The formation of multiple sclerosis (MS) lesions is a complex process involving inflammation, tissue damage, and tissue repair - all of which are visible on structural magnetic resonance imaging (MRI) and potentially modifiable by pharmacological therapy. In this paper, we introduce two statistical models for relating voxel-level, longitudinal, multi-sequence structural MRI intensities within MS lesions to clinical information and therapeutic interventions: (1) a principal component analysis (PCA) and regression model and (2) function-on-scalar regression models. To do so, we first characterize the post-lesion incidence repair process on longitudinal, multi-sequence structural MRI from 34 MS patients as voxel-level intensity profiles. For the PCA regression model, we perform PCA on the intensity profiles to develop a voxel-level biomarker for identifying slow and persistent, long-term intensity changes within lesion tissue voxels. The proposed biomarker's ability to identify such effects is validated by two experienced clinicians (a neuroradiologist and a neurologist). On a scale of 1 to 4, with 4 being the highest quality, the neuroradiologist gave the score on the first PC a median quality rating of 4 (95% CI: [4,4]), and the neurologist gave the score a median rating of 3 (95% CI: [3,3]). We then relate the biomarker to the clinical information in a mixed model framework. Treatment with disease-modifying therapies (p < 0.01), steroids (p < 0.01), and being closer to the boundary of abnormal signal intensity (p < 0.01) are all associated with return of a voxel to an intensity value closer to that of normal-appearing tissue. The function-on-scalar regression model allows for assessment of the post-incidence time points at which the covariates are associated with the profiles. In the function-on-scalar regression, both age and distance to the boundary were found to have a statistically significant association with the lesion intensities at some time point. The two models presented in this article show promise for understanding the mechanisms of tissue damage in MS and for evaluating the impact of treatments for the disease in clinical trials.
Keywords: Biomarker; CI, confidence interval; Expert rater trial; FLAIR, fluid-attenuated inversion recovery; Function-on-scalar regression; Longitudinal lesion behavior; Longitudinal study; MRI, magnetic resonance imaging; MS, multiple sclerosis; Multi-sequence imaging; Multiple sclerosis; NAWM, normal-appearing white matter; NINDS, National Institute of Neurological Disease and Stroke; PC, principal component; PCA, principal component analysis; PD, proton density-weighted; Principal component analysis and regression; RRMS, relapsing remitting MS; SPMS, secondary progressive MS; Structural magnetic resonance imaging; T, Tesla; T1, T1-weighted; T2, T2-weighted; sd, standard deviation.