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.

Understanding compressive viscoelastic properties of additively manufactured PLA for bone-mimetic scaffold design.

Bone tissue engineering has been recognized as a promising strategy to repair or replace damaged bone tissues. The mechanical properties of bone scaffolds play a critical role in successful bone regeneration, as it is essential to match the mechanical properties of the scaffold with the surrounding bone tissue. In this study, we investigated the effects of fused deposition modeling (FDM) process parameters, including printing speed, printing temperature, and layer thickness, on the compressive viscoelastic properties of polylactic acid (PLA) scaffolds. The compressive viscoelastic properties of bulk PLA specimens were characterized using a Zhu-Wang-Tang (ZWT) constitutive model under different compressive strain rates. A comprehensive statistical analysis comprising multivariate and univariate analysis of variance (MANOVA and ANOVA) and Tukey's post hoc analysis was utilized to quantify the effect of each FDM parameter on the viscoelastic mechanical properties of the PLA specimens. Subsequently, we fabricated modified face-centered cubic (MFCC) scaffolds using FDM and varied the FDM process parameters to achieve a compressive viscoelastic response that matched the natural trabecular bone tissue. The viscoelastic performance of the MFCC scaffolds was compared with traditional orthogonal cylindrical struts (OCS) scaffolds. Our methodology contributes to the design of bone-mimetic scaffolds with optimized mechanical properties by controlling FDM process parameters.

Gyral peaks: Novel gyral landmarks in developing macaque brains.

Cerebral cortex development undergoes a variety of processes, which provide valuable information for the study of the developmental mechanism of cortical folding as well as its relationship to brain structural architectures and brain functions. Despite the variability in the anatomy-function relationship on the higher-order cortex, recent studies have succeeded in identifying typical cortical landmarks, such as sulcal pits, that bestow specific functional and cognitive patterns and remain invariant across subjects and ages with their invariance being related to a gene-mediated proto-map. Inspired by the success of these studies, we aim in this study at defining and identifying novel cortical landmarks, termed gyral peaks, which are the local highest foci on gyri. By analyzing data from 156 MRI scans of 32 macaque monkeys with the age spanned from 0 to 36 months, we identified 39 and 37 gyral peaks on the left and right hemispheres, respectively. Our investigation suggests that these gyral peaks are spatially consistent across individuals and relatively stable within the age range of this dataset. Moreover, compared with other gyri, gyral peaks have a thicker cortex, higher mean curvature, more pronounced hub-like features in structural connective networks, and are closer to the borders of structural connectivity-based cortical parcellations. The spatial distribution of gyral peaks was shown to correlate with that of other cortical landmarks, including sulcal pits. These results provide insights into the spatial arrangement and temporal development of gyral peaks as well as their relation to brain structure and function.

Multi-objective Shape Optimization of Bone Scaffolds: Enhancement of Mechanical Properties and Permeability.

Porous scaffolds have recently attracted attention in bone tissue engineering. The implanted scaffolds are supposed to satisfy the mechanical and biological requirements. In this study, two porous structures named MFCC-1 (modified face centered cubic-1) and MFCC-2 (modified face centered cubic-2) are introduced. The proposed porous architectures are evaluated, optimized, and tested to enhance mechanical and biological properties. The geometric parameters of the scaffolds with porosities ranging from 70% to 90% are optimized to find a compromise between the effective Young's modulus and permeability, as well as satisfying the pore size and specific surface area requirements. To optimize the effective Young's modulus and permeability, we integrated a mathematical formulation, finite element analysis, and computational fluid dynamics simulations. For validation, the optimized scaffolds were 3D-printed, tested, and compared with two different orthogonal cylindrical struts (OCS) scaffold architectures. The MFCC designs are preferred to the generic OCS scaffolds from various perspectives: a) the MFCC architecture allows scaffold designs with porosities up to 96%; b) the very porous architecture of MFCC scaffolds allows achieving high permeabilities, which could potentially improve the cell diffusion; c) despite having a higher porosity compared to the OCS scaffolds, MFCC scaffolds improve mechanical performance regarding Young's modulus, stress concentration, and apparent yield strength; d) the proposed structures with different porosities are able to cover all the range of permeability for the human trabecular bones. The optimized MFCC designs have simple architectures and can be easily fabricated and used to improve the quality of load-bearing orthopedic scaffolds. STATEMENT OF SIGNIFICANCE: Porous scaffolds are increasingly being studied to repair large bone defects. A scaffold is supposed to withstand mechanical loads and provide an appropriate environment for bone cell growth after implantation. These mechanical and biological requirements are usually contradicting; improving the mechanical performance would require a reduction in porosity and a lower porosity is likely to reduce the biological performance of the scaffold. Various studies have shown that the mechanical and biological performance of bone scaffolds can be improved by internal architecture modification. In this study, we propose two scaffold architectures named MFCC-1 and MFCC-2 and provide an optimization framework to simultaneously optimize their stiffness and permeability to improve their mechanical and biological performances.

Shape optimization of orthopedic porous scaffolds to enhance mechanical performance.

Polymeric bone scaffolds are supposed to temporarily bear the external mechanical forces applied to the injured area. The implanted scaffolds should satisfy both mechanical and cell-proliferation requirements. In this study, to design an optimum scaffold structure from mechanical and cell growth perspectives, a new scaffold structure named MFCC (Modified Face Centered Cubic) is introduced, which is based on the Face Centered Cubic (FCC) arrangement of spherical pores. The geometric parameters of the scaffold structure are optimized to increase the stiffness of the scaffolds with 70%, 75%, and 80% porosities. The optimized MFCC scaffolds satisfy the cell growth requirements and show greater elastic modulus compared to regular OCS (Orthogonal Cylindrical Struts) scaffolds. For validation, the designed scaffolds made by the finite element optimization process were 3D printed, tested and compared with the OCS scaffolds. The results show that the gradual cross-section variation of the spheres in the optimized scaffold reduces the stress concentration and distributes the applied mechanical loads more uniformly compared to OCS scaffolds. Moreover, from the cell growth perspective, a spherical pore with a concave surface provides a better surface for the proliferation of cells. The optimized MFCC scaffolds are stiffer in small strains and have a greater apparent yield stress compared to the OCS scaffolds at the same porosity. The enhancement in the stiffness of the scaffold is shape attributed and is independent of the material used. Therefore, the same percentage increase in the stiffness is achievable for a broad range of materials. The presented new design with improved stiffness helps to enhance the quality of load-bearing scaffolds.

Effect of collagen degradation on the mechanical behavior and wrinkling of skin.

Chronological skin aging is a complex process that is controlled by numerous intrinsic and extrinsic factors. One major factor is the gradual degradation of the dermal collagen fiber network. As a step toward understanding the mechanistic importance of dermal tissue in the process of aging, this study employs analytical and multiscale computational models to elucidate the effect of collagen fiber bundle disintegration on the mechanical properties and topography of skin. Here, human skin is modeled as a soft composite with an anisotropic dermal layer. The anisotropy of the tissue is governed by collagen fiber bundles with varying densities, average fiber alignments, and normalized alignment distributions. In all finite element models examined, collagen fiber bundle degradation results in progressive decreases in dermal and full-thickness composite stiffness. This reduction is more profound when collagen bundles align with the compression axis. Aged skin models with low collagen fiber bundle densities under compression exhibit notably smaller critical wrinkling strains and larger critical wavelengths than younger skin models, in agreement with in vivo wrinkling behavior with age. The propensity for skin wrinkling can be directly attributable to the degradation of collagen fiber bundles, a relationship that has previously been assumed but unsubstantiated. While linear-elastic analytical models fail to capture the postbuckling behavior in skin, nonlinear finite element models can predict the complex bifurcations of the compressed skin with different densities of collagen bundles.

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.

Geometrical nonlinear elasticity of axon under tension: A coarse-grained computational study.

Axon bundles cross-linked by microtubule (MT) associate proteins and bounded by a shell skeleton are critical for normal function of neurons. Understanding effects of the complexly geometrical parameters on their mechanical properties can help gain a biomechanical perspective on the neurological functions of axons and thus brain disorders caused by the structural failure of axons. Here, the tensile mechanical properties of MT bundles cross-linked by tau proteins are investigated by systematically tuning MT length, axonal cross-section radius, and tau protein spacing in a bead-spring coarse-grained model. Our results indicate that the stress-strain curves of axons can be divided into two regimes, a nonlinear elastic regime dominated by rigid-body like inter-MT sliding, and a linear elastic regime dominated by affine deformation of both tau proteins and MTs. From the energetic analyses, first, the tau proteins dominate the mechanical performance of axons under tension. In the nonlinear regime, tau proteins undergo a rigid-body like rotating motion rather than elongating, whereas in the nonlinear elastic regime, tau proteins undergo a flexible elongating deformation along the MT axis. Second, as the average spacing between adjacent tau proteins along the MT axial direction increases from 25 to 125 nm, the Young's modulus of axon experiences a linear decrease whereas with the average space varying from 125 to 175 nm, and later reaches a plateau value with a stable fluctuation. Third, the increment of the cross-section radius of the MT bundle leads to a decrease in Young's modulus of axon, which is possibly attributed to the decrease in MT numbers per cross section. Overall, our research findings offer a new perspective into understanding the effects of geometrical parameters on the mechanics of MT bundles as well as serving as a theoretical basis for the development of artificial MT complexes potentially toward medical applications.

Effect of the Interfiber Bonding on the Mechanical Behavior of Electrospun Fibrous Mats.

Electrospun fibrous mats, characterized by their large surface-to-volume ratios, have unique and beneficial properties for various applications. The micro or nanoscale architectures of these structures significantly affects the mechanical properties of the material. The lack of knowledge for predicting the mechanical behavior of electrospun fibrous mats may prevent applications utilizing the se mats from reaching their full potential. In this paper, we propose a new computational model to predict the mechanical behavior of an electrospun fibrous mat by considering its microstructure and the percentage of the cross-points that are bonded. The model of the electrospun mat with randomly distributed fibers is considered in uniaxial and biaxial tension. Three cases are studied: (1) no interaction in cross-points of intersecting fibers, (2) half of the cross-points are bonded, (3) all of the cross-points are bonded. The results show that along with the mechanical properties of individual fibers, the fusion bonding of fibers is a critical parameter for tuning the mechanical properties of the bulk material. In a predefined porosity, the interfiber fusion enhanced the stiffness of the mat by 60%, which is independent of the loading mode and the mechanical property of individual fibers. For all ranges of porosities, bonding increases the stiffness of the mat; however, the bonding is more effective at stiffening when the porosity of the mat is low.

Analysis of mechanical deformation effect on the voltage generation of a vertical contact mode triboelectric generator.

One of the associated factors that controls the performance of a triboelectric generator (TEG) is the mechanical deformation of the dielectric layer. Therefore, a good contact model can be a prominent tool to find a more realistic and efficient way of determining the relationships between the contact and electrical output of the generator. In this study, experiments are conducted on a vertical contact mode triboelectric generator under an MTS machine. The open-circuit voltages are measured at different loads imposed by the MTS by controlling the cyclic displacement of the top tribo layer of the generator. A finite-element-based theoretical model is developed to explain the behavior of the generator during the experiments. The 2D-contact problem of the micro-structured tribo layers is simulated and then the contact results are integrated into 3D to find the actual contact area between the two surfaces. These numerical contact results improve the existing theoretical model by evaluating the correct surface charge density and contact area as a function of the input parameters. The excellent agreement between our experimental and theoretical results illustrates that theoretical modeling could be used as a robust approach to predict the mechanical and electrical performance of TEGs. In addition, some parametric studies of the harvester are presented here for different geometrical parameters of the microstructures.

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.

Denser Growing Fiber Connections Induce 3-hinge Gyral Folding.

Recent studies have shown that quantitative description of gyral shape patterns offers a novel window to examine the relationship between brain structure and function. Along this research line, this paper examines a unique and interesting type of cortical gyral region where 3 different gyral crests meet, termed 3-hinge gyral region. We extracted 3-hinge gyral regions in macaque/chimpanzee/human brains, quantified and compared the relevant DTI-derived fiber densities in 3-hinge and 2-hinge gyral regions. Our observations consistently showed that DTI-derived fiber densities in 3-hinge regions are much higher than those in 2-hinge regions. Therefore, we hypothesize that besides the cortical expansion, denser fiber connections can induce the formation of 3-hinge gyri. To examine the biomechanical basis of this hypothesis, we constructed a series of 3-dimensional finite element soft tissue models based on continuum growth theory to investigate fundamental biomechanical mechanisms of consistent 3-hinge gyri formation. Our computational simulation results consistently showed that during gyrification gyral regions with higher concentrations of growing axonal fibers tend to form 3-hinge gyri. Our integrative approach combining neuroimaging data analysis and computational modeling appears effective in probing a plausible theory of 3-hinge gyri formation and providing new insights into structural and functional cortical architectures and their relationship.

Radial Structure Scaffolds Convolution Patterns of Developing Cerebral Cortex.

Commonly-preserved radial convolution is a prominent characteristic of the mammalian cerebral cortex. Endeavors from multiple disciplines have been devoted for decades to explore the causes for this enigmatic structure. However, the underlying mechanisms that lead to consistent cortical convolution patterns still remain poorly understood. In this work, inspired by prior studies, we propose and evaluate a plausible theory that radial convolution during the early development of the brain is sculptured by radial structures consisting of radial glial cells (RGCs) and maturing axons. Specifically, the regionally heterogeneous development and distribution of RGCs controlled by Trnp1 regulate the convex and concave convolution patterns (gyri and sulci) in the radial direction, while the interplay of RGCs' effects on convolution and axons regulates the convex (gyral) convolution patterns. This theory is assessed by observations and measurements in literature from multiple disciplines such as neurobiology, genetics, biomechanics, etc., at multiple scales to date. Particularly, this theory is further validated by multimodal imaging data analysis and computational simulations in this study. We offer a versatile and descriptive study model that can provide reasonable explanations of observations, experiments, and simulations of the characteristic mammalian cortical folding.

4D Origami by Smart Embroidery.

There exist many methods for processing of materials: extrusion, injection molding, fibers spinning, 3D printing, to name a few. In most cases, materials with a static, fixed shape are produced. However, numerous advanced applications require customized elements with reconfigurable shape. The few available techniques capable of overcoming this problem are expensive and/or time-consuming. Here, the use of one of the most ancient technologies for structuring, embroidering, is proposed to generate sophisticated patterns of active materials, and, in this way, to achieve complex actuation. By combining experiments and computational modeling, the fundamental rules that can predict the folding behavior of sheets with a variety of stitch-patterns are elucidated. It is demonstrated that theoretical mechanics analysis is only suitable to predict the behavior of the simplest experimental setups, whereas computer modeling gives better predictions for more complex cases. Finally, the applicability of the rules by designing basic origami structures and wrinkling substrates with controlled thermal insulation properties is shown.

Mechanical role of a growing solid tumor on cortical folding.

Cortical folding, or convolution of the brain, is a vital process in mammals that causes the brain to have a wrinkled appearance. The existence of different types of prenatal solid tumors may alter this complex phenomenon and cause severe brain disorders. Here we interpret the effects of a growing solid tumor on the cortical folding in the fetal brain by virtue of theoretical analyses and computational modeling. The developing fetal brain is modeled as a simple, double-layered, and soft structure with an outer cortex and an inner core, in combination with a circular tumor model imbedded in the structure to investigate the developmental mechanism of cortical convolution. Analytical approaches offer introductory insight into the deformation field and stress distribution of a developing brain. After the onset of instability, analytical approaches fail to capture complex secondary evolution patterns, therefore a series of non-linear finite element simulations are carried out to study the crease formation and the influence from a growing solid tumor inside the structure. Parametric studies show the dependency of the cortical folding pattern on the size, location, and growth speed of a solid tumor in fetal brain. It is noteworthy to mention that there is a critical distance from the cortex/core interface where the growing tumor shows its pronounced effect on the cortical convolution, and that a growing tumor decreases the gyrification index of cortical convolution while its stiffness does not have a profound effect on the gyrification process.

Mechanisms of circumferential gyral convolution in primate brains.

Mammalian cerebral cortices are characterized by elaborate convolutions. Radial convolutions exhibit homology across primate species and generally are easily identified in individuals of the same species. In contrast, circumferential convolutions vary across species as well as individuals of the same species. However, systematic study of circumferential convolution patterns is lacking. To address this issue, we utilized structural MRI (sMRI) and diffusion MRI (dMRI) data from primate brains. We quantified cortical thickness and circumferential convolutions on gyral banks in relation to axonal pathways and density along the gray matter/white matter boundaries. Based on these observations, we performed a series of computational simulations. Results demonstrated that the interplay of heterogeneous cortex growth and mechanical forces along axons plays a vital role in the regulation of circumferential convolutions. In contrast, gyral geometry controls the complexity of circumferential convolutions. These findings offer insight into the mystery of circumferential convolutions in primate brains.

Commonly preserved and species-specific gyral folding patterns across primate brains.

Cortical folding pattern analysis is very important to understand brain organization and development. Since previous studies mostly focus on human brain cortex, the regularity and variability of cortical folding patterns across primate brains (macaques, chimpanzees and human) remain largely unknown. This paper presents a novel computational framework to identify common or unique gyral folding patterns in macaque, chimpanzee and human brains using magnetic resonance imaging (MRI) data. We quantitatively characterize gyral folding patterns via hinge numbers with cortical surfaces constructed from MRI data, and identify 6 common three-hinge gyral folds that exhibit consistent anatomical locations across these three species as well as 2 unique three hinges in macaque, 6 ones in chimpanzee and 14 ones in human. A novel morphology descriptor is then applied to classify three-hinge gyral folds, and the increasing complexity is identified among the species analyzed. This study may provide novel insights into the regularity and variability of the cerebral cortex from developmental perspective and may potentially facilitate novel neuroimage analyses such as cortical parcellation with correspondences across species in the future.

Mechanism of Consistent Gyrus Formation: an Experimental and Computational Study.

As a significant type of cerebral cortical convolution pattern, the gyrus is widely preserved across species. Although many hypotheses have been proposed to study the underlying mechanisms of gyrus formation, it is currently still far from clear which factors contribute to the regulation of consistent gyrus formation. In this paper, we employ a joint analysis scheme of experimental data and computational modeling to investigate the fundamental mechanism of gyrus formation. Experimental data on mature human brains and fetal brains show that thicker cortices are consistently found in gyral regions and gyral cortices have higher growth rates. We hypothesize that gyral convolution patterns might stem from heterogeneous regional growth in the cortex. Our computational simulations show that gyral convex patterns may occur in locations where the cortical plate grows faster than the cortex of the brain. Global differential growth can only produce a random gyrification pattern, but it cannot guarantee gyrus formation at certain locations. Based on extensive computational modeling and simulations, it is suggested that a special area in the cerebral cortex with a relatively faster growth speed could consistently engender gyri.