Characterising brain network topologies: A dynamic analysis approach using heat kernels.

Network theory provides a principled abstraction of the human brain: reducing a complex system into a simpler representation from which to investigate brain organisation. Recent advancement in the neuroimaging field is towards representing brain connectivity as a dynamic process in order to gain a deeper understanding of how the brain is organised for information transport. In this paper we propose a network modelling approach based on the heat kernel to capture the process of heat diffusion in complex networks. By applying the heat kernel to structural brain networks, we define new features which quantify change in heat propagation. Identifying suitable features which can classify networks between cohorts is useful towards understanding the effect of disease on brain architecture. We demonstrate the discriminative power of heat kernel features in both synthetic and clinical preterm data. By generating an extensive range of synthetic networks with varying density and randomisation, we investigate heat diffusion in relation to changes in network topology. We demonstrate that our proposed features provide a metric of network efficiency and may be indicative of organisational principles commonly associated with, for example, small-world architecture. In addition, we show the potential of these features to characterise and classify between network topologies. We further demonstrate our methodology in a clinical setting by applying it to a large cohort of preterm babies scanned at term equivalent age from which diffusion networks were computed. We show that our heat kernel features are able to successfully predict motor function measured at two years of age (sensitivity, specificity, F-score, accuracy = 75.0, 82.5, 78.6, and 82.3%, respectively).

Machine-learning to characterise neonatal functional connectivity in the preterm brain.

Brain development is adversely affected by preterm birth. Magnetic resonance image analysis has revealed a complex fusion of structural alterations across all tissue compartments that are apparent by term-equivalent age, persistent into adolescence and adulthood, and associated with wide-ranging neurodevelopment disorders. Although functional MRI has revealed the relatively advanced organisational state of the neonatal brain, the full extent and nature of functional disruptions following preterm birth remain unclear. In this study, we apply machine-learning methods to compare whole-brain functional connectivity in preterm infants at term-equivalent age and healthy term-born neonates in order to test the hypothesis that preterm birth results in specific alterations to functional connectivity by term-equivalent age. Functional connectivity networks were estimated in 105 preterm infants and 26 term controls using group-independent component analysis and a graphical lasso model. A random forest-based feature selection method was used to identify discriminative edges within each network and a nonlinear support vector machine was used to classify subjects based on functional connectivity alone. We achieved 80% cross-validated classification accuracy informed by a small set of discriminative edges. These edges connected a number of functional nodes in subcortical and cortical grey matter, and most were stronger in term neonates compared to those born preterm. Half of the discriminative edges connected one or more nodes within the basal ganglia. These results demonstrate that functional connectivity in the preterm brain is significantly altered by term-equivalent age, confirming previous reports of altered connectivity between subcortical structures and higher-level association cortex following preterm birth.

Construction of a fetal spatio-temporal cortical surface atlas from in utero MRI: Application of spectral surface matching.

In this study, we construct a spatio-temporal surface atlas of the developing cerebral cortex, which is an important tool for analysing and understanding normal and abnormal cortical development. In utero Magnetic Resonance Imaging (MRI) of 80 healthy fetuses was performed, with a gestational age range of 21.7 to 38.9 weeks. Topologically correct cortical surface models were extracted from reconstructed 3D MRI volumes. Accurate correspondences were obtained by applying a joint spectral analysis to cortices for sets of subjects close to a specific age. Sulcal alignment was found to be accurate in comparison to spherical demons, a state of the art registration technique for aligning 2D cortical representations (average Fréchet distance≈0.4 mm at 30 weeks). We construct consistent, unbiased average cortical surface templates, for each week of gestation, from age-matched groups of surfaces by applying kernel regression in the spectral domain. These were found to accurately capture the average cortical shape of individuals within the cohort, suggesting a good alignment of cortical geometry. Each spectral embedding and its corresponding cortical surface template provide a dual reference space where cortical geometry is aligned and a vertex-wise morphometric analysis can be undertaken.

Automatic quantification of normal cortical folding patterns from fetal brain MRI.

We automatically quantify patterns of normal cortical folding in the developing fetus from in utero MR images (N=80) over a wide gestational age (GA) range (21.7 to 38.9weeks). This work on data from healthy subjects represents a first step towards characterising abnormal folding that may be related to pathology, facilitating earlier diagnosis and intervention. The cortical boundary was delineated by automatically segmenting the brain MR image into a number of key structures. This utilised a spatio-temporal atlas as tissue priors in an expectation-maximization approach with second order Markov random field (MRF) regularization to improve the accuracy of the cortical boundary estimate. An implicit high resolution surface was then used to compute cortical folding measures. We validated the automated segmentations with manual delineations and the average surface discrepancy was of the order of 1mm. Eight curvature-based folding measures were computed for each fetal cortex and used to give summary shape descriptors. These were strongly correlated with GA (R(2)=0.99) confirming the close link between neurological development and cortical convolution. This allowed an age-dependent non-linear model to be accurately fitted to the folding measures. The model supports visual observations that, after a slow initial start, cortical folding increases rapidly between 25 and 30weeks and subsequently slows near birth. The model allows the accurate prediction of fetal age from an observed folding measure with a smaller error where growth is fastest. We also analysed regional patterns in folding by parcellating each fetal cortex using a nine-region anatomical atlas and found that Gompertz models fitted the change in lobar regions. Regional differences in growth rate were detected, with the parietal and posterior temporal lobes exhibiting the fastest growth, while the cingulate, frontal and medial temporal lobes developed more slowly.

Whole-brain mapping of structural connectivity in infants reveals altered connection strength associated with growth and preterm birth.

Cerebral white-matter injury is common in preterm-born infants and is associated with neurocognitive impairments. Identifying the pattern of connectivity changes in the brain following premature birth may provide a more comprehensive understanding of the neurobiology underlying these impairments. Here, we characterize whole-brain, macrostructural connectivity following preterm delivery and explore the influence of age and prematurity using a data-driven, nonsubjective analysis of diffusion magnetic resonance imaging data. T1- and T2-weighted and -diffusion MRI were obtained between 11 and 31 months postconceptional age in 49 infants, born between 25 and 35 weeks postconception. An optimized processing pipeline, combining anatomical, and tissue segmentations with probabilistic diffusion tractography, was used to map mean tract anisotropy. White-matter tracts where connection strength was related to age of delivery or imaging were identified using sparse-penalized regression and stability selection. Older children had stronger connections in tracts predominantly involving frontal lobe structures. Increasing prematurity at birth was related to widespread reductions in connection strength in tracts involving all cortical lobes and several subcortical structures. This nonsubjective approach to mapping whole-brain connectivity detected hypothesized changes in the strength of intracerebral connections during development and widespread reductions in connectivity strength associated with premature birth.

A combined manifold learning analysis of shape and appearance to characterize neonatal brain development.

Large medical image datasets form a rich source of anatomical descriptions for research into pathology and clinical biomarkers. Many features may be extracted from data such as MR images to provide, through manifold learning methods, new representations of the population's anatomy. However, the ability of any individual feature to fully capture all aspects morphology is limited. We propose a framework for deriving a representation from multiple features or measures which can be chosen to suit the application and are processed using separate manifold-learning steps. The results are then combined to give a single set of embedding coordinates for the data. We illustrate the framework in a population study of neonatal brain MR images and show how consistent representations, correlating well with clinical data, are given by measures of shape and of appearance. These particular measures were chosen as the developing neonatal brain undergoes rapid changes in shape and MR appearance and were derived from extracted cortical surfaces, nonrigid deformations, and image similarities. Combined single embeddings show improved correlations demonstrating their benefit for further studies such as identifying patterns in the trajectories of brain development. The results also suggest a lasting effect of age at birth on brain morphology, coinciding with previous clinical studies.

Combining morphological information in a manifold learning framework: application to neonatal MRI.

MR image data can provide many features or measures although any single measure is unlikely to comprehensively characterize the underlying morphology. We present a framework in which multiple measures are used in manifold learning steps to generate coordinate embeddings which are then combined to give an improved single representation of the population. An application to neonatal brain MRI data shows that the use of shape and appearance measures in particular leads to biologically plausible and consistent representations correlating well with clinical data. Orthogonality among the correlations suggests the embedding components relate to comparatively independent morphological features. The rapid changes that occur in brain shape and in MR image appearance during neonatal brain development justify the use of shape measures (obtained from a deformation metric) and appearance measures (obtained from image similarity). The benefit of combining separate embeddings is demonstrated by improved correlations with clinical data and we illustrate the potential of the proposed framework in characterizing trajectories of brain development.

A common neonatal image phenotype predicts adverse neurodevelopmental outcome in children born preterm.

Diffuse white matter injury is common in preterm infants and is a candidate substrate for later cognitive impairment. This injury pattern is associated with morphological changes in deep grey nuclei, the localization of which is uncertain. We test the hypotheses that diffuse white matter injury is associated with discrete focal tissue loss, and that this image phenotype is associated with impairment at 2years. We acquired magnetic resonance images from 80 preterm infants at term equivalent (mean gestational age 29(+6)weeks) and 20 control infants (mean GA 39(+2)weeks). Diffuse white matter injury was defined by abnormal apparent diffusion coefficient values in one or more white matter region (frontal, central or posterior white matter at the level of the centrum semiovale), and morphological difference between groups was calculated from 3D images using deformation based morphometry. Neurodevelopmental assessments were obtained from preterm infants at a mean chronological age of 27.5months, and from controls at a mean age of 31.1months. We identified a common image phenotype in 66 of 80 preterm infants at term equivalent comprising: diffuse white matter injury; and tissue volume reduction in the dorsomedial nucleus of the thalamus, the globus pallidus, periventricular white matter, the corona radiata and within the central region of the centrum semiovale (t=4.42 p<0.001 false discovery rate corrected). The abnormal image phenotype is associated with reduced median developmental quotient (DQ) at 2years (DQ=92) compared with control infants (DQ=112), p<0.001. These findings indicate that specific neural systems are susceptible to maldevelopment after preterm birth, and suggest that neonatal image phenotype may serve as a useful biomarker for studying mechanisms of injury and the effect of putative therapeutic interventions.

Multi-atlas based segmentation of brain images: atlas selection and its effect on accuracy.

Quantitative research in neuroimaging often relies on anatomical segmentation of human brain MR images. Recent multi-atlas based approaches provide highly accurate structural segmentations of the brain by propagating manual delineations from multiple atlases in a database to a query subject and combining them. The atlas databases which can be used for these purposes are growing steadily. We present a framework to address the consequent problems of scale in multi-atlas segmentation. We show that selecting a custom subset of atlases for each query subject provides more accurate subcortical segmentations than those given by non-selective combination of random atlas subsets. Using a database of 275 atlases, we tested an image-based similarity criterion as well as a demographic criterion (age) in a leave-one-out cross-validation study. Using a custom ranking of the database for each subject, we combined a varying number n of atlases from the top of the ranked list. The resulting segmentations were compared with manual reference segmentations using Dice overlap. Image-based selection provided better segmentations than random subsets (mean Dice overlap 0.854 vs. 0.811 for the estimated optimal subset size, n=20). Age-based selection resulted in a similar marked improvement. We conclude that selecting atlases from large databases for atlas-based brain image segmentation improves the accuracy of the segmentations achieved. We show that image similarity is a suitable selection criterion and give results based on selecting atlases by age that demonstrate the value of meta-information for selection.

Comparison and evaluation of segmentation techniques for subcortical structures in brain MRI.

The automation of segmentation of medical images is an active research area. However, there has been criticism of the standard of evaluation of methods. We have comprehensively evaluated four novel methods of automatically segmenting subcortical structures using volumetric, spatial overlap and distance-based measures. Two of the methods are atlas-based - classifier fusion and labelling (CFL) and expectation-maximisation segmentation using a dynamic brain atlas (EMS), and two model-based - profile active appearance models (PAM) and Bayesian appearance models (BAM). Each method was applied to the segmentation of 18 subcortical structures in 270 subjects from a diverse pool varying in age, disease, sex and image acquisition parameters. Our results showed that all four methods perform on par with recently published methods. CFL performed significantly better than the other three methods according to all three classes of metrics.

Automated morphological analysis of magnetic resonance brain imaging using spectral analysis.

Analysis of structural neuroimaging studies often relies on volume or shape comparisons of labeled neuroanatomical structures in two or more clinical groups. Such studies have common elements involving segmentation, morphological feature extraction for comparison, and subject and group discrimination. We combine two state-of-the-art analysis approaches, namely automated segmentation using label fusion and classification via spectral analysis to explore the relationship between the morphology of neuroanatomical structures and clinical diagnosis in dementia. We apply this framework to a cohort of normal controls and patients with mild dementia where accurate diagnosis is notoriously difficult. We compare and contrast our ability to discriminate normal and abnormal groups on the basis of structural morphology with (supervised) and without (unsupervised) knowledge of each individual's diagnosis. We test the hypothesis that morphological features resulting from Alzheimer disease processes are the strongest discriminator between groups.

Assessment of brain growth in early childhood using deformation-based morphometry.

We present methods for the quantitative analysis of brain growth based on the registration of longitudinal MR image data with the use of Jacobian determinant maps to characterise neuroanatomical changes. The individual anatomies, growth maps and tissue classes are also spatially normalised in an 'average space' and aggregated to provide atlases for the population at each timepoint. The average space representation is obtained using the average intersubject transformation within each timepoint. In an exemplar study, this approach is used to assess brain development in 25 infants between 1 and 2 years, and we show consistency in growth estimates between registration and segmentation approaches.

Classifier selection strategies for label fusion using large atlas databases.

Structural segmentations of brain MRI can be generated by propagating manually labelled atlas images from a repository to a query subject and combining them. This method has been shown to be robust, consistent and increasingly accurate with increasing numbers of classifiers. It outperforms standard atlas-based segmentation but suffers, however, from problems of scale when the number of atlases is large. For a large repository and a particular query subject, using a selection strategy to identify good classifiers is one way to address problems of scale. This work presents and compares different classifier selection strategies which are applied to a group of 275 subjects with manually labelled brain MR images. We approximate an upper limit for the accuracy or overlap that can be achieved for a particular structure in a given subject and compare this with the accuracy obtained using classifier selection. The accuracy of different classifier selection strategies are also rated against the distribution of overlaps generated by random groups of classifiers.

Interpolation artefacts in non-rigid registration.

Voxel based non-rigid registration of images involves finding a similarity maximising transformation that deforms a source image to the coordinate system of a target image. In order to do this, interpolation is required to estimate the source intensity values corresponding to transformed target voxels. These interpolated source intensities are used when calculating the similarity measure being optimised. In this work, we compare the extent and nature of artefactual displacements produced by voxel based non-rigid registration techniques for different interpolators and investigate their relationship to image noise and global transformation error. A per-voxel similarity gradient is calculated and the resulting vector field is used to characterise registration artefacts for each interpolator. Finally, we show that the resulting registration artefacts can generate spurious volume changes for image pairs with no expected volume change.

Spatial transformation of motion and deformation fields using nonrigid registration.

In this paper, we present a technique that can be used to transform the motion or deformation fields defined in the coordinate system of one subject into the coordinate system of another subject. Such a transformation accounts for the differences in the coordinate systems of the two subjects due to misalignment and size/shape variation, enabling the motion or deformation of each of the subjects to be directly quantitatively and qualitatively compared. The field transformation is performed by using a nonrigid registration algorithm to determine the intersubject coordinate system mapping from the first subject to the second subject. This fixes the relationship between the coordinate systems of the two subjects, and allows us to recover the deformation/motion vectors of the second subject for each corresponding point in the first subject. Since these vectors are still aligned with the coordinate system of the second subject, the inverse of the intersubject coordinate mapping is required to transform these vectors into the coordinate system of the first subject, and we approximate this inverse using a numerical line integral method. The accuracy of our numerical inversion technique is demonstrated using a synthetic example, after which we present applications of our method to sequences of cardiac and brain images.