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

&NA; 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. Graphical abstract Figure. No caption available.

[1]  Maciej A. Nowak,et al.  A random matrix approach to VARMA processes , 2010 .

[2]  William H. Thompson,et al.  A common framework for the problem of deriving estimates of dynamic functional brain connectivity , 2017, NeuroImage.

[3]  Hao He,et al.  Assessing dynamic brain graphs of time-varying connectivity in fMRI data: Application to healthy controls and patients with schizophrenia , 2015, NeuroImage.

[4]  Peter Fransson,et al.  Bursty properties revealed in large-scale brain networks with a point-based method for dynamic functional connectivity , 2016, Scientific Reports.

[5]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[6]  Tom Fawcett,et al.  An introduction to ROC analysis , 2006, Pattern Recognit. Lett..

[7]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[8]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[9]  J. Duyn,et al.  Time-varying functional network information extracted from brief instances of spontaneous brain activity , 2013, Proceedings of the National Academy of Sciences.

[10]  Russell A. Poldrack,et al.  Estimation of dynamic functional connectivity using Multiplication of Temporal Derivatives , 2015, NeuroImage.

[11]  R. Buxton,et al.  Dynamics of blood flow and oxygenation changes during brain activation: The balloon model , 1998, Magnetic resonance in medicine.

[12]  Catie Chang,et al.  Time–frequency dynamics of resting-state brain connectivity measured with fMRI , 2010, NeuroImage.

[13]  G. Livan,et al.  Asymmetric correlation matrices: an analysis of financial data , 2012, 1201.6535.

[14]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[15]  M. Nowak,et al.  Spectra of large time-lagged correlation matrices from random matrix theory , 2016, 1612.06552.

[16]  Dante R Chialvo,et al.  Brain organization into resting state networks emerges at criticality on a model of the human connectome. , 2012, Physical review letters.

[17]  Ravi S. Menon,et al.  Resting‐state networks show dynamic functional connectivity in awake humans and anesthetized macaques , 2013, Human brain mapping.

[18]  Alan J. Laub,et al.  Matrix analysis - for scientists and engineers , 2004 .

[19]  Stephen M. Smith,et al.  Temporally-independent functional modes of spontaneous brain activity , 2012, Proceedings of the National Academy of Sciences.

[20]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[21]  Laura C. Buchanan,et al.  The spatial structure of resting state connectivity stability on the scale of minutes , 2014, Front. Neurosci..

[22]  Mark W. Woolrich,et al.  Network modelling methods for FMRI , 2011, NeuroImage.

[23]  Craig G. Richter,et al.  A simulation and comparison of dynamic functional connectivity methods , 2017, bioRxiv.

[24]  Dimitri Van De Ville,et al.  The dynamic functional connectome: State-of-the-art and perspectives , 2017, NeuroImage.

[25]  Evan M. Gordon,et al.  On the Stability of BOLD fMRI Correlations , 2016, Cerebral cortex.