Enhancement of brain atlases with laminar coordinate systems: Flatmaps and barrel column annotations

Digital brain atlases define a hierarchy of brain regions and their locations in three-dimensional Cartesian space. They provide a standard coordinate system in which diverse datasets can be integrated for visualization and analysis. Although this coordinate system has well-defined anatomical axes, it does not provide the best context to work with the complex geometries of layered brain regions such as the neocortex. To address that, we introduce laminar coordinate systems that consider the curvature and the laminar structure of the region of interest. These new coordinate systems consist of a principal axis, locally aligned to the vertical direction and measuring depth, and two other axes that describe a flatmap, a two-dimensional representation of the horizontal extents of layers. The main property of the flatmap is that it allows seamless mapping of information back and forth between 2D and 3D spaces, in a way consistent with the principal axis. It involves a structured dimensionality reduction where information is aggregated along depth. We propose a method to enhance brain atlases with laminar coordinate systems and flatmaps based on user specifications and define a set of metrics to characterize the quality of flatmaps. We applied our method to an atlas of rat somatosensory cortex based on Paxinos and Watson’s rat brain atlas, enhancing it with a laminar coordinate system adapted to the geometry of this region. Further, we applied our method to enhance the Allen Mouse Brain Atlas Common Coordinate Framework version 3 with a flatmap of the whole isocortex. We used this flatmap to produce new annotations of 33 individual barrels and barrel columns in the barrel cortex. Thanks to the properties of the flatmap, the resulting annotations are non-overlapping and follow the curvature of the cortex. Additionally, we introduced several applications highlighting the utility of laminar coordinate systems for data visualization and data-driven modeling. We provide a free software implementation of our methods for the benefit of the community. ### Competing Interest Statement The authors have declared no competing interest.