A hyperelastic model for simulating cells in flow

Droplet dynamics in homogeneous isotropic turbulence with the immersed boundary-lattice Boltzmann method

We develop a numerical method for simulating the dynamics of a droplet immersed in a generic time-dependent velocity gradient field. This approach is grounded on the hybrid coupling between the lattice Boltzmann (LB) method, employed for the flow simulation, and the immersed boundary (IB) method, utilized to couple the droplet with the surrounding fluid. We show how to enrich the numerical scheme with a mesh regularization technique, allowing droplets to sustain large deformations. The resulting methodology is adapted to simulate the dynamics of droplets in homogeneous and isotropic turbulence, with the characteristic size of the droplet being smaller than the characteristic Kolmogorov scale of the outer turbulent flow. We report statistical results for droplet deformation and orientation collected from an ensemble of turbulent trajectories, as well as comparisons with theoretical models in the limit of small deformation.

Critical review of single-cell mechanotyping approaches for biomedical applications

Accurate mechanical measurements of cells has the potential to improve diagnostics, therapeutics and advance understanding of disease mechanisms, where high-resolution mechanical information can be measured by deforming individual cells. Here we evaluate recently developed techniques for measuring cell-scale stiffness properties; while many such techniques have been developed, much of the work examining single-cell stiffness is impacted by difficulties in standardization and comparability, giving rise to large variations in reported mechanical moduli. We highlight the role of underlying mechanical theories driving this variability, and note opportunities to develop novel mechanotyping devices and theoretical models that facilitate convenient and accurate mechanical characterisation. Moreover, many high-throughput approaches are confounded by factors including cell size, surface friction, natural population heterogeneity and convolution of elastic and viscous contributions to cell deformability. We nevertheless identify key approaches based on deformability cytometry as a promising direction for further development, where both high-throughput and accurate single-cell resolutions can be realized.

Mechanical complexity of living cells can be mapped onto simple homogeneous equivalents

Biological cells are built up from different constituents of varying size and stiffness which all contribute to the cell's mechanical properties. Despite this heterogeneity, in the analysis of experimental measurements one often assumes a strongly simplified homogeneous cell and thus a single elastic modulus is assigned to the entire cell. This ad-hoc simplification has so far mostly been used without proper justification. Here, we use computer simulations to show that indeed a mechanically heterogeneous cell can effectively be replaced by a homogeneous equivalent cell with a volume averaged elastic modulus. To demonstrate the validity of this approach, we investigate a hyperelastic cell with a heterogeneous interior under compression and in shear/channel flow mimicking atomic force and microfluidic measurements, respectively. We find that the homogeneous equivalent cell reproduces quantitatively the behavior of its heterogeneous counterpart, and that this equality is largely independent of the stiffness or spatial distribution of the heterogeneity.

Multi-scale characterization and analysis of cellular viscoelastic mechanical phenotypes by atomic force microscopy

The viscoelasticity of cells serves as a biomarker that reveals changes induced by malignant transformation, which aids the cytological examinations. However, differences in the measurement methods and parameters have prevented the consistent and effective characterization of the viscoelastic phenotype of cells. To address this issue, nanomechanical indentation experiments were conducted using an atomic force microscope (AFM). Multiple indentation methods were applied, and the indentation parameters were gradually varied to measure the viscoelasticity of normal liver cells and cancerous liver cells to create a database. This database was employed to train machine-learning algorithms in order to analyze the differences in the viscoelasticity of different types of cells and as well as to identify the optimal measurement methods and parameters. These findings indicated that the measurement speed significantly influenced viscoelasticity and that the classification difference between the two cell types was most evident at 5 μm/s. In addition, the precision and the area under the receiver operating characteristic curve were comparatively analyzed for various widely employed machine-learning algorithms. Unlike previous studies, this research validated the effectiveness of measurement parameters and methods with the assistance of machine-learning algorithms. Furthermore, the results confirmed that the viscoelasticity obtained from the multiparameter indentation measurement could be effectively used for cell classification. RESEARCH HIGHLIGHTS: This study aimed to analyze the viscoelasticity of liver cancer cells and liver cells. Different nano-indentation methods and parameters were used to measure the viscoelasticity of the two kinds of cells. The neural network algorithm was used to reverse analyze the dataset, and the methods and parameters for accurate classification and identification of cells are successfully found.

High-throughput viscoelastic characterization of cells in hyperbolic microchannels

Extensive research has demonstrated the potential of cell viscoelastic properties as intrinsic indicators of cell state, functionality, and disease. For this, several microfluidic techniques have been developed to measure cell viscoelasticity with high-throughput. However, current microchannel designs introduce complex stress distributions on cells, leading to inaccuracies in determining the stress-strain relationship and, consequently, the viscoelastic properties. Here, we introduce a novel approach using hyperbolic microchannels that enable precise measurements under a constant extensional stress and offer a straightforward stress-strain relationship, while operating at a measurement rate of up to 100 cells per second. We quantified the stresses acting in the channels using mechanical calibration particles made from polyacrylamide (PAAm) and found that the measurement buffer, a solution of methyl cellulose and phosphate buffered saline, shows strain-thickening following a power law up to 200 s-1. By measuring oil droplets with varying viscosities, we successfully detected changes in the relaxation times of the droplets and our approach could be used to get the interfacial tension and viscosity of liquid-liquid droplet systems from the same measurement. We further applied this methodology to PAAm microgel beads, demonstrating the accurate recovery of Young's moduli and the near-ideal elastic behavior of the beads. To explore the influence of altered cell viscoelasticity, we treated HL60 human leukemia cells with latrunculin B and nocodazole, resulting in clear changes in cell stiffness while relaxation times were only minimally affected. In conclusion, our approach offers a streamlined and time-efficient solution for assessing the viscoelastic properties of large cell populations and other microscale soft particles.

Experimental measurement and numerical modeling of deformation behavior of breast cancer cells passing through constricted microfluidic channels

During the multistep process of metastasis, cancer cells encounter various mechanical forces which make them deform drastically. Developing accurate in-silico models, capable of simulating the interactions between the mechanical forces and highly deformable cancer cells, can pave the way for the development of novel diagnostic and predictive methods for metastatic progression. Spring-network models of cancer cell, empowered by our recently proposed identification approach, promises a versatile numerical tool for developing experimentally validated models that can simulate complex interactions at cellular scale. Using this numerical tool, we presented spring-network models of breast cancer cells that can accurately replicate the experimental data of deformation behavior of the cells flowing in a fluidic domain and passing narrow constrictions comparable to microcapillary. First, using high-speed imaging, we experimentally studied the deformability of breast cancer cell lines with varying metastatic potential (MCF-7 (less invasive), SKBR-3 (medium-high invasive), and MDA-MB-231 (highly invasive)) in terms of their entry time to a constricted microfluidic channel. We observed that MDA-MB-231, that has the highest metastatic potential, is the most deformable cell among the three. Then, by focusing on this cell line, experimental measurements were expanded to two more constricted microchannel dimensions. The experimental deformability data in three constricted microchannel sizes for various cell sizes, enabled accurate identification of the unknown parameters of the spring-network model of the breast cancer cell line (MDA-MB-231). Our results show that the identified parameters depend on the cell size, suggesting the need for a systematic procedure for identifying the size-dependent parameters of spring-network models of cells. As the numerical results show, the presented cell models can simulate the entry process of the cell into constricted channels with very good agreements with the measured experimental data.

Effect of constitutive law on the erythrocyte membrane response to large strains

Three constitutive laws, that is the Skalak, neo-Hookean and Yeoh laws, commonly employed for describing the erythrocyte membrane mechanics are theoretically analyzed and numerically investigated to assess their accuracy for capturing erythrocyte deformation characteristics and morphology. Particular emphasis is given to the nonlinear deformation regime, where it is known that the discrepancies between constitutive laws are most prominent. Hence, the experiments of optical tweezers and micropipette aspiration are considered here, for which relationships between the individual shear elastic moduli of the constitutive laws can also be established through analysis of the tension-deformation relationship. All constitutive laws were found to adequately predict the axial and transverse deformations of a red blood cell subjected to stretching with optical tweezers for a constant shear elastic modulus value. As opposed to Skalak law, the neo-Hookean and Yeoh laws replicated the erythrocyte membrane folding, that has been experimentally observed, with the trade-off of sustaining significant area variations. For the micropipette aspiration, the suction pressure-aspiration length relationship could be excellently predicted for a fixed shear elastic modulus value only when Yeoh law was considered. Importantly, the neo-Hookean and Yeoh laws reproduced the membrane wrinkling at suction pressures close to those experimentally measured. None of the constitutive laws suffered from membrane area compressibility in the micropipette aspiration case.

Calcium supplementation of bioinks reduces shear stress-induced cell damage during bioprinting

During bioprinting, cells are suspended in a viscous bioink and extruded under pressure through small diameter printing needles. The combination of high pressure and small needle diameter exposes cells to considerable shear stress, which can lead to cell damage and death. Approaches to monitor and control shear stress-induced cell damage are currently not well established. To visualize the effects of printing-induced shear stress on plasma membrane integrity, we add FM 1-43 to the bioink, a styryl dye that becomes fluorescent when bound to lipid membranes, such as the cellular plasma membrane. Upon plasma membrane disruption, the dye enters the cell and also stains intracellular membranes. Extrusion of alginate-suspended NIH/3T3 cells through a 200µm printing needle led to an increased FM 1-43 incorporation at high pressure, demonstrating that typical shear stresses during bioprinting can transiently damage the plasma membrane. Cell imaging in a microfluidic channel confirmed that FM 1-43 incorporation is caused by cell strain. Notably, high printing pressure also impaired cell survival in bioprinting experiments. Using cell types of different stiffnesses, we find that shear stress-induced cell strain, FM 1-43 incorporation and cell death were reduced in stiffer compared to softer cell types and demonstrate that cell damage and death correlate with shear stress-induced cell deformation. Importantly, supplementation of the suspension medium with physiological concentrations of CaCl₂greatly reduced shear stress-induced cell damage and death but not cell deformation. As the sudden influx of calcium ions is known to induce rapid cellular vesicle exocytosis and subsequent actin polymerization in the cell cortex, we hypothesize that calcium supplementation facilitates the rapid resealing of plasma membrane damage sites. We recommend that bioinks should be routinely supplemented with physiological concentrations of calcium ions to reduce shear stress-induced cell damage and death during extrusion bioprinting.

Finite element analysis on mechanical state on the osteoclasts under gradient fluid shear stress

Mechanical loading, such as fluid shear stress (FSS), is regarded as the main factor that regulates the biological responses of bone cells. Our previous studies have demonstrated that the RAW264.7 osteoclast precursors migrate toward the low-FSS region under the gradient FSS field by a cone-and-plate flow chamber, in which the FSS in the outer region is larger than that in the inner region along the radial direction. Whether the FSS distribution on a cell depends on the gradient direction of FSS field should be clarified to explain this experimental observation. In this study, the finite element models of the discretely distributed or closely packed cells adherent on the bottom plate in a cone-and-plate flow chamber were constructed, and cells were regarded as compressible isotropic Hookean solid. Results showed that the average FSS of each discretely distributed cell at the quarter sector far from the center (SFC) was about 0.1% greater than that at the quarter sector near the center (SNC). In the bands with different orientations for a cell, the relative difference between the average FSS in the SFC and the SNC becomes smaller with increased band height. For the hexagonal closely packed cells, the relative value of SFC and SNC increases with increasing cell spacing. The difference between the local wall FSS in the SFC and the SNC may activate mechanosensitive ion channels and further regulate the migration of osteoclast precursors toward the low-FSS region under the gradient FSS field.