A cortical surface-based geodesic distance package for Python

The human cerebral cortex, whether tracing it through phylogeny or ontogeny, emerges through expansion and progressive differentiation into larger and more diverse areas. While current methodologies address this analytically by characterizing local cortical expansion in the form of surface area, several lines of research have proposed that the cortex in fact expands along trajectories from primordial anchor areas and furthermore, that the distance along the cortical surface is informative regarding cortical differentiation . We sought to investigate the geometric relationships that arise in the cortex based on expansion from such origin points. Towards this aim, we developed a Python package for measuring the geodesic distance along the cortical surface that restricts shortest paths from passing through nodes of non-cortical areas such as the non-cortical portions of the surface mesh described as the medial wall.<br>The calculation of geodesic distance along a mesh surface is based in the cumulative distance of the shortest path between two points. The first challenge that arises is the sensitivity of the calculation to the resolution of the mesh: the coarser the mesh, the longer the shortest path may be, as the distance becomes progressively less direct. This problem has been previously addressed and subsequently implemented in the Python package gdist, which calculates the exact geodesic distance along a mesh by subdividing the shortest path until a straight line along the cortex is approximated. <br>The second challenge, for which there was no prefabricated solution, was ensuring that the shortest path only traverses territory within the cortex proper, avoiding shortcuts through non-cortical areas included in the surface mesh most prominently, the non-cortical portions along the medial wall. Were the shortest paths between two nodes to traverse non-cortical regions, the distance between nodes would be artificially decreased, which would have artifactual impact on the interpretation of results. This concern would be especially relevant to the zones analysis described below, where the boundaries between regions would be altered. It was therefore necessary to remove mesh nodes prior to calculating the exact geodesic distance, which requires reconstructing the mesh and assigning the respective new node indices for any seed regions-of-interest.<br>Finally, to facilitate applications to neuroscience research questions, we enabled the loading and visualization of data from commonly used formats such as FreeSurfer and the Human Connectome Project (HCP). A Nipype pipeline for group-level batch processing has also been made available . The pipeline is wrapped in a command-line interface and allows for straightforward distance calculations of entire FreeSurfer-preprocessed datasets. Group-level data are stored as CSV files for each requested mesh resolution, source label and hemisphere, facilitating further statistical analyses.<br>The resultant package, SurfDist, achieves the aforementioned goals of faciliating the calculation of exact geodesic distance on the cortical surface. We present here the distance measures from the central and calcarine sulci labels on the FreeSurfer native surfaces. The distance measure provides a means to parcellate the cortex using the surface geometry. Towards that aim, we also implement a zones analysis, which constructs a Voronoi diagram, establishing partitions based on the greater proximity to a set of label nodes.<br>The SurfDist package is designed to enable investigation of intrinisic geometric properties of the cerebral cortex based on geodesic distance measures. Towards the aim of enabling applications specific to neuroimaging-based research question, we have designed the package to facilitate analysis and visualization of geodesic distance metrics using standard cortical surface meshes.

人类大脑皮层，无论从系统发育（phylogeny）还是个体发育（ontogeny）的视角追溯，均通过扩张与逐步分化，形成体积更大、类型更多样的脑区。当前主流分析方法多通过表征皮层局部扩张的表面积开展研究，但已有多条研究线索表明，皮层实则沿着源自原始锚定脑区的轨迹进行扩张，且皮层表面的距离信息可反映皮层分化程度。本研究旨在探究基于此类起源点的皮层扩张所产生的几何关系。为此，我们开发了一款Python工具包，用于测量皮层表面的测地线距离（geodesic distance），该工具包会限制最短路径不穿过非皮层区域的节点——例如被定义为内侧壁（medial wall）的表面网格中非皮层部分。
网格表面的测地线距离计算基于两点间最短路径的累积距离。首个挑战在于计算结果对网格分辨率的敏感性：网格越粗糙，最短路径的计算结果越长，因为距离近似的偏差会逐渐增大。此前已有研究针对该问题提出解决方案，并在Python工具包gdist中得以实现，该工具包通过细分最短路径直至近似得到皮层表面的直线距离，从而计算出网格表面的精确测地线距离。
第二个挑战尚无现成解决方案：需确保最短路径仅穿行于皮层本身的区域，避免绕行表面网格中包含的非皮层区域——最典型的即为内侧壁的非皮层部分。若两个节点间的最短路径穿过非皮层区域，节点间的距离会被人为低估，进而对结果解读产生人为误差，这一问题在下文所述的分区分析中尤为突出，会导致脑区边界出现偏差。因此，在计算精确测地线距离前，需移除网格中的非皮层节点，这要求我们重构网格，并为任意种子感兴趣区域分配对应的新节点索引。
最后，为便于应用于神经科学研究问题，我们支持加载并可视化FreeSurfer和人类连接组项目（Human Connectome Project, HCP）等常用格式的数据。此外，还提供了用于组水平批量处理的Nipype流水线（pipeline），该流水线封装了命令行界面，可直接对经过FreeSurfer预处理的完整数据集进行距离计算。组水平数据会按照每种请求的网格分辨率、源标签和大脑半球存储为CSV文件，便于后续开展统计分析。
最终得到的工具包SurfDist实现了前述目标，即实现在皮层表面上精确测地线距离的计算。我们在此展示了基于FreeSurfer原生表面的中央沟和距状沟标签的距离测量结果。该距离测量方法提供了一种利用表面几何特征对皮层进行分区的途径。为此，我们还实现了分区分析功能：该功能会构建沃罗诺伊图（Voronoi diagram），基于与一组标签节点的邻近性划分皮层区域。
SurfDist工具包旨在支持基于测地线距离测量的大脑皮层内在几何特性研究。为适配基于神经影像的特定研究问题应用，我们将该工具包设计为可通过标准皮层表面网格便捷分析和可视化测地线距离指标。