Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics

The complex interplay between mechanical forces, tissue response and individual susceptibility to pressure ulcers

OBJECTIVE

The most recent edition of the International Clinical Practice Guideline for the Prevention and Treatment of Pressure Ulcers/Injuries was released in 2019. Shortly after, in 2020, the first edition of the SECURE Prevention expert panel report, focusing on device-related pressure ulcers/injuries, was published as a special issue in the Journal of Wound Care. A second edition followed in 2022. This article presents a comprehensive summary of the current understanding of the causes of pressure ulcers/injuries (PU/Is) as detailed in these globally recognised consensus documents.

METHOD

The literature reviewed in this summary specifically addresses the impact of prolonged soft tissue deformations on the viability of cells and tissues in the context of PU/Is related to bodyweight or medical devices.

RESULTS

Prolonged soft tissue deformations initially result in cell death and tissue damage on a microscopic scale, potentially leading to development of clinical PU/Is over time. That is, localised high tissue deformations or mechanical stress concentrations can cause microscopic damage within minutes, but it may take several hours of continued mechanical loading for this initial cell and tissue damage to become visible and clinically noticeable. Superficial tissue damage primarily stems from excessive shear loading on fragile or vulnerable skin. In contrast, deeper PU/Is, known as deep tissue injuries, typically arise from stress concentrations in soft tissues at body regions over sharp or curved bony prominences, or under stiff medical devices in prolonged contact with the skin.

CONCLUSION

This review promotes deeper understanding of the pathophysiology of PU/Is, indicating that their primary prevention should focus on alleviating the exposure of cells and tissues to stress concentrations. This goal can be achieved either by reducing the intensity of stress concentrations in soft tissues, or by decreasing the exposure time of soft tissues to such stress concentrations.

Comparing the bone regeneration potential between a trabecular bone and a porous scaffold through osteoblast migration and differentiation: A multiscale approach

Both cell migration and osteogenic differentiation are critical for successful bone regeneration. Therefore, understanding the mechanobiological aspects that govern these two processes is essential in designing effective scaffolds that promote faster bone regeneration. Studying these two factors at different locations is necessary to manage bone regeneration in various sections of a scaffold. Hence, a multiscale computational model was used to observe the mechanical responses of osteoblasts placed in different positions of the trabecular bone and gyroid scaffold. Fluid shear stresses in scaffolds at cell seeded locations (representing osteogenic differentiation) and strain energy densities in cells at cell substrate interface (representing cell migration) were observed as mechanical response parameters in this study. Comparison of these responses, as two critical factors for bone regeneration, between the trabecular bone and gyroid scaffold at different locations, is the overall goal of the study. This study reveals that the gyroid scaffold exhibits higher osteogenic differentiation and cell migration potential compared to the trabecular bone. However, the responses in the gyroid only mimic the trabecular bone in two out of nine positions. These findings can guide us in predicting the ideal cell seeded sites within a scaffold for better bone regeneration and in replicating a replaced bone condition by altering the physical parameters of a scaffold.

Evaluating the cell migration potential of TiO2 nanorods incorporated in a Ti6Al4V scaffold: A multiscale approach

Improvement of cell migration by the nano-topographical modification of implant surface can directly or indirectly accelerate wound healing and osseointegration between bone and implant. Therefore, modification of the implant surface was done with TiO2 nanorod (NR) arrays to develop a more osseointegration-friendly implant in this study. Modulating the migration of a cell, adhered to a scaffold, by the variations of NR diameter, density and tip diameter in vitro is the primary objective of the study. The fluid structure interaction method was used, followed by the submodelling technique in this multiscale analysis. After completing a simulation over a global model, fluid structure interaction data was applied to the sub-scaffold finite element model to predict the mechanical response over cells at the cell-substrate interface. Special focus was given to strain energy density at the cell interface as a response parameter due to its direct correlation with the migration of an adherent cell. The results showed a huge rise in strain energy density after the addition of NRs on the scaffold surface. It also highlighted that variation in NR density plays a more effective role than the variation in NR diameter to control cell migration over a substrate. However, the effect of NR diameter becomes insignificant when the NR tip was considered. The findings of this study could be used to determine the best nanostructure parameters for better osseointegration.

Our contemporary understanding of the aetiology of pressure ulcers/pressure injuries

In 2019, the third and updated edition of the Clinical Practice Guideline (CPG) on Prevention and Treatment of Pressure Ulcers/Injuries has been published. In addition to this most up‐to‐date evidence‐based guidance for clinicians, related topics such as pressure ulcers (PUs)/pressure injuries (PIs) aetiology, classification, and future research needs were considered by the teams of experts. To elaborate on these topics, this is the third paper of a series of the CPG articles, which summarises the latest understanding of the aetiology of PUs/PIs with a special focus on the effects of soft tissue deformation. Sustained deformations of soft tissues cause initial cell death and tissue damage that ultimately may result in the formation of PUs/PIs. High tissue deformations result in cell damage on a microscopic level within just a few minutes, although it may take hours of sustained loading for the damage to become clinically visible. Superficial skin damage seems to be primarily caused by excessive shear strain/stress exposures, deeper PUs/PIs predominantly result from high pressures in combination with shear at the surface over bony prominences, or under stiff medical devices. Therefore, primary PU/PI prevention should aim for minimising deformations by either reducing the peak strain/stress values in tissues or decreasing the exposure time.

A new 3D finite element-based approach for computing cell surface tractions assuming nonlinear conditions

Advances in methods for determining the forces exerted by cells while they migrate are essential for attempting to understand important pathological processes, such as cancer or angiogenesis, among others. Precise data from three-dimensional conditions are both difficult to obtain and manipulate. For this purpose, it is critical to develop workflows in which the experiments are closely linked to the subsequent computational postprocessing. The work presented here starts from a traction force microscopy (TFM) experiment carried out on microfluidic chips, and this experiment is automatically joined to an inverse problem solver that allows us to extract the traction forces exerted by the cell from the displacements of fluorescent beads embedded in the extracellular matrix (ECM). Therefore, both the reconstruction of the cell geometry and the recovery of the ECM displacements are used to generate the inputs for the resolution of the inverse problem. The inverse problem is solved iteratively by using the finite element method under the hypothesis of finite deformations and nonlinear material formulation. Finally, after mathematical postprocessing is performed, the traction forces on the surface of the cell in the undeformed configuration are obtained. Therefore, in this work, we demonstrate the robustness of our computational-based methodology by testing it under different conditions in an extreme theoretical load problem and then by applying it to a real case based on experimental results. In summary, we have developed a new procedure that adds value to existing methodologies for solving inverse problems in 3D, mainly by allowing for large deformations and not being restricted to any particular material formulation. In addition, it automatically bridges the gap between experimental images and mechanical computations.

3D immuno-confocal image reconstruction of fibroblast cytoskeleton and nucleus architecture

Computational models of cellular structures generally rely on simplifying approximations and assumptions that limit biological accuracy. This study presents a comprehensive image processing pipeline for creating unified three-dimensional (3D) reconstructions of the cell cytoskeletal networks and nuclei. Confocal image stacks of these cellular structures were reconstructed to 3D isosurfaces (Imaris), then tessellations were simplified to reduce the number of elements in initial meshes by applying quadric edge collapse decimation with preserved topology boundaries (MeshLab). Geometries were remeshed to ensure uniformity (Instant Meshes) and the resulting 3D meshes exported (ABAQUS) for downstream application. The protocol has been applied successfully to fibroblast cytoskeletal reorganisation in the scleral connective tissue of the eye, under mechanical load that mimics internal eye pressure. While the method herein is specifically employed to reconstruct immunofluorescent confocal imaging data, it is also more widely applicable to other biological imaging modalities where accurate 3D cell structures are required.

Finite element analysis reveals an important role for cell morphology in response to mechanical compression

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.

An iterative finite element-based method for solving inverse problems in traction force microscopy

BACKGROUND AND OBJECTIVE

During the last years different model solutions were proposed for solving cell forces under different conditions. The solution relies on a deformation field that is obtained under cell relaxation with a chemical cocktail. Once the deformation field of the matrix is determined, cell forces can be computed by an inverse algorithm, given the mechanical properties of the matrix. Most of the Traction Force Microscopy (TFM) methods presented so far relied on a linear stress-strain response of the matrix. However, the mechanical response of some biopolymer networks, such as collagen gels is more complex. In this work, we present a numerical method for solving cell forces on non-linear materials.

METHODS

The proposed method relies on solving the inverse problem based on an iterative optimization. The objective function is defined by least-square minimization of the difference between the target and the current computed deformed configuration of the cell, and the iterative formulation is based on the solution of several direct mechanical problems. The model presents a well-posed discretized inverse elasticity problem in the absence of regularization. The algorithm can be easily implemented in any kind of Finite Element (FE) code as a sequence of different standard FE analysis.

RESULTS

To illustrate the proposed iterative formulation we apply the theoretical model to some illustrative examples by using real experimental data of Normal Human Dermal Fibroblast cells (NHDF) migrating inside a 2 mg/ml collagen-based gel. Different examples of application have been simulated to test the inverse numerical model proposed and to investigate the effect of introducing the correct cell properties onto the obtained cell forces. The algorithm converges after a small number of iterations, generating errors of around 5% for the tractions field in the cell contour domain. The resulting maximum traction values increased by 11% as a consequence of doubling the mechanical properties of the cell domain.

CONCLUSIONS

With the results generated from computations we demonstrate the application of the algorithm and explain how the mechanical properties of both, the cell and the gel, domains are important for arriving to the correct results when using inverse traction force reconstruction algorithms, however, have only a minor effect on the resulting traction values.

Micropipette aspiration method for characterizing biological materials with surface energy

Many soft biological tissues possess a considerable surface stress, which plays a significant role in their biophysical functions, but most previous methods for characterizing their mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration method to measure the mechanical properties of soft tissues and cells with surface effects. The neo-Hookean constitutive model is adopted to describe the hyperelasticity of the measured biological material, and the surface effect is taken into account by the finite element method. It is found that when the pipette radius or aspiration length is comparable to the elastocapillary length, surface energy may distinctly alter the aspiration response. Generally, both the aspiration length and the bulk normal stress decrease with increasing surface energy, and thus neglecting the surface energy would lead to an overestimation of elastic modulus. Through dimensional analysis and numerical simulations, we provide an explicit relation between the imposed pressure and the aspiration length. This method can be applied to determine the mechanical properties of soft biological tissues and organs, e.g., livers, tumors and embryos.

Endothelial cells on an aged subendothelial matrix display heterogeneous strain profiles in silico

Within the artery intima, endothelial cells respond to mechanical cues and changes in subendothelial matrix stiffness. Recently, we found that the aging subendothelial matrix stiffens heterogeneously and that stiffness heterogeneities are present on the scale of one cell length. However, the impacts of these complex mechanical micro-heterogeneities on endothelial cells have not been fully understood. Here, we simulate the effects of matrices that mimic young and aged vessels on single- and multi-cell endothelial cell models and examine the resulting cell basal strain profiles. Although there are limitations to the model which prohibit the prediction of intracellular strain distributions in alive cells, this model does introduce mechanical complexities to the subendothelial matrix material. More heterogeneous basal strain distributions are present in the single- and multi-cell models on the matrix mimicking an aged artery over those exhibited on the young artery. Overall, our data indicate that increased heterogeneous strain profiles in endothelial cells are displayed in silico when there is an increased presence of microscale arterial mechanical heterogeneities in the matrix.

The Nuclear Option: Evidence Implicating the Cell Nucleus in Mechanotransduction

Biophysical stimuli presented to cells via microenvironmental properties (e.g., alignment and stiffness) or external forces have a significant impact on cell function and behavior. Recently, the cell nucleus has been identified as a mechanosensitive organelle that contributes to the perception and response to mechanical stimuli. However, the specific mechanotransduction mechanisms that mediate these effects have not been clearly established. Here, we offer a comprehensive review of the evidence supporting (and refuting) three hypothetical nuclear mechanotransduction mechanisms: physical reorganization of chromatin, signaling at the nuclear envelope, and altered cytoskeletal structure/tension due to nuclear remodeling. Our goal is to provide a reference detailing the progress that has been made and the areas that still require investigation regarding the role of nuclear mechanotransduction in cell biology. Additionally, we will briefly discuss the role that mathematical models of cell mechanics can play in testing these hypotheses and in elucidating how biophysical stimulation of the nucleus drives changes in cell behavior. While force-induced alterations in signaling pathways involving lamina-associated polypeptides (LAPs) (e.g., emerin and histone deacetylase 3 (HDAC3)) and transcription factors (TFs) located at the nuclear envelope currently appear to be the most clearly supported mechanism of nuclear mechanotransduction, additional work is required to examine this process in detail and to more fully test alternative mechanisms. The combination of sophisticated experimental techniques and advanced mathematical models is necessary to enhance our understanding of the role of the nucleus in the mechanotransduction processes driving numerous critical cell functions.

Analytical modeling of the mechanics of early invasion of a merozoite into a human erythrocyte

In this study, we used a continuum model based on contact mechanics to understand the mechanics of merozoite invasion into human erythrocytes. This model allows us to evaluate the indentation force and work as well as the contact pressure between the merozoite and erythrocyte for an early stage of invasion (γ = 10%). The model predicted an indentation force of 1.3e ^-11N and an indentation work of 1e ^-18J. The present analytical model can be considered as a useful tool not only for investigations in mechanobiology and biomechanics but also to explore novel therapeutic targets for malaria and other parasite infections.

Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus [Formula: see text] on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of [Formula: see text], were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and [Formula: see text]140 KPa and (2) [Formula: see text], 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35[Formula: see text], 0.235[Formula: see text] and 0.6[Formula: see text]) than for FA attachment (0.0952[Formula: see text], 0.0472[Formula: see text] and 0.05[Formula: see text]). For increasing [Formula: see text], the largest maximum principal strain was 4.4[Formula: see text], 5[Formula: see text], 5.3[Formula: see text] and 5.3[Formula: see text] in the membrane, 9.5[Formula: see text], 1.1[Formula: see text], 1.2[Formula: see text] and 1.2[Formula: see text] in the cytosol, and 4.5[Formula: see text], 5.3[Formula: see text], 5.7[Formula: see text] and 5.7[Formula: see text] in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.

A phenomenological cohesive model for the macroscopic simulation of cell-matrix adhesions

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell-matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell-matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell-matrix adhesions.

Computational simulation of static/cyclic cell stimulations to investigate mechanical modulation of an individual mesenchymal stem cell using confocal microscopy

It has been found that cells react to mechanical stimuli, while the type and magnitude of these cells are different in various physiological and pathological conditions. These stimuli may affect cell behaviors via mechanotransduction mechanisms. The aim of this study is to evaluate mechanical responses of a mesenchymal stem cell (MSC) to a pressure loading using finite elements method (FEM) to clarify procedures of MSC mechanotransduction. The model is constructed based on an experimental set up in which statics and cyclic compressive loads are implemented on a model constructed from a confocal microscopy 3D image of a stem cell. Both of the applied compressive loads are considered in the physiological loading regimes. Moreover, a viscohyperelastic material model was assumed for the cell through which the finite elements simulation anticipates cell behavior based on strain and stress distributions in its components. As a result, high strain and stress values were captured from the viscohyperelastic model because of fluidic behavior of cytosol when compared with the obtained results through the hyperelastic models. It can be concluded that the generated strain produced by cyclic pressure is almost 8% higher than that caused by the static load and the von Mises stress distribution is significantly increased to about 150kPa through the cyclic loading. In total, the results does not only trace the efficacy of an individual 3D model of MSC using biomechanical experiments of cell modulation, but these results provide knowledge in interpretations from cell geometry. The current study was performed to determine a realistic aspect of cell behavior.

Effects of Frequency and Acceleration Amplitude on Osteoblast Mechanical Vibration Responses: A Finite Element Study

Bone cells are deformed according to mechanical stimulation they receive and their mechanical characteristics. However, how osteoblasts are affected by mechanical vibration frequency and acceleration amplitude remains unclear. By developing 3D osteoblast finite element (FE) models, this study investigated the effect of cell shapes on vibration characteristics and effect of acceleration (vibration intensity) on vibrational responses of cultured osteoblasts. Firstly, the developed FE models predicted natural frequencies of osteoblasts within 6.85-48.69 Hz. Then, three different levels of acceleration of base excitation were selected (0.5, 1, and 2 g) to simulate vibrational responses, and acceleration of base excitation was found to have no influence on natural frequencies of osteoblasts. However, vibration response values of displacement, stress, and strain increased with the increase of acceleration. Finally, stress and stress distributions of osteoblast models under 0.5 g acceleration in Z-direction were investigated further. It was revealed that resonance frequencies can be a monotonic function of cell height or bottom area when cell volumes and material properties were assumed as constants. These findings will be useful in understanding how forces are transferred and influence osteoblast mechanical responses during vibrations and in providing guidance for cell culture and external vibration loading in experimental and clinical osteogenesis studies.

Immersed Boundary Models for Quantifying Flow-Induced Mechanical Stimuli on Stem Cells Seeded on 3D Scaffolds in Perfusion Bioreactors

Perfusion bioreactors regulate flow conditions in order to provide cells with oxygen, nutrients and flow-associated mechanical stimuli. Locally, these flow conditions can vary depending on the scaffold geometry, cellular confluency and amount of extra cellular matrix deposition. In this study, a novel application of the immersed boundary method was introduced in order to represent a detailed deformable cell attached to a 3D scaffold inside a perfusion bioreactor and exposed to microscopic flow. The immersed boundary model permits the prediction of mechanical effects of the local flow conditions on the cell. Incorporating stiffness values measured with atomic force microscopy and micro-flow boundary conditions obtained from computational fluid dynamics simulations on the entire scaffold, we compared cell deformation, cortical tension, normal and shear pressure between different cell shapes and locations. We observed a large effect of the precise cell location on the local shear stress and we predicted flow-induced cortical tensions in the order of 5 pN/μm, at the lower end of the range reported in literature. The proposed method provides an interesting tool to study perfusion bioreactors processes down to the level of the individual cell's micro-environment, which can further aid in the achievement of robust bioprocess control for regenerative medicine applications.

Analytical and computational modeling of early penetration of non-enveloped icosahedral viruses into cells

BACKGROUND

As obligate intracellular parasites, all viruses penetrate target cells to initiate replication and infection.

OBJECTIVE

This study introduces two approaches for evaluating the contact loads applied to a cell during early penetration of non-enveloped icosahedral viruses.

METHODS

The first approach is analytical modeling which is based on Hertz's theory for the contact of two elastic bodies; here we model the virus capsid as a triangle and the cell as an order-of-magnitude larger sphere. The second approach is finite element modeling, where we simulate three types of viruses: adeno-, papilloma- and polio- viruses, each interacting with a cell section.

RESULTS

We find that the peak contact pressures and forces generated at the initial virus-cell contact depend on the virus geometry - that is both size and shape. With respect to shape, we show that the icosahedral virus shape induces greater peak pressures compared to a spherical virus shape. With respect to size, it is shown that the larger the virus is the greater are the contact loads in the attacked cell.

CONCLUSION

Utilization of our modeling can be substantially useful not only for basic science studies, but also in other, more applied fields, such as in the field of gene therapy, or in `phage' virus studies.

Fluid-Structure Interactions Analysis of Shear-Induced Modulation of a Mesenchymal Stem Cell: An Image-Based Study

Although effects of biochemical modulation of stem cells have been widely investigated, only recent advances have been made in the identification of mechanical conditioning on cell signaling pathways. Experimental investigations quantifying the micromechanical environment of mesenchymal stem cells (MSCs) are challenging while computational approaches can predict their behavior due to in vitro stimulations. This study introduces a 3D cell-specific finite element model simulating large deformations of MSCs. Here emphasizing cell mechanical modulation which represents the most challenging multiphysics phenomena in sub-cellular level, we focused on an approach attempting to elicit unique responses of a cell under fluid flow. Fluorescent staining of MSCs was performed in order to visualize the MSC morphology and develop a geometrically accurate model of it based on a confocal 3D image. We developed a 3D model of a cell fixed in a microchannel under fluid flow and then solved the numerical model by fluid-structure interactions method. By imposing flow characteristics representative of vigorous in vitro conditions, the model predicts that the employed external flow induces significant localized effective stress in the nucleo-cytoplasmic interface and average cell deformation of about 40%. Moreover, it can be concluded that a lower strain level is made in the cell by the oscillatory flow as compared with steady flow, while same ranges of effective stress are recorded inside the cell in both conditions. The deeper understanding provided by this study is beneficial for better design of single cell in vitro studies.

3D Reconstruction of Coronary Artery Vascular Smooth Muscle Cells

Aims

The 3D geometry of individual vascular smooth muscle cells (VSMCs), which are essential for understanding the mechanical function of blood vessels, are currently not available. This paper introduces a new 3D segmentation algorithm to determine VSMC morphology and orientation.

Methods and Results

A total of 112 VSMCs from six porcine coronary arteries were used in the analysis. A 3D semi-automatic segmentation method was developed to reconstruct individual VSMCs from cell clumps as well as to extract the 3D geometry of VSMCs. A new edge blocking model was introduced to recognize cell boundary while an edge growing was developed for optimal interpolation and edge verification. The proposed methods were designed based on Region of Interest (ROI) selected by user and interactive responses of limited key edges. Enhanced cell boundary features were used to construct the cell’s initial boundary for further edge growing. A unified framework of morphological parameters (dimensions and orientations) was proposed for the 3D volume data. Virtual phantom was designed to validate the tilt angle measurements, while other parameters extracted from 3D segmentations were compared with manual measurements to assess the accuracy of the algorithm. The length, width and thickness of VSMCs were 62.9±14.9μm, 4.6±0.6μm and 6.2±1.8μm (mean±SD). In longitudinal-circumferential plane of blood vessel, VSMCs align off the circumferential direction with two mean angles of -19.4±9.3° and 10.9±4.7°, while an out-of-plane angle (i.e., radial tilt angle) was found to be 8±7.6° with median as 5.7°.

Conclusions

A 3D segmentation algorithm was developed to reconstruct individual VSMCs of blood vessel walls based on optical image stacks. The results were validated by a virtual phantom and manual measurement. The obtained 3D geometries can be utilized in mathematical models and leads a better understanding of vascular mechanical properties and function.

A phase-contrast microscopy-based method for modeling the mechanical behavior of mesenchymal stem cells

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.

Finite element analysis of the pressure-induced deformation of Schlemm's canal endothelial cells

The endothelial cells lining the inner wall of Schlemm's canal (SC) in the eye are relatively unique in that they support a basal-to-apical pressure gradient that causes these cells to deform, creating giant vacuoles and transendothelial pores through which the aqueous humor flows. Glaucoma is associated with an increased resistance to this flow. We used finite element modeling and estimates of cell modulus made using atomic force microscopy to characterize the pressure-induced deformation of SC cells and to estimate the maximum pressure drop that SC cells can support. We examined the effects of cell geometry, cell stiffness, and the contribution of the cell cortex to support the pressure-generated load. We found that the maximum strain generated by this loading occurs at the points of cell-substrate attachment and that the cortex of the cells bears nearly all of this load. The ability of these cells to support a significant transcellular pressure drop is extremely limited (on the order of 5 mmHg or less) unless these cells either stiffen very considerably with increasing deformation or have substantial attachments to their substratum away from their periphery. This puts limits on the flow resistance that this layer can generate, which has implications regarding the site where the bulk of the flow resistance is generated in healthy and glaucomatous eyes.

Dynamic finite element analysis and moving particle simulation of human enamel on a microscale

BACKGROUND

The study of biomechanics of deformation and fracture of hard biological tissues involving organic matrix remains a challenge as variations in mechanical properties and fracture mode may have time-dependency. Finite element analysis (FEA) has been widely used but the shortcomings of FEA such as the long computation time owing to re-meshing in simulating fracture mechanics have warranted the development of alternative computational methods with higher throughput. The aim of this study was to compare dynamic two-dimensional FEA and moving particle simulation (MPS) when assuming a plane strain condition in the modeling of human enamel on a reduced scale.

METHODS

Two-dimensional models with the same geometry were developed for MPS and FEA and tested in tension generated with a single step of displacement. The displacement, velocity, pressure, and stress levels were compared and Spearman׳s rank-correlation coefficients R were calculated (p<0.001).

RESULTS

The MPS and FEA were significantly correlated for displacement, velocity, pressure, and Y-stress.

CONCLUSIONS

The MPS may be further developed as an alternative approach without mesh generation to simulate deformation and fracture phenomena of dental and potentially other hard tissues with complex microstructure.

Adipocyte stiffness increases with accumulation of lipid droplets

Adipogenesis and increase in fat tissue mass are mechanosensitive processes and hence should be influenced by the mechanical properties of adipocytes. We evaluated subcellular effective stiffnesses of adipocytes using atomic force microscopy (AFM) and interferometric phase microscopy (IPM), and we verified the empirical results using finite element (FE) simulations. In the AFM studies, we found that the mean ratio of stiffnesses of the lipid droplets (LDs) over the nucleus was 0.83 ± 0.14, from which we further evaluated the ratios of LDs over cytoplasm stiffness, as being in the range of 2.5 to 8.3. These stiffness ratios, indicating that LDs are stiffer than cytoplasm, were verified by means of FE modeling, which simulated the AFM experiments, and provided good agreement between empirical and model-predicted structural behavior. In the IPM studies, we found that LDs mechanically distort their intracellular environment, which again indicated that LDs are mechanically stiffer than the surrounding cytoplasm. Combining these empirical and simulation data together, we provide in this study evidence that adipocytes stiffen with differentiation as a result of accumulation of LDs. Our results are relevant to research of adipose-related diseases, particularly overweight and obesity, from a mechanobiology and cellular mechanics perspectives.

Computational models of the primary cilium and endothelial mechanotransmission

In endothelial cells (ECs), the mechanotransduction of fluid shear stress is partially dependent on the transmission of force from the fluid into the cell (mechanotransmission). The role of the primary cilium in EC mechanotransmission is not yet known. To motivate a framework towards quantifying cilia contribution to EC mechanotransmission, we have reviewed mechanical models of both (1) the primary cilium (three-dimensional and lower-dimensional) and (2) whole ECs (finite element, non-finite element, and tensegrity). Both the primary cilia and whole EC models typically incorporate fluid-induced wall shear stress and spatial geometry based on experimentally acquired images of cells. This paper presents future modelling directions as well as the major goals towards integrating primary cilium models into a multi-component EC mechanical model. Finally, we outline how an integrated cilium-EC model can be used to better understand mechanotransduction in the endothelium.

Structural finite element analysis to explain cell mechanics variability

The ability to model the mechanical responses of different cell types presents many opportunities to tissue engineering research to further identify changes from physiological conditions to disease. Using a previously validated finite element cell model we aim to show how variation of the material properties of the intracellular components affects cell response after compression and shearing. A parametric study was performed to understand the key mechanical features from different cell types, focussing on specific cytoskeleton components and prestress. Results show that actin cortex does not have a mechanical role in resisting shearing loading conditions. The sensitivity analysis predicted that cell force to compression and shearing is highly affected by changes in cortex thickness, cortex Young's modulus and rigidity of the remaining cytoplasm. Variation of prestress affects mainly the response of cells under shear loads and the model defines a relationship between cell force and prestress depending on the specific loading conditions, which is in good agreement with in vitro experiments. The results are used to make predictions that can relate mechanical properties with cell phenotype to be used as guidelines for individual cytoskeletal structures for future modelling efforts of the structure-function relationships of living cells.

A linear programming approach to reconstructing subcellular structures from confocal images for automated generation of representative 3D cellular models

This paper presents a novel computer vision algorithm to analyze 3D stacks of confocal images of fluorescently stained single cells. The goal of the algorithm is to create representative in silico model structures that can be imported into finite element analysis software for mechanical characterization. Segmentation of cell and nucleus boundaries is accomplished via standard thresholding methods. Using novel linear programming methods, a representative actin stress fiber network is generated by computing a linear superposition of fibers having minimum discrepancy compared with an experimental 3D confocal image. Qualitative validation is performed through analysis of seven 3D confocal image stacks of adherent vascular smooth muscle cells (VSMCs) grown in 2D culture. The presented method is able to automatically generate 3D geometries of the cell's boundary, nucleus, and representative F-actin network based on standard cell microscopy data. These geometries can be used for direct importation and implementation in structural finite element models for analysis of the mechanics of a single cell to potentially speed discoveries in the fields of regenerative medicine, mechanobiology, and drug discovery.

Sperm penetration to the zona pellucida of an oocyte: a computational model incorporating acrosome reaction

For fertilisation to occur, a spermatozoon needs to cross the zona pellucida (ZP), which is a glycoprotein layer surrounding the oocyte. Crossing the ZP requires an acrosome reaction (AR) where enzymes released from the spermatozoon head locally digest and soften the ZP so that the spermatozoon can penetrate deeper. Here, a biomechanical sperm-oocyte interaction model that considers the AR using the finite element method was formulated. This modelling is used to determine which of the following factors directly contribute to the crossing of the ZP: local ZP softening by AR, sperm head shape, ZP hardening elsewhere than in the AR site, ZP thickness and sperm hyperactivation (more flagellar beating). It has been found that an AR softening the ZP to over one-tenth of its basal stiffness is important for successful sperm penetration, and that 'sharper' heads have a biomechanical advantage in penetrating deeper. The approach is promising for understanding this exciting stage of reproduction.

A computational approach to understand phenotypic structure and constitutive mechanics relationships of single cells

The goal of this study is to construct a representative 3D finite element model (FEM) of individual cells based on their sub-cellular structures that predicts cell mechanical behavior. The FEM simulations replicate atomic force microscopy (AFM) nanoindentation experiments on live vascular smooth muscle cells. Individual cells are characterized mechanically with AFM and then imaged in 3D using a spinning disc confocal microscope. Using these images, geometries for the FEM are automatically generated via image segmentation and linear programming algorithms. The geometries consist of independent structures representing the nucleus, actin stress fiber network, and cytoplasm. These are imported into commercial software for mesh refinement and analysis. The FEM presented here is capable of predicting AFM results well for 500 nm indentations. The FEM results are relatively insensitive to both the exact number and diameter of fibers used. Despite the localized nature of AFM nanoindentation, the model predicts that stresses are distributed in an anisotropic manner throughout the cell body via the actin stress fibers. This pattern of stress distribution is likely a result of the geometric arrangement of the actin network.

Continuum modeling of a neuronal cell under blast loading

Traumatic brain injuries have recently been put under the spotlight as one of the most important causes of accidental brain dysfunctions. Significant experimental and modeling efforts are thus underway to study the associated biological, mechanical and physical mechanisms. In the field of cell mechanics, progress is also being made at the experimental and modeling levels to better characterize many of the cell functions, including differentiation, growth, migration and death. The work presented here aims to bridge both efforts by proposing a continuum model of a neuronal cell submitted to blast loading. In this approach, the cytoplasm, nucleus and membrane (plus cortex) are differentiated in a representative cell geometry, and different suitable material constitutive models are chosen for each one. The material parameters are calibrated against published experimental work on cell nanoindentation at multiple rates. The final cell model is ultimately subjected to blast loading within a complete computational framework of fluid-structure interaction. The results are compared to the nanoindentation simulation, and the specific effects of the blast wave on the pressure and shear levels at the interfaces are identified. As a conclusion, the presented model successfully captures some of the intrinsic intracellular phenomena occurring during the cellular deformation under blast loading that potentially lead to cell damage. It suggests, more particularly, that the localization of damage at the nucleus membrane is similar to what has already been observed at the overall cell membrane. This degree of damage is additionally predicted to be worsened by a longer blast positive phase duration. In conclusion, the proposed model ultimately provides a new three-dimensional computational tool to evaluate intracellular damage during blast loading.

Stretching Affects Intracellular Oxygen Levels: Three-Dimensional Multiphysics Studies

Multiphysics modeling is an emerging approach in cellular bioengineering research, used for simulating complex biophysical interactions and their effects on cell viability and function. Our goal in the present study was to integrate cell-specific finite element modeling—which we have developed in previous research to simulate deformation of individual cells subjected to external loading—with oxygen transport in the deformed cells at normoxic and hypoxic environments. We specifically studied individual and combined effects of substrate stretch levels, O2 concentration in the culture media, and temperature of the culture media on intracellular O2 levels in cultured myoblasts, in models of two individual cells. We found that (i) O2 transport became faster with the increasing levels of substrate stretch (ranging from 0 to 24%), and (ii) the effect of a 3  °C temperature drop on slowing down the O2 transport was milder with respect to the effect that strains had. The changes in cell geometry due to externally applied deformations could, hence, theoretically affect cell respiration, which should be a consideration in cellular mechanics experiments.

Cell-to-cell variability in deformations across compressed myoblasts

Many biological consequences of external mechanical loads applied to cells depend on localized cell deformations rather than on average whole-cell-body deformations. Such localized intracellular deformations are likely to depend, in turn, on the individual geometrical features of each cell, e.g., the local surface curvatures or the size of the nucleus, which always vary from one cell to another, even within the same culture. Our goal here was to characterize cell-to-cell variabilities in magnitudes and distribution patterns of localized tensile strains that develop in the plasma membrane (PM) and nuclear surface area (NSA) of compressed myoblasts, in order to identify resemblance or differences in mechanical performances across the cells. For this purpose, we utilized our previously developed confocal microscopy-based three-dimensional cell-specific finite element modeling methodology. Five different C2C12 undifferentiated cells belonging to the same culture were scanned confocally and modeled, and were then subjected to compression in the simulation setting. We calculated the average and peak tensile strains in the PM and NSA, the percentage of PM area subjected to tensile strains above certain thresholds and the coefficient of variation (COV) in average and peak strains. We found considerable COV values in tensile strains developing at the PM and NSA (up to ~35%) but small external compressive deformations induced greater variabilities in intracellular strains across cells compared to large deformations. Interestingly, the external deformations needed to cause localized PM or NSA strains exceeding each threshold were very close across the different cells. Better understanding of variabilities in mechanical performances of cells-either of the same type or of different types-is important for interpreting experimental data in any experiments involving delivery of mechanical loads to cells.

The Relationship Between Sperm Velocity and Pressures Applied to the Zona Pellucida During Early Sperm-Oocyte Penetration

Sperm velocity is long known to be an important indicator of sperm quality but without much biophysical theory explaining it. Contact mechanics based modeling was developed here to determine the effects that sperm velocity (vs) and sperm head density (ρs)—which is an indicator of the stiffness of the head, have on the peak sperm-zona pellucida contact pressure (pm) during the early phase of sperm penetration. The modeling identified vs as being more influential on pm compared with the influence that ρs has, which means that for spermatozoa competing on the same oocyte, greater vs is a more important advantage than higher ρs. Specifically, pm was more sensitive by a power of 2 to changes in vs than to changes in ρs. It was further demonstrated that each 0.1 g/cc increase in ρs (within the physiologically relevant range of 1.3–1.7 g/cc) would be equivalent to just ∼3% rise in vs, indicating again that faster swimming is a better strategy for spermatozoa compared with head stiffening. The modeling hence provided some useful insights regarding sperm biomechanics, which theoretically elucidate the well-recognized importance of sperm velocity measurements as being indicative of sperm quality.

Effects of Virus Size and Cell Stiffness on Forces, Work, and Pressures Driving Membrane Invagination in a Receptor-Mediated Endocytosis

A continuum model based on the contact mechanics theory was developed and used for evaluating virus indentation forces at the early stage of membrane invagination, as well as the work of the virus indentation forces and virus-cell contact pressures in a receptor-mediated endocytosis, depending on the virus size and virus/cell stiffnesses. The model indicated that early virus indentation forces are in the order of 1–10 pN and for a given extent of virus engulfment, they increase linearly with the elastic modulus of the host cell and also with the square of the virus radius. The work of invagination at the initial phase of virus endocytosis is in the order of tens of zeptojoules and peak virus-cell contact pressures at this stage are in the order of hundreds of Pascals to several kPa. For a given extent of virus engulfment, peak and average contact pressures increase linearly with the elastic modulus of the host cell but interestingly, they are negligibly affected by the virus size. The present model may be useful in the fields of cellular biomechanics, virology and nanodrug delivery to evaluate mechanical factors during the early phase of membrane invagination.