Longitudinal high-dimensional principal components analysis with application to diffusion tensor imaging of multiple sclerosis

Abstract

We develop a flexible framework for modeling high-dimensional imaging data observed longitudinally. The approach decomposes the observed variability of repeatedly measured high-dimensional observations into three additive components: a subject-specific imaging random intercept that quantifies the cross-sectional variability, a subject-specific imaging slope that quantifies the dynamic irreversible deformation over multiple realizations, and a subject-visit specific imaging deviation that quantifies exchangeable effects between visits. The proposed method is very fast, scalable to studies including ultra-high dimensional data, and can easily be adapted to and executed on modest computing infrastructures. The method is applied to the longitudinal analysis of diffusion tensor imaging (DTI) data of the corpus callosum of multiple sclerosis (MS) subjects. The study includes 176 subjects observed at 466 visits. For each subject and visit the study contains a registered DTI scan of the corpus callosum at roughly 30,000 voxels.

Parameterization of White Matter Manifold-Like Structures Using Principal Surfaces

“…In fact, it is possible that registering the 2D representation is preferable to whole brain registration a priori in certain applications. Note also that MFPCA (Di et al 2009) and LFPCA (Zipunnikov et al 2011; Zipunnikov et al 2014), methods have been shown to isolate registration error as a part of the model (Lee et al 2015), thus raising the intriguing possibility of DTI processing streams that dramatically decrease the need and importance of whole brain template-based registration.…”

Neuroimaging of corpus callosum in central nervous system demyelinating disorders

“…[11,[36][37][38] There has been also studies about the relationship between CC involvement's patterns and prognosis of MS. [7][8][9][10][11] Most of them showed that the damage to white matter network especially CC contributes to the reduced processing speed in task specific abilities. [39] A significant increase in CC's MD was observed in relapsing remitting MS, even in benign form. [40][41][42][43][44] Moreover, patterns of tract FA reduction for cognitive test, including localization of lesions in the body and splenium of the CC, only partially overlapped with T2 lesions, supporting that NAWM abnormality contributes to cognitive dysfunction.…”

“…On the other hand, in normal appearing brain tissue, CC's FA and axial diffusivity demonstrated further decline over time, while no significant change in radial diffusivity was observed. [47] Hence, the decline in axial diffusivity may suggest involvement of axonal loss and degeneration in normal appearing brain tissue at the early stage before active lesions develop, possibly attributing to poorer prognosis and progressive disability often observed in MS patients despite treatment. Many recent studies agree on the fact that longitudinal changes are most rapid in CC area of the brain in MS disorder in different types of imaging.…”

Functional Nonlinear Mixed Effects Models for Longitudinal Image Data

“…It should be noted that the estimation procedures used in [6, 17, 21] are not directly applicable here due to the nonlinear association map in (1). …”

“…Many parametric mixed effects models including both fixed and random effects are the predominant approach for characterizing both the temporal correlations and random individual variations. Although there is a great interest in the analysis of functional data with various levels of hierarchical structures [11, 18, 7], only a handful of them [6, 17, 21] focused on the development of linear mixed models for longitudinal image data. Recently, there was some attempt on the development of hierarchical geodesic models on diffeomorphism for longitudinal shape analysis [15].…”