Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

Prenatal muscle forces are necessary for vertebral segmentation and disc structure, but not for notochord involution in mice

Embryonic muscle forces are necessary for normal vertebral development and spinal curvature, but their involvement in intervertebral disc (IVD) development remains unclear. The aim of the current study was to determine how muscle contractions affect (1) notochord involution and vertebral segmentation, and (2) IVD development including the mechanical properties and morphology, as well as collagen fibre alignment in the annulus fibrosus. Muscular dysgenesis (mdg) mice were harvested at three prenatal stages: at Theiler Stage (TS)22 when notochord involution starts, at TS24 when involution is complete, and at TS27 when the IVD is formed. Vertebral and IVD development were characterised using histology, immunofluorescence, and indentation testing. The results revealed that notochord involution and vertebral segmentation occurred independently of muscle contractions between TS22 and TS24. However, in the absence of muscle contractions, we found vertebral fusion in the cervical region at TS27, along with (i) a displacement of the nucleus pulposus towards the dorsal side, (ii) a disruption of the structural arrangement of collagen in the annulus fibrosus, and (iii) an increase in viscous behaviour of the annulus fibrosus. These findings emphasise the important role of mechanical forces during IVD development, and demonstrate a critical role of muscle loading during development to enable proper annulus fibrosus formation. They further suggest a need for mechanical loading in the creation of fibre-reinforced tissue engineering replacement IVDs as a therapy for IVD degeneration.

Application of multi-element viscoelastic models to freshness evaluation of beef based on the viscoelasticity principle

The aims of this work were to develop multi-element viscoelastic models for beef and apply them to detect total volatile basic nitrogen (TVB-N) content for freshness evaluation. The deformation data were collected by a viscoelasticity detection system that employed the airflow and laser technique. Then, TVB-N contents were measured to determine the freshness of samples during storage. A universal global optimization (UGO) algorithm was applied to fit the deformation data. Various multi-element viscoelastic models including the Burgers, six-element and eight-element models were built using the obtained fitting parameters, and different viscoelastic parameters representing the degree of beef spoilage were obtained. All the viscoelastic parameters of each multi-element model and parameter combinations of the selected six-element model were employed to build mathematical models for predicting TVB-N content by support vector machine regression (SVR). In comparison, the six-element model with all the viscoelastic parameters performed the best and was determined to predict TVB-N content with correlation coefficient in the prediction set (R_P ) of 0.891 and root mean squared error in the prediction set (RMSEP) of 1.467 mg/100 g. Based on the results of parameter combinations, combination (E₂ , E₃ , E₁ , η₁ , η₂ ) from the six-element model performed the best, which was comparatively inferior to all the viscoelastic parameters of the six-element model. Results demonstrated that it was possible to predict TVB-N content for freshness evaluation by applying method of developing multi-element model based on the viscoelasticity with chemometrics.

Displacement of a bubble located at a fluid-viscoelastic medium interface

A model for estimating the displacement of a bubble located at a fluid-viscoelastic medium interface in response to acoustic radiation force is presented by extending the model for a spherical object embedded in a bulk material. The effects of the stiffness and viscosity of the viscoelastic medium and the amplitude and duration of the excitation force on bubble displacement were investigated using the proposed model. The results show that bubble displacement has a nonlinear relationship with excitation duration and viscosity. The time at which the steady state is reached increases with increasing medium viscosity and decreasing medium stiffness.

Correlation between stress drop and applied strain as a biomarker for tumor detection

This is the first study to measure the viscoelastic behavior of tumor tissues using stepwise compression-relaxation testing, and investigate the measured (Δσ-ε) relation between stress drop (Δσ) and applied strain (ε) as a biomarker for tumor detection. Stepwise compression-relaxation testing was implemented via a 2D tactile sensor to measure stress drop at each applied strain of a sample. Pearson correlation analysis was conducted to quantify the measured Δσ-ε relation as slope of stress drop versus applied strain (m=Δσ/ε) and coefficient of determination (R²). The measured results on soft materials revealed no dependency of coefficient of determination on the testing parameters and dependency of slope on them. Three groups of tissues: five mouse breast tumor (BT) tissues ex vivo, two mouse pancreatic tumor (PT) tissues in vivo and six normal tissues, were measured by using different testing parameters. Coefficient of determination was found to show significant difference among the center, edge and outside sites of all the BT tissues, and no difference between the BT outside sites and the normal tissues. Coefficient of determination also revealed significant difference between before and after treatment of the PT tissues, and no difference between the PT tissues after treatment and the normal tissues. Moreover, coefficient of determination of the PT tissues before treatment was found to be significantly different from that of the BT center sites, but slope failed to capture their difference. Dummy tumors made of silicon rubbers were found to behave differently from the native tumors. By removing the need of fitting the time-dependent data with a viscoelastic model, this study offered a time-efficient solution to quantifying the viscosity for tumor detection.

In Vivo Noninvasive Measurement of Young's Modulus of Elasticity in Human Eyes: A Feasibility Study

PURPOSE

Abnormal ocular biomechanical properties may be important for understanding the risk of glaucoma. However, there are no clinical methods for measuring standard material properties in patients. In this feasibility study we demonstrated proof-of-principle for a novel method, ultrasound surface wave elastography (USWE), to determine the in vivo Young's modulus of elasticity of corneas in normal human eyes.

METHODS

In total, 20 eyes of 10 healthy subjects (mean age, 51.4±7.2; ±SD; range, 43 to 64 y) were studied. A spherical-tipped probe (3-mm diameter) was placed on closed eyelids and generated a gentle harmonic vibration at 100 Hz for 0.1 second. Wave speed propagation in the cornea was measured by USWE, and Young's modulus was calculated from the wave speed. Associations between Young's modulus and intraocular pressure (IOP), age, central corneal thickness, and axial length were explored by the Pearson correlation. Statistical significance was determined by using generalized estimating equation models to account for possible correlation between fellow eyes.

RESULTS

Mean IOP was 12.8±2.7 mm Hg. Mean wave speed in the cornea was 1.82±0.10 m/s. Young's modulus of elasticity was 696±113 kPa and was correlated with IOP (r=0.57; P=0.004), but none of the other variables (P>0.1).

CONCLUSIONS

USWE is a novel noninvasive technique for measuring ocular biomechanical properties. Corneal Young's modulus in normal eyes is associated with IOP, consistent with measurements in cadaver eyes. Further work is needed to determine elasticity in other ocular tissues, particularly the sclera, and if elasticity is altered in glaucoma patients.

Manufacturing of hydrogel biomaterials with controlled mechanical properties for tissue engineering applications

Hydrogels have been recognized as crucial biomaterials in the field of tissue engineering, regenerative medicine, and drug delivery applications due to their specific characteristics. These biomaterials benefit from retaining a large amount of water, effective mass transfer, similarity to natural tissues and the ability to form different shapes. However, having relatively poor mechanical properties is a limiting factor associated with hydrogel biomaterials. Controlling the biomechanical properties of hydrogels is of paramount importance. In this work, firstly, mechanical characteristics of hydrogels and methods employed for characterizing these properties are explored. Subsequently, the most common approaches used for tuning mechanical properties of hydrogels including but are not limited to, interpenetrating polymer networks, nanocomposites, self-assembly techniques, and co-polymerization are discussed. The performance of different techniques used for tuning biomechanical properties of hydrogels is further compared. Such techniques involve lithography techniques for replication of tissues with complex mechanical profiles; microfluidic techniques applicable for generating gradients of mechanical properties in hydrogel biomaterials for engineering complex human tissues like intervertebral discs, osteochondral tissues, blood vessels and skin layers; and electrospinning techniques for synthesis of hybrid hydrogels and highly ordered fibers with tunable mechanical and biological properties. We finally discuss future perspectives and challenges for controlling biomimetic hydrogel materials possessing proper biomechanical properties.

STATEMENT OF SIGNIFICANCE

Hydrogels biomaterials are essential constituting components of engineered tissues with the applications in regenerative medicine and drug delivery. The mechanical properties of hydrogels play crucial roles in regulating the interactions between cells and extracellular matrix and directing the cells phenotype and genotype. Despite significant advances in developing methods and techniques with the ability of tuning the biomechanical properties of hydrogels, there are still challenges regarding the synthesis of hydrogels with complex mechanical profiles as well as limitations in vascularization and patterning of complex structures of natural tissues which barricade the production of sophisticated organs. Therefore, in addition to a review on advanced methods and techniques for measuring a variety of different biomechanical characteristics of hydrogels, the new techniques for enhancing the biomechanics of hydrogels are presented. It is expected that this review will profit future works for regulating the biomechanical properties of hydrogel biomaterials to satisfy the demands of a variety of different human tissues.

Lung Ultrasound Surface Wave Elastography: A Pilot Clinical Study

A lung ultrasound surface wave elastography (LUSWE) technique is developed to measure superficial lung tissue elastic properties. The purpose of this paper was to translate LUSWE into clinical studies for assessing patients with interstitial lung disease (ILD) and present the pilot data from lung measurements on 10 healthy subjects and 10 patients with ILD. ILD includes multiple lung disorders in which the lung tissue is distorted and stiffened by tissue fibrosis. Chest radiography and computed tomography are the most commonly used techniques for assessing lung disease, but they are associated with radiation and cannot directly measure lung elastic properties. LUSWE provides a noninvasive and nonionizing technique to measure the elastic properties of superficial lung tissue. LUSWE was used to measure regions of both lungs through six intercostal spaces for patients and healthy subjects. The data are presented as wave speed at 100, 150, and 200 Hz at the six intercostal spaces. As an example, the surface wave speeds are, respectively, 1.88 ± 0.11 m/s at 100 Hz, 2.74 ± 0.26 m/s at 150 Hz, and 3.62 ± 0.13 m/s at 200 Hz for a healthy subject in the upper right lung; this is in comparison to measurements from an ILD patient of 3.3 ± 0.37 m/s at 100 Hz, 4.38 ± 0.33 m/s at 150 Hz, and 5.24 ± 0.44 m/s at 200 Hz in the same lung space. Significant differences in wave speed between healthy subjects and ILD patients were found. LUSWE is a safe and noninvasive technique which may be useful for assessing ILD.

Measuring nanoscale viscoelastic parameters of cells directly from AFM force-displacement curves

Force-displacement (F-Z) curves are the most commonly used Atomic Force Microscopy (AFM) mode to measure the local, nanoscale elastic properties of soft materials like living cells. Yet a theoretical framework has been lacking that allows the post-processing of F-Z data to extract their viscoelastic constitutive parameters. Here, we propose a new method to extract nanoscale viscoelastic properties of soft samples like living cells and hydrogels directly from conventional AFM F-Z experiments, thereby creating a common platform for the analysis of cell elastic and viscoelastic properties with arbitrary linear constitutive relations. The method based on the elastic-viscoelastic correspondence principle was validated using finite element (FE) simulations and by comparison with the existed AFM techniques on living cells and hydrogels. The method also allows a discrimination of which viscoelastic relaxation model, for example, standard linear solid (SLS) or power-law rheology (PLR), best suits the experimental data. The method was used to extract the viscoelastic properties of benign and cancerous cell lines (NIH 3T3 fibroblasts, NMuMG epithelial, MDA-MB-231 and MCF-7 breast cancer cells). Finally, we studied the changes in viscoelastic properties related to tumorigenesis including TGF-β induced epithelial-to-mesenchymal transition on NMuMG cells and Syk expression induced phenotype changes in MDA-MB-231 cells.

Ultra-fast line-field low coherence holographic elastography using spatial phase shifting

Optical coherence elastography (OCE) is an emerging technique for quantifying tissue biomechanical properties. Generally, OCE relies on point-by-point scanning. However, long acquisition times make point-by-point scanning unfeasible for clinical use. Here we demonstrate a noncontact single shot line-field low coherence holography system utilizing an automatic Hilbert transform analysis based on a spatial phase shifting technique. Spatio-temporal maps of elastic wave propagation were acquired with only one air-pulse excitation and used to quantify wave velocity and sample mechanical properties at a line rate of 200 kHz. Results obtained on phantoms were correlated with data from mechanical testing. Finally, the stiffness of porcine cornea at different intraocular pressures was also quantified in situ.

Indentation Measurements to Validate Dynamic Elasticity Imaging Methods

We describe macro-indentation techniques for estimating the elastic modulus of soft hydrogels. Our study describes (a) conditions under which quasi-static indentation can validate dynamic shear-wave imaging estimates and (b) how each of these techniques uniquely biases modulus estimates as they couple to the sample geometry. Harmonic shear waves between 25 and 400 Hz were imaged using ultrasonic Doppler and optical coherence tomography methods to estimate shear dispersion. From the shear-wave speed of sound, average elastic moduli of homogeneous samples were estimated. These results are compared directly with macroscopic indentation measurements measured two ways. One set of measurements applied Hertzian theory to the loading phase of the force-displacement curves using samples treated to minimize surface adhesion forces. A second set of measurements applied Johnson-Kendall-Roberts theory to the unloading phase of the force-displacement curve when surface adhesions were significant. All measurements were made using gelatin hydrogel samples of different sizes and concentrations. Agreement within 5% among elastic modulus estimates was achieved for a range of experimental conditions. Consequently, a simple quasi-static indentation measurement using a common gel can provide elastic modulus measurements that help validate dynamic shear-wave imaging estimates.

Non-contact single shot elastography using line field low coherence holography

Optical elastic wave imaging is a powerful technique that can quantify local biomechanical properties of tissues. However, typically long acquisition times make this technique unfeasible for clinical use. Here, we demonstrate non-contact single shot elastographic holography using a line-field interferometer integrated with an air-pulse delivery system. The propagation of the air-pulse induced elastic wave was imaged in real time, and required a single excitation for a line-scan measurement. Results on tissue-mimicking phantoms and chicken breast muscle demonstrated the feasibility of this technique for accurate assessment of tissue biomechanical properties with an acquisition time of a few milliseconds using parallel acquisition.

Improving Displacement Signal-to-Noise Ratio for Low-Signal Radiation Force Elasticity Imaging Using Bayesian Techniques

Radiation force-based elasticity imaging is currently being investigated as a possible diagnostic modality for a number of clinical tasks, including liver fibrosis staging and the characterization of cardiovascular tissue. In this study, we evaluate the relationship between peak displacement magnitude and image quality and propose using a Bayesian estimator to overcome the challenge of obtaining viable data in low displacement signal environments. Displacement data quality were quantified for two common radiation force-based applications, acoustic radiation force impulse imaging, which measures the displacement within the region of excitation, and shear wave elasticity imaging, which measures displacements outside the region of excitation. Performance as a function of peak displacement magnitude for acoustic radiation force impulse imaging was assessed in simulations and lesion phantoms by quantifying signal-to-noise ratio (SNR) and contrast-to-noise ratio for varying peak displacement magnitudes. Overall performance for shear wave elasticity imaging was assessed in ex vivo chicken breast samples by measuring the displacement SNR as a function of distance from the excitation source. The results show that for any given displacement magnitude level, the Bayesian estimator can increase the SNR by approximately 9 dB over normalized cross-correlation and the contrast-to-noise ratio by a factor of two. We conclude from the results that a Bayesian estimator may be useful for increasing data quality in SNR-limited imaging environments.

On the mechanical characterization and modeling of polymer gel brain substitute under dynamic rotational loading

The use of highly sensitive soft materials has become increasingly apparent in the last few years in numerous industrial fields, due to their viscous and damping nature. Unfortunately these materials remain difficult to characterize using conventional techniques, mainly because of the very low internal forces supported by these materials especially under high strain-rates of deformation. The aim of this work is to investigate the dynamic response of a polymer gel brain analog material under specific rotational-impact experiments. The selected polymer gel commercially known as Sylgard 527 has been studied using a specific procedure for its experimental characterization and numerical modeling. At first an indentation experiment was conducted at several loading rates to study the strain rate sensitivity of the Sylgard 527 gel. During the unloading several relaxation tests were performed after indentation, to assess the viscous behavior of the material. A specific numerical procedure based on moving least square approximation and response surface method was then performed to determine adequate robust material parameters of the Sylgard 527 gel. A sensitivity analysis was assessed to confirm the robustness of the obtained material parameters. For the validation of the obtained material model, a second experiment was conducted using a dynamic rotational loading apparatus. It consists of a metallic cylindrical cup filled with the polymer gel and subjected to an eccentric transient rotational impact. Complete kinematics of the cup and the large strains induced in the Sylgard 527 gel, have been recorded at several patterns by means of optical measurement. The whole apparatus was modeled by the Finite Element Method using explicit dynamic time integration available within Ls-dyna(®) software. Comparison between the physical and the numerical models of the Sylgard 527 gel behavior under rotational choc shows excellent agreements.

Modeling transversely isotropic, viscoelastic, incompressible tissue-like materials with application in ultrasound shear wave elastography

In this paper, we propose a method to model the shear wave propagation in transversely isotropic, viscoelastic and incompressible media. The targeted application is ultrasound-based shear wave elastography for viscoelasticity measurements in anisotropic tissues such as the kidney and skeletal muscles. The proposed model predicts that if the viscoelastic parameters both across and along fiber directions can be characterized as a Voigt material, then the spatial phase velocity at any angle is also governed by a Voigt material model. Further, with the aid of Taylor expansions, it is shown that the spatial group velocity at any angle is close to a Voigt type for weakly attenuative materials within a certain bandwidth. The model is implemented in a finite element code by a time domain explicit integration scheme and shear wave simulations are conducted. The results of the simulations are analyzed to extract the shear wave elasticity and viscosity for both the spatial phase and group velocities. The estimated values match well with theoretical predictions. The proposed theory is further verified by an ex vivo tissue experiment measured in a porcine skeletal muscle by an ultrasound shear wave elastography method. The applicability of the Taylor expansion to analyze the spatial velocities is also discussed. We demonstrate that the approximations from the Taylor expansions are subject to errors when the viscosities across or along the fiber directions are large or the maximum frequency considered is beyond the bandwidth defined by radii of convergence of the Taylor expansions.