Abstract
Digital brain atlases define a hierarchy of brain regions and their locations in three-dimensional Cartesian space, providing 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 description of the complex geometries of layered brain regions such as the neocortex. As a better alternative, we proposelaminar coordinate systemsthat consider the curvature and laminar structure of the region of interest. These coordinate systems consist of a principal axis aligned to the local 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 flatmaps is that they allow a seamless mapping between 2D and 3D spaces through structured dimensionality reduction where information is aggregated along depth. We introduce a general method to define laminar coordinate systems and flatmaps based on digital brain atlases and according to user specifications. The method is complemented by a set of metrics to characterize the quality of the resulting flatmaps. We applied our method to two rodent atlases. First, 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. Second, to the Allen Mouse Brain Atlas Common Coordinate Framework version 3, enhancing it with two flatmaps of the whole isocortex. We used one of these flatmaps to define new annotations of 33 individual barrels and barrel columns that are nonoverlapping and follow the curvature of the cortex, therefore, producing the most accurate atlas of mouse barrel cortex to date. 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.