No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Finite Element Modeling of Cellular Mechanics Experiments
Abstract
The mechanical and biological response of cells to various loading regimes is a subject of great interest in the research
field of biomechanics. Extensive utilization of different cellular mechanics experimental designs has been made over the years
in order to provide better insight regarding the mechanical behavior of cells, and the mechanisms underlying the transduction
of the applied loads into biological reactions. These experimental protocols have limited ability in directly measuring different
mechanical parameters (e.g. internal cellular strains and stresses). In addition, they are very costly and involve highly
complex apparatuses and experimental designs. Thus, further understating of cellular response can be achieved by means of
computational models, such as the finite element (FE) method. FE modeling of cells is an emerging direction in the research
field of cellular mechanics. Its application has been rapidly growing over the last decade due to its ability to quantify
deformations, strains and stresses in and around cells, thus providing basic understating of the mechanical state of cells
and allowing identification of mechanical properties of cells and cellular organelles when coupled with appropriate experiments.
In this chapter, we review the two-dimensional (2D) and three-dimensional (3D) reported cell models of various cell types,
subjected to different applied mechanical stimuli, e.g. compression, micropipette aspiration, indentation.
... This well-established numerical analysis method is used in mechanics to model the deformation of complex structures for which an analytical solution is difficult to obtain. Moreover, FEM is well suited to modeling the effects of deformation due to local constraints [30,31]. Among the commonly used software solutions in the industry, Abaqus is an effective option providing many predefined elements for studying complex physical phenomena. ...
... This software provides powerful flexibility and modularity to approximate complete partition by polynomial functions on each element. Consequently, FEM, which provides a discrete solution to a continuous problem, has frequently been used for solid tissue modeling [31,32]. ...
... Moreover, to incorporate topological information, we calculated a spreading distance corresponding to the mean distance between a cell centroid and the centroids of the first order neighboring cells. Because having three or four direct neighbors is a very rare event [31], we decided to measure the mean distance to the five nearest neighbors. ...
Understanding the interplay between biology and mechanics in tissue architecture is challenging, particularly in terms of 3D tissue organization. Addressing this challenge requires a biological model enabling observations at multiple levels from cell to tissue, as well as theoretical and computational approaches enabling the generation of a synthetic model that is relevant to the biological model and allowing for investigation of the mechanical stresses experienced by the tissue. Using a monolayer human colon epithelium organoid as a biological model, freely available tools (Fiji, Cellpose, Napari, Morphonet, or Tyssue library), and the commercially available Abaqus FEM solver, we combined vertex and FEM approaches to generate a comprehensive viscoelastic finite element model of the human colon organoid and demonstrated its flexibility. We imaged human colon organoid development for 120 hours, following the evolution of the organoids from an immature to a mature morphology. According to the extracted architectural/geometric parameters of human colon organoids at various stages of tissue architecture establishment, we generated organoid active vertex models. However, this approach did not consider the mechanical aspects involved in the organoids’ morphological evolution. Therefore, we applied a finite element method considering mechanical loads mimicking osmotic pressure, external solicitation, or active contraction in the vertex model by using the Abaqus FEM solver. Integration of finite element analysis (FEA) into the vertex model achieved a better fit with the biological model. Therefore, the FEM model provides a basis for depicting cell shape, tissue deformation, and cellular-level strain due to imposed stresses. In conclusion, we demonstrated that a combination of vertex and FEM approaches, combining geometrical and mechanical parameters, improves modeling of alterations in organoid morphology over time and enables better assessment of the mechanical cues involved in establishing the architecture of the human colon epithelium.
... Responses of cells to external loading are composed of a complex combination of processes, which are difficult to separate experimentally. This has motivated researchers to combine cellular mechanics experiments with computational methods to segment the mechanostructural responses of loaded cells, accounting for the mechanical properties of cells, cellular structures and mechanical interactions between cells and their environment (Slomka and Gefen 2011b). Recent experimental works have shown the effects of increased hydrostatic pressure (uniform compression of cell surface), inducing changes in cell morphology and disruption of the cytoskeleton of adhered cells (Brooker et al. 2018) and reduction in viability of adherent and non-adherent cells (Yabuki et al. 2013). ...
... the medium were quantified through the global cell deformations, GCD (Slomka and Gefen 2011b): ...
Mechanical loading naturally controls cell phenotype, development, motility and various other biological functions; however, prolonged or substantial loading can cause cell damage and eventual death. Loading-induced mechanobiological and mechanostructural responses of different cell types affect their morphology and the internal architecture and the mechanics of the cellular components. Using single, mesenchymal stem cells, we have developed a cell-specific three-dimensional finite-element model; cell models were developed from phase-contrast microscopy images. This allowed us to evaluate the mechanostructural response of the naturally occurring variety of cell morphologies to increase sustained compressive loading. We focus on the morphology of the cytoplasm and the nucleus, as the main mechanically responsive elements, and evaluate formation of tensional strains and area changes in cells undergoing increasing uniaxial compressions. Here, we study mesenchymal stem cells as a model, due to their important role in tissue engineering and regenerative medicine; the method and findings are, however, applicable to any cell type. We observe variability in the cell responses to compression, which correlate directly with the morphology of the cells. Specifically, in cells with or without elongated protrusions (i.e., lamellipodia) tensional strains were, respectively, distributed mostly in the thin extensions or concentrated around the stiff nucleus. Thus, through cell-specific computational modeling of mechanical loading we have identified an underlying cause for stiffening (by actin recruitment) along the length of lamellipodia as well as a role for cell morphology in inducing cell-to-cell variability in mechanostructural response to loading.
... The mechanical parameters during microinjection (e.g. internal cellular strains and stresses) can be calculated from the model, which is difficult to measure directly by experiments 36,37 . These parameters can be used to explore deformations of the target cell, which can be used to describe cell damage. ...
Microinjecting yeast cells has been challenging for decades with no significant breakthrough due to the ultra-tough cell wall and low stiffness of the traditional injector tip at the micro-scale. Penetrating this protection wall is the key step for artificially bringing foreign substance into the yeast. In this paper, a yeast cell model was built by using finite element analysis (FEA) method to analyze the penetrating process. The key parameters of the yeast cell wall in the model (the Young’s modulus, the shear modulus, and the Lame constant) were calibrated according to a general nanoindentation experiment. Then by employing the calibrated model, the injection parameters were optimized to minimize the cell damage (the maximum cell deformation at the critical stress of the cell wall). Key guidelines were suggested for penetrating the cell wall during microinjection.
... 47 Models incorporating subcellular components, such as the nucleus and cytoskeletal fibers, may provide further insights into intracellular mechanotransduction mechanisms. 48 For such models, the assumption of continuous attachment between chondrocytes and their environment could also be updated to discrete focal cellmatrix attachment sites. 49 Direct validation of chondrocyte strains in the cartilage ECM have yet to be performed and may become more feasible in the near future with new developments in the field. ...
Understanding the mechanical factors that drive the biological responses of chondrocytes is central to our interpretation of the cascade of events that lead to osteoarthritic changes in articular cartilage. Chondrocyte mechanics is complicated by changes in tissue properties that can occur as osteoarthritis (OA) progresses and by the interaction between macro-scale, tissue level, properties and micro-scale pericellular matrix (PCM) and local extracellular matrix (ECM) properties, both of which cannot be easily studied using in vitro systems. Our objective was to study the influence of macro- and micro-scale OA-associated structural changes on chondrocyte strains. We developed a multi-scale finite element model of articular cartilage subjected to unconfined loading, for the following three conditions: (i) normal articular cartilage, (ii) OA cartilage (where macro and micro-scale changes in collagen content, matrix modulus and permeability were modeled), and (iii) early-stage OA cartilage (where only micro-scale changes in matrix modulus were modeled). In the macro-scale model, we found that a depth-dependent strain field was induced in both healthy and OA cartilage and that the middle and superficial zones of OA cartilage had increased tensile and compressive strains. At the micro-scale, chondrocyte shear strains were sensitive to PCM and local ECM properties. In the early-OA model, micro-scale spatial softening of PCM and ECM resulted in a substantial increase (30%) of chondrocyte shear strain, even with no structural changes in macro-scale tissue properties. Our study provides evidence that micromechanical changes at the cellular level may affect chondrocyte activities before macro-scale degradations at the tissue level become apparent. This article is protected by copyright. All rights reserved
... More advanced structural phenomena in mechanically loaded cells can be evaluated, with the same principles, using finite element (FE) modeling; a review of the body of work on computational cell modeling is available in [60] . In the context of the above discussion, however, Slomka and Gefen developed an approach to obtain three-dimensional (3D) cell-specific FE models to simulate experiments involving large cell deformations, based on analysis of confocal (z-stack) images of multiple undifferentiated skeletal muscle cells (C2C12 myoblasts) [61,62] . ...
The purpose of this review paper is to summarize the current knowledge on cell-scale mechanically-inflicted deformation-damage, which is at the frontier of cell mechanobiology and biomechanics science, specifically in the context of chronic wounds. The dynamics of the mechanostructure of cells and particularly, the damage occurring to the cytoskeleton and plasma-membrane when cells are chronically deformed (as in a weight-bearing static posture) is correlated to formation of the most common chronic wounds and injuries, such as pressure ulcers (injuries). The first occurrence is microscopic injury which onsets as damage in individual cells and then progresses macroscopically to the tissue-scale. Here, we specifically focus on sub-catastrophic and catastrophic damage to cells that can result from mechanical loads that are delivered statically or at physiological rates; this results in apoptosis at prolonged times or necrosis, rapidly. We start by providing a basic background of cell mechanics and dynamics, focusing on the plasma-membrane and the cytoskeleton, and discuss approaches to apply and estimate deformations in cells. We then consider the effects of different levels of mechanical loads, i.e. low, high and intermediate, and describe the expected damage in terms of time-scales of application and in terms of cell response, providing experimental examples where available. Finally, we review different theoretical and computational modeling approaches that have been used to describe cell responses to sustained deformation. We highlight the insights that those models provide to explain, for example, experimentally observed variabilities in cell damage and death under loading.
... The simple structural 3D cell simulations typically employ idealized-shaped geometrical models, usually halfspheres or half-ellipsoids to represent adhered cells in monolayers, or full spheres or ellipsoids to represent cells in a 3D matrix. Otherwise, more advanced geometrical models are reconstructed from confocal or multimodal fluorescence image sets, which provide realistic cell-specific geometries, including the nucleus, vesicles and sub-cellular components (Slomka and Gefen 2011b). ...
We present three-dimensional (3D) finite element (FE) models of single, mesenchymal stem cells (MSCs), generated from images obtained by optical phase-contrast microscopy and used to quantify the structural responses of the studied cells to externally applied mechanical loads. Mechanical loading has been shown to affect cell morphology and structure, phenotype, motility and other biological functions. Cells experience mechanical loads naturally, yet under prolonged or sizable loading, damage and cell death may occur, which motivates research regarding the structural behavior of loaded cells. For example, near the weight-bearing boney prominences of the buttocks of immobile persons, tissues may become highly loaded, eventually leading to massive cell death that manifests as pressure ulcers. Cell-specific computational models have previously been developed by our group, allowing simulations of cell deformations under compressive or stretching loads. These models were obtained by reconstructing specific cell structures from series of 2D fluorescence, confocal image-slices, requiring cell-specific fluorescent-staining protocols and costly (confocal) microscopy equipment. Alternative modeling approaches represent cells simply as half-spheres or half-ellipsoids (i.e. idealized geometries), which neglects the curvature details of the cell surfaces associated with changes in concentrations of strains and stresses. Thus, we introduce here for the first time an optical image-based FE modeling, where loads are simulated on reconstructed 3D geometrical cell models from a single 2D, phase-contrast image. Our novel modeling method eliminates the need for confocal imaging and fluorescent staining preparations (both expensive), and makes cell-specific FE modeling affordable and accessible to the biomechanics community. We demonstrate the utility of this cost-effective modeling method by performing simulations of compression of MSCs embedded in a gel.
Treatment options specifically targeting tumour cells are urgently needed in order to reduce the side effects accompanied by chemo- or radiotherapy. Differences in subcellular structure between tumour and normal cells determine their specific elasticity. These structural differences can be utilised by low-frequency ultrasound in order to specifically induce cytotoxicity of tumour cells. For further evaluation, we combined in silico FEM (finite element method) analyses and in vitro assays to bolster the significance of low-frequency ultrasound for tumour treatment. FEM simulations were able to calculate the first resonance frequency of MCF7 breast tumour cells at 21 kHz in contrast to 34 kHz for the MCF10A normal breast cells, which was due to the higher elasticity and larger size of MCF7 cells. For experimental validation of the in silico-determined resonance frequencies, equipment for ultrasonic irradiation with distinct frequencies was constructed. Differences for both cell lines in their response to low-frequent ultrasonic treatment were corroborated in 2D and in 3D cell culture assays. Treatment with ~ 24.5 kHz induced the death of MCF7 cells and MDA-MB-231 metastases cells possessing a similar elasticity; frequencies of > 29 kHz resulted in cytotoxicity of MCF10A. Fractionated treatments by ultrasonic irradiation of suspension myeloid HL60 cells resulted in a significant decrease of viable cells, mostly significant after threefold irradiation in intervals of 3 h. Most importantly in regard to a clinical application, combined ultrasonic treatment and chemotherapy with paclitaxel showed a significantly increased killing of MCF7 cells compared to both monotherapies. In summary, we were able to determine for the first time for different tumour cell lines a specific frequency of low-intensity ultrasound for induction of cell ablation. The cytotoxic effect of ultrasonic irradiation could be increased by either fractionated treatment or in combination with chemotherapy. Thus, our results will open new perspectives in tumour treatment.
This paper aims to review the current strategies for pelvic floor dysfunctions (PFDs). PFDs, such as stress urinary incontinence, foecal incontinence and vaginal prolapse affect the quality of life in women, involve high healthcare costs, and pose poor long-term success rates. As the problem progresses the cells in the pelvic tissues are impaired. The rheological relations between PFD and the damage of the tissues is not yet well established, bringing out clinical repair interventions, instead of knowing the root problem. As a consequence, the verification of damage mechanisms in the pelvic structures should be observed at cellular scales to correlate with the macroscopic phenomenological pathologies, namely, the changes in the mechanical properties and on the geometric configuration of the pelvic structures. Cells sense mechanical stimuli and respond biochemically via mechanotransduction mechanisms. Therefore, investigations on the cell dynamics must be performed, considering the physical conditions inside the bioreactors, to shed insight into the active behaviour of the cells during the treatment. These investigations should establish the conditions that push a cell to or keep a cell in a desired state during a regenerative treatment. This paper reviews the use of human adult stem cells to regenerate the defective muscles, ligaments and connective tissues in the pelvic floor, focusing on the role of the computational models as an assistive technology for these emergent tissue engineering treatments. First, the pelvic floor anatomy and physiology is related with the kinematic and mechanical behaviour of those structures at the tissue and cell scales. After, the relevance of the regenerative treatments is discussed and the requirements for their application are summarised. Later, the developments on computational models are exposed and the main guidelines for regeneration of the pelvic cavity tissues are proposed.
Insufficiency of mechanical properties of tissue-engineered (TE) cartilage grafts is still a limiting factor for their clinical application. It has been shown that mechanostimulation of chondrocytes enhances synthesis of extracellular matrix (ECM) and thereby improves the mechanical properties of the grafts. However, the optimal mechanical loading required to stimulate chondrocytes for sufficient matrix synthesis is still unknown. The properties of the pericellular matrix (PCM) and the ability of the chondrocyte to attach to its adjacent matrix may importantly determine the stimulation of the cell in loaded tissue. The aim of the present study is to numerically investigate the influence of tissue development and cell-matrix attachment on the mechanical environment of a chondrocyte embedded in agarose. Mechanical environment inside TE constructs are evaluated and compared to that in native cartilage under 10% unconfined-compression. A multi-scale finite element modeling approach in conjunction with a validated non-linear fiber-reinforced poroviscoelastic swelling cartilage model is used. Results indicate that without cell attachment, excessive local strains may be induced in the cell. With PCM development and the establishment of focal adhesions at the cell surface, the cell is strained more homogenously upon external loading. However, compared to chondrocytes in native cartilage the transmission of the external compression to the cells in TE constructs is less. This suggests that, over time, the loading magnitude may be increased to continue stimulation of chondrocytes at the physiological or even higher levels to possibly enhance matrix synthesis. These findings improve our insights into the micromechanical environment of cells in tissue engineering cultures.
Cells suspended in bodily fluids are routinely analyzed by cytopathologists as a means of diagnosing malignancies and other diseases. The physical and morphological properties of these suspended cells are evaluated in making diagnostic decisions, which often requires manual concentration, staining, and washing procedures to extract information about intracellular architecture. The need to manually prepare slides for analysis by a cytopathologist is a labor-intensive process, which is ripe for additional automation to reduce costs but also to potentially provide more repeatable and improved accuracy in diagnoses. We have developed a microfluidic system to perform several steps in the preparation of samples for cytopathology that (i) automates colorimetric staining on-chip, and (ii) images cells in flow, as well as provides (iii) additional quantitative analyses of captured images to aid cytopathologists. A flow-through approach provides benefits by allowing staining and imaging to be performed in a continuous, integrated manner, which also overcomes previous challenges with in-suspension colorimetric staining. We envision such a tool may reduce costs and aid cytopathologists in identifying rare or characteristic cells of interest by providing isolated images along with quantitative metrics on single cells from various rotational angles, allowing efficient determination of disease etiology.
Stress intensity factors due to surface crack propagation were analyzed
by using the influence function method and inherent strain analysis of
the residual stress fields caused by welding. The initial residual
stress in a plate welded-butt joint was calculated by using inherent
strain analysis, and the redistribution of residual stress and the
stress intensity factor due to crack propagation were analyzed as
changes in the structure's shape. Stress intensity factor was also
calculated by using an influence function database. The stress intensity
factor in the residual stress fields due to crack propagation obtained
by using inherent strain analysis completely agreed with that obtained
by using the influence function method. The results of the crack
propagation analysis were compared with the experimental results of a
fatigue test. It was validated that both the inherent strain analysis
and the influence function method were efficient for analyzing stress
intensity factors in residual stress fields caused by welding.
Tensile properties of vascular smooth muscle cells (VSMCs) of synthetic and contractile phenotypes were determined using a newly developed tensile test system. Synthetic and contractile VSMCs were isolated from the rabbit thoracic aorta with an explant and an enzymatic digestion method, respectively. Each cell floated in Hanks' balanced salt solution of 37°C was attached to the fine tips of a pair of micropipettes with a cell adhesive and, then, stretched at the rate of 6µm/sec by moving one of the micropipettes with a linear actuator. Load applied to the cell was measured with a cantilever-type load cell; its elongation was determined from the distance between the micropipette tips using a video dimension analyzer. The synthetic and contractile VSMCs were not broken even at the tensile force of 2.4µN and 3.4µN, respectively. Their stiffness was significantly higher in contractile phenotype (0.17N/m) than in synthetic one (0.09N/m). The different tensile properties between synthetic and contractile cells are attributable to the differences in cytoskeletal structures and contractile apparatus.
Numerous studies in tissue engineering and biomechanics use fluid flow stimulation, both unidirectional and oscillatory, to analyze the effects of shear stresses on cell behavior. However, it has typically been assumed that these shear stresses are uniform and that cell and substrate properties do not adversely affect these assumptions. With the increasing utilization of fluid flow in cell biology, it would be beneficial to determine the validity of various experimental protocols. Because it is difficult to determine the velocity profiles and shear stresses empirically, we used the finite element method (FEM). Using FEM, we determined the effects of cell confluence on fluid flow, the effects of cell height on the uniformity of shear stresses, apparent shear stresses exhibited by cells cultured on various substrates, and the effects of oscillatory fluid flow relative to the unidirectional flow. FEM analyses could successfully analyze flow patterns over cells for various cell confluence and shape and substrate characteristics. Our data suggest the benefits of the utilization of oscillatory fluid flow and the use of substrates that stimulate cell spreading in the distribution of more uniform shear stresses across the surface of cells. Also we demonstrated that the cells cultured on nanotopographies were exposed to greater apparent shear stresses than cells on flat controls when using the same fluid flow conditions. FEM thus provides an excellent tool for the development of experimental protocols and the design of bioreactor systems.
Previous studies on the intracellular force balance that forms the adherent cell structure have paid much attention to the mechanical behavior of cells seen in the horizontal project plane. By contrast, there are only few quantitative considerations on that in the vertical plane. Particularly, the contribution of the nucleus to the bearing of the vertical cell structure remains unclear. Here, we investigated the determinant of the vertical cell morphology from experimental and numerical approaches. The effect of cytoskeleton-affecting agents on the vascular endothelial cell height, as a measure of the vertical force balance, was examined by atomic force microscope indentation, demonstrating that actin depolymerization caused an increase in cell height. In contrast, disruption of microtubules lowered the cell height, whereas their stabilization elevated the cell plasma membrane. Time-lapse microscopy showed that intracellular vesicles moved radially outward after the microtubule disruption, together with an enlargement of the nuclear area in the project plane, that is probably associated with the decrease in cell height. Finite element analyses employing a 3D model were carried out to interpret the experimental results and examine potent parameters (such as prestress, elastic modulus, and Poisson's ratio) that affect vertical cell morphology. How the prestress in subcellular components influences cells subjected to extracellular tensile forces was also examined. These results indicate that the nuclear/cytoplasmic mechanical properties and degrees of prestress determine the vertical section structure of adhering cells.
Schlemm's canal (SC) endothelial cells are likely important in the physiology and pathophysiology of the aqueous drainage system of the eye, particularly in glaucoma. The mechanical stiffness of these cells determines, in part, the extent to which they can support a pressure gradient and thus can be used to place limits on the flow resistance that this layer can generate in the eye. However, little is known about the biomechanical properties of SC endothelial cells. Our goal in this study was to estimate the effective Young's modulus of elasticity of normal SC cells. To do so, we combined magnetic pulling cytometry of isolated cultured human SC cells with finite element modeling of the mechanical response of the cell to traction forces applied by adherent beads. Preliminary work showed that the immersion angles of beads attached to the SC cells had a major influence on bead response; therefore, we also measured bead immersion angle by confocal microscopy, using an empirical technique to correct for axial distortion of the confocal images. Our results showed that the upper bound for the effective Young's modulus of elasticity of the cultured SC cells examined in this study, in central, non-nuclear regions, ranged between 1,007 and 3,053 Pa, which is similar to, although somewhat larger than values that have been measured for other endothelial cell types. We compared these values to estimates of the modulus of primate SC cells in vivo, based on images of these cells under pressure loading, and found good agreement at low intraocular pressure (8-15 mm Hg). However, increasing intraocular pressure (22-30 mm Hg) appeared to cause a significant increase in the modulus of these cells. These moduli can be used to estimate the extent to which SC cells deform in response to the pressure drop across the inner wall endothelium and thereby estimate the extent to which they can generate outflow resistance.
Preventing femoral fractures is an important goal in osteoporosis research. In order to evaluate a person's fracture risk and to quantify response to treatment, bone competence is best assessed by bone strength. Finite-element (FE) modelling based on medical imaging is considered a very promising technique for the assessment of in vivo femoral bone strength. Over the past decades, a number of different FE models have been presented focusing on the effect of several methodological aspects, such as mesh type, material properties and loading conditions, on the precision and accuracy of these models. In this paper, a review of this work is presented. We conclude that moderate to good predictions can be made, especially when the models are tuned to specific loading scenarios. However, there is room for improvement when multiple loading conditions need to be evaluated. We hypothesize that including anisotropic material properties is the first target. As a proof of the concept, we demonstrate that the main orientation of the femoral bone structure can be calculated from clinical computed tomography scans. We hypothesize that this structural information can be used to estimate the anisotropic bone material properties, and that in the future this could potentially lead to a greater predictive value of FE models for femoral bone strength.
The acute respiratory distress syndrome (ARDS) is characterized by fluid accumulation in small pulmonary airways. The reopening of these fluid-filled airways involves the propagation of an air-liquid interface that exerts injurious hydrodynamic stresses on the epithelial cells (EpC) lining the airway walls. Previous experimental studies have demonstrated that these hydrodynamic stresses may cause rupture of the plasma membrane (i.e., cell necrosis) and have postulated that cell morphology plays a role in cell death. However, direct experimental measurement of stress and strain within the cell is intractable, and limited data are available on the mechanical response (i.e., deformation) of the epithelium during airway reopening. The goal of this study is to use image-based finite element models of cell deformation during airway reopening to investigate how cell morphology and mechanics influence the risk of cell injury/necrosis. Confocal microscopy images of EpC in subconfluent and confluent monolayers were used to generate morphologically accurate three-dimensional finite element models. Hydrodynamic stresses on the cells were calculated from boundary element solutions of bubble propagation in a fluid-filled parallel-plate flow channel. Results indicate that for equivalent cell mechanical properties and hydrodynamic load conditions, subconfluent cells develop higher membrane strains than confluent cells. Strain magnitudes were also found to decrease with increasing stiffness of the cell and membrane/cortex region but were most sensitive to changes in the cell's interior stiffness. These models may be useful in identifying pharmacological treatments that mitigate cell injury during airway reopening by altering specific biomechanical properties of the EpC.
The cell nucleus plays a central role in the response of the endothelium to mechanical forces, possibly by deforming during cellular adaptation. The goal of this work was to precisely quantify the mechanical properties of the nucleus. Individual endothelial cells were subjected to compression between glass microplates. This technique allows measurement of the uniaxial force applied to the cell and the resulting deformation. Measurements were made on round and spread cells to rule out the influence of cell morphology on the nucleus mechanical properties. Tests were also carried out with nuclei isolated from cell cultures by a chemical treatment. The non-linear force-deformation curves indicate that round cells deform at lower forces than spread cells and nuclei. Finite-element models were also built with geometries adapted to actual morphometric measurements of round cells, spread cells and isolated nuclei. The nucleus and the cytoplasm were modeled as separate homogeneous hyperelastic materials. The models simulate the compression and yield the force-deformation curve for a given set of elastic moduli. These parameters are varied to obtain a best fit between the theoretical and experimental data. The elastic modulus of the cytoplasm is found to be on the order of 500N/m(2) for spread and round cells. The elastic modulus of the endothelial nucleus is on the order of 5000N/m(2) for nuclei in the cell and on the order of 8000N/m(2) for isolated nuclei. These results represent an unambiguous measurement of the nucleus mechanical properties and will be important in understanding how cells perceive mechanical forces and respond to them.
Magnetic twisting cytometry probes mechanical properties of an adherent cell by applying a torque to a magnetic bead that is tightly bound to the cell surface. Here we have used a three-dimensional finite element model of cell deformation to compute the relationships between the applied torque and resulting bead rotation and lateral bead translation. From the analysis, we computed two coefficients that allow the cell elastic modulus to be estimated from measurements of either bead rotation or lateral bead translation, respectively, if the degree of bead embedding and the cell height are known. Although computed strains in proximity of the bead can be large, the relationships between applied torque and bead rotation or translation remain virtually linear up to bead rotations of 15 degrees, above which geometrical nonlinearities become significant. This appreciable linear range stands in contrast to the intrinsically nonlinear force-displacement relationship that is observed when cells are indented during atomic force microscopy. Finally, these computations support the idea that adhesive forces are sufficient to keep the bead firmly attached to the cell surface throughout the range of working torques.
Mechanical stimulation is known to cause alterations in the behaviour of cells adhering to a substrate. The mechanisms by which forces are transduced into biological responses within the cell remain largely unknown. Since cellular deformation is likely involved, further understanding of the biomechanical origins of alterations in cellular response can be aided by the use of computational models in describing cellular structural behaviour and in determining cellular deformation due to imposed loads of various magnitudes. In this paper, a finite element modelling approach that can describe the biomechanical behaviour of adherent eukaryotic cells is presented. It fuses two previous modelling approaches by incorporating, in an idealised geometry, all cellular components considered structurally significant, i.e. prestressed cytoskeleton, cytoplasm, nucleus and membrane components. The aim is to determine if we can use this model to describe the non-linear structural behaviour of an adherent cell and to determine the contribution of the various cellular components to cellular stability. Results obtained by applying forces (in the picoNewton range) to the model membrane nodes suggest a key role for the cytoskeleton in determining cellular stiffness. The model captures non-linear structural behaviours such as strain hardening and prestress effects (in the region of receptor sites), and variable compliance along the cell surface. The role of the cytoskeleton in stiffening a cell during the process of cell spreading is investigated by applying forces to five increasingly spread cell geometries. Parameter studies reveal that material properties of the cytoplasm (elasticity and compressibility) also have a large influence on cellular stiffness. The computational model of a single cell developed here is proposed as one that is sufficiently complex to capture the non-linear behaviours of the cell response to forces whilst not being so complex that the parameters cannot be specified. The model could be very useful in computing cellular structural behaviour in response to various in vitro mechanical stimuli (e.g. fluid flow, substrate strain), or for use in algorithms that attempt to simulate mechanobiological processes.
Quantification of the cell elastic modulus is a central issue of micromanipulation techniques used to analyze the mechanical properties of living adherent cells. In magnetic twisting cytometry (MTC), magnetic beads of radius R, linked to the cell cytoskeleton through transmembrane receptors, are twisted. The relationships between imposed external torque and measured resulting bead rotation or translation only provide values of the apparent cell stiffness. Thus, specific correcting coefficients have to be considered in order to derive the cell elastic modulus. This issue has been highlighted in previous studies, but general relationships forhandling such corrections are still lacking while they could help to understand and reduce the large dispersion of the reported values of cell elastic modulus. This work establishes generalized abacuses of the correcting coefficients from which the Young's modulus of a cell probed by MTC can be derived. Based on a 3D finite element analysis of an hyperelastic (neo-Hookean) cell, we show that the dimensionless ratio h(u)/2R, where h(u) is the cell height below the bead, is an essential parameter for quantification of the cell elasticity. This result could partly explain the still intriguing question of the large variation of measured elastic moduli with probe size.
Chondrocytes, the cells in articular cartilage, exhibit solid-like viscoelastic behavior in response to mechanical stress. In modeling the creep response of these cells during micropipette aspiration, previous studies have attributed the viscoelastic behavior of chondrocytes to either intrinsic viscoelasticity of the cytoplasm or to biphasic effects arising from fluid-solid interactions within the cell. However, the mechanisms responsible for the viscoelastic behavior of chondrocytes are not fully understood and may involve one or both of these phenomena. In this study, the micropipette aspiration experiment was modeled using a large strain finite element simulation that incorporated contact boundary conditions. The cell was modeled using finite strain incompressible and compressible elastic models, a two-mode compressible viscoelastic model, or a biphasic elastic or viscoelastic model. Comparison of the model to the experimentally measured response of chondrocytes to a step increase in aspiration pressure showed that a two-mode compressible viscoelastic formulation accurately captured the creep response of chondrocytes during micropipette aspiration. Similarly, a biphasic two-mode viscoelastic analysis could predict all aspects of the cell's creep response to a step aspiration. In contrast, a biphasic elastic formulation was not capable of predicting the complete creep response, suggesting that the creep response of the chondrocytes under micropipette aspiration is predominantly due to intrinsic viscoelastic phenomena and is not due to the biphasic behavior.
Previous work has established that mechanical forces can lead to quantifiable alterations in cell function. However, how forces change gene expression in a single cell and the mechanisms of force transmission to the nucleus are poorly understood. Here we demonstrate that the gene expression of proteins related to the extracellular matrix in single articular chondrocytes is modified by compressive forces in a dosage-dependent manner. Increasing force exposure catabolically shifts single-cell mRNA levels of aggrecan, collagen IIa, and tissue inhibitor of metalloproteinase-1. Cytohistochemistry reveals that the majority of strain experienced by the cell is also experienced by the nucleus, resulting in considerable changes in nuclear volume and structure. Transforming growth factor-beta1 and insulin-like growth factor-I offer mechanoprotection and recovery of gene expression of aggrecan and metalloproteinase-1. These results suggest that forces directly influence gene transcription and may do so by changing chromatin conformation.
We investigated the mechanotransduction pathway in endothelial cells between their nucleus and adhesions to the extracellular matrix. First, we measured nuclear deformations in response to alterations of cell shape as cells detach from a flat surface. We found that the nuclear deformation appeared to be in direct and immediate response to alterations of the cell adhesion area. The nucleus was then treated as a neo-Hookean compressible material, and we estimated the stress associated with the cytoskeleton and acting on the nucleus during cell rounding. With the obtained stress field, we estimated the magnitude of the forces deforming the nucleus. Considering the initial and final components of this adhesion-cytoskeleton-nucleus force transmission pathway, we found our estimate for the internal forces acting on the nucleus to be on the same order of magnitude as previously measured traction forces, suggesting a direct mechanical link between adhesions and the nucleus.
Country-Specific Mortality and Growth Failure in Infancy and Yound Children and
Association With Material Stature
Use interactive graphics and maps to view and sort country-specific infant and early
dhildhood mortality and growth failure data and their association with maternal
The threedimensional finite element (FE) model of eucaryotic cell presented in the paper is based on similar models published
recently; it comprehends elements representing cell membrane, cytoplasm and nucleus, and a complex tensegrity structure representing
cytoskeleton. In contrast to the previous models, this tensegrity structure consists of several parts. External and internal
parts count 30 struts and 60 cables each and their corresponding nodes are interconnected by 30 radial members; these parts
represent cortical, nuclear and deep cytoskeletons, respectively. This arrangement enables us to simulate the load transmission
from the extracellular space via membrane receptors (focal adhesions) to the central part of the cell (nucleus, centrosome);
this ability of the model was tested by simulation of some mechanical tests of isolated cells, in particular tension test
with micropipettes, indentation test and magnetic tweezer test. Although material properties of components have been defined
as realistic as possible on the base of the mechanical tests with vascular smooth muscle cells, they were not identified in
fact and are not unique probably. However, simulations of the tests have shown the ability of the model to simulate the global
load-deformation response of the cell under various types of loadings, as well as several substantial global features of the
cell behaviour, e.g. “at a distance effect”, non-linear stiffening with increasing load, or linear dependence of stiffness
on increasing prestrain.
Deep tissue injury (DTI) is a serious pressure ulcer, involving a mass of necrotic soft tissue under bony prominences as a
consequence of sustained tissue deformations. Though several processes are thought to participate in the onset and development
of DTI (e.g., cellular deformation, ischemia, and ischemia-reperfusion), the specific mechanisms responsible for it are currently
unknown. Recent work indicated that pathological processes at the cell level, which relate to cell deformation, are involved
in the etiology. We hypothesized that sustained tissue deformations can lead to elevated intracellular concentration of cell
metabolites, e.g., calcium ion (Ca2+), due to a stretch-induced increase in the local permeability of plasma membranes. This may ultimately lead to cell death
due to intracellular cytotoxic concentrations of metabolites. In order to investigate this hypothesis, computational models
were developed, for determining compression-induced membrane stretches and trends of times for reaching intracellular cytotoxic
Ca2+ levels due to uncontrolled Ca2+ influx through stretched membranes. The simulations indicated that elevated compressive cell deformations exceeding 25% induce
large tensional strains (>5%, and up to 11.5%) in membranes. These are likely to increase Ca2+ influx from the extracellular space into the cytosol through the stretched sites. Consistent with this assumption, the Ca2+ transport model showed high sensitivity of times for cell death to changes in membrane resistance. These results may open
a new path in pressure ulcer research, by indicating how global tissue deformations are transformed to plasma membrane deformations,
which in turn, affect transport properties and eventually, cell viability.
This study introduces a new confocal microscopy-based three-dimensional cell-specific finite element (FE) modeling methodology for simulating cellular mechanics experiments involving large cell deformations. Three-dimensional FE models of undifferentiated skeletal muscle cells were developed by scanning C2C12 myoblasts using a confocal microscope, and then building FE model geometries from the z-stack images. Strain magnitudes and distributions in two cells were studied when the cells were subjected to compression and stretching, which are used in pressure ulcer and deep tissue injury research to induce large cell deformations. Localized plasma membrane and nuclear surface area (NSA) stretches were observed for both the cell compression and stretching simulation configurations. It was found that in order to induce large tensile strains (>5%) in the plasma membrane and NSA, one needs to apply more than approximately 15% of global cell deformation in cell compression tests, or more than approximately 3% of tensile strains in the elastic plate substrate in cell stretching experiments. Utilization of our modeling can substantially enrich experimental cellular mechanics studies in classic cell loading designs that typically involve large cell deformations, such as static and cyclic stretching, cell compression, micropipette aspiration, shear flow and hydrostatic pressure, by providing magnitudes and distributions of the localized cellular strains specific to each setup and cell type, which could then be associated with the applied stimuli.
The viscoelastic properties of cells are important in predicting cell deformation under mechanical loading and may reflect cell phenotype or pathological transition. Previous studies have demonstrated that viscoelastic parameters estimated by finite element (FE) analyses of micropipette aspiration (MA) data differ from those estimated by the analytical half-space model. However, it is unclear whether these differences are statistically significant, as previous studies have been based on average cell properties or parametric analyses that do not reflect the inherent experimental and biological variability of real experimental data. To determine whether cell material parameters estimated by the half-space model are significantly different from those predicted by the FE method, we implemented an inverse FE method to estimate the viscoelastic parameters of a population of primary porcine aortic valve interstitial cells tested by MA. We found that inherent differences between the analytical and inverse FE estimation methods resulted in statistically significant differences in individual cell properties. However, in cases with small pipette to cell radius ratios and short loading periods, model-dependent differences were masked by experimental and cell-to-cell variability. Analytical models that account for finite cell-size and loading rate further relaxed the experimental conditions for which accurate cell material parameter estimates could be obtained. These data provide practical guidelines for analysis of MA data that account for the wide range of conditions encountered in typical experiments.
A substantial body of work has been reported in which the mechanical properties of adherent cells were characterized using compression testing in tandem with computational modeling. However, a number of important issues remain to be addressed. In the current study, using computational analyses, the effect of cell compressibility on the force required to deform spread cells is investigated and the possibility that stiffening of the cell cytoplasm occurs during spreading is examined based on published experimental compression test data. The effect of viscoelasticity on cell compression is considered and difficulties in performing a complete characterization of the viscoelastic properties of a cell nucleus and cytoplasm by this method are highlighted. Finally, a non-linear force-deformation response is simulated using differing linear viscoelastic properties for the cell nucleus and the cell cytoplasm.
The way in which the nucleus experiences mechanical forces has important implications for understanding mechanotransduction. Knowledge of nuclear material properties and, specifically, their relationship to the properties of the bulk cell can help determine if the nucleus directly experiences mechanical loads, or if it is a signal transduction mechanism secondary to cell membrane deformation that leads to altered gene expression. Prior work measuring nuclear material properties using micropipette aspiration suggests that the nucleus is substantially stiffer than the bulk cell [Guilak, F., Tedrow, J.R., Burgkart, R., 2000. Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269, 781-786], whereas recent work with unconfined compression of single chondrocytes showed a nearly one-to-one correlation between cellular and nuclear strains [Leipzig, N.D., Athanasiou, K.A., 2008. Static compression of single chondrocytes catabolically modifies single-cell gene expression. Biophys. J. 94, 2412-2422]. In this study, a linearly elastic finite element model of the cell with a nuclear inclusion was used to simulate the unconfined compression data. Cytoplasmic and nuclear stiffnesses were varied from 1 to 7 kPa for several combinations of cytoplasmic and nuclear Poisson's ratios. It was found that the experimental data were best fit when the ratio of cytoplasmic to nuclear stiffness was 1.4, and both cytoplasm and nucleus were modeled as incompressible. The cytoplasmic to nuclear stiffness ratio is significantly lower than prior reports for isolated nuclei. These results suggest that the nucleus may behave mechanically different in situ than when isolated.
We apply the wetting theory to predict the kinetics of fibroblast spreading onto an adhesive substrate, under simplifying assumptions on the cell structure and geometry. Three main parameters are used: cytoplasmic viscosity, cortical tension, and cell-to-substrate adhesion energy. The viscosity and tension values are taken from previous micromechanical studies. The adhesion energy, ill known, is adjusted by fitting the model predictions to available experimental data of contact radius versus time. The agreement is quite good, justifying such a "macroscopic" view of cell morphology.
Cell adhesion to material surfaces is a fundamental phenomenon in tissue response to implanted devices, and an important consideration in tissue engineering. For example, elucidation of phenomena associated with adhesion of chondrocytes to biomaterials is critical in addressing the difficult problem of articular cartilage regeneration. The first objective of this study was to measure the mechanical adhesiveness characteristics of individual rabbit articular chondrocytes as a function of seeding time to provide further understanding of the cell adhesion process. The second objective was to quantify the force required to separate the plasma membrane from the underlying cytoskeleton as a function of seeding time. After culturing chondrocytes on glass coverslips for 1, 2, 4, 6 h, two biomechanical tests were performed on single chondrocytes: (i) mechanical adhesiveness measurement by the cytodetacher; and (ii) plasma membrane tether formation force measurement by optical tweezers. Cell mechanical adhesiveness increased from 231 ± 149 Pa at 1 h to 1085 ± 211 Pa at 6 h. The cell contact area with the substrata increased from 161 ± 52 μm ² at 1 h to 369 ± 105 μm ² at 6 h. The tether formation force increased from 232 ± 23 pN at 1 h to 591 ± 17 pN at 6 h. Moreover, fluorescence staining by rhodamine‐phalloidin demonstrated the process of actin spreading within the cytoskeleton from 0.5 to 6 h and allowed for measurement of cell height which was found to decrease from 12.3 ± 2.9 μm at 0.5 h to 6.2 ± 0.9 μm at 6 h.
© 2002 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved.
Although osteoporosis is characterized by quantitative (mass) and qualitative (structural) changes, standard clinical techniques (dual-energy X-ray absorptiometry, DXA) only measure the former. Three-dimensional micro-finite-element (micro-FE) models based on high-resolution images can account for structural aspects as well, and it has recently been shown that an improved prediction of distal radius strength is possible with micro-FE analysis. A clinical application of this technique, however, is limited by its high imaging and computational demands. The objective of this study is to investigate if an improved prediction of bone strength can be obtained as well when only a small part of the radius is used for micro-FE modeling. Images of a 1-cm region of the metaphysis of the distal radius of 54 cadaver arms (mean age: 82 +/- 9 SD) made with a three-dimensional peripheral quantitative computed tomography (pQCT) device at 165- micro m resolution formed the basis for micro-FE models that were used to predict the bone failure load. Following imaging, specimens were experimentally compressed to failure to produce a Colles'-type fracture. Failure loads predicted from micro-FE analyses agreed well with those measured experimentally (R2 = 0.66, p < 0.001). Lower correlations were observed with bone mass (R2 = 0.48, p < 0.001) and microstructural parameters (R2 = 0.47, p < 0.001). Hence, even when only a small region is modeled, micro-FE analysis provides an improved prediction of radius strength.
We investigated the mechanotransduction pathway in endothelial cells between their nucleus and adhesions to the extracellular matrix. First, we measured nuclear deformations in response to alterations of cell shape as cells detach from a flat surface. We found that the nuclear deformation appeared to be in direct and immediate response to alterations of the cell adhesion area. The nucleus was then treated as a neo-Hookean compressible material, and we estimated the stress associated with the cytoskeleton and acting on the nucleus during cell rounding. With the obtained stress field, we estimated the magnitude of the forces deforming the nucleus. Considering the initial and final components of this adhesion-cytoskeleton-nucleus force transmission pathway, we found our estimate for the internal forces acting on the nucleus to be on the same order of magnitude as previously measured traction forces, suggesting a direct mechanical link between adhesions and the nucleus.
Eukaryotic cells are continuously subjected to mechanical forces under normal physiological conditions. These forces and associated cellular deformations induce a variety of biological processes. The degree of deformation depends on the mechanical properties of the cell. As most cells are anchorage dependent for normal functioning, it is important to study the mechanical properties of cells in their attached configuration. The goal of the present study was to obtain the mechanical and failure properties of attached cells. Individual, attached C2C12 mouse myoblasts were subjected to unconfined compression experiments using a recently developed loading device. The device allows global compression of the cell until cell rupture and simultaneously measures the associated forces. Cell bursting was characterized by a typical reduction in the force, referred to as the bursting force. Mean bursting forces were calculated as 8.7+/-2.5 microN at an axial strain of 72+/-4%. Visualization of the cell using confocal microscopy revealed that cell bursting was preceded by the formation of bulges at the cell membrane, which eventually led to rupturing of the cell membrane. Finite element calculations were performed to simulate the obtained force-deformation curves. A finite element mesh was built for each cell to account for its specific geometrical features. Using an axisymmetric approximation of the cell geometry, and a Neo-Hookean constitutive model, excellent agreement between predicted and measured force-deformation curves was obtained, yielding an average Young's modulus of 1.14+/-0.32 kPa.
Endothelial cells possess a mechanical network connecting adhesions on the basal surface, the cytoskeleton, and the nucleus. Transmission of force at adhesions via this pathway can deform the nucleus, ultimately resulting in an alteration of gene expression and other cellular changes (mechanotransduction). Previously, we measured cell adhesion area and apparent nuclear stretch during endothelial cell rounding. Here, we reconstruct the stress map of the nucleus from the observed strains using finite-element modeling. To simulate the disruption of adhesions, we prescribe displacement boundary conditions at the basal surface of the axisymmetric model cell. We consider different scenarios of the cytoskeletal arrangement, and represent the cytoskeleton as either discrete fibers or as an effective homogeneous layer When the nucleus is in the initial (spread) state, cytoskeletal tension holds the nucleus in an elongated, ellipsoidal configuration. Loss of cytoskeletal tension during cell rounding is represented by reactive forces acting on the nucleus in the model. In our simulations of cell rounding, we found that, for both representations of the cytoskeleton, the loss of cytoskeletal tension contributed more to the observed nuclear deformation than passive properties. Since the simulations make no assumption about the heterogeneity of the nucleus, the stress components both within and on the surface of the nucleus were calculated. The nuclear stress map showed that the nucleus experiences stress on the order of magnitude that can be significant for the function of DNA molecules and chromatin fibers. This study of endothelial cell mechanobiology suggests the possibility that mechanotransduction could result, in part, from nuclear deformation, and may be relevant to angiogenesis, wound healing, and endothelial barrier dysfunction.
Optical-sectioning, digital fluorescence microscopy provides images representing temporally- and spatially-resolved molecular-scale details of the substructures of living cells. To render such images into solid models for further computational analyses, we have developed an integrated system of image acquisition, processing, and rendering, which includes a new empirical technique to correct for axial distortions inherent in fluorescence microscopy due to refractive index mismatches between microscope objective immersion medium, coverslip glass, and water. This system takes advantage of the capabilities of ultra-high numerical aperture objectives (e.g. total internal reflection fluorescence microscopy) and enables faithful three-dimensional rendering of living cells into solid models amenable to further computational analysis. An example of solid modeling of bovine aortic endothelial cells and their nuclei is presented. Since many cellular level events are temporally and spatially confined, such integrated image acquisition, processing, rendering, and computational analysis, will enable, in silico, the generation of new computational models for cell mechanics and signaling.
A common but potentially severe malady afflicting permanent wheelchair users is pressure sores caused by elevated soft tissue strains and stresses over a critical prolonged period of time. Presently, there is paucity of information regarding deep soft tissue strains and stresses in the buttocks of humans during sitting. Strain and stress distributions in deep muscle and fat tissues were therefore calculated in six healthy subjects during sitting, in a double-donut Open-MR system, using a "reverse engineering" approach. Specifically, finite element (FE) models of the undeformed buttock were built for each subject using MR images taken at the coronal plane in a non-weight-bearing sitting posture. Using a second MR image taken from each subject during weight-bearing sitting we characterized the ischial tuberosity sagging toward the sitting surface in weight-bearing, and used these data as displacement boundary conditions for the FE models. These subject-specific FE analyses showed that maximal tissue strains and stresses occur in the gluteal muscles, not in fat or at the skin near the body-seat interface. Peak principal compressive strain and stress in the gluteus muscle were 74+/-7% and 32+/-9 kPa (mean+/-standard deviation), respectively. Peak principal compressive strain and stress in enveloping fat tissue were 46+/-7% and 18+/-4 kPa, respectively. Models were validated by comparing measured peak interface pressures under the ischial tuberosities (17+/-4 kPa) with those calculated by means of FE (18+/-3 kPa), for each subject. This is the first study to quantify sub-dermal tissue strain and stress distributions in sitting humans, in vivo. These data are essential for understanding the aetiology of pressure sores, particularly those that were recently termed "deep tissue injury" at the US National Pressure Ulcer Advisory Panel (NPUAP) 2005 Consensus Conference.
The paper deals with problems related to computational modelling of stress-strain states in vascular smooth muscle cells (SMCs). First, motivation for stress-strain analysis of SMCs is presented. Problems of their structure, geometry, constitutive models and initial (stress-free) state are analyzed on the basis of anatomical, histological and physiological knowledge. Various types of computational FE models of SMCs are presented; their constitutive models are identified on the basis of published mechanical tests carried out with SMCs cultured in vitro. Results of two models are presented; the former is a homogeneous model of the cell tension test with hyperelastic constitutive relations of the cell material. The latter model is more complex, it comprehends cortical and deep cytoskeleton, modelled as a tensegrity structure, and homogeneous linear elastic nucleus and remaining cytoplasm; it is used in computational modelling of indentation test. Perspectives, assumptions and limitations of computational modelling of SMCs under physiological load are discussed.
Hemodynamic forces applied at the apical surface of vascular endothelial cells may be redistributed to and amplified at remote intracellular organelles and protein complexes where they are transduced to biochemical signals. In this study we sought to quantify the effects of cellular material inhomogeneities and discrete attachment points on intracellular stresses resulting from physiological fluid flow. Steady-state shear- and magnetic bead-induced stress, strain, and displacement distributions were determined from finite-element stress analysis of a cell-specific, multicomponent elastic continuum model developed from multimodal fluorescence images of confluent endothelial cell (EC) monolayers and their nuclei. Focal adhesion locations and areas were determined from quantitative total internal reflection fluorescence microscopy and verified using green fluorescence protein-focal adhesion kinase (GFP-FAK). The model predicts that shear stress induces small heterogeneous deformations of the endothelial cell cytoplasm on the order of <100 nm. However, strain and stress were amplified 10-100-fold over apical values in and around the high-modulus nucleus and near focal adhesions (FAs) and stress distributions depended on flow direction. The presence of a 0.4 microm glycocalyx was predicted to increase intracellular stresses by approximately 2-fold. The model of magnetic bead twisting rheometry also predicted heterogeneous stress, strain, and displacement fields resulting from material heterogeneities and FAs. Thus, large differences in moduli between the nucleus and cytoplasm and the juxtaposition of constrained regions (e.g. FAs) and unattached regions provide two mechanisms of stress amplification in sheared endothelial cells. Such phenomena may play a role in subcellular localization of early mechanotransduction events.
Mechanical forces play an important role in many microbiological phenomena such as embryogenesis, regeneration, cell proliferation and differentiation. Micromanipulation of cells in a controlled environment is a widely used approach for understanding cellular responses with respect to external mechanical forces. While modern micromanipulation and imaging techniques provide useful optical information about the change of overall cell contours under the impact of external loads, the intrinsic mechanisms of energy and signal propagation throughout the cell structure are usually not accessible by direct observation. This work deals with the computational modelling and simulation of intracellular strain state of uniaxially stretched cells captured in a series of images. A nonlinear elastic finite element method on tetrahedral grids was applied for numerical analysis of inhomogeneous stretching of a rat embryonic fibroblast 52 (REF 52) using a simplified two-component model of a eukaryotic cell consisting of a stiffer nucleus surrounded by a softer cytoplasm. The difference between simulated and experimentally observed cell contours is used as a feedback criterion for iterative estimation of canonical material parameters of the two-component model such as stiffness and compressibility. Analysis of comparative simulations with varying material parameters shows that (i) the ratio between the stiffness of cell nucleus and cytoplasm determines intracellular strain distribution and (ii) large deformations result in increased stiffness and decreased compressibility of the cell cytoplasm. The proposed model is able to reproduce the evolution of the cellular shape over a sequence of observed deformations and provides complementary information for a better understanding of mechanical cell response.
Most trans-tibial amputation (TTA) patients use a prosthesis to retain upright mobility capabilities. Unfortunately, interaction between the residual limb and the prosthetic socket causes elevated internal strains and stresses in the muscle and fat tissues in the residual limb, which may lead to deep tissue injury (DTI) and other complications. Presently, there is paucity of information on the mechanical conditions in the TTA residual limb during load-bearing. Accordingly, our aim was to characterize the mechanical conditions in the muscle flap of the residual limb of a TTA patient after donning the prosthetic socket and during load-bearing. Knowledge of internal mechanical conditions in the muscle flap can be used to identify the risk for DTI and improve the fitting of the prosthesis. We used a patient-specific modelling approach which involved an MRI scan, interface pressure measurements between the residual limb and the socket of the prosthesis and three-dimensional non-linear large-deformation finite-element (FE) modelling to quantify internal soft tissue strains and stresses in a female TTA patient during static load-bearing. Movement of the truncated tibia and fibula during load-bearing was measured by means of MRI and used as displacement boundary conditions for the FE model. Subsequently, we calculated the internal strains, strain energy density (SED) and stresses in the muscle flap under the truncated bones. Internal strains under the tibia peaked at 85%, 129% and 106% for compression, tension and shear strains, respectively. Internal strains under the fibula peaked at substantially lower values, that is, 19%, 22% and 19% for compression, tension and shear strains, respectively. Strain energy density peaked at the tibial end (104kJ/m(3)). The von Mises stresses peaked at 215kPa around the distal end of the tibia. Stresses under the fibula were at least one order of magnitude lower than the stresses under the tibia. We surmise that our present patient-specific modelling method is an important tool in understanding the etiology of DTI in the residual limbs of TTA patients.