Combining anatomical manifold information via diffeomorphic metric mappings for studying cortical thinning of the cingulate gyrus in schizophrenia

Time multiscale regularization for nonlinear image registration

Regularization-based methods are commonly used for image registration. However, fixed regularizers have limitations in capturing details and describing the dynamic registration process. To address this issue, we propose a time multiscale registration framework for nonlinear image registration in this paper. Our approach replaces the fixed regularizer with a monotone decreasing sequence, and iteratively uses the residual of the previous step as the input for registration. Particularly, first, we introduce a dynamically varying regularization strategy that updates regularizers at each iteration and incorporates them with a multiscale framework. This approach guarantees an overall smooth deformation field in the initial stage of registration and fine-tunes local details as the images become more similar. We then deduce convergence analysis under certain conditions on the regularizers and parameters. Further, we introduce a TV-like regularizer to demonstrate the efficiency of our method. Finally, we compare our proposed multiscale algorithm with some existing methods on both synthetic images and pulmonary computed tomography (CT) images. The experimental results validate that our proposed algorithm outperforms the compared methods, especially in preserving details during image registration with sharp structures.

Voxel-based assessments of treatment effects on longitudinal brain changes in the Multidomain Alzheimer Preventive Trial cohort

The Multidomain Alzheimer Preventive Trial was designed to assess the effect of omega-3 supplementation and multidomain intervention on cognitive decline of subjects with subjective memory complaint. In terms of cognitive testing, no significant effect was found. In this paper, we evaluate the effect of the interventions on the brain morphological changes. Subjects with magnetic resonance imaging acquisitions at baseline and at 36 months were included (N = 376). Morphological changes were characterized by volume measurements and nonlinear deformation. The multidomain intervention was associated with a significant effect on the 3-year brain morphological changes in the deformation-based approach. Differences were mainly located in the left periventricular area next to the temporoparietal junction. These changes were associated with better cognitive performance and mood/behavior stabilization. No effect of the omega-3 supplementation was observed. This result suggests a possible effect on cognition, not yet observable after 3 years. We argue that neuroimaging could help define whether early intervention strategies are effective to delay cognitive decline and dementia.

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.

Analysis of mitochondrial shape dynamics using large deformation diffeomorphic metric curve matching

Mitochondrial shape changes are essential to mitochondrial functions. Quantification of mitochondrial shape changes is essential to understanding related physiology and disease mechanisms. In this study, we proposed a new automated pipeline for quantifying the shape changing patterns of mitochondria in the framework of large deformation diffeomorphic metric mapping for curve. We validated the accuracy of our pipeline on 32 mitochondria data, each having 6 sequential time-lapse frames. The contour of each mitochondrion is modeled by a curve consisting of a set of landmark points ranging from 39 to 358, with the moving distance between every two consecutive frames quantified for each localized point. The sensitivity of the proposed pipeline, with respect to different curve discretization, was investigated, with high robustness established. In addition, we quantified the uncertainty level of the proposed pipeline using 10 fixed mitochondria data with 6 time frames as well, with the mean between-frame moving distance found to be smaller than 28 nm for a majority of the 10 fixed mitochondria data. This indicates that the proposed pipeline has a very low level of uncertainty. The encouraging results from this work suggest that the proposed pipeline is potentially a powerful tool for quantifying shape dynamics, both globally and locally, of a variety of cellular components.

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

This paper proposes a method for primal-dual convex optimization in variational large deformation diffeomorphic metric mapping problems formulated with robust regularizers and robust image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We consider three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V-Huber and total generalized variation. The Huber norm is used in the image similarity term. The primal-dual equations are derived for the stationary and the non-stationary parameterizations of diffeomorphisms. The resulting algorithms have been implemented for running in the GPU using Cuda. For the most memory consuming methods, we have developed a multi-GPU implementation. The GPU implementations allowed us to perform an exhaustive evaluation study in NIREP and LPBA40 databases. The experiments showed that, for all the considered regularizers, the proposed method converges to diffeomorphic solutions while better preserving discontinuities at the boundaries of the objects compared to baseline diffeomorphic registration methods. In most cases, the evaluation showed a competitive performance for the robust regularizers, close to the performance of the baseline diffeomorphic registration methods.

Nonlinear image registration with bidirectional metric and reciprocal regularization

Nonlinear registration is an important technique to align two different images and widely applied in medical image analysis. In this paper, we develop a novel nonlinear registration framework based on the diffeomorphic demons, where a reciprocal regularizer is introduced to assume that the deformation between two images is an exact diffeomorphism. In detail, first, we adopt a bidirectional metric to improve the symmetry of the energy functional, whose variables are two reciprocal deformations. Secondly, we slack these two deformations into two independent variables and introduce a reciprocal regularizer to assure the deformations being the exact diffeomorphism. Then, we utilize an alternating iterative strategy to decouple the model into two minimizing subproblems, where a new closed form for the approximate velocity of deformation is calculated. Finally, we compare our proposed algorithm on two data sets of real brain MR images with two relative and conventional methods. The results validate that our proposed method improves accuracy and robustness of registration, as well as the gained bidirectional deformations are actually reciprocal.

Analysis of cortical morphometric variability using labeled cortical distance maps

Morphometric (i.e., shape and size) differences in the anatomy of cortical structures are associated with neurodevelopmental and neuropsychiatric disorders. Such differences can be quantized and detected by a powerful tool called Labeled Cortical Distance Map (LCDM). The LCDM method provides distances of labeled gray matter (GM) voxels from the GM/white matter (WM) surface for specific cortical structures (or tissues). Here we describe a method to analyze morphometric variability in the particular tissue using LCDM distances. To extract more of the information provided by LCDM distances, we perform pooling and censoring of LCDM distances. In particular, we employ Brown-Forsythe (BF) test of homogeneity of variance (HOV) on the LCDM distances. HOV analysis of pooled distances provides an overall analysis of morphometric variability of the LCDMs due to the disease in question, while the HOV analysis of censored distances suggests the location(s) of significant variation in these differences (i.e., at which distance from the GM/WM surface the morphometric variability starts to be significant). We also check for the influence of assumption violations on the HOV analysis of LCDM distances. In particular, we demonstrate that BF HOV test is robust to assumption violations such as the non-normality and within sample dependence of the residuals from the median for pooled and censored distances and are robust to data aggregation which occurs in analysis of censored distances. We recommend HOV analysis as a complementary tool to the analysis of distribution/location differences. We also apply the methodology on simulated normal and exponential data sets and assess the performance of the methods when more of the underlying assumptions are satisfied. We illustrate the methodology on a real data example, namely, LCDM distances of GM voxels in ventral medial prefrontal cortices (VMPFCs) to see the effects of depression or being of high risk to depression on the morphometry of VMPFCs. The methodology used here is also valid for morphometric analysis of other cortical structures.

Northwestern University schizophrenia data sharing for SchizConnect: A longitudinal dataset for large-scale integration

In this paper, we describe an instance of the Northwestern University Schizophrenia Data and Software Tool (NUSDAST), a schizophrenia-related dataset hosted at XNAT Central, and the SchizConnect data portal used for accessing and sharing the dataset. NUSDAST was built and extended upon existing, standard schemas available for data sharing on XNAT Central (http://central.xnat.org/). With the creation of SchizConnect, we were able to link NUSDAST to other neuroimaging data sources and create a powerful, federated neuroimaging resource.

The diffeomorphometry of regional shape change rates and its relevance to cognitive deterioration in mild cognitive impairment and Alzheimer's disease

We proposed a diffeomorphometry-based statistical pipeline to study the regional shape change rates of the bilateral hippocampus, amygdala, and ventricle in mild cognitive impairment (MCI) and Alzheimer's disease (AD) compared with healthy controls (HC), using sequential magnetic resonance imaging (MRI) scans of 713 subjects (3,123 scans in total). The subgroup shape atrophy rates of the bilateral hippocampus and amygdala, as well as the expansion rates of the bilateral ventricles, for a majority of vertices were found to follow the order of AD>MCI>HC. The bilateral hippocampus and the left amygdala were subsegmented into multiple functionally meaningful subregions with the help of high-field MRI scans. The largest group differences in localized shape atrophy rates on the hippocampus were found to occur in CA1, followed by subiculum, CA2, and finally CA3/dentate gyrus, which is consistent with the neurofibrillary tangle accumulation trajectory. Highly nonuniform group differences were detected on the amygdala; vertices on the core amygdala (basolateral and lateral nucleus) revealed much larger atrophy rates, whereas those on the noncore amygdala (mainly centromedial) displayed similar or even smaller atrophy rates in AD relative to HC. The temporal horns of the ventricles were observed to have the largest localized ventricular expansion rate differences; with the AD group showing larger localized expansion rates on the anterior horn and the body part of the ventricles as well. Significant correlations were observed between the localized shape change rates of each of these six structures and the cognitive deterioration rates as quantified by the Alzheimer's Disease Assessment Scale-Cognitive Behavior Section increase rate and the Mini Mental State Examination decrease rate.

Gauss-Newton inspired preconditioned optimization in large deformation diffeomorphic metric mapping

In this work, we propose a novel preconditioned optimization method in the paradigm of Large Deformation Diffeomorphic Metric Mapping (LDDMM). The preconditioned update scheme is formulated for the non-stationary and the stationary parameterizations of diffeomorphisms, yielding three different LDDMM methods. The preconditioning matrices are inspired in the Hessian approximation used in Gauss-Newton method. The derivatives are computed using Frechet differentials. Thus, optimization is performed in a Sobolev space, in contrast to optimization in L(2) commonly used in non-rigid registration literature. The proposed LDDMM methods have been evaluated and compared with their respective implementations of gradient descent optimization. Evaluation has been performed using real and simulated images from the Non-rigid Image Registration Evaluation Project (NIREP). The experiments conducted in this work reported that our preconditioned LDDMM methods achieved a performance similar or superior to well-established-in-literature gradient descent non-stationary LDDMM in the great majority of cases. Moreover, preconditioned optimization showed a substantial reduction in the execution time with an affordable increase of the memory usage per iteration. Additional experiments reported that optimization using Frechet differentials should be preferable to optimization using L(2) differentials.

Shape abnormalities of subcortical and ventricular structures in mild cognitive impairment and Alzheimer's disease: detecting, quantifying, and predicting

This article assesses the feasibility of using shape information to detect and quantify the subcortical and ventricular structural changes in mild cognitive impairment (MCI) and Alzheimer's disease (AD) patients. We first demonstrate structural shape abnormalities in MCI and AD as compared with healthy controls (HC). Exploring the development to AD, we then divide the MCI participants into two subgroups based on longitudinal clinical information: (1) MCI patients who remained stable; (2) MCI patients who converted to AD over time. We focus on seven structures (amygdala, hippocampus, thalamus, caudate, putamen, globus pallidus, and lateral ventricles) in 754 MR scans (210 HC, 369 MCI of which 151 converted to AD over time, and 175 AD). The hippocampus and amygdala were further subsegmented based on high field 0.8 mm isotropic 7.0T scans for finer exploration. For MCI and AD, prominent ventricular expansions were detected and we found that these patients had strongest hippocampal atrophy occurring at CA1 and strongest amygdala atrophy at the basolateral complex. Mild atrophy in basal ganglia structures was also detected in MCI and AD. Stronger atrophy in the amygdala and hippocampus, and greater expansion in ventricles was observed in MCI converters, relative to those MCI who remained stable. Furthermore, we performed principal component analysis on a linear shape space of each structure. A subsequent linear discriminant analysis on the principal component values of hippocampus, amygdala, and ventricle leads to correct classification of 88% HC subjects and 86% AD subjects.

Morphometric differences in planum temporale in schizophrenia and bipolar disorder revealed by statistical analysis of labeled cortical depth maps

Differences in cortical thickness in the lateral temporal lobe, including the planum temporale (PT), have been reported in MRI studies of schizophrenia (SCZ) and bipolar disorder (BPD) patients. Most of these studies have used a single-valued global or local measure for thickness. However, additional and complementary information can be obtained by generating labeled cortical distance maps (LCDMs), which are distances of labeled gray matter (GM) voxels from the nearest point on the GM/white matter (WM) (inner) cortical surface. Statistical analyses of pooled and censored LCDM distances reveal subtle differences in PT between SCZ and BPD groups from data generated by Ratnanather et al. (Schizophrenia Research, http://dx.doi.org/10.1016/j.schres.2013.08.014). These results confirm that the left planum temporale (LPT) is more sensitive than the right PT in distinguishing between SCZ, BPD, and healthy controls. Also confirmed is a strong gender effect, with a thicker PT seen in males than in females. The differences between groups at smaller distances in the LPT revealed by pooled and censored LCDM analysis suggest that SCZ and BPD have different effects on the cortical mantle close to the GM/WM surface. This is consistent with reported subtle changes in the cortical mantle observed in post-mortem studies.

Northwestern University Schizophrenia Data and Software Tool (NUSDAST)

The schizophrenia research community has invested substantial resources on collecting, managing and sharing large neuroimaging datasets. As part of this effort, our group has collected high resolution magnetic resonance (MR) datasets from individuals with schizophrenia, their non-psychotic siblings, healthy controls and their siblings. This effort has resulted in a growing resource, the Northwestern University Schizophrenia Data and Software Tool (NUSDAST), an NIH-funded data sharing project to stimulate new research. This resource resides on XNAT Central, and it contains neuroimaging (MR scans, landmarks and surface maps for deep subcortical structures, and FreeSurfer cortical parcellation and measurement data), cognitive (cognitive domain scores for crystallized intelligence, working memory, episodic memory, and executive function), clinical (demographic, sibling relationship, SAPS and SANS psychopathology), and genetic (20 polymorphisms) data, collected from more than 450 subjects, most with 2-year longitudinal follow-up. A neuroimaging mapping, analysis and visualization software tool, CAWorks, is also part of this resource. Moreover, in making our existing neuroimaging data along with the associated meta-data and computational tools publically accessible, we have established a web-based information retrieval portal that allows the user to efficiently search the collection. This research-ready dataset meaningfully combines neuroimaging data with other relevant information, and it can be used to help facilitate advancing neuroimaging research. It is our hope that this effort will help to overcome some of the commonly recognized technical barriers in advancing neuroimaging research such as lack of local organization and standard descriptions.

Censoring distances based on labeled cortical distance maps in cortical morphometry

It has been demonstrated that shape differences in cortical structures may be manifested in neuropsychiatric disorders. Such morphometric differences can be measured by labeled cortical distance mapping (LCDM) which characterizes the morphometry of the laminar cortical mantle of cortical structures. LCDM data consist of signed/labeled distances of gray matter (GM) voxels with respect to GM/white matter (WM) surface. Volumes and other summary measures for each subject and the pooled distances can help determine the morphometric differences between diagnostic groups, however they do not reveal all the morphometric information contained in LCDM distances. To extract more information from LCDM data, censoring of the pooled distances is introduced for each diagnostic group where the range of LCDM distances is partitioned at a fixed increment size; and at each censoring step, the distances not exceeding the censoring distance are kept. Censored LCDM distances inherit the advantages of the pooled distances but also provide information about the location of morphometric differences which cannot be obtained from the pooled distances. However, at each step, the censored distances aggregate, which might confound the results. The influence of data aggregation is investigated with an extensive Monte Carlo simulation analysis and it is demonstrated that this influence is negligible. As an illustrative example, GM of ventral medial prefrontal cortices (VMPFCs) of subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy control (Ctrl) subjects are used. A significant reduction in laminar thickness of the VMPFC in MDD and HR subjects is observed compared to Ctrl subjects. Moreover, the GM LCDM distances (i.e., locations with respect to the GM/WM surface) for which these differences start to occur are determined. The methodology is also applicable to LCDM-based morphometric measures of other cortical structures affected by disease.

Deformable medical image registration: a survey

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.

Regionally selective atrophy of subcortical structures in prodromal HD as revealed by statistical shape analysis

Huntington disease (HD) is a neurodegenerative disorder that involves preferential atrophy in the striatal complex and related subcortical nuclei. In this article, which is based on a dataset extracted from the PREDICT-HD study, we use statistical shape analysis with deformation markers obtained through "Large Deformation Diffeomorphic Metric Mapping" of cortical surfaces to highlight specific atrophy patterns in the caudate, putamen, and globus pallidus, at different prodromal stages of the disease. On the basis of the relation to cortico-basal ganglia circuitry, we propose that statistical shape analysis, along with other structural and functional imaging studies, may help expand our understanding of the brain circuitry affected and other aspects of the neurobiology of HD, and also guide the most effective strategies for intervention.

The Singapore flagship programme in translational and clinical research in psychosis

AIM

This paper describes the rationale, aims and development of the Singapore Translational and Clinical Research in Psychosis, which is a 5-year programme.

METHODS

The authors provide a selective review of the pertinent findings from the clinical, neuropsychological, genetics and neuroimaging studies on high-risk population and how they were factored in the hypotheses and design of this translational clinical research programme.

RESULTS

This programme, which draws upon the previous work of various groups and the experience of the investigators of this consortium, comprises three interlinked studies. The first is a genome-wide association and copy number variation analysis using the diagnostic phenotype of schizophrenia and cognitive phenotypes, and a joint genome-wide analysis performed by combining our data with other datasets to increase the power to detect genetic risk factors. The second is a prospective study of a large group of individuals who are assessed to be at ultra-high risk of psychosis, and the third is a randomized controlled trial to improve neurocognition in patients with schizophrenia.

CONCLUSION

The convergence of various factors including the unique structured characteristics of the Singaporean society, the presence of political will with availability of funding and the established research infrastructure make it possible to accrue the sample size for adequate power to elucidate biomarkers of disease risk and resilience.

Topological correction of brain surface meshes using spherical harmonics

Surface reconstruction methods allow advanced analysis of structural and functional brain data beyond what can be achieved using volumetric images alone. Automated generation of cortical surface meshes from 3D brain MRI often leads to topological defects and geometrical artifacts that must be corrected to permit subsequent analysis. Here, we propose a novel method to repair topological defects using a surface reconstruction that relies on spherical harmonics. First, during reparameterization of the surface using a tiled platonic solid, the original MRI intensity values are used as a basis to select either a "fill" or "cut" operation for each topological defect. We modify the spherical map of the uncorrected brain surface mesh, such that certain triangles are favored while searching for the bounding triangle during reparameterization. Then, a low-pass filtered alternative reconstruction based on spherical harmonics is patched into the reconstructed surface in areas that previously contained defects. Self-intersections are repaired using a local smoothing algorithm that limits the number of affected points to less than 0.1% of the total, and as a last step, all modified points are adjusted based on the T1 intensity. We found that the corrected reconstructions have reduced distance error metrics compared with a "gold standard" surface created by averaging 12 scans of the same brain. Ninety-three percent of the topological defects in a set of 10 scans of control subjects were accurately corrected. The entire process takes 6-8 min of computation time. Further improvements are discussed, especially regarding the use of the T1-weighted image to make corrections.

STATISTICAL ANALYSIS OF CORTICAL MORPHOMETRICS USING POOLED DISTANCES BASED ON LABELED CORTICAL DISTANCE MAPS

Neuropsychiatric disorders have been demonstrated to manifest shape differences in cortical structures. Labeled Cortical Distance Mapping (LCDM) is a powerful tool in quantifying such morphometric differences and characterizes the morphometry of the laminar cortical mantle of cortical structures. Specifically, LCDM data are distances of labeled gray matter (GM) voxels with respect to the gray/white matter cortical surface. Volumes and descriptive measures (such as means and variances for each subject) based on LCDM distances provide descriptive summary information on some of the shape characteristics. However, additional morphometrics are contained in the data and their analysis may provide additional clues to underlying differences in cortical characteristics. To use more of this information, we pool (merge) LCDM distances from subjects in the same group. These pooled distances can help detect morphometric differences between groups, but do not provide information about the locations of such differences in the tissue in question. In this article, we check for the influence of the assumption violations on the analysis of pooled LCDM distances. We demonstrate that the classical parametric tests are robust to the non-normality and within sample dependence of LCDM distances and nonparametric tests are robust to within sample dependence of LCDM distances. We specify the types of alternatives for which the tests are more sensitive. We also show that the pooled LCDM distances provide powerful results for group differences in distribution of LCDM distances. As an illustrative example, we use GM in the ventral medial prefrontal cortex (VMPFC) in subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy subjects. Significant morphometric differences were found in VMPFC due to MDD or being at HR. In particular, the analysis indicated that distances in left and right VMPFCs tend to decrease due to MDD or being at HR, possibly as a result of thinning. The methodology can also be applied to other cortical structures.

Regionally specific white matter disruptions of fornix and cingulum in schizophrenia

Limbic circuitry disruptions have been implicated in the psychopathology and cognitive deficits of schizophrenia, which may involve white matter disruptions of the major tracts of the limbic system, including the fornix and the cingulum. Our study aimed to investigate regionally specific abnormalities of the fornix and cingulum in schizophrenia using diffusion tensor imaging (DTI). We determined the fractional anisotropy (FA), radial diffusivity (RD), and axial diffusivity (AD) profiles along the fornix and cingulum tracts using a fibertracking technique and a brain mapping algorithm, the large deformation diffeomorphic metric mapping (LDDMM), in the DTI scans of 33 patients with schizophrenia and 31 age-, gender-, and handedness-matched healthy controls. We found that patients with schizophrenia showed reduction in FA and increase in RD in bilateral fornix, and increase in RD in left anterior cingulum when compared to healthy controls. In addition, tract-based analysis revealed specific loci of these white matter differences in schizophrenia, that is, FA reductions and AD and RD increases occur in the region of the left fornix further from the hippocampus, FA reductions and RD increases occur in the rostral portion of the left anterior cingulum, and RD and AD increases occur in the anterior segment of the left middle cingulum. In patients with schizophrenia, decreased FA in the specific loci of the left fornix and increased AD in the right cingulum adjoining the hippocampus correlated with greater severity of psychotic symptoms. These findings support precise disruptions of limbic-cortical integrity in schizophrenia and disruption of these structural networks may contribute towards the neural basis underlying the syndrome of schizophrenia and clinical symptomatology.

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.

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.

Anatomical abnormalities of the anterior cingulate cortex in schizophrenia: bridging the gap between neuroimaging and neuropathology

The anterior cingulate cortex (ACC) is a functionally heterogeneous region involved in diverse cognitive and emotional processes that support goal-directed behaviour. Structural magnetic resonance imaging (MRI) and neuropathological findings over the past two decades have converged to suggest abnormalities in the region may represent a neurobiological basis for many of the clinical manifestations of schizophrenia. However, while each approach offers complimentary information that can provide clues regarding underlying patholophysiological processes, the findings from these 2 fields are seldom integrated. In this article, we review structural neuroimaging and neuropathological studies of the ACC, focusing on the unique information they provide. The available imaging data suggest grey matter reductions in the ACC precede psychosis onset in some categories of high-risk individuals, show sub-regional specificity, and may progress with illness duration. The available post-mortem findings indicate these imaging-related changes are accompanied by reductions in neuronal, synaptic, and dendritic density, as well as increased afferent input, suggesting the grey matter differences observed with MRI arise from alterations in both neuronal and non-neuronal tissue compartments. We discuss the potential mechanisms that might facilitate integration of these findings and consider strategies for future research.

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.

Feasibility of geometric-intensity-based semi-automated delineation of the tentorium cerebelli from MRI scans

This paper describes a feasibility study of a method for delineating the tentorium cerebelli in magnetic resonance imaging (MRI) brain scans. The tentorium cerebelli is a thin sheet of dura matter covering the cerebellum and separating it from the posterior part of the temporal lobe and the occipital lobe of the cerebral hemispheres. Cortical structures such as the parahippocampal gyrus can be indistinguishable from tentorium in magnetized prepared rapid gradient echo and T1-weighted MRI scans. Similar intensities in these neighboring regions make it difficult to perform accurate cortical analysis in neuroimaging studies of schizophrenia and Alzheimer's disease. A semi-automated, geometric, intensity-based procedure for delineating the tentorium from a whole-brain scan is described. Initial and final curves are traced within the tentorium. A cost function, based on intensity and Euclidean distance, is computed between the two curves using the Fast Marching method. The initial curve is then evolved to the final curve based on the gradient of the computed costs, generating a series of intermediate curves. These curves are then used to generate a triangulated surface of the tentorium. For 3 scans, surfaces were found to be within 2 voxels from hand segmentations.

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.

The emerging discipline of Computational Functional Anatomy

Computational Functional Anatomy (CFA) is the study of functional and physiological response variables in anatomical coordinates. For this we focus on two things: (i) the construction of bijections (via diffeomorphisms) between the coordinatized manifolds of human anatomy, and (ii) the transfer (group action and parallel transport) of functional information into anatomical atlases via these bijections. We review advances in the unification of the bijective comparison of anatomical submanifolds via point-sets including points, curves and surface triangulations as well as dense imagery. We examine the transfer via these bijections of functional response variables into anatomical coordinates via group action on scalars and matrices in DTI as well as parallel transport of metric information across multiple templates which preserves the inner product.

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.

Evolutions equations in computational anatomy

One of the main purposes in computational anatomy is the measurement and statistical study of anatomical variations in organs, notably in the brain or the heart. Over the last decade, our group has progressively developed several approaches for this problem, all related to the Riemannian geometry of groups of diffeomorphisms and the shape spaces on which these groups act. Several important shape evolution equations that are now used routinely in applications have emerged over time. Our goal in this paper is to provide an overview of these equations, placing them in their theoretical context, and giving examples of applications in which they can be used. We introduce the required theoretical background before discussing several classes of equations of increasingly complexity. These equations include energy minimizing evolutions deriving from Riemannian gradient descent, geodesics, parallel transport and Jacobi fields.

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.

Validation of alternating Kernel mixture method: application to tissue segmentation of cortical and subcortical structures

This paper describes the application of the alternating Kernel mixture (AKM) segmentation algorithm to high resolution MRI subvolumes acquired from a 1.5T scanner (hippocampus, n = 10 and prefrontal cortex, n = 9) and a 3T scanner (hippocampus, n = 10 and occipital lobe, n = 10). Segmentation of the subvolumes into cerebrospinal fluid, gray matter, and white matter tissue is validated by comparison with manual segmentation. When compared with other segmentation methods that use traditional Bayesian segmentation, AKM yields smaller errors (P < .005, exact Wilcoxon signed rank test) demonstrating the robustness and wide applicability of AKM across different structures. By generating multiple mixtures for each tissue compartment, AKM mimics the increased variation of manual segmentation in partial volumes due to the highly folded tissues. AKM's superior performance makes it useful for tissue segmentation of subcortical and cortical structures in large-scale neuroimaging studies.

Large Deformation Diffeomorphic Metric Curve Mapping

We present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping (LDDMM) scheme for computing an optimal transformation between two curves embedded in Euclidean space ℝ(d). Curves are first represented as vector-valued measures, which incorporate both location and the first order geometric structure of the curves. Then, a Hilbert space structure is imposed on the measures to build the norm for quantifying the closeness between two curves. We describe a discretized version of this, in which discrete sequences of points along the curve are represented by vector-valued functionals. This gives a convenient and practical way to define a matching functional for curves. We derive and implement the curve matching in the large deformation framework and demonstrate mapping results of curves in ℝ(2) and ℝ(3). Behaviors of the curve mapping are discussed using 2D curves. The applications to shape classification is shown and experiments with 3D curves extracted from brain cortical surfaces are presented.

Intrinsic and extrinsic analysis in computational anatomy

We present intrinsic and extrinsic methods for studying anatomical coordinates in order to perform statistical inference on random physiological signals F across clinical populations. In both intrinsic and extrinsic methods, we introduce generalized partition functions of the coordinates, psi(x), x epsilon M, which are used to construct a random field of F on M as statistical model. In the intrinsic analysis, such partition functions are built intrinsically for individual anatomical coordinate based on Courant's theorem on nodal analysis via self-adjoint linear elliptic differential operators. In contrast, the extrinsic method needs only one set of partition functions for a template coordinate system, and then applies to each anatomical coordinate system via diffeomorphic transformation. For illustration, we apply both intrinsic and extrinsic methods to a clinical study: cortical thickness variation of the left cingulate gyrus in schizophrenia. Both methods show that the left cingulate gyrus tends to become thinner in schizophrenia relative to the healthy control population. However, the intrinsic method increases the statistical power.