Preserving Derivative Information while Transforming Neuronal CurvesThe international neuroscience community is building the first comprehensive
atlases of brain cell types to understand how the brain functions from a higher
resolution, and more integrated perspective than ever before. In order to build
these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal
cortical neurons etc.) are traced in individual brain samples by placing points
along dendrites and axons. Then, the traces are mapped to common coordinate
systems by transforming the positions of their points, which neglects how the
transformation bends the line segments in between. In this work, we apply the
theory of jets to describe how to preserve derivatives of neuron traces up to
any order. We provide a framework to compute possible error introduced by
standard mapping methods, which involves the Jacobian of the mapping
transformation. We show how our first order method improves mapping accuracy in
both simulated and real neuron traces, though zeroth order mapping is generally
adequate in our real data setting. Our method is freely available in our
open-source Python package brainlit.
arxiv.org