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. Recently, Permutation Entropy for Graph signals (PE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</inf> ) has been proposed to extend PE to data residing on irregular domains. However, PE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</inf> 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 PE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</inf> , can be discerned using our graph-based patterns. These are then validated in 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 in individual brain regions change as the disease progresses, demonstrating potential as a method of analyzing graph-signals at a granular scale.