  Structural magnetic resonance imaging (MRI) can be used to detect lesions in
the brains of multiple sclerosis (MS) patients. The formation of these lesions
is a complex process involving inflammation, tissue damage, and tissue repair,
all of which are visible on MRI. Here we characterize the lesion formation
process on longitudinal, multi-sequence structural MRI from 34 MS patients and
relate the longitudinal changes we observe within lesions to therapeutic
interventions. In this article, we first outline a pipeline to extract voxel
level, multi-sequence longitudinal profiles from four MRI sequences within
lesion tissue. We then propose two models to relate clinical covariates to the
longitudinal profiles. The first model is a principal component analysis (PCA)
regression model, which collapses the information from all four profiles into a
scalar value. We find that the score on the first PC identifies areas of slow,
long-term intensity changes within the lesion at a voxel level, as validated by
two experienced clinicians, a neuroradiologist and a neurologist. On a quality
scale of 1 to 4 (4 being the highest) the neuroradiologist gave the score on
the first PC a median rating of 4 (95% CI: [4,4]), and the neurologist gave it
a median rating of 3 (95% CI: [3,3]). In the PCA regression model, we find that
treatment with disease modifying therapies (p-value < 0.01), steroids (p-value
< 0.01), and being closer to the boundary of abnormal signal intensity (p-value
< 0.01) are associated with a return of a voxel to intensity values closer to
that of normal-appearing tissue. The second model is a function-on-scalar
regression, which allows for assessment of the individual 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 profiles.
