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

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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.