Structural Variability in the Human Brain Reflects Fine-Grained Functional Architecture at the Population Level.

Human brain structure topography is thought to be related in part to functional specialization. However, the extent of such relationships is unclear. Here, using a data-driven, multimodal approach for studying brain structure across the lifespan (N = 484, n = 260 females), we demonstrate that numerous structural networks, covering the entire brain, follow a functionally meaningful architecture. These gray matter networks (GMNs) emerge from the covariation of gray matter volume and cortical area at the population level. We further reveal fine-grained anatomical signatures of functional connectivity. For example, within the cerebellum, a structural separation emerges between lobules that are functionally connected to distinct, mainly sensorimotor, cognitive and limbic regions of the cerebral cortex and subcortex. Structural modes of variation also replicate the fine-grained functional architecture seen in eight well defined visual areas in both task and resting-state fMRI. Furthermore, our study shows a structural distinction corresponding to the established segregation between anterior and posterior default-mode networks (DMNs). These fine-grained GMNs further cluster together to form functionally meaningful larger-scale organization. In particular, we identify a structural architecture bringing together the functional posterior DMN and its anticorrelated counterpart. In summary, our results demonstrate that the relationship between structural and functional connectivity is fine-grained, widespread across the entire brain, and driven by covariation in cortical area, i.e. likely differences in shape, depth, or number of foldings. These results suggest that neurotrophic events occur during development to dictate that the size and folding pattern of distant, functionally connected brain regions should vary together across subjects.SIGNIFICANCE STATEMENT Questions about the relationship between structure and function in the human brain have engaged neuroscientists for centuries in a debate that continues to this day. Here, by investigating intersubject variation in brain structure across a large number of individuals, we reveal modes of structural variation that map onto fine-grained functional organization across the entire brain, and specifically in the cerebellum, visual areas, and default-mode network. This functionally meaningful structural architecture emerges from the covariation of gray matter volume and cortical folding. These results suggest that the neurotrophic events at play during development, and possibly evolution, which dictate that the size and folding pattern of distant brain regions should vary together across subjects, might also play a role in functional cortical specialization.

A common brain network links development, aging, and vulnerability to disease.

Several theories link processes of development and aging in humans. In neuroscience, one model posits for instance that healthy age-related brain degeneration mirrors development, with the areas of the brain thought to develop later also degenerating earlier. However, intrinsic evidence for such a link between healthy aging and development in brain structure remains elusive. Here, we show that a data-driven analysis of brain structural variation across 484 healthy participants (8-85 y) reveals a largely--but not only--transmodal network whose lifespan pattern of age-related change intrinsically supports this model of mirroring development and aging. We further demonstrate that this network of brain regions, which develops relatively late during adolescence and shows accelerated degeneration in old age compared with the rest of the brain, characterizes areas of heightened vulnerability to unhealthy developmental and aging processes, as exemplified by schizophrenia and Alzheimer's disease, respectively. Specifically, this network, while derived solely from healthy subjects, spatially recapitulates the pattern of brain abnormalities observed in both schizophrenia and Alzheimer's disease. This network is further associated in our large-scale healthy population with intellectual ability and episodic memory, whose impairment contributes to key symptoms of schizophrenia and Alzheimer's disease. Taken together, our results suggest that the common spatial pattern of abnormalities observed in these two disorders, which emerge at opposite ends of the life spectrum, might be influenced by the timing of their separate and distinct pathological processes in disrupting healthy cerebral development and aging, respectively.

Probabilistic inference of regularisation in non-rigid registration.

A long-standing issue in non-rigid image registration is the choice of the level of regularisation. Regularisation is necessary to preserve the smoothness of the registration and penalise against unnecessary complexity. The vast majority of existing registration methods use a fixed level of regularisation, which is typically hand-tuned by a user to provide "nice" results. However, the optimal level of regularisation will depend on the data which is being processed; lower signal-to-noise ratios require higher regularisation to avoid registering image noise as well as features, and different pairs of images require registrations of varying complexity depending on their anatomical similarity. In this paper we present a probabilistic registration framework that infers the level of regularisation from the data. An additional benefit of this proposed probabilistic framework is that estimates of the registration uncertainty are obtained. This framework has been implemented using a free-form deformation transformation model, although it would be generically applicable to a range of transformation models. We demonstrate our registration framework on the application of inter-subject brain registration of healthy control subjects from the NIREP database. In our results we show that our framework appropriately adapts the level of regularisation in the presence of noise, and that inferring regularisation on an individual basis leads to a reduction in model over-fitting as measured by image folding while providing a similar level of overlap.

Benefits of multi-modal fusion analysis on a large-scale dataset: life-span patterns of inter-subject variability in cortical morphometry and white matter microstructure.

Neuroimaging studies have become increasingly multimodal in recent years, with researchers typically acquiring several different types of MRI data and processing them along separate pipelines that provide a set of complementary windows into each subject's brain. However, few attempts have been made to integrate the various modalities in the same analysis. Linked ICA is a robust data fusion model that takes multi-modal data and characterizes inter-subject variability in terms of a set of multi-modal components. This paper examines the types of components found when running Linked ICA on a large magnetic resonance imaging (MRI) morphometric and diffusion tensor imaging (DTI) data set comprising 484 healthy subjects ranging from 8 to 85 years of age. We find several strong global features related to age, sex, and intracranial volume; in particular, one component predicts age to a high accuracy (r=0.95). Most of the remaining components describe spatially localized modes of variability in white or gray matter, with many components including both tissue types. The multimodal components tend to be located in anatomically-related brain areas, suggesting a morphological and possibly functional relationship. The local components show relationships between surface-based cortical thickness and arealization, voxel-based morphometry (VBM), and between three different DTI measures. Further, we report components related to artifacts (e.g. scanner software upgrades) which would be expected in a dataset of this size. Most of the 100 extracted components showed interpretable spatial patterns and were found to be reliable using split-half validation. This work provides novel information about normal inter-subject variability in brain structure, and demonstrates the potential of Linked ICA as a feature-extracting data fusion approach across modalities. This exploratory approach automatically generates models to explain structure in the data, and may prove especially powerful for large-scale studies, where the population variability can be explored in increased detail.

MEG beamforming using Bayesian PCA for adaptive data covariance matrix regularization.

Beamformers are a commonly used method for doing source localization from magnetoencephalography (MEG) data. A key ingredient in a beamformer is the estimation of the data covariance matrix. When the noise levels are high, or when there is only a small amount of data available, the data covariance matrix is estimated poorly and the signal-to-noise ratio (SNR) of the beamformer output degrades. One solution to this is to use regularization whereby the diagonal of the covariance matrix is amplified by a pre-specified amount. However, this provides improvements at the expense of a loss in spatial resolution, and the parameter controlling the amount of regularization must be chosen subjectively. In this paper, we introduce a method that provides an adaptive solution to this problem by using a Bayesian Principle Component Analysis (PCA). This provides an estimate of the data covariance matrix to give a data-driven, non-arbitrary solution to the trade-off between the spatial resolution and the SNR of the beamformer output. This also provides a method for determining when the quality of the data covariance estimate maybe under question. We apply the approach to simulated and real MEG data, and demonstrate the way in which it can automatically adapt the regularization to give good performance over a range of noise and signal levels.

Linked independent component analysis for multimodal data fusion.

In recent years, neuroimaging studies have increasingly been acquiring multiple modalities of data and searching for task- or disease-related changes in each modality separately. A major challenge in analysis is to find systematic approaches for fusing these differing data types together to automatically find patterns of related changes across multiple modalities, when they exist. Independent Component Analysis (ICA) is a popular unsupervised learning method that can be used to find the modes of variation in neuroimaging data across a group of subjects. When multimodal data is acquired for the subjects, ICA is typically performed separately on each modality, leading to incompatible decompositions across modalities. Using a modular Bayesian framework, we develop a novel "Linked ICA" model for simultaneously modelling and discovering common features across multiple modalities, which can potentially have completely different units, signal- and contrast-to-noise ratios, voxel counts, spatial smoothnesses and intensity distributions. Furthermore, this general model can be configured to allow tensor ICA or spatially-concatenated ICA decompositions, or a combination of both at the same time. Linked ICA automatically determines the optimal weighting of each modality, and also can detect single-modality structured components when present. This is a fully probabilistic approach, implemented using Variational Bayes. We evaluate the method on simulated multimodal data sets, as well as on a real data set of Alzheimer's patients and age-matched controls that combines two very different types of structural MRI data: morphological data (grey matter density) and diffusion data (fractional anisotropy, mean diffusivity, and tensor mode).

Combined spatial and non-spatial prior for inference on MRI time-series.

When modelling FMRI and other MRI time-series data, a Bayesian approach based on adaptive spatial smoothness priors is a compelling alternative to using a standard generalized linear model (GLM) on presmoothed data. Another benefit of the Bayesian approach is that biophysical prior information can be incorporated in a principled manner; however, this requirement for a fixed non-spatial prior on a parameter would normally preclude using spatial regularization on that same parameter. We have developed a Gaussian-process-based prior to apply adaptive spatial regularization while still ensuring that the fixed biophysical prior is correctly applied on each voxel. A parameterized covariance matrix provides separate control over the variance (the diagonal elements) and the between-voxel correlation (due to off-diagonal elements). Analysis proceeds using evidence optimization (EO), with variational Bayes (VB) updates used for some parameters. The method can also be applied to non-linear forward models by using a linear Taylor expansion centred on the latest parameter estimates. Applying the method to FMRI with a constrained haemodynamic response function (HRF) shape model shows improved fits in simulations, compared to using either the non-spatial or spatial-smoothness prior alone. We also analyse multi-inversion arterial spin labelling data using a non-linear perfusion model to estimate cerebral blood flow and bolus arrival time. By combining both types of prior information, this new prior performs consistently well across a wider range of situations than either prior alone, and provides better estimates when both types of prior information are relevant.

Two-dimensional spatial compounding with warping.

Spatial compounding aims to improve image quality through signal averaging, but speed-of-sound (SoS) and refraction errors can misalign the component frames and blur the compound image. A 2-D compounding system is demonstrated that uses a nonrigid registration (warping) to realign the frames before compounding. Block-based estimates of local misalignments are interpolated smoothly to compute the warp vectors. Simulations and a specialized phantom, both with a 9% SoS distortion, were created, and compound images with and without warping were compared to the conventional image. Image sharpness was compared by measuring the diameter of point targets and directional edge sharpness. The average registration accuracy was 0.06 to 0.07 mm (approximately one pixel). The diameter of point targets increased only 2% with warping vs. 32% without warping and directional edge sharpness dropped 3.7% vs. 20.0%. Furthermore, most of the speckle reduction due to compounding is retained when warping is used. The tests on simulated and phantom data demonstrate that the method is capable of making a small, but significant, improvement to image quality. The examinations in vitro and in vivo show the correct operation of the method with real tissue features. Further clinical studies should be performed to compare spatial compounding with and without warping to see which applications would benefit from the small improvement.

Ensemble learning incorporating uncertain registration.

This paper proposes a novel approach for improving the accuracy of statistical prediction methods in spatially normalized analysis. This is achieved by incorporating registration uncertainty into an ensemble learning scheme. A probabilistic registration method is used to estimate a distribution of probable mappings between subject and atlas space. This allows the estimation of the distribution of spatially normalized feature data, e.g., grey matter probability maps. From this distribution, samples are drawn for use as training examples. This allows the creation of multiple predictors, which are subsequently combined using an ensemble learning approach. Furthermore, extra testing samples can be generated to measure the uncertainty of prediction. This is applied to separating subjects with Alzheimer's disease from normal controls using a linear support vector machine on a region of interest in magnetic resonance images of the brain. We show that our proposed method leads to an improvement in discrimination using voxel-based morphometry and deformation tensor-based morphometry over bootstrap aggregating, a common ensemble learning framework. The proposed approach also generates more reasonable soft-classification predictions than bootstrap aggregating. We expect that this approach could be applied to other statistical prediction tasks where registration is important.

Longitudinal brain MRI analysis with uncertain registration.

In this paper we propose a novel approach for incorporating measures of spatial uncertainty, which are derived from non-rigid registration, into spatially normalised statistics. Current approaches to spatially normalised statistical analysis use point-estimates of the registration parameters. This is limiting as the registration will rarely be completely accurate, and therefore data smoothing is often used to compensate for the uncertainty of the mapping. We derive localised measurements of spatial uncertainty from a probabilistic registration framework, which provides a principled approach to image smoothing. We evaluate our method using longitudinal deformation features from a set of MR brain images acquired from the Alzheimer's Disease Neuroimaging Initiative. These images are spatially normalised using our probabilistic registration algorithm. The spatially normalised longitudinal features are adaptively smoothed according to the registration uncertainty. The proposed adaptive smoothing shows improved classification results, (84% correct Alzheimer's Disease vs. controls), over either not smoothing (79.6%), or using a Gaussian filter with sigma = 2mm (78.8%).