Sustained Physiological Stretch Induces Abdominal Skin Growth in Pregnancy

Supraphysiological stretches are exploited in skin expanders to induce tissue growth for autologous implants. As pregnancy is associated with large levels of sustained stretch, we investigated whether skin growth occurs in pregnancy. Therefore, we combined a mechanical model of skin and the observations from suction experiments on several body locations of five pregnant women at different gestational ages. The measurements show a continuous increase in stiffness, with the largest change observed during the last trimester. A comparison with numerical simulations indicates that the measured increase in skin stiffness is far below the level expected for the corresponding deformation of abdominal skin. A new set of simulations accounting for growth could rationalize all observations. The predicted amount of tissue growth corresponds to approximately 40% area increase before delivery. The results of the simulations also offered the opportunity to investigate the biophysical cues present in abdominal skin along gestation and to compare them with those arising in skin expanders. Alterations of the skin mechanome were quantified, including tissue stiffness, hydrostatic and osmotic pressure of the interstitial fluid, its flow velocity and electrical potential. The comparison between pregnancy and skin expansion highlights similarities as well as differences possibly influencing growth and remodeling.

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.

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.

Control of hydrostatic pressure and osmotic stress in 3D cell culture for mechanobiological studies

Hydrostatic pressure (HP) and osmotic stress (OS) play an important role in various biological processes, such as cell proliferation and differentiation. In contrast to canonical mechanical signals transmitted through the anchoring points of the cells with the extracellular matrix, the physical and molecular mechanisms that transduce HP and OS into cellular functions remain elusive. Three-dimensional cell cultures show great promise to replicate physiologically relevant signals in well-defined host bioreactors with the goal of shedding light on hidden aspects of the mechanobiology of HP and OS. This review starts by introducing prevalent mechanisms for the generation of HP and OS signals in biological tissues that are subject to pathophysiological mechanical loading. We then revisit various mechanisms in the mechanotransduction of HP and OS, and describe the current state of the art in bioreactors and biomaterials for the control of the corresponding physical signals.

On multiscale tension-compression asymmetry in skeletal muscle

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

Risky interpretations across the length scales: continuum vs. discrete models for soft tissue mechanobiology

Modelling and simulation in mechanobiology play an increasingly important role to unravel the complex mechanisms that allow resident cells to sense and respond to mechanical cues. Many of the in vivo mechanical loads occur on the tissue length scale, thus raising the essential question how the resulting macroscopic strains and stresses are transferred across the scales down to the cellular and subcellular levels. Since cells anchor to the collagen fibres within the extracellular matrix, the reliable representation of fibre deformation is a prerequisite for models that aim at linking tissue biomechanics and cell mechanobiology. In this paper, we consider the two-scale mechanical response of an affine structural model as an example of a continuum mechanical approach and compare it with the results of a discrete fibre network model. In particular, we shed light on the crucially different mechanical properties of the 'fibres' in these two approaches. While assessing the capability of the affine structural approach to capture the fibre kinematics in real tissues is beyond the scope of our study, our results clearly show that neither the macroscopic tissue response nor the microscopic fibre orientation statistics can clarify the question of affinity.

Tailoring the multiscale architecture of electrospun membranes to promote 3D cellular infiltration

Controlling the architecture of engineered scaffolds is of outmost importance to induce a targeted cell response and ultimately achieve successful tissue regeneration upon implantation. Robust, reliable and reproducible methods to control scaffold properties at different levels are timely and highly important. However, the multiscale architectural properties of electrospun membranes are very complex, in particular the role of fiber-to-fiber interactions on mechanical properties, and their effect on cell response remain largely unexplored. The work reported here reveals that the macroscopic membrane stiffness, observed by stress-strain curves, cannot be predicted solely based on the Young's moduli of the constituting fibers but is rather influenced by interactions on the microscale, namely the number of fiber-to-fiber bonds. To specifically control the formation of these bonds, solvent systems of the electrospinning solution were fine-tuned, affecting the membrane properties at every length-scale investigated. In contrast to dichloromethane that is characterized by a high vapor pressure, the use of trifluoroacetic acid, a solvent with a lower vapor pressure, favors the generation of fiber-to-fiber bonds. This ultimately led to an overall increased Young's modulus and yield stress of the membrane despite a lower stiffness of the constituting fibers. With respect to tissue engineering applications, an experimental setup was developed to investigate the effect of architectural parameters on the ability of cells to infiltrate and migrate within the scaffold. The results reveal that differences in fiber-to-fiber bonds significantly affect the infiltration of normal human dermal fibroblasts into the membranes. Membranes of loose fibers with low numbers of fiber-to-fiber bonds, as obtained from spinning solutions using dichloromethane, promote cellular infiltration and are thus promising candidates for the formation of a 3D tissue.

Visco- and poroelastic contributions of the zona pellucida to the mechanical response of oocytes

Probing mechanical properties of cells has been identified as a means to infer information on their current state, e.g. with respect to diseases or differentiation. Oocytes have gained particular interest, since mechanical parameters are considered potential indicators of the success of in vitro fertilisation procedures. Established tests provide the structural response of the oocyte resulting from the material properties of the cell's components and their disposition. Based on dedicated experiments and numerical simulations, we here provide novel insights on the origin of this response. In particular, polarised light microscopy is used to characterise the anisotropy of the zona pellucida, the outermost layer of the oocyte composed of glycoproteins. This information is combined with data on volumetric changes and the force measured in relaxation/cyclic, compression/indentation experiments to calibrate a multi-phasic hyper-viscoelastic model through inverse finite element analysis. These simulations capture the oocyte's overall force response, the distinct volume changes observed in the zona pellucida, and the structural alterations interpreted as a realignment of the glycoproteins with applied load. The analysis reveals the presence of two distinct timescales, roughly separated by three orders of magnitude, and associated with a rapid outflow of fluid across the external boundaries and a long-term, progressive relaxation of the glycoproteins, respectively. The new results allow breaking the overall response down into the contributions from fluid transport and the mechanical properties of the zona pellucida and ooplasm. In addition to the gain in fundamental knowledge, the outcome of this study may therefore serve an improved interpretation of the data obtained with current methods for mechanical oocyte characterisation.

Direct measurement of the direction-dependent mechanical behaviour of skeletal muscle extracellular matrix

This paper reports the first comprehensive data set on the anisotropic mechanical properties of isolated endo- and perimysial extracellular matrix of skeletal muscle, and presents the corresponding protocols for preparing and testing the samples. In particular, decellularisation of porcine skeletal muscle is achieved with caustic soda solution, and mechanical parameters are defined based on compressive and tensile testing in order to identify the optimal treatment time such that muscle fibres are dissolved whereas the extracellular matrix remains largely intact and mechanically functional. At around 18 h, a time window was found and confirmed by histology, in which axial tensile experiments were performed to characterise the direction-dependent mechanical response of the extracellular matrix samples, and the effect of lateral pre-compression was studied. The typical, large variability in the experimental stress response could be largely reduced by varying a single scalar factor, which was attributed to the variation of the fraction of extracellular matrix within the tissue. While experimental results on the mechanical properties of intact muscle tissue and single muscle fibres are increasingly available in literature, there is a lack of information on the properties of the collagenous components of skeletal muscle. The present work aims at closing this gap and thus contributes to an improved understanding of the mechanics of skeletal muscle tissue and provides a missing piece of information for the development of corresponding constitutive and computational models.

3D finite element models from serial section histology of skeletal muscle tissue - The role of micro-architecture on mechanical behaviour

In this contribution we create three-dimensional (3D) finite element models from a series of histological sections of porcine skeletal muscle tissue. Image registration is performed on the stained sections by affinely aligning them using auxiliary markers, followed by image segmentation to determine muscle fibres and the extracellular matrix in each section, with particular regard to the continuity of the fibres through the stack. With this information, 3D virtual tissue samples are reconstructed, discretised, and associated with appropriate non-linear elastic anisotropic material models. While the gross anatomy is directly obtained from the images, the local directions of anisotropy were determined by the use of an analogy with steady state diffusion. The influence of the number of histological sections considered for reconstruction on the numerically simulated mechanical response of the virtual tissue samples is then studied. The results show that muscle tissue is fairly heterogeneous along the fascicles, and that transverse isotropy is inadequate in describing their material symmetry at the typical length scale of a fascicle. Numerical simulations of different load cases suggest that ignoring the undulations of fibres and their non-uniform cross-sections only moderately affects the passive response of the tissue in tensile and compressive modes, but can become crucial when predicting the response to generic loads and activation.

Random auxetics from buckling fibre networks

Auxetic materials have gained increasing interest in the last decades, fostered by auspicious applications in various fields. While the design of new auxetics has largely focused on meta-materials with deterministic, periodically arranged structures, we show here by theoretical and numerical analysis that pronounced auxetic behaviour with negative Poisson's ratios of very large magnitude can occur in random fibre networks with slender, reasonably straight fibre segments that buckle and deflect. We further demonstrate in experiments that such auxetic fibre networks, which increase their thickness by an order of magnitude and more than quintuple their volume when moderately extended, can be produced by electrospinning. Our results thus augment the class of auxetics by a large group of straightforwardly fabricable meta-materials with stochastic microstructure.

On the defect tolerance of fetal membranes

A series of mechanical experiments were performed to quantify the strength and fracture toughness of human amnion and chorion. The experiments were complemented with computational investigations using a 'hybrid' model that includes an explicit representation of the collagen fibre network of amnion. Despite its much smaller thickness, amnion is shown to be stiffer, stronger and tougher than chorion, and thus to determine the mechanical response of fetal membranes, with respect to both, deformation and fracture behaviour. Data from uniaxial tension and fracture tests were used to inform and validate the computational model, which was then applied to rationalize measurements of the tear resistance of tissue samples containing crack-like defects. Experiments and computations show that the strength of amnion is not significantly reduced by defects smaller than 1 mm, but the crack size induced by perforations for amniocentesis and fetal membrane suturing during fetal surgery might be larger than this value. In line with previous experimental observations, the computational model predicts a very narrow near field at the crack tip of amnion, due to localized fibre alignment and collagen compaction. This mechanism shields the tissue from the defect and strongly reduces the interaction of multiple adjacent cracks. These findings were confirmed through corresponding experiments, showing that no interaction is expected for multiple sutures for an inter-suture distance larger than 1 mm and 3 mm for amnion and chorion, respectively. The experimental procedures and numerical models applied in the present study might be used to optimize needle and/or staple dimensions and inter-suture distance, and thus to reduce the risk of iatrogenic preterm premature rupture of the membranes from amniocentesis, fetoscopic and open prenatal surgery.

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.

Inverse poroelasticity as a fundamental mechanism in biomechanics and mechanobiology

Understanding the mechanisms of deformation of biological materials is important for improved diagnosis and therapy, fundamental investigations in mechanobiology, and applications in tissue engineering. Here we demonstrate the essential role of interstitial fluid mobility in determining the mechanical properties of soft tissues. Opposite to the behavior expected for a poroelastic material, the tissue volume of different collagenous membranes is observed to strongly decrease with tensile loading. Inverse poroelasticity governs monotonic and cyclic responses of soft biomembranes, and induces chemo-mechanical coupling, such that tensile forces are modulated by the chemical potential of the interstitial fluid. Correspondingly, the osmotic pressure varies with mechanical loads, thus providing an effective mechanism for mechanotransduction. Water mobility determines the tissue's ability to adapt to deformation through compaction and dilation of the collagen fiber network. In the near field of defects this mechanism activates the reversible formation of reinforcing collagen structures which effectively avoid propagation of cracks.How soft tissues respond to mechanical load is essential to their biological function. Here, the authors discover that - contrary to predictions of poroelasticity - fluid mobility in collagenous tissues induces drastic volume decrease with tensile loading and pronounced chemo-mechanical coupling.

A 2.5D approach to the mechanics of electrospun fibre mats

In this paper, a discrete random network modelling approach specific to electrospun networks is presented. Owing to the manufacturing process, fibres in these materials systems have an enormous length, as compared to their diameters, and form sparse networks since fibre contact over thickness is limited to a narrow range. Representative volume elements are generated, in which fibres span the entire domain, and a technique is developed to apply computationally favourable periodic boundary conditions despite the initial non-periodicity of the networks. To capture sparsity, a physically motivated method is proposed to distinguish true fibre cross-links, in which mechanical interaction takes place, from mere fibre intersections. The model is exclusively informed by experimentally accessible parameters, demonstrates excellent agreement with the mechanical response of electrospun fibre mats, captures typical microscopic deformation patterns, and provides information on the kinematics of fibres and pores. This ability to address relevant mechanisms of deformation at both micro- and macroscopic length scales, together with the moderate computational cost, render the proposed modelling approach a highly qualified tool for the computer-based design and optimization of electrospun networks.

The suture retention test, revisited and revised

A systematic investigation of the factors affecting the suture retention test is performed. The specimen width w and the distance a of the suture bite from the specimen free edge emerge as the most influential geometrical parameters. A conservative approach for the quantification of suture retention strength is identified, based on the use of a camera to monitor the incipient failure and detect the instant of earliest crack propagation. The corresponding critical force, called break starting strength, is extremely robust against test parameter variations and its dependence on the specimen geometry becomes negligible when a≥ 2mm and w≥ 10mm. Comparison of suture retention and mode I crack opening tests reveals a linear correlation between break starting strength and tearing energy. This suggests that the defect created by the needle and the load applied by the suture thread lead to a fracture mechanics problem, which dominates the initiation of failure.

Microstructure based prediction of the deformation behavior of soft collagenous membranes

The response of human amnion (HA) and bovine Glisson's capsule (GC) to uniaxial and biaxial tensile loading is analyzed on tissue (∼mm) and collagen fiber (∼μm) length scales. The mechanical behavior of the membranes is rationalized based on a discrete fiber network model that relates model parameters with microstructural features of the tissues. Parameters were first determined for GC based on the quantity and organization of collagen fibers in the tissue. Next, parameters for HA were defined by comparing the microstructures of the two membranes, which differ in fiber organization in that collagen forms μm-thick fiber bundles in GC while 50 nm-thin fibrils constitute the network in HA. The flexural behavior of these structures is phenomenologically represented in the model, indicating that shear forces are transmitted through fibrils within GC bundles, but to a much lesser extent than in a corresponding solid cross section. The model provides excellent predictions of the uniaxial and biaxial mechanical response, as well as of the progressive reorientation of fibers associated with uniaxial loading. The results are particularly relevant since model parameters were not obtained through a fitting procedure of the tissue's tension-stretch curve. Furthermore, simulations of representative in vivo deformation states indicated that a large part of the fibers are expected to be un-crimped under physiological loading conditions. Thus, the crimped shape of collagen fibers in the initial test configuration, and typically observed in histological analyses, might be a consequence of the contraction occurring when membranes are extracted from their environment in the body.

Factors influencing the determination of cell traction forces

Methods summarized by the term Traction Force Microscopy are widely used to quantify cellular forces in mechanobiological studies. These methods are inverse, in the sense that forces must be determined such that they comply with a measured displacement field. This study investigates how several experimental and analytical factors, originating in the realization of the experiments and the procedures for the analysis, affect the determined traction forces. The present results demonstrate that even for very high resolution measurements free of noise, traction forces can be significantly underestimated, while traction peaks are typically overestimated by 50% or more, even in the noise free case. Compared to this errors, which are inherent to the nature of the mechanical problem and its discretization, the effect of ignoring the out-of-plane displacement component, the interpolation scheme used between the discrete measurement points and the disregard of the geometrical non-linearities when using a nearly linear substrate material are less consequential. Nevertheless, a nonlinear elastic substrate, with strain-stiffening response and some degree of compressibility, can substantially improve the robustness of the reconstruction of traction forces over a wide range of magnitudes. This poses the need for a correct mechanical representation of these non-linearities during the traction reconstruction and a correct mechanical characterization of the substrate itself, especially for the large strain shear domain which is shown to plays a major role in the deformations induced by cells.

Confocal reference free traction force microscopy

The mechanical wiring between cells and their surroundings is fundamental to the regulation of complex biological processes during tissue development, repair or pathology. Traction force microscopy (TFM) enables determination of the actuating forces. Despite progress, important limitations with intrusion effects in low resolution 2D pillar-based methods or disruptive intermediate steps of cell removal and substrate relaxation in high-resolution continuum TFM methods need to be overcome. Here we introduce a novel method allowing a one-shot (live) acquisition of continuous in- and out-of-plane traction fields with high sensitivity. The method is based on electrohydrodynamic nanodrip-printing of quantum dots into confocal monocrystalline arrays, rendering individually identifiable point light sources on compliant substrates. We demonstrate the undisrupted reference-free acquisition and quantification of high-resolution continuous force fields, and the simultaneous capability of this method to correlatively overlap traction forces with spatial localization of proteins revealed using immunofluorescence methods.

Traction force microscopy is an effective method of measuring forces between cells and their environment, but requires removing the cells to obtain a reference image. Here the authors use nanodrip printing of quantum dots into compliant substrates to provide a regular array of fiducial spots, removing the need for a reference image.

Mechanical Characteristics of Bovine Glisson's Capsule as a Model Tissue for Soft Collagenous Membranes

An extensive multiaxial experimental campaign on the monotonic, time- and history-dependent mechanical response of bovine Glisson's capsule (GC) is presented. Reproducible characteristics were observed such as J-shaped curves in uniaxial and biaxial configurations, large lateral contraction, cyclic tension softening, large tension relaxation, and moderate creep strain accumulation. The substantial influence of the reference state selection on the kinematic response and the tension versus stretch curves is demonstrated and discussed. The parameters of a large-strain viscoelastic constitutive model were determined based on the data of uniaxial tension relaxation experiments. The model is shown to well predict the uniaxial and biaxial viscoelastic responses in all other configurations. GC, the corresponding model, and the experimental protocols are proposed as a useful basis for future studies on the relation between microstructure and tissue functionality and on the factors influencing the mechanical response of soft collagenous membranes.

Deformation mechanisms of human amnion: Quantitative studies based on second harmonic generation microscopy

Multiphoton microscopy has proven to be a versatile tool to analyze the three-dimensional microstructure of the fetal membrane and the mechanisms of deformation on the length scale of cells and the collagen network. In the present contribution, dedicated microscopic tools for in situ mechanical characterization of tissue under applied mechanical loads and the related methods for data interpretation are presented with emphasis on new stepwise monotonic uniaxial experiments. The resulting microscopic parameters are consistent with previous ones quantified for cyclic and relaxation tests, underlining the reliability of these techniques. The thickness reduction and the substantial alignment of collagen fiber bundles in the compact and fibroblast layer starting at very small loads are highlighted, which challenges the definition of a reference configuration in terms of a force threshold. The findings presented in this paper intend to inform the development of models towards a better understanding of fetal membrane deformation and failure, and thus of related problems in obstetrics and other clinical conditions.

Time-dependent mechanical behavior of human amnion: macroscopic and microscopic characterization

Characterizing the mechanical response of the human amnion is essential to understand and to eventually prevent premature rupture of fetal membranes. In this study, a large set of macroscopic and microscopic mechanical tests have been carried out on fresh unfixed amnion to gain insight into the time-dependent material response and the underlying mechanisms. Creep and relaxation responses of amnion were characterized in macroscopic uniaxial tension, biaxial tension and inflation configurations. For the first time, these experiments were complemented by microstructural information from nonlinear laser scanning microscopy performed during in situ uniaxial relaxation tests. The amnion showed large tension reduction during relaxation and small inelastic strain accumulation in creep. The short-term relaxation response was related to a concomitant in-plane and out-of-plane contraction, and was dependent on the testing configuration. The microscopic investigation revealed a large volume reduction at the beginning, but no change of volume was measured long-term during relaxation. Tension-strain curves normalized with respect to the maximum strain were highly repeatable in all configurations and allowed the quantification of corresponding characteristic parameters. The present data indicate that dissipative behavior of human amnion is related to two mechanisms: (i) volume reduction due to water outflow (up to ∼20 s) and (ii) long-term dissipative behavior without macroscopic deformation and no systematic global reorientation of collagen fibers.

On the anisotropy of skeletal muscle tissue under compression

This paper deals with the role of the muscle fibres and extracellular matrix (ECM) components when muscle tissue is subjected to compressive loads. To this end, dissected tissue samples were tested in compression modes which induced states of fibres in compression (I), in tension (II) or at constant length (III), respectively. A comparison of the stress responses indicated that the tissue behaviour is significantly different for these modes, including differences between the modes (I) and (III). This contradicts the paradigm of many constitutive models that the stress response can be decomposed into an isotropic part relating to the ECM and an anisotropic fibre part the contribution of which can be neglected under compression. Conversely, the results provide experimental evidence that there is an anisotropic contribution of the fibre direction to the compressive stress. Interpreting these results in terms of recent microscopical studies, potential connections between the observed behaviour and the structure of muscle ECM are established.

On a staggered iFEM approach to account for friction in compression testing of soft materials

An inverse finite element method (iFEM) to estimate material parameters from compression tests of soft materials is presented, where alginate hydrogel was used as a phantom material. The method applies if the boundary conditions at the loaded surfaces are not ideal, i.e. neither free of friction nor fully constrained, as it may be the case in most realistic testing set-ups. Assuming a linear friction law, the friction coefficient μ was considered unknown and estimated in a first step by minimising the difference between the contours of the sample, obtained by optical measurements, and the simulated shape. Force-displacement data were used in a second step to determine the parameters of the constitutive law. Staggering these two steps, both friction and material parameters were identified by optimisation. Skipping the first step and predefining μ instead, a unique parameter set could only be clearly identified if the deviations of the contours were considered in addition to the deviations in the force-displacement data. Finally, forward FEM calculations with differently shaped specimens were used to verify the goodness of the obtained parameter sets.

Modelling mechanical characteristics of microbial biofilms by network theory

In this contribution, we present a constitutive model to describe the mechanical behaviour of microbial biofilms based on classical approaches in the continuum theory of polymer networks. Although the model is particularly developed for the well-studied biofilms formed by mucoid Pseudomonas aeruginosa strains, it could easily be adapted to other biofilms. The basic assumption behind the model is that the network of extracellular polymeric substances can be described as a superposition of worm-like chain networks, each connected by transient junctions of a certain lifetime. Several models that were applied to biofilms previously are included in the presented approach as special cases, and for small shear strains, the governing equations are those of four parallel Maxwell elements. Rheological data given in the literature are very adequately captured by the proposed model, and the simulated response for a series of compression tests at large strains is in good qualitative agreement with reported experimental behavior.

Myocardial material parameter estimation: a comparison of invariant based orthotropic constitutive equations

This study investigated a number of invariant based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. A number of orthotropic laws based on Green strain components and one microstructurally based law have previously been investigated to fit experimental measurements of stress-strain behaviour. Here we extend this investigation to include several recently proposed functional forms, i.e. invariant based orthotropic and transversely isotropic constitutive relations. These laws were compared on the basis of (i) 'goodness of fit': how well they fit a set of six shear deformation tests, (ii) 'variability': how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive laws. It was found that a specific form of the polyconvex type as well as the exponential Fung-type law from the previous study were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.

A polyconvex anisotropic strain-energy function for soft collagenous tissues

Polyconvexity of a strain-energy function is a very important mathematical condition, especially in the context of a boundary-value problem. In the present paper, we propose an exponential polyconvex anisotropic strain-energy function. It is given by a series with an arbitrary number of terms and associated material constants. Each term of this series a priori satisfies the condition of the energy- and stress-free natural state so that no additional restrictions have to be imposed. Due to the exponential form, the proposed hyperelastic model is suitable for soft biological tissues. Thus, a good agreement with experimental data on different types of tissues is achieved.