Lu Wang

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.

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.

This paper studies the problem of classifying longitudinal structural brain networks to identify meaningful substructures and their time‐varying effects. The problem is motivated by a subpopulation of healthy older adults who can maintain excellent cognitive functions across time, while others usually have cognitive decline in aging. It is of substantial scientific interest to study neurological mechanisms behind this successful aging phenomena; however, existing statistical tools for longitudinal networks are very limited. We propose a structured classification method that could identify a set of small outcome‐relevant subgraphs and estimate the age effect of each signal subgraph from the longitudinal network predictors, as well as an efficient algorithm for model estimation. Application of this method to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data identifies a small set of brain regions whose connectivity strengths are predictive of successful cognitive aging, which has more appealing interpretation and better predictive performance compared with unstructured classification methods.

Structural brain networks constructed from diffusion MRI are important biomarkers for understanding human brain structure and its relation to cognitive functioning. There is increasing interest in learning differences in structural brain networks between groups of subjects in neuroimaging studies, leading to a variable selection problem in network classification. Traditional methods often use independent edgewise tests or unstructured generalized linear model (GLM) with regularization on vectorized networks to select edges distinguishing the groups, which ignore the network structure and make the results hard to interpret. In this paper, we develop a symmetric bilinear logistic regression (SBLR) with elastic-net penalty to identify a set of small clique subgraphs in network classification. Clique subgraphs, consisting of all the interconnections among a subset of brain regions, have appealing neurological interpretations as they may correspond to some anatomical circuits in the brain related to the outcome. We apply this method to study differences in the structural connectome between adolescents with high and low crystallized cognitive ability, using the crystallized cognition composite score, picture vocabulary and oral reading recognition tests from NIH Toolbox. A few clique subgraphs containing several small sets of brain regions are identified between different levels of functioning, indicating their importance in crystallized cognition.

There is an increasing interest in learning a set of small outcome-relevant subgraphs in network-predictor regression. The extracted signal subgraphs can greatly improve the interpretation of the association between the network predictor and the response. In brain connectomics, the brain network for an individual corresponds to a set of interconnections among brain regions and there is a strong interest in linking the brain connectome to human cognitive traits. Modern neuroimaging technology allows a very fine segmentation of the brain, producing very large structural brain networks. Therefore, accurate and efficient methods for identifying a set of small predictive subgraphs become crucial, leading to discovery of key interconnected brain regions related to the trait and important insights on the mechanism of variation in human cognitive traits. We propose a symmetric bilinear model with $L_1$ penalty to search for small clique subgraphs that contain useful information about the response. A coordinate descent algorithm is developed to estimate the model where we derive analytical solutions for a sequence of conditional convex optimizations. Application of this method on human connectome and language comprehension data shows interesting discovery of relevant interconnections among several small sets of brain regions and better predictive performance than competitors.