Metric optimization for surface analysis in the Laplace-Beltrami embedding space

PLO3S: Protein LOcal Surficial Similarity Screening

The study of protein molecular surfaces enables to better understand and predict protein interactions. Different methods have been developed in computer vision to compare surfaces that can be applied to protein molecular surfaces. The present work proposes a method using the Wave Kernel Signature: Protein LOcal Surficial Similarity Screening (PLO3S). The descriptor of the PLO3S method is a local surface shape descriptor projected on a unit sphere mapped onto a 2D plane and called Surface Wave Interpolated Maps (SWIM). PLO3S allows to rapidly compare protein surface shapes through local comparisons to filter large protein surfaces datasets in protein structures virtual screening protocols.

Preterm Birth Alters the Regional Development and Structural Covariance of Cerebellum at Term-Equivalent Age

Preterm birth is associated with increased risk for a spectrum of neurodevelopmental disabilities. The cerebellum is implicated in a wide range of cognitive functions extending beyond sensorimotor control and plays an increasingly recognized role in brain development. Morphometric studies based on volume analyses have revealed impaired cerebellar development in preterm infants. However, the structural covariance between the cerebellum and cerebral cortex has not been studied during the neonatal period, and the extent to which structural covariance is affected by preterm birth remains unknown. In this study, using the structural MR images of 52 preterm infants scanned at term-equivalent age and 312 full-term controls from the Developing Human Connectome Project, we compared volumetric growth, local cerebellum shape development and cerebello-cerebral structural covariance between the two groups. We found that although there was no significant difference in the overall volume measurements between preterm and full-term infants, the shape measurements were different. Compared with the control infants, preterm infants had significantly larger thickness in the vermis and lower thickness in the lateral portions of the bilateral cerebral hemispheres. The structural covariance between the cerebellum and frontal and parietal lobes was significantly greater in preterm infants than in full-term controls. The findings in this study suggested that cerebellar development and cerebello-cerebral structural covariance may be affected by premature birth.

Morphological changes in the cerebellum during aging: evidence from convolutional neural networks and shape analysis

The morphology and function of the cerebellum are associated with various developmental disorders and healthy aging. Changes in cerebellar morphology during the aging process have been extensively investigated, with most studies focusing on changes in cerebellar regional volume. The volumetric method has been used to quantitatively demonstrate the decrease in the cerebellar volume with age, but it has certain limitations in visually presenting the morphological changes of cerebellar atrophy from a three-dimensional perspective. Thus, we comprehensively described cerebellar morphological changes during aging through volume measurements of subregions and shape analysis. This study included 553 healthy participants aged 20-80 years. A novel cerebellar localized segmentation algorithm based on convolutional neural networks was utilized to analyze the volume of subregions, followed by shape analysis for localized atrophy assessment based on the cerebellar thickness. The results indicated that out of the 28 subregions in the absolute volume of the cerebellum, 15 exhibited significant aging trends, and 16 exhibited significant sex differences. Regarding the analysis of relative volume, only 11 out of the 28 subregions of the cerebellum exhibited significant aging trends, and 4 exhibited significant sex differences. The results of the shape analysis revealed region-specific atrophy of the cerebellum with increasing age. Regions displaying more significant atrophy were predominantly located in the vermis, the lateral portions of bilateral cerebellar hemispheres, lobules I-III, and the medial portions of the posterior lobe. This atrophy differed between sexes. Men exhibited slightly more severe atrophy than women in most of the cerebellar regions. Our study provides a comprehensive perspective for observing cerebellar atrophy during the aging process.

Aging pattern of the brainstem based on volumetric measurement and optimized surface shape analysis

The brainstem, a small and crucial structure, is connected to the cerebrum, spinal cord, and cerebellum, playing a vital role in regulating autonomic functions, transmitting motor and sensory information, and modulating cognitive processes, emotions, and consciousness. While previous research has indicated that changes in brainstem anatomy can serve as a biomarker for aging and neurodegenerative diseases, the structural changes that occur in the brainstem during normal aging remain unclear. This study aimed to examine the age- and sex-related differences in the global and local structural measures of the brainstem in 187 healthy adults (ranging in age from 18 to 70 years) using structural magnetic resonance imaging. The findings showed a significant negative age effect on the volume of the two major components of the brainstem: the medulla oblongata and midbrain. The shape analysis revealed that atrophy primarily occurs in specific structures, such as the pyramid, cerebral peduncle, superior and inferior colliculi. Surface area and shape analysis showed a trend of flattening in the aging brainstem. There were no significant differences between the sexes or sex-by-age interactions in brainstem structural measures. These findings provide a systematic description of age associations with brainstem structures in healthy adults and may provide a reference for future research on brain aging and neurodegenerative diseases.

Morphological development of the human fetal striatum during the second trimester

The morphological development of the fetal striatum during the second trimester has remained poorly described. We manually segmented the striatum using 7.0-T MR images of the fetal specimens ranging from 14 to 22 gestational weeks. The global development of the striatum was evaluated by volume measurement. The absolute volume (Vabs) of the caudate nucleus (CN) increased linearly with gestational age, while the relative volume (Vrel) showed a quadratic growth. Both Vabs and Vrel of putamen increased linearly. Through shape analysis, the changes of local structure in developing striatum were specifically demonstrated. Except for the CN tail, the lateral and medial parts of the CN grew faster than the middle regions, with a clear rostral-caudal growth gradient as well as a distinct "outside-in" growth gradient. For putamen, the dorsal and ventral regions grew obviously faster than the other regions, with a dorsal-ventral bidirectional developmental pattern. The right CN was larger than the left, whereas there was no significant hemispheric asymmetry in the putamen. By establishing the developmental trajectories, spatial heterochrony, and hemispheric dimorphism of human fetal striatum, these data bring new insight into the fetal striatum development and provide detailed anatomical references for future striatal studies.

G-RMOS: GPU-accelerated Riemannian Metric Optimization on Surfaces

Surface mapping is used in various brain imaging studies, such as for mapping gray matter atrophy patterns in Alzheimer's disease. Riemannian metrics on surface (RMOS) is a state-of-the-art surface mapping algorithm that optimizes Riemannian metrics to establish one-to-one correspondences between surfaces in the Laplace-Beltrami embedding space. However, owing to the complex calculation with accurate one-to-one correspondences, RMOS registration takes a long time. In this study, we propose G-RMOS, a graphics processing unit (GPU)-accelerated RMOS registration pipeline that uses three GPU kernel design strategies: 1. using GPU computing capability with a batch scheme; 2. using the cache in the GPU block to minimize memory latency in register and shared memory; and 3. maximizing the effective number of instructions per GPU cycle using instruction level parallelism. Using the experimental results, we compare the acceleration speed of the G-RMOS framework with that of RMOS using hippocampus and cortical surfaces, and show that G-RMOS achieves a significant speedup in surface mapping. We also compare the memory requirements for cortical surface mapping and show that G-RMOS uses less memory than RMOS.

Shape analysis of subcortical structures in obsessive-compulsive disorder and the relationship with comorbid anxiety, depression, and medication use: A meta-analysis by the OCD Brain Imaging Consortium

OBJECTIVE

Neuroimaging studies of obsessive-compulsive disorder (OCD) patients have highlighted the important role of deep gray matter structures. Less work has however focused on subcortical shape in OCD patients.

METHODS

Here we pooled brain MRI scans from 412 OCD patients and 368 controls to perform a meta-analysis utilizing the ENIGMA-Shape protocol. In addition, we investigated modulating effects of medication status, comorbid anxiety or depression, and disease duration on subcortical shape.

RESULTS

There was no significant difference in shape thickness or surface area between OCD patients and healthy controls. For the subgroup analyses, OCD patients with comorbid depression or anxiety had lower thickness of the hippocampus and caudate nucleus and higher thickness of the putamen and pallidum compared to controls. OCD patients with comorbid depression had lower shape surface area in the thalamus, caudate nucleus, putamen, hippocampus, and nucleus accumbens and higher shape surface area in the pallidum. OCD patients with comorbid anxiety had lower shape surface area in the putamen and the left caudate nucleus and higher shape surface area in the pallidum and the right caudate nucleus. Further, OCD patients on medication had lower shape thickness of the putamen, thalamus, and hippocampus and higher thickness of the pallidum and caudate nucleus, as well as lower shape surface area in the hippocampus and amygdala and higher surface area in the putamen, pallidum, and caudate nucleus compared to controls. There were no significant differences between OCD patients without co-morbid anxiety and/or depression and healthy controls on shape measures. In addition, there were also no significant differences between OCD patients not using medication and healthy controls.

CONCLUSIONS

The findings here are partly consistent with prior work on brain volumes in OCD, insofar as they emphasize that alterations in subcortical brain morphology are associated with comorbidity and medication status. Further work is needed to understand the biological processes contributing to subcortical shape.

Hippocampal Asymmetry of Regional Development and Structural Covariance in Preterm Neonates

Premature birth is associated with a high prevalence of neurodevelopmental impairments in surviving infants. The hippocampus is known to be critical for learning and memory, yet the putative effects of hippocampal dysfunction remain poorly understood in preterm neonates. In particular, while asymmetry of the hippocampus has been well noted both structurally and functionally, how preterm birth impairs hippocampal development and to what extent the hippocampus is asymmetrically impaired by preterm birth have not been well delineated. In this study, we compared volumetric growth and shape development in the hippocampal hemispheres and structural covariance (SC) between hippocampal vertices and cortical thickness in cerebral cortex regions between two groups. We found that premature infants had smaller volumes of the right hippocampi only. Lower thickness was observed in the hippocampal head in both hemispheres for preterm neonates compared with full-term peers, though preterm neonates exhibited an accelerated age-related change of hippocampal thickness in the left hippocampi. The SC between the left hippocampi and the limbic lobe of the premature infants was severely impaired compared with the term-born neonates. These findings suggested that the development of the hippocampus during the third trimester may be altered following early extrauterine exposure with a high degree of asymmetry.

Tetrahedral spectral feature-Based bayesian manifold learning for grey matter morphometry: Findings from the Alzheimer's disease neuroimaging initiative

Structural and anatomical analyses of magnetic resonance imaging (MRI) data often require a reconstruction of the three-dimensional anatomy to a statistical shape model. Our prior work demonstrated the usefulness of tetrahedral spectral features for grey matter morphometry. However, most of the current methods provide a large number of descriptive shape features, but lack an unsupervised scheme to automatically extract a concise set of features with clear biological interpretations and that also carries strong statistical power. Here we introduce a new tetrahedral spectral feature-based Bayesian manifold learning framework for effective statistical analysis of grey matter morphology. We start by solving the technical issue of generating tetrahedral meshes which preserve the details of the grey matter geometry. We then derive explicit weak-form tetrahedral discretizations of the Hamiltonian operator (HO) and the Laplace-Beltrami operator (LBO). Next, the Schrödinger's equation is solved for constructing the scale-invariant wave kernel signature (SIWKS) as the shape descriptor. By solving the heat equation and utilizing the SIWKS, we design a morphometric Gaussian process (M-GP) regression framework and an active learning strategy to select landmarks as concrete shape descriptors. We evaluate the proposed system on publicly available data from the Alzheimers Disease Neuroimaging Initiative (ADNI), using subjects structural MRI covering the range from cognitively unimpaired (CU) to full blown Alzheimer's disease (AD). Our analyses suggest that the SIWKS and M-GP compare favorably with seven other baseline algorithms to obtain grey matter morphometry-based diagnoses. Our work may inspire more tetrahedral spectral feature-based Bayesian learning research in medical image analysis.

Selective morphological and volumetric alterations in the hippocampus of children exposed in utero to gestational diabetes mellitus

Prior epidemiological studies have found that in utero exposure to gestational diabetes mellitus (GDM) is associated with increased risk for neurodevelopmental disorders. However, brain alterations associated with GDM are not known. The hippocampus is pivotal for cognition and emotional regulation. Therefore, we assessed relationships between in utero exposure to GDM and hippocampal morphology and subfield structure during childhood. One hundred seventeen children aged 7–11 years (57% girls, 57% exposed to GDM), born at Kaiser Permanente Southern California, participated in the BrainChild Study. Maternal GDM status was determined from electronic medical records. Children underwent brain magnetic resonance imaging. Freesurfer 6.0 was used to measure hippocampal and individual hippocampal subfield gray matter volume (mm³). Morphological analyses on the hippocampal surface were carried out using shape analysis. GDM‐exposed children exhibited reduced radial thickness in a small, spatially‐restricted portion of the left inferior body of the hippocampus that corresponds to the CA1 subfield. There was a significant interaction between GDM‐exposure and sex on the right hippocampal CA1 subfield. GDM‐exposed boys had reduced right CA1 volume compared to unexposed boys, but this association was no longer significant after controlling for age. No significant group differences were observed in girls. Our results suggest that GDM‐exposure impacts shape of the left hippocampal CA1 subfield in both boys and girls and may reduce volume of right hippocampal CA1 only in boys. These in‐depth findings illuminate the unique properties of the hippocampus impacted by prenatal GDM‐exposure and could have important implications for hippocampal‐related functions.

The effect of body mass index on hippocampal morphology and memory performance in late childhood and adolescence

Childhood obesity is associated with negative physiological and cognitive health outcomes. The hippocampus is a diverse subcortical structure involved in learned feeding behaviors and energy regulation, and research has shown that the hippocampus is vulnerable to the effects of excess adiposity. Previous studies have demonstrated reduced hippocampal volume in overweight and obese children; however, it is unclear if certain subregions are selectively affected. The purpose of this study was to determine how excess body weight influences regional hippocampal surface morphology and memory performance in a large cross-sectional cohort of 588 children and adolescents between 8.33 and 19.92 years of age using body mass index expressed as a percentage of the 95th percentile cutoff (%BMIp95). We demonstrate %BMIp95 is associated with reduced radial thickness in the superior anterior region of the left hippocampus, and this relationship is predominantly driven by children younger than 14 years. We also found %BMIp95 was associated with worse performance on a spatial episodic memory task and this relationship was partially mediated by the radial thickness of the significant shape cluster. These results demonstrate the differential influence of excess body weight on regional hippocampal structure and hippocampal-dependent behavior in children and adolescents.

Longitudinal changes in blood-based biomarkers in chronic moderate to severe traumatic brain injury: preliminary findings

Objectives: This longitudinal study aims at 1) providing preliminary evidence of changes in blood-based biomarkers across time in chronic TBI and 2) relating these changes to outcome measures and cerebral structure and activity.Methods: Eight patients with moderate-to-severe TBI (7 males, 35 ± 7.6 years old, 5 severe TBI, 17.52 ± 3.84 months post-injury) were evaluated at monthly intervals across 6 time-points using: a) Blood-based biomarkers (GFAP, NSE, S100A12, SDBP145, UCH-L1, T-tau, P-tau, P-tau/T-tau ratio); b) Magnetic Resonance Imaging to evaluate changes in brain structure; c) Resting-state electroencephalograms to evaluate changes in brain function; and d) Outcome measures to assess cognition, emotion, and functional recovery (MOCA, RBANS, BDI-II, and DRS).Results: Changes in P-tau levels were found across time [p = .007]. P-tau was positively related to functional [p < .001] and cognitive [p = .006] outcomes, and negatively related to the severity of depression, 6 months later [R = -0.901; p =.006]. P-tau and P-tau/T-tau ratio were also positively correlated to shape change in subcortical areas such as brainstem [T(7) = 4.71, p = .008] and putamen [T(7) = 3.25, p = .012].Conclusions: Our study provides preliminary findings that suggest a positive relationship between P-tau and the recovery of patients with chronic TBI.

Surface Registration with Eigenvalues and Eigenvectors

This paper presents a novel surface registration technique using the spectrum of the shapes, which can facilitate accurate localization and visualization of non-isometric deformations of the surfaces. In order to register two surfaces, we map both eigenvalues and eigenvectors of the Laplace-Beltrami of the shapes through optimizing an energy function. The function is defined by the integration of a smoothness term to align the eigenvalues and a distance term between the eigenvectors at feature points to align the eigenvectors. The feature points are generated using the static points of certain eigenvectors of the surfaces. By using both the eigenvalues and the eigenvectors on these feature points, the computational efficiency is improved considerably without losing the accuracy in comparison to the approaches that use the eigenvectors for all vertices. In our technique, the variation of the shape is expressed using a scale function defined at each vertex. Consequently, the total energy function to align the two given surfaces can be defined using the linear interpolation of the scale function derivatives. Through the optimization of the energy function, the scale function can be solved and the alignment is achieved. After the alignment, the eigenvectors can be employed to calculate the point-to-point correspondence of the surfaces. Therefore, the proposed method can accurately define the displacement of the vertices. We evaluate our method by conducting experiments on synthetic and real data using hippocampus, heart, and hand models. We also compare our method with non-rigid Iterative Closest Point (ICP) and a similar spectrum-based methods. These experiments demonstrate the advantages and accuracy of our method.

Hippocampal Shape Maturation in Childhood and Adolescence

The hippocampus is a subcortical structure critical for learning and memory, and a thorough understanding of its neurodevelopment is important for studying these processes in health and disease. However, few studies have quantified the typical developmental trajectory of the structure in childhood and adolescence. This study examined the cross-sectional age-related changes and sex differences in hippocampal shape in a multisite, multistudy cohort of 1676 typically developing children (age 1-22 years) using a novel intrinsic brain mapping method based on Laplace-Beltrami embedding of surfaces. Significant age-related expansion was observed bilaterally and nonlinear growth was observed primarily in the right head and tail of the hippocampus. Sex differences were also observed bilaterally along the lateral and medial aspects of the surface, with females exhibiting relatively larger surface expansion than males. Additionally, the superior posterior lateral surface of the left hippocampus exhibited an age-sex interaction with females expanding faster than males. Shape analysis provides enhanced sensitivity to regional changes in hippocampal morphology over traditional volumetric approaches and allows for the localization of developmental effects. Our results further support evidence that hippocampal structures follow distinct maturational trajectories that may coincide with the development of learning and memory skills during critical periods of development.

3D Shape Modeling and Analysis of Retinal Microvasculature in OCT-Angiography Images

3D optical coherence tomography angiography (OCT-A) is a novel and non-invasive imaging modality for analyzing retinal diseases. The studies of microvasculature in 2D en face projection images have been widely implemented, but comprehensive 3D analysis of OCT-A images with rich depth-resolved microvascular information is rarely considered. In this paper, we propose a robust, effective, and automatic 3D shape modeling framework to provide a high-quality 3D vessel representation and to preserve valuable 3D geometric and topological information for vessel analysis. Effective vessel enhancement and extraction steps by means of curvelet denoising and optimally oriented flux (OOF) filtering are first designed to produce 3D microvascular networks. Afterwards, a novel 3D data representation of OCT-A microvasculature is reconstructed via advanced mesh reconstruction techniques. Based on the 3D surfaces, shape analysis is established to extract novel shape-based microvascular area distortion via the Laplace-Beltrami eigen-projection. The extracted feature is integrated into a graph-cut segmentation system to categorize large vessels and small capillaries for more precise shape analysis. The proposed framework is validated on a dedicated repeated scan dataset including 260 volume images and shows high repeatability. Statistical analysis using the surface area biomarker is performed on small capillaries to avoid the effect of tailing artifact from large vessels. It shows significant differences ( ) between DR stages on 100 subjects in a OCTA-DR dataset. The proposed shape modeling and analysis framework opens the possibility for further investigating OCT-A microvasculature in a new perspective.

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.

3-D Shape Matching and Non-Rigid Correspondence for Hippocampi Based on Markov Random Fields

The purpose of this paper is to recover dense correspondence between non-rigid shapes for anatomical objects, which is a key element of disease diagnosis and analysis. We proposed a shape matching framework based on Markov random fields to obtain non-rigid correspondence. We constructed an energy function by summing up two terms where one was a unary term and the other was a binary term. By using this formulation, shape matching was represented as an energy function minimisation problem. Loopy belief propagation (LBP) was then used to minimize the energy function. We adopted a new sparse update technique for LBP update to increase computational efficiency. At the same time, we also proposed to use a novel clamping technique, an expectation-maximization (EM) like approach, to enhance matching accuracy. Experiments with the hippocampal data from OASIS and PATH showed that the sparse update was 160 times faster than standard BP. By iteratively running the EM-like clamping procedure, we were able to obtain high quality non-rigid correspondence results to achieve 97% matching rate between two hippocampi. Our shape matching based approach overcomes the flip problem of first-order ellipsoid and does not assume pre-alignment unlike iterative closest point.

Holistic Mapping of Striatum Surfaces in the Laplace-Beltrami Embedding Space

In brain shape analysis, the striatum is typically divided into three parts: the caudate, putamen, and accumbens nuclei for its analysis. Recent connectivity and animal studies, however, indicate striatum-cortical inter-connections do not always follow such subdivisions. For the holistic mapping of striatum surfaces, conventional spherical registration techniques are not suitable due to the large metric distortions in spherical parameterization of striatal surfaces. To overcome this difficulty, we develop a novel striatal surface mapping method using the recently proposed Riemannian metric optimization techniques in the Laplace-Beltrami (LB) embedding space. For the robust resolution of sign ambiguities in the LB spectrum, we also devise novel anatomical contextual features to guide the surface mapping in the embedding space. In our experimental results, we compare with spherical registration tools from FreeSurfer and FSL to demonstrate that our novel method provides a superior solution to the striatal mapping problem. We also apply our method to map the striatal surfaces from 211 subjects of the Human Connectome Project (HCP), and use the surface maps to construct a cortical connectivity atlas. Our atlas results show that the striato-cortical connectivity is not distinctive according to traditional structural subdivision of the striatum, and further confirms the holistic approach for mapping striatal surfaces.

Connectome imaging for mapping human brain pathways

With the fast advance of connectome imaging techniques, we have the opportunity of mapping the human brain pathways in vivo at unprecedented resolution. In this article we review the current developments of diffusion magnetic resonance imaging (MRI) for the reconstruction of anatomical pathways in connectome studies. We first introduce the background of diffusion MRI with an emphasis on the technical advances and challenges in state-of-the-art multi-shell acquisition schemes used in the Human Connectome Project. Characterization of the microstructural environment in the human brain is discussed from the tensor model to the general fiber orientation distribution (FOD) models that can resolve crossing fibers in each voxel of the image. Using FOD-based tractography, we describe novel methods for fiber bundle reconstruction and graph-based connectivity analysis. Building upon these novel developments, there have already been successful applications of connectome imaging techniques in reconstructing challenging brain pathways. Examples including retinofugal and brainstem pathways will be reviewed. Finally, we discuss future directions in connectome imaging and its interaction with other aspects of brain imaging research.

eCurves: A Temporal Shape Encoding

OBJECTIVE

This paper presents a framework for temporal shape analysis to capture the shape and changes of anatomical structures from three-dimensional+t(ime) medical scans.

METHOD

We first encode the shape of a structure at each time point with the spectral signature, i.e., the eigenvalues and eigenfunctions of the Laplace operator. We then expand it to capture morphing shapes by tracking the eigenmodes across time according to the similarity of their eigenfunctions. The similarity metric is motivated by the fact that small-shaped deformations lead to minor changes in the eigenfunctions. Following each eigenmode from the beginning to end results in a set of eigenmode curves representing the shape and its changes over time.

RESULTS

We apply our encoding to a cardiac dataset consisting of series of segmentations outlining the right and left ventricles over time. We measure the accuracy of our encoding by training classifiers on discriminating healthy adults from patients that received reconstructive surgery for Tetralogy of Fallot (TOF). The classifiers based on our encoding significantly surpass deformation-based encodings of the right ventricle, the structure most impacted by TOF.

CONCLUSION

The strength of our framework lies in its simplicity: It only assumes pose invariance within a time series but does not assume point-to-point correspondence across time series or a (statistical or physical) model. In addition, it is easy to implement and only depends on a single parameter, i.e., the number of curves.

Towards a Holistic Cortical Thickness Descriptor: Heat Kernel-Based Grey Matter Morphology Signatures

In this paper, we propose a heat kernel based regional shape descriptor that may be capable of better exploiting volumetric morphological information than other available methods, thereby improving statistical power on brain magnetic resonance imaging (MRI) analysis. The mechanism of our analysis is driven by the graph spectrum and the heat kernel theory, to capture the volumetric geometry information in the constructed tetrahedral meshes. In order to capture profound brain grey matter shape changes, we first use the volumetric Laplace-Beltrami operator to determine the point pair correspondence between white-grey matter and CSF-grey matter boundary surfaces by computing the streamlines in a tetrahedral mesh. Secondly, we propose multi-scale grey matter morphology signatures to describe the transition probability by random walk between the point pairs, which reflects the inherent geometric characteristics. Thirdly, a point distribution model is applied to reduce the dimensionality of the grey matter morphology signatures and generate the internal structure features. With the sparse linear discriminant analysis, we select a concise morphology feature set with improved classification accuracies. In our experiments, the proposed work outperformed the cortical thickness features computed by FreeSurfer software in the classification of Alzheimer's disease and its prodromal stage, i.e., mild cognitive impairment, on publicly available data from the Alzheimer's Disease Neuroimaging Initiative. The multi-scale and physics based volumetric structure feature may bring stronger statistical power than some traditional methods for MRI-based grey matter morphology analysis.

Visualizing Shape Deformations with Variation of Geometric Spectrum

This paper presents a novel approach based on spectral geometry to quantify and visualize non-isometric deformations of 3D surfaces by mapping two manifolds. The proposed method can determine multi-scale, non-isometric deformations through the variation of Laplace-Beltrami spectrum of two shapes. Given two triangle meshes, the spectra can be varied from one to another with a scale function defined on each vertex. The variation is expressed as a linear interpolation of eigenvalues of the two shapes. In each iteration step, a quadratic programming problem is constructed, based on our derived spectrum variation theorem and smoothness energy constraint, to compute the spectrum variation. The derivation of the scale function is the solution of such a problem. Therefore, the final scale function can be solved by integral of the derivation from each step, which, in turn, quantitatively describes non-isometric deformations between two shapes. To evaluate the method, we conduct extensive experiments on synthetic and real data. We employ real epilepsy patient imaging data to quantify the shape variation between the left and right hippocampi in epileptic brains. In addition, we use longitudinal Alzheimer data to compare the shape deformation of diseased and healthy hippocampus. In order to show the accuracy and effectiveness of the proposed method, we also compare it with spatial registration-based methods, e.g., non-rigid Iterative Closest Point (ICP) and voxel-based method. These experiments demonstrate the advantages of our method.

Heritability of the shape of subcortical brain structures in the general population

The volumes of subcortical brain structures are highly heritable, but genetic underpinnings of their shape remain relatively obscure. Here we determine the relative contribution of genetic factors to individual variation in the shape of seven bilateral subcortical structures: the nucleus accumbens, amygdala, caudate, hippocampus, pallidum, putamen and thalamus. In 3,686 unrelated individuals aged between 45 and 98 years, brain magnetic resonance imaging and genotyping was performed. The maximal heritability of shape varies from 32.7 to 53.3% across the subcortical structures. Genetic contributions to shape extend beyond influences on intracranial volume and the gross volume of the respective structure. The regional variance in heritability was related to the reliability of the measurements, but could not be accounted for by technical factors only. These findings could be replicated in an independent sample of 1,040 twins. Differences in genetic contributions within a single region reveal the value of refined brain maps to appreciate the genetic complexity of brain structures.

Riemannian Metric Optimization for Connectivity-driven Surface Mapping

With the advance of human connectome research, there are great interests in computing diffeomorphic maps of brain surfaces with rich connectivity features. In this paper, we propose a novel framework for connectivity-driven surface mapping based on Riemannian metric optimization on surfaces (RMOS) in the Laplace-Beltrami (LB) embedding space. The mathematical foundation of our method is that we can use the pullback metric to define an isometry between surfaces for an arbitrary diffeomorphism, which in turn results in identical LB embeddings from the two surfaces. For connectivity-driven surface mapping, our goal is to compute a diffeomorphism that can match a set of connectivity features defined over anatomical surfaces. The proposed RMOS approach achieves this goal by iteratively optimizing the Riemannian metric on surfaces to match the connectivity features in the LB embedding space. At the core of our framework is an optimization approach that converts the cost function of connectivity features into a distance measure in the LB embedding space, and optimizes it using gradients of the LB eigen-system with respect to the Riemannian metric. We demonstrate our method on the mapping of thalamic surfaces according to connectivity to ten cortical regions, which we compute with the multi-shell diffusion imaging data from the Human Connectome Project (HCP). Comparisons with a state-of-the-art method show that the RMOS method can more effectively match anatomical features and detect thalamic atrophy due to normal aging.

Cortical folding of the preterm brain: a longitudinal analysis of extremely preterm born neonates using spectral matching

INTRODUCTION

Infants born extremely preterm (<28 weeks of gestation) are at risk of significant neurodevelopmental sequelae. In these infants birth coincides with a period of rapid brain growth and development, when the brain is also vulnerable to a range of insults. Mapping these changes is crucial for identifying potential biomarkers to predict early impairment.

METHODS

In this study we use surface-based spectral matching techniques to find an intrasubject longitudinal surface correspondence between the white-grey matter boundary at 30 and 40 weeks equivalent gestational age in nine extremely preterm born infants.

RESULTS

Using the resulting surface correspondence, we identified regions that undergo more cortical folding of the white-grey matter boundary during the preterm period by looking at changes in well-known curvature measures. We performed Hotelling T(2) statistics to evaluate the significance of our findings.

DISCUSSION

The prefrontal and temporal lobes exhibit most development during the preterm period, especially in the left hemisphere. Such correspondences are a promising result as longitudinal measurements of change in cortical folding could provide insightful information about the mechanical properties of the underlying tissue and may be useful in inferring changes during growth and development in this vulnerable period.

Fiber Orientation and Compartment Parameter Estimation From Multi-Shell Diffusion Imaging

Diffusion MRI offers the unique opportunity of assessing the structural connections of human brains in vivo. With the advance of diffusion MRI technology, multi-shell imaging methods are becoming increasingly practical for large scale studies and clinical application. In this work, we propose a novel method for the analysis of multi-shell diffusion imaging data by incorporating compartment models into a spherical deconvolution framework for fiber orientation distribution (FOD) reconstruction. For numerical implementation, we develop an adaptively constrained energy minimization approach to efficiently compute the solution. On simulated and real data from Human Connectome Project (HCP), we show that our method not only reconstructs sharp and clean FODs for the modeling of fiber crossings, but also generates reliable estimation of compartment parameters with great potential for clinical research of neurological diseases. In comparisons with publicly available DSI-Studio and BEDPOSTX of FSL, we demonstrate that our method reconstructs sharper FODs with more precise estimation of fiber directions. By applying probabilistic tractography to the FODs computed by our method, we show that more complete reconstruction of the corpus callosum bundle can be achieved. On a clinical, two-shell diffusion imaging data, we also demonstrate the feasibility of our method in analyzing white matter lesions.

Development of the human fetal hippocampal formation during early second trimester

Development of the fetal hippocampal formation has been difficult to fully describe because of rapid changes in its shape during the fetal period. The aims of this study were to: (1) segment the fetal hippocampal formation using 7.0 T MR images from 41 specimens with gestational ages ranging from 14 to 22 weeks and (2) reveal the developmental course of the fetal hippocampal formation using volume and shape analyses. Differences in hemispheric volume were observed, with the right hippocampi being larger than the left. Absolute volume changes showed a linear increase, while relative volume changes demonstrated an inverted-U shape trend during this period. Together these exhibited a variable developmental rate among different regions of the fetal brain. Different sub-regional growth of the fetal hippocampal formation was specifically observed using shape analysis. The fetal hippocampal formation possessed a prominent medial-lateral bidirectional shape growth pattern during its rotation process. Our results provide additional insight into 3D hippocampal morphology in the assessment of fetal brain development and can be used as a reference for future hippocampal studies.

Medial Demons Registration Localizes The Degree of Genetic Influence Over Subcortical Shape Variability: An N= 1480 Meta-Analysis

We present a multi-cohort shape heritability study, extending the fast spherical demons registration to subcortical shapes via medial modeling. A multi-channel demons registration based on vector spherical harmonics is applied to medial and curvature features, while controlling for metric distortion. We registered and compared seven subcortical structures of 1480 twins and siblings from the Queensland Twin Imaging Study and Human Connectome Project: Thalamus, Caudate, Putamen, Pallidum, Hippocampus, Amygdala, and Nucleus Accumbens. Radial distance and tensor-based morphometry (TBM) features were found to be highly heritable throughout the entire basal ganglia and limbic system. Surface maps reveal subtle variation in heritability across functionally distinct parts of each structure. Medial Demons reveals more significantly heritable regions than two previously described surface registration methods. This approach may help to prioritize features and measures for genome-wide association studies.

A Riemannian Framework for Intrinsic Comparison of Closed Genus-Zero Shapes

We present a framework for intrinsic comparison of surface metric structures and curvatures. This work parallels the work of Kurtek et al. on parameterization-invariant comparison of genus zero shapes. Here, instead of comparing the embedding of spherically parameterized surfaces in space, we focus on the first fundamental form. To ensure that the distance on spherical metric tensor fields is invariant to parameterization, we apply the conjugation-invariant metric arising from the L2 norm on symmetric positive definite matrices. As a reparameterization changes the metric tensor by a congruent Jacobian transform, this metric perfectly suits our purpose. The result is an intrinsic comparison of shape metric structure that does not depend on the specifics of a spherical mapping. Further, when restricted to tensors of fixed volume form, the manifold of metric tensor fields and its quotient of the group of unitary diffeomorphisms becomes a proper metric manifold that is geodesically complete. Exploiting this fact, and augmenting the metric with analogous metrics on curvatures, we derive a complete Riemannian framework for shape comparison and reconstruction. A by-product of our framework is a near-isometric and curvature-preserving mapping between surfaces. The correspondence is optimized using the fast spherical fluid algorithm. We validate our framework using several subcortical boundary surface models from the ADNI dataset.