Multifractal analysis of white matter structural changes on 3D magnetic resonance imaging between normal aging and early Alzheimer's disease

Applications of multifractal analysis to white matter structure changes on magnetic resonance imaging (MRI) have recently received increasing attentions. Although some progresses have been made, there is no evident study on applying multifractal analysis to evaluate the white matter structural changes on MRI for Alzheimer's disease (AD) research. In this paper, to explore multifractal analysis of white matter structural changes on 3D MRI volumes between normal aging and early AD, we not only extend the traditional box-counting multifractal analysis (BCMA) into the 3D case, but also propose a modified integer ratio based BCMA (IRBCMA) algorithm to compensate for the rigid division rule in BCMA. We verify multifractal characteristics in 3D white matter MRI volumes. In addition to the previously well studied multifractal feature, Δα, we also demonstrated Δf as an alternative and effective multifractal feature to distinguish NC from AD subjects. Both Δα and Δf are found to have strong positive correlation with the clinical MMSE scores with statistical significance. Moreover, the proposed IRBCMA can be an alternative and more accurate algorithm for 3D volume analysis. Our findings highlight the potential usefulness of multifractal analysis, which may contribute to clarify some aspects of the etiology of AD through detection of structural changes in white matter.