Differential Equations and Data-Driven Methods for Modeling Microglial Cells During Ischemic Stroke

Amato, Sara

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Differential Equations and Data-Driven Methods for Modeling Microglial Cells During Ischemic Stroke

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Neuroinflammation immediately follows the onset of ischemic stroke. During this process, microglial cells are activated in and recruited to the tissue surrounding the irreversibly injured infarct core, the so-called penumbra. Microglial cells can be activated into two different phenotypes: M1, which can worsen brain injury; or M2, which can aid in long-term recovery. In this thesis, we contribute a summary of experimental data on microglial cell counts in the penumbra following ischemic stroke induced by middle cerebral artery occlusion (MCAO) in mice and compile available data sets into a single set suitable for time series analysis. Further, we formulate data-inspired and data-driven models of microglial cells in the penumbra during ischemic stroke due to MCAO. Through use of machine learning algorithms, differential equations, parameter estimation, sensitivity analysis, and uncertainty quantification, we computationally explore microglial cell dynamics in the short-term and long-term. Results emphasize an initial M2 dominance followed by a takeover of M1 cells, show the importance of microglial cell switching on model outputs, and suggest a lingering inflammatory response.

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