Local Spectral Analysis of the Cerebral Cortex: New Gyrification Indices

Curvature analysis of perisylvian epilepsy

PURPOSE

We assess whether alterations in the convolutional anatomy of the deep perisylvian area (DPSA) might indicate focal epileptogenicity.

MATERIALS AND METHODS

The DPSA of each hemisphere was segmented on MRI and a 3D gray-white matter interface (GWMI) geometrical model was constructed. Comparative visual and quantitative assessment of the convolutional anatomy of both the left and right DPSA models was performed. Both the density of thorn-like contours (peak percentage) and coarse interface curvatures was computed using Gaussian curvature and shape index, respectively. The proposed method was applied to a total of 14 subjects; 7 patients with an epileptogenic DPSA and 7 non-epileptic subjects.

RESULTS

A high peak percentage correlated well with the epileptogenic DPSA. It distinguished between patients and non-epileptic subjects (P = 0.029) and identified laterality of the epileptic focus in all but one case. A diminished regional curvature also identified epileptogenicity (P = 0.016) and, moreover, its laterality (P = 0.001).

CONCLUSION

An increased peak percentage from a global view of the GWMI of the DPSA provides some indication of a propensity toward a focal or regional DPSA epileptogenicity. A diminished convolutional anatomy (i.e., smoothing effect) appears also to coincide with the epileptogenic site in the DPSA and to distinguish laterality.

Population-wise labeling of sulcal graphs using multi-graph matching

Population-wise matching of the cortical folds is necessary to compute statistics, a required step for e.g. identifying biomarkers of neurological or psychiatric disorders. The difficulty arises from the massive inter-individual variations in the morphology and spatial organization of the folds. The task is challenging both methodologically and conceptually. In the widely used registration-based techniques, these variations are considered as noise and the matching of folds is only implicit. Alternative approaches are based on the extraction and explicit identification of the cortical folds. In particular, representing cortical folding patterns as graphs of sulcal basins-termed sulcal graphs-enables to formalize the task as a graph-matching problem. In this paper, we propose to address the problem of sulcal graph matching directly at the population level using multi-graph matching techniques. First, we motivate the relevance of the multi-graph matching framework in this context. We then present a procedure for generating populations of artificial sulcal graphs, which allows us to benchmark several state-of-the-art multi-graph matching methods. Our results on both artificial and real data demonstrate the effectiveness of multi-graph matching techniques in obtaining a population-wise consistent labeling of cortical folds at the sulcal basin level.

Ensemble learning for the detection of pli-de-passages in the superior temporal sulcus

The surface of the cerebral cortex is very convoluted, with a large number of folds, the cortical sulci. These folds are extremely variable from one individual to another, and this large variability is a problem for many applications in neuroscience and brain imaging. In particular, sulcal geometry (shape) and sulcal topology (branches, number of pieces) are very variable. "Plis de passages" (PPs) or "annectant gyri" can explain part of the topological variability, namely why sulci have a variable number of pieces across subjects. The concept of PPs was first introduced by Gratiolet (1854) to describe transverse gyri that interconnect both sides of a sulcus, that are frequently buried in the depth of sulci, and that are sometimes apparent on the cortical surface, hence seemingly interrupting the course of sulci and separating them in several pieces. Nevertheless, the difficulty of identifying PPs and the lack of systematic methods to automatically detect them has limited their use. However, based on a recent characterization of PPs in the superior temporal sulcus, we present here a method to automatically detect PPs in the superior temporal sulcus. Local morphology within the sulcus is characterized using cortical surface profiling, and the three-dimensional PP recognition problem is performed as a two-dimensional image classification problem with class-imbalance. This is solved by using an ensemble support vector machine model (EnsSVM) with a rebalancing strategy. Cross validation and quantitative experimental results on an external dataset show the effectiveness and robustness of our approach.

Diffusion-informed spatial smoothing of fMRI data in white matter using spectral graph filters

Brain activation mapping using functional magnetic resonance imaging (fMRI) has been extensively studied in brain gray matter (GM), whereas in large disregarded for probing white matter (WM). This unbalanced treatment has been in part due to controversies in relation to the nature of the blood oxygenation level-dependent (BOLD) contrast in WM and its detectability. However, an accumulating body of studies has provided solid evidence of the functional significance of the BOLD signal in WM and has revealed that it exhibits anisotropic spatio-temporal correlations and structure-specific fluctuations concomitant with those of the cortical BOLD signal. In this work, we present an anisotropic spatial filtering scheme for smoothing fMRI data in WM that accounts for known spatial constraints on the BOLD signal in WM. In particular, the spatial correlation structure of the BOLD signal in WM is highly anisotropic and closely linked to local axonal structure in terms of shape and orientation, suggesting that isotropic Gaussian filters conventionally used for smoothing fMRI data are inadequate for denoising the BOLD signal in WM. The fundamental element in the proposed method is a graph-based description of WM that encodes the underlying anisotropy observed across WM, derived from diffusion-weighted MRI data. Based on this representation, and leveraging graph signal processing principles, we design subject-specific spatial filters that adapt to a subject's unique WM structure at each position in the WM that they are applied at. We use the proposed filters to spatially smooth fMRI data in WM, as an alternative to the conventional practice of using isotropic Gaussian filters. We test the proposed filtering approach on two sets of simulated phantoms, showcasing its greater sensitivity and specificity for the detection of slender anisotropic activations, compared to that achieved with isotropic Gaussian filters. We also present WM activation mapping results on the Human Connectome Project's 100-unrelated subject dataset, across seven functional tasks, showing that the proposed method enables the detection of streamline-like activations within axonal bundles.

Imaging evolution of the primate brain: the next frontier?

Evolution, as we currently understand it, strikes a delicate balance between animals' ancestral history and adaptations to their current niche. Similarities between species are generally considered inherited from a common ancestor whereas observed differences are considered as more recent evolution. Hence comparing species can provide insights into the evolutionary history. Comparative neuroimaging has recently emerged as a novel subdiscipline, which uses magnetic resonance imaging (MRI) to identify similarities and differences in brain structure and function across species. Whereas invasive histological and molecular techniques are superior in spatial resolution, they are laborious, post-mortem, and oftentimes limited to specific species. Neuroimaging, by comparison, has the advantages of being applicable across species and allows for fast, whole-brain, repeatable, and multi-modal measurements of the structure and function in living brains and post-mortem tissue. In this review, we summarise the current state of the art in comparative anatomy and function of the brain and gather together the main scientific questions to be explored in the future of the fascinating new field of brain evolution derived from comparative neuroimaging.

Independent components of human brain morphology

Quantification of brain morphology has become an important cornerstone in understanding brain structure. Measures of cortical morphology such as thickness and surface area are frequently used to compare groups of subjects or characterise longitudinal changes. However, such measures are often treated as independent from each other. A recently described scaling law, derived from a statistical physics model of cortical folding, demonstrates that there is a tight covariance between three commonly used cortical morphology measures: cortical thickness, total surface area, and exposed surface area. We show that assuming the independence of cortical morphology measures can hide features and potentially lead to misinterpretations. Using the scaling law, we account for the covariance between cortical morphology measures and derive novel independent measures of cortical morphology. By applying these new measures, we show that new information can be gained; in our example we show that distinct morphological alterations underlie healthy ageing compared to temporal lobe epilepsy, even on the coarse level of a whole hemisphere. We thus provide a conceptual framework for characterising cortical morphology in a statistically valid and interpretable manner, based on theoretical reasoning about the shape of the cortex.

A gyrification analysis approach based on Laplace Beltrami eigenfunction level sets

An accurate measure of the complexity of patterns of cortical folding or gyrification is necessary for understanding normal brain development and neurodevelopmental disorders. Conventional gyrification indices (GIs) are calculated based on surface curvature (curvature-based GI) or an outer hull surface of the cortex (outer surface-based GI). The latter is dependent on the definition of the outer hull surface and a corresponding function between surfaces. In the present study, we propose the Laplace Beltrami-based gyrification index (LB-GI). This is a new curvature-based local GI computed using the first three Laplace Beltrami eigenfunction level sets. As with outer surface-based GI methods, this method is based on the hypothesis that gyrification stems from a flat surface during development. However, instead of quantifying gyrification with reference to corresponding points on an outer hull surface, LB-GI quantifies the gyrification at each point on the cortical surface with reference to their surrounding gyral points, overcoming several shortcomings of existing methods. The LB-GI was applied to investigate the cortical maturation profile of the human brain from preschool to early adulthood using the PING database. The results revealed more detail in patterns of cortical folding than conventional curvature-based methods, especially on frontal and posterior tips of the brain, such as the frontal pole, lateral occipital, lateral cuneus, and lingual. Negative associations of cortical folding with age were observed at cortical regions, including bilateral lingual, lateral occipital, precentral gyrus, postcentral gyrus, and superior frontal gyrus. The results also indicated positive significant associations between age and the LB-GI of bilateral insula, the medial orbitofrontal, frontal pole and rostral anterior cingulate regions. It is anticipated that the LB-GI will be advantageous in providing further insights in the understanding of brain development and degeneration in large clinical neuroimaging studies.

Surface Regularity via the Estimation of Fractional Brownian Motion Index

The recent definition of fractional Brownian motions on surfaces has raised the statistical issue of estimating the Hurst index characterizing these models. To deal with this open issue, we propose a method which is based on a spectral representation of surfaces built upon their Laplace-Beltrami operator. This method includes a first step where the surface supporting the motion is recovered using a mean curvature flow, and a second one where the Hurst index is estimated by linear regression on the motion spectrum. The method is evaluated on synthetic surfaces. The interest of the method is further illustrated on some fetal cortical surfaces extracted from magnetic resonance images as a means to quantify the brain complexity during the gestational age.

Quantitative Evaluations of Geometrical Distortion Corrections in Cortical Surface-Based Analysis of High-Resolution Functional MRI Data at 7T

Background

Although 7T functional MRI (fMRI) provides better signal‐to‐noise ratio and higher spatial resolution than 3T fMRI, geometric distortions become more challenging because fMRI is more susceptible to distortions than structural MRI. Accurate alignment of 7T fMRI to structural MRI data is critical for precise cortical surface‐based analysis.

Purpose

To quantify the effectiveness of distortion corrections of 7T fMRI data.

Study Type

Prospective.

Subjects

Fifteen healthy individuals aged 19–26 years (mean: 21.9 years).

Field Strength/Sequence

Multiband gradient‐echo echo‐planar imaging sequence at 7T; 3D T₁/T₂‐weighted sequences (magnetization prepared rapid acquisition with gradient echo [MPRAGE] and sampling perfection with application optimized contrast using different flip angle evolution [SPACE]) at 3T.

Assessment

fMRI data at 7T were registered to cortical surfaces reconstructed from 3T structural data acquired in the same subjects. Distortions induced by B₀ inhomogeneity and gradient nonlinearity (B₀ and gradient distortions) were evaluated as cortical fallout (misregistration of noncortical areas) and displacement (misregistration along gray matter).

Statistical Tests

Repeated measures analyses of variance with post‐hoc t‐tests with Bonferroni correction.

Results

The accuracy of fully corrected fMRI images based on the intensity distribution was 89.2%. Without any corrections, 9.7% of vertices in the whole surfaces were fallout and the average displacement was 0.96 mm for the rest of the vertices. B₀ and gradient distortion corrections significantly reduced the fallout (to 2.1% and 8.7%) and displacement (to 0.29 mm and 0.86 mm). These corrections were effective even around regions with moderate distortions (the somatosensory and visual cortices for B₀ distortion, and the anterior frontal, inferior temporal, and posterior occipital cortices for gradient distortion).

Data Conclusion

B₀ distortion correction is crucial for surface‐based analysis of fine‐resolution fMRI at 7T. Gradient distortion correction should be considered when regions of interest include regions distant from the isocenter of scanners.

Evidence Level

1

Technical Efficacy Stage

1

Cortical gyrification and its relationships with molecular measures and cognition in children with the FMR1 premutation

Neurobiological basis for cognitive development and psychiatric conditions remains unexplored in children with the FMR1 premutation (PM). Knock-in mouse models of PM revealed defects in embryonic cortical development that may affect cortical folding. Cortical-folding complexity quantified using local gyrification index (LGI) was examined in 61 children (age 8–12 years, 19/14 male/female PM carriers, 15/13 male/female controls). Whole-brain vertex-wise analysis of LGI was performed for group comparisons and correlations with IQ. Individuals with aberrant gyrification in 68 cortical areas were identified using Z-scores of LGI (hyper: Z ≥ 2.58, hypo: Z ≤ − 2.58). Significant group-by-sex-by-age interaction in LGI was detected in right inferior temporal and fusiform cortices, which correlated negatively with CGG repeat length in the PM carriers. Sixteen PM boys (hyper/hypo: 7/9) and 10 PM girls (hyper/hypo: 2/5, 3 both) displayed aberrant LGI in 1–17 regions/person while 2 control boys (hyper/hypo: 0/2) and 2 control girls (hyper/hypo: 1/1) met the same criteria in only 1 region/person. LGI in the precuneus and cingulate cortices correlated positively with IQ scores in PM and control boys while negatively in PM girls and no significant correlation in control girls. These findings reveal aberrant gyrification, which may underlie cognitive performance in children with the PM.