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

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.

Mechanical properties of external confinement modulate the rounding dynamics of cells

Many studies have demonstrated that mitotic cells can round up against external impediments. However, how the stiffness of external confinement affects the dynamics of rounding force/pressure and cell volume remains largely unknown. Here, we develop a theoretical framework to study the rounding of adherent cells confined between a substrate and a cantilever. We show that the rounding force and pressure increase exclusively with the effective confinement on the cell, which is related to the cantilever stiffness and the separation between cantilever and substrate. Remarkably, an increase of cantilever stiffness from 0.001 to 1 N/m can lead to a 100-fold change in rounding force. This model also predicts an active role of confinement stiffness in regulating the dynamics of cell volume and hydrostatic pressure. We find that the dynamic changes of cellular volume and hydrostatic pressure after osmotic shocks are opposite if the cantilever is soft, whereas the dynamic changes of cellular volume and pressure are the same if the cantilever is stiff. Taken together, this work demonstrates that confinement stiffness appears as a critical regulator in regulating the dynamics of rounding force and pressure. Our findings also indicate that the difference in cantilever stiffness need to be considered when comparing the measured rounding force and pressure from various experiments.

Biomechanics of Collective Cell Migration in Cancer Progression: Experimental and Computational Methods

Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is associated with some biomechanical particularities such as restructuring of extracellular matrix (ECM), stress and force distribution profiles, and reorganization of the cytoskeleton. Therefore, the phenomenon could be understood by an in-depth study of cells' behavior determinants, including but not limited to mechanical cues from the environment and from fellow "travelers". This review article aims to cover the recent development of experimental and computational methods for studying the biomechanics of collective cell migration during cancer progression and invasion. We also summarized the tested hypotheses regarding the mechanism underlying collective cell migration enabled by these methods. Together, the paper enables a broad overview on the methods and tools currently available to unravel the biophysical mechanisms pertinent to cell collective migration as well as providing perspectives on future development toward eventually deciphering the key mechanisms behind the most lethal feature of cancer.

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.

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.

Effects of methotrexate on the viscoelastic properties of single cells probed by atomic force microscopy

Methotrexate is a commonly used anti-cancer chemotherapy drug. Cellular mechanical properties are fundamental parameters that reflect the physiological state of a cell. However, so far the role of cellular mechanical properties in the actions of methotrexate is still unclear. In recent years, probing the behaviors of single cells with the use of atomic force microscopy (AFM) has contributed much to the field of cell biomechanics. In this work, with the use of AFM, the effects of methotrexate on the viscoelastic properties of four types of cells were quantitatively investigated. The inhibitory and cytotoxic effects of methotrexate on the proliferation of cells were observed by optical and fluorescence microscopy. AFM indenting was used to measure the changes of cellular viscoelastic properties (Young's modulus and relaxation time) by using both conical tip and spherical tip, quantitatively showing that the stimulation of methotrexate resulted in a significant decrease of both cellular Young's modulus and relaxation times. The morphological changes of cells induced by methotrexate were visualized by AFM imaging. The study improves our understanding of methotrexate action and offers a novel way to quantify drug actions at the single-cell level by measuring cellular viscoelastic properties, which may have potential impacts on developing label-free methods for drug evaluation.

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.

Osteoarthritis year in review 2015: mechanics

Motivated by the conceptual framework of multi-scale biomechanics, this narrative review highlights recent major advances with a focus on gait and joint kinematics, then tissue-level mechanics, cell mechanics and mechanotransduction, matrix mechanics, and finally the nanoscale mechanics of matrix macromolecules. A literature review was conducted from January 2014 to April 2015 using PubMed to identify major developments in mechanics related to osteoarthritis (OA). Studies of knee adduction, flexion, rotation, and contact mechanics have extended our understanding of medial compartment loading. In turn, advances in measurement methodologies have shown how injuries to both the meniscus and ligaments, together, can alter joint kinematics. At the tissue scale, novel findings have emerged regarding the mechanics of the meniscus as well as cartilage superficial zone. Moving to the cell level, poroelastic and poro-viscoelastic mechanisms underlying chondrocyte deformation have been reported, along with the response to osmotic stress. Further developments have emerged on the role of calcium signaling in chondrocyte mechanobiology, including exciting findings on the function of mechanically activated cation channels newly found to be expressed in chondrocytes. Finally, AFM-based nano-rheology systems have enabled studies of thin murine tissues and brush layers of matrix molecules over a wide range of loading rates including high rates corresponding to impact injury. With OA acknowledged to be a disease of the joint as an organ, understanding mechanical behavior at each length scale helps to elucidate the connections between cell biology, matrix biochemistry and tissue structure/function that may play a role in the pathomechanics of OA.