Spectral Quantification of Nonlinear Elasticity Using Acoustoelasticity and Shear-Wave Dispersion

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.

Imaging the Local Nonlinear Viscoelastic Properties of Soft Tissues: Initial Validation and Expected Benefits

Imaging tissue mechanical properties has shown promise in noninvasive assessment of numerous pathologies. Researchers have successfully measured many linear tissue mechanical properties in laboratory and clinical settings. Currently, multiple complex mechanical effects such as frequency-dependence, anisotropy, and nonlinearity are being investigated separately. However, a concurrent assessment of these complex effects may enable more complete characterization of tissue biomechanics and offer improved diagnostic sensitivity. In this work, we report for the first time a method to map the frequency-dependent nonlinear parameters of soft tissues on a local scale. We recently developed a nonlinear elastography model that combines strain measurements from arbitrary tissue compression with radiation-force-based broadband shear wave speed (WS) measurements. Here, we extended this model to incorporate local measurements of frequency-dependent shear modulus. This combined approach provides a local frequency-dependent nonlinear parameter that can be obtained with arbitrary, clinically realizable tissue compression. Initial assessments using simulations and phantoms validate the accuracy of this approach. We also observed improved contrast in nonlinearity parameter at higher frequencies. Results from ex-vivo liver experiments show 32, 25, 34, and 38 dB higher contrast in elastograms than traditional linear elasticity, elastic nonlinearity, viscosity, and strain imaging methods, respectively. A lesion, artificially created by injection of glutaraldehyde into a liver specimen, showed a 59% increase in the frequency-dependent nonlinear parameter and a 17% increase in contrast ratio.

Nonlinear Characterization of Tissue Viscoelasticity With Acoustoelastic Attenuation of Shear Waves

Shear-wave elastography (SWE) measures shear-wave speed (SWS), which is related to the underlying shear modulus of soft tissue. SWS in soft tissue changes depending on the amount of external strain that soft tissue is subjected to due to the acoustoelastic (AE) phenomenon. In the literature, variations of SWS as a function of applied uniaxial strain were used for nonlinear characterization, assuming soft tissues to be elastic, although soft tissues are indeed viscoelastic in nature. Hence, nonlinear characterization using SWS alone is insufficient. In this work, we use SWS together with shear-wave attenuation (SWA) during incremental quasi-static compressions in order to derive biomechanical characterization based on the AE theory in terms of well-defined storage and loss moduli. As part of this study, we also quantify the effect of applied strain on measurements of SWS and SWA since such confounding effects need to be taken into account when using SWS and/or SWA, e.g., for staging a disease state, while such effects can also serve as an additional imaging biomarker. Our results from tissue-mimicking phantoms with varying oil percentages and ex vivo porcine liver experiments demonstrate the feasibility of our proposed methods. In both experiments, SWA was observed to decrease with applied strain. For 10% compression in ex vivo livers, shear-wave attenuation decreased, on average, by 28% (93 Np/m), while SWS increased, on average, by 20% (0.26 m/s).

Measured Hyperelastic Properties of Cervical Tissue with Shear-Wave Elastography

The nonlinear mechanical behaviour of cervical tissue causes unpredictable changes in measured elastograms when pressure is applied. These uncontrolled variables prevent the reliable measurement of tissue elasticity in a clinical setting. Measuring the nonlinear properties of tissue is difficult due to the need for both shear modulus and strain to be taken simultaneously. A simulation-based method is proposed in this paper to resolve this. This study describes the nonlinear behaviour of cervical tissue using the hyperelastic material models of Demiray–Fung and Veronda–Westmann. Elastograms from 33 low-risk patients between 18 and 22 weeks gestation were obtained. The average measured properties of the hyperelastic material models are: Demiray–Fung—A1α = 2.07 (1.65–2.58) kPa, α = 6.74 (4.07–19.55); Veronda–Westmann—C1C2 = 4.12 (3.24–5.04) kPa, C2 = 4.86 (2.86–14.28). The Demiray–Fung and Veronda–Westmann models performed similarly in fitting to the elastograms with an average root mean square deviation of 0.41 and 0.47 ms−1, respectively. The use of hyperelastic material models to calibrate shear-wave speed measurements improved the consistency of measurements. This method could be applied in a large-scale clinical setting but requires updated models and higher data resolution.

Speed of sound and shear wave speed for calf soft tissue composition and nonlinearity assessment

Background

The purpose of this study was threefold: (I) to study the correlation of speed-of-sound (SoS) and shear-wave-speed (SWS) ultrasound (US) in the gastrocnemius muscle, (II) to use reproducible tissue compression to characterize tissue nonlinearity effects, and (III) to compare the potential of SoS and SWS for tissue composition assessment.

Methods

Twenty gastrocnemius muscles of 10 healthy young subjects (age range, 23-34 years, two females and eight males) were prospectively examined with both clinical SWS (GE Logiq E9, in m/s) and a prototype system that measures SoS (in m/s). A reflector was positioned opposite the US probe as a timing reference for SoS, with the muscle in between. Reproducible tissue compression was applied by reducing probe-reflector distance in 5 mm steps. The Ogden hyperelastic model and the acoustoelastic theory were used to characterize SoS and SWS variations with tissue compression and extract novel metrics related to tissue nonlinearity. The body fat percentage (BF%) of the subjects was estimated using bioelectrical impedance analysis.

Results

A weak negative correlation was observed between SWS and SoS (r=-0.28, P=0.002). SWS showed an increasing trend with increasing tissue compression (P=0.10) while SoS values decayed nonlinearly (P<0.001). The acoustoelastic modeling showed a weak correlation for SWS (r=-0.36, P<0.001) but a very strong correlation for SoS (r=0.86, P<0.001), which was used to extract the SoS acoustoelastic parameter. SWS showed higher variability between both calves [intraclass correlation coefficient (ICC) =0.62, P=0.08] than SoS (ICC =0.91, P<0.001). Correlations with BF% were strong and positive for SWS (r=0.60, P<0.001), moderate and negative for SoS (r=-0.43, P=0.05), and moderate positive for SoS acoustoelastic parameter (r=0.48, P=0.03).

Conclusions

SWS and SoS provide independent information about tissue elastic properties. SWS correlated stronger with BF% than SoS, but measurements were less reliable. SoS enabled the extraction of novel metrics related to tissue nonlinearity with potential complementary information.

Acousto-elasticity of transversely isotropic incompressible soft tissues: characterization of skeletal striated muscle

Using shear wave elastography, we measure the changes in the wave speed with the stress produced by a striated muscle during isometric voluntary contraction. To isolate the behaviour of an individual muscle from complementary or antagonistic actions of adjacent muscles, we select theflexor digiti minimimuscle, whose sole function is to extend the little finger. To link the wave speed to the stiffness, we develop an acousto-elastic theory for shear waves in homogeneous, transversely isotropic, incompressible solids subject to an uniaxial stress. We then provide measurements of the apparent shear elastic modulus along, and transversely to, the fibre axis for six healthy human volunteers of different age and sex. The results display a great variety across the six subjects. We find that the slope of the apparent shear elastic modulus along the fibre direction changes inversely to the maximum voluntary contraction (MVC) produced by the volunteer. We propose an interpretation of our results by introducing the S (slow) or F (fast) nature of the fibres, which harden the muscle differently and accordingly, produce different MVCs. A natural follow-up on this study is to apply the method to patients with musculoskeletal disorders or neurodegenerative diseases.