, it will help to bring together the computer science and the medical community.