Cell Wall Curvature Research Articles

Viscoelastic circular cell honeycomb helmet liners for reducing head rotation and brain strain in oblique impacts

Rotational head motion is one of the major contributors to brain tissue strain during head impacts, which damages axons and vessels and leads to traumatic brain injury. Helmet technologies have come to market promising enhanced protection against such rotational head motion. We recently introduced novel air-filled viscoelastic cell arrays and showed that their shear response under oblique impacts can be tailored through altering the cell wall curvature. We found that concave cells provide shear stiffness that is a few folds larger than that of convex cells. Here we test whether altering the cell curvature can reduce head rotational kinematics and brain strain and whether the viscoelastic cell arrays outperform the reference EPS foam-based liner. To test these hypotheses, we incorporate the viscoelastic cell arrays in a bicycle helmet liner. We use validated finite element models of the helmet and replace the liner with validated finite element models of the cellular cell arrays. We simulate oblique impacts at different locations to represent a wide range of real-world bicycle head impacts. In all cases, the head kinematics and brain deformation metrics indicate significant improvements with the novel cell arrays over the conventional EPS liner. We show that the shear-compliant cell arrays can reduce head rotational acceleration by as much as 64 % and brain strain by 69 %, but not in all impact locations. Cell arrays with similar axial stiffness yet lower shear stiffness often bottomed out, indicating that a considerable amount of energy is dissipated via cell shearing around the impact zone. Our results show that placement of cells with varying amounts of shear stiffness should be optimised, with the most shear-compliant cells near the crown and the least near the temples. This study shows the promising performance of viscoelastic cell arrays in protecting the head and brain under oblique impacts and provides avenues for optimising the distribution of their compressive-shear properties.

The semi-automated development of plant cell wall finite element models

This study presents a methodology for a high-throughput digitization and quantification process of plant cell walls characterization, including the automated development of two-dimensional finite element models. Custom algorithms based on machine learning can also analyze the cellular microstructure for phenotypes such as cell size, cell wall curvature, and cell wall orientation. To demonstrate the utility of these models, a series of compound microscope images of both herbaceous and woody representatives were observed and processed. In addition, parametric analyses were performed on the resulting finite element models. Sensitivity analyses of the structural stiffness of the resulting tissue based on the cell wall elastic modulus and the cell wall thickness; demonstrated that the cell wall thickness has a three-fold larger impact of tissue stiffness than cell wall elastic modulus.

The role of network topology on the uniaxial tensile behaviour of low density random open cellular structures

The effect of cellular structure on the mechanical properties of cellular solids is included in the prefactors of the relative density term in the Gibson and Ashby scaling laws. The effect of cell shape, cell size distribution, cell shape anisotropy, cell wall curvature and strut cross sectional variation have been known to affect these prefactors. This paper investigates the dependence of these prefactors on the network connectivity in random honeycombs and three-dimensional random open cellular structures. Beginning with intact structures, the network connectivity is reduced by randomly removing struts. A scaled genus density, that remains independent of sample volume, absolute cell size, and the relative density, has been defined and taken as a quantitative measure of the global connectivity. The variation in the overall stiffness and offset yield stress due to loss in connectivity was found to clearly depend on the scaled genus density when the relative density is kept constant, indicating that the geometric prefactors are functions of scaled genus density. The prefactors for intact perturbed cubic voronoi, perturbed BCC voronoi structures, and perturbed cubic body diagonal lattices with widely differing scaled genus density also confirm this strong correlation. We also show that the prefactors can be factored to quantitatively decouple the effects of anisotropy and scaled genus density.

Efficient computational modelling of closed cell metallic foams using a morphologically controlled shell geometry

This contribution addresses the finite element modelling of closed cell metallic foams using Representative Volume Elements (RVEs) based on shell geometries directly extracted from implicitly defined 3D geometries. 3D RVEs of closed cell foam materials are produced by means of a generation strategy allowing a close morphological control reproducing fine scale geometrical features incorporating cell size, cell wall thickness and cell wall curvature distributions. The strategy is built on three computational ingredients: (i) a random packing algorithm based on random sequential addition assisted by neighbour distance control, (ii) a distance field-based shape tessellation (morphing) that allows incorporating cell wall curvatures and varying cell wall thicknesses and (iii) a close control on the shape of the cells. In order to decrease the computational cost of a full 3D finite element model, an original approach is proposed to produce a shell-based geometry directly from 3D information. Extracting the shell geometry from the implicitly defined 3D geometry based on the zero level of distance fields that would represent the cell walls is computationally impossible. Therefore, a novel robust procedure is proposed using careful cutting operations on distance fields for this purpose. The effect of the different microstructural geometrical features of interest on the average mechanical behaviour of the foam is investigated using shell-based finite element analyses. The computational cost and the accuracy of the proposed shell models are then assessed by comparing their results to full 3D simulations. The macroscopic behaviour of the generated shell-based model under compressive loading is then assessed up to the densification stage (including contact), and compared qualitatively with experiments from the literature. The macroscopic behaviour of the shell-based model is explained by linking it to cell/wall level deformation mechanisms.

English

English

In-plane homogenization of commercial hexagonal honeycombs considering the cell wall curvature and adhesive layer influence

In the present paper a general parameterization of a periodic hexagonal honeycomb with double vertical walls (commercial honeycomb) is proposed and a new analytic model is established. More attention is paid to account for the radius of curvature of the inclined walls, the adhesive layer thickness, and adhesive fillet at nodes. Then, neglecting the skin effect, in plane elastic constants is obtained analytically using the beam theory. The deformation mechanisms of the honeycomb cells include flexure, stretching, shearing and hinging. The mechanism of hinging is included through small fictitious beams in order to balance the local effects which cannot be captured using the beam theory. Hinging can be neglected when the thickness of these beams becomes infinite or optimally chosen by a proper thickness as to minimize the cumulative errors of the analytical assumptions. The new analytic model presented in this paper can be particularized to the extended Balawi and Abot model if some parameters are adequately modified. The finite element modeling of a representative volume element is used for model calibration and validation considering different relative densities of real honeycombs. The numerical results obtained as a reference for the effective elastic constants are discussed by comparing them to the ones given by the analytic model; its advantages and pitfalls are discussed and explained through a case study and some sensitivity analyses. Numerical simulations are also done in order to establish the distribution of the stresses in cell walls and nodes to confirm the hypotheses used for determining the analytical relations and to explain some limits of the analytic model. The results provide new insights into understanding the mechanics of honeycombs and facilitate the design of new types of cellular materials, including composite hexagonal cell cores.

Consideration of Internal Board Camera Optics for Triaxial Testing Applications

Abstract The application of small board cameras, located within a triaxial cell to determine radial and axial strain, was investigated. Specifically, charge-coupled device (CCD) sensors were utilized in conjunction with precision pinhole apertures to capture images from within the triaxial cell. The cameras were fully immersed in electronics-grade silicone oil and were able to withstand cell pressures that are common to triaxial testing (up to 1034 kPa (150 psi)). The small size of the cameras allowed for implementation within the triaxial cell, thereby avoiding: (1) the cumbersome corrections that are required to account for refraction at the confining fluid–cell wall–air interfaces and magnification due to cell wall curvature, and (2) the amount of space required for outside-of-the-cell monitoring systems that utilize cameras. The final design of the cameras was based on an iterative testing process in which various types of small board cameras, lenses, and finally pinhole apertures were investigated. The advantages of the lensless pinhole aperture camera design included: (1) lack of optical aberrations, such as those encountered in traditional lensed camera systems, (2) practically infinite depth of field, allowing for sharp, close-up images, and (3) wide-angle field of view without the distortions that are associated with the use of wide-angle lenses. As discussed herein, the pinhole cameras were optimized for optical resolution and light entry to minimize the effect of diffraction patterns that are commonly associated with pinhole apertures. The resolution of the cameras was determined to be sufficient for the potential application of the cameras (volume measurements). The instrumentation presented herein provides a novel alternative to the state-of-the-art outside-of-the-cell photogrammetric instrumentation that is currently employed to monitor soil specimens during triaxial tests.

Studying biomolecule localization by engineering bacterial cell wall curvature.

In this article we describe two techniques for exploring the relationship between bacterial cell shape and the intracellular organization of proteins. First, we created microchannels in a layer of agarose to reshape live bacterial cells and predictably control their mean cell wall curvature, and quantified the influence of curvature on the localization and distribution of proteins in vivo. Second, we used agarose microchambers to reshape bacteria whose cell wall had been chemically and enzymatically removed. By combining microstructures with different geometries and fluorescence microscopy, we determined the relationship between bacterial shape and the localization for two different membrane-associated proteins: i) the cell-shape related protein MreB of Escherichia coli, which is positioned along the long axis of the rod-shaped cell; and ii) the negative curvature-sensing cell division protein DivIVA of Bacillus subtilis, which is positioned primarily at cell division sites. Our studies of intracellular organization in live cells of E. coli and B. subtilis demonstrate that MreB is largely excluded from areas of high negative curvature, whereas DivIVA localizes preferentially to regions of high negative curvature. These studies highlight a unique approach for studying the relationship between cell shape and intracellular organization in intact, live bacteria.

Quantification of microfibril angle in secondary cell walls at subcellular resolution by means of polarized light microscopy

The cell walls constitute the mechanical support of plants. Crystalline cellulose building the walls forms rigid microfibrils that set the stiffness of the cell and the direction in which it expands during growth. Therefore, the determination of the directions of the microfibrils is important in both mechanical and developmental assays. We adapted polarized light microscopy to estimate the cellulose microfibril orientations at subcellular resolution. The optical information supplements X-ray scattering data, Raman microspectroscopy, and electron microscopy. We analyzed samples from three plant tissues: cells from an Araucaria excels branch, in which we revealed lower cellulose density in regions where the cell wall curvature becomes bigger, namely, the cell wall corners; a wheat (Triticum turgidum) awn's hygroscopically active region, which revealed a gradient in the cellulose microfibril angles that spans across four cell rows; and a stork's bill's (Erodium gruinum) coiling awn, which revealed that the cellulose in the cell wall is organized in two orientations seamed together, rather than in a continuous helix. The unique spatial information is easily obtained from microscopic specimens and further illuminates new aspects in the mechanical tissues.

Study on parameterisation of plant tissue microstructure by confocal microscopy for finite elements modelling

This paper reviews three different methods for parameterisation of plant tissues which can be applied to images obtained with a confocal scanning laser microscope to create models for the simulation of the mechanical behaviour of biological cellular structures. Vectorisation, Voronoi tessellation and ellipse tessellation were tested. Potato tuber and carrot parenchyma were chosen as examples. For each method tested, five geometrical parameters were analysed: area, perimeter, orientation, elongation and a local indicator of spatial association of all individual regions which represented cells. The reconstruction accuracy of the original tissue microstructure by each parameterisation method was investigated by the comparison of the geometrical properties of the cells from the segmentation with their virtual equivalents. Linear regression models between the reference and modelled parameters were built. The model performance was expressed in terms of the coefficient of determination ( R 2), the slope of the regression line and the root mean square errors for prediction (RMSEP). Based on the results, Voronoi tessellation was considered to be inaccurate for tissue modelling. The vectorisation procedure only allowed for reproduction of the general shapes of cells, and the curvature of cell walls was neglected in this method. For both the Voronoi tessellation as well as vectorisation, created cells completely filled the space with no additional gaps and possessed sharp, angular shapes. The best overall reconstruction accuracy was obtained with ellipse tessellation. Models created with this method can be considered as representative equivalents of real tissues in terms of cell area, orientation, perimeter, shape and spatial arrangement.

Changes in topology and geometry of the embryonic epithelium of Xenopus during relaxation of mechanical tension

The paper presents the results of statistical evaluation of the changes of cellular apex connections, apical angles, and apical indices of ventral cells of the epiectodermal gastrula of Xenopus during the first HC-four hours after the relaxation of mechanical tension. In the unrelaxed epithelium, an overwhelming majority of cells have three apical connections, apical angles close to 120 degrees, and apical indices around one (isodiametric cells); after relaxation, the number of cells with more than three connections, the number of apical angles deviating substantially from 120 degrees, and the percentage of columnar cells with high apical index increase. Apices with more than three connections tend to gather in enclosed groups, forming a smooth line of cell walls. The length and curvature of cell walls with four apical connections significantly exceeds those same indicators for cells with three apical connections. The observed changes in topology and geometry of cells correspond to reconstructions observed during normal morphogenesis. They are considered in terms of the hyper-restoration model of mechanical tension in relaxed epithelial layers.

Strain rate sensitivity and defects in steel foam

Steel foams fabricated by a powder metallurgical process were subjected to uniaxial compression tests to explore the dependence on strain rate. The yield strength of foam samples showed stronger strain rate dependence at higher strain rates, while the energy absorption increased linearly with strain rate. Measurements of cell wall curvature showed that an increased mean curvature correlated with a reduction in yield strength, and foam strengths generally fell below predictions of the Gibson–Ashby theory. Morphological defects (corrugations of cell walls) also reduced yield strength and altered the dependence on density.

Relationships between growth, morphology and wall stress in the stalk of Acetabularia acetabulum.

With carbon particles we analyzed patterns of growth in Acetabularia acetabulum (Lam.) P.C. Silva, a giant unicell famous for classic development studies. We focused on the stalk apex, which generates the stalk, whorls of hairs, and whorls of gametophores. To gain visual and physical accessibility, we amputated the youngest whorls of hair and the original apex and performed experiments on the apex that regenerated. Video analysis indicated that most growth occurred near the tip of the new apex. Less growth occured throughout the cut-interwhorl. We also analyzed cell wall thickness along stalks cleared of cytoplasm. Correlating growth data to wall morphology suggests growth near the apex may be proportional to stress on the cell wall. We propose that turgor-pressure wall stress modulates local apical cell wall growth rates. A supplementary model, relating cell wall curvature and growth rate in the cut-interwhorl, characterizes how the stalk's final dimensions and nearly cylindrical shap may arise. See http://faculty.washington.edu/mandoli/vondassow for supplementary data, analysis, and mathematical appendices. We believe this is the first quantiative description of apex morphogenesis of A. acetabulum.

The role of cellular structure in creep of two-dimensional cellular solids

The creep response of cellular solids is sensitive to the details of the microstructure. Here, finite element simulations were used to model the steady state, secondary creep rate of several two-dimensional cellular solids: a Voronoi honeycomb, representing a structure with a random variation in cell shape; a plane section of a micrograph of a commercially available closed-cell aluminum foam; and the same plane section of the foam, but with the curvature of the cell walls suppressed. The solid was assumed to follow power-law creep. Both periodic boundary conditions and boundary conditions corresponding to a finite size sample were analyzed. The results of the models are compared with the analytical results for a regular hexagonal honeycomb of the same relative density. The creep rates of all of the other structures are higher than that of the regular hexagonal honeycomb. The results indicate that the details of the microstructure can have a significant effect on the creep rate, and thus the lifetime, of the cellular solid. Cell wall curvature plays the most significant role, but the distribution of cell shape and size also influences the creep rate.

Reduction In Young's Modulus Of Aluminum Foams Due To Cell Wall Curvature And Corrugation

ABSTRACTMeasurements of the Young's modulus and compressive strength of several closedcell aluminum foams indicate that they are lower than expected from models for foam behaviour. Microstructural characterization has revealed that there are a number of defects in the cell structure which may contribute to the reduction in mechanical properties. These include: cell wall curvature, cell wall corrugations, density variations and non-equiaxed cell shape. Finite element analysis of a closed-cell tetrakaidecahedral unit cell with idealized curved or corrugated cell walls indicates that these two types of defects can reduce the Young's modulus and compressive strength by up to 70%. In this paper we report the results of measurements of the curvature of the cell walls and of the amplitude and frequency of corrugations in the cell walls and use simple bounds to estimate the reduction in modulus that they are responsible for.