Penalized functional regression analysis of white-matter tract profiles in multiple sclerosis

Diffusion tensor imaging (DTI) enables noninvasive parcellation of cerebral white matter into its component fiber bundles or tracts. These tracts often subserve specific functions, and damage to the tracts can therefore result in characteristic forms of disability. Attempts to quantify the extent of tract-specific damage have been limited in part by substantial spatial variation of imaging properties from one end of a tract to the other, variation that can be compounded by the effects of disease. Here, we develop a "penalized functional regression" procedure to analyze spatially normalized tract profiles, which powerfully characterize such spatial variation. The central idea is to identify and emphasize portions of a tract that are more relevant to a clinical outcome score, such as case status or degree of disability. The procedure also yields a "tract abnormality score" for each tract and MRI index studied. Importantly, the weighting function used in this procedure is constrained to be smooth, and the statistical associations are estimated using generalized linear models. We test the method on data from a cross-sectional MRI and functional study of 115 multiple-sclerosis cases and 42 healthy volunteers, considering a range of quantitative MRI indices, white-matter tracts, and clinical outcome scores, and using training and testing sets to validate the results. We show that attention to spatial variation yields up to 15% (mean across all tracts and MRI indices: 6.4%) improvement in the ability to discriminate multiple sclerosis cases from healthy volunteers. Our results confirm that comprehensive analysis of white-matter tract-specific imaging data improves with knowledge and characterization of the normal spatial variation.