Fitting Splines to Axonal Arbors Quantifies Relationship Between Branch Order and Geometry

Frontiers in Neuroinformatics

Jacopo Teneggi²  Thomas L. Athey²  Daniel J. Tward⁴  Ulrich Mueller⁵  Joshua T. Vogelstein⁷  Michael I. Miller⁷ 

[1] Center for Imaging Science, Johns Hopkins University, Baltimore, MD, United States;Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, United States;Department of Computational Medicine, University of California, Los Angeles, Los Angeles, CA, United States;Department of Neurology, University of California, Los Angeles, Los Angeles, CA, United States;Department of Neuroscience, Johns Hopkins University, Baltimore, MD, United States;Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, United States;Kavli Neuroscience Discovery Institute, Johns Hopkins University, Baltimore, MD, United States;

关键词: neuron;    morphology;    axon;    curvature;    projection;    mouse;   

DOI  :  10.3389/fninf.2021.704627

来源: DOAJ

【 摘 要 】

Neuromorphology is crucial to identifying neuronal subtypes and understanding learning. It is also implicated in neurological disease. However, standard morphological analysis focuses on macroscopic features such as branching frequency and connectivity between regions, and often neglects the internal geometry of neurons. In this work, we treat neuron trace points as a sampling of differentiable curves and fit them with a set of branching B-splines. We designed our representation with the Frenet-Serret formulas from differential geometry in mind. The Frenet-Serret formulas completely characterize smooth curves, and involve two parameters, curvature and torsion. Our representation makes it possible to compute these parameters from neuron traces in closed form. These parameters are defined continuously along the curve, in contrast to other parameters like tortuosity which depend on start and end points. We applied our method to a dataset of cortical projection neurons traced in two mouse brains, and found that the parameters are distributed differently between primary, collateral, and terminal axon branches, thus quantifying geometric differences between different components of an axonal arbor. The results agreed in both brains, further validating our representation. The code used in this work can be readily applied to neuron traces in SWC format and is available in our open-source Python package brainlit: http://brainlit.neurodata.io/.

【 授权许可】

Unknown