Single cell active force generation under dynamic loading - Part I: AFM experiments

Active viscoelastic models for cell and tissue mechanics

Living cells are out of equilibrium active materials. Cell-generated forces are transmitted across the cytoskeleton network and to the extracellular environment. These active force interactions shape cellular mechanical behaviour, trigger mechano-sensing, regulate cell adaptation to the microenvironment and can affect disease outcomes. In recent years, the mechanobiology community has witnessed the emergence of many experimental and theoretical approaches to study cells as mechanically active materials. In this review, we highlight recent advancements in incorporating active characteristics of cellular behaviour at different length scales into classic viscoelastic models by either adding an active tension-generating element or adjusting the resting length of an elastic element in the model. Summarizing the two groups of approaches, we will review the formulation and application of these models to understand cellular adaptation mechanisms in response to various types of mechanical stimuli, such as the effect of extracellular matrix properties and external loadings or deformations.

Development of an FEA framework for analysis of subject-specific aortic compliance based on 4D flow MRI

This paper presents a subject-specific in-silico framework in which we uncover the relationship between the spatially varying constituents of the aorta and the non-linear compliance of the vessel during the cardiac cycle uncovered through our MRI investigations. A microstructurally motivated constitutive model is developed, and simulations reveal that internal vessel contractility, due to pre-stretched elastin and actively generated smooth muscle cell stress, must be incorporated, along with collagen strain stiffening, in order to accurately predict the non-linear pressure-area relationship observed in-vivo. Modelling of elastin and smooth muscle cell contractility allows for the identification of the reference vessel configuration at zero-lumen pressure, in addition to accurately predicting high- and low-compliance regimes under a physiological range of pressures. This modelling approach is also shown to capture the key features of elastin digestion and SMC activation experiments. The volume fractions of the constituent components of the aortic material model were computed so that the in-silico pressure-area curves accurately predict the corresponding MRI data at each location. Simulations reveal that collagen and smooth muscle volume fractions increase distally, while elastin volume fraction decreases distally, consistent with reported histological data. Furthermore, the strain at which collagen transitions from low to high stiffness is lower in the abdominal aorta, again supporting the histological finding that collagen waviness is lower distally. The analyses presented in this paper provide new insights into the heterogeneous structure-function relationship that underlies aortic biomechanics. Furthermore, this subject-specific MRI/FEA methodology provides a foundation for personalised in-silico clinical analysis and tailored aortic device development. STATEMENT OF SIGNIFICANCE: This study provides a significant advance in in-silico medicine by capturing the structure/function relationship of the subject-specific human aorta presented in our previous MRI analyses. A physiologically based aortic constitutive model is developed, and simulations reveal that internal vessel contractility must be incorporated, along with collagen strain stiffening, to accurately predict the in-vivo non-linear pressure-area relationship. Furthermore, this is the first subject-specific model to predict spatial variation in the volume fractions of aortic wall constituents. Previous studies perform phenomenological hyperelastic curve fits to medical imaging data and ignore the prestress contribution of elastin, collagen, and SMCs and the associated zero-pressure reference state of the vessel. This novel MRI/FEA framework can be used as an in-silico diagnostic tool for the early stage detection of aortic pathologies.

Influence of multi-axial dynamic constraint on cell alignment and contractility in engineered tissues

In this study an experimental rig is developed to investigate the influence of tissue constraint and cyclic loading on cell alignment and active cell force generation in uniaxial and biaxial engineered tissues constructs. Addition of contractile cells to collagen hydrogels dramatically increases the measured forces in uniaxial and biaxial constructs under dynamic loading. This increase in measured force is due to active cell contractility, as is evident from the decreased force after treatment with cytochalasin D. Prior to dynamic loading, cells are highly aligned in uniaxially constrained tissues but are uniformly distributed in biaxially constrained tissues, demonstrating the importance of tissue constraints on cell alignment. Dynamic uniaxial stretching resulted in a slight increase in cell alignment in the centre of the tissue, whereas dynamic biaxial stretching had no significant effect on cell alignment. Our active modelling framework accurately predicts our experimental trends and suggests that a slightly higher (3%) total SF formation occurs at the centre of a biaxial tissue compared to the uniaxial tissue. However, high alignment of SFs and lateral compaction in the case of the uniaxially constrained tissue results in a significantly higher (75%) actively generated cell contractile stress, compared to the biaxially constrained tissue. These findings have significant implications for engineering of contractile tissue constructs.

Regional biomechanical imaging of liver cancer cells

Liver cancer is one of the leading cancers, especially in developing countries. Understanding the biomechanical properties of the liver cancer cells can not only help to elucidate the mechanisms behind the cancer progression, but also provide important information for diagnosis and treatment. At the cellular level, we used well-established atomic force microscopy (AFM) techniques to characterize the heterogeneity of mechanical properties of two different types of human liver cancer cells and a normal liver cell line. Stiffness maps with a resolution of 128x128 were acquired for each cell. The distributions of the indentation moduli of the cells showed significant differences between cancerous cells and healthy controls. Significantly, the variability was even greater amongst different types of cancerous cells. Fitting of the histogram of the effective moduli using a normal distribution function showed the Bel7402 cells were stiffer than the normal cells while HepG2 cells were softer. Morphological analysis of the cell structures also showed a higher cytoskeleton content among the cancerous cells. Results provided a foundation for applying knowledge of cell stiffness heterogeneity to search for tissue-level, early-stage indicators of liver cancer.

Finite element investigation into the use of carbon fibre reinforced PEEK laminated composites for distal radius fracture fixation implants

Carbon fibre reinforced PEEK (CF/PEEK) laminates provide mechanical advantages over homogenous metal osteo-synthesis implants, e.g. radiolucency, fatigue strength and strength to weight ratio. Implants can be designed with custom anisotropic material properties, thus enabling the engineer to tailor the overall stiffness of the implant to the specific loading conditions it will experience in vivo. In the current study a multi-scale computational investigation of idealised distal radius fracture fixation plate (DRP) is conducted. Physiological loading conditions are applied to macro-scale finite element models of DRPs. The mechanical response is compared for several CF/PEEK laminate layups to examine the effect of ply layup design. The importance of ply orientation in laminated DRPs is highlighted. A high number of 0° plies near the outer surfaces results in a greater bending strength while the addition of 45° plies increases the torsional strength of the laminates. Intra-laminar transverse tensile failure is predicted as the primary mode of failure. A micro-mechanical analysis of the CF/PEEK microstructure uncovers the precise mechanism under-lying intra-laminar transverse tensile crack to be debonding of the PEEK matrix from carbon fibres. Plastic strains in the matrix material are not sufficiently high to result in ductile failure of the matrix. The findings of this study demonstrate the significant challenge in the design and optimisation of fibre reinforced laminated composites for orthopaedic applications, highlighting the importance of multi-scale modelling for identification of failure mechanisms.

Transient active force generation and stress fibre remodelling in cells under cyclic loading

The active cytoskeleton is known to play an important mechanistic role in cellular structure, spreading, and contractility. Contractility is actively generated by stress fibres (SF), which continuously remodel in response to physiological dynamic loading conditions. The influence of actin-myosin cross-bridge cycling on SF remodelling under dynamic loading conditions has not previously been uncovered. In this study, a novel SF cross-bridge cycling model is developed to predict transient active force generation in cells subjected to dynamic loading. Rates of formation of cross-bridges within SFs are governed by the chemical potentials of attached and unattached myosin heads. This transient cross-bridge cycling model is coupled with a thermodynamically motivated framework for SF remodelling to analyse the influence of transient force generation on cytoskeletal evolution. A 1D implementation of the model is shown to correctly predict complex patterns of active cell force generation under a range of dynamic loading conditions, as reported in previous experimental studies.

Study of the Mechanical Environment of Chondrocytes in Articular Cartilage Defects Repaired Area under Cyclic Compressive Loading

COMSOL finite element software was used to establish a solid-liquid coupling biphasic model of articular cartilage and a microscopic model of chondrocytes, using modeling to take into account the shape and number of chondrocytes in cartilage lacuna in each layer. The effects of cyclic loading at different frequencies on the micromechanical environment of chondrocytes in different regions of the cartilage were studied. The results showed that low frequency loading can cause stress concentration of superficial chondrocytes. Moreover, along with increased frequency, the maximum value of stress response curve of chondrocytes decreased, while the minimum value increased. When the frequency was greater than 0.2 Hz, the extreme value stress of response curve tended to be constant. Cyclic loading had a large influence on the distribution of liquid pressure in chondrocytes in the middle and deep layers. The concentration of fluid pressure changed alternately from intracellular to peripheral in the middle layer. Both the range of liquid pressure in the upper chondrocytes and the maximum value of liquid pressure in the lower chondrocytes in the same lacunae varied greatly in the deep layer. At the same loading frequency, the elastic modulus of artificial cartilage had little effect on the mechanical environment of chondrocytes.

The role of adhesion junctions in the biomechanical behaviour and osteogenic differentiation of 3D mesenchymal stem cell spheroids

Osteogenesis of mesenchymal stem cells (MSC) can be regulated by the mechanical environment. MSCs grown in 3D spheroids (mesenspheres) have preserved multi-lineage potential, improved differentiation efficiency, and exhibit enhanced osteogenic gene expression and matrix composition in comparison to MSCs grown in 2D culture. Within 3D mesenspheres, mechanical cues are primarily in the form of cell-cell contraction, mediated by adhesion junctions, and as such adhesion junctions are likely to play an important role in the osteogenic differentiation of mesenspheres. However the precise role of N- and OB-cadherin on the biomechanical behaviour of mesenspheres remains unknown. Here we have mechanically tested mesenspheres cultured in suspension using parallel plate compression to assess the influence of N-cadherin and OB-cadherin adhesion junctions on the viscoelastic properties of the mesenspheres during osteogenesis. Our results demonstrate that N-cadherin and OB-cadherin have different effects on mesensphere viscoelastic behaviour and osteogenesis. When OB-cadherin was silenced, the viscosity, initial and long term Young's moduli and actin stress fibre formation of the mesenspheres increased in comparison to N-cadherin silenced mesenspheres and mesenspheres treated with a scrambled siRNA (Scram) at day 2. Additionally, the increased viscoelastic material properties correlate with evidence of calcification at an earlier time point (day 7) of OB-cadherin silenced mesenspheres but not Scram. Interestingly, both N-cadherin and OB-cadherin silenced mesenspheres had higher BSP2 expression than Scram at day 14. Taken together, these results indicate that N-cadherin and OB-cadherin both influence mesensphere biomechanics and osteogenesis, but play different roles.

Single cell active force generation under dynamic loading - Part II: Active modelling insights

In Part I of this two-part study a novel single cell AFM experimental investigation reveals a complex force-strain response of cells to cyclic loading. The biomechanisms underlying such complex behaviour cannot be fully understood without a detailed mechanistic analysis incorporating the key features of active stress generation and remodelling of the actin cytoskeleton. In order to simulate untreated contractile cells an active bio-chemo-mechanical model is developed, incorporating the key features of stress fibre (SF) remodelling and active tension generation. It is demonstrated that a fading memory SF contractility model accurately captures the transient response of cells to dynamic loading. Simulations reveal that high stretching forces during unloading half-cycles (probe retraction) occur due to tension actively generated by axially oriented SFs. On the other hand, hoop oriented SFs generate tension during loading half-cycles, providing a coherent explanation for the elevated compression resistance of contractile cells. Finally, it is also demonstrated that passive non-linear visco-hyperelastic material laws, traditionally used to simulate cell mechanical behaviour, are not appropriate for untreated contractile cells, and their use should be limited to the simulation of cells in which the active force generation machinery of the actin cytoskeleton has been chemically disrupted. In summary, our active modelling framework provides a coherent understanding of the biomechanisms underlying the complex patterns of experimentally observed single cell force generation presented in the first part of this study.

STATEMENT OF SIGNIFICANCE

A novel computational investigation into the active and passive response of cells to dynamic loading is performed. An active formulation that considers key features of actin cytoskeleton active contractility and remodelling throughout the cytoplasm is implemented. Simulations provide new insights into the sub-cellular biomechanical response, providing a coherent explanation for the complex patterns of cell force uncovered experimentally in the first part of this study. Our computational models also reveal that passive non-linear visco-hyperelastic material laws, traditionally used to simulate cell mechanical behaviour, are not appropriate for untreated contractile cells, and their use should be limited to the simulation of cells in which the active force generation machinery of the actin cytoskeleton has been chemically disrupted.