Detection and skeletonization of single neurons and tracer injections using topological methods

Abstract

Neuroscientific data analysis has traditionally relied on linear algebra and stochastic process theory. However, the tree-like shapes of neurons cannot be described easily as points in a vector space (the subtraction of two neuronal shapes is not a meaningful operation), and methods from computational topology are better suited to their analysis. Here we introduce methods from Discrete Morse (DM) Theory to extract the tree-skeletons of individual neurons from volumetric brain image data, and to summarize collections of neurons labelled by tracer injections. Since individual neurons are topologically trees, it is sensible to summarize the collection of neurons using a consensus tree-shape that provides a richer information summary than the traditional regional 'connectivity matrix' approach. The conceptually elegant DM approach lacks handtuned parameters and captures global properties of the data as opposed to previous approaches which are inherently local. For individual skeletonization of sparsely labelled neurons we obtain substantial performance gains over state-of-the-art non-topological methods (over 10% improvements in precision and faster proofreading). The consensus-tree summary of tracer injections incorporates the regional connectivity matrix information, but in addition captures the collective collateral branching patterns of the set of neurons connected to the injection site, and provides a bridge between single-neuron morphology and tracer-injection data. SummaryNeuroscientific data analysis has traditionally involved methods for statistical signal and image processing, drawing on linear algebra and stochastic process theory. However, digitized neuroanatomical datasets containing labelled neurons, either individually or in groups labelled by tracer injections, do not fit into this classical framework. The tree-like shapes of neurons cannot be adequately described as points in a vector space (e.g. the subtraction of two neuronal shapes is not a meaningful operation). There is therefore a need for new approaches, which has become more urgent given the growth in whole-brain datasets with sparsely labelled neurons or tracer injections.Methods from computational topology and geometry are naturally suited to the analysis of neuronal shapes. In this paper we introduce methods from Discrete Morse Theory to extract tree-skeletons of individual neurons from volumetric brain image data, and to summarize collections of neurons labelled by anterograde tracer injections. Since individual neurons are topologically trees, it is sensible to summarize the collection of neurons using a consensus tree-shape. This consensus tree provides a richer information summary than the regional or voxel-based "connectivity matrix" approach that has previously been used in the literature.The algorithmic procedure for single neuron skeletonization includes an initial neurite-detection step to extract a density field from the raw volumetric image data, followed by Dis-crete Morse theoretic skeleton extraction from the density field us...

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