Integrating topological data analysis and biology-based modeling to characterize murine tumor growth and angiogenesis

David A.Hormuth, II

The University of Texas at Austin

"Integrating topological data analysis and biology-based modeling to characterize murine tumor growth and angiogenesis"

Biology-based modeling and topological data analysis (TDA) are powerful techniques for characterizing properties of tumors and vascular networks, but there has been limited effort to integrate these approaches to characterize in vivo tumor growth. Persistent homology offers a systematic approach to identify features such as connected components, loops, and voids across different scales in high-dimensional datasets. Likewise, biology-based models can be calibrated to longitudinal data to yield tumor-specific parameters describing tumor and vascular growth. In this study, we applied TDA and biology-based modeling to longitudinal MRI collected in nine animals with C6 glioma tumors. Animals were imaged up to seven times over a two week period to measure the cell density and blood volume fraction. We computed persistent homology of cubical complexes filtered by the ratio of blood volume fraction to normalized tumor cell density to characterise connected components, loops, and voids in the 3D data. We summarised the output in 15 topological features which quantify known biological properties of the data. For the biology-based modeling approach, a two-species reaction-diffusion model describing tumor growth and angiogenesis was calibrated to longitudinal data to estimate parameters describing tumor growth, invasion, angiogenesis, and vessel death. We then performed k-means clustering on a combined set of topological and biology-based modeling features yielding three clusters. Clusters 1 and 2 consisted of tumors that exhibited voids (necrosis), while Cluster 3 consisted of tumors without well-defined voids. Notably animals in Clusters 1 and 2 had a lower ratio of vascular proliferation to tumor proliferation than Cluster 3. This preliminary study indicates that there may be relationships between topological features and biology-based parameters. Further development of these methods could yield a framework to assign improved model parameters of tumor growth and response.
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