CDS&E-MSS: Geometric and Statistical Foundations for Modeling Cell Shapes

该项目旨在通过结合数学、统计学和生物学等多个领域的知识，开发用于研究细胞形状的新的数学和统计工具。它涉及处于这些领域前沿的综合研究和教育计划。该项目将使用数学和统计相结合的建模和模拟来了解细胞形态的潜在机制。将这些有价值的细胞形状信息结合到分析中可以导致对细胞功能的新发现，并有可能促进对潜在生物过程的新理解，如细胞形态，这在理解癌症机制方面非常重要。该奖项将通过研究为研究生培养提供支持。该项目的主要目标是开发新的几何和统计框架，允许从业者将有价值的细胞形状信息纳入分析。几何基础将首先通过表征细胞形状空间(细胞形状空间)的内在和外在几何来发展。接下来，我们将开发一套新的统计模型和工具，用于细胞形状分析，可以适当地结合细胞形状空间的几何形状。提出了用几何演化方程研究细胞形态的新数学模型。我们研究的另一个关键主题是将数学建模与统计推理相结合，形成一种系统的细胞研究方法。我们将使用统计数据进行数学模型验证和改进，并使用改进后的数学模型中模拟的数据进行统计模型验证。开发的方法将被应用于一项关于红细胞(红细胞)形态在血栓形成过程中的作用的重要研究。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The project aims to develop new mathematical and statistical tools for studying cell shapes by combining knowledge from several fields such as mathematics, statistics and biology. It concerns an integrated research and education program at the forefront of these fields. The project will use combined mathematical and statistical modeling and simulation to learn underlying the mechanisms of cell morphology. Incorporating this valuable information of cell shapes into analysis can lead to new discoveries of cell functions and has the potential of advancing new understanding of the underlying biological processes such as cell morphology, which is very important for example in understanding cancer mechanisms. The award will provide support of graduate student training through research.The main goal of the project is to develop new geometric and statistical framework that allows practitioners to incorporate valuable information of cell shapes into analysis. Geometric foundations will be first developed by characterizing both the intrinsic and extrinsic geometry of the space of cell shapes (the cell shape space). Next we will develop a new suite of statistical models and tools for cell shape analysis that can appropriately incorporate the geometry of the cell shape space. A new mathematical model for studying morphology of cells by geometric evolution equations will be proposed. Another key theme of our research is to combine mathematical modeling with statistical inference to form a systematic approach for cell studies. We will use statistics for mathematical model validation and refinements, and employ data simulated from the refined mathematical model for statistical model validations. The developed methods will be applied to an important study on the role of RBCs (red blood cells) morphology during the formation of blood clots.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.