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A Data-Informed Mathematical Model of Microglial Cell Dynamics During Ischemic Stroke in the Middle Cerebral Artery
Sara Amato1, Andrea Arnold2,3
1Bioinformatics and Computational Biology Program, Worcester Polytechnic Institute, Worcester, MA, USA.
Abstract:
Neuroinflammation immediately follows the onset of ischemic stroke in the middle cerebral artery. During this process, microglial cells are activated in and recruited to the 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 study, 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 a mathematical model of microglial cells in the penumbra during ischemic stroke due to MCAO. Through use of global sensitivity analysis and Markov Chain Monte Carlo (MCMC)-based parameter estimation, we analyze the effects of the model parameters on the number of M1 and M2 cells in the penumbra and fit identifiable parameters to the compiled experimental data set. We utilize results from MCMC parameter estimation to ascertain uncertainty bounds and forward predictions for the number of M1 and M2 microglial cells over time. Results demonstrate the significance of parameters related to M1 and M2 activation on the number of M1 and M2 microglial cells. Simulations further suggest that potential outliers in the observed data may be omitted and forecast predictions suggest a lingering inflammatory response.
Insights
This study models microglial cell responses after ischemic stroke. Mathematical analysis reveals key factors influencing M1 (harmful) and M2 (helpful) cell numbers, predicting a prolonged inflammatory response.
Area of Science:
- Neuroscience
- Computational Biology
- Immunology
Background:
- Ischemic stroke triggers neuroinflammation, involving microglial cells in the brain's penumbra.
- Microglial cells adopt M1 (detrimental) or M2 (beneficial) phenotypes, impacting stroke outcomes.
Purpose of the Study:
- To compile and analyze experimental data on microglial cell counts post-ischemic stroke.
- To develop a mathematical model predicting M1 and M2 microglial cell dynamics in the penumbra.
- To identify key parameters influencing microglial phenotypes and their temporal evolution.
Main Methods:
- Data compilation for time series analysis of microglial cell counts.
- Mathematical modeling of microglial cell behavior following middle cerebral artery occlusion (MCAO).
- Global sensitivity analysis and Markov Chain Monte Carlo (MCMC) for parameter estimation and uncertainty quantification.
Main Results:
- Identified significant model parameters affecting M1 and M2 microglial cell numbers.
- Fitted model parameters to compiled experimental data, providing uncertainty bounds.
- Model simulations suggest potential data outliers and a persistent inflammatory response.
Conclusions:
- Model parameters related to M1 and M2 activation are crucial for predicting microglial cell dynamics.
- Forward predictions indicate a sustained neuroinflammatory state post-stroke.
- The study provides a framework for understanding and potentially modulating microglial responses in ischemic stroke.
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