Qualitative Unbiased Shape Analysis with Geometry & Topology

The convergence of biology and mathematics is unlocking new frontiers in understanding the complexities of cellular behaviour. This project aims to advance the analysis of human mesenchymal stem cells (hMSCs) through cutting-edge mathematical techniques. By employing geometric and topological data analysis (GTDA), this research seeks to provide deeper insights into cell self-organization and differentiation, which could have profound implications for regenerative medicine. At the heart of this project lies the application of GTDA, a powerful mathematical framework that enables the study of the shape and structure of data. GTDA allows researchers to capture the multi-scale features of complex biological systems. By analysing the topological features of biological cells, the project aims to identify subpopulations of cells with distinct behaviours and properties. This innovative approach offers a new lens through which to examine cellular processes, providing a level of detail and insight that traditional methods often miss. We focus on analysing hMSCs due to their ability to differentiate into various cell types and their potential in tissue repair. By analysing hMSCs, this project addresses a pivotal question in stem cell research: how to identify and characterise distinct subpopulations of cells. The project leverages tools from geometry and topology which have not been extensivey applied in biological contexts. By developing tools that allow for the transformation and analysis of cellular structures in a way that preserves essential geometric properties, we can accurately model cell behaviour. Combined with persistent homology, which tracks the evolution of topological features across multiple scales, these techniques provide a robust framework for analysing dynamic cellular processes. Beyond its immediate scientific goals, this project aims to release an open-source software package that encapsulates the developed techniques and findings. This resource will empower researchers worldwide to apply these advanced mathematical tools to their own biological data, fostering further innovation and discovery. Additionally, the project emphasizes the importance of ethical considerations in using ML/AI for biological analysis. All in all, this project is a significant step towards understanding cellular behaviour. By integrating advanced mathematical techniques with cutting-edge biological research, it illuminates new dimensions of cellular behaviour, paving the way for applications in medicine and biotechnology. The project`s commitment to open science and interdisciplinary collaboration ensures that its impact will be felt across multiple fields, driving progress and innovation for the future.