Graph-based permutation patterns for the analysis of task-related fMRI signals on DTI networks in mild cognitive impairment

Permutation Entropy (PE) is a powerful nonlinear analysis technique for univariate time series. Very recently, Permutation Entropy for Graph signals (PEG) has been proposed to extend PE to data residing on irregular domains. However, PEG is limited as it provides a single value to characterise a whole graph signal. Here, we introduce a novel approach to evaluate graph signals at the vertex level: graph-based permutation patterns. Synthetic datasets show the efficacy of our method. We reveal that dynamics in graph signals, undetectable with PEG, can be discerned using our graph-based permutation patterns. These are then validated in the analysis of DTI and fMRI data acquired during a working memory task in mild cognitive impairment, where we explore functional brain signals on structural white matter networks. Our findings suggest that graph-based permutation patterns change in individual brain regions as the disease progresses. Thus, graph-based permutation patterns offer promise by enabling
the granular scale analysis of graph signals.