Homology analysis detects topological changes of Iba1 localization accompanied by microglial activation

The state of microglial activation provides important information about the central nervous system. However, a reliable index of microglial activation in histological samples has yet to be established. Here, we show that microglial activation induces topological changes of Iba1 localization that can be detected by analysis based on homology theory. Analysis of homology was applied to images of Iba1-stained tissue sections, and the 0-dimentional Betti number (b0: the number of solid components) and the 1-dimentional Betti number (b1: the number of windows surrounded by solid components) were obtained. We defined b1/b0 as the Homology Value (HV), and investigated its validity as an index of microglial activation using cerebral ischemia model mice. Microglial activation was accompanied by changes to Iba1 localization and morphology of microglial processes. In single microglial cells, the change of Iba1 localization increased b1. Conversely, thickening or retraction of microglial processes decreased b0. Consequently, microglial activation increased the HV. The HV of a tissue area increased with proximity to the ischemic core and showed a high degree of concordance with the number of microglia expressing activation makers. Furthermore, the HV of human metastatic brain tumor tissue also increased with proximity to the tumor. These results suggest that our index, based on homology theory, can be used to correctly evaluate microglial activation in various tissue images.