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.

翻译：神经炎症紧随大脑中动脉缺血性卒中发作而出现。在此过程中，小胶质细胞在半暗带被激活并募集。小胶质细胞可被激活为两种不同表型：M1型（可加重脑损伤）或M2型（有助于长期恢复）。本研究对小鼠大脑中动脉闭塞（MCAO）诱发缺血性卒中后半暗带小胶质细胞计数的实验数据进行了汇总，并将现有数据集整理为适用于时间序列分析的统一集合。进一步地，我们构建了MCAO所致缺血性卒中过程中半暗带小胶质细胞的数学模型。通过全局敏感性分析和基于马尔可夫链蒙特卡洛（MCMC）的参数估计，我们分析了模型参数对半暗带中M1与M2细胞数量的影响，并将可辨识参数拟合至整理后的实验数据集。利用MCMC参数估计结果，我们确定了M1与M2小胶质细胞数量随时间变化的置信区间及正向预测。结果显示，与M1和M2激活相关的参数对两类细胞数量具有显著影响。模拟进一步表明，观测数据中的潜在异常值可被剔除，而预测提示炎症反应将持续存在。