Mark Fiecas

Genetic topography of brain morphology

Significance How diverse functional cortical regions develop is an important neuroscience question. Animal experiments show that regional differentiation is controlled by genes that express in a graded and regionalized pattern; however, such investigation in humans is scarce. Using noninvasive imaging techniques to acquire brain structure data of genetically related subjects (i.e., twins), we estimated the spatial pattern of genetic influences on cortical structure. We developed a genetic parcellation of cortical thickness to delineate the boundaries of cortical divisions that are—within each division—maximally under control of shared genetic influences. We also found differences in genetic influences on cortical surface area and thickness along two orthogonal axes. The concept of gradations is crucial for understanding the organization of the human brain. Animal data show that cortical development is initially patterned by genetic gradients largely along three orthogonal axes. We previously reported differences in genetic influences on cortical surface area along an anterior-posterior axis using neuroimaging data of adult human twins. Here, we demonstrate differences in genetic influences on cortical thickness along a dorsal-ventral axis in the same cohort. The phenomenon of orthogonal gradations in cortical organization evident in different structural and functional properties may originate from genetic gradients. Another emerging theme of cortical patterning is that patterns of genetic influences recapitulate the spatial topography of the cortex within hemispheres. The genetic patterning of both cortical thickness and surface area corresponds to cortical functional specializations. Intriguingly, in contrast to broad similarities in genetic patterning, two sets of analyses distinguish cortical thickness and surface area genetically. First, genetic contributions to cortical thickness and surface area are largely distinct; there is very little genetic correlation (i.e., shared genetic influences) between them. Second, organizing principles among genetically defined regions differ between thickness and surface area. Examining the structure of the genetic similarity matrix among clusters revealed that, whereas surface area clusters showed great genetic proximity with clusters from the same lobe, thickness clusters appear to have close genetic relatedness with clusters that have similar maturational timing. The discrepancies are in line with evidence that the two traits follow different mechanisms in neurodevelopment. Our findings highlight the complexity of genetic influences on cortical morphology and provide a glimpse into emerging principles of genetic organization of the cortex.

A comparison of heritability maps of cortical surface area and thickness and the influence of adjustment for whole brain measures: A magnetic resonance imaging twin study

Understanding the genetic and environmental contributions to measures of brain structure such as surface area and cortical thickness is important for a better understanding of the nature of brain-behavior relationships and changes due to development or disease. Continuous spatial maps of genetic influences on these structural features can contribute to our understanding of regional patterns of heritability, since it remains to be seen whether genetic contributions to brain structure respect the boundaries of any traditional parcellation approaches. Using data from magnetic resonance imaging scans collected on a large sample of monozygotic and dizygotic twins in the Vietnam Era Twin Study of Aging, we created maps of the heritability of areal expansion (a vertex-based area measure) and cortical thickness and examined the degree to which these maps were affected by adjustment for total surface area and mean cortical thickness. We also compared the approach of estimating regional heritability based on the average heritability of vertices within the region to the more traditional region-of-interest (ROI)-based approach. The results suggested high heritability across the cortex for areal expansion and, to a slightly lesser degree, for cortical thickness. There was a great deal of genetic overlap between global and regional measures for surface area, so maps of region-specific genetic influences on surface area revealed more modest heritabilities. There was greater inter-regional variability in heritabilities when calculated using the traditional ROI-based approach compared to summarizing vertex-by-vertex heritabilities within regions. Discrepancies between the approaches were greatest in small regions and tended to be larger for surface area than for cortical thickness measures. Implications regarding brain phenotypes for future genetic association studies are discussed.

The Genetic Association Between Neocortical Volume and General Cognitive Ability Is Driven by Global Surface Area Rather Than Thickness

Total gray matter volume is associated with general cognitive ability (GCA), an association mediated by genetic factors. It is expectable that total neocortical volume should be similarly associated with GCA. Neocortical volume is the product of thickness and surface area, but global thickness and surface area are unrelated phenotypically and genetically in humans. The nature of the genetic association between GCA and either of these 2 cortical dimensions has not been examined. Humans possess greater cognitive capacity than other species, and surface area increases appear to be the primary driver of the increased size of the human cortex. Thus, we expected neocortical surface area to be more strongly associated with cognition than thickness. Using multivariate genetic analysis in 515 middle-aged twins, we demonstrated that both the phenotypic and genetic associations between neocortical volume and GCA are driven primarily by surface area rather than thickness. Results were generally similar for each of 4 specific cognitive abilities that comprised the GCA measure. Our results suggest that emphasis on neocortical surface area, rather than thickness, could be more fruitful for elucidating neocortical-GCA associations and identifying specific genes underlying those associations.

Quantifying temporal correlations: A test–retest evaluation of functional connectivity in resting-state fMRI

There have been many interpretations of functional connectivity and proposed measures of temporal correlations between BOLD signals across different brain areas. These interpretations yield from many studies on functional connectivity using resting-state fMRI data that have emerged in recent years. However, not all of these studies used the same metrics for quantifying the temporal correlations between brain regions. In this paper, we use a public-domain test-retest resting-state fMRI data set to perform a systematic investigation of the stability of the metrics that are often used in resting-state functional connectivity (FC) studies. The fMRI data set was collected across three different sessions. The second session took place approximately eleven months after the first session, and the third session was an hour after the second session. The FC metrics composed of cross-correlation, partial cross-correlation, cross-coherence, and parameters based on an autoregressive model. We discussed the strengths and weaknesses of each metric. We performed ROI-level and full-brain seed-based voxelwise test-retest analyses using each FC metric to assess its stability. For both ROI-level and voxel-level analyses, we found that cross-correlation yielded more stable measurements than the other metrics. We discussed the consequences of this result on the utility of the FC metrics. We observed that for negatively correlated ROIs, their partial cross-correlation is shrunk towards zero, thus affecting the stability of their FC. For the present data set, we found greater stability in FC between the second and third sessions (one hour between sessions) compared to the first and second sessions (approximately 11months between sessions). Finally, we report that some of the metrics showed a positive association between strength and stability. In summary, the results presented in this paper suggest important implications when choosing metrics for quantifying and assessing various types of functional connectivity for resting-state fMRI studies.

The generalized shrinkage estimator for the analysis of functional connectivity of brain signals

We develop a new statistical method for estimating functional connectivity between neurophysiological signals represented by a multivariate time series. We use partial coherence as the measure of functional connectivity. Partial coherence identifies the frequency bands that drive the direct linear association between any pair of channels. To estimate partial coherence, one would first need an estimate of the spectral density matrix of the multivariate time series. Parametric estimators of the spectral density matrix provide good frequency resolution but could be sensitive when the parametric model is misspecified. Smoothing-based nonparametric estimators are robust to model misspecification and are consistent but may have poor frequency resolution. In this work, we develop the generalized shrinkage estimator, which is a weighted average of a parametric estimator and a nonparametric estimator. The optimal weights are frequency-specific and derived under the quadratic risk criterion so that the estimator, either the parametric estimator or the nonparametric estimator, that performs better at a particular frequency receives heavier weight. We validate the proposed estimator in a simulation study and apply it on electroencephalogram recordings from a visual-motor experiment.

Functional connectivity: shrinkage estimation and randomization test.

We develop new statistical methods for estimating functional connectivity between components of a multivariate time series and for testing differences in functional connectivity across experimental conditions. Here, we characterize functional connectivity by partial coherence, which identifies the frequency band (or bands) that drives the direct linear association between any pair of components of a multivariate time series after removing the linear effects of the other components. Partial coherence can be efficiently estimated using the inverse of the spectral density matrix. However, when the number of components is large and the components of the multivariate time series are highly correlated, the spectral density matrix estimate may be numerically unstable and consequently gives partial coherence estimates that are highly variable. To address the problem of numerical instability, we propose a shrinkage-based estimator which is a weighted average of a smoothed periodogram estimator and a scaled identity matrix with frequency-specific weight computed objectively so that the resulting shrinkage estimator minimizes the mean-squared error criterion. Compared to typical smoothing-based estimators, the shrinkage estimator is more computationally stable and gives a lower mean squared error. In addition, we develop a randomization method for testing differences in functional connectivity networks between experimental conditions. Finally, we report results from numerical experiments and analyze an EEG data set recorded during a visually-guided hand movement task.

Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment

ABSTRACT We develop a new time series model to investigate the dynamic interactions between the nucleus accumbens and the hippocampus during an associative learning experiment. Preliminary analyses indicated that the spectral properties of the local field potentials at these two regions changed over the trials of the experiment. While many models already take into account nonstationarity within a single trial, the evolution of the dynamics across trials is often ignored. Our proposed model, the slowly evolving locally stationary process (SEv-LSP), is designed to capture nonstationarity both within a trial and across trials. We rigorously define the evolving evolutionary spectral density matrix, which we estimate using a two-stage procedure. In the first stage, we compute the within-trial time-localized periodogram matrix. In the second stage, we develop a data-driven approach that combines information from trial-specific local periodogram matrices. Through simulation studies, we show the utility of our proposed method for analyzing time series data with different evolutionary structures. Finally, we use the SEv-LSP model to demonstrate the evolving dynamics between the hippocampus and the nucleus accumbens during an associative learning experiment. Supplementary materials for this article are available online.

Hierarchical vector auto-regressive models and their applications to multi-subject effective connectivity

Vector auto-regressive (VAR) models typically form the basis for constructing directed graphical models for investigating connectivity in a brain network with brain regions of interest (ROIs) as nodes. There are limitations in the standard VAR models. The number of parameters in the VAR model increases quadratically with the number of ROIs and linearly with the order of the model and thus due to the large number of parameters, the model could pose serious estimation problems. Moreover, when applied to imaging data, the standard VAR model does not account for variability in the connectivity structure across all subjects. In this paper, we develop a novel generalization of the VAR model that overcomes these limitations. To deal with the high dimensionality of the parameter space, we propose a Bayesian hierarchical framework for the VAR model that will account for both temporal correlation within a subject and between subject variation. Our approach uses prior distributions that give rise to estimates that correspond to penalized least squares criterion with the elastic net penalty. We apply the proposed model to investigate differences in effective connectivity during a hand grasp experiment between healthy controls and patients with residual motor deficit following a stroke.

Cognitive reserve moderates the association between hippocampal volume and episodic memory in middle age

Cognitive reserve is hypothesized to help people withstand greater brain pathology without manifesting clinical symptoms, and may be regarded as a preventive factor of dementia. It is unclear whether the effect of cognitive reserve is evident only among the older adults or after conversion to dementia, or if it can also be seen earlier in life before the prominent effects of cognitive aging become apparent. While finding a main effect of cognitive reserve on cognitive outcome may be consistent with the reserve hypothesis, in our view, it is unnecessary to invoke the idea of reserve if only a main effect is present. Rather, it is the interaction between a measure of reserve and a brain measure on cognitive outcome that is key for confirming that the effects of brain pathology affect people differently according to their cognitive reserve. We studied whether general cognitive ability at an average age of 20 years, as a direct measure of cognitive reserve, moderates the association between hippocampal volume and episodic memory performance in 494 middle-aged men ages 51 to 60. Whereas there was no statistically significant direct relationship between hippocampal volume and episodic memory performance in middle age, we found a statistically significant interaction such that there was a positive association between hippocampal volume and episodic memory only among people with lower general cognitive ability at age 20, i.e., lower levels of cognitive reserve. Our results provide support for the hypothesis that cognitive reserve moderates the relationship between brain structure and cognition in middle age, well before the onset of dementia.

Data-driven shrinkage of the spectral density matrix of a high-dimensional time series

Time series data obtained from neurophysiological signals is often high-dimensional and the length of the time series is often short relative to the number of dimensions. Thus, it is difficult or sometimes impossible to compute statistics that are based on the spectral density matrix because estimates of these matrices are often numerically unstable. In this work, we discuss the importance of regularization for spectral analysis of high-dimensional time series and propose shrinkage estimation for estimating high-dimensional spectral density matrices. We use and develop the multivariate Time-frequency Toggle (TFT) bootstrap procedure for multivariate time series to estimate the shrinkage parameters, and show that the multivariate TFT bootstrap is theoretically valid. We show via simulations and an fMRI data set that failure to regularize the estimates of the spectral density matrix can yield unstable statistics, and that this can be alleviated by shrinkage estimation.