A poroviscohyperelastic model for numerical analysis of mechanical behavior of single chondrocyte

An in-silico study on the mechanical behavior of colorectal cancer cell lines in the micropipette aspiration process

Cancer alters the structural integrity and morphology of cells. Consequently, the cell function is overshadowed. In this study, the micropipette aspiration process is computationally modeled to predict the mechanical behavior of the colorectal cancer cells. The intended cancer cells are modeled as an incompressible Neo-Hookean visco-hyperelastic material. Also, the micropipette is assumed to be rigid with no deformation. The proposed model is validated with an in-vitro study. To capture the equilibrium and time-dependent behaviors of cells, ramp, and creep tests are respectively performed using the finite element method. Through the simulations, the effects of the micropipette geometry and the aspiration pressure on the colorectal cancer cell lines are investigated. Our findings indicate that, as the inner radius of the micropipette increases, despite the increase in deformation rate and aspirated length, the time to reach the equilibrium state increases. Nevertheless, it is obvious that increasing the tip curvature radius has a small effect on the change of the aspirated length. But, due to the decrease in the stress concentration, it drastically reduces the equilibrium time and increases the deformation rate significantly. Interestingly, our results demonstrate that increasing the aspiration pressure somehow causes the cell stiffening, thereby reducing the upward trend of deformation rate, equilibrium time, and aspirated length. Our findings provide valuable insights for researchers in cell therapy and cancer treatment and can aid in developing more precise microfluidic.

Time-dependent plastic behavior of bacteria leading to rupture

A study of the mechanical response of bacteria is essential in designing an antibacterial surface for implants and food packaging applications. This research evaluated the mechanical response of Escherichia coli under different loading conditions. Indentation and prolonged creep tests were performed to understand their viscoelastic-plastic response. The results indicate that varying loading rates from 1 μm/s to 5 μm/s show an increase in modulus of 182% and 90%, calculated in the loading and unloading cycles, respectively, and a decrease in adhesion force by 42%. However, on varying loads from 5 nN to 25 nN, nominal change is observed in both modulus and adhesion force. The rupture curve at 100 nN load shows elastic and a small plastic deformation accompanied by a sharp peak indicating the cell wall rupture. The rupture force at the peak was found to be 34.38 ± 5.15 nN, irrespective of the loading rate, making it a failure criterion for bacteria rupture. The creep response of bacteria increases (for 6 s) and then remains constant (for 15 s) with time, indicating that a standard linear solid (SLS) model applies to this behavior. This work attempts to evaluate the mechanical properties of E. coli bacteria focusing on its rupture by contact killing mechanism.

Visco- and poroelastic contributions of the zona pellucida to the mechanical response of oocytes

Probing mechanical properties of cells has been identified as a means to infer information on their current state, e.g. with respect to diseases or differentiation. Oocytes have gained particular interest, since mechanical parameters are considered potential indicators of the success of in vitro fertilisation procedures. Established tests provide the structural response of the oocyte resulting from the material properties of the cell's components and their disposition. Based on dedicated experiments and numerical simulations, we here provide novel insights on the origin of this response. In particular, polarised light microscopy is used to characterise the anisotropy of the zona pellucida, the outermost layer of the oocyte composed of glycoproteins. This information is combined with data on volumetric changes and the force measured in relaxation/cyclic, compression/indentation experiments to calibrate a multi-phasic hyper-viscoelastic model through inverse finite element analysis. These simulations capture the oocyte's overall force response, the distinct volume changes observed in the zona pellucida, and the structural alterations interpreted as a realignment of the glycoproteins with applied load. The analysis reveals the presence of two distinct timescales, roughly separated by three orders of magnitude, and associated with a rapid outflow of fluid across the external boundaries and a long-term, progressive relaxation of the glycoproteins, respectively. The new results allow breaking the overall response down into the contributions from fluid transport and the mechanical properties of the zona pellucida and ooplasm. In addition to the gain in fundamental knowledge, the outcome of this study may therefore serve an improved interpretation of the data obtained with current methods for mechanical oocyte characterisation.

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.

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.

A novel approach for extracting viscoelastic parameters of living cells through combination of inverse finite element simulation and Atomic Force Microscopy

Dynamic mechanical behaviour of living cells has been described by viscoelasticity. However, quantitation of the viscoelastic parameters for living cells is far from sophisticated. In this paper, combining inverse finite element (FE) simulation with Atomic Force Microscope characterization, we attempt to develop a new method to evaluate and acquire trustworthy viscoelastic index of living cells. First, influence of the experiment parameters on stress relaxation process is assessed using FE simulation. As suggested by the simulations, cell height has negligible impact on shape of the force-time curve, i.e. the characteristic relaxation time; and the effect originates from substrate can be totally eliminated when stiff substrate (Young's modulus larger than 3 GPa) is used. Then, so as to develop an effective optimization strategy for the inverse FE simulation, the parameters sensitivity evaluation is performed for Young's modulus, Poisson's ratio, and characteristic relaxation time. With the experiment data obtained through typical stress relaxation measurement, viscoelastic parameters are extracted through the inverse FE simulation by comparing the simulation results and experimental measurements. Finally, reliability of the acquired mechanical parameters is verified with different load experiments performed on the same cell.

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.