Acoustoelasticity in transversely isotropic soft tissues: Quantification of muscle nonlinear elasticity

3D Ultrasound Shear Wave Elastography for Musculoskeletal Tissue Assessment Under Compressive Load: A Feasibility Study

Given its real-time capability to quantify mechanical tissue properties, ultrasound shear wave elastography holds significant promise in clinical musculoskeletal imaging. However, existing shear wave elastography methods fall short in enabling full-limb analysis of 3D anatomical structures under diverse loading conditions, and may introduce measurement bias due to sonographer-applied force on the transducer. These limitations pose numerous challenges, particularly for 3D computational biomechanical tissue modeling in areas like prosthetic socket design. In this feasibility study, a clinical linear ultrasound transducer system with integrated shear wave elastography capabilities was utilized to scan both a calibrated phantom and human limbs in a water tank imaging setup. By conducting 2D and 3D scans under varying compressive loads, this study demonstrates the feasibility of volumetric ultrasound shear wave elastography of human limbs. Our preliminary results showcase a potential method for evaluating 3D spatially varying tissue properties, offering future extensions to computational biomechanical modeling of tissue for various clinical scenarios.

Mechanical properties change of immobilized skeletal muscle in short position measured by shear wave elastography and pure shearing test

The purpose of this study was to evaluate the effects of immobilization on mechanical properties of skeletal muscle over the time. An in vivo rat model was used to investigate the shear modulus change of the flexor carpi ulnaris (FCU) in a short position. Measurements were performed by shear wave elastography (SWE) to compare contralateral and immobilized cases. The results showed a significant increase of 18.1% (p = 3.86. 10-7) in the shear modulus of immobilized skeletal muscle after two weeks (D14) when compared with the contralateral case. For the purposes of comparison, in vitro mechanical pure shearing tests were performed on samples collected from the skeletal muscles of the same rats. Although the difference between contralateral and immobilized cases was 17.6% (p = 0.32) at D14, the shear modulus difference was 35.7% (p = 0.0126 and p = 1.57.10-5 for immobilization and contralateral respectively) between in vivo and in vitro approaches. The mechanical properties changes were then correlated with the density of collagen from histological analysis, and it was shown that the contralateral collagen surface density was 25.4% higher than the immobilized density at D14 (p = 0.001). Thus, the results showed the feasibility of the comparison between the two approaches, which can surely be improved by optimizing the experimental protocols.

Unravelling anisotropic nonlinear shear elasticity in muscles: Towards a non-invasive assessment of stress in living organisms

Acoustoelasticity theory describes propagation of shear waves in uniaxially stressed medium and allows the retrieval of nonlinear elastic coefficients of tissues. In transverse isotropic medium such as muscles the theory leads to 9 different configurations of propagating shear waves (stress axis vs. fibers axis vs. shear wave polarization axis vs. shear wave propagation axis). In this work we propose to use 4 configurations to quantify these nonlinear parameters ex vivo and in vivo. Ex vivo experiments combining ultrasound shear wave elastography and mechanical testing were conducted on iliopsoas pig muscles to quantify three third-order nonlinear coefficients A, H and K that are possibly linked to the architectural structure of muscles. In vivo experiments were performed with human volunteers on biceps brachii during a stretching exercise on an ergometer. A combination of the third order nonlinear elastic parameters was assessed. The knowledge of this nonlinear elastic parameters paves the way to quantify in vivo the local forces produced by muscle during exercise, contraction or movements.

Comparison of ultrasound elastography, magnetic resonance elastography and finite element model to quantify nonlinear shear modulus

Objective. The aim of this study is to validate the estimation of the nonlinear shear modulus (A) from the acoustoelasticity theory with two experimental methods, ultrasound (US) elastography and magnetic resonance elastography (MRE), and a finite element method.Approach. Experiments were performed on agar (2%)-gelatin (8%) phantom considered as homogeneous, elastic and isotropic. Two specific setups were built to ensure a uniaxial stress step by step on the phantom, one for US and a nonmagnetic version for MRE. The stress was controlled identically in both imaging techniques, with a water tank placed on the top of the phantom and filled with increasing masses of water during the experiment. In US, the supersonic shear wave elastography was implemented on an ultrafast US device, driving a 6 MHz linear array to measure shear wave speed. In MRE, a gradient-echo sequence was used in which the three spatial directions of a 40 Hz continuous wave displacement generated with an external driver were encoded successively. Numerically, a finite element method was developed to simulate the propagation of the shear wave in a uniaxially stressed soft medium.Main results. Similar shear moduli were estimated at zero stress using experimental methods,μ0US= 12.3 ± 0.3 kPa andμ0MRE= 11.5 ± 0.7 kPa. Numerical simulations were set with a shear modulus of 12 kPa and the resulting nonlinear shear modulus was found to be -58.1 ± 0.7 kPa. A very good agreement between the finite element model and the experimental models (AUS= -58.9 ± 9.9 kPa andAMRE= -52.8 ± 6.5 kPa) was obtained.Significance. These results show the validity of such nonlinear shear modulus measurement quantification in shear wave elastography. This work paves the way to develop nonlinear elastography technique to get a new biomarker for medical diagnosis.

Nonlinear propagation of quasiplanar shear wave beams in soft elastic media with transverse isotropy

Model equations are developed for shear wave propagation in a soft elastic material that include effects of nonlinearity, diffraction, and transverse isotropy. A theory for plane wave propagation by Cormack [J. Acoust. Soc. Am. 150, 2566 (2021)] is extended to include leading order effects of wavefront curvature by assuming that the motion is quasiplanar, which is consistent with other paraxial model equations in nonlinear acoustics. The material is modeled using a general expansion of the strain energy density to fourth order in strain that comprises thirteen terms defining the elastic moduli. Equations of motion for the transverse displacement components are obtained using Hamilton's principle. The coupled equations of motion describe diffraction, anisotropy of the wave speeds, quadratic and cubic plane wave nonlinearity, and quadratic nonlinearity associated with wavefront curvature. Two illustrative special cases are investigated. Spatially varying shear vertical wave motion in the fiber direction excites a quadratic nonlinear interaction unique to transversely isotropic soft solids that results in axial second harmonic motion with longitudinal polarization. Shear horizontal wave motion in the fiber plane reveals effects of anisotropy on third harmonic generation, such as beam steering and dependence of harmonic generation efficiency on the propagation and fiber directions.

Viscoelasticity assessment for in vivo quantification of muscle contusion injury in rats using shear wave elastography

The aim of the study described here was to investigate the role of viscoelasticity in assessing muscle fibrosis and inflammation in a rat model of contusion using quantitative shear wave elastography (SWE). Unilateral gastrocnemius muscle contusion was induced in 32 male rats using an impactor apparatus. The contralateral muscles served as the control group. SWE was applied to the control group and rats 1, 3, 14 and 21 d after successful modeling (each time point group, n = 8). Histologic features were used as reference standards. The degree of fibrosis was moderately correlated with shear wave speed (r = 0.53), whereas the degree of inflammation was well correlated with shear wave dispersion (SWD) slope (r = 0.74). The area under the receiver operating characteristic curve (AUC) for the dispersion slope for muscle inflammation and fibrosis assessment was 0.87 (95% confidence interval: 0.705-0.963), which exceeded that of the shear wave speed (0.68, 95% confidence interval: 0.494-0.834). The larger decline in dispersion slope in the fibrotic stage than in the inflammation stage (1-d group vs. 14-d group or 21-d group, p < 0.05) indicated better predictive performance than the shear wave speed.

Non-destructive mapping of stress and strain in soft thin films through sound waves

Measuring the in-plane mechanical stress in a taut membrane is challenging, especially if its material parameters are unknown or altered by the stress. Yet being able to measure the stress is of fundamental interest to basic research and practical applications that use soft membranes, from engineering to tissues. Here we present a robust non-destructive technique to measure directly in-situ stress and strain in soft thin films without the need to calibrate material parameters. Our method relies on measuring the speed of elastic waves propagating in the film. Using optical coherence tomography, we verify our method experimentally for a stretched rubber membrane, a piece of cling film (about 10 μm thick), and the leather skin of a traditional Irish frame drum. We find that our stress predictions are highly accurate and anticipate that our technique could be useful in applications ranging from soft matter devices to biomaterial engineering and medical diagnosis.