CAREER: Topology-Driven Learning for Biomedical Imaging Informatics

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。由于几十年的技术发展，科学家们现在能够可视化高质量的复杂生物医学结构，如神经元、血管、小梁和乳腺组织。这些复杂而动态的结构编码了有关潜在生物机制的重要信息。需要创新的方法来充分利用这些结构并预测生物学和临床结果。通过识别关键的结构模式，科学家可以更好地解释疾病进展，并发现新的结构诊断和预后生物标志物。挑战在于，这些结构在几何和拓扑结构上往往非常复杂，而且变化很大。拓扑学是抽象数学的一个分支，研究连接和环路等结构；该项目结合了拓扑学的先进数学理论（特别是持久同源性）和现代深度学习，开发了精确重建和分析这些复杂、动态和异构生物医学结构的新方法。该项目的结果不仅将产生更适合这些拓扑丰富的结构的新颖学习方法，而且还将促进对不同生物医学结构系统功能的理解。该项目还通过精心整合的教育和外联计划培训下一代研究人员和教育工作者。通过实施数据游戏（PWD）原则，研究者将通过与真实世界的数据直接互动来吸引学生和公众。该项目的目标是为生物医学结构创建一个基础拓扑驱动的学习范例，包括分割、生成和分析。使用持久同调理论，它提供了涉及拓扑的鲁棒和可微表示，研究者将(1)明确地在拓扑特征空间中捕获和推理，(2)以端到端的方式无缝地将拓扑推理融入现代学习中，以便可以以数据驱动和任务驱动的方式学习关键拓扑模式。提出了技术贡献，以解决关键的理论和算法挑战，制定拓扑信息作为拓扑损失。该损失用于训练具有高拓扑精度的图像分割模型，这对结构分析至关重要。研究者还将开发拓扑感知深度生成模型，可以从实际数据中学习拓扑。将开发新的拓扑表示和学习算法，以充分利用拓扑丰富的结构并识别区分种群的关键模式。研究者还将研究新的时变拓扑表示，并解决学习动力学的挑战性问题。由此产生的技术和软件将在公共数据集和现实世界的生物医学问题上得到验证。要开发的方法是一般的，并将影响其他科学领域的数据，例如生态学和地理信息科学，这些领域存在内在的复杂和动态结构。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).Thanks to decades of technology development, scientists are now able to visualize in high quality complex biomedical structures such as neurons, vessels, trabeculae and breast tissues. These complex and dynamic structures encode important information about underlying biological mechanisms. Innovative approaches are needed to fully exploit these structures and to predict biological and clinical outcomes. By identifying crucial structural patterns, scientists can better explain disease progression and discover novel structure-informed diagnosis and prognosis biomarkers. The challenge is that the structures are often highly complex in geometry and topology, and highly variable. Topology is the branch of abstract mathematics that deals with structures such as connections and loops; this project combines advanced mathematical theory from topology (in particular, persistent homology) and modern deep learning to develop novel methodology for accurate reconstruction and analysis of these complex, dynamic and heterogeneous biomedical structures. The outcome of the project will not only generate novel learning methods that are better suited for these topology-rich structures, but also advance the understanding of the functionality of different biomedical structural systems. This project also trains the next generation of researchers and educators through a carefully integrated educational and outreach plan. By implementing a Play-With-Data (PWD) principle, the investigator will engage students and the public through direct interactions with real-world data. The goal of this project is to create a foundational topology-driven learning paradigm for biomedical structures, including segmentation, generation, and analysis. Using the theory of persistent homology, which provides robust and differentiable representations involving topology, the investigator will (1) explicitly capture and reason in a topological feature space, and (2) seamlessly incorporate topological reasoning into modern learning in an end-to-end fashion, so that critical topological patterns can be learned in a data-driven and task-driven manner. Technical contributions are proposed to address key theoretical and algorithmic challenges in formulating topological information as a topological loss. The loss is used to train image-segmentation models with high topological accuracy, which is crucial for structural analysis. The investigator will also develop topology-aware deep generative models that can learn topology from the real data. Novel topological representation and learning algorithms will be developed to fully exploit the topology-rich structures and identify crucial patterns differentiating populations. The investigator will also investigate new time-varying topology representations and address the challenging problem of learning the dynamics. The resulting techniques and software will be validated on public datasets and real-world biomedical problems. The methods to be developed are general and will impact data from other scientific domains, such as ecology and geographic information science, where intrinsic complex and dynamic structures exist.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.