A mechanical model predicts morphological abnormalities in the developing human brain

Comparative anatomy of the caudate nucleus in canids and felids: Associations with brain size, curvature, cross-sectional properties, and behavioral ecology

The evolutionary history of canids and felids is marked by a deep time separation that has uniquely shaped their behavior and phenotype toward refined predatory abilities. The caudate nucleus is a subcortical brain structure associated with both motor control and cognitive, emotional, and executive functions. We used a combination of three-dimensional imaging, allometric scaling, and structural analyses to compare the size and shape characteristics of the caudate nucleus. The sample consisted of MRI scan data obtained from six canid species (Canis lupus lupus, Canis latrans, Chrysocyon brachyurus, Lycaon pictus, Vulpes vulpes, Vulpes zerda), two canid subspecies (Canis lupus familiaris, Canis lupus dingo), as well as three felids (Panthera tigris, Panthera uncia, Felis silvestris catus). Results revealed marked conservation in the scaling and shape attributes of the caudate nucleus across species, with only slight deviations. We hypothesize that observed differences in caudate nucleus size and structure for the domestic canids are reflective of enhanced cognitive and emotional pathways that possibly emerged during domestication.

Molecular signatures of cortical expansion in the human fetal brain

The third trimester of human gestation is characterised by rapid increases in brain volume and cortical surface area. A growing catalogue of cells in the prenatal brain has revealed remarkable molecular diversity across cortical areas.1,2 Despite this, little is known about how this translates into the patterns of differential cortical expansion observed in humans during the latter stages of gestation. Here we present a new resource, μBrain, to facilitate knowledge translation between molecular and anatomical descriptions of the prenatal developing brain. Built using generative artificial intelligence, μBrain is a three-dimensional cellular-resolution digital atlas combining publicly-available serial sections of the postmortem human brain at 21 weeks gestation3 with bulk tissue microarray data, sampled across 29 cortical regions and 5 transient tissue zones.4 Using μBrain, we evaluate the molecular signatures of preferentially-expanded cortical regions during human gestation, quantified in utero using magnetic resonance imaging (MRI). We find that differences in the rates of expansion across cortical areas during gestation respect anatomical and evolutionary boundaries between cortical types5 and are founded upon extended periods of upper-layer cortical neuron migration that continue beyond mid-gestation. We identify a set of genes that are upregulated from mid-gestation and highly expressed in rapidly expanding neocortex, which are implicated in genetic disorders with cognitive sequelae. Our findings demonstrate a spatial coupling between areal differences in the timing of neurogenesis and rates of expansion across the neocortical sheet during the prenatal epoch. The μBrain atlas is available from: https://garedaba.github.io/micro-brain/ and provides a new tool to comprehensively map early brain development across domains, model systems and resolution scales.

Accuracy meets simplicity: A constitutive model for heterogenous brain tissue

We present a general, hyperelastic, stretch-based potential that shows promise for modeling the mechanics of brain tissue. A specific four-parameter model derived from this general potential outperforms alternative models, such as the modified Ogden model, the Gent model, Demiray model, and machine-learning models, in capturing brain tissue elasticity. Specifically, the stretch-based model achieved R2 values of 0.997, 0.992, and 0.993 (tension, compression, and shear) for the cortex, 0.995, 0.983, and 0.983 for the basal ganglia, 0.994, 0.929, and 0.970 for the corona radiata, and 0.990, 0.896, and 0.969 for the corpus callosum. This work has the potential to advance our understanding of brain tissue mechanics and provides a valuable tool to improve finite element models for the investigation of brain development, injuries, and disease.

Multi-scale measurement of stiffness in the developing ferret brain

Cortical folding is an important process during brain development, and aberrant folding is linked to disorders such as autism and schizophrenia. Changes in cell numbers, size, and morphology have been proposed to exert forces that control the folding process, but these changes may also influence the mechanical properties of developing brain tissue. Currently, the changes in tissue stiffness during brain folding are unknown. Here, we report stiffness in the developing ferret brain across multiple length scales, emphasizing changes in folding cortical tissue. Using rheometry to measure the bulk properties of brain tissue, we found that overall brain stiffness increases with age over the period of cortical folding. Using atomic force microscopy to target the cortical plate, we found that the occipital cortex increases in stiffness as well as stiffness heterogeneity over the course of development and folding. These findings can help to elucidate the mechanics of the cortical folding process by clarifying the concurrent evolution of tissue properties.

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.

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.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Orchestrating human neocortex development across the scales; from micro to macro

How our brains have developed to perform the many complex functions that make us human has long remained a question of great interest. Over the last few decades, many scientists from a wide range of fields have tried to answer this question by aiming to uncover the mechanisms that regulate the development of the human neocortex. They have approached this on different scales, focusing microscopically on individual cells all the way up to macroscopically imaging entire brains within living patients. In this review we will summarise these key findings and how they fit together.

PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data

We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through a spatial transformation function. We start from our previously reported work, which uses 3D tensor product B-spline basis functions to interpolate 3D space. Here, the movement of the B-spline control points, composed with an implicit function describing the shape of the tissue, yields the total deformation gradient field. The deformation gradient is then split into growth and elastic contributions. The growth tensor captures addition of mass, i.e. growth, and evolves according to a constitutive equation which is usually a function of the elastic deformation. Stress is generated in the material due to the elastic component of the deformation alone. The result of the registration is obtained by minimizing a total energy functional which includes: a distance measure reflecting similarity between the shapes, and the total elastic energy accounting for the growth of the tissue. We apply the proposed shape registration framework to study zebrafish embryo epiboly process and tissue expansion during skin reconstruction surgery. We anticipate that our PDE-constrained shape registration method will improve our understanding of biological and medical problems in which tissues undergo extreme deformations over time.

Tissue-Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models

Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time-dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.

A Minireview on Brain Models Simulating Geometrical, Physical, and Biochemical Properties of the Human Brain

There is a growing body of evidences that brain surrogates will be of great interest for researchers and physicians in the medical field. They are currently mainly used for education and training purposes or to verify the appropriate functionality of medical devices. Depending on the purpose, a variety of materials have been used with specific and accurate mechanical and biophysical properties, More recently they have been used to assess the biocompatibility of implantable devices, but they are still not validated to study the migration of leaching components from devices. This minireview shows the large diversity of approaches and uses of brain phantoms, which converge punctually. All these phantoms are complementary to numeric models, which benefit, reciprocally, of their respective advances. It also suggests avenues of research for the analysis of leaching components from implantable devices.

Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons and dendrites—to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

Cortex tissue relaxation and slow to medium load rates dependency can be captured by a two-phase flow poroelastic model

This paper investigates the complex time-dependent behavior of cortex tissue, under adiabatic condition, using a two-phase flow poroelastic model. Motivated by experiments and Biot's consolidation theory, we tackle time-dependent uniaxial loading, confined and unconfined, with various geometries and loading rates from 1μm/s to 100μm/s. The cortex tissue is modeled as the porous solid saturated by two immiscible fluids, with dynamic viscosities separated by four orders, resulting in two different characteristic times. These are respectively associated to interstitial fluid and glial cells. The partial differential equations system is discretized in space by the finite element method and in time by Euler-implicit scheme. The solution is computed using a monolithic scheme within the open-source computational framework FEniCS. The parameters calibration is based on Sobol sensitivity analysis, which divides them into two groups: the tissue specific group, whose parameters represent general properties, and sample specific group, whose parameters have greater variations. Our results show that the experimental curves can be reproduced without the need to resort to viscous solid effects, by adding an additional fluid phase. Through this process, we aim to present multiphase poromechanics as a promising way to a unified brain tissue modeling framework in a variety of settings.

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.

Neocortical development and epilepsy: insights from focal cortical dysplasia and brain tumours

During the past decade, there have been considerable advances in understanding of the genetic and morphogenic processes underlying cortical malformations and developmental brain tumours. Focal malformations are caused by somatic (postzygotic) variants in genes related to cell growth (ie, in the mTOR pathway in focal cortical dysplasia type 2), which are acquired in neuronal progenitors during neurodevelopment. In comparison, developmental brain tumours result from somatic variants in genes related to cell proliferation (eg, in the MAP-kinase pathway in ganglioglioma), which affect proliferating glioneuronal precursors. The timing of the genetic event and the specific gene involved during neurodevelopment will drive the nature and size of the lesion, whether it is a developmental malformation or a brain tumour. There is also emerging evidence that epigenetic processes underlie a molecular memory in epileptogenesis. This knowledge will together facilitate understanding of why and how patients with these lesions have epilepsy, and could form a basis for a move towards precision medicine for this challenging cohort of patients.

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.

A unifying theory of physics and biological information through consciousness

This article represents a transdisciplinary theory that attempts, in a nonmathematical way, to reconcile some contemporary concepts of physics with a novel theory of the mind. It represents a thought experiment that consolidates complexity by melding certain unifying natural science concepts into a coherent reality. The foundations of quantum mechanics and the cosmological mysteries of dark energy, dark matter, and normal matter non-dogmatically explained may be accessible to individuals other than those immersed in mathematical formulas. Through reasoning and models, terms are defined and illustrations provided, further clarifying concepts. In this theory, consciousness represents dynamic differences that come to an end. It exists through interdependent relationships between dark energy, focal points of dark matter (FPDMs), and normal matter with associated states of mind: pure awareness, pure mental state, and mental images state, respectively. Consciousness enables the emergence of an observing ego, a viewpoint that defines conscious events but which is not consciousness in and of itself. For topics described throughout the article, there is a mental and physical aspect that through relationship produces change that makes a difference. In this way, the reader, an 'observing ego,' with a human cognitive viewpoint, may bridge the 'gap' connecting the mental and physical domains. Although the theory can be developed mathematically in more detail, the main emphasis is to provide an intriguing explanation of how physics melds with 'mind,' thus laying the foundation for future explorations into how this theoretical framework of the mind reciprocates with other areas of science.

Growth and form, Lie algebras and special functions

The formation of a biological organism, or an organ within it, can often be regarded as the unfolding of successive equilibria of a mechanical system. In a mathematical model, these changes of equilibria may be considered to be responses of mechanically constrained systems to a change of a reference configuration and of a reference metric, which are in turn driven by genes and their expression. This paper brings together three major threads of research. These are: Lie-type symmetries of equations; models as well as data on growth and pattern formation; and the relation between Lie algebras (and groups) and special functions associated with them. We show that symmetry methods can be generalized to map between solutions to models with different reference metrics. In the case in which we attempt to obtain such equations, they seem too complicated to be of any immediate service to the community of researchers on cortical growth. However, models and data on growth may be used to obtain generators of these Lie algebras empirically and numerically. These generators result in new classes of special functions. The paper is an invitation to develop what we may call empirical Lie algebras and associated functions. The hypothesis that remains to be tested is whether the confluence of ideas described in the paper, namely the Lie algebraic-related consequences of pattern formation and growth, prove useful for deepened understanding of biological growth patterns.

The influence of biophysical parameters in a biomechanical model of cortical folding patterns

Abnormal cortical folding patterns, such as lissencephaly, pachygyria and polymicrogyria malformations, may be related to neurodevelopmental disorders. In this context, computational modeling is a powerful tool to provide a better understanding of the early brain folding process. Recent studies based on biomechanical modeling have shown that mechanical forces play a crucial role in the formation of cortical convolutions. However, the effect of biophysical parameters in these models remain unclear. In this paper, we investigate the effect of the cortical growth, the initial geometry and the initial cortical thickness on folding patterns. In addition, we not only use several descriptors of the folds such as the dimensionless mean curvature, the surface-based three-dimensional gyrification index and the sulcal depth, but also propose a new metric to quantify the folds orientation. The results demonstrate that the cortical growth mode does almost not affect the complexity degree of surface morphology; the variation in the initial geometry changes the folds orientation and depth, and in particular, the slenderer the shape is, the more folds along its longest axis could be seen and the deeper the sulci become. Moreover, the thinner the initial cortical thickness is, the higher the spatial frequency of the folds is, but the shallower the sulci become, which is in agreement with the previously reported effects of cortical thickness.

An inverse modelling study on the local volume changes during early morphoelastic growth of the fetal human brain

We take a data-driven approach to deducing the local volume changes accompanying early development of the fetal human brain. Our approach uses fetal brain atlas MRI data for the geometric changes in representative cases. Using a nonlinear continuum mechanics model of morphoelastic growth, we invert the deformation obtained from MRI registration to arrive at a field for the growth deformation gradient tensor. Our field inversion uses a combination of direct and adjoint methods for computing gradients of the objective function while constraining the optimization by the physics of morphoelastic growth. We thus infer a growth deformation gradient field that obeys the laws of morphoelastic growth. The errors between the MRI data and the forward displacement solution driven by the inverted growth deformation gradient field are found to be smaller than the reference displacement by well over an order of magnitude, and can be driven even lower. The results thus reproduce the three-dimensional growth during the early development of the fetal brain with controllable error. Our findings confirm that early growth is dominated by in plane cortical expansion rather than thickness increase.

A Micropatterned Human-Specific Neuroepithelial Tissue for Modeling Gene and Drug-Induced Neurodevelopmental Defects

The generation of structurally standardized human pluripotent stem cell (hPSC)-derived neural embryonic tissues has the potential to model genetic and environmental mediators of early neurodevelopmental defects. Current neural patterning systems have so far focused on directing cell fate specification spatio-temporally but not morphogenetic processes. Here, the formation of a structurally reproducible and highly-organized neuroepithelium (NE) tissue is directed from hPSCs, which recapitulates morphogenetic cellular processes relevant to early neurulation. These include having a continuous, polarized epithelium and a distinct invagination-like folding, where primitive ectodermal cells undergo E-to-N-cadherin switching and apical constriction as they acquire a NE fate. This is accomplished by spatio-temporal patterning of the mesoendoderm, which guides the development and self-organization of the adjacent primitive ectoderm into the NE. It is uncovered that TGFβ signaling emanating from endodermal cells support tissue folding of the prospective NE. Evaluation of NE tissue structural dysmorphia, which is uniquely achievable in the model, enables the detection of apical constriction and cell adhesion dysfunctions in patient-derived hPSCs as well as differentiating between different classes of neural tube defect-inducing drugs.

A mesoscale finite element modeling approach for understanding brain morphology and material heterogeneity effects in chronic traumatic encephalopathy

Chronic Traumatic Encephalopathy (CTE) affects a significant portion of athletes in contact sports but is difficult to quantify using clinical examinations and modeling approaches. We use an in silico approach to quantify CTE biomechanics using mesoscale Finite Element (FE) analysis that bridges with macroscale whole head FE analysis. The sulci geometry produces complex stress waves that interact with one another to create increased shear stresses at the sulci depth that are significantly larger than in analyses without sulci (from 0.5 to 18.0 kPa). Sulci peak stress concentration regions coincide with experimentally observed CTE sites documented in the literature. HighlightsSulci introduce stress localizations at their depth in the gray matterSulci stress fields interact to produce stress concentration sites in white matterDifferentiating brain tissue properties did not significantly affect peak stresses.

Definitions and classification of malformations of cortical development: practical guidelines

Malformations of cortical development are a group of rare disorders commonly manifesting with developmental delay, cerebral palsy or seizures. The neurological outcome is extremely variable depending on the type, extent and severity of the malformation and the involved genetic pathways of brain development. Neuroimaging plays an essential role in the diagnosis of these malformations, but several issues regarding malformations of cortical development definitions and classification remain unclear. The purpose of this consensus statement is to provide standardized malformations of cortical development terminology and classification for neuroradiological pattern interpretation. A committee of international experts in paediatric neuroradiology prepared systematic literature reviews and formulated neuroimaging recommendations in collaboration with geneticists, paediatric neurologists and pathologists during consensus meetings in the context of the European Network Neuro-MIG initiative on Brain Malformations (https://www.neuro-mig.org/). Malformations of cortical development neuroimaging features and practical recommendations are provided to aid both expert and non-expert radiologists and neurologists who may encounter patients with malformations of cortical development in their practice, with the aim of improving malformations of cortical development diagnosis and imaging interpretation worldwide.

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.

An inverse modelling study on the local volume changes during early morphoelastic growth of the fetal human brain

We take a data-driven approach to deducing the local volume changes accompanying early development of the fetal human brain. Our approach uses fetal brain atlas MRI data for the geometric changes in representative cases. Using a nonlinear continuum mechanics model of morphoelastic growth, we invert the deformation obtained from MRI registration to arrive at a field for the growth deformation gradient tensor. Our field inversion uses a combination of direct and adjoint methods for computing gradients of the objective function while constraining the optimization by the physics of morphoelastic growth. We thus infer a growth deformation gradient field that obeys the laws of morphoelastic growth. The errors between the MRI data and the forward displacement solution driven by the inverted growth deformation gradient field are found to be smaller than the reference displacement by well over an order of magnitude, and can be driven even lower. The results thus reproduce the three-dimensional growth during the early development of the fetal brain with controllable error. Our findings confirm that early growth is dominated by in plane cortical expansion rather than thickness increase.

Continuum modeling for neuronal lamination during cerebral morphogenesis considering cell migration and tissue growth

For neuronal lamination during cerebral morphogenesis, later-born neurons must migrate through already-accumulated neurons. This neuronal migration is biochemically regulated by signaling molecules and mechanically affected by tissue deformation. To understand the neuronal lamination mechanisms, we constructed a continuum model of neuronal migration in a growing deformable tissue. We performed numerical analyses considering the migration promoted by signaling molecules and the tissue growth induced by neuron accumulation. The results suggest that the promoted migration and the space ensured by tissue growth are essential for neuronal lamination. The proposed model can describe the coupling of mechanical and biochemical mechanisms for neuronal lamination.

Numerical investigation of biomechanically coupled growth in cortical folding

Cortical folding-the process of forming the characteristic gyri (hills) and sulci (valleys) of the cortex-is a highly dynamic process that results from the interaction between gene expression, cellular mechanisms, and mechanical forces. Like many other cells, neurons are sensitive to their mechanical environment. Because of this, cortical growth may not happen uniformly throughout gyri and sulci after the onset of cortical folding, which is accompanied by patterns of tension and compression in the surrounding tissue. Here, as an extension of our previous work, we introduce a biomechanically coupled growth model to investigate the importance of interaction between biological growth and mechanical cues during brain development. Our earlier simulations of cortical growth consisted of a homogeneous growing cortex attached to an elastic subcortex. Here, we let the evolution of cortical growth depend on a geometrical quantity-the mean curvature of the cortex-to achieve preferential growth in either gyri or sulci. As opposed to the popular pre-patterning hypothesis, our model treats inhomogeneous cortical growth as the result of folding rather than the cause. The model is implemented numerically in a commercial finite element software Abaqus/Explicit in Abaqus reference manuals, Dassault Systemes Simulia, Providence (2019) by writing user-defined material subroutine (VUMAT). Our simulations show that gyral-sulcal thickness variations are a phenomenon particular to low stiffness ratios. In comparison with cortical thickness measurements of [Formula: see text] human brains via a consistent sampling scheme, our simulations with similar cortical and subcortical stiffnesses suggest that cortical growth is higher in gyri than in sulci.

Folding drives cortical thickness variations

The cortical thickness is a characteristic biomarker for a wide variety of neurological disorders. While the structural organization of the cerebral cortex is tightly regulated and evolutionarily preserved, its thickness varies widely between 1.5 and 4.5 mm across the healthy adult human brain. It remains unclear whether these thickness variations are a cause or consequence of cortical development. Recent studies suggest that cortical thickness variations are primarily a result of genetic effects. Previous studies showed that a simple homogeneous bilayered system with a growing layer on an elastic substrate undergoes a unique symmetry breaking into a spatially heterogeneous system with discrete gyri and sulci. Here, we expand on that work to explore the evolution of cortical thickness variations over time to support our finding that cortical pattern formation and thickness variations can be explained - at least in part - by the physical forces that emerge during cortical folding. Strikingly, as growth progresses, the developing gyri universally thicken and the sulci thin, even in the complete absence of regional information. Using magnetic resonance images, we demonstrate that these naturally emerging thickness variations agree with the cortical folding pattern in n = 9 healthy adult human brains, in n = 564 healthy human brains ages 7-64, and in n = 73 infant brains scanned at birth, and at ages one and two. Additionally, we show that cortical organoids develop similar patterns throughout their growth. Our results suggest that genetic, geometric, and physical events during brain development are closely interrelated. Understanding regional and temporal variations in cortical thickness can provide insight into the evolution and causative factors of neurological disorders, inform the diagnosis of neurological conditions, and assess the efficacy of treatment options.

The Subplate: A Potential Driver of Cortical Folding?

In many species of Mammalia, the surface of the brain develops from a smooth structure to one with many fissures and folds, allowing for vast expansion of the surface area of the cortex. The importance of understanding what drives cortical folding extends beyond mere curiosity, as conditions such as preterm birth, intrauterine growth restriction, and fetal alcohol syndrome are associated with impaired folding in the infant and child. Despite being a key feature of brain development, the mechanisms driving cortical folding remain largely unknown. In this review we discuss the possible role of the subplate, a developmentally transient compartment, in directing region-dependent development leading to sulcal and gyral formation. We discuss the development of the subplate in species with lissencephalic and gyrencephalic cortices, the characteristics of the cells found in the subplate, and the possible presence of molecular cues that guide axons into, and out of, the overlying and multilayered cortex before the appearance of definitive cortical folds. An understanding of what drives cortical folding is likely to help in understanding the origins of abnormal folding patterns in clinical pathologies.

On folding morphogenesis, a mechanical problem

Tissue folding is a fundamental process that sculpts a simple flat epithelium into a complex three-dimensional organ structure. Whether it is the folding of the brain, or the looping of the gut, it has become clear that to generate an invagination or a fold of any form, mechanical asymmetries must exist in the epithelium. These mechanical asymmetries can be generated locally, involving just the invaginating cells and their immediate neighbours, or on a more global tissue-wide scale. Here, we review the different mechanical mechanisms that epithelia have adopted to generate folds, and how the use of precisely defined mathematical models has helped decipher which mechanisms are the key driving forces in different epithelia. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

Genetic and microstructural differences in the cortical plate of gyri and sulci during gyrification in fetal sheep

Gyrification of the cerebral cortex is a developmentally important process, but the mechanisms that drive cortical folding are not fully known. Theories propose that changes within the cortical plate (CP) cause gyrification, yet differences between the CP below gyri and sulci have not been investigated. Here we report genetic and microstructural differences in the CP below gyri and sulci assessed before (at 70 days of gestational age [GA] 70), during (GA 90), and after (GA 110) gyrification in fetal sheep. The areal density of BDNF, CDK5, and NeuroD6 immunopositive cells were increased, and HDAC5 and MeCP2 mRNA levels were decreased in the CP below gyri compared with sulci during gyrification, but not before. Only the areal density of BDNF-immunopositive cells remained increased after gyrification. MAP2 immunoreactivity and neurite outgrowth were also increased in the CP below gyri compared with sulci at GA 90, and this was associated with microstructural changes assessed via diffusion tensor imaging and neurite orientation dispersion and density imaging at GA 98. Differential neurite outgrowth may therefore explain the localized changes in CP architecture that result in gyrification.

Nonuniform growth and surface friction determine bacterial biofilm morphology on soft substrates

During development, organisms acquire three-dimensional (3D) shapes with important physiological consequences. While basic mechanisms underlying morphogenesis are known in eukaryotes, it is often difficult to manipulate them in vivo. To circumvent this issue, here we present a study of developing Vibrio cholerae biofilms grown on agar substrates in which the spatiotemporal morphological patterns were altered by varying the agar concentration. Expanding biofilms are initially flat but later undergo a mechanical instability and become wrinkled. To gain mechanistic insights into this dynamic pattern-formation process, we developed a model that considers diffusion of nutrients and their uptake by bacteria, bacterial growth/biofilm matrix production, mechanical deformation of both the biofilm and the substrate, and the friction between them. Our model shows quantitative agreement with experimental measurements of biofilm expansion dynamics, and it accurately predicts two distinct spatiotemporal patterns observed in the experiments-the wrinkles initially appear either in the peripheral region and propagate inward (soft substrate/low friction) or in the central region and propagate outward (stiff substrate/high friction). Our results, which establish that nonuniform growth and friction are fundamental determinants of stress anisotropy and hence biofilm morphology, are broadly applicable to bacterial biofilms with similar morphologies and also provide insight into how other bacterial biofilms form distinct wrinkle patterns. We discuss the implications of forming undulated biofilm morphologies, which may enhance the availability of nutrients and signaling molecules and serve as a "bet hedging" strategy.

Absorption of Polyunsaturated Fatty Acid (PUFA) Is Related to IgG Blood Levels of Neonatal Pigs during the First 48 Hours Postpartum

The current study is aimed at highlighting the impact of enterally or parenterally applied immunoglobulins (Igs) on polyunsaturated fatty acid (PUFA) absorption in newborn pigs. Piglets were chosen as the appropriate model since they are born agammaglobulinemic and any effects of Ig addition can thus be easily monitored. Twenty-one, new born piglets were used in the study. Plasma levels of PUFAs, ARA, DHA, and EPA dropped (similarly to that seen in human infants) by between 40 and 50% in newborn, unsuckled piglets fed an infant formula for 48 h. However, piglets fed the same infant formula but supplied with immunoglobulins (Igs) either orally, by feeding piglets with swine or bovine colostrum, or intravenously, by i.u.a. (intraumbilical artery) infusion of swine or human Ig preparations or swine serum, demonstrated improved growth and PUFA levels similar to those observed at birth. The significant positive correlation was found between the body weight gain, as well as levels of ARA and EPA, and plasma immunoglobulins concentration. These results indicate the importance of the presence of Ig in the blood for appropriate absorption of dietary PUFAs and probably other nutrients in newborn piglets. This may have an impact on the dietary guidelines for human neonates, especially those born prematurely with low plasma Ig levels, since PUFAs are important factors for brain development in early life.

Global Perturbation of Initial Geometry in a Biomechanical Model of Cortical Morphogenesis

Cortical folding pattern is a main characteristic of the geometry of the human brain which is formed by gyri (ridges) and sulci (grooves). Several biological hypotheses have suggested different mechanisms that attempt to explain the development of cortical folding and its abnormal evolutions. Based on these hypotheses, biomechanical models of cortical folding have been proposed. In this work, we compare biomechanical simulations for several initial conditions by using an adaptive spherical parameterization approach. Our approach allows us to study and explore one of the most potential sources of reproducible cortical folding pattern: the specification of initial geometry of the brain.

On early brain folding patterns using biomechanical growth modeling

Abnormal cortical folding patterns may be related to neurodevelopmental disorders such as lissencephaly and polymicrogyria. In this context, computational modeling is a powerful tool to provide a better understanding of the early brain folding process. Recent studies based on biomechanical modeling have shown that mechanical forces play a crucial role in the formation of cortical convolutions. However, the correlation between simulation results and biological facts, and the effect of physical parameters in these models remain unclear. In this paper, we propose a new brain longitudinal length growth model to improve brain model growth. In addition, we investigate the effect of the initial cortical thickness on folding patterns, quantifying the folds by the surface-based three-dimensional gyrification index and a spectral analysis of gyrification. The results tend to show that the use of such biomechanical models could highlight the links between neurodevelopmental diseases and physical parameters.

A Model of Brain Folding Based on Strong Local and Weak Long-Range Connectivity Requirements

Throughout the animal kingdom, the structure of the central nervous system varies widely from distributed ganglia in worms to compact brains with varying degrees of folding in mammals. The differences in structure may indicate a fundamentally different circuit organization. However, the folded brain most likely is a direct result of mechanical forces when considering that a larger surface area of cortex packs into the restricted volume provided by the skull. Here, we introduce a computational model that instead of modeling mechanical forces relies on dimension reduction methods to place neurons according to specific connectivity requirements. For a simplified connectivity with strong local and weak long-range connections, our model predicts a transition from separate ganglia through smooth brain structures to heavily folded brains as the number of cortical columns increases. The model reproduces experimentally determined relationships between metrics of cortical folding and its pathological phenotypes in lissencephaly, polymicrogyria, microcephaly, autism, and schizophrenia. This suggests that mechanical forces that are known to lead to cortical folding may synergistically contribute to arrangements that reduce wiring. Our model provides a unified conceptual understanding of gyrification linking cellular connectivity and macroscopic structures in large-scale neural network models of the brain.

Instability of Incompatible Bilayered Soft Tissues and the Role of Interface Conditions

Mechanical stability analysis is instructive in explaining biological processes like morphogenesis, organogenesis, and pathogenesis of soft tissues. Consideration of the layered, residually stressed structure of tissues, requires accounting for the joint effects of interface conditions and layer incompatibility. This paper is concerned with the influence of imposed rate (incremental) interface conditions (RICs) on critical loads in soft tissues, within the context of linear bifurcation analysis. Aiming at simplicity, we analyze a model of bilayered isotropic hyperelastic (neo-Hookean) spherical shells with residual stresses generated by “shrink-fitting” two perfectly bonded layers with radial interfacial incompatibility. This setting allows a comparison between available, seemingly equivalent, interface conditions commonly used in the literature of layered media stability. We analytically determine the circumstances under which the interface conditions are equivalent or not, and numerically demonstrate significant differences between interface conditions with increasing level of layer incompatibility. Differences of more than tenfold in buckling and 30% in inflation instability critical loads are recorded using the different RICs. Contrasting instability characteristics are also revealed using the different RICs in the presence of incompatibility: inflation instability can occur before pressure maximum, and spontaneous instability may be excluded for thin shells. These findings are relevant to the growing body of stability studies of layered and residually stressed tissues. The impact of interface conditions on critical thresholds is significant in studies that use concepts of instability to draw conclusions about the normal development and the pathologies of tissues like arteries, esophagus, airways, and the brain.

The Shrinking Brain: Cerebral Atrophy Following Traumatic Brain Injury

Cerebral atrophy in response to traumatic brain injury is a well-documented phenomenon in both primary investigations and review articles. Recent atrophy studies focus on exploring the region-specific patterns of cerebral atrophy; yet, there is no study that analyzes and synthesizes the emerging atrophy patterns in a single comprehensive review. Here we attempt to fill this gap in our current knowledge by integrating the current literature into a cohesive theory of preferential brain tissue loss and by identifying common risk factors for accelerated atrophy progression. Our review reveals that observations for mild traumatic brain injury remain inconclusive, whereas observations for moderate-to-severe traumatic brain injury converge towards robust patterns: brain tissue loss is on the order of 5% per year, and occurs in the form of generalized atrophy, across the entire brain, or focal atrophy, in specific brain regions. The most common regions of focal atrophy are the thalamus, hippocampus, and cerebellum in gray matter and the corpus callosum, corona radiata, and brainstem in white matter. We illustrate the differences of generalized and focal gray and white matter atrophy on emerging deformation and stress profiles across the whole brain using computational simulation. The characteristic features of our atrophy simulations-a widening of the cortical sulci, a gradual enlargement of the ventricles, and a pronounced cortical thinning-agree well with clinical observations. Understanding region-specific atrophy patterns in response to traumatic brain injury has significant implications in modeling, simulating, and predicting injury outcomes. Computational modeling of brain atrophy could open new strategies for physicians to make informed decisions for whom, how, and when to administer pharmaceutical treatment to manage the chronic loss of brain structure and function.

Non-uniform curvature and anisotropic deformation control wrinkling patterns on tori

We investigate wrinkling patterns in a tri-layer torus consisting of an expanding thin outer layer, an intermediate soft layer and an inner core with a tunable shear modulus, inspired by pattern formation in developmental biology, such as follicle pattern formation during the development of chicken embryos. We show from large-scale finite element simulations that hexagonal wrinkling patterns form for stiff cores whereas stripe wrinkling patterns develop for soft cores. Hexagons and stripes co-exist to form hybrid patterns for cores with intermediate stiffness. The governing mechanism for the pattern transition is that the stiffness of the inner core controls the degree to which the major radius of the torus expands - this has a greater effect on deformation in the long direction as compared to the short direction of the torus. This anisotropic deformation alters stress states in the outer layer which change from biaxial (preferred hexagons) to uniaxial (preferred stripes) compression as the core stiffness is reduced. As the outer layer continues to expand, stripe and hexagon patterns will evolve into zigzags and segmented labyrinths, respectively. Stripe wrinkles are observed to initiate at the inner surface of the torus while hexagon wrinkles start from the outer surface as a result of curvature-dependent stresses in the torus. We further discuss the effects of elasticities and geometries of the torus on the wrinkling patterns.

Cortical neurodevelopment in pre-manifest Huntington's disease

Background

The expression of the HTT CAG repeat expansion mutation causes neurodegeneration in Huntington's disease (HD). Objectives: In light of the – mainly in-vitro – evidence suggesting an additional role of huntingtin in neurodevelopment we used 3T MRI to test the hypothesis that in CAG-expanded individuals without clinical signs of HD (preHD) there is evidence for neurodevelopmental abnormalities.

Methods

We specifically investigated the complexity of cortical folding, a measure of cortical neurodevelopment, employing a novel method to quantify local fractal dimension (FD) measures that uses spherical harmonic reconstructions.

Results

The complexity of cortical folding differed at a group level between preHD (n = 57) and healthy volunteers (n = 57) in areas of the motor and visual system as well as temporal cortical areas. However, there was no association between the complexity of cortical folding and the loss in putamen volume that was clearly evident in preHD.

Conclusions

Our results suggest that HTT CAG repeat length may have an influence on cortical folding without evidence that this leads to developmental pathology or was clinically meaningful. This suggests that the HTT CAG-repeat expansion mutation may influence the processes governing cortical neurodevelopment; however, that influence seems independent of the events that lead to neurodegeneration.

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Measures of cortical neurodevelopment in preclinical Huntington's disease (HD) gene carriers differ from healthy volunteers

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The influence on cortical folding of the HD gene was not associated with developmental pathology or clinically meaningful

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The influence of the HD gene on cortical neurodevelopment may differ from that on neurodegeneration

Revisiting the wrinkling of elastic bilayers I: linear analysis

Wrinkling is a universal instability occurring in a wide variety of engineering and biological materials. It has been studied extensively for many different systems but a full description is still lacking. Here, we provide a systematic analysis of the wrinkling of a thin hyperelastic film over a substrate in plane strain using stream functions. For comparison, we assume that wrinkling is generated either by the isotropic growth of the film or by the lateral compression of the entire system. We perform an exhaustive linear analysis of the wrinkling problem for all stiffness ratios and under a variety of additional boundary and material effects. Namely, we consider the effect of added pressure, surface tension, an upper substrate and fibres. We obtain analytical estimates of the instability in the two asymptotic regimes of long and short wavelengths. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.

On the Variable Clinical Presentation of Molar-Incisor Hypomineralization

Molar-incisor hypomineralization (MIH) is a condition that is defined based on its peculiar clinical presentation. Original reports on the etiology of the condition and possible risk factors were inconclusive, and we refuted the original suggestion that MIH is an idiopathic condition and suggested that MIH has complex inheritance and is due to the interaction of more than one gene and the environment. Our group was the first to suggest MIH has a genetic component that involves genetic variation in genes expressed during dental enamel formation. Later we expanded this work to include genes related to the immune response. In this report, we provide a rationale to explain the variation seen in the clinical presentation of MIH, which can affect just one molar out of the four or just a portion of a particular molar.

Mechanical instability and interfacial energy drive biofilm morphogenesis

Surface-attached bacterial communities called biofilms display a diversity of morphologies. Although structural and regulatory components required for biofilm formation are known, it is not understood how these essential constituents promote biofilm surface morphology. Here, using Vibrio cholerae as our model system, we combine mechanical measurements, theory and simulation, quantitative image analyses, surface energy characterizations, and mutagenesis to show that mechanical instabilities, including wrinkling and delamination, underlie the morphogenesis program of growing biofilms. We also identify interfacial energy as a key driving force for mechanomorphogenesis because it dictates the generation of new and the annihilation of existing interfaces. Finally, we discover feedback between mechanomorphogenesis and biofilm expansion, which shapes the overall biofilm contour. The morphogenesis principles that we discover in bacterial biofilms, which rely on mechanical instabilities and interfacial energies, should be generally applicable to morphogenesis processes in tissues in higher organisms.

Engineers have long studied how mechanical instabilities cause patterns to form in inanimate materials, and recently more attention has been given to how such forces affect biological systems. For example, stresses can build up within a tissue if one layer grows faster than an adjacent layer. The tissue can release this stress by wrinkling, folding or creasing.

Though ancient and single-celled, bacteria can also develop spectacular patterns when they exist in the lifestyle known as a biofilm: a community of cells adhered to a surface. But do mechanical instabilities drive the patterns seen in biofilms?

To investigate, Yan, Fei, Mao et al. grew biofilms of the bacterium called Vibrio cholerae – which causes the disease cholera – on solid, non-growing ‘substrates’. This work revealed that as the biofilms grow, their expansion is constrained by the substrate, and this situation generates mechanical stresses. To release the stresses, the biofilm initially folds to form wrinkles. Later, as the biofilm expands further, small parts of it detach from the substrate to form blisters. The same forces that keep water droplets spherical (known as interfacial forces) dictate how the blisters evolve, interact, and eventually shape the expanding biofilm. Using these principles, Yan et al. could engineer the biofilm into desired shapes.

Collectively, the results presented by Yan et al. connect the shape of the biofilm surface with its material properties, in particular its stiffness. Understanding this relationship could help researchers to develop new ways to remove harmful biofilms, such as those that cause disease or that damage underwater structures. The stiffness of biofilms is already known to affect how well bacteria can resist antibiotics. Future studies could look for new genes or compounds that change the material properties of a biofilm, thereby altering the biofilm surface.

How Forces Fold the Cerebral Cortex

Improved understanding of the factors that govern folding of the cerebral cortex is desirable for many reasons. The existence of consistent patterns in folding within and between species suggests a fundamental role in brain function. Abnormal folding patterns found in individuals affected by a diverse array of neurodevelopmental disorders underline the clinical relevance of understanding the folding process. Recent experimental and computational efforts to elucidate the biomechanical forces involved in cerebral cortical folding have converged on a consistent approach. Brain growth is modeled with two components: an expanding outer zone, destined to become the cerebral cortex, is mechanically coupled to an inner zone, destined to become white matter, that grows at a slower rate, perhaps in response to stress induced by expansion from the outer layer. This framework is consistent with experimentally observed internal forces in developing brains, and with observations of the folding process in physical models. In addition, computational simulations based on this foundation can produce folding patterns that recapitulate the characteristics of folding patterns found in gyroencephalic brains. This perspective establishes the importance of mechanical forces in our current understanding of how brains fold, and identifies realistic ranges for specific parameters in biophysical models of developing brain tissue. However, further refinement of this approach is needed. An understanding of mechanical forces that arise during brain development and their cellular-level origins is necessary to interpret the consequences of abnormal brain folding and its role in functional deficits as well as neurodevelopmental disease.Dual Perspectives Companion Paper: How Cells Fold the Cerebral Cortex, by Víctor Borrell.

A mechanical method of cerebral cortical folding development based on thermal expansion

Cortical folding malformations are associated with several severe neurological disorders, including epilepsy, schizophrenia and autism. However, the mechanism behind cerebral cortical folding development is not yet clear. In this paper, we propose a mechanical method based on thermal expansion to simulate the development of human cerebral cortical folding. The influences of stiffness ratio, growth rate ratio, and initial cortical plate thickness on cortical folding are discussed. The results of our thermal expansion model are consistent with previous studies, indicating that abnormal values of the aforementioned three factors could directly lead to cortical folding malformation in a generally fixed pattern.