Generative probabilistic models of neuron morphology

Abstract

Thanks to automation in ultrathin sectioning and confocal and electron microscopy, it is now possible to image large populations of neurons at single-cell resolution. This imaging capability promises to create a new field of neural circuit microanatomy. Three goals of such a field would be to trace multi-cell neural networks, to classify neurons into morphological cell types, and to compare patterns and statistics of connectivity in large networks to meaningful null models. However, those goals raise significant computational challenges. In particular, since neural morphology spans six orders of magnitude in length (roughly 1 nm-1 mm), a spatial hierarchy of representations is needed to capture micron-scale morphological features in nanometer resolution images. For this thesis, I have built and characterized a system that learns such a representation as a Multivariate Hidden Markov Model over skeletonized neurons. I have developed and implemented a maximum likelihood method for learning an HMM over a directed, unrooted tree structure of arbitrary degree. In addition, I have developed and implemented a set of object-oriented data structures to support this HMM, and to produce a directed tree given a division of the leaf nodes into inputs and outputs. Furthermore, I have developed a set of features on which to train the HMM based only on information in the skeletonized neuron, and I have tested this system on a dataset consisting of confocal microscope images of 14 fluorescence-labeled mouse retinal ganglion cells. Additionally, I have developed a system to simulate neurons of varying difficulty for the HMM, and analyzed its performance on those neurons. Finally, I have explored whether the HMMs this system learns could successfully detect errors in simulated and, eventually, neural datasets.