Morphology and fractal-based classifications of neurons and microglia

Microglia and neurons live physically intertwined, intimately related structurally and functionally in a dynamic relationship in which microglia change continuously over a much shorter timescale than neurons. Although microglia may unwind and depart from the neurons they attend under certain circumstances, in general, together both contribute to the fractal topology of the brain that defines its computational capabilities. Both neuronal and microglial morphologies are well described using fractal analysis complementary to more traditional measures. For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has contributed substantially to classifying functional categories, where in general, the more pathological the biological status, the lower the fractal dimension for individual cells, with some exceptions including hyper-ramification. Here we briefly review the intimate relationships between neurons and microglia, and survey work applying fractal analysis to their respective morphologies, summarizing key results and highlighting methodological issues.