The 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.

翻译：国际神经科学界正在构建首个全面的大脑细胞类型图谱，旨在从更高分辨率和更整合的视角理解大脑功能。为构建这些图谱，研究人员通过沿树突和轴突放置标记点的方式，在单个脑样本中追踪特定神经元亚群（如血清素能神经元、前额叶皮层神经元等）。随后，通过变换这些标记点的空间位置将追踪结果映射至通用坐标系，但该方法忽略了变换对标记点之间线段弯曲形态的影响。本研究应用流形上的射流理论，描述了如何保留神经元追踪结果任意阶导数的信息。我们提出一个框架，用于计算标准映射方法可能引入的误差，该误差与映射变换的雅可比矩阵相关。实验证明，尽管在真实数据场景中零阶映射通常足够，但我们的一阶方法在模拟和真实神经追踪数据中均能提升映射精度。本方法已开源集成至Python工具包brainlit中免费使用。