轴索树状结构的样条拟合量化了分支顺序与几何结构的关系
Fitting Splines to Axonal Arbors Quantifies Relationship between Branch Order and Geometry
摘要：
神经形态学对于识别神经元亚型和理解学习至关重要。它也与神经系统疾病有关。然而，标准的形态学分析侧重于宏观特征，如分支频率和区域之间的连接，往往忽略了神经元的内部几何结构。在这项工作中，我们把神经元迹点作为一个采样的可微曲线和适合他们与一组分支B样条。我们设计了我们的表示与Frenet-Serret公式从微分几何铭记。Frenet-Serret公式完全刻画了光滑曲线的特征，并且包含两个参数：曲率和挠率。我们的表示使得有可能从封闭形式的神经元迹线计算这些参数。这些参数是沿着曲线连续定义的，与依赖于起点和终点的其他参数（如弯曲度）相反。我们将我们的方法应用于在两个小鼠大脑中追踪的皮质投射神经元的数据集，并发现参数在初级，侧支和末端轴突分支之间分布不同，从而量化轴突乔木的不同组成部分之间的几何差异。结果在两个大脑中一致，进一步验证了我们的陈述。这项工作中使用的代码可以很容易地应用于SWC格式的神经元轨迹，并且可以在我们的开源Python包brainlit中获得：http://brainlit.neurodata.io/。
英文摘要：
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/.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
