Analysis of complex data is still a challenge in medical image analysis. Due to the heterogeneous information that can be extracted from magnetic resonance imaging (MRI) it can be difficult to fuse such data in a proper way. One interesting case is given by the analysis of diffusion imaging (DI) data. DI techniques give an important variety of information about the status of microstructure in the brain. This is interesting information to use especially in longitudinal setting where the temporal evolution of the pathology is an important added value. In this paper, we propose a new tensor-based framework capable to detect longitudinal changes appearing in DI data in multiple sclerosis (MS) patients. We focus our attention to the analysis of longitudinal changes occurring along different white matter (WM) fiber-bundles. Our main goal is to detect which subset of fibers (within a bundle) and which sections of these fibers contain "pathological" longitudinal changes. The framework consists of three main parts: i) preprocessing of longitudinal diffusion acquisitions and WM fiber-bundles extraction, ii) data tensorization and rank selection, iii) application of a parallelized constrained tensor factorization algorithm to detect longitudinal "pathological" changes. The proposed method was applied on simulated longitudinal variations and on real MS data. High level of accuracy and precision were obtained in the detection of small longitudinal changes along the WM fiber-bundles.