Discrete quasi-linear viscoelastic damping analysis of connective tissues, and the biomechanics of stretching

The fibrous character of pericellular matrix mediates cell mechanotransduction

Cells in solid tissues sense and respond to mechanical signals that are transmitted through extracellular matrix (ECM) over distances that are many times their size. This long-range force transmission is known to arise from strain-stiffening and buckling in the collagen fiber ECM network, but must also pass through the denser pericellular matrix (PCM) that cells form by secreting and compacting nearby collagen. However, the role of the PCM in the transmission of mechanical signals is still unclear. We therefore studied an idealized computational model of cells embedded within fibrous collagen ECM and PCM. Our results suggest that the smaller network pore sizes associated with PCM attenuates tension-driven collagen-fiber alignment, undermining long-range force transmission and shielding cells from mechanical stress. However, elongation of the cell body or anisotropic cell contraction can compensate for these effects to enable long distance force transmission. Results are consistent with recent experiments that highlight an effect of PCM on shielding cells from high stresses. Results have implications for the transmission of mechanical signaling in development, wound healing, and fibrosis.

Effects of tendon viscoelasticity on the distribution of forces across sutures in a model tendon-to-bone repair

Tears to the rotator cuff often require surgical repair. These repairs often culminate in re-tearing when sutures break through the tendon in the weeks following repair. Although numerous studies have been performed to identify suturing strategies that reduce this risk by balancing forces across sutures, none have accounted for how the viscoelastic nature of tendon influences load sharing. With the aim of providing insight into this problem, we studied how tendon viscoelasticity, tendon stiffness, and suture anchor spacing affect this balancing of forces across sutures. Results from a model of a three-row sutured re-attachment demonstrated that optimized distributions of suture stiffnesses and of the spacing of suture anchors can balance the forces across sutures to within a few percent, even when accounting for tendon viscoelasticity. Non-optimized distributions resulted in concentrated force, typically in the outermost sutures. Results underscore the importance of accounting for viscoelastic effects in the design of tendon to bone repairs.

A Biosynthetic Hybrid Spidroin-Amyloid-Mussel Foot Protein for Underwater Adhesion on Diverse Surfaces

Strong underwater adhesives are attractive materials for biomedical healing and underwater repair, but their success in applications has been limited, owing to challenges with underwater setting and with balancing surface adhesion and cohesion. Here, we applied synthetic biology approaches to overcome these challenges through design and synthesis of a novel hybrid protein consisting of the zipper-forming domains of an amyloid protein, flexible spider silk sequences, and a dihydroxyphenylalanine (DOPA)-containing mussel foot protein (Mfp). This partially structured, hybrid protein can self-assemble into a semi-crystalline hydrogel that exhibits high strength and toughness as well as strong underwater adhesion to a variety of surfaces, including difficult-to-adhere plastics, tendon, and skin. The hydrogel allows selective debonding by oxidation or iron-chelating treatments. Both the material design and the biosynthetic approach explored in this study will inspire future work for a wide range of hybrid protein-based materials with tunable properties and broad applications.

Quasi-Linear Viscoelastic Characterization of Soft Tissue-Mimicking Materials

We present a novel method based on the quasi-linear viscoelastic (QLV) theory to describe the time-dependent behavior of soft materials. Unlike previous methods for deriving QLV parameters, we characterize the elastic and viscous behavior of materials separately by using two different sets of experiments. To model the nonlinear elastic behavior, we fit the elastic stress response with a one-term Ogden model. Then, we model the relaxation behavior with a Prony series to compare the stress relaxation of the material at different timescales. This new method allows us to characterize materials with narrow confidence intervals (high accuracy), independently from the loading conditions. We validate our model using samples made of phantom materials that mimic normal and cancerous prostate tissues in terms of Young's modulus. Our model is shown to distinguish materials with similar elastic (viscous) properties but different viscous (elastic) properties. Drawing a precise distinction between the phantoms, this method could be useful for prostate cancer (PCa) diagnosis; but significant clinical studies will be needed in the future.

Rheological characterization of poly-dimethyl siloxane formulations with tunable viscoelastic properties

Studies from the past two decades have demonstrated convincingly that cells are able to sense the mechanical properties of their surroundings. Cells make major decisions in response to this mechanosensation, including decisions regarding cell migration, proliferation, survival, and differentiation. The vast majority of these studies have focused on the cellular mechanoresponse to changing substrate stiffness (or elastic modulus) and have been conducted on purely elastic substrates. In contrast, most soft tissues in the human body exhibit viscoelastic behavior; that is, they generate responsive force proportional to both the magnitude and rate of strain. While several recent studies have demonstrated that viscous effects of an underlying substrate affect cellular mechanoresponse, there is not a straightforward experimental method to probe this, particularly for investigators with little background in biomaterial fabrication. In the current work, we demonstrate that polymers comprised of differing polydimethylsiloxane (PDMS) formulations can be generated that allow for control over both the strain-dependent storage modulus and the strain rate-dependent loss modulus. These substrates requires no background in biomaterial fabrication to fabricate, are shelf-stable, and exhibit repeatable mechanical properties. Here we demonstrate that these substrates are biocompatible and exhibit similar protein adsorption characteristics regardless of mechanical properties. Finally, we develop a set of empirical equations that predicts the storage and loss modulus for a given blend of PDMS formulations, allowing users to tailor substrate mechanical properties to their specific needs.

We have generated novel formulations of polydimethyl siloxane with varying viscoelastic properties that can be used to study cellular response. We present equations that can be used to predict the storage and loss moduli of these polymers.

Characterizing poroelasticity of biological tissues by spherical indentation: an improved theory for large relaxation

Flow of fluids within biological tissues often meets with resistance that causes a rate- and size-dependent material behavior known as poroelasticity. Characterizing poroelasticity can provide insight into a broad range of physiological functions, and is done qualitatively in the clinic by palpation. Indentation has been widely used for characterizing poroelasticity of soft materials, where quantitative interpretation of indentation requires a model of the underlying physics, and such existing models are well established for cases of small strain and modest force relaxation. We showed here that existing models are inadequate for large relaxation, where the force on the indenter at a prescribed depth at long-time scale drops to below half of the initially peak force (i.e., F(0)/F(∞) > 2). We developed an indentation theory for such cases of large relaxation, based on Biot theory and a generalized Hertz contact model. We demonstrated that our proposed theory is suitable for biological tissues (e.g., spleen, kidney, skin and human cirrhosis liver) with both small and large relaxations. The proposed method would be a powerful tool to characterize poroelastic properties of biological materials for various applications such as pathological study and disease diagnosis.

Evaluating Plastic Deformation and Damage as Potential Mechanisms for Tendon Inelasticity using a Reactive Modeling Framework

Inelastic behaviors, such as softening, a progressive decrease in modulus before failure, occur in tendon and are important aspect in degeneration and tendinopathy. These inelastic behaviors are generally attributed to two potential mechanisms: plastic deformation and damage. However, it is not clear which is primarily responsible. In this study, we evaluated these potential mechanisms of tendon inelasticity by using a recently developed reactive inelasticity model (RIE), which is a structurally-inspired continuum mechanics framework that models tissue inelasticity based on the molecular bond kinetics. Using RIE, we formulated two material models, one specific to plastic deformation and the other to damage. The models were independently fit to published experimental tensile tests of rat tail tendons. We quantified the inelastic effects and compared the performance of the two models in fitting the mechanical response during loading, relaxation, unloading, and reloading phases. Additionally, we validated the models by using the resulting fit parameters to predict an independent set of experimental stress-strain curves from ramp-to-failure tests. Overall, the models were both successful in fitting the experiments and predicting the validation data. However, the results did not strongly favor one mechanism over the other. As a result, to distinguish between plastic deformation and damage, different experimental protocols will be needed. Nevertheless, these findings suggest the potential of RIE as a comprehensive framework for studying tendon inelastic behaviors.

An Analysis of the Mechanical Properties of the Ponseti Method in Clubfoot Treatment

Congenital clubfoot is a complex pediatric foot deformity, occurring in approximately 1 in 1000 live births and resulting in significant disability, deformity, and pain if left untreated. The Ponseti method of manipulation is widely recognized as the gold standard treatment for congenital clubfoot; however, its mechanical aspects have not yet been fully explored. During the multiple manipulation-casting cycles, the tendons and ligaments on the medial and posterior aspect of the foot and ankle, which are identified as the rate-limiting tissues, usually undergo weekly sequential stretches, with a plaster of Paris cast applied after the stretch to maintain the length gained. This triggers extracellular matrix remodeling and tissue growth, but due to the viscoelastic properties of tendons and ligaments, the initial strain size, rate, and loading history will affect the relaxation behavior and mechanical strength of the tissue. To increase the efficiency of the Ponseti treatment, we discuss the theoretical possibilities of decreasing the size of the strain step and interval of casting and/or increasing the overall number of casts. This modification may provide more tensile stimuli, allow more time for remodeling, and preserve the mechanical integrity of the soft tissues.

Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix

Characterizing how a tissue's constituents give rise to its viscoelasticity is important for uncovering how hidden timescales underlie multiscale biomechanics. These constituents are viscoelastic in nature, and their mechanics must typically be assessed from the uniaxial behavior of a tissue. Confounding the challenge is that tissue viscoelasticity is typically associated with nonlinear elastic responses. Here, we experimentally assessed how fibroblasts and extracellular matrix (ECM) within engineered tissue constructs give rise to the nonlinear viscoelastic responses of a tissue. We applied a constant strain rate, "triangular-wave" loading and interpreted responses using the Fung quasi-linear viscoelastic (QLV) material model. Although the Fung QLV model has several well-known weaknesses, it was well suited to the behaviors of the tissue constructs, cells, and ECM tested. Cells showed relatively high damping over certain loading frequency ranges. Analysis revealed that, even in cases where the Fung QLV model provided an excellent fit to data, the the time constant derived from the model was not in general a material parameter. Results have implications for design of protocols for the mechanical characterization of biological materials, and for the mechanobiology of cells within viscoelastic tissues.

Role of extracellular matrix in the biomechanical behavior of pancreatic tissue

Correlating the biomechanical properties of tissue with its function is an emerging area of research with potential impact in diagnostics, therapeutics, and prognostics. A critical stepping-stone in developing structure-function models is creating methods that can correlate the tissue structure with its mechanical behavior. As an initial step in addressing this challenge, we have characterized the mechanical behavior of unprocessed pancreatic tissue using optical fiber polarimetric elastography. To correlate the observed behavior to physiologically relevant structural features, a series of architectures are designed and fabricated using 3D printing. The mechanical response of the 3D printed elastomeric structures is analyzed using compressive testing and modeled using finite element analysis. The biomechanical behavior and buckling point of the 3D printed structures is used to create a calibration curve to understand the measured response of the resected pancreatic tissue. Based on the modeling and biomimetic results, the biomechanical behavior of pancreatic tissue is likely due to the collagen IV network.

Viscoelastic shear lag model to predict the micromechanical behavior of tendon under dynamic tensile loading

Owing to its viscoelastic nature, tendon exhibits stress rate-dependent breaking and stiffness function. A Kelvin-Voigt viscoelastic shear lag model is proposed to illustrate the micromechanical behavior of the tendon under dynamic tensile conditions. Theoretical closed-form expressions are derived to predict the deformation and stress transfer between fibrils and interfibrillar matrix while tendon is dynamically stretched. The results from the analytical solutions demonstrate that how the fibril overlap length and fibril volume fraction affect the stress transfer and mechanical properties of tendon. We find that the viscoelastic property of interfibrillar matrix mainly results in collagen fibril failure under fast loading rate or creep rupture of tendon. However, discontinuous fibril model and hierarchical structure of tendon ensure relative sliding under slow loading rate, helping dissipate energy and protecting fibril from damage, which may be a key reason why regularly staggering alignment microstructure is widely selected in nature. According to the growth, injury, healing and healed process of tendon observed by many researchers, the conclusions presented in this paper agrees well with the experimental findings. Additionally, the emphasis of this paper is on micromechanical behavior of tendon, whereas this analytical viscoelastic shear lag model can be equally applicable to other soft or hard tissues, owning the similar microstructure.