Fiber microstructure quantile (FMQ) regression: A novel statistical approach for analyzing white matter bundles from periphery to core

The structural connections of the brain's white matter are critical for brain function. Diffusion MRI tractography enables the in-vivo reconstruction of white matter fiber bundles and the study of their relationship to covariates of interest, such as neurobehavioral or clinical factors. In this work, we introduce Fiber Microstructure Quantile (FMQ) Regression, a new statistical approach for studying the association between white matter fiber bundles and scalar factors (e.g., cognitive scores). Our approach analyzes tissue microstructure measures based on<i>quantile-specific bundle regions</i>. These regions are defined in a data-driven fashion according to the quantiles of fractional anisotropy (FA) of a<i>population fiber bundle</i>, which pools all individuals' bundles. The FA quantiles induce a natural subdivision of a fiber bundle, defining regions from the periphery (low FA) to the core (high FA) of the population fiber bundle. To investigate how fiber bundle tissue microstructure relates to covariates of interest, we employ the statistical technique of quantile regression. Unlike ordinary regression, which only models a conditional mean, quantile regression models the conditional quantiles of a response variable. This enables the proposed analysis, where a quantile regression is fitted for each quantile-specific bundle region. To demonstrate FMQ Regression, we perform an illustrative study in a large healthy young adult tractography dataset derived from the Human Connectome Project-Young Adult (HCP-YA), focusing on particular bundles expected to relate to particular aspects of cognition and motor function. In comparison with traditional regression analyses based on FA Mean and Automated Fiber Quantification (AFQ), we find that FMQ Regression provides a superior model fit with the lowest mean squared error. This demonstrates that FMQ Regression captures the relationship between scalar factors and white matter microstructure more effectively than the compared approaches. Our results suggest that FMQ Regression, which enables FA analysis in data-driven regions defined by FA quantiles, is more powerful for detecting brain-behavior associations than AFQ, which enables FA analysis in regions defined along the trajectory of a bundle. FMQ Regression finds significant brain-behavior associations in multiple bundles, including findings unique to males or to females. In both males and females, language performance is significantly associated with FA in the left arcuate fasciculus, with stronger associations in the bundle's periphery. In males only, memory performance is significantly associated with FA in the left uncinate fasciculus, particularly in intermediate regions of the bundle. In females only, motor performance is significantly associated with FA in the left and right corticospinal tracts, with a slightly lower relationship at the bundle periphery and a slightly higher relationship toward the bundle core. No significant relationships are found between executive function and cingulum bundle FA. Our study demonstrates that FMQ Regression is a powerful statistical approach that can provide insight into associations from bundle periphery to bundle core. Our results also identify several brain-behavior relationships unique to males or to females, highlighting the importance of considering sex differences in future research.