Characterising soft tissues under large amplitude oscillatory shear and combined loading

Beyond stiffness: deciphering the role of viscoelasticity in cancer evolution and treatment response

There is increasing evidence that cancer progression is linked to tissue viscoelasticity, which challenges the commonly accepted notion that stiffness is the main mechanical hallmark of cancer. However, this new insight has not reached widespread clinical use, as most clinical trials focus on the application of tissue elasticity and stiffness in diagnostic, therapeutic, and surgical planning. Therefore, there is a need to advance the fundamental understanding of the effect of viscoelasticity on cancer progression, to develop novel mechanical biomarkers of clinical significance. Tissue viscoelasticity is largely determined by the extracellular matrix (ECM), which can be simulatedin vitrousing hydrogel-based platforms. Since the mechanical properties of hydrogels can be easily adjusted by changing parameters such as molecular weight and crosslinking type, they provide a platform to systematically study the relationship between ECM viscoelasticity and cancer progression. This review begins with an overview of cancer viscoelasticity, describing how tumor cells interact with biophysical signals in their environment, how they contribute to tumor viscoelasticity, and how this translates into cancer progression. Next, an overview of clinical trials focused on measuring biomechanical properties of tumors is presented, highlighting the biomechanical properties utilized for cancer diagnosis and monitoring. Finally, this review examines the use of biofabricated tumor models for studying the impact of ECM viscoelasticity on cancer behavior and progression and it explores potential avenues for future research on the production of more sophisticated and biomimetic tumor models, as well as their mechanical evaluation.

Strain-dependent shear properties of human adipose tissue in vivo

INTRODUCTION

Human adipose tissue (fat) deforms substantially under normal physiological loading and during impact. Thus, accurate data on strain-dependent stiffness of fat is essential for the creation of accurate biomechanical models. Previous studies on ex vivo samples reported human fat to be nonlinear and viscoelastic. When static compression is combined with magnetic resonance (MR) elastography (an imaging technique used to measure viscoelasticity in vivo), the large deformation properties of tissues can be determined. Here, we use magnetic resonance elastography to quantify fat shear modulus in vivo under increasing compressive strain and compare it to the underlying passive gluteal muscle.

METHODS

The right buttocks of ten female participants were incrementally compressed at four levels while MR elastography (50 Hz) and mDixon images were acquired. Maps of tissue shear modulus (G*) were reconstructed from the MR elastography phase images. Tissue strain was estimated from registration of deformed and undeformed mDixon images. Linear mixed models were fit to the natural logarithm of the compressive strain and shear modulus data for each tissue.

RESULTS

Shear modulus increased in an exponential relationship with compressive strain in fat: Gfat*=748.5*Cyy-1.18Pa, and to a lesser extent in muscle: Gmuscle*=956.4*Cyy-0.36Pa. The baseline (undeformed) stiffness of fat was significantly lower than that of muscle (mean G*fat = 752 Pa, mean G*muscle = 1000 Pa, paired samples t-test, t = -4.24, p = 0.001). However, fat exhibited a significantly higher degree of strain dependence (characterised by the exponent of the curve, t = -6.47, p = 0.0001).

CONCLUSION

Static compression of human adipose tissue results in an increase in apparent viscoelastic shear modulus (stiffness), in an exponentially increasing relationship. The relationships defined here can be used in the development of physiologically realistic computational models for impact, injury and biomechanical modelling.

Local fat content determines global and local stiffness in livers with simple steatosis

Fat accumulation during liver steatosis precedes inflammation and fibrosis in fatty liver diseases, and is associated with disease progression. Despite a large body of evidence that liver mechanics play a major role in liver disease progression, the effect of fat accumulation by itself on liver mechanics remains unclear. Thus, we conducted ex vivo studies of liver mechanics in rodent models of simple steatosis to isolate and examine the mechanical effects of intrahepatic fat accumulation, and found that fat accumulation softens the liver. Using a novel adaptation of microindentation to permit association of local mechanics with microarchitectural features, we found evidence that the softening of fatty liver results from local softening of fatty regions rather than uniform softening of the liver. These results suggest that fat accumulation itself exerts a softening effect on liver tissue. This, along with the localized heterogeneity of softening within the liver, has implications in what mechanical mechanisms are involved in the progression of liver steatosis to more severe pathologies and disease. Finally, the ability to examine and associate local mechanics with microarchitectural features is potentially applicable to the study of the role of heterogeneous mechanical microenvironments in both other liver pathologies and other organ systems.

Linear and nonlinear rheology of liberase-treated breast cancer tumors

Extracellular matrix (ECM) rigidity has been shown to increase the invasive properties of breast cancer cells, promoting transformation and metastasis through mechanotransduction. Reducing ECM stiffness via enzymatic digestion could be a promising approach to slowing breast cancer development by de-differentiation of breast cancer cells to less aggressive phenotypes and enhancing the effectiveness of existing chemotherapeutics via improved drug penetrance throughout the tumor. In this study, we examine the effects of injectable liberase (a blend of collagenase and thermolysin enzymes) treatments on the linear and nonlinear rheology of allograft 4T1 mouse mammary tumors. We perform two sets of in vivo mouse studies, in which either one or multiple treatment injections occur before the tumors are harvested for rheological analysis. The treatment groups in each study consist of a buffer control, free liberase enzyme in buffer, a thermoresponsive copolymer called LiquoGel (LQG) in buffer, and a combined, localized injection of LQG and liberase. All tumor samples exhibit gel-like linear rheological behavior with the elastic modulus significantly larger than the viscous modulus and both independent of frequency. Tumors that receive a single injection of localized liberase have significantly lower tumor volumes and lower tissue moduli at both the center and edge compared to buffer- and free liberase-injected control tumors, while tissue viscoelasticity remains relatively unaffected. Tumors injected multiple times with LQG and liberase also have lower tissue volumes but possess higher tissue moduli and lower viscoelasticities compared to the other treatment groups. We propose that a mechanotransductive mechanism could cause the formation of smaller but stiffer tumors after repeated, localized liberase injections. Large amplitude oscillatory shear (LAOS) experiments are also performed on tissues from the multiple injection study and the results are analyzed using MITlaos. LAOS analysis reveals that all 4T1 tumors from the multiple injection study exhibit nonlinear rheological behavior at high strains and strain rates. Examination of the Lissajous-Bowditch curves, Chebyshev coefficient ratios, elastic moduli, and dynamic viscosities demonstrate that the onset and type of nonlinear behavior is independent of treatment type and elastic modulus, suggesting that multiple liberase injections do not affect the nonlinear viscoelasticity of 4T1 tumors.

Ex vivo bovine liver nonlinear viscoelastic properties: MR elastography and rheological measurements

INTRODUCTION

Knowledge of the nonlinear viscoelastic properties of the liver is important, but the complex tissue behavior outside the linear viscoelastic regime has impeded their characterization, particularly in vivo. Combining static compression with magnetic resonance (MR) elastography has the potential to be a useful imaging method for assessing large deformation mechanical properties of soft tissues in vivo. However, this remains to be verified. Therefore this study aims first to determine whether MR elastography can measure the nonlinear mechanical properties of ex vivo bovine liver tissue under varying levels of uniform and focal preloads (up to 30%), and second to compare MR elastography-derived complex shear modulus with standard rheological measurements.

METHOD

Nine fresh bovine livers were collected from a local abattoir, and experiments were conducted within 12hr of death. Two cubic samples (∼10 × 10 × 10 cm³) were dissected from each liver and imaged using MR elastography (60 Hz) under 4 levels of uniform and focal preload (1, 10, 20, and 30% of sample width) to investigate the relationship between MR elastography-derived complex shear modulus (G∗) and the maximum principal Right Cauchy Green Strain (C₁₁). Three tissue samples from each of the same 9 livers underwent oscillatory rheometry under the same 4 preloads (1, 10, 20, and 30% strain). MR elastography-derived complex shear modulus (G∗) from the uniform preload was validated against rheometry by fitting the frequency dependence of G∗ with a power-law and extrapolating rheometry-derived G∗ to 60 Hz.

RESULTS

MR elastography-derived G∗ increased with increasing compressive large deformation strain, and followed a power-law curve (G∗ = 1.73 × C₁₁^-0.38, R² = 0.96). Similarly, rheometry-derived G∗ at 1 Hz, increasing from 0.66 ± 1.03 kPa (1% strain) to 1.84 ± 1.65 kPa (30% strain, RM one-way ANOVA, P < 0.001), and the frequency dependence of G∗ followed a power-law with the exponent decreasing from 0.13 to 0.06 with increasing preload. MR elastography-derived G∗ was 1.4-3.1 times higher than the extrapolated rheometry-derived G∗ at 60 Hz, but the strain dependence was consistent between rheometry and MR elastography measurements.

CONCLUSIONS

This study demonstrates that MR elastography can detect changes in ex vivo bovine liver complex shear modulus due to either uniform or focal preload and therefore can be a useful technique to characterize nonlinear viscoelastic properties of soft tissue, provided that strains applied to the tissue can be quantified. Although MR elastography could reliably characterize the strain dependence of the ex vivo bovine liver, MR elastography overestimated the complex shear modulus of the tissue compared to rheological measurements, particularly at lower preload (<10%). That is likely to be important in clinical hepatic MR elastography diagnosis studies if preload is not carefully considered. A limitation is the absence of overlapping frequency between rheometry and MR elastography for formal validation.

Dynamic viscoelastic properties of porcine gastric tissue: Effects of loading frequency, region and direction

The gastric biomechanics influences digestive function as well as a range of topics of medical and scientific interests such as interaction between the stomach and gastric devices. Hence, the mechanical properties are essential for understanding gastric tissue and function in health and disease, and for the development of diagnostic or therapeutic devices. A key characteristic to be characterized is the time dependent mechanical tissue properties. The aim of this study was to characterize viscoelastic properties of the stomach across a frequency range. Longitudinal and circumferential stomach samples from the porcine fundus, corpus and antrum were pre-stretched 10 % and sinusoidally loaded with 10 % dynamic strain. The viscoelastic properties were assessed from 0.01 - 15 Hz using dynamic mechanical analysis. The storage moduli, loss moduli and tan δ had a significant second-order polynomial trend with increasing frequency. For the loss moduli, significant differences were observed between 0.01 and 15 Hz and between 0.05 and 15 Hz (p = 0.023 to 0.041). Significant differences were not found for storage moduli. Tan δ was frequency-independent, indicating that the two moduli varied proportionally. Fundus had significantly smaller storage moduli for longitudinal samples compared to corpus (p = 0.034) and antrum (p = 0.014) but was not significantly different for circumferential samples. Analysis of direction-dependency showed significant differences between longitudinal and circumferential samples (p = 0.002 to 0.042). The presented work provides insight into tensile viscoelastic properties of gastric tissue, which is useful for developing biomaterials, devices and computational models for device development specification calibrations.

Comprehensive experimental assessments of rheological models' performance in elastography of soft tissues

Elastography researchers have utilized several rheological models to characterize soft tissue viscoelasticity over the past thirty years. Due to the frequency-dependent behavior of viscoelastic parameters as well as the different techniques and frequencies employed in various studies of soft tissues, rheological models have value in standardizing disparate techniques via explicit mathematical representations. However, the important question remains: which of the several available models should be considered for widespread adoption within a theoretical framework? We address this by evaluating the performance of three well established rheological models to characterize ex vivo bovine liver tissues: the Kelvin-Voigt (KV) model as a 2-parameter model, and the standard linear solid (SLS) and Kelvin-Voigt fractional derivative (KVFD) models as 3-parameter models. The assessments were based on the analysis of time domain behavior (using stress relaxation tests) and frequency domain behavior (by measuring shear wave speed (SWS) dispersion). SWS was measured over a wide range of frequency from 1 Hz to 1 kHz using three different tests: (i) harmonic shear tests using a rheometer, (ii) reverberant shear wave (RSW) ultrasound elastography scans, and (iii) RSW optical coherence elastography scans, with each test targeting a distinct frequency range. Our results demonstrated that the KVFD model produces the only mutually consistent rendering of time and frequency domain data for liver. Furthermore, it reduces to a 2-parameter model for liver (correspondingly to a 2-parameter "spring-pot" or power-law model for SWS dispersion) and provides the most accurate predictions of the material viscoelastic behavior in time (>98% accuracy) and frequency (>96% accuracy) domains. STATEMENT OF SIGNIFICANCE: Rheological models are applied in quantifying tissues viscoelastic properties. This study is unique in presenting comprehensive assessments of rheological models.

Hyaluronic acid and chitosan-based electrospun wound dressings: Problems and solutions

To date, available review papers related to the electrospinning of biopolymers including polysaccharides for wound healing were focused on summarizing the process conditions for two candidates, namely chitosan and hyaluronic acid. However, most reviews lack the discussion of problems of hyaluronan and chitosan electrospun nanofibers for wound dressing applications. For this reason, it is required to update information by providing a comprehensive overview of all factors which may play a role in the electrospinning of hyaluronic acid and chitosan for applications of wound dressings. This review summarizes the fabricated chitosan and hyaluronic acid electrospun nanofibers as wound dressings in the last years, including methods of preparations of nanofibers and challenges for the electrospinning of both pure chitosan and hyaluronic acid and strategies how to overcome the existing difficulties. Moreover, in this review the biological roles and mechanisms of chitosan and hyaluronic acid in the wound healing process are explained including the advantages of nanofibers for ideal wound management using the common solvents, copolymers enhancing spinning process, and the most biologically active incorporated substances thereby providing drug delivery in wound healing.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells’ migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

A parameter reduced adaptive quasi-linear viscoelastic model for soft biological tissue in uniaxial tension

Mechanical characterisation of soft viscous materials is essential for many applications including aerospace industries, material models for surgical simulation, and tissue mimicking materials for anatomical models. Constitutive material models are, therefore, necessary to describe soft biological tissues in physiologically relevant strain ranges. Hereby, the adaptive quasi-linear viscoelastic (AQLV) model enables accurate modelling of the strain-dependent non-linear viscoelastic behaviour of soft tissues with a high flexibility. However, the higher flexibility produces a large number of model parameters. In this study, porcine muscle and liver tissue samples were modelled in the framework of the originally published AQLV (3-layers of Maxwell elements) model using four incremental ramp-hold experiments in uniaxial tension. AQLV model parameters were reduced by decreasing model layers (M) as well as the number of experimental ramp-hold steps (N). Leave One out cross validation tests show that the original AQLV model (3M4N) with 19 parameters, accurately describes porcine muscle tissue with an average R² of 0.90 and porcine liver tissue, R² of 0.86. Reducing the number of layers (N) in the model produced acceptable model fits for 1-layer (R² of 0.83) and 2-layer models (R² of 0.89) for porcine muscle tissue and 1-layer (R² of 0.84) and 2-layer model (R² of 0.85) for porcine liver tissue. Additionally, a 2 step (2N) ramp-hold experiment was performed on additional samples of porcine muscle tissue only to further reduce model parameters. Calibrated spring constant values for 2N ramp-hold tests parameters k₁ and k₂ had a 16.8% and 38.0% deviation from those calibrated for a 4 step (4N) ramp hold experiment. This enables further reduction of material parameters by means of step reduction, effectively reducing the number of parameters required to calibrate the AQLV model from 19 for a 3M4N model to 8 for a 2M2N model, with the added advantage of reducing the time per experiment by 50%. This study proposes a 'reduced-parameter' AQLV model (2M2N) for the modelling of soft biological tissues at finite strain ranges. Sequentially, the comparison of model parameters of soft tissues is easier and the experimental burden is reduced.

Using rheology to quantify the effects of localized collagenase treatments on uterine fibroid digestion

Uterine fibroids are stiff, benign tumors containing excessive, disordered collagens that occur in 70-80% of women before age 50 and cause bleeding and pain. Collagenase Clostridium histolyticum (CCH) is a bacterial enzyme capable of digesting the collagens present in fibroids. By combining CCH with injectable drug delivery systems to enhance effectiveness, a new class of treatments could be developed to reduce the stiffness of fibroids, preventing the need for surgical removal and preserving fertility. In this work, we achieved localization of CCH via physical entrapment by co-injecting a thermoresponsive pNIPAM-based polymeric delivery system called LiquoGel (LQG), which undergoes a sol-gel transition upon heating. Toxicity study results for LQG injected subcutaneously into mice demonstrate that LQG does not induce lesions or other adverse effects. We then used rheology to quantify the effects of localized CCH injections on the modulus and viscoelasticity of uterine fibroids, which exhibit gel-like behavior, through ex vivo and in vivo digestion studies. Ex vivo CCH injections reduce the tissue modulus by over two orders of magnitude and co-injection of LQG enhances this effect. Rheological results from an in vivo digestion study in mice show a significant reduction in tissue modulus and increase in tissue viscoelasticity 7 days after a single injection of LQG+CCH. Parallel histological staining validates that the observed rheological changes correspond to an increase in collagen lysis after treatment by LQG+CCH. These results show promise for development of injectable and localized enzymatic therapies for uterine fibroids and other dense tumors. STATEMENT OF SIGNIFICANCE: Uterine fibroids are stiff, benign tumors containing high collagen levels that cause bleeding and pain in women. Fertility-preserving and minimally-invasive treatments to soften fibroids are needed as an alternative to surgical removal via hysterectomy. We demonstrate through ex vivo and in vivo studies that co-injecting a thermoresponsive polymer delivery system (LQG) alongside a bacterial collagenase (CCH) enzyme significantly increases treatment effectiveness at softening fibroids through CCH localization. We use rheology to measure the modulus and viscoelasticity of fibroids and histology to show that fibroid softening corresponds to a decrease in collagen after treatment with LQG+CCH. These results highlight the utility of rheology at quantifying tissue properties and present a promising injectable therapy for fibroids and other dense tumors.

How growing tumour impacts intracranial pressure and deformation mechanics of brain

Brain is an actuator for control and coordination. When a pathology arises in cranium, it may leave a degenerative, disfiguring and destabilizing impact on brain physiology. However, the leading consequences of the same may vary from case to case. Tumour, in this context, is a special type of pathology which deforms brain parenchyma permanently. From translational perspective, deformation mechanics and pressures, specifically the intracranial cerebral pressure (ICP) in a tumour-housed brain, have not been addressed holistically in literature. This is an important area to investigate in neuropathy prognosis. To address this, we aim to solve the pressure mystery in a tumour-based brain in this study and present a fairly workable methodology. Using image-based finite-element modelling, we reconstruct a tumour-based brain and probe resulting deformations and pressures (ICP). Tumour is grown by dilating the voxel region by 16 and 30 mm uniformly. Cumulatively three cases are studied including an existing stage of the tumour. Pressures of cerebrospinal fluid due to its flow inside the ventricle region are also provided to make the model anatomically realistic. Comparison of obtained results unequivocally shows that as the tumour region increases its area and size, deformation pattern changes extensively and spreads throughout the brain volume with a greater concentration in tumour vicinity. Second, we conclude that ICP pressures inside the cranium do increase substantially; however, they still remain under the normal values (15 mmHg). In the end, a correlation relationship of ICP mechanics and tumour is addressed. From a diagnostic purpose, this result also explains why generally a tumour in its initial stage does not show symptoms because the required ICP threshold has not been crossed. We finally conclude that even at low ICP values, substantial deformation progression inside the cranium is possible. This may result in plastic deformation, midline shift etc. in the brain.

Foaming and rheological properties of aqueous solutions: an interfacial study

Although aqueous foam is composed of simple fluids, air and water, it shows a complex rheological behavior. It exhibits solid-like behavior at low shear and fluid-like behavior at high shear rate. Therefore, understanding such behavior is important for many industrial applications in foods, pharmaceuticals, and cosmetics. Additionally, air–water interface of bubble surface plays an important role in the stabilizing mechanism of foams. Therefore, the rheological properties associated with the aqueous foam highly depend on its interfacial properties. In this review, a systematic study of aqueous foam are presented primarily from rheology point of view. Firstly, foaming agents, surfactants and particles are described; then foam structure was explained, followed by change in structure under applied shear. Finally, foam rheology was linked to interfacial rheology for the interface containing particles whose surface properties were altered by surfactants.

Hyperelastic and viscoelastic characterization of hepatic tissue under uniaxial tension in time and frequency domain

In order to create accurate anatomical models for medical training and research, mechanical properties of biological tissues need to be studied. However, non-linear and viscoelastic behaviour of most soft biological tissues complicates the evaluation of their mechanical properties. In the current study, a method for measuring hyperelasticity and viscoelasticity of bovine and porcine hepatic parenchyma in tension is presented. First, non-linear stress-stretch curves resulting from ramp loading and unloading, were interpreted based on a hyperelastic framework, using a Veronda-Westmann strain energy function. Strain-specific elastic moduli, such as initial stiffness E_I, were thereupon defined in certain parts of the stress-stretch curves. Furthermore, dissipated and stored energy density were calculated. Next, the viscoelastic nature of liver tissue was examined with two different methods: stress relaxation and dynamic cyclic testing. Both tests yielded dissipated and stored energy density, as well as loss tangent (tanδ), storage modulus (E^'), and loss modulus (E^''). In tension, stress relaxation was experimentally more convenient than dynamic cyclic testing. Thus we considered whether relaxation could be used for approximating the results of the cyclic tests. Regarding the resulting elastic moduli, initial stiffness was similar for porcine and bovine liver (E_I∼30kPa), while porcine liver was stiffer for higher strains. Comparing stress relaxation with dynamic cyclic testing, tanδ of porcine and bovine liver was the same for both methods (tanδ=0.05-0.25 at 1 Hz). Storage and loss moduli matched well for bovine, but not as well for porcine tissue. In conclusion, the utilized Veronda-Westmann model was appropriate for representing the hyperelasticity of liver tissue seen in ramp tests. Concerning viscoelasticity, both chosen testing methods - stress relaxation and dynamic cyclic testing - yielded comparable results for E^', E^'', and tanδ, as long as elasticity non-linearities were heeded. The here presented method provides novel insight into the tensile viscoelastic properties of hepatic tissue, and provides guidelines for convenient evaluation of soft tissue mechanical properties.

An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials

Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelastic, current biomechanical models in the computational community often assume hyperelastic material models. Fractional viscoelastic constitutive models have been successfully used in literature to capture viscoelastic material response; however, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic constitutive models are not suitable for three-dimensional simulations. Furthermore, the use of fractional derivatives can be computationally prohibitive, with a number of current numerical approximations having a computational cost that is 𝒪 ( N T 2 ) and a storage cost that is 𝒪(N_T ) (N_T denotes the number of time steps). In this paper, we present a novel numerical approximation to the Caputo derivative which exploits a recurrence relation similar to those used to discretize classic temporal derivatives, giving a computational cost that is 𝒪(N_T ) and a storage cost that is fixed over time. The approximation is optimized for numerical applications, and an error estimate is presented to demonstrate the efficacy of the method. The method, integrated into a finite element solid mechanics framework, is shown to be unconditionally stable in the linear viscoelastic case. It was then integrated into a computational biomechanical framework, with several numerical examples verifying the accuracy and computational efficiency of the method, including in an analytic test, in an analytic fractional differential equation, as well as in a computational biomechanical model problem.

Nonlinear viscoelastic constitutive model for bovine liver tissue

Soft tissue mechanical characterisation is important in many areas of medical research. Examples span from surgery training, device design and testing, sudden injury and disease diagnosis. The liver is of particular interest, as it is the most commonly injured organ in frontal and side motor vehicle crashes, and also assessed for inflammation and fibrosis in chronic liver diseases. Hence, an extensive rheological characterisation of liver tissue would contribute to advancements in these areas, which are dependent upon underlying biomechanical models. The aim of this paper is to define a liver constitutive equation that is able to characterise the nonlinear viscoelastic behaviour of liver tissue under a range of deformations and frequencies. The tissue response to large amplitude oscillatory shear (1–50%) under varying preloads (1–20%) and frequencies (0.5–2 Hz) is modelled using viscoelastic-adapted forms of the Mooney–Rivlin, Ogden and exponential models. These models are fit to the data using classical or modified objective norms. The results show that all three models are suitable for capturing the initial nonlinear regime, with the latter two being capable of capturing, simultaneously, the whole deformation range tested. The work presented here provides a comprehensive analysis across several material models and norms, leading to an identifiable constitutive equation that describes the nonlinear viscoelastic behaviour of the liver.

Prestrain and cholinergic receptor-dependent differential recruitment of mechanosensitive energy loss and energy release elements in airway smooth muscle

We tested the hypothesis that oscillatory airway smooth muscle (ASM) mechanics is governed by mechanosensitive energy loss and energy release elements that can be recruited by prestrain and cholinergic stimulation. We measured mechanical energy loss and mechanical energy release in unstimulated and carbachol-stimulated bovine ASM held at prestrains ranging from 0.3 to 1.0 L_o (reference length) and subjected to sinusoidal length oscillation at 1 hz with oscillatory strain amplitudes ranging from 0.1 to 1.5% L_o. We found that oscillatory ASM mechanics during sinusoidal length oscillation is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. The greater mechanosensitivity of the energy loss element than energy release element may explain the bronchodilatory effect of deep inspiration. Prestrain, an important determinant of ASM responsiveness, differentially increased energy loss and energy release in unstimulated and carbachol-stimulated ASM. Cholinergic stimulation, an important cause of bronchoconstriction and airway inflammation, also differentially increased energy loss and energy release. When prestrain and cholinergic stimulation were combined, we found that prestrain and cholinergic stimulation synergistically increased energy loss and energy release by ASM. The relationship between recruitment of energy loss elements and recruitment of energy release elements was nonlinear, suggesting that energy loss and energy release elements are not coupled in ASM cells. These findings imply that large lung volume and cholinergic ASM activation would synergistically increase mechanical energy expenditure during inspiration and mechanical recoil of ASM during expiration. NEW & NOTEWORTHY We report for the first time that oscillatory airway smooth muscle mechanics is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. Prestrain and cholinergic stimulation synergistically and differentially recruit energy loss and energy release elements. The greater mechanosensitivity of the energy loss element than the energy release element may explain the bronchodilatory effect of deep inspiration.

Soft tissue rheology and its implications for elastography: Challenges and opportunities

Magnetic resonance elastography and related shear wave ultrasound elastography techniques can be used to estimate the mechanical properties of soft tissues in vivo by using the relationships between wave propagation and the elastic properties of materials. These techniques have found numerous clinical and research applications, tracking changes in tissue properties as a result of disease or other interventions. Most dynamic elastography approaches estimate tissue elastic (or viscoelastic) properties from a simplified version of the equations for the propagation of acoustic waves through a homogeneous linear (visco)elastic medium. However, soft tissue rheology is complex and departs significantly from this idealized picture. In particular, soft tissues are nonlinearly viscoelastic, inhomogeneous and often anisotropic, and their apparent stiffness can vary with the current loading state. All of these features have implications for the reliability and reproducibility of elastography measurements, from data acquisition to analysis and interpretation. New developments in inversion algorithms for elastography are beginning to offer solutions to account for the complex rheology of tissues, including inhomogeneity and anisotropy. There remains considerable potential to further refine elastography to capture the full spectrum of tissue rheology, and thus to better understand the underlying tissue microstructural changes in a broad range of clinical disorders.

Characterizing viscoelastic mechanical properties of highly compliant polymers and biological tissues using impact indentation

Precise and accurate measurement of viscoelastic mechanical properties becomes increasingly challenging as sample stiffness decreases to elastic moduli <1 kPa, largely due to difficulties detecting initial contact with the compliant sample surface. This limitation is particularly relevant to characterization of biological soft tissues and compliant gels. Here, we employ impact indentation which, in contrast to shear rheology and conventional indentation, does not require contact detection a priori, and present a novel method to extract viscoelastic moduli and relaxation time constants directly from the impact response. We first validate our approach by using both impact indentation and shear rheology to characterize polydimethylsiloxane (PDMS) elastomers of stiffness ranging from 100 s of Pa to nearly 10 kPa. Assuming a linear viscoelastic constitutive model for the material, we find that the moduli and relaxation times obtained from fitting the impact response agree well with those obtained from fitting the rheological response. Next, we demonstrate our validated method on hydrated, biological soft tissues obtained from porcine brain, murine liver, and murine heart, and report the equilibrium shear moduli, instantaneous shear moduli, and relaxation time constants for each tissue. Together, our findings provide a new and straightforward approach capable of probing local mechanical properties of highly compliant viscoelastic materials with millimeter scale spatial resolution, mitigating complications involving contact detection or sample geometric constraints.

STATEMENT OF SIGNIFICANCE

Characterization and optimization of mechanical properties can be essential for the proper function of biomaterials in diverse applications. However, precise and accurate measurement of viscoelastic mechanical properties becomes increasingly difficult with increased compliance (particularly for elastic moduli <1 kPa), largely due to challenges detecting initial contact with the compliant sample surface and measuring response at short timescale or high frequency. By contrast, impact indentation has highly accurate contact detection and can be used to measure short timescale (glassy) response. Here, we demonstrate an experimental and analytical method that confers significant advantages over existing approaches to extract spatially resolved viscoelastic moduli and characteristic time constants of biological tissues (e.g., brain and heart) and engineered biomaterials.

Changes in Rat Brain Tissue Microstructure and Stiffness during the Development of Experimental Obstructive Hydrocephalus

Understanding neural injury in hydrocephalus and how the brain changes during the course of the disease in-vivo remain unclear. This study describes brain deformation, microstructural and mechanical properties changes during obstructive hydrocephalus development in a rat model using multimodal magnetic resonance (MR) imaging. Hydrocephalus was induced in eight Sprague-Dawley rats (4 weeks old) by injecting a kaolin suspension into the cisterna magna. Six sham-injected rats were used as controls. MR imaging (9.4T, Bruker) was performed 1 day before, and at 3, 7 and 16 days post injection. T2-weighted MR images were collected to quantify brain deformation. MR elastography was used to measure brain stiffness, and diffusion tensor imaging (DTI) was conducted to observe brain tissue microstructure. Results showed that the enlargement of the ventricular system was associated with a decrease in the cortical gray matter thickness and caudate-putamen cross-sectional area (P < 0.001, for both), an alteration of the corpus callosum and periventricular white matter microstructure (CC+PVWM) and rearrangement of the cortical gray matter microstructure (P < 0.001, for both), while compression without gross microstructural alteration was evident in the caudate-putamen and ventral internal capsule (P < 0.001, for both). During hydrocephalus development, increased space between the white matter tracts was observed in the CC+PVWM (P < 0.001), while a decrease in space was observed for the ventral internal capsule (P < 0.001). For the cortical gray matter, an increase in extracellular tissue water was significantly associated with a decrease in tissue stiffness (P = 0.001). To conclude, this study characterizes the temporal changes in tissue microstructure, water content and stiffness in different brain regions and their association with ventricular enlargement. In summary, whilst diffusion changes were larger and statistically significant for majority of the brain regions studied, the changes in mechanical properties were modest. Moreover, the effect of ventricular enlargement is not limited to the CC+PVWM and ventral internal capsule, the extent of microstructural changes vary between brain regions, and there is regional and temporal variation in brain tissue stiffness during hydrocephalus development.

Normal and Fibrotic Rat Livers Demonstrate Shear Strain Softening and Compression Stiffening: A Model for Soft Tissue Mechanics

Tissues including liver stiffen and acquire more extracellular matrix with fibrosis. The relationship between matrix content and stiffness, however, is non-linear, and stiffness is only one component of tissue mechanics. The mechanical response of tissues such as liver to physiological stresses is not well described, and models of tissue mechanics are limited. To better understand the mechanics of the normal and fibrotic rat liver, we carried out a series of studies using parallel plate rheometry, measuring the response to compressive, extensional, and shear strains. We found that the shear storage and loss moduli G’ and G” and the apparent Young's moduli measured by uniaxial strain orthogonal to the shear direction increased markedly with both progressive fibrosis and increasing compression, that livers shear strain softened, and that significant increases in shear modulus with compressional stress occurred within a range consistent with increased sinusoidal pressures in liver disease. Proteoglycan content and integrin-matrix interactions were significant determinants of liver mechanics, particularly in compression. We propose a new non-linear constitutive model of the liver. A key feature of this model is that, while it assumes overall liver incompressibility, it takes into account water flow and solid phase compressibility. In sum, we report a detailed study of non-linear liver mechanics under physiological strains in the normal state, early fibrosis, and late fibrosis. We propose a constitutive model that captures compression stiffening, tension softening, and shear softening, and can be understood in terms of the cellular and matrix components of the liver.

A comparison of hyperelastic constitutive models applicable to brain and fat tissues

In some soft biological structures such as brain and fat tissues, strong experimental evidence suggests that the shear modulus increases significantly under increasing compressive strain, but not under tensile strain, whereas the apparent Young's elastic modulus increases or remains almost constant when compressive strain increases. These tissues also exhibit a predominantly isotropic, incompressible behaviour. Our aim is to capture these seemingly contradictory mechanical behaviours, both qualitatively and quantitatively, within the framework of finite elasticity, by modelling a soft tissue as a homogeneous, isotropic, incompressible, hyperelastic material and comparing our results with available experimental data. Our analysis reveals that the Fung and Gent models, which are typically used to model soft tissues, are inadequate for the modelling of brain or fat under combined stretch and shear, and so are the classical neo-Hookean and Mooney-Rivlin models used for elastomers. However, a subclass of Ogden hyperelastic models are found to be in excellent agreement with the experiments. Our findings provide explicit models suitable for integration in large-scale finite-element computations.

Stimulus-responsive hydrogels: Theory, modern advances, and applications

Over the past century, hydrogels have emerged as effective materials for an immense variety of applications. The unique network structure of hydrogels enables very high levels of hydrophilicity and biocompatibility, while at the same time exhibiting the soft physical properties associated with living tissue, making them ideal biomaterials. Stimulus-responsive hydrogels have been especially impactful, allowing for unprecedented levels of control over material properties in response to external cues. This enhanced control has enabled groundbreaking advances in healthcare, allowing for more effective treatment of a vast array of diseases and improved approaches for tissue engineering and wound healing. In this extensive review, we identify and discuss the multitude of response modalities that have been developed, including temperature, pH, chemical, light, electro, and shear-sensitive hydrogels. We discuss the theoretical analysis of hydrogel properties and the mechanisms used to create these responses, highlighting both the pioneering and most recent work in all of these fields. Finally, we review the many current and proposed applications of these hydrogels in medicine and industry.

Compression stiffening of brain and its effect on mechanosensing by glioma cells

Many cell types, including neurons, astrocytes and other cells of the central nervous system respond to changes in extracellular matrix or substrate viscoelasticity, and increased tissue stiffness is a hallmark of several disease states including fibrosis and some types of cancers. Whether the malignant tissue in brain, an organ that lacks the protein-based filamentous extracellular matrix of other organs, exhibits the same macroscopic stiffening characteristic of breast, colon, pancreatic, and other tumors is not known. In this study we show that glioma cells like normal astrocytes, respond strongly in vitro to substrate stiffness in the range of 100 to 2000 Pa, but that macroscopic (mm to cm) tissue samples isolated from human glioma tumors have elastic moduli on the order of 200 Pa that are indistinguishable from those of normal brain. However, both normal brain and glioma tissues increase their shear elastic moduli under modest uniaxial compression, and glioma tissue stiffens more strongly under compression than does normal brain. These findings suggest that local tissue stiffness has the potential to alter glial cell function, and that stiffness changes in brain tumors might arise not from increased deposition or crosslinking of collagen-rich extracellular matrix but from pressure gradients that form within the tumors in vivo.

Nonequilibrium dynamics of a confined colloidal bilayer in a planar shear flow

Using Brownian dynamics (BD) simulations we investigate the impact of shear flow on structural and dynamical properties of a system of charged colloids confined to a narrow slit pore. Our model consists of spherical microions interacting through a Derjaguin-Landau-Verwey-Overbeek (DLVO) and a soft-sphere potential. The DLVO parameters were chosen according to a system of moderately charged silica particles (with valence Z~35) in a solvent of low ionic strength. At the confinement conditions considered, the colloids form two well-pronounced layers. In the present study we investigate shear-induced transitions of the translational order and dynamics in the layers, including a discussion of the translational diffusion. In particular, we show that diffusion in the shear-melted state can be described by an analytical model involving a single shear-driven particle in a harmonic trap. We also explore the emergence of zigzag motion characterized by spatiotemporal oscillations of the particles in the layers in the vorticity direction. Similar behavior has been recently observed in experiments of much thicker colloidal films.