A model of tension-induced fiber growth predicts white matter organization during brain folding

Altered thalamocortical tract trajectory growth with undisrupted thalamic parcellation pattern in human lissencephaly brain at mid-gestational stage

Proper topographically organized neural connections between the thalamus and the cerebral cortex are mandatory for thalamus function. Thalamocortical (TC) fiber growth begins during the embryonic period and completes by the third trimester of gestation, so that human neonates at birth have a thalamus with a near-facsimile of adult functional parcellation. Whether congenital neocortical anomaly (e.g., lissencephaly) affects TC connection in humans is unknown. Here, via diffusion MRI fiber-tractography analysis of long-term formalin-fixed postmortem fetal brain diagnosed as lissencephaly in comparison with an age-matched normal one, we found similar topological patterns of thalamic subregions and of internal capsule parcellated by TC fibers. However, lissencephaly fetal brain showed white matter structural changes, including fewer/less organized TC fibers and optic radiations, and much less cortical plate invasion by TC fibers - particularly around the shallow central sulcus. Diffusion MRI fiber tractography of normal fetal brains at 15, 23, and 26 gestational weeks (GW) revealed dynamic volumetric change of each parcellated thalamic subregion, suggesting coupled developmental progress of the thalamus with the corresponding cortex. Moreover, from GW23 and GW26 normal fetal brains, TC endings in the cortical plate could be delineated to reflect cumulative progressive TC invasion of cortical plate. By contrast, lissencephaly brain showed a dramatic decrease in TC invasion of the cortical plate. Our study thus shows the feasibility of diffusion MRI fiber tractography in postmortem long-term formalin-fixed fetal brains to disclose the developmental progress of TC tracts coordinating with thalamic and neocortical growth both in normal and lissencephaly fetal brains at mid-gestational stage.

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.

Longitudinal MRI of the developing ferret brain reveals regional variations in timing and rate of growth

Normative ferret brain development was characterized using magnetic resonance imaging. Brain growth was longitudinally monitored in 10 ferrets (equal numbers of males and females) from postnatal day 8 (P8) through P38 in 6-d increments. Template T2-weighted images were constructed at each age, and these were manually segmented into 12 to 14 brain regions. A logistic growth model was used to fit data from whole brain volumes and 8 of the individual regions in both males and females. More protracted growth was found in males, which results in larger brains; however, sex differences were not apparent when results were corrected for body weight. Additionally, surface models of the developing cortical plate were registered to one another using the anatomically-constrained Multimodal Surface Matching algorithm. This, in turn, enabled local logistic growth parameters to be mapped across the cortical surface. A close similarity was observed between surface area expansion timing and previous reports of the transverse neurogenic gradient in ferrets. Regional variation in the extent of surface area expansion and the maximum expansion rate was also revealed. This characterization of normative brain growth over the period of cerebral cortex folding may serve as a reference for ferret studies of brain development.

Structural connectome architecture shapes the maturation of cortical morphology from childhood to adolescence

Cortical thinning is an important hallmark of the maturation of brain morphology during childhood and adolescence. However, the connectome-based wiring mechanism that underlies cortical maturation remains unclear. Here, we show cortical thinning patterns primarily located in the lateral frontal and parietal heteromodal nodes during childhood and adolescence, which are structurally constrained by white matter network architecture and are particularly represented using a network-based diffusion model. Furthermore, connectome-based constraints are regionally heterogeneous, with the largest constraints residing in frontoparietal nodes, and are associated with gene expression signatures of microstructural neurodevelopmental events. These results are highly reproducible in another independent dataset. These findings advance our understanding of network-level mechanisms and the associated genetic basis that underlies the maturational process of cortical morphology during childhood and adolescence.

Changed cortical thickness and sulcal depth in pediatric acute lymphoblastic leukemia survivors treated with chemotherapy only

The purpose of this study is to observe the changes of cortical morphological characteristics and their potential contribution to cognitive function in ALL survivors by using surface-based morphometry (SBM). Using SBM analysis, we calculated and compared group differences in cortical thickness, sulcal depth, gyrification, and fractal dimension of the cerebral cortex between 18 pediatric ALL survivors treated on chemotherapy-only protocols and off treatment within 2 years, and 18 healthy controls (HCs) with two-sample t-tests [P < 0.05, family-wise error (FWE) corrected]. Relationships between abnormal cortical characteristic values and cognitive function parameters were investigated with partial correlation analysis, taking age as a covariate. We found decreased cortical thickness mainly located in the prefrontal and temporal region, and increased sulcal depth in left rostral middle frontal cortex and left pars orbitalis in the ALL survivors compared to HCs. There were no statistically significant differences in the gyrification and fractal dimension between the two groups. In ALL survivors, cortical thickness and sulcal depth of above areas values revealed no significant correlation with the cognitive function parameters. In conclusion, pediatric ALL survivors show decreased cortical thickness in prefrontal and temporal regions, and increased sulcal depth in prefrontal region. These results suggest that SBM-based approach can be used to assess changes of cortical morphological characteristics in pediatric ALL survivors.

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

We review our recent contributions to anisotropic soft matter models for liquid crystal interfaces, drops and membranes, emphasizing validations with experimental and biological data, and with related theory and simulation literature. The presentation aims to illustrate and characterize the rich output and future opportunities of using a methodology based on the liquid crystal-membrane shape equation applied to static and dynamic pattern formation phenomena. The geometry of static and kinetic shapes is usually described with dimensional curvatures that co-mingle shape and curvedness. In this review, we systematically show how the application of a novel decoupled shape-curvedness framework to practical and ubiquitous soft matter phenomena, such as the shape of drops and tactoids and bending of evolving membranes, leads to deeper quantitative insights than when using traditional dimensional mean and Gaussian curvatures. The review focuses only on (1) statics of wrinkling and shape selection in liquid crystal interfaces and membranes; (2) kinetics and dissipative dynamics of shape evolution in membranes; and (3) computational methods for shape selection and shape evolution; due to various limitations other important topics are excluded. Finally, the outlook follows a similar structure. The main results include: (1) single and multiple wavelength corrugations in liquid crystal interfaces appear naturally in the presence of surface splay and bend orientation distortions with scaling laws governed by ratios of anchoring-to-isotropic tension energy; adding membrane elasticity to liquid crystal anchoring generates multiple scales wrinkling as in tulips; drops of liquid crystals encapsulates in membranes can adopt, according to the ratios of anchoring/tension/bending, families of shapes as multilobal, tactoidal, and serrated as observed in biological cells. (2) Mapping the liquid crystal director to a membrane unit normal. The dissipative shape evolution model with irreversible thermodynamics for flows dominated by bending rates, yields new insights. The model explains the kinetic stability of cylinders, while spheres and saddles are attractors. The model also adds to the evolving understanding of outer hair cells in the inner ear. (3) Computational soft matter geometry includes solving shape equations, trajectories on energy and orientation landscapes, and shape-curvedness evolutions on entropy production landscape with efficient numerical methods and adaptive approaches.

Ultrafast and facile construction of programmable, multidimensional wrinkled-patterned polyacrylamide/sodium alginate hydrogels for human skin-like tactile perception

Customizable structures and patterns are becoming powerful tools for biomimetic design and application of soft materials. The construction of long-range ordered self-wrinkled structures on multi-dimensional and complex-shaped surfaces with facile, fast and efficient strategies still faces serious challenges. During the stretch-recovery process, the carboxyl groups in the polyacrylamide/sodium alginate dual network gel form robust coordination with Fe3+ to achieve a hard shell layer, resulting in a modulus mismatch between the inner soft layer and the outer hard layer, thereby forming a wrinkled surface. This flexible strategy allows simultaneous construction of complex topologies from 1D to 3D wits well-organized microstructure and controllable dimensions. The mechanism of the influence of ion treating time and pre-stretching ratio on wrinkle wavelength was explored in detail. The finite element simulations matched well with the experimental results. Due to the unique surface and dual crosslinking network, the self-wrinkled hydrogel maintains a high sensitivity of up to 67.47 kPa-1 in 1000 compression cycles. As a high-sensitivity pressure sensor integrated into the detection system, it can be efficiently applied to the contact dynamic tactile perception and monitoring of various movement behaviors of the human body.

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.

Biomechanical models and mechanisms of cellular morphogenesis and cerebral cortical expansion and folding

Morphogenesis of the nervous system involves a highly complex spatio-temporal pattern of physical forces (mainly tension and pressure) acting on cells and tissues that are pliable but have an intricately organized cytoskeletal infrastructure. This review begins by covering basic principles of biomechanics and the core cytoskeletal toolkit used to regulate the shapes of cells and tissues during embryogenesis and neural development. It illustrates how the principle of 'tensegrity' provides a useful conceptual framework for understanding how cells dynamically respond to forces that are generated internally or applied externally. The latter part of the review builds on this foundation in considering the development of mammalian cerebral cortex. The main focus is on cortical expansion and folding - processes that take place over an extended period of prenatal and postnatal development. Cortical expansion and folding are likely to involve many complementary mechanisms, some related to regulating cell proliferation and migration and others related to specific types and patterns of mechanical tension and pressure. Three distinct multi-mechanism models are evaluated in relation to a set of 18 key experimental observations and findings. The Composite Tension Plus (CT+) model is introduced as an updated version of a previous multi-component Differential Expansion Sandwich Plus (DES+) model (Van Essen, 2020); the new CT+ model includes 10 distinct mechanisms and has the greatest explanatory power among published models to date. Much needs to be done in order to validate specific mechanistic components and to assess their relative importance in different species, and important directions for future research are suggested.

Effects of stress-dependent growth on evolution of sulcal direction and curvature in models of cortical folding

The majority of human brain folding occurs during the third trimester of gestation. Although many studies have investigated the physical mechanisms of brain folding, a comprehensive understanding of this complex process has not yet been achieved. In mechanical terms, the "differential growth hypothesis" suggests that the formation of folds results from a difference in expansion rates between cortical and subcortical layers, which eventually leads to mechanical instability akin to buckling. It has also been observed that axons, a substantial component of subcortical tissue, can elongate or shrink under tensile or compressive stress, respectively. Previous work has proposed that this cell-scale behavior in aggregate can produce stress-dependent growth in the subcortical layers. The current study investigates the potential role of stress-dependent growth on cortical surface morphology, in particular the variations in folding direction and curvature over the course of development. Evolution of sulcal direction and mid-cortical surface curvature were calculated from finite element simulations of three-dimensional folding in four different initial geometries: (i) sphere; (ii) axisymmetric oblate spheroid; (iii) axisymmetric prolate spheroid; and (iv) triaxial spheroid. The results were compared to mid-cortical surface reconstructions from four preterm human infants, imaged and analyzed at four time points during the period of brain folding. Results indicate that models incorporating subcortical stress-dependent growth predict folding patterns that more closely resemble those in the developing human brain.

Statement of Significance

Cortical folding is a critical process in human brain development. Aberrant folding is associated with disorders such as autism and schizophrenia, yet our understanding of the physical mechanism of folding remains limited. Ultimately mechanical forces must shape the brain. An important question is whether mechanical forces simply deform tissue elastically, or whether stresses in the tissue modulate growth. Evidence from this paper, consisting of quantitative comparisons between patterns of folding in the developing human brain and corresponding patterns in simulations, supports a key role for stress-dependent growth in cortical folding.

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.

Orchestrated neuronal migration and cortical folding: A computational and experimental study

Brain development involves precisely orchestrated genetic, biochemical, and mechanical events. At the cellular level, neuronal proliferation in the innermost zone of the brain followed by migration towards the outermost layer results in a rapid increase in brain surface area, outpacing the volumetric growth of the brain, and forming the highly folded cortex. This work aims to provide mechanistic insights into the process of brain development and cortical folding using a biomechanical model that couples cell division and migration with volumetric growth. Unlike phenomenological growth models, our model tracks the spatio-temporal development of cohorts of neurons born at different times, with each cohort modeled separately as an advection-diffusion process and the total cell density determining the extent of volume growth. We numerically implement our model in Abaqus/Standard (2020) by writing user-defined element (UEL) subroutines. For model calibration, we apply in utero electroporation (IUE) to ferret brains to visualize and track cohorts of neurons born at different stages of embryonic development. Our calibrated simulations of cortical folding align qualitatively with the ferret experiments. We have made our experimental data and finite-element implementation available online to offer other researchers a modeling platform for future study of neurological disorders associated with atypical neurodevelopment and cortical malformations.

Brain development and cortical folding is a highly dynamic process that results from the interaction between gene expression, cellular mechanisms, and mechanical forces. Here, we expand on existing mathematical models of brain development and cortical folding to capture the behavior of multiple different subpopulations of neurons. By calibrating our biomechanical model to our novel experiments on ferrets, we can track the distribution of neurons over time and observe how the brain grows and develops its characteristic folds. Our calibrated model captures interactions between cell behavior and tissue deformation and offers more detailed information about the orchestrated migration of neuronal subpopulations. This work offers new mechanistic insights into brain development and opens the door to future investigations of atypical brain development caused by disrupted neuronal activities, particularly those alterations associated with injury, exposure, or treatment at a specific location or time during development. Finally, our experimental data and numerical implementations are provided as a resource online for the use of other researchers.