Exploring 3-hinge gyral folding patterns among HCP Q3 868 human subjects

Axonal tension contributes to consistent fold placement

Cortical folding is a critical process during brain development, resulting in morphologies that are both consistent and distinct between individuals and species. While earlier studies have highlighted important aspects of cortical folding, most existing computational models, based on the differential growth theory, fall short of explaining why folds tend to appear in particular locations. The axon tension hypothesis may provide insight into this conundrum; however, there has been significant controversy about a potential role of axonal tension during the gyrification. The common opinion in the field is that axonal tension is inadequate to drive gyrification, but we currently run the risk of discarding this hypothesis without comprehensively studying the role of axonal tension. Here we propose a novel bi-layered finite element model incorporating the two theories, including characteristic axonal tension in the subcortex and differential cortical growth. We show that axon tension can serve as a perturbation sufficient to trigger buckling in simulations; similarly to other types of perturbations, the natural stability behavior of the system tends to determine some characteristics of the folding morphology (e.g. the wavelength) while the perturbation determines the location of folds. Certain geometries, however, can interact or compete with the natural stability of the system to change the wavelength. When multiple perturbations are present, they similarly compete with each other. We found that an axon bundle of reasonable size will overpower up to a 5% thickness perturbation (typical in the literature) and determine fold placement. Finally, when multiple axon tracts are present, even a slight difference in axon stiffness, representing the heterogeneity of axonal connections, is enough to significantly change the folding pattern. While the simulations presented here are a very simple representation of white matter connectivity, our findings point to urgent future research on the role of axon connectivity in cortical folding.

Mechanical hierarchy in the formation and modulation of cortical folding patterns

The important mechanical parameters and their hierarchy in the growth and folding of the human brain have not been thoroughly understood. In this study, we developed a multiscale mechanical model to investigate how the interplay between initial geometrical undulations, differential tangential growth in the cortical plate, and axonal connectivity form and regulate the folding patterns of the human brain in a hierarchical order. To do so, different growth scenarios with bilayer spherical models that features initial undulations on the cortex and uniform or heterogeneous distribution of axonal fibers in the white matter were developed, statistically analyzed, and validated by the imaging observations. The results showed that the differential tangential growth is the inducer of cortical folding, and in a hierarchal order, high-amplitude initial undulations on the surface and axonal fibers in the substrate regulate the folding patterns and determine the location of gyri and sulci. The locations with dense axonal fibers after folding settle in gyri rather than sulci. The statistical results also indicated that there is a strong correlation between the location of positive (outward) and negative (inward) initial undulations and the locations of gyri and sulci after folding, respectively. In addition, the locations of 3-hinge gyral folds are strongly correlated with the initial positive undulations and locations of dense axonal fibers. As another finding, it was revealed that there is a correlation between the density of axonal fibers and local gyrification index, which has been observed in imaging studies but not yet fundamentally explained. This study is the first step in understanding the linkage between abnormal gyrification (surface morphology) and disruption in connectivity that has been observed in some brain disorders such as Autism Spectrum Disorder. Moreover, the findings of the study directly contribute to the concept of the regularity and variability of folding patterns in individual human brains.

An integrated finite element method and machine learning algorithm for brain morphology prediction

The human brain development experiences a complex evolving cortical folding from a smooth surface to a convoluted ensemble of folds. Computational modeling of brain development has played an essential role in better understanding the process of cortical folding, but still leaves many questions to be answered. A major challenge faced by computational models is how to create massive brain developmental simulations with affordable computational sources to complement neuroimaging data and provide reliable predictions for brain folding. In this study, we leveraged the power of machine learning in data augmentation and prediction to develop a machine-learning-based finite element surrogate model to expedite brain computational simulations, predict brain folding morphology, and explore the underlying folding mechanism. To do so, massive finite element method (FEM) mechanical models were run to simulate brain development using the predefined brain patch growth models with adjustable surface curvature. Then, a GAN-based machine learning model was trained and validated with these produced computational data to predict brain folding morphology given a predefined initial configuration. The results indicate that the machine learning models can predict the complex morphology of folding patterns, including 3-hinge gyral folds. The close agreement between the folding patterns observed in FEM results and those predicted by machine learning models validate the feasibility of the proposed approach, offering a promising avenue to predict the brain development with given fetal brain configurations.

Identification for the cortical 3-Hinges folding pattern based on cortical morphological and structural features

The Cortical 3-Hinges Folding Pattern (i.e., 3-Hinges) is one of the brain's hallmarks, and it is of great reference for predicting human intelligence, diagnosing eurological diseases and understanding the brain functional structure differences among gender. Given the significant morphological variability among individuals, it is challenging to identify 3-Hinges, but current 3-Hinges researches are mainly based on the computationally expensive Gyral-net method. To address this challenge, this paper aims to develop a deep network model to realize the fast identification of 3-Hinges based on cortical morphological and structural features. The main work includes: (1) The morphological and structural features of the cerebral cortex are extracted to relieve the imbalance between the number of 3-Hinges and each brain image's voxels; (2) The feature vector is constructed with the K nearest neighbor algorithm from the extracted scattered features of the morphological and structural features to alleviate over-fitting in training; (3) The squeeze excitation module combined with the deep U-shaped network structure is used to learn the correlation of the channels among the feature vectors; (4) The functional structure roles that 3-Hinges plays between adolescent males and females are discussed in this work. The experimental results on both adolescent and adult MRI datasets show that the proposed model achieves better performance in terms of time consumption. Moreover, this paper reveals that cortical sulcus information plays a critical role in the procedure of identification, and the cortical thickness, cortical surface area, and volume characteristics can supplement valuable information for 3-Hinges identification to some extent. Furthermore, there are significant structural differences on 3-Hinges among adolescent gender.

BIRGU Net: deformable brain magnetic resonance image registration using gyral-net map and 3D Res-Unet

Deformable image registration is a fundamental procedure in medical imaging. Recently, deep learning-based deformable image registrations have achieved fast registration by learning the spatial correspondence from image pairs. However, it remains challenging in brain image registration due to the structural complexity of individual brains and the lack of ground truth for anatomical correspondences between the brain image pairs. This work devotes to achieving an end-to-end unsupervised brain deformable image registration method using the gyral-net map and 3D Res-Unet (BIRGU Net). Firstly, the gyral-net map was introduced to represent the 3D global cortex complex information of the brain image since it was considered as one of the anatomical landmarks, which can help to extract the salient structural feature of individual brains for registration. Secondly, the variant of 3D U-net architecture involving dual residual strategies was designed to map the image into the deformation field effectively and to prevent the gradient from vanishing as well. Finally, double regularized terms were imposed on the deformation field to guide the network training for leveraging the smoothness and the topology preservation of the deformation field. The registration procedure was trained in an unsupervised manner, which addressed the lack of ground truth for anatomical correspondences between the brain image pairs. The experimental results on four public data sets demonstrate that the extracted gyral-net can be an auxiliary feature for registration and the proposed network with the designed strategies can improve the registration performance since the Dice similarity coefficient (DSC) and normalized mutual information (NMI) are higher and the time consumption is comparable than the state-of-the-art. The code is available at https://github.com/mynameiswode/BIRGU-Net .

Gyral and sulcal connectivity in the human cerebral cortex

The rapid evolution of image acquisition and data analytic methods has established in vivo whole-brain tractography as a routine technology over the last 20 years. Imaging-based methods provide an additional approach to classic neuroanatomical studies focusing on biomechanical principles of anatomical organization and can in turn overcome the complexity of inter-individual variability associated with histological and tractography studies. In this work we propose a novel, reliable framework for determining brain tracts resolving the anatomical variance of brain regions. We distinguished 4 region types based on anatomical considerations: (i) gyral regions at borders between cortical communities; (ii) gyral regions within communities; (iii) sulcal regions at invariant locations across subjects; and (iv) other sulcal regions. Region types showed strikingly different anatomical and connection properties. Results allowed complementing the current understanding of the brain’s communication structure with a model of its anatomical underpinnings.

Cortical thickness systematically varies with curvature and depth in healthy human brains

Cortical thickness varies throughout the cortex in a systematic way. However, it is challenging to investigate the patterns of cortical thickness due to the intricate geometry of the cortex. The cortex has a folded nature both in radial and tangential directions which forms not only gyri and sulci but also tangential folds and intersections. In this article, cortical curvature and depth are used to characterize the spatial distribution of the cortical thickness with much higher resolution than conventional regional atlases. To do this, a computational pipeline was developed that is capable of calculating a variety of quantitative measures such as surface area, cortical thickness, curvature (mean curvature, Gaussian curvature, shape index, intrinsic curvature index, and folding index), and sulcal depth. By analyzing 501 neurotypical adult human subjects from the ABIDE‐I dataset, we show that cortex has a very organized structure and cortical thickness is strongly correlated with local shape. Our results indicate that cortical thickness consistently increases along the gyral–sulcal spectrum from concave to convex shape, encompassing the saddle shape along the way. Additionally, tangential folds influence cortical thickness in a similar way as gyral and sulcal folds; outer folds are consistently thicker than inner.

Cortical development coupling between surface area and sulcal depth on macaque brains

Postnatal development of cerebral cortex is associated with a variety of neuronal processes and is thus critical to development of brain function and cognition. Longitudinal changes of cortical morphology and topology, such as postnatal cortical thinning and flattening have been widely studied. However, thorough and systematic investigation of such cortical change, including how to quantify it from multiple spatial directions and how to relate it to surface topology, is rarely found. In this work, based on a longitudinal macaque neuroimaging dataset, we quantified local changes in gyral white matter's surface area and sulcal depth during early development. We also investigated how these two metrics are coupled and how this coupling is linked to cortical surface topology, underlying white matter, and positions of functional areas. Semi-parametric generalized additive models were adopted to quantify the longitudinal changes of surface area (A) and sulcal depth (D), and the coupling patterns between them. This resulted in four classes of regions, according to how they change compared with global change throughout early development: slower surface area change and slower sulcal depth change (slowA_slowD), slower surface area change and faster sulcal depth change (slowA_fastD), faster surface area change and slower sulcal depth change (fastA_slowD), and faster surface area change and faster sulcal depth change (fastA_fastD). We found that cortex-related metrics, including folding pattern and cortical thickness, vary along slowA_fastD-fastA_slowD axis, and structural connection-related metrics vary along fastA_fastD-slowA_slowD axis, with which brain functional sites align better. It is also found that cortical landmarks, including sulcal pits and gyral hinges, spatially reside on the borders of the four patterns. These findings shed new lights on the relationship between cortex development, surface topology, axonal wiring pattern and brain functions.

NAS-optimized topology-preserving transfer learning for differentiating cortical folding patterns

Increasing evidence suggests that cortical folding patterns of human cerebral cortex manifest overt structural and functional differences. However, for interpretability, few studies leverage advanced techniques (e.g., deep learning) to investigate the difference among cortical folds, resulting in more differences yet to be extensively explored. To this end, we proposed an effective topology-preserving transfer learning framework to differentiate cortical fMRI time series extracted from cortical folds. Our framework consists of three main parts: (1) Neural architecture search (NAS), which is used to devise a well-performing network structure based on an initialized hand-designed super-graph in an image dataset; (2) Topology-preserving transfer, which takes the model searched by NAS as the source network, keeping the topological connectivity in the network unchanged, while transforming all 2D operations including convolution and pooling into 1D, therefore resulting in a topology-preserving network, named TPNAS-Net; (3) Classification and correlation analysis, which involves using the TPNAS-Net to classify 1D cortical fMRI time series for each individual brain, and performing a group difference analysis between autism spectrum disorder (ASD) and healthy control (HC) and correlation analysis with clinical information (i.e., age). Extensive experiments on two ASD datasets obtain consistent results, demonstrating that the TPNAS-Net not only discriminates cortical folding patterns at high classification accuracy, but also captures subtle differences between ASD and HC (p-value = 0.042). In addition, we discover that there is a positive correlation between the classification accuracy and age in ASD (r = 0.39, p-value = 0.04). These findings together suggest that structural and functional differences in cortical folding patterns between ASD and HC may provide a potentially useful biomarker for the diagnosis of ASD.

Computational models of cortical folding: A review of common approaches

The process of gyrification, by which the brain develops the intricate pattern of gyral hills and sulcal valleys, is the result of interactions between biological and mechanical processes during brain development. Researchers have developed a vast array of computational models in order to investigate cortical folding. This review aims to summarize these studies, focusing on five essential elements of the brain that affect development and gyrification and how they are represented in computational models: (i) the constraints of skull, meninges, and cerebrospinal fluid; (ii) heterogeneity of cortical layers and regions; (iii) anisotropic behavior of subcortical fiber tracts; (iv) material properties of brain tissue; and (v) the complex geometry of the brain. Finally, we highlight areas of need for future simulations of brain development.

Mechanism Exploration of 3-Hinge Gyral Formation and Pattern Recognition

The 3-hinge gyral folding is the conjunction of gyrus crest lines from three different orientations. Previous studies have not explored the possible mechanisms of formation of such 3-hinge gyri, which are preserved across species in primate brains. We develop a biomechanical model to mimic the formation of 3-hinge patterns on a real brain and determine how special types of 3-hinge patterns form in certain areas of the model. Our computational and experimental imaging results show that most tertiary convolutions and exact locations of 3-hinge patterns after growth and folding are unpredictable, but they help explain the consistency of locations and patterns of certain 3-hinge patterns. Growing fibers within the white matter is posited as a determining factor to affect the location and shape of these 3-hinge patterns. Even if the growing fibers do not exert strong enough forces to guide gyrification directly, they still may seed a heterogeneous growth profile that leads to the formation of 3-hinge patterns in specific locations. A minor difference in initial morphology between two growing model brains can lead to distinct numbers and locations of 3-hinge patterns after folding.

Surface-based single-subject morphological brain networks: Effects of morphological index, brain parcellation and similarity measure, sample size-varying stability and test-retest reliability

Morphological brain networks, in particular those at the individual level, have become an important approach for studying the human brain connectome; however, relevant methodology is far from being well-established in their formation, description and reproducibility. Here, we extended our previous study by constructing and characterizing single-subject morphological similarity networks from brain volume to surface space and systematically evaluated their reproducibility with respect to effects of different choices of morphological index, brain parcellation atlas and similarity measure, sample size-varying stability and test-retest reliability. Using the Human Connectome Project dataset, we found that surface-based single-subject morphological similarity networks shared common small-world organization, high parallel efficiency, modular architecture and bilaterally distributed hubs regardless of different analytical strategies. Nevertheless, quantitative values of all interregional similarities, global network measures and nodal centralities were significantly affected by choices of morphological index, brain parcellation atlas and similarity measure. Moreover, the morphological similarity networks varied along with the number of participants and approached stability until the sample size exceeded ~70. Using an independent test-retest dataset, we found fair to good, even excellent, reliability for most interregional similarities and network measures, which were also modulated by different analytical strategies, in particular choices of morphological index. Specifically, fractal dimension and sulcal depth outperformed gyrification index and cortical thickness, higher-resolution atlases outperformed lower-resolution atlases, and Jensen-Shannon divergence-based similarity outperformed Kullback-Leibler divergence-based similarity. Altogether, our findings propose surface-based single-subject morphological similarity networks as a reliable method to characterize the human brain connectome and provide methodological recommendations and guidance for future research.

Physical aspects of cortical folding

The characteristically folded surface of the human brain is critical for brain function and allows for higher cognitive abilities. Recent mostly computational research advances have shown that mechanical instabilities play a crucial role during early brain development and cortical folding. However, it is difficult to investigate such mechanisms in vivo. To experimentally gain deeper insights into the physical mechanisms that underlie the development of brain shape, we use a setup of swelling polymers. We investigate the influence of cortical thickness and the stiffness ratio between cortex and subcortex on the resulting surface pattern by taking the initially smooth fetal brain geometry at week 22 into consideration. The gel specimens possess a two-layered structure accounting for gray and white matter tissue and yield complex surface morphologies that well resemble patterns in the human brain. The results are in good agreement with analytical predictions. Through the variation of cortical thickness and stiffness, it is possible to reproduce cortical malformations such as polymicrogyria and lissencephaly. The results suggest that wrinkling with subsequent transition into folding is the driving instability mechanism during brain development. In addition, the experiments provide valuable insights towards the distinction between wrinkling and creasing instabilities. Taken together, the presented swelling experiments impressively demonstrate the purely physical aspects of brain shape and constitute a valuable tool to advance our understanding of human brain development.

Cortical 3-hinges could serve as hubs in cortico-cortical connective network

Mapping the relation between cortical convolution and structural/functional brain architectures could provide deep insights into the mechanisms of brain development, evolution and diseases. In our previous studies, we found a unique gyral folding pattern, termed a 3-hinge, which was defined as the conjunction of three gyral crests. The uniqueness of the 3-hinge was evidenced by its thicker cortex and stronger fiber connections than other gyral regions. However, the role that 3-hinges play in cortico-cortical connective architecture remains unclear. To this end, we conducted MRI studies by constructing structural cortico-cortical connective networks based on a fine-granular cortical parcellation, the parcels of which were automatically labeled as 3-hinge, 2-hinge (ordinary gyrus) or sulcus. On human brains, 3-hinges possess significantly higher degrees, strengths and betweennesses than 2-hinges, suggesting that 3-hinges could serve more like hubs in the cortico-cortical connective network. This hypothesis gains supports from human functional network analyses, in which 3-hinges are involved in more global functional networks than ordinary gyri. In addition, 3-hinges could serve as 'connector' hubs rather than 'provincial' hubs and they account for a dominant proportion of nodes in the high-level 'backbone' of the network. These structural results are reproduced on chimpanzee and macaque brains, while the roles of 3-hinges as hubs become more pronounced in higher order primates. Our new findings could provide a new window to the relation between cortical convolution, anatomical connection and brain function.

Identifying Cross-individual Correspondences of 3-hinge Gyri

Human brain alignment based on imaging data has long been an intriguing research topic. One of the challenges is the huge inter-individual variabilities, which are pronounced not only in cortical folding patterns, but also in the underlying structural and functional patterns. Also, it is still not fully understood how to link the cross-subject similarity of cortical folding patterns to the correspondences of structural brain wiring diagrams and brain functions. Recently, a specific cortical gyral folding pattern was identified, which is the conjunction of gyri from multiple directions and termed a "gyral hinge". These gyral hinges are characterized by the thickest cortices, the densest long-range fibers, and the most complex functional profiles in contrast to other gyri. In addition to their structural and functional importance, a small portion of 3-hinges found correspondences across subjects and even species by manual labeling. However, it is unclear if such cross-subject correspondences can be found for all 3-hinges, or if the correspondences are interpretable from structural and functional aspects. Given the huge variability of cortical folding patterns, we proposed a novel algorithm which jointly uses structural MRI-derived cortical folding patterns and diffusion-MRI-derived fiber shape features to estimate the correspondences. This algorithm was executed in a group-wise manner, whereby 3-hinges of all subjects were simultaneously aligned. The effectiveness of the algorithm was demonstrated by higher cross-subject 3-hinges' consistency with respect to structural and functional metrics, when compared with other methods. Our findings provide a novel approach to brain alignment and an insight to the linkage between cortical folding patterns and the underlying structural connective diagrams and brain functions.

Exploring 3-hinge gyral folding patterns among HCP Q3 868 human subjects

Comparison and integration of neuroimaging data from different brains and populations are fundamental in neuroscience. Over the past decades, the neuroimaging field has largely depended on image registration to compare and integrate neuroimaging data from individuals in a common reference space, with a basic assumption that the brains are similar. However, the intrinsic neuroanatomical complexity and huge interindividual cortical folding variation remain underexplored. Here we focus on a specific cortical convolution pattern, termed 3-hinge gyral folding, which is the conjunction of gyri from multiple orientations and has unique and consistent anatomically, structurally, and functionally connective patterns across subjects. By developing a novel shape descriptor and a two-stage clustering pipeline, we devise an automatic method to identify 3-hinges in the Human Connectome Project Q3 868 human brains, and further parameterize the complexity of such a pattern and quantify its regularity and variation in terms of 3-hinge number, position, and morphology. Our results not only exhibit the huge interindividual variations, but also reveal regular relationship between gyral hinges and other factors, such as their locations and cortical morphologies. It is found that "line-shape" cortices have relatively more consistent 3-hinge shape pattern distributions, and certain types of 3-hinge patterns favor particular cortical morphologies. In addition, more 3-hinges are found on "line-shape" cortices while their numbers vary more across subjects than those on "non-line-shape" cortices. This study adds new insights into a better understanding of the regularity and variability of human brain anatomy, and their functional aspects.