Multiscale strain analysis of tissue equivalents using a custom-designed biaxial testing device

Biaxial tensile testing system for measuring mechanical properties of both sides of biological tissues

The aortic wall exhibits a unique elastic behavior, periodically expanding in aortic diameter by approximately 10% during heartbeats. This elastic behavior of the aortic wall relies on the distinct yet interacting mechanical properties of its three layers: intima, media, and adventitia. Aortic aneurysms develop as a result of multifactorial remodeling influenced by mechanical vulnerability of the aortic wall. Therefore, investigating the mechanical response of the aneurysmal wall, in conjunction with changes in microstructural parameters on both the intimal and adventitial sides, may offer valuable insights into the mechanisms of aortic aneurysm development or rupture. This study aimed to develop a biaxial tensile testing system to measure the mechanical properties of both sides of the tissue to gain insights concerning the interactions in anisotropic layered tissue. The biaxial tensile test set-up consisted of four motors, four cameras, four load cells, and a toggle switch. Porcine ascending aortas were chosen as the test subject. Graphite particles with diameters of approximately 5-11 [μm] were randomly applied to both sides of the aorta. Strain measurements were obtained using the stereo digital-image correlation method. Because stretching a rectangular specimen with a thread inevitably concentrates and localizes stress, to reduce this effect the specimen's shape was investigated using finite element analysis. The finite element analysis showed that a cross-shaped specimen with diagonally cut edges would be suitable. Therefore, we prepared specimens with this novel shape. This test system showed that mechanical response of the aortic tissue was significantly different between the intimal and adventitial side in the high-strain range, due to the disruption of collagen fibers. The adventitia side exhibited a smaller elastic modulus than the intimal side, accompanied by disruption of collagen fibers in the adventitia, which were more pronounced in the longitudinal direction. In contrast, in the mid-strain range, the elastic modulus did not differ between the intimal and adventitial sides, irrespective of longitudinal or circumferential direction, and collagen fibers were not disrupted but elongated. A biaxial tensile test system, which measures the mechanical properties of both sides of biological tissues and the shape of the specimen for reducing the concentration of stress at the chuck region, was developed in this study. The biaxial tensile testing system developed here is useful for better understanding the influences of mechanical loads and tissue degeneration on anisotropic, layered biological tissues.

Biaxial testing system for characterization of mechanical and rupture properties of small samples

The study of damage and rupture of soft tissues using a tensile testing system is essential to understand the limits of mechanical behavior and loss of function in diseased tissues. However, commercial material testing systems are often expensive and may not be fully suitable for rupture tests of small samples. While several research laboratories have developed custom, less expensive, uniaxial or biaxial devices, there is a need for an open source, inexpensive, accurate and easy to customize biaxial material testing system to perform rupture tests in small soft samples. We designed a testing system (BiMaTS) that (a) was shown able to perform uniaxial and biaxial tests, (b) offers a large travel range for rupture tests of small samples, (c) maintains a centered field of view for effective strain mapping using digital image correlation, (d) provides a controlled temperature environment, (e) utilize many off-the-shelve components for easy manufacture and customization, and it is cost effective (∼$15 K). The instrument performance was characterized using 80%-scaled down, ASTM D412-C shaped PDMS samples. Our results demonstrate the ability of this open source, customizable, low-cost, biaxial materials testing system to successfully characterize the mechanical and rupture properties of small samples with high repeatability and accuracy.

Biaxial test and hyperelastic material models of silicone elastomer fabricated by extrusion-based additive manufacturing for wearable biomedical devices

Biaxial tensile testing of the silicone elastomer fabricated by additive manufacturing (AM) for wearable biomedical devices is presented. Silicone elastomer has unique mechanical properties ideal for stretchable parts in wearable biomedical devices. Biaxial tensile testing, in comparison to the uniaxial tensile and compression tests, is more representative for materials with large, multidirectional stretch. This study investigates the experimental setup and methods to measure and characterize mechanical properties of AM solid and porous silicone elastomer sheets on equi-biaxial stretch (with the stretch ratio up to 2). Four hyperelastic material models were applied to characterize the AM silicone sheet and evaluated through the finite element analysis (FEA) to quantify the fit to biaxial tensile test results. The Yeoh model with C₁₀ = 80.7 kPa, C₂₀ = -2.11 kPa, and C₃₀ = 0.22 kPa has the best match to the experimentally measured stress-strain curve as well as the force and strain in FEA. This study demonstrates that the effects of raster angle and thickness are insignificant in the stress-strain curve of an AM silicone elastomer with solid cross-section. This study also demonstrates that AM can fabricate anisotropic porous silicone elastomer parts with different stiffness in x- and y-directions.

Integrating structural heterogeneity, fiber orientation, and recruitment in multiscale ECM mechanics

Extracellular matrix (ECM) plays critical roles in establishing tissue structure-function relationships and controlling cell fate. However, the mechanisms by which ECM mechanics influence cell and tissue behavior remain to be elucidated since the events associated with this process span length scales from the tissue to molecular level. Entirely new methods are needed in order to better understand the multiscale mechanics of ECM. In this study, a multiscale experimental approach was established by integrating Optical Magnetic Twisting Cytometry (OMTC) with a biaxial tensile tester to study the microscopic (local) ECM mechanical properties under controlled tissue-level (global) loading. Adventitial layer of porcine thoracic artery was used as a collagen-based ECM. Multiphoton microscopy imaging was performed to capture the changes in ECM fiber structure during biaxial deformation. As visualized from multiphoton microscopy images, biaxial stretch induces gradual fiber straightening and the fiber families become evident at higher stretch levels. The OMTC measurements show that the local apparent storage and loss modulus increases with the global biaxial stretch, however there exists a complex interplay among local ECM mechanical properties, ECM structural heterogeneity, and fiber distribution and engagement. The phase lag does not change significantly with global biaxial stretch. Our results also show a much faster increase in global tissue tangent modulus compared to the local apparent complex modulus with biaxial stretch, indicating the scale dependency of ECM mechanics.

The multiscale stiffness of electrospun substrates and aspects of their mechanical biocompatibility

In contrast to homogeneous materials, the mechanical properties of fibrous substrates depend on the probing lengthscale. This suggests that cells feel very different mechanical cues than expected from the macroscale characterisation of the substrate materials. By means of multiscale computational analyses we study here the mechanical environment of cells adhering to typical electrospun networks used in biomedical applications, with comparable macroscopic stiffness but different fibre diameters. The stiffness evaluated at the level of focal adhesions varies significantly, and the overall magnitude is strongly affected by the fibre diameter. The microscopic stiffness evaluated at cell scale depends substantially on the network topology and is about one order of magnitude lower than the macroscopic stiffness of the substrate, and two to three orders of magnitude below the fibres' elastic modulus. Moreover, the translation of stiffness over the scales is modulated by global deformations of the scaffold. In particular, uniaxial or biaxial stretching of the substrate induces nonlinear microscopic stiffening. Finally, although electrospun networks allow long-range transmission of cell-induced deformations, the comparison between the range of forces measured in cell traction force microscopy and those required to markedly deform typical electrospun networks reveals an order of magnitude difference, suggesting that these scaffolds provide a rather rigid environment for cells. All these results underline that the achievement of mechanical biocompatibility at all relevant lengthscales, and over the whole range of physiological loading states is extremely challenging. At the same time, the study shows that the diameter, length and curvature of fibre segments might be tunable towards achieving this goal. STATEMENT OF SIGNIFICANCE: Electrospun fabrics have growing use as substrates and scaffolds in tissue engineering and other biomedical applications. Based on multiscale computational analyses, this study shows that substrates of comparable macroscopic stiffness can provide tremendously different mechanical micro-environments, and that cells adhering to fibrous substrates may thus experience by orders of magnitude different mechanical cues than it would be expected from macroscale material characterisation. The simulations further reveal that the transfer of stiffness over the length scales changes with macroscopic deformation, and identify some key parameters that govern the transfer ratio. We believe that such refined understanding of the multiscale aspects of mechanical biocompatibility is key to the development of successful scaffold materials.

Multiscale Modeling of Bone Healing: Toward a Systems Biology Approach

Bone is a living part of the body that can, in most situations, heal itself after fracture. However, in some situations, healing may fail. Compromised conditions, such as large bone defects, aging, immuno-deficiency, or genetic disorders, might lead to delayed or non-unions. Treatment strategies for those conditions remain a clinical challenge, emphasizing the need to better understand the mechanisms behind endogenous bone regeneration. Bone healing is a complex process that involves the coordination of multiple events at different length and time scales. Computer models have been able to provide great insights into the interactions occurring within and across the different scales (organ, tissue, cellular, intracellular) using different modeling approaches [partial differential equations (PDEs), agent-based models, and finite element techniques]. In this review, we summarize the latest advances in computer models of bone healing with a focus on multiscale approaches and how they have contributed to understand the emergence of tissue formation patterns as a result of processes taking place at the lower length scales.

In Vivo Multiscale and Spatially-Dependent Biomechanics Reveals Differential Strain Transfer Hierarchy in Skeletal Muscle

Biological tissues have a complex hierarchical architecture that spans organ to subcellular scales and comprises interconnected biophysical and biochemical machinery. Mechanotransduction, gene regulation, gene protection, and structure-function relationships in tissues depend on how force and strain are modulated from macro to micro scales, and vice versa. Traditionally, computational and experimental techniques have been used in common model systems (e.g., embryos) and simple strain measures were applied. But the hierarchical transfer of mechanical parameters like strain in mammalian systems is largely unexplored in vivo. Here, we experimentally probed complex strain transfer processes in mammalian skeletal muscle tissue over multiple biological scales using complementary in vivo ultrasound and optical imaging approaches. An iterative hyperelastic warping technique quantified the spatially-dependent strain distributions in tissue, matrix, and subcellular (nuclear) structures, and revealed a surprising increase in strain magnitude and heterogeneity in active muscle as the spatial scale also increased. The multiscale strain heterogeneity indicates tight regulation of mechanical signals to the nuclei of individual cells in active muscle, and an emergent behavior appearing at larger (e.g. tissue) scales characterized by dramatically increased strain complexity.

Characterization of a novel bioreactor system for 3D cellular mechanobiology studies

In vitro engineering systems can be powerful tools for studying tissue development in response to biophysical stimuli as well as for evaluating the functionality of engineered tissue grafts. It has been challenging, however, to develop systems that adequately integrate the application of biomimetic mechanical strain to engineered tissue with the ability to assess functional outcomes in real time. The aim of this study was to design a bioreactor system capable of real-time conditioning (dynamic, uniaxial strain, and electrical stimulation) of centimeter-long 3D tissue engineered constructs simultaneously with the capacity to monitor local strains. The system addresses key limitations of uniform sample loading and real-time imaging capabilities. Our system features an electrospun fibrin scaffold, which exhibits physiologically relevant stiffness and uniaxial alignment that facilitates cell adhesion, alignment, and proliferation. We have demonstrated the capacity for directly incorporating human adipose-derived stromal/stem cells into the fibers during the electrospinning process and subsequent culture of the cell-seeded constructs in the bioreactor. The bioreactor facilitates accurate pre-straining of the 3D constructs as well as the application of dynamic and static uniaxial strains while monitoring bulk construct tensions. The incorporation of fluorescent nanoparticles throughout the scaffolds enables in situ monitoring of local strain fields using fluorescent digital image correlation techniques, since the bioreactor is imaging compatible, and allows the assessment of local sample stiffness and stresses when coupled with force sensor measurements. In addition, the system is capable of measuring the electromechanical coupling of skeletal muscle explants by applying an electrical stimulus and simultaneously measuring the force of contraction. The packaging of these technologies, biomaterials, and analytical methods into a single bioreactor system has produced a powerful tool that will enable improved engineering of functional 3D ligaments, tendons, and skeletal muscles. Biotechnol. Bioeng. 2016;113: 1825-1837. © 2016 Wiley Periodicals, Inc.

Device-Based In Vitro Techniques for Mechanical Stimulation of Vascular Cells: A Review

The most common cause of death in the developed world is cardiovascular disease. For decades, this has provided a powerful motivation to study the effects of mechanical forces on vascular cells in a controlled setting, since these cells have been implicated in the development of disease. Early efforts in the 1970 s included the first use of a parallel-plate flow system to apply shear stress to endothelial cells (ECs) and the development of uniaxial substrate stretching techniques (Krueger et al., 1971, “An in Vitro Study of Flow Response by Cells,” J. Biomech., 4(1), pp. 31–36 and Meikle et al., 1979, “Rabbit Cranial Sutures in Vitro: A New Experimental Model for Studying the Response of Fibrous Joints to Mechanical Stress,” Calcif. Tissue Int., 28(2), pp. 13–144). Since then, a multitude of in vitro devices have been designed and developed for mechanical stimulation of vascular cells and tissues in an effort to better understand their response to in vivo physiologic mechanical conditions. This article reviews the functional attributes of mechanical bioreactors developed in the 21st century, including their major advantages and disadvantages. Each of these systems has been categorized in terms of their primary loading modality: fluid shear stress (FSS), substrate distention, combined distention and fluid shear, or other applied forces. The goal of this article is to provide researchers with a survey of useful methodologies that can be adapted to studies in this area, and to clarify future possibilities for improved research methods.

Cytoplasmic dynein pushes the cytoskeletal meshwork forward during axonal elongation

During development, neurons send out axonal processes that can reach lengths hundreds of times longer than the diameter of their cell bodies. Recent studies indicate that en masse microtubule translocation is a significant mechanism underlying axonal elongation, but how cellular forces drive this process is unknown. Cytoplasmic dynein generates forces on microtubules in axons to power their movement through 'stop-and-go' transport, but whether these forces influence the bulk translocation of long microtubules embedded in the cytoskeletal meshwork has not been tested. Here, we use both function-blocking antibodies targeted to the dynein intermediate chain and the pharmacological dynein inhibitor ciliobrevin D to ask whether dynein forces contribute to en bloc cytoskeleton translocation. By tracking docked mitochondria as fiducial markers for bulk cytoskeleton movements, we find that translocation is reduced after dynein disruption. We then directly measure net force generation after dynein disruption and find a dramatic increase in axonal tension. Taken together, these data indicate that dynein generates forces that push the cytoskeletal meshwork forward en masse during axonal elongation.

Biaxial tension of fibrous tissue: using finite element methods to address experimental challenges arising from boundary conditions and anisotropy

Planar biaxial tension remains a critical loading modality for fibrous soft tissue and is widely used to characterize tissue mechanical response, evaluate treatments, develop constitutive formulas, and obtain material properties for use in finite element studies. Although the application of tension on all edges of the test specimen represents the in situ environment, there remains a need to address the interpretation of experimental results. Unlike uniaxial tension, in biaxial tension the applied forces at the loading clamps do not transmit fully to the region of interest (ROI), which may lead to improper material characterization if not accounted for. In this study, we reviewed the tensile biaxial literature over the last ten years, noting experimental and analysis challenges. In response to these challenges, we used finite element simulations to quantify load transmission from the clamps to the ROI in biaxial tension and to formulate a correction factor that can be used to determine ROI stresses. Additionally, the impact of sample geometry, material anisotropy, and tissue orientation on the correction factor were determined. Large stress concentrations were evident in both square and cruciform geometries and for all levels of anisotropy. In general, stress concentrations were greater for the square geometry than the cruciform geometry. For both square and cruciform geometries, materials with fibers aligned parallel to the loading axes reduced stress concentrations compared to the isotropic tissue, resulting in more of the applied load being transferred to the ROI. In contrast, fiber-reinforced specimens oriented such that the fibers aligned at an angle to the loading axes produced very large stress concentrations across the clamps and shielding in the ROI. A correction factor technique was introduced that can be used to calculate the stresses in the ROI from the measured experimental loads at the clamps. Application of a correction factor to experimental biaxial results may lead to more accurate representation of the mechanical response of fibrous soft tissue.

Evaluation of a post-processing approach for multiscale analysis of biphasic mechanics of chondrocytes

Understanding the mechanical behaviour of chondrocytes as a result of cartilage tissue mechanics has significant implications for both evaluation of mechanobiological function and to elaborate on damage mechanisms. A common procedure for prediction of chondrocyte mechanics (and of cell mechanics in general) relies on a computational post-processing approach where tissue-level deformations drive cell-level models. Potential loss of information in this numerical coupling approach may cause erroneous cellular-scale results, particularly during multiphysics analysis of cartilage. The goal of this study was to evaluate the capacity of first- and second-order data passing to predict chondrocyte mechanics by analysing cartilage deformations obtained for varying complexity of loading scenarios. A tissue-scale model with a sub-region incorporating representation of chondron size and distribution served as control. The post-processing approach first required solution of a homogeneous tissue-level model, results of which were used to drive a separate cell-level model (same characteristics as the sub-region of control model). The first-order data passing appeared to be adequate for simplified loading of the cartilage and for a subset of cell deformation metrics, for example, change in aspect ratio. The second-order data passing scheme was more accurate, particularly when asymmetric permeability of the tissue boundaries was considered. Yet, the method exhibited limitations for predictions of instantaneous metrics related to the fluid phase, for example, mass exchange rate. Nonetheless, employing higher order data exchange schemes may be necessary to understand the biphasic mechanics of cells under lifelike tissue loading states for the whole time history of the simulation.

Prediction of equibiaxial loading stress in collagen-based extracellular matrix using a three-dimensional unit cell model

Mechanical signals are important factors in determining cell fate. Therefore, insights as to how mechanical signals are transferred between the cell and its surrounding three-dimensional collagen fibril network will provide a basis for designing the optimum extracellular matrix (ECM) microenvironment for tissue regeneration. Previously we described a cellular solid model to predict fibril microstructure-mechanical relationships of reconstituted collagen matrices due to unidirectional loads (Acta Biomater 2010;6:1471-86). The model consisted of representative volume elements made up of an interconnected network of flexible struts. The present study extends this work by adapting the model to account for microstructural anisotropy of the collagen fibrils and a biaxial loading environment. The model was calibrated based on uniaxial tensile data and used to predict the equibiaxial tensile stress-stretch relationship. Modifications to the model significantly improved its predictive capacity for equibiaxial loading data. With a comparable fibril length (model 5.9-8μm, measured 7.5μm) and appropriate fibril anisotropy the anisotropic model provides a better representation of the collagen fibril microstructure. Such models are important tools for tissue engineering because they facilitate prediction of microstructure-mechanical relationships for collagen matrices over a wide range of microstructures and provide a framework for predicting cell-ECM interactions.