Revisiting correlation-based functional connectivity and its relationship with structural connectivity

Abstract

Patterns of brain structural connectivity (SC) and functional connectivity (FC) are known to be related. In SC-FC comparisons, FC has classically been evaluated from correlations between functional time series, and more recently from partial correlations or their unnormalized version encoded in the precision matrix. The latter FC metrics yields more meaningful comparisons to SC because they capture ‘direct’ statistical dependencies, i.e., discarding the effects of mediators, but their use has been limited because of estimation issues. With the rise of high-quality and large neuroimaging datasets, we revisit relevance of different FC metrics in the context of SC-FC comparisons. Using data from 100 unrelated HCP subjects, we first explore the amount of functional data required to reliably estimate various FC metrics. We find that precision-based FC yields a better match to SC than correlation-based FC when using 5 minutes of functional data or more. Finally, using a linear model linking SC and FC, we show that the SC-FC match can be used to further interrogate various aspects of brain structure and function such as the timescales of functional dynamics in different resting-state networks or the intensity of anatomical self-connections.

Whenmakes you unique: temporality of the human brain fingerprint

“…This work opens also the avenue of relating functional brainprints with underlying structural architecture. Recent studies have shown that building FC matrices from (very) long RS fMRI sessions leads to very good proxies for SC 30 . Similarly, it has been shown that longer fMRI sessions (up to a plateau 10 ) improve identification.…”

Regional structural-functional connectome coupling is heritable and associated with age, sex and cognitive scores in adults

“…Here, we calculated FC using a regularized precision approach, which aims to capture only the “direct” connections between brain regions. We chose to use precision-based FC as it was recently shown to result in FC matrices that had stronger correlations with SC than more conventional Pearson correlation-based FC 32 . For completeness and comparison to previous work 24, 25 , Pearson correlation-based FC results are provided in the Supplemental Information.…”

“…Statistical, communication, biophysical and machine learning models have been applied to better align FC and SC 3, 7, 8, 38 . Recent work has also found the strength of global SC-FC correlation depends on how FC is calculated 32 . In particular, this work showed FC calculated using partial correlation (precision), which aims to isolate direct and remove the effect of indirect functional connections, had stronger correlations with SC than standard FC calculated using full (Pearson) correlation.…”

“…To compute precision-based FC, we first computed the unregularized inverse of the correlation matrix for each individual, and averaged them over the population to obtain the population-level precision matrix. We then calculated the individuals’ precision matrices using Tikhonov regularization, which adds a full-rank regularization term (scaled identity) to the correlation matrix before inversion 32 : where I is the identity matrix and λ is the regularization parameter. The regularization parameter λ ∈ [0, 1] was chosen via grid search to be the value that minimized the sum of the Frobenius norms between the regularized subject precision matrices and the group-averaged unregularized precision matrix, resulting in λ opt = 0.3.…”

“…To compute precision-based FC, we first computed the unregularized inverse of the correlation matrix for each individual, and averaged them over the population to obtain the population-level precision matrix. We then calculated the individuals' precision matrices using Tikhonov regularization, which adds a full-rank regularization term (scaled identity) to the correlation matrix before inversion 32 :…”