On the pros and cons of using temporal derivatives to assess brain functional connectivity

TL;DR

This paper critically evaluates the 'Multiplication of Temporal Derivatives' metric for brain connectivity analysis, finding it offers no clear advantages over traditional correlation methods and has lower sensitivity and signal-to-noise ratio.

Contribution

The study provides a formal comparison of MTD with Pearson correlation, highlighting its limitations and lack of significant benefits in brain connectivity analysis.

Findings

MTD is similar to Pearson correlation of derivatives with minor differences.

MTD has lower sensitivity to low frequency drifts and autocorrelations.

MTD exhibits lower signal-to-noise ratio compared to traditional methods.

Abstract

The study of correlations between brain regions is an important chapter of the analysis of large-scale brain spatiotemporal dynamics. In particular, novel methods suited to extract dynamic changes in mutual correlations are needed. Here we scrutinize a recently reported metric dubbed "Multiplication of Temporal Derivatives" (MTD) which is based on the temporal derivative of each time series. The formal comparison of the MTD formula with the Pearson correlation of the derivatives reveals only minor differences, which we find negligible in practice. A comparison with the sliding window Pearson correlation of the raw time series in several stationary and non-stationary set-ups, including a realistic stationary network detection, reveals lower sensitivity of derivatives to low frequency drifts and to autocorrelations but also lower signal-to-noise ratio. It does not indicate any evident mathematical advantages of the proposed metric over commonly used correlation methods.