Is Pearson's correlation coefficient enough for functional connectivity in fMRI?

Abstract

Functional connectivity (FC) is commonly defined as the temporal coincidence of neurophysiological events, often quantified by the statistical dependency among signals from different brain regions and measured by Pearson's correlation coefficient in fMRI. However, Pearson's r captures only linear dependencies, potentially overlooking nonlinear interactions. Recently, Multiscale Graph Correlation (MGC) was introduced to measure statistical dependencies of both linear and nonlinear relationships across multiple scales, offering an "optimal scale" at which such dependencies can be inferred. In this study, we systematically compared FC measurements by Pearson's r and MGC across datasets, evaluating their reliability, sensitivity to data quantity, and ability to capture distinct experimental conditions (deeper anesthesia in macaques) and brain-behavior association. Results showed highly similar spatial connectivity patterns and strong alignment between Pearson's r and MGC for within-network FC, where optimal scales were frequently global. However, local optimal scales emerged between networks, suggesting the presence of nonlinear dependencies of FC. Reliability was higher for Pearson's r overall, but both measurements improved as the quantity of data increased. Notably, MGC revealed variability in the optimal scales under altered brain states in deeper anesthesia, highlighting its potential for detecting local-scale dependencies across states. Despite these advantages, MGC required greater computational resources and did not outperform Pearson's r in detecting brain-behavior associations. Consequently, Pearson's r remains a sufficient and reliable measure for many standard applications, whereas MGC can offer more nuanced insights in scenarios where nonlinear dynamics are of particular interest. Researchers should, therefore, balance the potential gains from MGC against its added complexity and computational cost when selecting methods to quantify FC.

Keywords: Multiscale Graph Correlation; Pearson’s correlation coefficient; fMRI; functional connectivity; nonlinear dependencies.

Fig. 1.

Example demonstrating homotopic connectivity measured by MGC, depicting linear and nonlinear time series along with their corresponding local correlation maps.

Fig. 2.

FC measured by Pearson’s r, MGC statistics, and its optimal scale. (A) Distributions of individual FC values as measured by Pearson’s r, MGC statistic, and optimal scale: a density plot of Pearson’s r and MGC statistic with contour lines and histograms on the edges (left), scatter plot colored by optimal scale (middle), and a density plot of Pearson’s r and MGC optimal scale (right). (B) Group-level FC matrix measured by Pearson’s r, MGC statistics, and its optimal scale. (C) Individual-level similarity between Pearson’s r, MGC statistics, and optimal scale: Pearson’s r exhibited a strong similarity with MGC statistics and optimal scale, particularly for the FCs estimated within networks.

Fig. 3.

Comparison of FC measured by Pearson’s r, MGC statistics, and optimal scale across different data quantities per subject: 200 time points (1 scan), 400 time points (averaging FC of 2 scans, each consisting of 200 time points), and 800 time points (averaging FC of 4 scans, each consisting of 200 time points). (A) Pearson’s r, MGC statistics, and optimal scale of FC across data quantities. Higher Pearson’s r, MGC statistics, and optimal scales were observed within networks compared to those between networks. (B) Similarity between Pearson’s r, MGC statistics, and optimal scale: Higher similarities were consistently observed within networks, increasing with data quantities.

Fig. 4.

Test-retest reliability for the HCP dataset in Study 2, using 400 time points and 800 time points on Glasser360 (Glasser et al., 2016) parcellations.

Fig. 5.

Homotopic connectivity measured by Pearson’s r, MGC statistics, and optimal scale across different data quantities (200, 400, and 800 time points per scan for each individual). (A) Group-averaged homotopic connectivity maps plotted on the left hemisphere and (B) Network-level connectivity values. The optimal scale of MGC in various acquisition durations showed a shift from local to global optimal scales as the duration increased.

Fig. 6.

Macaque homotopic connectivity measured by Pearson’s r, MGC statistics, and the optimal scale of MGC across awake and anesthetized states at isoflurane concentrations of 0.75%, 1.00%, 1.50%, and 2.00%. The optimal scale of MGC in the macaque showed a shift from global to local as the isoflurane concentration increased.