Characterizing Whole Brain Temporal Variation of Functional Connectivity via Zero and First Order Derivatives of Sliding Window Correlations

Abstract

Brain functional connectivity has been shown to change over time during resting state fMRI experiments. Close examination of temporal changes have revealed a small set of whole-brain connectivity patterns called dynamic states. Dynamic functional network connectivity (dFNC) studies have demonstrated that it is possible to replicate the dynamic states across several resting state experiments. However, estimation of states and their temporal dynamicity still suffers from noisy and imperfect estimations. In regular dFNC implementations, states are estimated by comparing connectivity patterns through the data without considering time, in other words only zero order changes are examined. In this work we propose a method that includes first order variations of dFNC in the searching scheme of dynamic connectivity patterns. Our approach, referred to as temporal variation of functional network connectivity (tvFNC), estimates the derivative of dFNC, and then searches for reoccurring patterns of concurrent dFNC states and their derivatives. The tvFNC method is first validated using a simulated dataset and then applied to a resting-state fMRI sample including healthy controls (HC) and schizophrenia (SZ) patients and compared to the standard dFNC approach. Our dynamic approach reveals extra patterns in the connectivity derivatives complementing the already reported state patterns. State derivatives consist of additional information about increment and decrement of connectivity among brain networks not observed by the original dFNC method. The tvFNC shows more sensitivity than regular dFNC by uncovering additional FNC differences between the HC and SZ groups in each state. In summary, the tvFNC method provides a new and enhanced approach to examine time-varying functional connectivity.

An imbalance between functional segregation and integration in patients with pontine stroke: A dynamic functional network connectivity study

“…In addition to these observations; the results of our study may provide a new clue to the functional impairment in patients with PS; in terms of whole-brain functional network connectivity. The same finding that patients had a longer duration in the sparsely connected state also has been reported in multiple brain diseases, such as depressive disorders( Zhi et al, 2018 , Wang et al, 2020 ), schizophrenia( Yu et al, 2015 , Rabany et al, 2019 , Espinoza et al, 2019 ), Huntington's disease( Espinoza et al, 2019 , Espinoza et al, 2019 ); and neurofibromatosis( Mennigen et al, 2019 , Mennigen et al, 2019 ). Given the above research, such abnormalities in dFNC may be the underlying mechanism of similar dysfunctions in different brain disorders.…”

The chronnectome as a model for Charcot’s ‘dynamic lesion’ in functional movement disorders

“…First, the functional chronnectome was investigated not only by focusing on component functional connectivity at certain points in time, but also from a first-order-derivative-perspective, which encompasses the changes of connectivity between two consecutive windows (‘speed’ of connectivity change; ( Calhoun et al, 2014 , Espinoza et al, 2019 ). It has been shown that including these first order derivatives facilitates the estimation of the optimal number of dynamic brain states, and ultimately results in a higher sensitivity of finding neuropsychiatric disease-related patterns ( Espinoza et al, 2019 ). Second, by including derivatives we demonstrated that dynamic brain states seem to adhere to specific transition sequences, called attractors, with dynamic connectivity increasing and decreasing in orbiting patterns.…”

“…Successive windows were shifted in steps of 1 TR each, which means that windows are overlapping. Subsequently, average sliding window correlations (ASWC; window size = 25 TR) and the first order derivatives were calculated for every subject, resulting in 175 windows per subject, with each window containing 1378 × 2 = 2756 values ( Espinoza et al, 2019 , Vergara et al, 2019a ). We opted for the ASWC approach, as this requires smaller window lengths, and thus a more accurate estimation of dFC, by reducing spurious fluctuations, as compared to the standard sliding window correlation approach ( Vergara et al, 2019a ).…”

“…We opted for the ASWC approach, as this requires smaller window lengths, and thus a more accurate estimation of dFC, by reducing spurious fluctuations, as compared to the standard sliding window correlation approach ( Vergara et al, 2019a ). The first-order derivatives encompass the connectivity changes between two contiguous windows (‘speed’ of connectivity change; Calhoun et al, 2014 , Espinoza et al, 2019 ). We included these first order derivatives in our analysis as it has been shown that this facilitates the estimation of the optimal number of dynamic brain states, and thus results in a higher sensitivity of finding neuropsychiatric disease-related patterns ( Espinoza et al, 2019 ).…”

Functional outcome is tied to dynamic brain states after mild to moderate traumatic brain injury

“…Subsequently, k‐means clustering was performed (maximum iterations of 4,000, correlation distance method, 33 replicates) using both the ASWC as well as their first derivatives of all subjects (derivatives were normalized for every subject to match the variance of the correlations). Including the first derivatives has been shown to result in higher sensitivity for capturing group‐differences in dynamic FNC (Espinoza et al, ). To estimate the optimal number of clusters (k), the following cluster validity indexes were computed for a range of k (1–10) using GIFT: Elbow method, Bayesian information criterion (BIC), Dunn's index, Gap statistic, Akaike information criterion (AIC), and Silhouette method (Supporting Information S1).…”