B0527
Title: Elastic shape analysis of neuronal trees
Authors: Anuj Srivastava - Florida State University (United States) [presenting]
Abstract: There is a great interest neuronal morphology, which seeks tools for comparing neuronal shapes, modeling variability within and across neuron populations, and for clustering/testing/classifying neurons. The challenges include: (1) tremendous variability in size and shape of the main branch (axon), and (2) different numbers, sizes, and shapes of the side branches. That is, the neurons differ in both geometry and topology, and that makes it difficult to model their shapes. An important sub-problem is the registration of points across neurons. An elastic framework for shape analysis of neuronal tree is presented. It is an extension of elastic functional data analysis, where one compares individual curves while being invariant to certain shape-preserving transformations. We define a shape space of these tree representations and impose an elastic Riemannian metric on it to compare different trees. The resulting geodesic paths between neurons show the main branch of one tree deforming into the main branch of the other, while optimally deforming/sliding/creating/destroying the side branches of one into the side branches of other. Using this metric, we define sample mean and variances, and perform principal component analysis of shape data. Furthermore, we cluster and classify neurons into wild types and mutations using this approach. We present some preliminary results using axonal trees taken from the Neuromorpho database.
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