We have continued to employ the concepts of Mandelbrot's fractal geometry to the quantitative studies of central nervous system neurons, and other cell types grown in tissue culture or from whole animals. We do this by employing image processing techniques to measure the fractal dimension (FD), which is a measure of the complexity of the structure under investigation. In particular, the FD relates to the degree of branching (e.g., of dendrites), the ruggedness of borders, and the degree of space- filling of the object of interest. We have undertaken, in separate studies, how the fractal dimension changes during the differentiation and growth of glial and neuronal cells in tissue culture, We have found that optic nerve-derived oligodendrocytes differentiate faster and to a greater extent than do nerve-derived astrocytes. A subsequent study has found that nerve- derived glia also differentiate faster and to a greater extent than do brain-derived glia. Interestingly, the rates of differentiation as measured by the FD can be described by a single time constant. The work on cultured spinal neurons shows that they differentiate in a similarly simple fashion. We have proposed that the FD is a useful, quantitative measure of morphological differentiation. We have begun studies of the development of the internal and surface structures of cultured rat hippocampal neurons with fluorescence and confocal microscopy in order to localize the position of GABA during growth and differentiation.
