This is the final paper in a Comments and Controversies series dedicated to "The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution". We argue that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations. These models have to be endowed with priors on unknown parameters and afford checks for model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger Causal Modeling and other approaches. We establish links between past and current statistical causal modeling, in terms of Bayesian dependency graphs and Wiener-Akaike-Granger-Schweder influence measures. We show that some of the challenges faced in this field have promising solutions and speculate on future developments.

There is much current interest in identifying the anatomical and functional circuits that are the basis of the brain's computations, with hope that functional neuroimaging techniques will allow the in vivo study of these neural processes through the statistical analysis of the time-series they produce. Ideally, the use of techniques such as multivariate autoregressive (MAR) modelling should allow the identification of effective connectivity by combining graphical modelling methods with the concept of Granger causality. Unfortunately, current time-series methods perform well only for the case that the length of the time-series Nt is much larger than p , the number of brain sites studied, which is exactly the reverse of the situation in neuroimaging for which relatively short time-series are measured over thousands of voxels. Methods are introduced for dealing with this situation by using sparse MAR models. These can be estimated in a two-stage process involving (i) penalized regression and (ii) pruning of unlikely connections by means of the local false discovery rate developed by Efron. Extensive simulations were performed with idealized cortical networks having small world topologies and stable dynamics. These show that the detection efficiency of connections of the proposed procedure is quite high. Application of the method to real data was illustrated by the identification of neural circuitry related to emotional processing as measured by BOLD.

Which reference is appropriate for the scalp ERP and EEG studies? This unsettled problem still inspires unceasing debate. The ideal reference should be the one with zero or constant potential but unfortunately it is well known that no point on the body fulfills this condition. Consequently, more than ten references are used in the present EEG-ERP studies. This diversity seriously undermines the reproducibility and comparability of results across laboratories. A comprehensive review accompanied by a brief communication with rigorous derivations and notable properties (Hu et al. Brain Topogr, 2019. https://doi.org/10.1007/s10548-019-00706-y) is thus necessary to provide application-oriented principled recommendations. In this paper current popular references are classified into two categories: (1) unipolar references that construct a neutral reference, including both online unipolar references and offline re-references. Examples of unipolar references are the reference electrode standardization technique (REST), average reference (AR), and linked-mastoids/ears reference (LM); (2) non-unipolar references that include the bipolar reference and the Laplacian reference. We show that each reference is derived with a different assumption and serves different aims. We also note from (Hu et al. 2019) that there is a general form for the reference problem, the ‘no memory’ property of the unipolar references, and a unified estimator for the potentials at infinity termed as the regularized REST (rREST) which has more advantageous statistical evidence than AR. A thorough discussion of the advantages and limitations of references is provided with recommendations in the hope to clarify the role of each reference in the ERP and EEG practice.

Brain clocks, which quantify discrepancies between brain age and chronological age, hold promise for understanding brain health and disease. However, the impact of diversity (including geographical, socioeconomic, sociodemographic, sex and neurodegeneration) on the brain-age gap is unknown. We analyzed datasets from 5,306 participants across 15 countries (7 Latin American and Caribbean countries (LAC) and 8 non-LAC countries). Based on higher-order interactions, we developed a brain-age gap deep learning architecture for functional magnetic resonance imaging (2,953) and electroencephalography (2,353). The datasets comprised healthy controls and individuals with mild cognitive impairment, Alzheimer disease and behavioral variant frontotemporal dementia. LAC models evidenced older brain ages (functional magnetic resonance imaging: mean directional error = 5.60, root mean square error (r.m.s.e.) = 11.91; electroencephalography: mean directional error = 5.34, r.m.s.e. = 9.82) associated with frontoposterior networks compared with non-LAC models. Structural socioeconomic inequality, pollution and health disparities were influential predictors of increased brain-age gaps, especially in LAC (R² = 0.37, F² = 0.59, r.m.s.e. = 6.9). An ascending brain-age gap from healthy controls to mild cognitive impairment to Alzheimer disease was found. In LAC, we observed larger brain-age gaps in females in control and Alzheimer disease groups compared with the respective males. The results were not explained by variations in signal quality, demographics or acquisition methods. These findings provide a quantitative framework capturing the diversity of accelerated brain aging.