Computational anatomy and neuropsychiatric disease: probabilistic assessment of variation and statistical inference of group difference, hemispheric asymmetry, and time-dependent change

Progressive deformation of deep brain nuclei and hippocampal-amygdala formation in schizophrenia

BACKGROUND

Progressive decreases in cortical gray matter volume have been reported in schizophrenia. However, studies of progressive change in deep brain nuclei and hippocampal-amygdala formation have not yielded consistent findings.

METHODS

Two high-resolution, T1-weighted magnetic resonance images were collected 2 years apart in 56 schizophrenia and 62 control subjects. Large-deformation high-dimensional brain mapping was used to generate surfaces for deep brain nuclei and hippocampal-amygdala formation at baseline and follow-up. Repeated-measures analysis of variance was used to test for longitudinal changes in volume and shape.

RESULTS

The pattern of progressive changes in the deep brain nuclei and hippocampal-amygdala formation in schizophrenia and control subjects was variable. Of the structures that receive direct projections from the cortex, the thalamus, caudate nucleus, nucleus accumbens, and hippocampus showed changes specific to subjects with schizophrenia, and changes in the amygdala and putamen were similar in both groups. Although different at baseline, no progressive change was observed in the globus pallidus, which does not receive direct projections from the cortex.

CONCLUSIONS

These findings suggest that the disease process of schizophrenia is associated with progressive effects on brain structure and that brain structures that receive direct, excitatory connections from the cortex may be more likely to show progressive changes, compared with brain structures that receive indirect, inhibitory connections from the cortex. These findings are also somewhat consistent with the hypothesis that overactivity of excitatory pathways in the brain may contribute to the neural degeneration that occurs in at least a subgroup of individuals with schizophrenia.

Automated mapping of hippocampal atrophy in 1-year repeat MRI data from 490 subjects with Alzheimer's disease, mild cognitive impairment, and elderly controls

As one of the earliest structures to degenerate in Alzheimer's disease (AD), the hippocampus is the target of many studies of factors that influence rates of brain degeneration in the elderly. In one of the largest brain mapping studies to date, we mapped the 3D profile of hippocampal degeneration over time in 490 subjects scanned twice with brain MRI over a 1-year interval (980 scans). We examined baseline and 1-year follow-up scans of 97 AD subjects (49 males/48 females), 148 healthy control subjects (75 males/73 females), and 245 subjects with mild cognitive impairment (MCI; 160 males/85 females). We used our previously validated automated segmentation method, based on AdaBoost, to create 3D hippocampal surface models in all 980 scans. Hippocampal volume loss rates increased with worsening diagnosis (normal=0.66%/year; MCI=3.12%/year; AD=5.59%/year), and correlated with both baseline and interval changes in Mini-Mental State Examination (MMSE) scores and global and sum-of-boxes Clinical Dementia Rating scale (CDR) scores. Surface-based statistical maps visualized a selective profile of ongoing atrophy in all three diagnostic groups. Healthy controls carrying the ApoE4 gene atrophied faster than non-carriers, while more educated controls atrophied more slowly; converters from MCI to AD showed faster atrophy than non-converters. Hippocampal loss rates can be rapidly mapped, and they track cognitive decline closely enough to be used as surrogate markers of Alzheimer's disease in drug trials. They also reveal genetically greater atrophy in cognitively intact subjects.

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 a fully automated 3D hippocampal segmentation method using subjects with Alzheimer's disease mild cognitive impairment, and elderly controls

We introduce a new method for brain MRI segmentation, called the auto context model (ACM), to segment the hippocampus automatically in 3D T1-weighted structural brain MRI scans of subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI). In a training phase, our algorithm used 21 hand-labeled segmentations to learn a classification rule for hippocampal versus non-hippocampal regions using a modified AdaBoost method, based on approximately 18,000 features (image intensity, position, image curvatures, image gradients, tissue classification maps of gray/white matter and CSF, and mean, standard deviation, and Haar filters of size 1x1x1 to 7x7x7). We linearly registered all brains to a standard template to devise a basic shape prior to capture the global shape of the hippocampus, defined as the pointwise summation of all the training masks. We also included curvature, gradient, mean, standard deviation, and Haar filters of the shape prior and the tissue classified images as features. During each iteration of ACM - our extension of AdaBoost - the Bayesian posterior distribution of the labeling was fed back in as an input, along with its neighborhood features as new features for AdaBoost to use. In validation studies, we compared our results with hand-labeled segmentations by two experts. Using a leave-one-out approach and standard overlap and distance error metrics, our automated segmentations agreed well with human raters; any differences were comparable to differences between trained human raters. Our error metrics compare favorably with those previously reported for other automated hippocampal segmentations, suggesting the utility of the approach for large-scale studies.

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.

Symmetric abnormalities in sulcal patterning in schizophrenia

To compare the morphology of the cerebral cortex and its characteristic pattern of gyri and sulci in individuals with and without schizophrenia, T1-weighted magnetic resonance scans were collected, along with clinical and cognitive information, from 33 individuals with schizophrenia and 30 healthy individuals group-matched for age, gender, race and parental socioeconomic status. Sulcal depth was measured across the entire cerebral cortex by reconstructing surfaces of cortical mid-thickness (layer 4) in each hemisphere and registering them to the human PALS cortical atlas. Group differences in sulcal depth were tested using methods for cluster size analysis and interhemispheric symmetry analysis. A significant group difference was found bilaterally in the parietal operculum, where the average sulcal depth was shallower in individuals with schizophrenia. In addition, group differences in sulcal depth showed significant bilateral symmetry across much of the occipital, parietal, and temporal cortices. In individuals with schizophrenia, sulcal depth in the left hemisphere was correlated with the severity of impaired performance on tests of working memory and executive function.

Multi-structure network shape analysis via normal surface momentum maps

We present a shape analysis pipeline for the assessment of anatomical variations in subcortical networks in MR images. The shape analysis pipeline injects the global shape properties of the CFA subcortical template into the subcortical parcellations generated from FreeSurfer via large deformation diffeomorphic metric mapping (LDDMM). Examples are shown for this injection in several subcortical structures whose raw MR images were sampled from the database of Open Access Series of Imaging Studies (OASIS). The shape analysis is performed on random field representation of the template surface momentum maps that encode the shape variation of subcortical structure targets of each individual subject relative to the template. The momentum maps have the optimum property that they are supported only on the boundary of the subcortical structures with the direction normal to the subcortical nuclei boundary thereby reducing the dimension of shape variation significantly. A two-level statistical model was built on these momentum maps to assess anatomical connectivity among the subcortical structures on the basis of similar surface deformation (compression or expansion). Results in the study of healthy aging on the hippocampus-amygdala network indicate the anatomical connectivity between the basolateral complex of the amygdala and the subiculum of the hippocampus on the basis of shape compression in healthy elders relative to young adults.

FreeSurfer-initiated fully-automated subcortical brain segmentation in MRI using Large Deformation Diffeomorphic Metric Mapping

Fully-automated brain segmentation methods have not been widely adopted for clinical use because of issues related to reliability, accuracy, and limitations of delineation protocol. By combining the probabilistic-based FreeSurfer (FS) method with the Large Deformation Diffeomorphic Metric Mapping (LDDMM)-based label-propagation method, we are able to increase reliability and accuracy, and allow for flexibility in template choice. Our method uses the automated FreeSurfer subcortical labeling to provide a coarse-to-fine introduction of information in the LDDMM template-based segmentation resulting in a fully-automated subcortical brain segmentation method (FS+LDDMM). One major advantage of the FS+LDDMM-based approach is that the automatically generated segmentations generated are inherently smooth, thus subsequent steps in shape analysis can directly follow without manual post-processing or loss of detail. We have evaluated our new FS+LDDMM method on several databases containing a total of 50 subjects with different pathologies, scan sequences and manual delineation protocols for labeling the basal ganglia, thalamus, and hippocampus. In healthy controls we report Dice overlap measures of 0.81, 0.83, 0.74, 0.86 and 0.75 for the right caudate nucleus, putamen, pallidum, thalamus and hippocampus respectively. We also find statistically significant improvement of accuracy in FS+LDDMM over FreeSurfer for the caudate nucleus and putamen of Huntington's disease and Tourette's syndrome subjects, and the right hippocampus of Schizophrenia subjects.

Open Access Series of Imaging Studies (OASIS): cross-sectional MRI data in young, middle aged, nondemented, and demented older adults

The Open Access Series of Imaging Studies is a series of magnetic resonance imaging data sets that is publicly available for study and analysis. The initial data set consists of a cross-sectional collection of 416 subjects aged 18 to 96 years. One hundred of the included subjects older than 60 years have been clinically diagnosed with very mild to moderate Alzheimer's disease. The subjects are all right-handed and include both men and women. For each subject, three or four individual T1-weighted magnetic resonance imaging scans obtained in single imaging sessions are included. Multiple within-session acquisitions provide extremely high contrast-to-noise ratio, making the data amenable to a wide range of analytic approaches including automated computational analysis. Additionally, a reliability data set is included containing 20 subjects without dementia imaged on a subsequent visit within 90 days of their initial session. Automated calculation of whole-brain volume and estimated total intracranial volume are presented to demonstrate use of the data for measuring differences associated with normal aging and Alzheimer's disease.

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.

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

Spatial normalization is a crucial step in assessing patterns of neuroanatomical structure and function associated with health and disease. Errors that occur during spatial normalization can influence hypothesis testing due to the dimensionalities of mapping algorithms and anatomical manifolds (landmarks, curves, surfaces, volumes) used to drive the mapping algorithms. The primary aim of this paper is to improve statistical inference using multiple anatomical manifolds and large deformation diffeomorphic metric mapping (LDDMM) algorithms. We propose that combining information generated by the various manifolds and algorithms improves the reliability of hypothesis testing. We used this unified approach to assess variation in the thickness of the cingulate gyrus in subjects with schizophrenia and healthy comparison subjects. Three different LDDMM algorithms for mapping landmarks, curves and triangulated meshes were used to transform thickness maps of the cingulate surfaces into an atlas coordinate system. We then tested for group differences by combining the information from the three types of anatomical manifolds and LDDMM mapping algorithms. The unified approach provided reliable statistical results and eliminated ambiguous results due to surface mismatches. Subjects with schizophrenia had non-uniform cortical thinning over the left and right cingulate gyri, especially in the anterior portion, as compared to healthy comparison subjects.

Abnormalities of cingulate gyrus neuroanatomy in schizophrenia

OBJECTIVE AND METHODS

Abnormalities of the neuroanatomy of the gray matter of the cingulate gyrus, especially its anterior segment, have been suggested to be an important characteristic of schizophrenia. In this study, T1-weighted magnetic resonance scans were collected in 53 individuals with schizophrenia and 68 comparison subjects matched for age, gender, race and parental socioeconomic status. We applied Labeled Cortical Mantle Distance Mapping to assess the volume, surface area and thickness of the cortical mantle within the anterior (AC) and posterior (PC) segments of the cingulate gyrus, excluding the paracingulate gyrus, and related these anatomical measures to measures of psychopathology and illness duration.

RESULTS

After covarying for total cerebral volume, individuals with schizophrenia showed smaller AC gray matter volume (p=0.024), thickness (trend, p=0.081), but not surface area (p=0.16), than comparison subjects. Similar group differences were found for PC gray matter volume (p=0.0005) and thickness (trend, p=0.055), but not surface area (p=0.15). Across both groups, there was a significant L>R asymmetry in thickness of the AC, and a significant L>R asymmetry in the surface area of the PC. However, there were no significant group-by-hemisphere interactions. In the individuals with schizophrenia, thinning of the AC, but not the PC, was correlated with a longer duration of illness and a greater severity of psychotic symptoms.

CONCLUSIONS

Individuals with schizophrenia showed smaller gray matter volumes across the entire cingulate gyrus, mostly due to a reduction in cortical mantle thickness. However, structural measures of the AC were more closely related to clinical features of the illness.

Validity of large-deformation high dimensional brain mapping of the basal ganglia in adults with Tourette syndrome

The basal ganglia and thalamus may play a critical role for behavioral inhibition mediated by prefrontal, parietal, temporal, and cingulate cortices. The cortico-basal ganglia-thalamo-cortical loop with projections from frontal cortex to striatum, then to globus pallidus or to substantia nigra pars reticulata, to thalamus and back to cortex, provides the anatomical substrate for this function. In-vivo neuroimaging studies have reported reduced volumes in the thalamus and basal ganglia in individuals with Tourette Syndrome (TS) when compared with healthy controls. However, patterns of neuroanatomical shape that may be associated with these volume differences have not yet been consistently characterized. Tools are being developed at a rapid pace within the emerging field of computational anatomy that allow for the precise analysis of neuroanatomical shape derived from magnetic resonance (MR) images, and give us the ability to characterize subtle abnormalities of brain structures that were previously undetectable. In this study, T1-weighted MR scans were collected in 15 neuroleptic-naïve adults with TS or chronic motor tics and 15 healthy, tic-free adult subjects matched for age, gender and handedness. We demonstrated the validity and reliability of large-deformation high dimensional brain mapping (HDBM-LD) as a tool to characterize the basal ganglia (caudate, globus pallidus and putamen) and thalamus. We found no significant volume or shape differences in any of the structures in this small sample of subjects.

Shape variability of the human striatum—Effects of age and gender

Human striatum is involved in the regulation of movement, reinforcement, learning, reward, cognitive functioning, and addiction. Previous classical volumetric MRI studies have implicated age-, disease- and medication-related changes in striatal structures. Yet, no studies to date have addressed the effects of these factors on the shape variability and local structural alterations in the striatum. The local alterations may provide meaningful additional information in the context of functional neuroanatomy and brain connectivity. We developed image analysis methodology for the measurement of the volume and local shape variability of the human striatum. The method was applied in a group of 43 healthy controls to study the effects of age and gender on striatal shape variability. In the volume analysis, the volume of the striatum was normalized using the volume of the whole brain. In the local shape analysis, the deviations from a mean surface were studied for each surface point using high-dimensional mapping. Also, discriminant functions were constructed from a statistical shape model. The accuracy and reproducibility of the methods used were evaluated. The results confirmed that the volume of the striatum decreases as a function of age. However, the volume decrease was not uniform and age-related shape differences were observed in several subregions of the human striatum whereas no local gender differences were seen. Examination of the variability of striatal shape in the healthy population will pave the way for applying this method in clinical settings. This method will be particularly useful for investigating neuropsychiatric disorders that are associated with subtle morphological alterations of the brain, such as schizophrenia.

Smooth functional and structural maps on the neocortex via orthonormal bases of the Laplace-Beltrami operator

Functional and structural maps, such as a curvature, cortical thickness, and functional magnetic resonance imaging (MRI) maps, indexed over the local coordinates of the cortical manifold play an important role in neuropsychiatric studies. Due to the highly convoluted nature of the cerebral cortex and image quality, these functions are generally uninterpretable without proper methods of association and smoothness onto the local coordinate system. In this paper, we generalized the spline smoothing problem (Wahba, 1990) from a sphere to any arbitrary two-dimensional (2-D) manifold with boundaries. We first seek a numerical solution to orthonormal basis functions of the Laplace-Beltrami (LB) operator with Neumann boundary conditions for a 2-D manifold M then solve the spline smoothing problem in a reproducing kernel Hilbert space (r.k.h.s.) of real-valued functions on manifold M with kernel constructed from the basis functions. The explicit discrete LB representation is derived using the finite element method calculated directly on the manifold coordinates so that finding discrete LB orthonormal basis functions is equivalent to solving an algebraic eigenvalue problem. And then smoothed functions in r.k.h.s can be represented as a linear combination of the basis functions. We demonstrate numerical solutions of spherical harmonics on a unit sphere and brain orthonormal basis functions on a planum temporale manifold. Then synthetic data is used to quantify the goodness of the smoothness compared with the ground truth and discuss how many basis functions should be incorporated in the smoothing. We present applications of our approach to smoothing sulcal mean curvature, cortical thickness, and functional statistical maps on submanifolds of the neocortex.

3D mapping of ventricular and corpus callosum abnormalities in HIV/AIDS

OBJECTIVE

40 million people worldwide are now infected with HIV/AIDS, an illness that often leads to rapidly progressing dementia and death. Even so, little is known about how AIDS affects the brain. Using computational anatomy techniques, we mapped how AIDS impacts the corpus callosum (CC) and ventricular system, two systems that show prominent changes on MRI. We (1) identified regions with greatest differences between AIDS patients and healthy controls and (2) correlated specific 3D patterns of structural differences with measures of immune system deterioration and cognitive decline.

METHODS

51 3D brain MRI scans from 30 non-demented AIDS patients (age: 43.4 years +/- 7.6 SD) and 21 HIV-seronegative controls (age: 39.5 years +/- 12.2) were aligned to ICBM standard space. 3D surface mesh reconstructions of the lateral ventricles and CC were spatially averaged and compared across diagnostic groups. Structural alterations were correlated with viral load, T cell counts, and cognitive impairment.

RESULTS

Statistical maps revealed the 3D profile of ventricular expansion and callosal thinning in AIDS. Specific 3D ventricular changes were linked with immune system decline (CD4+ T cell counts; P < 0.001) and cognitive impairment (P < 0.009), but not viral load. Frontal horn maps distinguished AIDS patients from controls better than occipital and temporal horn measures. T cell decline linked with callosal thinning in anterior regions connecting frontal areas with greatest cortical atrophy.

CONCLUSION

These maps (1) reveal how brain changes in HIV/AIDS relate to immune decline and impaired cognition, and, after further validation and testing, (2) may offer possible neuroimaging markers for anti-viral drug trials, which gauge how well treatments oppose disease progression in the brain.

Computational anatomy: shape, growth, and atrophy comparison via diffeomorphisms

Computational anatomy (CA) is the mathematical study of anatomy I in I = I(alpha) o G, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g in G of anatomical exemplars I(alpha) in I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g in G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(.) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.