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

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.

Personalized Patch-based Normality Assessment of Brain Atrophy in Alzheimer's Disease

Cortical thickness is an important biomarker associated with gray matter atrophy in neurodegenerative diseases. In order to conduct meaningful comparisons of cortical thickness between different subjects, it is imperative to establish correspondence among surface meshes. Conventional methods achieve this by projecting surface onto canonical domains such as the unit sphere or averaging feature values in anatomical regions of interest (ROIs). However, due to the natural variability in cortical topography, perfect anatomically meaningful one-to-one mapping can be hardly achieved and the practice of averaging leads to the loss of detailed information. For example, two subjects may have different number of gyral structures in the same region, and thus mapping can result in gyral/sulcal mismatch which introduces noise and averaging in detailed local information loss. Therefore, it is necessary to develop new method that can overcome these intrinsic problems to construct more meaningful comparison for atrophy detection. To address these limitations, we propose a novel personalized patch-based method to improve cortical thickness comparison across subjects. Our model segments the brain surface into patches based on gyral and sulcal structures to reduce mismatches in mapping method while still preserving detailed topological information which is potentially discarded in averaging. Moreover,the personalized templates for each patch account for the variability of folding patterns, as not all subjects are comparable. Finally, through normality assessment experiments, we demonstrate that our model performs better than standard spherical registration in detecting atrophy in patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD).

Hierarchical particle optimization for cortical shape correspondence in temporal lobe resection

BACKGROUND

Anterior temporal lobe resection is an effective treatment for temporal lobe epilepsy. The post-surgical structural changes could influence the follow-up treatment. Capturing post-surgical changes necessitates a well-established cortical shape correspondence between pre- and post-surgical surfaces. Yet, most cortical surface registration methods are designed for normal neuroanatomy. Surgical changes can introduce wide ranging artifacts in correspondence, for which conventional surface registration methods may not work as intended.

METHODS

In this paper, we propose a novel particle method for one-to-one dense shape correspondence between pre- and post-surgical surfaces with temporal lobe resection. The proposed method can handle partial structural abnormality involving non-rigid changes. Unlike existing particle methods using implicit particle adjacency, we consider explicit particle adjacency to establish a smooth correspondence. Moreover, we propose hierarchical optimization of particles rather than full optimization of all particles at once to avoid trappings of locally optimal particle update.

RESULTS

We evaluate the proposed method on 25 pairs of T1-MRI with pre- and post-simulated resection on the anterior temporal lobe and 25 pairs of patients with actual resection. We show improved accuracy over several cortical regions in terms of ROI boundary Hausdorff distance with 4.29 mm and Dice similarity coefficients with average value 0.841, compared to existing surface registration methods on simulated data. In 25 patients with actual resection of the anterior temporal lobe, our method shows an improved shape correspondence in qualitative and quantitative evaluation on parcellation-off ratio with average value 0.061 and cortical thickness changes. We also show better smoothness of the correspondence without self-intersection, compared with point-wise matching methods which show various degrees of self-intersection.

CONCLUSION

The proposed method establishes a promising one-to-one dense shape correspondence for temporal lobe resection. The resulting correspondence is smooth without self-intersection. The proposed hierarchical optimization strategy could accelerate optimization and improve the optimization accuracy. According to the results on the paired surfaces with temporal lobe resection, the proposed method outperforms the compared methods and is more reliable to capture cortical thickness changes.

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.

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.

Labeling lateral prefrontal sulci using spherical data augmentation and context-aware training

The inference of cortical sulcal labels often focuses on deep (primary and secondary) sulcal regions, whereas shallow (tertiary) sulcal regions are largely overlooked in the literature due to the scarcity of manual/well-defined annotations and their large neuroanatomical variability. In this paper, we present an automated framework for regional labeling of both primary/secondary and tertiary sulci of the dorsal portion of lateral prefrontal cortex (LPFC) using spherical convolutional neural networks. We propose two core components that enhance the inference of sulcal labels to overcome such large neuroanatomical variability: (1) surface data augmentation and (2) context-aware training. (1) To take into account neuroanatomical variability, we synthesize training data from the proposed feature space that embeds intermediate deformation trajectories of spherical data in a rigid to non-rigid fashion, which bridges an augmentation gap in conventional rotation data augmentation. (2) Moreover, we design a two-stage training process to improve labeling accuracy of tertiary sulci by informing the biological associations in neuroanatomy: inference of primary/secondary sulci and then their spatial likelihood to guide the definition of tertiary sulci. In the experiments, we evaluate our method on 13 deep and shallow sulci of human LPFC in two independent data sets with different age ranges: pediatric (N=60) and adult (N=36) cohorts. We compare the proposed method with a conventional multi-atlas approach and spherical convolutional neural networks without/with rotation data augmentation. In both cohorts, the proposed data augmentation improves labeling accuracy of deep and shallow sulci over the baselines, and the proposed context-aware training offers further improvement in the labeling of shallow sulci over the proposed data augmentation. We share our tools with the field and discuss applications of our results for understanding neuroanatomical-functional organization of LPFC and the rest of cortex (https://github.com/ilwoolyu/SphericalLabeling).

Unsupervised Learning for Spherical Surface Registration

Current spherical surface registration methods achieve good performance on alignment and spatial normalization of cortical surfaces across individuals in neuroimaging analysis. However, they are computationally intensive, since they have to optimize an objective function independently for each pair of surfaces. In this paper, we present a fast learning-based algorithm that makes use of the recent development in spherical Convolutional Neural Networks (CNNs) for spherical cortical surface registration. Given a set of surface pairs without supervised information such as ground truth deformation fields or anatomical landmarks, we formulate the registration as a parametric function and learn its parameters by enforcing the feature similarity between one surface and the other one warped by the estimated deformation field using the function. Then, given a new pair of surfaces, we can quickly infer the spherical deformation field registering one surface to the other one. We model this parametric function using three orthogonal Spherical U-Nets and use spherical transform layers to warp the spherical surfaces, while imposing smoothness constraints on the deformation field. All the layers in the network are well-defined and differentiable, thus the parameters can be effectively learned. We show that our method achieves accurate cortical alignment results on 102 subjects, comparable to two state-of-the-art methods: Spherical Demons and MSM, while runs much faster.

Morphometric development of the human fetal cerebellum during the early second trimester

The protracted nature of development makes the cerebellum vulnerable to a broad spectrum of pathologic conditions, especially during the early fetal period. This study aims to characterize normal cerebellar growth in human fetuses during the early second trimester. We manually segmented the fetal cerebellum using 7.0-T high-resolution MR images obtained in 35 specimens with gestational ages ranging from 15 to 22 weeks. Volume measurements and shape analysis were performed to quantitatively evaluate global and regional cerebellar growth. The absolute volume of the fetal cerebellum showed a quadratic growth with increasing gestational age, while the pattern of relative volume changes revealed that the cerebellum grew at a greater pace than the cerebrum after 17 gestational weeks. Shape analysis was used to examine the distinctive development of subregions of the cerebellum. The extreme lateral portions of both cerebellar hemispheres showed the lowest rate of growth. The anterior lobe grew faster than most of the posterior lobe. These findings expand our understanding of the early growth pattern of the human cerebellum and could be further used to assess the developmental conditions of the fetal brain.

Surface-based Tracking of U-fibers in the Superficial White Matter

The superficial white matter (SWM) lies directly underneath the cortical ribbon and contains the short association fibers, or U-fibers, that connect neighboring gyri. Connectivity of these U-fibers is important for various neuroscientific research from the development to the aging of the brain. Nonetheless, conventional tractography methods can only provide a partial representation of these connections. Moreover, previous studies on U-fibers mainly extract tracts based on their shape characteristics without imposing the biologically critical condition that they should tightly follow the cortical surface. In this work we leverage the high resolution diffusion imaging data from the Human Connectome Project (HCP), and develop a novel surface-based framework for reconstructing the U-fibers. Guided by the projected fiber orientation distributions (FODs) on cortical surfaces, our method tracks the U-fibers from sulcal seed regions to neighboring gyrus on the triangular mesh representation of the cortex. Compared to volume-based tractography, the main advantage of our method is that it is intrinsic to the cortical geometry. More specifically, we define a novel approach for measuring the change of angles on the tangent space of the surface and use them to determine the U-fiber passing through a sulcal seed point. In experimental results, we compare our surface-based method with state-of-the-art FOD-based tractography from MRtrix on a large-scale dataset of 484 HCP subjects, and demonstrate that our method clearly achieves superior performance on the reconstruction of U-fibers between the precentral and postcentral gyrus.

Hierarchical spherical deformation for cortical surface registration

We present hierarchical spherical deformation for a group-wise shape correspondence to address template selection bias and to minimize registration distortion. In this work, we aim at a continuous and smooth deformation field to guide accurate cortical surface registration. In conventional spherical registration methods, a global rigid alignment and local deformation are independently performed. Motivated by the composition of precession and intrinsic rotation, we simultaneously optimize global rigid rotation and non-rigid local deformation by utilizing spherical harmonics interpolation of local composite rotations in a single framework. To this end, we indirectly encode local displacements by such local composite rotations as functions of spherical locations. Furthermore, we introduce an additional regularization term to the spherical deformation, which maximizes its rigidity while reducing registration distortion. To improve surface registration performance, we employ the second order approximation of the energy function that enables fast convergence of the optimization. In the experiments, we validate our method on healthy normal subjects with manual cortical surface parcellation in registration accuracy and distortion. We show an improved shape correspondence with high accuracy in cortical surface parcellation and significantly low registration distortion in surface area and edge length. In addition to validation, we discuss parameter tuning, optimization, and implementation design with potential acceleration.