Biological connective tissues exhibit viscoelastic and poroelastic behavior at different frequency regimes: Application to tendon and skin biophysics

Tissue-scale in vitro epithelial wrinkling and wrinkle-to-fold transition

Although epithelial folding is commonly studied using in vivo animal models, such models exhibit critical limitations in terms of real-time observation and independent control of experimental parameters. Here, we develop a tissue-scale in vitro epithelial bilayer folding model that incorporates an epithelium and extracellular matrix (ECM) hydrogel, thereby emulating various folding structures found in in vivo epithelial tissue. Beyond mere folding, our in vitro model realizes a hierarchical transition in the epithelial bilayer, shifting from periodic wrinkles to a single deep fold under compression. Experimental and theoretical investigations of the in vitro model imply that both the strain-stiffening of epithelium and the poroelasticity of ECM influence the folded structures of epithelial tissue. The proposed in vitro model will aid in investigating the underlying mechanism of tissue-scale in vivo epithelial folding relevant to developmental biology and tissue engineering.

A quadriphasic mechanical model of the human dermis

The present study investigates the multiphasic nature of the mechanical behavior of human dermis. Motivated by experimental observations and by consideration of its composition, a quadriphasic model of the dermis is proposed, distinguishing solid matrix components, interstitial fluid and charged constituents moving within the fluid, i.e., anions and cations. Compression and tensile experiments with and without change of osmolarity of the bath are performed to characterize the chemo-mechanical coupling in the dermis. Model parameters are determined through inverse analysis. The computations predict a dominant role of the permeability in the determination of the temporal evolution of the mechanical response of the tissue. In line with the previous studies on other tissues, the analysis shows that an ideal model based on Donnan's equilibrium overestimates the osmotic pressure in skin for the case of very dilute solutions. The quadriphasic model is applied to predict changes in dermal cell environment and therefore alterations in what is called the "mechanome," associated with skin stretch. The simulations indicate that skin deformation causes a variation in several local variables, including in particular the electric field associated with a deformation-induced non-homogeneous distribution of fixed charges.

Poroelastic Characterization and Modeling of Subcutaneous Tissue Under Confined Compression

Subcutaneous tissue mechanics are important for drug delivery. Yet, even though this material is poroelastic, its mechanical characterization has focused on its hyperelastic response. Moreover, advancement in subcutaneous drug delivery requires effective tissue mimics such as hydrogels for which similar gaps of poroelastic data exist. Porcine subcutaneous samples and gelatin hydrogels were tested under confined compression at physiological conditions and strain rates of 0.01%/s in 5% strain steps with 2600 s of stress relaxation between loading steps. Force-time data were used in an inverse finite element approach to obtain material parameters. Tissues and gels were modeled as porous neo-Hookean materials with properties specified via shear modulus, effective solid volume fraction, initial hydraulic permeability, permeability exponent, and normalized viscous relaxation moduli. The constitutive model was implemented into an isogeometric analysis (IGA) framework to study subcutaneous injection. Subcutaneous tissue exhibited an initial spike in stress due to compression of the solid and fluid pressure buildup, with rapid relaxation explained by fluid drainage, and longer time-scale relaxation explained by viscous dissipation. The inferred parameters aligned with the ranges reported in the literature. Hydraulic permeability, the most important parameter for drug delivery, was in the rangek 0 ∈ [ 0.142 , 0.203 ] mm4 /(N s). With these parameters, IGA simulations showed peak stresses due to a 1-mL injection to reach 48.8 kPa at the site of injection, decaying after drug volume disperses into the tissue. The poro-hyper-viscoelastic neo-Hookean model captures the confined compression response of subcutaneous tissue and gelatin hydrogels. IGA implementation enables predictive simulations of drug delivery.

Emergence of nanoscale viscoelasticity from single cancer cells to established tumors

Tumors are complex materials whose physical properties dictate growth and treatment outcomes. Recent evidence suggests time-dependent physical properties, such as viscoelasticity, are crucial, distinct mechanical regulators of cancer progression and malignancy, yet the genesis and consequences of tumor viscoelasticity are poorly understood. Here, using Wide-bandwidth AFM-based ViscoElastic Spectroscopy (WAVES) coupled with mathematical modeling, we probe the origins of tumor viscoelasticity. From single carcinoma cells to increasingly sized carcinoma spheroids to established tumors, we describe a stepwise evolution of dynamic mechanical properties that create a nanorheological signature of established tumors: increased stiffness, decreased rate-dependent stiffening, and reduced energy dissipation. We dissect this evolution of viscoelasticity by scale, and show established tumors use fluid-solid interactions as the dominant mechanism of mechanical energy dissipation as opposed to fluid-independent intrinsic viscoelasticity. Additionally, we demonstrate the energy dissipation mechanism in spheroids and established tumors is negatively correlated with the cellular density, and this relationship strongly depends on an intact actin cytoskeleton. These findings define an emergent and targetable signature of the physical tumor microenvironment, with potential for deeper understanding of tumor pathophysiology and treatment strategies.

Nanorheology and Nanoindentation Revealed a Softening and an Increased Viscous Fluidity of Adherent Mammalian Cells upon Increasing the Frequency

The nanomechanical response of a cell depends on the frequency at which the cell is probed. The components of the cell that contribute to this property and their interplay are not well understood. Here, two force microscopy methods are integrated to characterize the frequency and/or the velocity-dependent properties of living cells. It is shown on HeLa and fibroblasts, that cells soften and fluidize upon increasing the frequency or the velocity of the deformation. This property was independent of the type and values (25 or 1000 nm) of the deformation. At low frequencies (2-10 Hz) or velocities (1-10 µm s-1 ), the response is dominated by the mechanical properties of the cell surface. At higher frequencies (>10 Hz) or velocities (>10 µm s-1 ), the response is dominated by the hydrodynamic drag of the cytosol. Softening and fluidization does not seem to involve any structural remodeling. It reflects a redistribution of the applied stress between the solid and liquid-like elements of the cell as the frequency or the velocity is changed. The data indicates that the quasistatic mechanical properties of a cell featuring a cytoskeleton pathology might be mimicked by the response of a non-pathological cell which is probed at a high frequency.

On the contribution of solid and fluid behavior to the modeling of the time-dependent mechanics of tendons under semi-confined compression

The present work aims to investigate whether it is possible to identify and quantify the contributions of the interstitial fluid and the solid skeleton to the overall time-dependent behavior of tendons based on a single mechanical test. For this purpose, the capabilities of three different time-dependent models (a viscoelastic, a poroelastic and a poroviscoelastic) were investigated in the modeling of the experimental behavior obtained from semi-confined compression with stress relaxation tests transverse to collagen fibers. The main achieved result points out that the poroviscoelastic model was the only one capable to characterize both the experimental responses of the force and volume changes of the tissue samples. Moreover, further analysis of this model shows that while the kinematics of the sample are mainly governed by the fluid flow (pore pressure contribution of the model), the behavior intrinsically associated with the viscoelastic solid skeleton makes a significant contribution to the experimental force response. This study reinforces the importance of taking both the experimental kinematics and kinetics of tendon tissues into account during the constitutive characterization procedure.

Multiscale mechanical analysis of the elastic modulus of skin

The mechanical properties of the skin determine tissue function and regulate dermal cell behavior. Yet measuring these properties remains challenging, as evidenced by the large range of elastic moduli reported in the literature-from below one kPa to hundreds of MPa. Here, we reconcile these disparate results by dedicated experiments at both tissue and cellular length scales and by computational models considering the multiscale and multiphasic tissue structure. At the macroscopic tissue length scale, the collective behavior of the collagen fiber network under tension provides functional tissue stiffness, and its properties determine the corresponding elastic modulus (100-200 kPa). The compliant microscale environment (0.1-10 kPa), probed by atomic force microscopy, arises from the ground matrix without engaging the collagen fiber network. Our analysis indicates that indentation-based elasticity measurements, although probing tissue properties at the cell-relevant length scale, do not assess the deformation mechanisms activated by dermal cells when exerting traction forces on the extracellular matrix. Using dermal-equivalent collagen hydrogels, we demonstrate that indentation measurements of tissue stiffness do not correlate with the behavior of embedded dermal fibroblasts. These results provide a deeper understanding of tissue mechanics across length scales with important implications for skin mechanobiology and tissue engineering. STATEMENT OF SIGNIFICANCE: Measuring the mechanical properties of the skin is essential for understanding dermal cell mechanobiology and designing tissue-engineered skin substitutes. However, previous results reported for the elastic modulus of skin vary by six orders of magnitude. We show that two distinct deformation mechanisms, related to the tension-compression nonlinearity of the collagen fiber network, can explain the large variations in elastic moduli. Furthermore, we show that microscale indentation, which is frequently used to assess the stiffness perceived by cells, fails to engage the fiber network, and therefore cannot predict the behavior of dermal fibroblasts in stiffness-tunable fibrous hydrogels. This has important implications for how to measure and interpret the mechanical properties of soft tissues across length scales.

Poroelastic behavior and water permeability of human skin at the nanoscale

Topical skin care products and hydrating compositions (moisturizers or injectable fillers) have been used for years to improve the appearance of, for example facial wrinkles, or to increase "plumpness". Most of the studies have addressed these changes based on the overall mechanical changes associated with an increase in hydration state. However, little is known about the water mobility contribution to these changes as well as the consequences to the specific skin layers. This is important as the biophysical properties and the biochemical composition of normal stratum corneum, epithelium, and dermis vary tremendously from one another. Our current studies and results reported here have focused on a novel approach (dynamic atomic force microscopy-based nanoindentation) to quantify biophysical characteristics of individual layers of ex vivo human skin. We have discovered that our new methods are highly sensitive to the mechanical properties of individual skin layers, as well as their hydration properties. Furthermore, our methods can assess the ability of these individual layers to respond to both compressive and shear deformations. In addition, since human skin is mechanically loaded over a wide range of deformation rates (frequencies), we studied the biophysical properties of skin over a wide frequency range. The poroelasticity model used helps to quantify the hydraulic permeability of the skin layers, providing an innovative method to evaluate and interpret the impact of hydrating compositions on water mobility of these different skin layers.

Single and bi-compartment poro-elastic model of perfused biological soft tissues: FEniCSx implementation and tutorial

Soft biological tissues demonstrate strong time-dependent and strain-rate mechanical behavior, arising from their intrinsic visco-elasticity and fluid-solid interactions. The time-dependent mechanical properties of soft tissues influence their physiological functions and are related to several pathological processes. Poro-elastic modeling represents a promising approach because it allows the integration of multiscale/multiphysics data to probe biologically relevant phenomena at a smaller scale and embeds the relevant mechanisms at the larger scale. The implementation of multiphase flow poro-elastic models however is a complex undertaking, requiring extensive knowledge. The open-source software FEniCSx Project provides a novel tool for the automated solution of partial differential equations by the finite element method. This paper aims to provide the required tools to model the mixed formulation of poro-elasticity, from the theory to the implementation, within FEniCSx. Several benchmark cases are studied. A column under confined compression conditions is compared to the Terzaghi analytical solution, using the L2-norm. An implementation of poro-hyper-elasticity is proposed. A bi-compartment column is compared to previously published results (Cast3m implementation). For all cases, accurate results are obtained in terms of a normalized Root Mean Square Error (RMSE). Furthermore, the FEniCSx computation is found three times faster than the legacy FEniCS one. The benefits of parallel computation are also highlighted.

Elasticity of whole blood clots measured via Volume Controlled Cavity Expansion

Measuring and understanding the mechanical properties of blood clots can provide insights into disease progression and the effectiveness of potential treatments. However, several limitations hinder the use of standard mechanical testing methods to measure the response of soft biological tissues, like blood clots. These tissues can be difficult to mount, and are inhomogeneous, irregular in shape, scarce, and valuable. To remedy this, we employ in this work Volume Controlled Cavity Expansion (VCCE), a technique that was recently developed, to measure local mechanical properties of soft materials in their natural environment. Through highly controlled volume expansion of a water bubble at the tip of an injection needle, paired with simultaneous measurement of the resisting pressure, we obtain a local signature of whole blood clot mechanical response. Comparing this data with predictive theoretical models, we find that a 1-term Ogden model is sufficient to capture the nonlinear elastic response observed in our experiments and produces shear modulus values that are comparable to values reported in the literature. Moreover, we find that bovine whole blood stored at 4 °C for greater than 2 days exhibits a statistically significant shift in the shear modulus from 2.53 ± 0.44 kPa on day 2 (N = 13) to 1.23 ± 0.18 kPa on day 3 (N = 14). In contrast to previously reported results, our samples did not exhibit viscoelastic rate sensitivity within strain rates ranging from 0.22 - 21.1 s-1. By surveying existing data on whole blood clots for comparison, we show that this technique provides highly repeatable and reliable results, hence we propose the more widespread adoption of VCCE as a path forward to building a better understanding of the mechanics of soft biological materials.

Solute Transport across the Lymphatic Vasculature in a Soft Skin Tissue

Convective transport of drug solutes in biological tissues is regulated by the interstitial fluid pressure, which plays a crucial role in drug absorption into the lymphatic system through the subcutaneous (SC) injection. In this paper, an approximate continuum poroelasticity model is developed to simulate the pressure evolution in the soft porous tissue during an SC injection. This poroelastic model mimics the deformation of the tissue by introducing the time variation of the interstitial fluid pressure. The advantage of this method lies in its computational time efficiency and simplicity, and it can accurately model the relaxation of pressure. The interstitial fluid pressure obtained using the proposed model is validated against both the analytical and the numerical solution of the poroelastic tissue model. The decreasing elasticity elongates the relaxation time of pressure, and the sensitivity of pressure relaxation to elasticity decreases with the hydraulic permeability, while the increasing porosity and permeability due to deformation alleviate the high pressure. An improved Kedem-Katchalsky model is developed to study solute transport across the lymphatic vessel network, including convection and diffusion in the multi-layered poroelastic tissue with a hybrid discrete-continuum vessel network embedded inside. At last, the effect of different structures of the lymphatic vessel network, such as fractal trees and Voronoi structure, on the lymphatic uptake is investigated. In this paper, we provide a novel and time-efficient computational model for solute transport across the lymphatic vasculature connecting the microscopic properties of the lymphatic vessel membrane to the macroscopic drug absorption.

Is the fluid volume fraction equal to the water content in tendons? Insights on biphasic modeling

The mass density of highly hydrated soft tissues is generally assumed to be very close to that of the water, resulting that the fluid mass fraction (water content) being equal to the fluid volume fraction. Within this context, the present study aims to investigate whether such an assumption actually holds for tendon tissues and to what extent it may affect the constitutive characterizations based on biphasic (poroelastic) models. Once the water content was assessed by a classical drying assay, the fluid volume fraction was obtained based on an image segmentation approach. The main achieved results point out that the fluid volume fraction is ∼20% higher than the water content in the studied tendons (flexor digitorum profundus bovine tendons). Based on this, it is shown that the use of the water content instead of the fluid volume fraction may considerably bias the results drawn by biphasic modeling of tendons. Accordingly, a proper measurement of the fluid volume fraction is then required.

Static and Dynamic: Evolving Biomaterial Mechanical Properties to Control Cellular Mechanotransduction

The extracellular matrix (ECM) is a highly dynamic system that constantly offers physical, biological, and chemical signals to embraced cells. Increasing evidence suggests that mechanical signals derived from the dynamic cellular microenvironment are essential controllers of cell behaviors. Conventional cell culture biomaterials, with static mechanical properties such as chemistry, topography, and stiffness, have offered a fundamental understanding of various vital biochemical and biophysical processes, such as cell adhesion, spreading, migration, growth, and differentiation. At present, novel biomaterials that can spatiotemporally impart biophysical cues to manipulate cell fate are emerging. The dynamic properties and adaptive traits of new materials endow them with the ability to adapt to cell requirements and enhance cell functions. In this review, an introductory overview of the key players essential to mechanobiology is provided. A biophysical perspective on the state-of-the-art manipulation techniques and novel materials in designing static and dynamic ECM-mimicking biomaterials is taken. In particular, different static and dynamic mechanical cues in regulating cellular mechanosensing and functions are compared. This review to benefit the development of engineering biomechanical systems regulating cell functions is expected.

Multi-Step Extracellular Matrix Remodelling and Stiffening in the Development of Idiopathic Pulmonary Fibrosis

The extracellular matrix (ECM) of the lung is a filamentous network composed mainly of collagens, elastin, and proteoglycans that provides structural and physical support to its populating cells. Proliferation, migration and overall behaviour of those cells is greatly determined by micromechanical queues provided by the ECM. Lung fibrosis displays an aberrant increased deposition of ECM which likely changes filament organization and stiffens the ECM, thus upregulating the profibrotic profile of pulmonary cells. We have previously used AFM to assess changes in the Young's Modulus (E) of the ECM in the lung. Here, we perform further ECM topographical, mechanical and viscoelastic analysis at the micro- and nano-scale throughout fibrosis development. Furthermore, we provide nanoscale correlations between topographical and elastic properties of the ECM fibres. Firstly, we identify a softening of the ECM after rats are instilled with media associated with recovery of mechanical homeostasis, which is hindered in bleomycin-instilled lungs. Moreover, we find opposite correlations between fibre stiffness and roughness in PBS- vs bleomycin-treated lung. Our findings suggest that changes in ECM nanoscale organization take place at different stages of fibrosis, with the potential to help identify pharmacological targets to hinder its progression.

Recent advances in electronic skins: material progress and applications

Electronic skins are currently in huge demand for health monitoring platforms and personalized medicine applications. To ensure safe monitoring for long-term periods, high-performance electronic skins that are softly interfaced with biological tissues are required. Stretchability, self-healing behavior, and biocompatibility of the materials will ensure the future application of electronic skins in biomedical engineering. This mini-review highlights recent advances in mechanically active materials and structural designs for electronic skins, which have been used successfully in these contexts. Firstly, the structural and biomechanical characteristics of biological skins are described and compared with those of artificial electronic skins. Thereafter, a wide variety of processing techniques for stretchable materials are reviewed, including geometric engineering and acquiring intrinsic stretchability. Then, different types of self-healing materials and their applications in electronic skins are critically assessed and compared. Finally, the mini-review is concluded with a discussion on remaining challenges and future opportunities for materials and biomedical research.

A multiphasic model for determination of water and solute transport across the arterial wall: effects of elastic fiber defects

Transport of solute across the arterial wall is a process driven by both convection and diffusion. In disease, the elastic fibers in the arterial wall are disrupted and lead to altered fluid and mass transport kinetics. A computational mixture model was used to numerically match previously published data of fluid and solute permeation experiments in groups of mouse arteries with genetic (knockout of fibulin-5) or chemical (treatment with elastase) disruption of elastic fibers. A biphasic model of fluid permeation indicated the governing property to be the hydraulic permeability, which was estimated to be 1.52×10^-9, 1.01×10^-8, and 1.07×10^-8 mm⁴/μN.s for control, knockout, and elastase groups, respectively. A multiphasic model incorporating solute transport was used to estimate effective diffusivities that were dependent on molecular weight, consistent with expected transport behaviors in multiphasic biological tissues. The effective diffusivity for the 4 kDA FITC-dextran solute, but not the 70 or 150 kDa FITC-dextran solutes, was dependent on elastic fiber structure, with increasing values from control to knockout to elastase groups, suggesting that elastic fiber disruption affects transport of lower molecular weight solutes. The model used here sets the groundwork for future work investigating transport through the arterial wall.

The role of cell-matrix interactions in connective tissue mechanics

Living tissue is able to withstand large stresses in everyday life, yet it also actively adapts to dynamic loads. This remarkable mechanical behaviour emerges from the interplay between living cells and their non-living extracellular environment. Here we review recent insights into the biophysical mechanisms involved in the reciprocal interplay between cells and the extracellular matrix and how this interplay determines tissue mechanics, with a focus on connective tissues. We first describe the roles of the main macromolecular components of the extracellular matrix in regards to tissue mechanics. We then proceed to highlight the main routes via which cells sense and respond to their biochemical and mechanical extracellular environment. Next we introduce the three main routes via which cells can modify their extracellular environment: exertion of contractile forces, secretion and deposition of matrix components, and matrix degradation. Finally we discuss how recent insights in the mechanobiology of cell-matrix interactions are furthering our understanding of the pathophysiology of connective tissue diseases and cancer, and facilitating the design of novel strategies for tissue engineering.

Assessment of the viscoelastic mechanical properties of the porcine optic nerve head using micromechanical testing and finite element modeling

Optic nerve head (ONH) biomechanics is centrally involved in the pathogenesis of glaucoma, a blinding ocular condition often characterized by elevation and fluctuation of the intraocular pressure and resulting loads on the ONH. Further, tissue viscoelasticity is expected to strongly influence the mechanical response of the ONH to mechanical loading, yet the viscoelastic mechanical properties of the ONH remain unknown. To determine these properties, we conducted micromechanical testing on porcine ONH tissue samples, coupled with finite element modeling based on a mixture model consisting of a biphasic material with a viscoelastic solid matrix. Our results provide a detailed description of the viscoelastic properties of the porcine ONH at each of its four anatomical quadrants (i.e., nasal, superior, temporal, and inferior). We showed that the ONH's viscoelastic mechanical response can be explained by a dual mechanism of fluid flow and solid matrix viscoelasticity, as is common in other soft tissues. We obtained porcine ONH properties as follows: matrix Young's modulus E=1.895[1.056,2.391] kPa (median [min., max.]), Poisson's ratio ν=0.142[0.060,0.312], kinetic time-constant τ=214[89,921] sec, and hydraulic permeability k=3.854×10^-1[3.457×10^-2,9.994×10^-1] mm⁴/(N.sec). These values can be used to design and fabricate physiologically appropriate ex vivo test environments (e.g., 3D cell culture) to further understand glaucoma pathophysiology. STATEMENT OF SIGNIFICANCE: Optic nerve head (ONH) biomechanics is an important aspect of the pathogenesis of glaucoma, the leading cause of irreversible blindness. The ONH experiences time-varying loads, yet the viscoelastic behavior of this tissue has not been characterized. Here, we measure the time-dependent response of the ONH in porcine eyes and use mechanical modeling to provide time-dependent mechanical properties of the ONH. This information allows us to identify time-varying stimuli in vivo which have timescales matching the characteristic response times of the ONH, and can also be used to design and fabricate ex vivo 3D cultures to study glaucoma pathophysiology in a physiologically relevant environment, enabling the discovery of new generations of glaucoma medications focusing on neuroprotection.

Transport and Lymphatic Uptake of Biotherapeutics Through Subcutaneous Injection

Drug transport and uptake in the subcutaneous tissue receives increasing attention in biomechanical and pharmaceutical researches, as subcutaneous administration becomes a common approach for the delivery of biotherapeutics, such as monoclonal antibodies. In this paper, high-fidelity numerical simulations are used to investigate the mechanisms governing drug transport and absorption in the subcutaneous tissue, which is expressed as a porous medium modeled by Darcy's law. The effects of tissue properties (permeability and porosity), the injection flow rate, and the vascular permeability of lymphatic vessels on the lymphatic uptake are studied. Additionally, an empirical formula for the lymphatic uptake during the injection is developed based on the numerical results. The roles of lymphatic drainage, blood perfusion, osmotic pressure, and the drug binding to the cells and the extracellular matrix in the lymphatic uptake are systematically studied. Furthermore, the drug distribution and absorption in a multi-layered porous medium are investigated to illustrate the effect of heterogeneity of permeability, as the permeability varies over a wide range in different layers of the tissue (such as dermis, subcutaneous tissue, muscle). While the interstitial pressure plays an essential role in the mechanisms regulating the absorption of free monoclonal antibodies, the binding and metabolism of drug proteins also affect the drug absorption by reducing the total free monoclonal antibodies.

A method to analyze the influence of mechanical strain on dermal collagen morphologies

Collagen fibers and their orientation play a major role in the mechanical behavior of soft biological tissue such as skin. Here, we present a proof-of-principle study correlating mechanical properties with collagen fiber network morphologies. A dedicated multiphoton stretching device allows for mechanical deformations in combination with a simultaneous analysis of its collagen fiber network by second harmonic generation imaging (SHG). The recently introduced Fiber Image Network Evaluation (FINE) algorithm is used to obtain detailed information about the morphology with regard to fiber families in collagen network images. To demonstrate the potential of our method, we investigate an isotropic and an anisotropic ex-vivo dorsal pig skin sample under quasi-static cyclic stretching and relaxation sequences. Families of collagen fibers are found to form a partially aligned collagen network under strain. We find that the relative force uptake is accomplished in two steps. Firstly, fibers align within their fiber families and, secondly, fiber families orient in the direction of force. The maximum alignment of the collagen fiber network is found to be determined by the largest strain. Isotropic and anisotropic samples reveal a different micro structural behavior under repeated deformation leading to a similar force uptake after two stretching cycles. Our method correlates mechanical properties with morphologies in collagen fiber networks.

A biphasic multilayer computational model of human skin

The present study investigates the layer-specific mechanical behavior of human skin. Motivated by skin’s histology, a biphasic model is proposed which differentiates between epidermis, papillary and reticular dermis, and hypodermis. Inverse analysis of ex vivo tensile and in vivo suction experiments yields mechanical parameters for each layer and predicts a stiff reticular dermis and successively softer papillary dermis, epidermis and hypodermis. Layer-specific analysis of simulations underlines the dominating role of the reticular dermis in tensile loading. Furthermore, it shows that the observed out-of-plane deflection in ex vivo tensile tests is a direct consequence of the layered structure of skin. In in vivo suction experiments, the softer upper layers strongly influence the mechanical response, whose dissipative part is determined by interstitial fluid redistribution within the tissue. Magnetic resonance imaging-based visualization of skin deformation in suction experiments confirms the deformation pattern predicted by the multilayer model, showing a consistent decrease in dermal thickness for large probe opening diameters.

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.

Comparison of material models for anterior cruciate ligament in tension: from poroelastic to a novel fibril-reinforced nonlinear composite model

Computational models of the knee joint are useful for evaluating stresses and strains within the joint tissues. However, the outcome of those models is sensitive to the material model and material properties chosen for ligaments, the collagen reinforced tissues connecting bone to bone. The purpose of this study was to investigate different compositionally motivated material models and further to develop a model that can accurately reproduce experimentally measured stress-relaxation data of bovine anterior cruciate ligament (ACL). Tensile testing samples were extracted from ACLs of bovine knee joints (N = 10) and subjected to a three-step stress-relaxation test at the toe region. Data from the experiments was averaged and one average finite element model was generated to replicate the experiment. Poroelastic and different fibril-reinforced poro(visco)elastic material models were applied, and their material parameters were optimized to reproduce the experimental force-time response. Material models with only fluid flow mediated relaxation were not able to capture the stress-relaxation behavior (R² = 0.806, 0.803 and 0.938). The inclusion of the viscoelasticity of the fibrillar network improved the model prediction (R² = 0.978 and 0.976), but the complex stress-relaxation behavior was best captured by a poroelastic model with a nonlinear two-relaxation-time strain-recruited viscoelastic fibrillar network (R² = 0.997). The results suggest that in order to replicate the multi-step stress-relaxation behavior of ACL in tension, the fibrillar network formulation should include the complex nonlinear viscoelastic phenomena.

Nonuniformity in Periodontal Ligament: Mechanics and Matrix Composition

The periodontal ligament (PDL) plays a critical role in providing immediate response to abrupt high loads during mastication while also facilitating slow remodeling of the alveolar bone. The PDL exceptional functionality is permitted by the unique nonuniform structure of the tissue. Two distinct areas that are critical to PDL function were previously identified: the furcation and the dense collar. Despite their hypothesized functions in tooth movement and maintenance, these 2 regions have not yet been compared within the context of their native environment. Therefore, the objective of this study is to elucidate the extracellular matrix (ECM) structure, composition, and biomechanical function of the furcation and the collar regions while maintaining the 3-dimensional (3D) structure in the murine PDL. We identify significant difference between the collar and furcation regions in both structure and mechanical properties. Specifically, we observed unique longitudinal structures in the dense collar that correlate with type VI collagen and LOX, both of which are associated with increased type I collagen density and tissue stiffness and are therefore proposed to function as scaffolds for tooth stabilization. We also found that the collar region is stiffer than the furcation region and therefore suggest that the dense collar acts as a suspense structure of the tooth within the bone during physiological loading. The furcation region of the PDL contained more proteins associated with reduced stiffness and higher tissue remodeling, as well as a dual mechanical behavior, suggesting a critical function in loads transfer and remodeling of the alveolar bone. In summary, this work unravels the nonuniform nature of the PDL within the 3D structural context and establishes understanding of regional PDL function, which opens new avenues for future studies of remodeling, regeneration, and disease.

Transient swelling behavior of the bovine caudal disc

The intervertebral disc is an avascular composite structure, comprised of the nucleus pulposus (NP) and the annulus fibrosus (AF). Previous tissue-level experiments either examined relative differences in swelling capacity of the two disc regions at a single time point or tested explant structures that did not replicate in situ boundary conditions. Previous joint-level studies that investigated time-dependent fluid flow into the disc provided limited information about swelling-induced intradiscal strains with respect to time and boundary constraints. Therefore, the objective of this study was to investigate time-dependent swelling behavior of the intervertebral disc ex situ. The first study investigated time-dependent free-swelling response of the whole disc and the disc's subcomponents separately (i.e., NP and AF). Findings from this study showed that the swelling rate and swelling capacity of NP explants under free-swelling conditions were greater than AF explants. The second study evaluated the effect of boundary conditions on in-plane strain distributions of intact discs and AF rings. Swelling-induced strain was highly heterogeneous in AF rings, where negative circumferential strains were observed in the inner AF and tensile circumferential strains were observed in the outer AF. Radial strains in AF rings were an order of magnitude greater than circumferential strains. Restricting fluid flow only to the outer AF periphery reduced the swelling of the inner AF. Swelling of intact discs affected both NP and AF swelling behaviors, where NP hydration decreased by 60%. Furthermore, the presence of the NP reduced peak radial strains in the AF and resulted in uniform strain distribution throughout the AF. In conclusion, these studies highlight that tissue hydration and swelling-induced strains largely depend on regional biochemical composition and geometric boundary constraints.

New bioreactor for mechanical stimulation of cultured tendon-like constructs: design and validation

OBJECTIVE

Although several different types of bioreactors are currently available with mechanical stimulation of constructs or prostheses for tendon regeneration, they are in many cases expensive and difficult to operate. This paper proposes a simple bioreactor to mechanically stimulate up to three constructs for tendon and ligament repair, composed of a stainless-steel frame and an electric motor.

METHODS

The deformation is produced by a cam wheel, whose eccentricity defines the maximum deformation. The test samples, braids of PLA seeded in surface with mouse fibroblasts, are immersed in the culture medium during mechanical stimulation.

RESULTS

Its advantages over existing similar bioreactor designs include: easy renewal of the culture medium and an external electric motor to avoid heating and contamination issues. After 14 days of stretching, the culture samples showed enhanced cellular proliferation and cell fiber alignment in addition to higher production of type I collagen. The cells initially seeded on the braid surface migrated to the inside of the braid.

CONCLUSION

Although the results obtained have a poor statistical basis, they do suggest that the bioreactor could be usefully applied to stimulate constructs for tendon and ligament repair. Anyway, further experiments should be conducted in the future.

Effects of extracellular matrix viscoelasticity on cellular behaviour

Substantial research over the past two decades has established that extracellular matrix (ECM) elasticity, or stiffness, affects fundamental cellular processes, including spreading, growth, proliferation, migration, differentiation and organoid formation. Linearly elastic polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers coated with ECM proteins are widely used to assess the role of stiffness, and results from such experiments are often assumed to reproduce the effect of the mechanical environment experienced by cells in vivo. However, tissues and ECMs are not linearly elastic materials-they exhibit far more complex mechanical behaviours, including viscoelasticity (a time-dependent response to loading or deformation), as well as mechanical plasticity and nonlinear elasticity. Here we review the complex mechanical behaviours of tissues and ECMs, discuss the effect of ECM viscoelasticity on cells, and describe the potential use of viscoelastic biomaterials in regenerative medicine. Recent work has revealed that matrix viscoelasticity regulates these same fundamental cell processes, and can promote behaviours that are not observed with elastic hydrogels in both two- and three-dimensional culture microenvironments. These findings have provided insights into cell-matrix interactions and how these interactions differentially modulate mechano-sensitive molecular pathways in cells. Moreover, these results suggest design guidelines for the next generation of biomaterials, with the goal of matching tissue and ECM mechanics for in vitro tissue models and applications in regenerative medicine.

In situ AFM-based nanoscale rheology reveals regional non-uniformity in viscoporoelastic mechanical behavior of the murine periodontal ligament

The periodontal ligament (PDL) is a critical player in the maintenance of tooth health, acting as the primary stabilizer of tooth position. Recent studies have identified two unique regions within the PDL, the 'dense collar' region and the 'furcation' region, which exhibit distinct structural and compositional differences. However, specific functional differences between these regions have yet to be investigated. We adapted an AFM-based nanoscale rheology method to regionally assess mechanical properties and poroelasticity in the mouse PDL while minimizing the disruption of the 3-dimensional native boundary conditions, and then explored tissue mechanical function in four different regions within the dense collar as well as in the furcation region. We found significant differences between the collar and furcation regions, with the collar acting as a stabilizing ligamentous structure and the furcation acting as both a compressive cushion for vertical forces and a conduit for nutrient transport. While this finding supports our hypothesis, based on previous studies investigating structural and compositional differences, we also found surprising inhomogeneity within the collar region itself. This inhomogeneity supports previous findings of a tilting movement in the buccal direction of mandibular molar teeth and the structural adaptation to prevent lingual movement. Future work will aim to understand how different regions of the PDL change functionally during biological or mechanical perturbations, such as orthodontic tooth movement, development, or aging, with the ultimate goal of better understanding the mechanobiology of the PDL function in health and disease.

Structure-Function Relationships of Healthy and Osteoarthritic Human Tibial Cartilage: Experimental and Numerical Investigation

Relationships between composition, structure and constituent-specific functional properties of human articular cartilage at different stages of osteoarthritis (OA) are poorly known. We established these relationships by comparison of elastic, viscoelastic and fibril-reinforced poroelastic mechanical properties with microscopic and spectroscopic analysis of structure and composition of healthy and osteoarthritic human tibial cartilage (n = 27). At a low frequency (0.005 Hz), proteoglycan content correlated negatively and collagen content correlated positively with the phase difference (i.e. tissue viscosity). At a high-frequency regime (> 0.05 Hz), proteoglycan content correlated negatively and collagen orientation angle correlated positively with the phase difference. Proteoglycans were lost in the early and advanced OA groups compared to the healthy group, while the superficial collagen orientation angle was greater only in the advanced OA group compared to the healthy group. Simultaneously, the initial fibril network modulus (fibril pretension) was smaller in the early and advanced OA groups compared to the healthy group. These findings suggest different mechanisms contribute to cartilage viscosity in low and high frequencies, and that the loss of superficial collagen pretension during early OA is due to lower tissue swelling (PG loss), while in advanced OA, both collagen disorganization and lower swelling modulate the collagen fibril pretension.

Evaluation of transverse poroelastic mechanics of tendon using osmotic loading and biphasic mixture finite element modeling

Tendon's viscoelastic behaviors are important to the tissue mechanical function and cellular mechanobiology. When loaded in longitudinal tension, tendons often have a large Poisson's ratio (ν>2) that exceeds the limit of incompressibility for isotropic material (ν=0.5), indicating that tendon experiences volume loss, inducing poroelastic fluid exudation in the transverse direction. Therefore, transverse poroelasticity is an important contributor to tendon material behavior. Tendon hydraulic permeability which is required to evaluate the fluid flow contribution to viscoelasticity, is mostly unavailable, and where available, varies by several orders of magnitude. In this manuscript, we quantified the transverse poroelastic material parameters of rat tail tendon fascicles by conducting transverse osmotic loading experiments, in both tension and compression. We used a multi-start optimization method to evaluate the parameters using biphasic finite element modeling. Our tendon samples had a transverse hydraulic permeability of 10^-4 to 10^-5 mm⁴. (Ns)^-1 and showed a significant tension-compression nonlinearity in the transverse direction. Further, using these results, we predict hydraulic permeability during longitudinal (fiber-aligned) tensile loading, and the spatial distribution of fluid flow during osmotic loading. These results reveal novel aspects of tendon mechanics and can be used to study the physiomechanical response of tendon in response to mechanical loading.

Nonlinear stress-dependent recovery behavior of the intervertebral disc

The intervertebral disc exhibits complex mechanics due to its heterogeneous structure, inherent viscoelasticity, and interstitial fluid-matrix interactions. Sufficient fluid flow into the disc during low loading periods is important for maintaining mechanics and nutrient transport. However, there is a lack of knowledge on the effect of loading magnitude on time-dependent recovery behavior and the relative contribution of multiple recovery mechanisms during recovery. In most studies that have evaluated disc recovery behavior, a single load condition has been considered, making it difficult to compare findings across studies. Hence, the objective of this study was to quantify unloaded disc recovery behavior after compressive creep loading under a wide range of physiologically relevant stresses (0.2-2 MPa). First, the repeatability of disc recovery behavior was assessed. Once repeatable recovery behavior was confirmed, each motion segment was subject to three cycles of creep-recovery loading, where each cycle consisted of a 24-h creep at a pre-assigned load (100, 200, 300, 600, 900, or 1200 N), followed by an 18-h recovery period at a nominal load (10 N). Results showed that disc recovery behavior was strongly influenced by the magnitude of loading. The magnitude of instantaneous and time-dependent recovery deformations increased nonlinearly with an increase in compressive stress during creep. In conclusion, this study highlights that elastic deformation, intrinsic viscoelasticity, and poroelasticity all have substantial contributions to disc height recovery during low loading periods. However, their relative contributions to disc height recovery largely depend on the magnitude of loading. While loading history does not influence the contribution of the short-term recovery, the contribution of long-term recovery is highly sensitive to loading magnitude.

The regional-dependent biaxial behavior of young and aged mouse skin: A detailed histomechanical characterization, residual strain analysis, and constitutive model

Skin fulfills several vital functions, many of which are dependent on its mechanical properties. Therefore, as mice have become an invaluable model for skin research, determining murine skin's mechanical properties is important. Specifically, skin's mechanical properties are important for functional tests as well as for prognostic and diagnostic purposes. Additionally, computational simulations of skin behavior are becoming commonplace, rendering accurate models of murine skin's constitutive behavior necessary. To date, our knowledge of mouse skin mechanics shows significant gaps. For example, there are no comprehensive reports correlating skin's mechanical properties with region, age, and direction. Moreover, mouse skin's residual strain behavior has not been reported on. In our current work, we set out to fill these gaps. Based on histology, 2-photon microscopy, and planar biaxial testing, while accurately tracking various reference configurations, we report on differences in gross structure, microstructural organization, and constitutive response of skin, and cast those properties into a versatile Fung-type hyperelastic constitutive law for three reference configurations. Our data is the most comprehensive report contrasting the mechanical properties of young (12 weeks) and aged (52 weeks) mouse skin and will, thus, be valuable to basic science as control data, and provide accurate constitutive laws for mouse skin modeling. STATEMENT OF SIGNIFICANCE: Our findings are significant as they fill several gaps in our understanding of mouse skin mechanics. This is particularly important as mouse skin is becoming a frequent and critical model of human skin for cosmetic and medical science. Specifically, we quantified how mechanical properties of mice skin vary with age, with location, and with direction. Additionally, we cast our findings into constitutive models that can be used by others for predictive computer simulations of skin behavior.

Micro-indentation and optical coherence tomography for the mechanical characterization of embryos: Experimental setup and measurements on chicken embryos

The investigation of the mechanical properties of embryos is expected to provide valuable information on the phenomenology of morphogenesis. It is thus believed that, by mapping the viscoelastic features of an embryo at different stages of growth, it may be possible to shed light on the role of mechanics in embryonic development. To contribute to this field, we present a new instrument that can determine spatiotemporal distributions of mechanical properties of embryos over a wide area and with unprecedented accuracy. The method relies on combining ferrule-top micro-indentation, which provides local measurements of viscoelasticity, with Optical Coherence Tomography, which can reveal changes in tissue morphology and help the user identify the indentation point. To prove the working principle, we have collected viscoelasticity maps of fixed and live HH11-HH12 chicken embryos. Our study shows that the instrument can reveal correlations between tissue morphology and mechanical behavior. STATEMENT OF SIGNIFICANCE: Local mechanical properties of soft biological tissue play a crucial role in several biological processes, including cell differentiation, cell migration, and body formation; therefore, measuring tissue properties at high resolution is of great interest in biology and tissue engineering. To provide an efficient method for the biomechanical characterization of soft biological tissues, we introduce a new tool in which the combination of non-invasive Optical Coherence Tomography imaging and depth-controlled indentation measurements allows one to map the viscoelastic properties of biological tissue and investigate correlations between local mechanical features and tissue morphology with unprecedented resolution.

Indentation response of soft viscoelastic matter with hard skin

The structure of a hard film mounted on a soft viscoelastic substrate exists widely in nature and in industrial production, in which the hard film plays an important role. In this study, in order to accurately describe the indentation behaviors of hard film/soft viscoelastic substrate systems and to separate the mechanical properties of the hard film from the overall indentation response, an analytical relationship between the indentation loads and displacements was derived and presented herein based on plate theory, Hankel transformation, the elastic-viscoelastic correspondence principle, and Boltzmann superposition principle. In addition, finite element simulations and experiments were performed to investigate the effectiveness and applicability of the theoretical model. The results showed that the analytical solution agreed extremely well with the experiments and simulations. By analyzing the analytical solution, it was found that, due to the presence of the hard film, the viscous behaviors of the hard film/soft viscoelastic substrate system depended not only on the viscous properties of the soft substrate but also on the elastic properties of the soft substrate. Surprisingly, the relaxation time of the hard film/soft viscoelastic substrate system became longer than that of the soft substrate, but the ratio of the decay modulus to the equilibrium modulus was lower than that of the soft substrate. The above findings remind us that it is impossible to simply judge whether the hard film inhibits or promotes the soft substrate viscous behaviors. Our research can help readers gain insights into the indentation response characteristics of hard film/soft viscoelastic substrate systems, and it provide a theoretical basis for the measurement of the mechanical properties of a hard film mounted on a soft viscoelastic substrate.

Exploiting Viscoelastic Experimental Observations and Numerical Simulations to Infer Biomimetic Artificial Tendon Fiber Designs

Designing biomimetic artificial tendons requires a thorough, data-based understanding of the tendon's inner material properties. The current work exploits viscoelastic experimental observations at the tendon fascicle scale, making use of mechanical and data analysis methods. More specifically, based on reported elastic, volumetric and relaxation fascicle scale properties, we infer most probable, mechanically compatible material attributes at the fiber scale. In particular, the work provides pairs of elastic and viscous fiber-scale moduli, which can reproduce the upper scale tendon mechanics. The computed range of values for the fiber-scale tendon viscosity attest to the substantial stress relaxation capabilities of tendons. More importantly, the reported mechanical parameters constitute a basis for the design of tendon-specific restoration materials, such as fiber-based, engineering scaffolds.

Understanding how reduced loading affects Achilles tendon mechanical properties using a fibre-reinforced poro-visco-hyper-elastic model

Understanding tendon mechanobiology is important for gaining insight into the development of tendon pathology and subsequent repair processes. The aim of this study was to investigate how experimentally observed mechanobiological adaptation of rat Achilles tendons translate to changes in constitutive mechanical properties and biomechanical behavior. In addition, we assessed the ability of the model to simulate tendon creep and stress-relaxation. A three dimensional finite element framework of rat Achilles tendon was implemented with a fibre-reinforced poro-visco-hyper-elastic constitutive model. Stress-relaxation and creep data from Achilles tendons of Sprague Dawley rats that had been subjected to both daily loading and a period of reduced loading were used to determine the constitutive properties of the tendons. Our results showed that the constitutive model captures creep and stress-relaxation data from rat Achilles tendons for both loaded and unloaded tendons with good accuracy (normalized root mean square error between model and experimental data were 0.010-0.027). Only when the model parameters were fitted to data from both mechanical tests simultaneously, were we able to also capture similar increase in elastic energy (increased stiffness) and decreased viscoelasticity in response to unloading, as was reported experimentally. Our study is the first to show that experimentally observed mechanobiological changes in tendon biomechanics, such as stiffness and viscoelasticity, can be designated to mechanical quantities in a constitutive model. Further investigation in this direction has potential to discriminate tissue components responsible for specific biomechanical response, and enable targeted treatment strategies for tendon health.

On the compressibility and poroelasticity of human and murine skin

A total of 37 human and 33 murine skin samples were subjected to uniaxial monotonic, cyclic, and relaxation experiments. Detailed analysis of the three-dimensional kinematic response showed that skin volume is significantly reduced as a consequence of a tensile elongation. This behavior is most pronounced in monotonic but persists in cyclic tests. The dehydration associated with volume loss depends on the osmolarity of the environment, so that tension relaxation changes as a consequence of modifying the ionic strength of the environmental bath. Similar to ex vivo observations, complementary in vivo stretching experiments on human volar forearms showed strong in-plane lateral contraction. A biphasic homogenized model is proposed which allows representing all relevant features of the observed mechanical response.

Electroadhesion with application to touchscreens

There is growing interest in touchscreens displaying tactile feedback due to their tremendous potential in consumer electronics. In these systems, the friction between the user's fingerpad and the surface of the touchscreen is modulated to display tactile effects. One of the promising techniques used in this regard is electrostatic actuation. If, for example, an alternating voltage is applied to the conductive layer of a surface capacitive touchscreen, an attractive electrostatic force is generated between the finger and the surface, which results in an increase in frictional forces acting on the finger moving on the surface. By altering the amplitude, frequency, and waveform of this signal, a rich set of tactile effects can be generated on the touchscreen. Despite the ease of implementation and its powerful effect on our tactile sensation, the contact mechanics leading to an increase in friction due to electroadhesion has not been fully understood yet. In this paper, we present experimental results for how the friction between a finger and a touchscreen depends on the electrostatic attraction and the applied normal pressure. The dependency of the finger-touchscreen interaction on the applied voltage and on several other parameters is also investigated using a mean field theory based on multiscale contact mechanics. We present detailed theoretical analysis of how the area of real contact and the friction force depend on contact parameters, and show that it is possible to further augment the friction force, and hence the tactile feedback displayed to the user by carefully choosing those parameters.