Diffeomorphic metric surface mapping in subregion of the superior temporal gyrus

New insights into the variability of upper airway morphology in modern humans

The biological adaptation of the human lineage to its environment is a recurring question in paleoanthropology. Particularly, how eco-geographic factors (e.g., environmental temperature and humidity) have shaped upper airway morphology in hominins have been subject to continuing debate. Nasal shape is the result of many intertwined factors that include, but are not limited to, genetic drift, sexual selection, or adaptation to climate. A quantification of nasal airway (NA) morphological variation in modern human populations is crucial to better understand these multiple factors. In the present research, we study 195 in vivo CT scans of adult individuals collected in five different geographic areas (Chile, France, Cambodia, Russia, and South Africa). After segmentation of the nasal airway, we reconstruct 3D meshes that are analyzed with a landmark-free geometric morphometrics method based on surface deformation. Our results highlight subtle but statistically significant morphological differences between our five samples. The two morphologically closest groups are France and Russia, whose NAs are longer and narrower, with an important protrusion of the supero-anterior part. The Cambodian sample is the most morphologically distinct and clustered sample, with a mean NA that is wider and shorter. On the contrary, the Chilean sample form the most scattered cluster with the greatest intra-population variation. The South African sample is morphologically close to the Cambodian sample, but also partially overlaps the French and Russian variation. Interestingly, we record no correlation between NA volume and geographic groups, which raises the question of climate-related metabolic demands for oxygen consumption. The other factors of variation (sex and age) have no influence on the NA shape in our samples. However, NA volume varies significantly according both to sex and age: it is higher in males than in females and tends to increase with age. In contrast, we observe no effect of temperature or humidity on NA volume. Finally, we highlight the important influence of asymmetries related to nasal septum deviations in NA shape variation.

A meta-analysis of deep brain structural shape and asymmetry abnormalities in 2,833 individuals with schizophrenia compared with 3,929 healthy volunteers via the ENIGMA Consortium

Schizophrenia is associated with widespread alterations in subcortical brain structure. While analytic methods have enabled more detailed morphometric characterization, findings are often equivocal. In this meta-analysis, we employed the harmonized ENIGMA shape analysis protocols to collaboratively investigate subcortical brain structure shape differences between individuals with schizophrenia and healthy control participants. The study analyzed data from 2,833 individuals with schizophrenia and 3,929 healthy control participants contributed by 21 worldwide research groups participating in the ENIGMA Schizophrenia Working Group. Harmonized shape analysis protocols were applied to each site's data independently for bilateral hippocampus, amygdala, caudate, accumbens, putamen, pallidum, and thalamus obtained from T1-weighted structural MRI scans. Mass univariate meta-analyses revealed more-concave-than-convex shape differences in the hippocampus, amygdala, accumbens, and thalamus in individuals with schizophrenia compared with control participants, more-convex-than-concave shape differences in the putamen and pallidum, and both concave and convex shape differences in the caudate. Patterns of exaggerated asymmetry were observed across the hippocampus, amygdala, and thalamus in individuals with schizophrenia compared to control participants, while diminished asymmetry encompassed ventral striatum and ventral and dorsal thalamus. Our analyses also revealed that higher chlorpromazine dose equivalents and increased positive symptom levels were associated with patterns of contiguous convex shape differences across multiple subcortical structures. Findings from our shape meta-analysis suggest that common neurobiological mechanisms may contribute to gray matter reduction across multiple subcortical regions, thus enhancing our understanding of the nature of network disorganization in schizophrenia.

Nonlinear interaction between APOE ε4 allele load and age in the hippocampal surface of cognitively intact individuals

The ε4 allele of the gene Apolipoprotein E is the major genetic risk factor for Alzheimer's Disease. APOE ε4 has been associated with changes in brain structure in cognitively impaired and unimpaired subjects, including atrophy of the hippocampus, which is one of the brain structures that is early affected by AD. In this work we analyzed the impact of APOE ε4 gene dose and its association with age, on hippocampal shape assessed with multivariate surface analysis, in a ε4‐enriched cohort of n = 479 cognitively healthy individuals. Furthermore, we sought to replicate our findings on an independent dataset of n = 969 individuals covering the entire AD spectrum. We segmented the hippocampus of the subjects with a multi‐atlas‐based approach, obtaining high‐dimensional meshes that can be analyzed in a multivariate way. We analyzed the effects of different factors including APOE, sex, and age (in both cohorts) as well as clinical diagnosis on the local 3D hippocampal surface changes. We found specific regions on the hippocampal surface where the effect is modulated by significant APOE ε4 linear and quadratic interactions with age. We compared between APOE and diagnosis effects from both cohorts, finding similarities between APOE ε4 and AD effects on specific regions, and suggesting that age may modulate the effect of APOE ε4 and AD in a similar way.

Efficacy of diffeomorphic surface matching and 3D geometric morphometrics for taxonomic discrimination of Early Pleistocene hominin mandibular molars

Morphometric assessments of the dentition have played significant roles in hypotheses relating to taxonomic diversity among extinct hominins. In this regard, emphasis has been placed on the statistical appraisal of intraspecific variation to identify morphological criteria that convey maximum discriminatory power. Three-dimensional geometric morphometric (3D GM) approaches that utilize landmarks and semi-landmarks to quantify shape variation have enjoyed increasingly popular use over the past twenty-five years in assessments of the outer enamel surface (OES) and enamel-dentine junction (EDJ) of fossil molars. Recently developed diffeomorphic surface matching (DSM) methods that model the deformation between shapes have drastically reduced if not altogether eliminated potential methodological inconsistencies associated with the a priori identification of landmarks and delineation of semi-landmarks. As such, DSM has the potential to better capture the geometric details that describe tooth shape by accounting for both homologous and non-homologous (i.e., discrete) features, and permitting the statistical determination of geometric correspondence. We compare the discriminatory power of 3D GM and DSM in the evaluation of the OES and EDJ of mandibular permanent molars attributed to Australopithecus africanus, Paranthropus robustus and early Homo sp. from the sites of Sterkfontein and Swartkrans. For all three molars, classification and clustering scores demonstrate that DSM performs better at separating the A. africanus and P. robustus samples than does 3D GM. The EDJ provided the best results. P. robustus evinces greater morphological variability than A. africanus. The DSM assessment of the early Homo molar from Swartkrans reveals its distinctiveness from either australopith sample, and the "unknown" specimen from Sterkfontein (Stw 151) is notably more similar to Homo than to A. africanus.

Computational anatomy and diffeomorphometry: A dynamical systems model of neuroanatomy in the soft condensed matter continuum

The nonlinear systems models of computational anatomy that have emerged over the past several decades are a synthesis of three significant areas of computational science and biological modeling. First is the algebraic model of biological shape as a Riemannian orbit, a set of objects under diffeomorphic action. Second is the embedding of anatomical shapes into the soft condensed matter physics continuum via the extension of the Euler equations to geodesic, smooth flows with inverses, encoding divergence for the compressibility of atrophy and expansion of growth. Third, is making human shape and form a metrizable space via geodesic connections of coordinate systems. These three themes place our formalism into the modern data science world of personalized medicine supporting inference of high-dimensional anatomical phenotypes for studying neurodegeneration and neurodevelopment. The dynamical systems model of growth and atrophy that emerges is one which is organized in terms of forces, accelerations, velocities, and displacements, with the associated Hamiltonian momentum and the diffeomorphic flow acting as the state, and the smooth vector field the control. The forces that enter the model derive from external measurements through which the dynamical system must flow, and the internal potential energies of structures making up the soft condensed matter. We examine numerous examples on growth and atrophy. This article is categorized under: Analytical and Computational Methods > Computational Methods Laboratory Methods and Technologies > Imaging Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Riemannian metric optimization on surfaces (RMOS) for intrinsic brain mapping in the Laplace-Beltrami embedding space

Surface mapping methods play an important role in various brain imaging studies from tracking the maturation of adolescent brains to mapping gray matter atrophy patterns in Alzheimer's disease. Popular surface mapping approaches based on spherical registration, however, have inherent numerical limitations when severe metric distortions are present during the spherical parameterization step. In this paper, we propose a novel computational framework for intrinsic surface mapping in the Laplace-Beltrami (LB) embedding space based on Riemannian metric optimization on surfaces (RMOS). Given a diffeomorphism between two surfaces, an isometry can be defined using the pullback metric, which in turn results in identical LB embeddings from the two surfaces. The proposed RMOS approach builds upon this mathematical foundation and achieves general feature-driven surface mapping in the LB embedding space by iteratively optimizing the Riemannian metric defined on the edges of triangular meshes. At the core of our framework is an optimization engine that converts an energy function for surface mapping into a distance measure in the LB embedding space, which can be effectively optimized using gradients of the LB eigen-system with respect to the Riemannian metrics. In the experimental results, we compare the RMOS algorithm with spherical registration using large-scale brain imaging data, and show that RMOS achieves superior performance in the prediction of hippocampal subfields and cortical gyral labels, and the holistic mapping of striatal surfaces for the construction of a striatal connectivity atlas from substantia nigra.

Predicting auditory feedback control of speech production from subregional shape of subcortical structures

Although a growing body of research has focused on the cortical sensorimotor mechanisms that support auditory feedback control of speech production, much less is known about the subcortical contributions to this control process. This study examined whether subregional anatomy of subcortical structures assessed by statistical shape analysis is associated with vocal compensations and cortical event-related potentials in response to pitch feedback errors. The results revealed significant negative correlations between the magnitudes of vocal compensations and subregional shape of the right thalamus, between the latencies of vocal compensations and subregional shape of the left caudate and pallidum, and between the latencies of cortical N1 responses and subregional shape of the left putamen. These associations indicate that smaller local volumes of the basal ganglia and thalamus are predictive of slower and larger neurobehavioral responses to vocal pitch errors. Furthermore, increased local volumes of the left hippocampus and right amygdala were predictive of larger vocal compensations, suggesting that there is an interplay between the memory-related subcortical structures and auditory-vocal integration. These results, for the first time, provide evidence for differential associations of subregional morphology of the basal ganglia, thalamus, hippocampus, and amygdala with neurobehavioral processing of vocal pitch errors, suggesting that subregional shape measures of subcortical structures can predict behavioral outcome of auditory-vocal integration and associated neural features. Hum Brain Mapp 39:459-471, 2018. © 2017 Wiley Periodicals, Inc.

Minimum action principle and shape dynamics

In this paper, we propose a new method for computing a distance between two shapes embedded in three-dimensional space. Instead of comparing directly the geometric properties of the two shapes, we measure the cost of deforming one of the two shapes into the other. The deformation is computed as the geodesic between the two shapes in the space of shapes. The geodesic is found as a minimizer of the Onsager-Machlup action, based on an elastic energy for shapes that we define. Its length is set to be the integral of the action along that path; it defines an intrinsic quasi-metric on the space of shapes. We illustrate applications of our method to geometric morphometrics using three datasets representing bones and teeth of primates. Experiments on these datasets show that the variational quasi-metric we have introduced performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.

Large Deformation Multiresolution Diffeomorphic Metric Mapping for Multiresolution Cortical Surfaces: A Coarse-to-Fine Approach

Brain surface registration is an important tool for characterizing cortical anatomical variations and understanding their roles in normal cortical development and psychiatric diseases. However, surface registration remains challenging due to complicated cortical anatomy and its large differences across individuals. In this paper, we propose a fast coarse-to-fine algorithm for surface registration by adapting the large diffeomorphic deformation metric mapping (LDDMM) framework for surface mapping and show improvements in speed and accuracy via a multiresolution analysis of surface meshes and the construction of multiresolution diffeomorphic transformations. The proposed method constructs a family of multiresolution meshes that are used as natural sparse priors of the cortical morphology. At varying resolutions, these meshes act as anchor points where the parameterization of multiresolution deformation vector fields can be supported, allowing the construction of a bundle of multiresolution deformation fields, each originating from a different resolution. Using a coarse-to-fine approach, we show a potential reduction in computation cost along with improvements in sulcal alignment when compared with LDDMM surface mapping.

Statistical shape analysis using 3D Poisson equation--A quantitatively validated approach

Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc. Unfortunately, the proposed methods are rarely quantitatively evaluated, and as shown in recent studies, when they are evaluated, significant discrepancies exist in their outputs. In this work, we concentrate on the problem of finding the consistent location of deformation between two population of shapes. We propose a new shape analysis algorithm along with a framework to perform a quantitative evaluation of its performance. Specifically, the algorithm constructs a Signed Poisson Map (SPoM) by solving two Poisson equations on the volumetric shapes of arbitrary topology, and statistical analysis is then carried out on the SPoMs. The method is quantitatively evaluated on synthetic shapes and applied on real shape data sets in brain structures.

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

Multiresolution Diffeomorphic Mapping for Cortical Surfaces

Due to the convoluted folding pattern of the cerebral cortex, accurate alignment of cortical surfaces remains challenging. In this paper, we present a multiresolution diffeomorphic surface mapping algorithm under the framework of large deformation diffeomorphic metric mapping (LDDMM). Our algorithm takes advantage of multiresolution analysis (MRA) for surfaces and constructs cortical surfaces at multiresolution. This family of multiresolution surfaces are used as natural sparse priors of the cortical anatomy and provide the anchor points where the parametrization of deformation vector fields is supported. This naturally constructs tangent bundles of diffeomorphisms at different resolution levels and hence generates multiresolution diffeomorphic transformation. We show that our construction of multiresolution LDDMM surface mapping can potentially reduce computational cost and improves the mapping accuracy of cortical surfaces.

Network Neurodegeneration in Alzheimer's Disease via MRI Based Shape Diffeomorphometry and High-Field Atlasing

This paper examines MRI analysis of neurodegeneration in Alzheimer’s Disease (AD) in a network of structures within the medial temporal lobe using diffeomorphometry methods coupled with high-field atlasing in which the entorhinal cortex is partitioned into eight subareas. The morphometry markers for three groups of subjects (controls, preclinical AD, and symptomatic AD) are indexed to template coordinates measured with respect to these eight subareas. The location and timing of changes are examined within the subareas as it pertains to the classic Braak and Braak staging by comparing the three groups. We demonstrate that the earliest preclinical changes in the population occur in the lateral most sulcal extent in the entorhinal cortex (alluded to as transentorhinal cortex by Braak and Braak), and then proceeds medially which is consistent with the Braak and Braak staging. We use high-field 11T atlasing to demonstrate that the network changes are occurring at the junctures of the substructures in this medial temporal lobe network. Temporal progression of the disease through the network is also examined via changepoint analysis, demonstrating earliest changes in entorhinal cortex. The differential expression of rate of atrophy with progression signaling the changepoint time across the network is demonstrated to be signaling in the intermediate caudal subarea of the entorhinal cortex, which has been noted to be proximal to the hippocampus. This coupled to the findings of the nearby basolateral involvement in amygdala demonstrates the selectivity of neurodegeneration in early AD.

Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template.

Landmark constrained genus-one surface Teichmüller map applied to surface registration in medical imaging

We address the registration problem of genus-one surfaces (such as vertebrae bones) with prescribed landmark constraints. The high-genus topology of the surfaces makes it challenging to obtain a unique and bijective surface mapping that matches landmarks consistently. This work proposes to tackle this registration problem using a special class of quasi-conformal maps called Teichmüller maps (T-Maps). A landmark constrained T-Map is the unique mapping between genus-1 surfaces that minimizes the maximal conformality distortion while matching the prescribed feature landmarks. Existence and uniqueness of the landmark constrained T-Map are theoretically guaranteed. This work presents an iterative algorithm to compute the T-Map. The main idea is to represent the set of diffeomorphism using the Beltrami coefficients (BC). The BC is iteratively adjusted to an optimal one, which corresponds to our desired T-Map that matches the prescribed landmarks and satisfies the periodic boundary condition on the universal covering space. Numerical experiments demonstrate the effectiveness of our proposed algorithm. The method has also been applied to register vertebrae bones with prescribed landmark points and curves, which gives accurate surface registrations.

Individualized diffeomorphic mapping of brains with large cortical infarcts

Whole brain mapping of stroke patients with large cortical infarcts is not trivial due to the complexity of infarcts' anatomical location and appearance in magnetic resonance image. In this study, we proposed an individualized diffeomorphic mapping framework for solving this problem. This framework is based on our recent work of large deformation diffeomorphic metric mapping (LDDMM) in Du et al. (2011) and incorporates anatomical features, such as sulcal/gyral curves, cortical surfaces, brain intensity image, and masks of infarcted regions, in order to align a normal brain to the brain of stroke patients. We applied this framework to synthetic data and data of stroke patients and validated the mapping accuracy in terms of the alignment of gyral/sulcal curves, sulcal regions, and brain segmentation. Our results revealed that this framework provided comparable mapping results for stroke patients and healthy controls, suggesting the importance of incorporating individualized anatomical features in whole brain mapping of brains with large cortical infarcts.

Morphometry of anatomical shape complexes with dense deformations and sparse parameters

We propose a generic method for the statistical analysis of collections of anatomical shape complexes, namely sets of surfaces that were previously segmented and labeled in a group of subjects. The method estimates an anatomical model, the template complex, that is representative of the population under study. Its shape reflects anatomical invariants within the dataset. In addition, the method automatically places control points near the most variable parts of the template complex. Vectors attached to these points are parameters of deformations of the ambient 3D space. These deformations warp the template to each subject's complex in a way that preserves the organization of the anatomical structures. Multivariate statistical analysis is applied to these deformation parameters to test for group differences. Results of the statistical analysis are then expressed in terms of deformation patterns of the template complex, and can be visualized and interpreted. The user needs only to specify the topology of the template complex and the number of control points. The method then automatically estimates the shape of the template complex, the optimal position of control points and deformation parameters. The proposed approach is completely generic with respect to any type of application and well adapted to efficient use in clinical studies, in that it does not require point correspondence across surfaces and is robust to mesh imperfections such as holes, spikes, inconsistent orientation or irregular meshing. The approach is illustrated with a neuroimaging study of Down syndrome (DS). The results demonstrate that the complex of deep brain structures shows a statistically significant shape difference between control and DS subjects. The deformation-based modelingis able to classify subjects with very high specificity and sensitivity, thus showing important generalization capability even given a low sample size. We show that the results remain significant even if the number of control points, and hence the dimension of variables in the statistical model, are drastically reduced. The analysis may even suggest that parsimonious models have an increased statistical performance. The method has been implemented in the software Deformetrica, which is publicly available at www.deformetrica.org.

Inferring changepoint times of medial temporal lobe morphometric change in preclinical Alzheimer's disease

This paper uses diffeomorphometry methods to quantify the order in which statistically significant morphometric change occurs in three medial temporal lobe regions, the amygdala, entorhinal cortex (ERC), and hippocampus among subjects with symptomatic and preclinical Alzheimer's disease (AD). Magnetic resonance imaging scans were examined in subjects who were cognitively normal at baseline, some of whom subsequently developed clinical symptoms of AD. The images were mapped to a common template, using shape-based diffeomorphometry. The multidimensional shape markers indexed through the temporal lobe structures were modeled using a changepoint model with explicit parameters, specifying the number of years preceding clinical symptom onset. Our model assumes that the atrophy rate of a considered brain structure increases years before detectable symptoms.

The results demonstrate that the atrophy changepoint in the ERC occurs first, indicating significant change 8–10 years prior to onset, followed by the hippocampus, 2–4 years prior to onset, followed by the amygdala, 3 years prior to onset. The ERC is significant bilaterally, in both our local and global measures, with estimates of ERC surface area loss of 2.4% (left side) and 1.6% (right side) annually. The same changepoint model for ERC volume gives 3.0% and 2.7% on the left and right sides, respectively. Understanding the order in which changes in the brain occur during preclinical AD may assist in the design of intervention trials aimed at slowing the evolution of the disease.

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We use diffeomorphometry to quantify the order in which statistically significant morphometric change occurs in three medial temporal lobe regions, the amygdala, entorhinal cortex (ERC), and hippocampus among subjects with symptomatic and preclinical Alzheimer's disease (AD).

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We introduce a model on anatomical shape change in which changepoint is inferred, taking place some period of time before cognitive onset of AD.

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The analysis uses a dataset arising from the BIOCARD study, in which all subjects were cognitively normal at baseline, some of whom subsequently developed clinical symptoms of AD.

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The results demonstrate that the atrophy changepoint in the ERC occurs first, indicating significant change 8-10 years prior to onset, followed by hippocampus, 2-4 years prior to onset, followed by amygdala, 3 years prior to onset.

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The ERC is significant bilaterally, in both our local and global measures, with estimates of ERC surface area loss of 2.4% (left side) and 1.6% (right side) annually.

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Understanding the order in which changes in the brain occur during preclinical AD may assist in the design of intervention trials aimed at slowing the evolution of the disease.

Shape analysis, a field in need of careful validation

In the last two decades, the statistical analysis of shape has become an actively studied field and finds applications in a wide range of areas. In addition to algorithmic development, many researchers have distributed end-user orientated toolboxes, which further enable the utilization of the algorithms in an "off the shelf" fashion. However, there is little work on the evaluation and validation of these techniques, which poses a rather serious challenge when interpreting their results. To address this lack of validation, we design a validation framework and then use it to test some of the most widely used toolboxes. Our initial results show inconsistencies and disagreement among four different methods. We believe this type of analysis to be critical not only for the community of algorithm designers but also perhaps more importantly to researchers who use these tools without knowing the algorithm details and seek objective criteria for tool selection.

The diffeomorphometry of temporal lobe structures in preclinical Alzheimer's disease

This paper examines morphometry of MRI biomarkers derived from the network of temporal lobe structures including the amygdala, entorhinal cortex and hippocampus in subjects with preclinical Alzheimer's disease (AD). Based on template-centered population analysis, it is demonstrated that the structural markers of the amygdala, hippocampus and entorhinal cortex are statistically significantly different between controls and those with preclinical AD. Entorhinal cortex is the most strongly significant based on the linear effects model (p < .0001) for the high-dimensional vertex- and Laplacian-based markers corresponding to localized atrophy. The hippocampus also shows significant localized high-dimensional change (p < .0025) and the amygdala demonstrates more global change signaled by the strength of the low-dimensional volume markers. The analysis of the three structures also demonstrates that the volume measures are only weakly discriminating between preclinical and control groups, with the average atrophy rates of the volume of the entorhinal cortex higher than amygdala and hippocampus. The entorhinal cortex thickness also exhibits an atrophy rate nearly a factor of two higher in the ApoE4 positive group relative to the ApoE4 negative group providing weak discrimination between the two groups.

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We examine MRI measures in controls vs. subjects with ‘preclinical AD’.

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Morphometry shape markers of the entorhinal cortex were most discriminating.

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The mean atrophy rate of the entorhinal cortex exceeded the hippocampus or amygdala.

Surface fluid registration of conformal representation: application to detect disease burden and genetic influence on hippocampus

In this paper, we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1-forms, inverse consistent surface fluid registration, and multivariate tensor-based morphometry (mTBM). First, we conformally map a surface onto a planar rectangle space with holomorphic 1-forms. Second, we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface. Third, we align the feature image with a chosen template image via the fluid image registration algorithm, which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization. The inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images. This alignment induces a corresponding deformation on the surface. We tested the system on Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline dataset to study AD symptoms on hippocampus. In our system, by modeling a hippocampus as a 3D parametric surface, we nonlinearly registered each surface with a selected template surface. Then we used mTBM to analyze the morphometry difference between diagnostic groups. Experimental results show that the new system has better performance than two publicly available subcortical surface registration tools: FIRST and SPHARM. We also analyzed the genetic influence of the Apolipoprotein E[element of]4 allele (ApoE4), which is considered as the most prevalent risk factor for AD. Our work successfully detected statistically significant difference between ApoE4 carriers and non-carriers in both patients of mild cognitive impairment (MCI) and healthy control subjects. The results show evidence that the ApoE genotype may be associated with accelerated brain atrophy so that our work provides a new MRI analysis tool that may help presymptomatic AD research.

Amygdala-hippocampal shape and cortical thickness abnormalities in first-episode schizophrenia and mania

BACKGROUND

Abnormalities in cortical thickness and subcortical structures have been studied in schizophrenia but little is known about corresponding changes in mania and brain structural differences between these two psychiatric conditions, especially early in the stage of the illness. In this study we aimed to compare cortical thickness and shape of the amygdala-hippocampal complex in first-episode schizophrenia (FES) and mania (FEM). Method Structural magnetic resonance imaging (MRI) was performed on 28 FES patients, 28 FEM patients and 28 healthy control subjects who were matched for age, gender and handedness.

RESULTS

Overall, the shape of the amygdala was deformed in both patient groups, relative to controls. Compared to FEM patients, FES patients had significant inward shape deformation in the left hippocampal tail, right hippocampal body and a small region in the right amygdala. Cortical thinning was more widespread in FES patients, with significant differences found in the temporal brain regions when compared with FEM and controls.

CONCLUSIONS

Significant differences were observed between the two groups of patients with FES and FEM in terms of the hippocampal shape and cortical thickness in the temporal region, highlighting that distinguishable brain structural changes are present early in the course of schizophrenia and mania.

Applying tensor-based morphometry to parametric surfaces can improve MRI-based disease diagnosis

Many methods have been proposed for computer-assisted diagnostic classification. Full tensor information and machine learning with 3D maps derived from brain images may help detect subtle differences or classify subjects into different groups. Here we develop a new approach to apply tensor-based morphometry to parametric surface models for diagnostic classification. We use this approach to identify cortical surface features for use in diagnostic classifiers. First, with holomorphic 1-forms, we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so-called slit domain. Next, the surface parameterization approach provides a natural way to register anatomical surfaces across subjects using a constrained harmonic map. To analyze anatomical differences, we then analyze the full Riemannian surface metric tensors, which retain multivariate information on local surface geometry. As the number of voxels in a 3D image is large, sparse learning is a promising method to select a subset of imaging features and to improve classification accuracy. Focusing on vertices with greatest effect sizes, we train a diagnostic classifier using the surface features selected by an L1-norm based sparse learning method. Stability selection is applied to validate the selected feature sets. We tested the algorithm on MRI-derived cortical surfaces from 42 subjects with genetically confirmed Williams syndrome and 40 age-matched controls, multivariate statistics on the local tensors gave greater effect sizes for detecting group differences relative to other TBM-based statistics including analysis of the Jacobian determinant and the largest eigenvalue of the surface metric. Our method also gave reasonable classification results relative to the Jacobian determinant, the pair of eigenvalues of the Jacobian matrix and volume features. This analysis pipeline may boost the power of morphometry studies, and may assist with image-based classification.

Hyperbolic harmonic brain surface registration with curvature-based landmark matching

Brain Cortical surface registration is required for inter-subject studies of functional and anatomical data. Harmonic mapping has been applied for brain mapping, due to its existence, uniqueness, regularity and numerical stability. In order to improve the registration accuracy, sculcal landmarks are usually used as constraints for brain registration. Unfortunately, constrained harmonic mappings may not be diffeomorphic and produces invalid registration. This work conquer this problem by changing the Riemannian metric on the target cortical surface o a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism while the landmark constraints are enforced as boundary matching condition. The computational algorithms are based on the Ricci flow method and yperbolic heat diffusion. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic, with higher qualities in terms of landmark alignment, curvature matching, area distortion and overlapping of region of interests.

Evolution of hippocampal shapes across the human lifespan

Aberrant hippocampal morphology plays an important role in the pathophysiology of aging. Volumetric analysis of the hippocampus has been performed in aging studies; however, the shape morphometry--which is potentially more informative in terms of related cognition--has yet to be examined. In this paper, we employed an advanced brain mapping technique, large deformation diffeomorphic metric mapping (LDDMM), and a dimensionality reduction approach, locally linear diffeomorphic metric embedding (LLDME), to explore age-related changes in hippocampal shape as delineated from magnetic resonance (MR) images of 302 healthy adults aged from 18 to 94 years. Compared with the hippocampal volumes, the hippocampal shapes clearly showed the nonlinear trajectory of biological aging across the human lifespan, where the variation of hippocampal shapes by age was characterized by a cubic polynomial. By integrating of LDDMM and LLDME, we were also able to illustrate the average hippocampal shapes in each individual decade. In addition, LDDMM and LLDME facilitated the identification of 63 years as a threshold beyond which hippocampal morphological changes were accelerated. Adults over 63 years of age showed the inward-deformation bilaterally in the head of the hippocampi and the left subiculum regardless of hippocampal volume reduction when compared to adults younger than 63. Hence, we demonstrated that the shape of anatomical structures added another dimension of structural morphological quantification beyond the volume in understanding aging.

Inattention and hyperactivity predict alterations in specific neural circuits among 6-year-old boys

OBJECTIVE

Assessment of inattention and hyperactivity in preschoolers is highly dependent upon parental reports. Such reports are compromised by parental attitudes and mental health. Our study aimed to examine associations of inattention and hyperactivity/impulsivity from maternal reports on the Conners' Parent Rating Scale (CPRS) with brain morphology assessed using structural magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI) in 6-year-old boys.

METHOD

Large deformation diffeomorphic metric brain mapping was used to assess brain morphology on MRI and DTI in 96 six-year-old boys, including cortical thickness, subcortical shapes, and fractional anisotropy (FA) of deep white matter tracts (DWMTs). Linear regression examined associations between these measures of brain structures and mothers' CPRS ratings of their child's inattention and hyperactivity/impulsivity.

RESULTS

Our results revealed that temporal and parietal cortices, as well as posterior white matter and callosal tracts are associated with inattention and hyperactivity/impulsivity symptoms among six-year-old boys. Inattention and hyperactivity/impulsivity symptoms share common neural circuits, but hyperactivity/impulsivity ratings associate with more extensive cortical areas, such as frontal regions, and with white matter tracts emphasizing executive control. There were no associations detected between inattention (or hyperactivity/impulsivity) and the shape of subcortical structures.

CONCLUSIONS

Our results suggested specific rather than widespread neural circuits involved in inattention and hyperactivity/impulsivity in young children, which is congruent with existing findings in older children and adolescents, and in adults with attention-deficit/hyperactivity disorder (ADHD). Hence, our study supported the dimensional view of ADHD, that is, that symptoms of inattention and hyperactivity/impulsivity lie on a continuum.

Principal component based diffeomorphic surface mapping

We present a new diffeomorphic surface mapping algorithm under the framework of large deformation diffeomorphic metric mapping (LDDMM). Unlike existing LDDMM approaches, this new algorithm reduces the complexity of the estimation of diffeomorphic transformations by incorporating a shape prior in which a nonlinear diffeomorphic shape space is represented by a linear space of initial momenta of diffeomorphic geodesic flows from a fixed template. In addition, for the first time, the diffeomorphic mapping is formulated within a decision-theoretic scheme based on Bayesian modeling in which an empirical shape prior is characterized by a low dimensional Gaussian distribution on initial momentum. This is achieved using principal component analysis (PCA) to construct the eigenspace of the initial momentum. A likelihood function is formulated as the conditional probability of observing surfaces given any particular value of the initial momentum, which is modeled as a random field of vector-valued measures characterizing the geometry of surfaces. We define the diffeomorphic mapping as a problem that maximizes a posterior distribution of the initial momentum given observable surfaces over the eigenspace of the initial momentum. We demonstrate the stability of the initial momentum eigenspace when altering training samples using a bootstrapping method. We then validate the mapping accuracy and show robustness to outliers whose shape variation is not incorporated into the shape prior.

Approximations of the diffeomorphic metric and their applications in shape learning

In neuroimaging studies based on anatomical shapes, it is well-known that the dimensionality of the shape information is much higher than the number of subjects available. A major challenge in shape analysis is to develop a dimensionality reduction approach that is able to efficiently characterize anatomical variations in a low-dimensional space. For this, there is a need to characterize shape variations among individuals for N given subjects. Therefore, one would need to calculate (2(N)) mappings between any two shapes and obtain their distance matrix. In this paper, we propose a method that reduces the computational burden to N mappings. This is made possible by making use of the first- and second-order approximations of the metric distance between two brain structural shapes in a diffeomorphic metric space. We directly derive these approximations based on the so-called conservation law of momentum, i.e., the diffeomorphic transformation acting on anatomical shapes along the geodesic is completely determined by its velocity at the origin of a fixed template. This allows for estimating morphological variation of two shapes through the first- and second-order approximations of the initial velocity in the tangent space of the diffeomorphisms at the template. We also introduce an alternative representation of these approximations through the initial momentum, i.e., a linear transformation of the initial velocity, and provide a simple computational algorithm for the matrix of the diffeomorphic metric. We employ this algorithm to compute the distance matrix of hippocampal shapes among an aging population used in a dimensionality reduction analysis, namely, ISOMAP. Our results demonstrate that the first- and second-order approximations are sufficient to characterize shape variations when compared to the diffeomorphic metric constructed through (2(N)) mappings in ISOMAP analysis.

Whole brain diffeomorphic metric mapping via integration of sulcal and gyral curves, cortical surfaces, and images

This paper introduces a novel large deformation diffeomorphic metric mapping algorithm for whole brain registration where sulcal and gyral curves, cortical surfaces, and intensity images are simultaneously carried from one subject to another through a flow of diffeomorphisms. To the best of our knowledge, this is the first time that the diffeomorphic metric from one brain to another is derived in a shape space of intensity images and point sets (such as curves and surfaces) in a unified manner. We describe the Euler-Lagrange equation associated with this algorithm with respect to momentum, a linear transformation of the velocity vector field of the diffeomorphic flow. The numerical implementation for solving this variational problem, which involves large-scale kernel convolution in an irregular grid, is made feasible by introducing a class of computationally friendly kernels. We apply this algorithm to align magnetic resonance brain data. Our whole brain mapping results show that our algorithm outperforms the image-based LDDMM algorithm in terms of the mapping accuracy of gyral/sulcal curves, sulcal regions, and cortical and subcortical segmentation. Moreover, our algorithm provides better whole brain alignment than combined volumetric and surface registration (Postelnicu et al., 2009) and hierarchical attribute matching mechanism for elastic registration (HAMMER) (Shen and Davatzikos, 2002) in terms of cortical and subcortical volume segmentation.

Locally Linear Diffeomorphic Metric Embedding (LLDME) for surface-based anatomical shape modeling

This paper presents the algorithm, Locally Linear Diffeomorphic Metric Embedding (LLDME), for constructing efficient and compact representations of surface-based brain shapes whose variations are characterized using Large Deformation Diffeomorphic Metric Mapping (LDDMM). Our hypothesis is that the shape variations in the infinite-dimensional diffeomorphic metric space can be captured by a low-dimensional space. To do so, traditional Locally Linear Embedding (LLE) that reconstructs a data point from its neighbors in Euclidean space is extended to LLDME that requires interpolating a shape from its neighbors in the infinite-dimensional diffeomorphic metric space. This is made possible through the conservation law of momentum derived from LDDMM. It indicates that initial momentum, a linear transformation of the initial velocity of diffeomorphic flows, at a fixed template shape determines the geodesic connecting the template to a subject's shape in the diffeomorphic metric space and becomes the shape signature of an individual subject. This leads to the compact linear representation of the nonlinear diffeomorphisms in terms of the initial momentum. Since the initial momentum is in a linear space, a shape can be approximated by a linear combination of its neighbors in the diffeomorphic metric space. In addition, we provide efficient computations for the metric distance between two shapes through the first order approximation of the geodesic using the initial momentum as well as for the reconstruction of a shape given its low-dimensional Euclidean coordinates using the geodesic shooting with the initial momentum as the initial condition. Experiments are performed on the hippocampal shapes of 302 normal subjects across the whole life span (18-94years). Compared with Principal Component Analysis and ISOMAP, LLDME provides the most compact and efficient representation of the age-related hippocampal shapes. Even though the hippocampal volumes among young adults are as variable as those in older adults, LLDME disentangles the hippocampal local shape variation from the hippocampal size and thus reveals the nonlinear relationship of the hippocampal morphometry with age.

Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents

This paper proposes a generic framework for the registration, the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images. This framework is based on the metric on currents for the comparison of fiber bundles. This metric measures anatomical differences between fiber bundles, seen as global homologous structures across subjects. It avoids the need to establish correspondences between points or between individual fibers of different bundles. It can measure differences both in terms of the geometry of the bundles (like its boundaries) and in terms of the density of fibers within the bundle. It is robust to fiber interruptions and reconnections. In addition, a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents. First, we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects. A dense deformation of the underlying white matter is estimated, which is constrained by the bundles seen as global anatomical landmarks. By contrast, the alignment obtained from image registration is driven only by the local gradient of the image. Second, we propose a generative statistical model for the analysis of a collection of homologous bundles. This model consistently estimates prototype fiber bundles (called template), which capture the anatomical invariants in the population, a set of deformations, which align the geometry of the template to that of each subject and a set of residual perturbations. The statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry (stretching, torque, etc.) and "texture" (fiber density, etc.). Third, this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability. This gives a way to interpret the anatomical features that the model detects consistently across the subjects. This may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles.

Atlas generation for subcortical and ventricular structures with its applications in shape analysis

Atlas-driven morphometric analysis has received great attention for studying anatomical shape variation across clinical populations in neuroimaging research as it provides a local coordinate representation for understanding the family of anatomic observations. We present a procedure for generating atlas of subcortical and ventricular structures, including amygdala, hippocampus, caudate, putamen, globus pallidus, thalamus, and lateral ventricles, using the large deformation diffeomorphic metric atlas generation algorithm. The atlas was built based on manually labeled volumes of 41 subjects randomly selected from the database of Open Access Series of Imaging Studies (OASIS, 10 young adults, 10 middle-age adults, 10 healthy elders, and 11 patients with dementia). We show that the estimated atlas is representative of the population in terms of its metric distance to each individual subject in the population. In the application of detecting shape variations, using the estimated atlas may potentially increase statistical power in identifying group shape difference when comparing with using a single subject atlas. In shape-based classification, the metric distances between subjects and each of within-class estimated atlases construct a shape feature space, which allows for performing a variety of classification algorithms to distinguish anatomies.

Basal ganglia shapes predict social, communication, and motor dysfunctions in boys with autism spectrum disorder

OBJECTIVE

Basal ganglia abnormalities have been suggested as contributing to motor, social, and communicative impairments in autism spectrum disorder (ASD). Volumetric analyses offer limited ability to detect localized differences in basal ganglia structure. Our objective was to investigate basal ganglia shape abnormalities and their association with behavioral features of ASD, which may involve multiple frontal-subcortical circuits.

METHOD

Basal ganglia were manually delineated from MR images of 32 boys with ASD and 45 typically developing (TD) boys. Large deformation diffeomorphic metric mapping (LDDMM) was used to assess between-group differences in basal ganglia shape and to examine associations with motor, praxis, and reciprocal social and communicative impairments in ASD.

RESULTS

Boys with ASD showed changes in right basal ganglia shape as compared with TD boys; surface deformation was present in the caudate, putamen, and globus pallidus but did not stand up to correction for multiple comparisons. Brain-behavior correlation findings were more robust; analyses accounting for multiple comparisons revealed, in boys with ASD, surface inward deformation of the right posterior putamen predicted poorer motor skill, whereas surface inward deformation of the bilateral anterior and posterior putamen predicted poorer praxis. Surface outward deformation in the bilateral medial caudate head predicted greater reciprocal social and communicative impairment.

CONCLUSIONS

Motor, social, and communicative impairments in boys with ASD are associated with shape abnormalities in the basal ganglia. The findings suggest abnormalities within parallel frontal-subcortical circuits are differentially associated with impaired acquisition of motor and reciprocal social and communicative skills in ASD.

A local technique based on vectorized surfaces for craniofacial reconstruction

In this paper, we focus on the automation of facial reconstruction. Since they consider the whole head as the object of interest, usual reconstruction techniques are global and involve a large number of parameters to be estimated. We present a local technique which aims at reaching a good trade-off between bias and variance following the paradigm of non-parametric statistics. The estimation is localized on patches delimited by surface geodesics between anatomical points of the skull. The technique relies on a continuous representation of the individual surfaces embedded in the vectorial space of extended normal vector fields. This allows to compute deformations and averages of surfaces. It consists in estimating the soft-tissue surface over patches. Using a homogeneous database described in [31], we obtain results on the chin and nasal regions with an average error below 1mm, outperforming the global reconstruction techniques.

Quantitative evaluation of LDDMM, FreeSurfer, and CARET for cortical surface mapping

Cortical surface mapping has been widely used to compensate for individual variability of cortical shape and topology in anatomical and functional studies. While many surface mapping methods were proposed based on landmarks, curves, spherical or native cortical coordinates, few studies have extensively and quantitatively evaluated surface mapping methods across different methodologies. In this study we compared five cortical surface mapping algorithms, including large deformation diffeomorphic metric mapping (LDDMM) for curves (LDDMM-curve), for surfaces (LDDMM-surface), multi-manifold LDDMM (MM-LDDMM), FreeSurfer, and CARET, using 40 MRI scans and 10 simulated datasets. We computed curve variation errors and surface alignment consistency for assessing the mapping accuracy of local cortical features (e.g., gyral/sulcal curves and sulcal regions) and the curvature correlation for measuring the mapping accuracy in terms of overall cortical shape. In addition, the simulated datasets facilitated the investigation of mapping error distribution over the cortical surface when the MM-LDDMM, FreeSurfer, and CARET mapping algorithms were applied. Our results revealed that the LDDMM-curve, MM-LDDMM, and CARET approaches best aligned the local curve features with their own curves. The MM-LDDMM approach was also found to be the best in aligning the local regions and cortical folding patterns (e.g., curvature) as compared to the other mapping approaches. The simulation experiment showed that the MM-LDDMM mapping yielded less local and global deformation errors than the CARET and FreeSurfer mappings.

Surface-based analysis on shape and fractional anisotropy of white matter tracts in Alzheimer's disease

Background

White matter disruption has been suggested as one of anatomical features associated with Alzheimer's disease (AD). Diffusion tensor imaging (DTI), which has been widely used in AD studies, obtains new insights into the white matter structure.

Methods

We introduced surface-based geometric models of the deep white matter tracts extracted from DTI, allowing the characterization of their shape variations relative to an atlas as well as fractional anisotropy (FA) variations on the atlas surface through large deformation diffeomorphic metric mapping (LDDMM). We applied it to assess local shapes and FA variations of twenty-three deep white matter tracts in 13 patients with AD and 19 healthy control subjects.

Results

Our results showed regionally-specific shape abnormalities and FA reduction in the cingulum tract and the sagittal stratum tract in AD, suggesting that disruption in the white matter tracts near the temporal lobe may represent the secondary consequence of the medial temporal lobe pathology in AD. Moreover, the regionally-specific patterns of FA and shape of the white matter tracts were shown to be of sufficient sensitivity to robustly differentiate patients with AD from healthy comparison controls when compared with the mean FA and volumes within the regions of the white matter tracts. Finally, greater FA or deformation abnormalities of the white matter tracts were associated with lower MMSE scores.

Conclusion

The regionally-specific shape and FA patterns could be potential imaging markers for differentiating AD from normal aging.

Collaborative computational anatomy: an MRI morphometry study of the human brain via diffeomorphic metric mapping

This article describes a large multi-institutional analysis of the shape and structure of the human hippocampus in the aging brain as measured via MRI. The study was conducted on a population of 101 subjects including nondemented control subjects (n = 57) and subjects clinically diagnosed with Alzheimer's Disease (AD, n = 38) or semantic dementia (n = 6) with imaging data collected at Washington University in St. Louis, hippocampal structure annotated at the Massachusetts General Hospital, and anatomical shapes embedded into a metric shape space using large deformation diffeomorphic metric mapping (LDDMM) at the Johns Hopkins University. A global classifier was constructed for discriminating cohorts of nondemented and demented subjects based on linear discriminant analysis of dimensions derived from metric distances between anatomical shapes, demonstrating class conditional structure differences measured via LDDMM metric shape (P < 0.01). Localized analysis of the control and AD subjects only on the coordinates of the population template demonstrates shape changes in the subiculum and the CA1 subfield in AD (P < 0.05). Such large scale collaborative analysis of anatomical shapes has the potential to enhance the understanding of neurodevelopmental and neuropsychiatric disorders.

Multi-manifold diffeomorphic metric mapping for aligning cortical hemispheric surfaces

Cortical surface-based analysis has been widely used in anatomical and functional studies because it is geometrically appropriate for the cortex. One of the main challenges in the cortical surface-based analysis is to optimize the alignment of the cortical hemispheric surfaces across individuals. In this paper, we introduce a multi-manifold large deformation diffeomorphic metric mapping (MM-LDDMM) algorithm that allows simultaneously carrying the cortical hemispheric surface and its sulcal curves from one to the other through a flow of diffeomorphisms. We present an algorithm based on recent derivation of a law of momentum conservation for the geodesics of diffeomorphic flow. Once a template is fixed, the space of initial momentum becomes an appropriate space for studying shape via geodesic flow since the flow at any point on curves and surfaces along the geodesic is completely determined by the momentum at the origin. We solve for trajectories (geodesics) of the kinetic energy by computing its variation with respect to the initial momentum and by applying a gradient descent scheme. The MM-LDDMM algorithm optimizes the initial momenta encoding the anatomical variation of each individual relative to a common coordinate system in a linear space, which provides a natural scheme for shape deformation average and template (or atlas) generation. We applied the MM-LDDMM algorithm for constructing the templates for the cortical surface and 14 sulcal curves of each hemisphere using a group of 40 subjects. The estimated template shape reflects regions which are highly variable across these subjects. Compared with existing single-manifold LDDMM algorithms, such as the LDDMM-curve mapping and the LDDMM-surface mapping, the MM-LDDMM mapping provides better results in terms of surface to surface distances in five predefined regions.

Neuroanatomical asymmetry patterns in individuals with schizophrenia and their non-psychotic siblings

Neuroanatomical endophenotypes may reveal insights into the processes by which genetic factors increase the risk of developing schizophrenia. To determine whether patterns of neuroanatomical asymmetries may be useful as schizophrenia-related endophenotypes, we compared patterns of structural asymmetries in patients with schizophrenia, healthy controls, and their respective siblings. The surfaces of the left and right amygdala, hippocampus, thalamus, caudate nucleus, putamen, globus pallidus, and nucleus accumbens were assessed in 40 pairs of healthy comparison controls (CON) and their siblings (CON-SIB) and 25 pairs of patients with schizophrenia (SCZ) and their siblings (SCZ-SIB) in magnetic resonance (MR) images using large deformation diffeomorphic metric mapping (LDDMM) and parallel transport techniques. The within-subject asymmetry deformation of each structure was first measured via LDDMM, and then translated to a global template via parallel transport for evaluation of the patterns of asymmetry both within and across siblings. Our results revealed that asymmetries observed in CON subjects occurred in the amygdala and the anterior segment of the hippocampus with more pronounced expansion deformation in the right-sided structures (R>L asymmetry) but not in the basal ganglia and thalamus. Disturbance in this pattern of asymmetries was observed in both SCZ and SCZ-SIB subjects. More specifically, exaggerations and reductions in the normative pattern of asymmetries were observed in the amygdala-hippocampus formation, basal ganglia, and thalamus. These altered patterns of asymmetries are present in subjects with schizophrenia and their siblings, and therefore may represent a schizophrenia-related endophenotype.

Regional shape abnormalities in mild cognitive impairment and Alzheimer's disease

Magnetic resonance (MR) based shape analysis provides an opportunity to detect regional specificity of volumetric changes that may distinguish mild cognitive impairment (MCI) and Alzheimer's disease (AD) from healthy elderly controls (CON), and predict future conversion to AD. We assessed the surface deformation of seven structures (amygdala, hippocampus, thalamus, caudate, putamen, globus pallidus, body and temporal horn of the lateral ventricles) in 383 MRI volumes, based on data shared through the publicly available Alzheimer's Disease Neuroimaging Initiative (ADNI), to identify regionally-specific shape abnormalities in MCI and AD. Large deformation diffeomorphic metric mapping (LDDMM) was used to generate the shapes of seven structures based on template shapes injected into segmented subcortical volumes. LDDMM then constructed the surface deformation maps encoding the local shape variation of each subject relative to the template. Hierarchical models were developed to detect differences in local shape in MCI and AD relative to CON. Our findings revealed that surface inward-deformation in MCI and AD is most prominent in the anterior hippocampal segment and the basolateral complex of the amygdala. Most pronounced surface outward-deformation in MCI and AD occurs in the lateral ventricles. Mild surface inward-deformation in MCI and AD occurs in the anterior-lateral and ventral-lateral aspects of the thalamus, with no evidence of regionally-specific deformation in the putamen or globus pallidus. Although the locations of the shape abnormalities in MCI and AD are primarily within the mesial temporal region, analyses support distinct components of correlated shape variation that may help predict future MCI conversion.

Basal ganglia volume and shape in children with attention deficit hyperactivity disorder

OBJECTIVE

Volumetric abnormalities of basal ganglia have been associated with attention deficit hyperactivity disorder (ADHD), especially in boys. To specify localization of these abnormalities, large deformation diffeomorphic metric mapping (LDDMM) was used to examine the effects of ADHD, sex, and their interaction on basal ganglia shapes.

METHOD

The basal ganglia (caudate, putamen, globus pallidus) were manually delineated on magnetic resonance imaging from 66 typically developing children (35 boys) and 47 children (27 boys) with ADHD. LDDMM mappings from 35 typically developing children were used to generate basal ganglia templates. Shape variations of each structure relative to the template were modeled for each subject as a random field using Laplace-Beltrami basis functions in the template coordinates. Linear regression was used to examine group differences in volumes and shapes of the basal ganglia.

RESULTS

Boys with ADHD showed significantly smaller basal ganglia volumes compared with typically developing boys, and LDDMM revealed the groups remarkably differed in basal ganglia shapes. Volume compression was seen bilaterally in the caudate head and body and anterior putamen as well as in the left anterior globus pallidus and right ventral putamen. Volume expansion was most pronounced in the posterior putamen. No volume or shape differences were revealed in girls with ADHD.

CONCLUSIONS

The shape compression pattern of basal ganglia in boys with ADHD suggests that ADHD-associated deviations from typical brain development involve multiple frontal-subcortical control loops, including circuits with premotor, oculomotor, and prefrontal cortices. Further investigations employing brain-behavior analyses will help to discern the task-dependent contributions of these circuits to impaired response control that is characteristic of ADHD.

Time sequence diffeomorphic metric mapping and parallel transport track time-dependent shape changes

Serial MRI human brain scans have facilitated the detection of brain development and of the earliest signs of neuropsychiatric and neurodegenerative diseases, monitoring disease progression, and resolving drug effects in clinical trials for preventing or slowing the rate of brain degeneration. To track anatomical shape changes in serial images, we introduce new point-based time sequence large deformation diffeomorphic metric mapping (TS-LDDMM) to infer the time flow of within-subject geometric shape changes that carry known observations through a period. Its Euler-Lagrange equation is generalized for anatomies whose shapes are characterized by point sets, such as landmarks, curves, and surfaces. The time-dependent momentum obtained from the TS-LDDMM encodes within-subject shape changes. For the purpose of across-subject shape comparison, we then propose a diffeomorphic analysis framework to translate within-subject deformation in a global template without incorporating across-subject anatomical variations via parallel transport technique. The analysis involves the retraction of the within-subject time-dependent momentum along the TS-LDDMM trajectory from each time to the baseline, the translation of the momentum in a global template, and the reconstruction of the TS-LDDMM trajectory starting from the global template.

APOE related hippocampal shape alteration in geriatric depression

Late-onset depression often precedes the onset of dementia associated with the hippocampal degeneration. Using large deformation diffeomorphic metric mapping (LDDMM), we evaluated apolipoprotein E epsilon-4 allele (apoE E4) effects on hippocampal volume and shape in 38 depressed patients without the apoE E4, 14 depressed patients with one apoE E4, and 31 healthy comparison subjects without the apoE E4. The hippocampal volumes were manually assessed. We applied a diffeomorphic template generation procedure for creating the hippocampal templates based on a subset of the population. The LDDMM mappings were used to generate the hippocampal shape of each subject and characterize the surface deformation of each hippocampus relative to the template. Such deformation was modeled as random field characterized by the Laplace-Beltrami basis functions in the template coordinates. Linear regression was used to examine group differences in the hippocampal volume and shape. We found that there were significant hippocampal shape alternations in both depressed groups while the groups of depressed patients and the group of healthy subjects did not differ in the hippocampal volume. The depressed patients with one apoE E4 show more pronounced shape inward-compression in the anterior CA1 than the depressed patients without the apoE E4 when compared with the healthy controls without the apoE E4. Thus, hippocampal shape abnormalities in late-onset depressed patients with one apoE E4 may indicate future conversion of this group to AD at higher risk than depressed patients without the apoE E4.

Region-of-interest-based analysis with application of cortical thickness variation of left planum temporale in schizophrenia and psychotic bipolar disorder

In neuroimaging studies, spatial normalization and multivariate testing are central problems in characterizing group variation of functions (e.g., cortical thickness, curvature, functional response) in an atlas coordinate system across clinical populations. We present a region-of-interest (ROI)-based analysis framework for detecting such a group variation. This framework includes two main techniques: ROI-based registration via large deformation diffeomorphic metric surface mapping and a multivariate testing using a Gaussian random field (GRF) model on the cortical surface constructed by the eigenfunctions of the Laplace-Beltramioperator. We compared our GRF statistical model with a pointwise hypothesis testing approach, whose P-value is corrected using false discovery rate or random field theory at several smoothness scales. As an illustration, we applied this framework to a clinical study of the cortical thickness of the left planum temporale (PT) in subjects with psychotic bipolar disorder, schizophrenia, and healthy comparison controls. Our results show that the anterior portion of the left PT is thinner in the psychotic bipolar and schizophrenic groups than in the healthy control group, and the posterior portion of the left PT shows the reversal finding. Moreover, there may be a greater thickness variation in the left PT in psychotic bipolar patients when compared with that in schizophrenic patients.