Spatially regularized multifractal analysis for fMRI data

Scale-free dynamics is nowadays a massively used paradigm to model infraslow macroscopic brain activity. Multifractal analysis is becoming the standard tool to characterize scale-free dynamics. It is commonly used on various modalities of neuroimaging data to evaluate whether arrhythmic fluctuations in ongoing or evoked brain activity are related to pathologies (Alzheimer, epilepsy) or task performance. The success of multifractal analysis in neurosciences remains however so far contrasted: While it lead to relevant findings on M/EEG data, less clear impact was shown when applied to fMRI data. This is mostly due to their poor time resolution and very short duration as well as to the fact that analysis remains performed voxelwise. To take advantage of the large amount of voxels recorded jointly in fMRI, the present contribution proposes the use of a recently introduced Bayesian formalism for multifractal analysis, that regularizes the estimation of the multifractality parameter of a given voxel using information from neighbor voxels. The benefits of this regularized multifractal analysis are illustrated by comparison against classical multifractal analysis on fMRI data collected on one subject, at rest and during a working memory task: Though not yet statistically significant, increased multifractality is observed in task-negative and task-positive networks, respectively.