Optimizing the measurement of sample entropy in resting-state fMRI data
Authors: Roediger Donovan J. , Butts Jessica , Falke Chloe , Fiecas Mark B. , Klimes-Dougan Bonnie , Mueller Bryon A. , Cullen Kathryn R. 
Published: February 2024

Introduction

The complexity of brain signals may hold clues to understand brain-based disorders. Sample entropy, an index that captures the predictability of a signal, is a promising tool to measure signal complexity. However, measurement of sample entropy from fMRI signals has its challenges, and numerous questions regarding preprocessing and parameter selection require research to advance the potential impact of this method. For one example, entropy may be highly sensitive to the effects of motion, yet standard approaches to addressing motion (e.g., scrubbing) may be unsuitable for entropy measurement. For another, the parameters used to calculate entropy need to be defined by the properties of data being analyzed, an issue that has frequently been ignored in fMRI research. The current work sought to rigorously address these issues and to create methods that could be used to advance this field.

Methods

We developed and tested a novel windowing approach to select and concatenate (ignoring connecting volumes) low-motion windows in fMRI data to reduce the impact of motion on sample entropy estimates. We created utilities (implementing autoregressive models and a grid search function) to facilitate selection of the matching length m parameter and the error tolerance r parameter. We developed an approach to apply these methods at every grayordinate of the brain, creating a whole-brain dense entropy map. These methods and tools have been integrated into a publicly available R package (“powseR”). We demonstrate these methods using data from the ABCD study. After applying the windowing procedure to allow sample entropy calculation on the lowest-motion windows from runs 1 and 2 (combined) and those from runs 3 and 4 (combined), we identified the optimal m and r parameters for these data. To confirm the impact of the windowing procedure, we compared entropy values and their relationship with motion when entropy was calculated using the full set of data vs. those calculated using the windowing procedure. We then assessed reproducibility of sample entropy calculations using the windowed procedure by calculating the intraclass correlation between the earlier and later entropy measurements at every grayordinate.

Results

When applying these optimized methods to the ABCD data (from the subset of individuals who had enough windows of continuous “usable” volumes), we found that the novel windowing procedure successfully mitigated the large inverse correlation between entropy values and head motion seen when using a standard approach. Furthermore, using the windowed approach, entropy values calculated early in the scan (runs 1 and 2) are largely reproducible when measured later in the scan (runs 3 and 4), although there is some regional variability in reproducibility.

Discussion

We developed an optimized approach to measuring sample entropy that addresses concerns about motion and that can be applied across datasets through user-identified adaptations that allow the method to be tailored to the dataset at hand. We offer preliminary results regarding reproducibility. We also include recommendations for fMRI data acquisition to optimize sample entropy measurement and considerations for the field.