Evaluating the influence on osteocyte mechanobiology within the lacunar-canalicular system for varying lacunar equancy and perilacunar elasticity: A multiscale fluid-structure interaction analysis

The lacunar morphology and perilacunar tissue properties of osteocytes in bone can vary under different physiological and pathological conditions. How these alterations collectively change the overall micromechanics of osteocytes in the lacunar-canalicular system (LCS) of an osteon still requires special focus. Therefore, a Haversian canal and LCS-based osteon model was established to evaluate the changes in the hydrodynamic environment around osteocytes under physiological loading using fluid-structure interaction analysis, followed by a sub-modelled finite element analysis to assess the mechanical responses of osteocytes and their components. Osteocytes were modelled with detailed configurations, including cytoplasm, nucleus, and cytoskeleton, and parametric variations in lacunar equancy (L.Eq) and perilacunar elasticity (Pl.E) were considered within the osteon model. The study aimed to conduct a comparative study among osteon models with varying L. Eq and Pl. E to check the resulting differences in osteocyte mechanobiology. The results demonstrated that the average mechanical stimulation of each subcellular component of osteocytes increased with decreases in L. Eq and Pl. E, reflecting conditions typically seen in young, healthy bone as per previous literature. However, hydrodynamic responses, such as fluid flow and fluid shear stress on osteocytes, varied proportionally with the elasticity difference between the bone matrix and the perilacunar region during Pl. E variation. Additionally, the findings revealed that a minimal percentage of energy was used to transmit mechanical responses through microtubules from the cell membrane to the nucleus, and this energy percentage increased with higher L. Eq. The outcomes of the study could help to quantify how the osteocyte microenvironment and its mechanosensitivity within cortical bone changes with L. Eq and Pl. E alterations in different bone conditions, from young to aged and healthy to diseased.

2D vs. 3D Evaluation of Osteocyte Lacunae - Methodological Approaches, Recommended Parameters, and Challenges: A Narrative Review by the European Calcified Tissue Society (ECTS)

PURPOSE OF REVIEW

Quantification of the morphology of osteocyte lacunae has become a powerful tool to investigate bone metabolism, pathologies and aging. This review will provide a brief overview of 2D and 3D imaging methods for the determination of lacunar shape, orientation, density, and volume. Deviations between 2D-based and 3D-based lacunar volume estimations are often not sufficiently addressed and may give rise to contradictory findings. Thus, the systematic error arising from 2D-based estimations of lacunar volume will be discussed, and an alternative calculation proposed. Further, standardized morphological parameters and best practices for sampling and segmentation are suggested.

RECENT FINDINGS

We quantified the errors in reported estimation methods of lacunar volume based on 2D cross-sections, which increase with variations in lacunar orientation and histological cutting plane. The estimations of lacunar volume based on common practice in 2D imaging methods resulted in an underestimation of lacunar volume of up to 85% compared to actual lacunar volume in an artificial dataset. For a representative estimation of lacunar size and morphology based on 2D images, at least 400 lacunae should be assessed per sample.

Analysis of the Adherent Cell Response to the Substrate Stiffness Using Tensegrity

Cell's shape is dependent on the cytoskeleton mechanical properties. Hybrid models were developed that combine the discrete structure for the cytoskeleton and continuum parts for other cell organelles. Tensegrity-based structures that consist of tensile and compression elements are useful models to understand the cytoskeleton mechanical behavior. In this study, we are looking to examine the reaction of the cell to a variety of substrate stiffnesses and explain the relationship between cell behavior and substrate mechanical properties. However, which tensegrity structure is appropriate for modeling a living cell? Is the structure's complexity play a major role? We used two spherical tensegrities with different complexities to assess the impact of the structure on the cell's mechanical response versus substrate's stiffness. Six- and twelve-strut tensegrities together with membrane, cytoplasm, nucleoskeleton, and nucleus envelope were assembled in Abaqus package to create a hybrid cell model. A compressive load was applied to the cell model and the reaction forces versus deflection curves were analyzed for number of substrate stiffness values. By analyzing the difference due to two different tensegrities it became clear that the lower density structure is a better choice for modeling stiffer cells. It was also found that the six-strut tensegrity is sensitive to higher range of substrate stiffness.

Biomechanics of Chondrocytes and Chondrons in Healthy Conditions and Osteoarthritis: A Review of the Mechanical Characterisations at the Microscale

Biomechanical studies are expanding across a variety of fields, from biomedicine to biomedical engineering. From the molecular to the system level, mechanical stimuli are crucial regulators of the development of organs and tissues, their growth and related processes such as remodelling, regeneration or disease. When dealing with cell mechanics, various experimental techniques have been developed to analyse the passive response of cells; however, cell variability and the extraction process, complex experimental procedures and different models and assumptions may affect the resulting mechanical properties. For these purposes, this review was aimed at collecting the available literature focused on experimental chondrocyte and chondron biomechanics with direct connection to their biochemical functions and activities, in order to point out important information regarding the planning of an experimental test or a comparison with the available results. In particular, this review highlighted (i) the most common experimental techniques used, (ii) the results and models adopted by different authors, (iii) a critical perspective on features that could affect the results and finally (iv) the quantification of structural and mechanical changes due to a degenerative pathology such as osteoarthritis.

Finite Element Models of Osteocytes and Their Load-Induced Activation

PURPOSE OF REVIEW

Osteocytes are the conductors of bone adaptation and remodelling. Buried inside the calcified matrix, they sense mechanical cues and signal osteoclasts in case of low activity, and osteoblasts when stresses are high. How do osteocytes detect mechanical stress? What physical signal do they perceive? Finite element analysis is a useful tool to address these questions as it allows calculating stresses, strains and fluid flow where they cannot be measured. The purpose of this review is to evaluate the capabilities and challenges of finite element models of bone, in particular the osteocytes and load-induced activation mechanisms.

RECENT FINDINGS

High-resolution imaging and increased computational power allow ever more detailed modelling of osteocytes, either in isolation or embedded within the mineralised matrix. Over the years, homogeneous models of bone and osteocytes got replaced by heterogeneous and microstructural models, including, e.g. the lacuno-canalicular network and the cytoskeleton. The lacuno-canalicular network induces strain amplifications and the osteocyte protrusions seem to be stimulated much more than the cell body, both by strain and fluid flow. More realistic cell geometries, like minute constrictions of the canaliculi, increase this effect. Microstructural osteocyte models describe the transduction of external stimuli to the nucleus. Supracellular multiscale models (e.g. of a tunnelling osteon) allow to study differential loading of osteocytes and to distinguish between strain and fluid flow as the pivotal stimulatory cue. In the future, the finite element models may be enhanced by including chemical transport and intercellular communication between osteocytes, osteoclasts and osteoblasts.

Impact of Nanoparticle Uptake on the Biophysical Properties of Cell for Biomedical Engineering Applications

Nanomaterials are currently the state-of-the-art in the development of advanced biomedical devices and applications where classical approaches have failed. To date, majority of the literature on nanomaterial interaction with cells have largely focused on the biological responses of cells obtained via assays, with little interest on their biophysical responses. However, recent studies have shown that the biophysical responses of cells, such as stiffness and adhesive properties, play a significant role in their physiological function. In this paper, we investigate cell biophysical responses after uptake of nanoparticles. Atomic force microscopy was used to study changes in cell stiffness and adhesion upon boron nitride (BN) and hydroxyapatite (HAP) nanoparticle uptake. Results show increase in cell stiffness with varying nanoparticle (BN and HAP) concentration, while a decrease in cell adhesion trigger by uptake of HAP. In addition, changes in the biochemical response of the cell membrane were observed via Raman spectroscopy of nanoparticle treated cells. These findings have significant implications in biomedical applications of nanoparticles, e.g. in drug delivery, advanced prosthesis and surgical implants.

Comparison of cell mechanical measurements provided by Atomic Force Microscopy (AFM) and Micropipette Aspiration (MPA)

A comparative analysis of T-lymphocyte mechanical data obtained from Micropipette Aspiration (MPA) and Atomic Force Microscopy (AFM) is presented. Results obtained by fitting the experimental data to simple Hertz and Theret models led to non-Gaussian distributions and significantly different values of the elastic moduli obtained by both techniques. The use of more refined models, taking into account the finite size of cells (simplified double contact and Zhou models) reduces the differences in the values calculated for the elastic moduli. Several possible sources for the discrepancy between the techniques are considered. The analysis suggests that the local nature of AFM measurements compared with the more general character of MPA measurements probably contributed to the differences observed.

Effect of Substrate Stiffness on Mechanical Coupling and Force Propagation at the Infarct Boundary

Heterogeneous intercellular coupling plays a significant role in mechanical and electrical signal transmission in the heart. Although many studies have investigated the electrical signal conduction between myocytes and nonmyocytes within the heart muscle tissue, there are not many that have looked into the mechanical counterpart. This study aims to investigate the effect of substrate stiffness and the presence of cardiac myofibroblasts (CMFs) on mechanical force propagation across cardiomyocytes (CMs) and CMFs in healthy and heart-attack-mimicking matrix stiffness conditions. The contractile forces generated by the CMs and their propagation across the CMFs were measured using a bio-nanoindenter integrated with fluorescence microscopy for fast calcium imaging. Our results showed that softer substrates facilitated stronger and further signal transmission. Interestingly, the presence of the CMFs attenuated the signal propagation in a stiffness-dependent manner. Stiffer substrates with CMFs present attenuated the signal ∼24-32% more compared to soft substrates with CMFs, indicating a synergistic detrimental effect of increased matrix stiffness and increased CMF numbers after myocardial infarction on myocardial function. Furthermore, the beating pattern of the CMF movement at the CM-CMF boundary also depended on the substrate stiffness, thereby influencing the waveform of the propagation of CM-generated contractile forces. We performed computer simulations to further understand the occurrence of different force transmission patterns and showed that cell-matrix focal adhesions assembled at the CM-CMF interfaces, which differs depending on the substrates stiffness, play important roles in determining the efficiency and mechanism of signal transmission. In conclusion, in addition to substrate stiffness, the degree and type of cell-cell and cell-matrix interactions, affected by the substrate stiffness, influence mechanical signal conduction between myocytes and nonmyocytes in the heart muscle tissue.

Finite Element Formulation of Multiphasic Shell Elements for Cell Mechanics Analyses in FEBio

With the recent implementation of multiphasic materials in the open-source finite element (FE) software FEBio (febio.org), 3D models of cells embedded within the tissue may now be analyzed, accounting for porous solid matrix deformation, transport of interstitial fluid and solutes, membrane potential, and reactions. The cell membrane is a critical component in cell models, which selectively regulates the transport of fluid and solutes in the presence of large concentration and electric potential gradients, while also facilitating the transport of various proteins. The cell membrane is much thinner than the cell; therefore, in an FE environment, shell elements formulated as 2D surfaces in 3D space would be preferred for modeling the cell membrane, for the convenience of mesh generation from image-based data, especially for convoluted membranes. However, multiphasic shell elements are yet to be developed in the FE literature and commercial FE software. This study presents a novel formulation of multiphasic shell elements and its implementation in FEBio. The shell model includes front- and back-face nodal degrees of freedom for the solid displacement, effective fluid pressure and effective solute concentrations, and a linear interpolation of these variables across the shell thickness. This formulation was verified against classical models of cell physiology and validated against reported experimental measurements in chondrocytes. This implementation of passive transport of fluid and solutes across multiphasic membranes makes it possible to model the biomechanics of isolated cells or cells embedded in their extracellular matrix, accounting for solvent and solute transport.

Computational Investigation on the Biomechanical Responses of the Osteocytes to the Compressive Stimulus: A Poroelastic Model

Osteocytes, the major type of bone cells embedded in the bone matrix and surrounded by the lacunar and canalicular system, can serve as biomechanosensors and biomechanotranducers of the bone. Theoretical analytical methods have been employed to investigate the biomechanical responses of osteocytes in vivo; the poroelastic properties have not been taken into consideration in the three-dimensional (3D) finite element model. In this study, a 3D poroelastic idealized finite element model was developed and was used to predict biomechanical behaviours (maximal principal strain, pore pressure, and fluid velocity) of the osteocyte-lacunar-canalicular system under 150-, 1000-, 3000-, and 5000-microstrain compressive loads, respectively, representing disuse, physiological, overuse, and pathological overload loading stimuli. The highest local strain, pore pressure, and fluid velocity were found to be highest at the proximal region of cell processes. These data suggest that the strain, pore pressure, and fluid velocity of the osteocyte-lacunar-canalicular system increase with the global loading and that the poroelastic material property affects the biomechanical responses to the compressive stimulus. This new model can be used to predict the mechanobiological behaviours of osteocytes under the four different compressive loadings and may provide an insight into the mechanisms of mechanosensation and mechanotransduction of the bone.

Investigation of Cell-Substrate Adhesion Properties of Living Chondrocyte by Measuring Adhesive Shear Force and Detachment Using AFM and Inverse FEA

It is well-known that cell adhesion is important in many biological processes such as cell migration and proliferation. A better understanding of the cell adhesion process will shed insight into these cellular biological responses as well as cell adhesion-related diseases treatment. However, there is little research which has attempted to investigate the process of cell adhesion and its mechanism. Thus, this paper aims to study the time-dependent adhesion properties of single living chondrocytes using an advanced coupled experimental-numerical approach. Atomic Force Microscopy (AFM) tips will be used to apply lateral forces to detach chondrocytes that are seeded for three different periods. An advanced Finite Element Analysis (FEA) model combining porohyperelastic (PHE) constitutive model and cohesive zone formulation is developed to explore the mechanism of adhesion. The results revealed that the cells can resist normal traction better than tangential traction in the beginning of adhesion. This is when the cell adhesion molecules establish early attachment to the substrates. After that when the cells are spreading, stress fiber bundles generate tangential traction on the substrate to form strong adhesion. Both simulation and experimental results agree well with each other, providing a powerful tool to study the cellular adhesion process.

Investigation of the Effects of Extracellular Osmotic Pressure on Morphology and Mechanical Properties of Individual Chondrocyte

It has been demonstrated that most cells of the body respond to osmotic pressure in a systematic manner. The disruption of the collagen network in the early stages of osteoarthritis causes an increase in water content of cartilage which leads to a reduction of pericellular osmolality in chondrocytes distributed within the extracellular environment. It is therefore arguable that an insight into the mechanical properties of chondrocytes under varying osmotic pressure would provide a better understanding of chondrocyte mechanotransduction and potentially contribute to knowledge on cartilage degeneration. In this present study, the chondrocyte cells were exposed to solutions with different osmolality. Changes in their dimensions and mechanical properties were measured over time. Atomic force microscopy (AFM) was used to apply load at various strain-rates and the force-time curves were logged. The thin-layer elastic model was used to extract the elastic stiffness of chondrocytes at different strain-rates and at different solution osmolality. In addition, the porohyperelastic (PHE) model was used to investigate the strain-rate-dependent responses under the loading and osmotic pressure conditions. The results revealed that the hypo-osmotic external environment increased chondrocyte dimensions and reduced Young's modulus of the cells at all strain-rates tested. In contrast, the hyper-osmotic external environment reduced dimensions and increased Young's modulus. Moreover, using the PHE model coupled with inverse FEA simulation, we established that the hydraulic permeability of chondrocytes increased with decreasing extracellular osmolality which is consistent with previous work in the literature. This could be due to a higher intracellular fluid volume fraction with lower osmolality.

Microscale consolidation analysis of relaxation behavior of single living chondrocytes subjected to varying strain-rates

Besides the elastic stiffness, the relaxation behavior of single living cells is also of interest of various researchers when studying cell mechanics. It is hypothesized that the relaxation response of the cells is governed by both intrinsic viscoelasticity of the solid phase and fluid-solid interactions mechanisms. There are a number of mechanical models have been developed to investigate the relaxation behavior of single cells. However, there is lack of model enable to accurately capture both of the mechanisms. Therefore, in this study, the porohyperelastic (PHE) model, which is an extension of the consolidation theory, combined with inverse Finite Element Analysis (FEA) technique was used at the first time to investigate the relaxation response of living chondrocytes. This model was also utilized to study the dependence of relaxation behavior of the cells on strain-rates. The stress-relaxation experiments under the various strain-rates were conducted with the Atomic Force Microscopy (AFM). The results have demonstrated that the PHE model could effectively capture the stress-relaxation behavior of the living chondrocytes, especially at intermediate to high strain-rates. Although this model gave some errors at lower strain-rates, its performance was acceptable. Therefore, the PHE model is properly a promising model for single cell mechanics studies. Moreover, it has been found that the hydraulic permeability of living chondrocytes reduced with decreasing of strain-rates. It might be due to the intracellular fluid volume fraction and the fluid pore pressure gradients of chondrocytes were higher when higher strain-rates applied.