One Rule to Grow Them All: A General Theory of Neuronal Branching and Its Practical Application
(A) Example of an additional application of the algorithm: automated model-based tree reconstruction from image stacks. Maximum intensity projection of tiled image stacks containing a sample sub-tree of a fluorescently labelled neuronal tree. Blue overlay in top panel corresponds to the output of a non-linear thresholding. The resulting binary matrix is then reduced to single points in space (green dots) via a skeletonization procedure. After a distance graph is obtained which describes the probability of a connection between these points due to the image data the points are used as carrier points for the growth algorithm to obtain the corresponding tree using the distance graph as an additional cost factor. After unlikely branches are removed the underlying tree structure is captured (green tree structure in the lower panel, see text for more detail; note absence of scale bar since this a sample image stack). (B) Maximum intensity projections of tiled 2-photon fluorescent image stacks acquired at 820 nm from primary visual cortex of a p13 JAX transgenic mouse (strain #007677, ) expressing GFP in parvalbumin interneurons, of which one is present. Three further layer 5 pyramidal neurons are also imaged; all cells were filled with a fluorescent dye Alexa 594 via whole cell patch-clamp recording. Data courtesy of Kate Buchanan and Jesper Sjöström. (C) Corresponding reconstructions (with the interneuron in green) grown in a competitive manner on the image stacks after manual post-processing.