Growth and instability of soft tissue in confined environment

Soft tissues are complex materials with typical nonlinear, anisotropic, inhomogeneous behaviors subjected to large strains and stresses. Growth or atrophy of soft materials (refer both of them as growth in the next) in media may lead to instability and formation of surface wrinkling, folding or creasing which depends on a variety of factors, such as geometry and material properties. Instabilities in the soft materials to adjust the shape configuration and dictate morphological evolution is playing a crucial role in the healthy behavior of soft biological tissues like artery, heart, brain, and airway. Inappropriate growth process may cause physiological and pathological disorders in organs such as asthma, mucosal inflammation, gastroenteritis, chronic bronchitis, and tumor invasion. Growth of soft biological materials without confined boundary condition has been studied analytically and numerically in several recent articles [1]. The results show that growth induces residual stresses in the material that often cause large enough compressive stress to initiate instability in the structures [2]. However, constrained or anisotropic growth in the soft materials remains to be further explored. This article presents an isotropic growth of a tube with Neo-Hookean hyperelastic material in the confined boundary. To produce the deformation field and stress distributions, multiplicative decomposition of deformation gradient theory has been adapted and critical growth factors for trigger of creases or detaching have been calculated analytically and numerically. Free energy content of creased structure can be calculated and compared with energy content of deformed but without creases status. Result shows creased or detached tubes have lower energy content and releasing of energy by creasing causes system to be more stabilized. These primary results may provide some fundamental understandings to growth modeling of complicated phenomenon like cortical folding of brain

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

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

Mechanical role of a growing solid tumor on cortical folding

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

Nanoscale Surface Creasing Induced by Post-polymerization Modification

Creasing in soft polymeric films is a result of substantial compressive stresses that trigger instability beyond a critical strain and have been directly related to failure mechanisms in different materials. However, it has been shown that programming these instabilities into soft materials can lead to new applications, such as particle sorting, deformable capillaries, and stimuli-responsive interfaces. In this work, we present a method for fabricating reproducible nanoscale surface instabilities using reactive microcontacting printing (μCP) on activated ester polymer brush layers of poly(pentafluorophenyl acrylate). The sizes and structures of the nanoscale creases can be modulated by varying the grafting density of the brush substrate and pressure applied during μCP. Stress is generated in the film under confinement due to the molecular weight increase of the side chains during post-polymerization modification, which results in substantial in-plane growth in the film and leads to the observed nanoscale creases

Mechanical hierarchy in the formation and modulation of cortical folding patterns

Abstract 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

Role of axonal fibers in the cortical folding patterns: A tale of variability and regularity

Cortical folding is one of the most complex processes that occur during the normal development of the human brain. Despite variability in folding patterns of different individuals, there are a few specific types of preserved folding patterns within individuals or across species. The origin and formation mechanism of variable or regular folding patterns in the human brain yet remains to be thoroughly explored. This study aims to delineate how the interplay between the differential tangential growth of cerebral cortex and axonal fiber tension induces and regulates the folding patterns in a developing human brain. To achieve this aim, an image-based multiscale mechanical model on the basis of the embedded nonlinear finite element method is employed to investigate a set of growth and folding scenarios. Our results show that the differential growth between cortical and subcortical layers is the main inducer of cortical folding. In addition, the gyrification of the cortex pulls the areas with a high density of stiff axonal fiber bundles towards gyri rather than sulci; therefore, axonal fiber bundles induce symmetry breaking, and regulate the folding patterns. In particular, spatial distribution of axonal fiber bundles is the determinant factor to control the locations of gyri and sulci. In conclusion, we propose that neural wiring might be the main regulator of folding patterns responsible for the formation of regular cortical folding patterns. This study provides a deeper understanding of cortical folding and its morphogenesis which are the key to interpreting normal brain development and growth