Macro- to Microscale Strain Transfer in Fibrous Tissues is Heterogeneous and Tissue-Specific

Mechanical deformation applied at the joint or tissue level is transmitted through the macroscale extracellular matrix to the microscale local matrix, where it is transduced to cells within these tissues and modulates tissue growth, maintenance, and repair. The objective of this study was to investigate how applied tissue strain is transferred through the local matrix to the cell and nucleus in meniscus, tendon, and the annulus fibrosus, as well as in stem cell-seeded scaffolds engineered to reproduce the organized microstructure of these native tissues. To carry out this study, we developed a custom confocal microscope-mounted tensile testing device and simultaneously monitored strain across multiple length scales. Results showed that mean strain was heterogeneous and significantly attenuated, but coordinated, at the local matrix level in native tissues (35–70% strain attenuation). Conversely, freshly seeded scaffolds exhibited very direct and uniform strain transfer from the tissue to the local matrix level (15–25% strain attenuation). In addition, strain transfer from local matrix to cells and nuclei was dependent on fiber orientation and tissue type. Histological analysis suggested that different domains exist within these fibrous tissues, with most of the tissue being fibrous, characterized by an aligned collagen structure and elongated cells, and other regions being proteoglycan (PG)-rich, characterized by a dense accumulation of PGs and rounder cells. In meniscus, the observed heterogeneity in strain transfer correlated strongly with cellular morphology, where rounder cells located in PG-rich microdomains were shielded from deformation, while elongated cells in fibrous microdomains deformed readily. Collectively, these findings suggest that different tissues utilize distinct strain-attenuating mechanisms according to their unique structure and cellular phenotype, and these differences likely alter the local biologic response of such tissues and constructs in response to mechanical perturbation.     

Macro- to Microscale Strain Transfer in Fibrous Tissues is Heterogeneous and Tissue-Specific

Mechanical deformation applied at the joint or tissue level is transmitted through the macroscale extracellular matrix to the microscale local matrix, where it is transduced to cells within these tissues and modulates tissue growth, maintenance, and repair. The objective of this study was to investigate how applied tissue strain is transferred through the local matrix to the cell and nucleus in meniscus, tendon, and the annulus fibrosus, as well as in stem cell-seeded scaffolds engineered to reproduce the organized microstructure of these native tissues. To carry out this study, we developed a custom confocal microscope-mounted tensile testing device and simultaneously monitored strain across multiple length scales. Results showed that mean strain was heterogeneous and significantly attenuated, but coordinated, at the local matrix level in native tissues (35–70% strain attenuation). Conversely, freshly seeded scaffolds exhibited very direct and uniform strain transfer from the tissue to the local matrix level (15–25% strain attenuation). In addition, strain transfer from local matrix to cells and nuclei was dependent on fiber orientation and tissue type. Histological analysis suggested that different domains exist within these fibrous tissues, with most of the tissue being fibrous, characterized by an aligned collagen structure and elongated cells, and other regions being proteoglycan (PG)-rich, characterized by a dense accumulation of PGs and rounder cells. In meniscus, the observed heterogeneity in strain transfer correlated strongly with cellular morphology, where rounder cells located in PG-rich microdomains were shielded from deformation, while elongated cells in fibrous microdomains deformed readily. Collectively, these findings suggest that different tissues utilize distinct strain-attenuating mechanisms according to their unique structure and cellular phenotype, and these differences likely alter the local biologic response of such tissues and constructs in response to mechanical perturbation.     

Micromechanical model of a surrogate for collagenous soft tissues: development, validation and analysis of mesoscale size effects

Aligned, collagenous tissues such as tendons and ligaments are composed primarily of water and type I collagen, organized hierarchically into nanoscale fibrils, microscale fibers and mesoscale fascicles. Force transfer across scales is complex and poorly understood. Since innervation, the vasculature, damage mechanisms and mechanotransduction occur at the microscale and mesoscale, understanding multiscale interactions is of high importance. This study used a physical model in combination with a computational model to isolate and examine the mechanisms of force transfer between scales. A collagen-based surrogate served as the physical model. The surrogate consisted of extruded collagen fibers embedded within a collagen gel matrix. A micromechanical finite element model of the surrogate was validated using tensile test data that were recorded using a custom tensile testing device mounted on a confocal microscope. Results demonstrated that the experimentally measured macroscale strain was not representative of the microscale strain, which was highly inhomogeneous. The micromechanical model, in combination with a macroscopic continuum model, revealed that the microscale inhomogeneity resulted from size effects in the presence of a constrained boundary. A sensitivity study indicated that significant scale effects would be present over a range of physiologically relevant inter-fiber spacing values and matrix material properties. The results indicate that the traditional continuum assumption is not valid for describing the macroscale behavior of the surrogate and that boundary-induced size effects are present.     

Cytoplasmic strains and strain rates in motile polymorphonuclear leukocytes.

A new method is presented to measure local cytoplasmic deformation and rate of deformation in motile active neutrophils. The deformation is expressed in terms of biomechanical strains and strain rates. For this purpose small phagocytosed latex microspheres were used as intracellular markers. Planar Lagrangian and Eulerian strains and the rate of strain were estimated from the positions of a triad of internalized markers. Principal strains, stretch ratios, and principal directions were computed. The intracellular strains were found to be large relative to the overall cell shape change. Principal cytoplasmic stretch ratios showed large extension in the direction of pseudopod formation and cell locomotion and contraction in perpendicular directions. Regional strain analysis showed contractile strains to predominate in the vicinity of the pseudopod or leading edge of motion. The transitional region between the pseudopod and the main cell body exhibited large shear strains. The posterior region, where the uropod is located, also revealed large extensions but small contractile strains. The rate of strains are relatively small, nonuniform in time, and largely independent of the strain. The method we propose to measure cytoplasmic strain can be applied to a variety of problems in cell mechanics.     

Stress and strain localization in stretched collagenous tissues via a multiscale modelling approach

Mechanobiology of cells in soft collagenous tissues is highly affected by both tissue response at the macroscale and stress/strain localization mechanisms due to features at lower scales. In this paper, the macroscale mechanical behaviour of soft collagenous tissues is modelled by a three-level multiscale approach, based on a multi-step homogenisation technique from nanoscale up to the macroscale. Nanoscale effects, related to both intermolecular cross-links and collagen mechanics, are accounted for, together with geometric nonlinearities at the microscale. Moreover, an effective submodelling procedure is conceived in order to evaluate the local stress and strain fields at the microscale, which is around and within cells. Numerical results, obtained by using an incremental finite element formulation and addressing stretched tendinous tissues, prove consistency and accuracy of the model at both macroscale and microscale, confirming also the effectiveness of the multiscale modelling concept for successfully analysing physiopathological processes in biological tissues.     

Mechanical properties of a mature biofilm from a wastewater system: from microscale to macroscale level

A fundamental understanding of biofilm mechanical stability is critical in order to describe detachment and develop biofouling control strategies. It is thus important to characterise the elastic deformation and flow behaviour of the biofilm under different modes of applied force. In this study, the mechanical properties of a mature wastewater biofilm were investigated with methods including macroscale compression and microscale indentation using atomic force microscopy (AFM). The mature biofilm was found to be mechanically isotropic at the macroscale level as its mechanical properties did not depend on the scales and modes of loading. However, the biofilm showed a tendency for mechanical inhomogeneity at the microscale level as indentation progressed deeper into the matrix. Moreover, it was observed that the adhesion force had a significant influence on the elastic properties of the biofilm at the surface, subjected to microscale tensile loading. These results are expected to inform a damage-based model for biofilm detachment.     

Strain transfer in the annulus fibrosus under applied flexion

A detailed understanding of the anatomical and mechanical environment in the intervertebral disc at the scale of the cell is necessary for the design of tissue engineering repair strategies and to elucidate the role of mechanical factors in pathology. The objective of this study was to measure and compare the macroscale to microscale strains in the outer annulus fibrosus in various cellular regions of intact discs over a range of applied flexion. Macroscale strains were measured on the annulus fibrosus surface, and contrasted to in situ microscale strains using novel confocal microscopy techniques for dual labeling of the cell and the extracellular matrix. Fiber oriented surface strains were significantly higher than in situ fiber strains, which implies a mechanism of load redistribution that minimizes strain along the fibers. Non-uniformity of the strains and matrix distortion occurred immediately and most interestingly varied little with increase in flexion (3–16°), suggesting that inter-fiber shear is important in the initial stages of strain redistribution. Fiber oriented intercellular strains were significantly larger and compressive compared to in situ strains in other regions of the extracellular matrix indicating that the mechanical environment in this region may be unique. Further examination of the structural morphology in this pericellular region is needed to fully understand the pathway of strain transfer from the tissue to the cell. This study provides new knowledge on the complex in situ micro-mechanical environment of the annulus fibrosus that is essential to understanding the mechanobiological behavior of this tissue.     

Shear properties of passive ventricular myocardium

We examined the shear properties of passive ventricular myocardium in six pig hearts. Samples (3 x 3 x 3 mm) were cut from adjacent regions of the lateral left ventricular midwall, with sides aligned with the principal material axes. Four cycles of sinusoidal simple shear (maximum shear displacements of 0.1-0.5) were applied separately to each specimen in two orthogonal directions. Resulting forces along the three axes were measured. Three specimens from each heart were tested in different orientations to cover all six modes of simple shear deformation. Passive myocardium has nonlinear viscoelastic shear properties with reproducible, directionally dependent softening as strain is increased. Shear properties were clearly anisotropic with respect to the three principal material directions: passive ventricular myocardium is least resistant to simple shear displacements imposed in the plane of the myocardial layers and most resistant to shear deformations that produce extension of the myocyte axis. Comparison of results for the six different shear modes suggests that simple shear deformation is resisted by elastic elements aligned with the microstructural axes of the tissue.     

Regional Variations in Growth Plate Chondrocyte Deformation as Predicted By Three-Dimensional Multi-Scale Simulations

The physis, or growth plate, is a complex disc-shaped cartilage structure that is responsible for longitudinal bone growth. In this study, a multi-scale computational approach was undertaken to better understand how physiological loads are experienced by chondrocytes embedded inside chondrons when subjected to moderate strain under instantaneous compressive loading of the growth plate. Models of representative samples of compressed bone/growth-plate/bone from a 0.67 mm thick 4-month old bovine proximal tibial physis were subjected to a prescribed displacement equal to 20% of the growth plate thickness. At the macroscale level, the applied compressive deformation resulted in an overall compressive strain across the proliferative-hypertrophic zone of 17%. The microscale model predicted that chondrocytes sustained compressive height strains of 12% and 6% in the proliferative and hypertrophic zones, respectively, in the interior regions of the plate. This pattern was reversed within the outer 300 μm region at the free surface where cells were compressed by 10% in the proliferative and 26% in the hypertrophic zones, in agreement with experimental observations. This work provides a new approach to study growth plate behavior under compression and illustrates the need for combining computational and experimental methods to better understand the chondrocyte mechanics in the growth plate cartilage. While the current model is relevant to fast dynamic events, such as heel strike in walking, we believe this approach provides new insight into the mechanical factors that regulate bone growth at the cell level and provides a basis for developing models to help interpret experimental results at varying time scales.     

Strain transfer through the aortic valve

The complex structural organization of the aortic valve (AV) extracellular matrix (ECM) enables large and highly nonlinear tissue level deformations. The collagen and elastin (elastic) fibers within the ECM form an interconnected fibrous network (FN) and are known to be the main load-bearing elements of the AV matrix. The role of the FN in enabling deformation has been investigated and documented. However, there is little data on the correlation between tissue level and FN-level strains. Investigating this correlation will help establish the mode of strain transfer (affine or nonaffine) through the AV tissue as a key feature in microstructural modeling and will also help characterize the local FN deformation across the AV sample in response to applied tissue level strains. In this study, the correlation between applied strains at tissue level, macrostrains across the tissue surface, and local FN strains were investigated. Results showed that the FN strain distribution across AV samples was inhomogeneous and nonuniform, as well as anisotropic. There was no direct transfer of the deformation applied at tissue level to the fibrous network. Loading modes induced in the FN are different than those applied at the tissue as a result of different local strains in the valve layers. This nonuniformity of local strains induced internal shearing within the FN of the AV, possibly exposing the aortic valve interstitial cells (AVICs) to shear strains and stresses.     

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

Interbody fusion device subsidence has been reported clinically. An enhanced understanding of the mechanical behaviour of the surrounding bone would allow for accurate predictions of vertebral subsidence. The multiaxial inelastic behaviour of trabecular bone is investigated at a microscale and macroscale level. The post-yield behaviour of trabecular bone under hydrostatic and confined compression is investigated using microcomputed tomography-derived microstructural models, elucidating a mechanism of pressure-dependent yielding at the macroscopic level. Specifically, microstructural trabecular simulations predict a distinctive yield point in the apparent stress–strain curve under uniaxial, confined and hydrostatic compression. Such distinctive apparent stress–strain behaviour results from localised stress concentrations and material yielding in the trabecular microstructure. This phenomenon is shown to be independent of the plasticity formulation employed at a trabecular level. The distinctive response can be accurately captured by a continuum model using a crushable foam plasticity formulation in which pressure-dependent yielding occurs. Vertebral device subsidence experiments are also performed, providing measurements of the trabecular plastic zone. It is demonstrated that a pressure-dependent plasticity formulation must be used for continuum level macroscale models of trabecular bone in order to replicate the experimental observations, further supporting the microscale investigations. Using a crushable foam plasticity formulation in the simulation of vertebral subsidence, it is shown that the predicted subsidence force and plastic zone size correspond closely with the experimental measurements. In contrast, the use of von Mises, Drucker–Prager and Hill plasticity formulations for continuum trabecular bone models lead to over prediction of the subsidence force and plastic zone.     

Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue

Bone tissue is a complex multilevel composite which has the ability to sense ad respond to its mechanical environment. It is believed that bone cells called osteocytes within the bone matrix sense the mechanical environment and determine whether structural alterations are needed. At present it is not known, however, how loads are transferred from the whole bone level to cells. A computational procedure combining representative volume element (RVE) based homogenization theory with digital imaging is proposed to estimate strains at various levels of bone structure. Bone tissue structural organization and RVE based analysis are briefly reviewed. The digital image based computational procedure was applied to estimate strains in individual trabeculae (first-level microstructure). Homogenization analysis of an idealized model was used to estimate strains at one level of bone structure around osteocyte lacunae (second-level trabecular microstructure). The results showed that strain at one level of bone structure is amplified to a broad range at the next microstructural level. In one case, a zeor-level tensile principal strain of 495 muE engendered strains ranging between -1000 and 7000 muE in individual trabeculae (first-level microstructure). Subsequently, a first-level tensile principal strains of 1325 muE within an inidividual trabecula engendered strains ranging between 782 and 2530 muE around osteocyte lacunae. Lacunar orientation was found to influence strains around osteocyte lacunae much more than lacunar ellipticity. In conclusion, the computational procedure combining homogenization theory with digital imaging can proveide estimates of cell level strains within whole bones. Such results may be used to bridge experimental studies of bone adaptation at the whole bone and cell culture level. (c) 1994 John Wiley & Sons, Inc.     

Tools for studying and modulating (cardiac muscle) cell mechanics and mechanosensing across the scales

Cardiomyocytes generate force for the contraction of the heart to pump blood into the lungs and body. At the same time, they are exquisitely tuned to the mechanical environment and react to e.g. changes in cell and extracellular matrix stiffness or altered stretching due to reduced ejection fraction in heart disease, by adapting their cytoskeleton, force generation and cell mechanics. Both mechanical sensing and cell mechanical adaptations are multiscale processes. Receptor interactions with the extracellular matrix at the nanoscale will lead to clustering of receptors and modification of the cytoskeleton. This in turn alters mechanosensing, force generation, cell and nuclear stiffness and viscoelasticity at the microscale. Further, this affects cell shape, orientation, maturation and tissue integration at the microscale to macroscale. A variety of tools have been developed and adapted to measure cardiomyocyte receptor-ligand interactions and forces or mechanics at the different ranges, resulting in a wealth of new information about cardiomyocyte mechanobiology. Here, we take stock at the different tools for exploring cardiomyocyte mechanosensing and cell mechanics at the different scales from the nanoscale to microscale and macroscale.     

Biofilm engineering: linking biofilm development at different length and time scales

Biofilms are heterogeneous and dynamic systems. Evaluation of biofilm structure and function at the microscale has been greatly advanced through the application of multidimensional imaging, in-situ identification of the microbial community composition, function, and genetic regulation. Biofilm reactors are being applied for advanced biological treatment processes and their overall (macroscale) operation is well understood and controlled. What is missing is the link between micro and macroscale. In this horizon paper we suggest how understanding the overall biofilm ecosystem will require an integrated evaluation of the different length and time scales.     

Macroscale versus microscale methods for physiological analysis of biofilms formed in 96-well microtiter plates

Microtiter plates with 96 wells have become one of the preferred platforms for biofilm studies mainly because they enable high-throughput assays. In this work, macroscale and microscale methods were used to study the impact of hydrodynamic conditions on the physiology and location of Escherichia coli JM109(DE3) biofilms formed in microtiter plates. Biofilms were formed in shaking and static conditions, and two macroscale parameters were assayed: the total amount of biofilm was measured by the crystal violet assay and the metabolic activity was determined by the resazurin assay. From the macroscale point of view, there were no statistically significant differences between the biofilms formed in static and shaking conditions. However, at a microscale level, the differences between both conditions were revealed using scanning electron microscopy (SEM). It was observed that biofilm morphology and spatial distribution along the wall were different in these conditions. Simulation of the hydrodynamic conditions inside the wells at a microscale was performed by computational fluid dynamics (CFD). These simulations showed that the shear strain rate was unevenly distributed on the walls during shaking conditions and that regions of higher shear strain rate were obtained closer to the air/liquid interface. Additionally, it was shown that wall regions subjected to higher shear strain rates were associated with the formation of biofilms containing cells of smaller size. Conversely, regions with lower shear strain rate were prone to have a more uniform spatial distribution of adhered cells of larger size. The results presented on this work highlight the wealth of information that may be gathered by complementing macroscale approaches with a microscale analysis of the experiments.     

Kinematics of cytoplasmic deformation in neutrophils during active motion

A procedure is proposed to measure the cytoplasmic deformation in active motile neutrophils in the form of cytoplasmic strains and strain rates. Three neighboring microspheres in a local region of the cytoplasm serve as markers for local motion. Their positions are tracked by means of a high resolution light microscope and serve to compute nonlinear measures of strains and strain rates together with the principal strains and principal directions. Active neutrophils exhibit large cytoplasmic strains both during periodic pseudopod projections and during continuous locomotion in a polarized shape. The cytoplasmic motion is often synchronized with the whole cell deformation. The local cytoplasmic strains exceed the strains estimated for the whole cell and are not reversible except in some cases of single pseudopod projections. Large strains are observed both in attached and freely suspended cells. Strain rates are relatively constant but show an increase during the pseudopod retraction phase. Local cytoplasmic strains in neutrophils are inhomogeneous and reach large values during passage of the contraction rings. Neutrophils rendered passive by treatment with cytochalasin or EDTA show a random motion of microspheres with much smaller displacements. These observations suggest that the cytoplasm of active neutrophil exhibits large cytoplasmic strains and strain rates in the absence of an external stress resulting in a high degree of intracellular mixing. The proposed technique may be applied to a wide range of problems in cell biology.     

Measurement of intracellular strain on deformable substrates with texture correlation

Mechanical stimuli are important factors that regulate cell proliferation, survival, metabolism and motility in a variety of cell types. The relationship between mechanical deformation of the extracellular matrix and intracellular deformation of cellular sub-regions and organelles has not been fully elucidated, but may provide new insight into the mechanisms involved in transducing mechanical stimuli to biological responses. In this study, a novel fluorescence microscopy and image analysis method was applied to examine the hypothesis that mechanical strains are fully transferred from a planar, deformable substrate to cytoplasmic and intranuclear regions within attached cells. Intracellular strains were measured in cells derived from the anulus fibrosus of the intervertebral disc when attached to an elastic silicone membrane that was subjected to tensile stretch. Measurements indicated cytoplasmic strains were similar to those of the underlying substrate, with a strain transfer ratio (STR) of 0.79. In contrast, nuclear strains were much smaller than those of the substrate, with an STR of 0.17. These findings are consistent with previous studies indicating nuclear stiffness is significantly greater than cytoplasmic stiffness, as measured using other methods. This study provides a novel method for the study of cellular mechanics, including a new technique for measuring intranuclear deformations, with evidence of differential magnitudes and patterns of strain transferred from the substrate to cell cytoplasm and nucleus.     

A microscale anisotropic biaxial cell stretching device for applications in mechanobiology

A multi-layered polydimethylsiloxane microfluidic device with an integrated suspended membrane has been fabricated that allows dynamic and multi-axial mechanical deformation and simultaneous live-cell microscopy imaging. The transparent membrane’s strain field can be controlled independently along two orthogonal directions. Human foreskin fibroblasts were immobilized on the membrane’s surface and stretched along two orthogonal directions sequentially while performing live-cell imaging. Cyclic deformation of the cells induced a reversible reorientation perpendicular to the direction of the applied strain. Cells remained viable in the microdevice for several days. As opposed to existing microfluidic or macroscale stretching devices, this device can impose changing, anisotropic and time-varying strain fields in order to more closely mimic the complexities of strains occurring in vivo.     

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.     

Microfluidics meet cell biology: bridging the gap by validation and application of microscale techniques for cell biological assays

Microscale techniques have been applied to biological assays for nearly two decades, but haven't been widely integrated as common tools in biological laboratories. The significant differences between several physical phenomena at the microscale versus the macroscale have been exploited to provide a variety of new types of assays (such as gradient production or spatial cell patterning). However, the use of these devices by biologists seems to be limited by issues regarding biological validation, ease of use, and the limited available readouts for assays done using microtechnology. Critical validation work has been done recently that highlights the current challenges for microfluidic methods and suggest ways in which future devices might be improved to better integrate with biological assays. With more validation and improved designs, microscale techniques hold immense promise as a platform to study aspects of cell biology that are not possible using current macroscale techniques.