Riemannian diffusion kernel-smoothed continuous structural connectivity on cortical surface

Atlas-free continuous structural connectivity has garnered increasing attention due to the limitations of atlas-based approaches, including the arbitrary selection of brain atlases and potential information loss. Typically, continuous structural connectivity is represented by a probability density function, with kernel density estimation as a common estimation method. However, constructing an appropriate kernel function on the cortical surface poses significant challenges. Current methods often inflate the cortical surface into a sphere and apply the spherical heat kernel, introducing distortions to density estimation. In this study, we propose a novel approach using the Riemannian diffusion kernel derived from the Laplace-Beltrami operator on the cortical surface to smooth streamline endpoints into a continuous density. Our method inherently accounts for the complex geometry of the cortical surface and exhibits computational efficiency, even with dense tractography datasets. Additionally, we investigate the number of streamlines or fiber tracts required to achieve a reliable continuous representation of structural connectivity. Through simulations and analyses of data from the Adolescent Brain Cognitive Development (ABCD) Study, we demonstrate the potential of the Riemannian diffusion kernel in enhancing the estimation and analysis of continuous structural connectivity.