AitF: Collaborative Research: Topological Algorithms for 3D/4D Cardiac Images: Understanding Complex and Dynamic Structures

人类心脏心室的内部由难以分辨的肌肉纤维的细网跨越，即使在高分辨率CT图像中也是如此。 然而，对这些结构的准确描述可以改善心脏疾病的诊断、心脏功能的评估、中风风险的评估和心脏血流的模拟。拓扑学是抽象数学中处理连接的分支;本项目使用持久同源性理论来确定关键的拓扑手柄，这些拓扑手柄可用于精确重建和分析这些CT图像中的复杂心脏动力学。该项目的成果不仅将促进我们对心脏功能的理解，而且还将产生新的计算拓扑方法，这些方法对于实际应用更有效。该项目不仅弥合了计算拓扑学理论与心脏图像分析实际问题之间的差距，而且通过精心整合的教育计划培养了下一代研究人员和教育工作者。该项目的目标是开发一种拓扑方法，从复杂和动态的3D/4D心脏数据中揭示内在结构，并提供定量分析这些结构的原则性工具。PI将创建新的计算拓扑方法和算法，以从心脏数据的内在结构中提取丰富的信息。他们将开发新的方法来提取局部拓扑特征，并根据它们的空间和时间一致性对其进行跟踪。他们还计划设计新的算法来解决模糊和不确定的情况，以通过时间序列数据跟踪结构。由此产生的技术和软件将在心脏CT数据上进行验证，以产生准确性的定量评估，并表征这些方法的优点和局限性。领域专家将通过科学假设和数据探索来验证方法的质量。要开发的方法是通用的，将影响其他科学领域的内在复杂和动态结构存在。

The interiors of ventricles of a human heart are spanned by a fine net of muscle fibers that are difficult to resolve, even in high resolution CT images. An accurate account of these structures, however, could improve diagnosis of cardiac disease, evaluation of cardiac function, assessment of stroke risk, and simulation of cardiac blood flow. Topology is the branch of abstract mathematics that deals with connections; this project uses the theory of persistent homology to identify crucial topological handles that can be useful for accurate reconstruction and analysis of the complex cardiac dynamics from these CT images. The outcome of the project will not only advance our understanding of cardiac function, but also generate novel computational topology methods that are more efficient and effective for practical applications. This project not only bridges the gap between the theory of computational topology and the practical problem of cardiac image analysis, but also trains the next generation of researchers and educators to do so by a carefully integrated education plan. The PIs will engage undergraduate students, high school students, women and other underrepresented students in their proposed research.The goal of this project is to develop a topological approach to unveil the intrinsic structures from complex and dynamic 3D/4D cardiac data, and furthermore, to provide principled tools to quantitatively analyze these structures. The PIs will create new computational topology methodologies and algorithms to extract rich information from the intrinsic structure of cardiac data. They will develop novel methodologies to extract localized topological features and to track them based on their spatial and temporal coherence. They also plan to design new algorithms to untangle ambiguous and uncertain situations for tracking structures through time sequence data. The resulting techniques and software will be validated on cardiac CT data to produce quantitative assessments of accuracy and to characterize the advantages and limitations of these approaches. Domain experts will validate the quality of the approaches via scientific hypotheses and data exploration. The methods to be developed are general and will impact other scientific fields where intrinsic complex and dynamic structures exist.