Fourier-Domain Shift Matching: A Robust Time-of-Flight Approach for Shear Wave Speed Estimation

Fourier energy spectrum centroid: a robust and efficient approach for shear wave speed estimation inω-kspace

Objective.The propagation speed of a shear wave, whether externally or internally induced, in biological tissues is directly linked to the tissue's stiffness. The group shear wave speed (SWS) can be estimated using a class of time-of-flight (TOF) methods in the time-domain or phase speed-based methods in the frequency domain. However, these methods suffer from biased estimations or time-consuming computations, and they are especially prone to wave distortions inin vivocases. In this work, we present a parameter-free, robust, and efficient group SWS estimation method coined as Fourier energy spectrum centroid (FESC).Approach.The proposed FESC method is based on the center of mass inω-kspace. It was evaluated on data from computer simulations with additive Gaussian noise, a commercial elasticity phantom, anex vivopig liver, andin vivobiceps brachii muscles of three young healthy male subjects. The FESC method was compared with two 2D frequency-domain methods: Max-fre, which considers phase SWS at the peak ofk-space, and Fre-regre, which applies linear regression of phase SWS within a fixed bandwidth. Two additional benchmarks included time-domain methods based on cross-correlation (X-Corr) and radon sum transformation (RD).Main results.Statistical results showed that our FESC method and the RD method had comparable accuracy and robustness, outperforming the other benchmark methods. In the simulation and phantom studies, when the signal-to-noise ratio was higher than 25 dB, our FESC showed higher accuracy than RD. In thein vivostudy, our FESC method had better repeatability than RD. Furthermore, the proposed FESC method was 100 times faster than the runner-up method, X-Corr, and 3,000 times faster than the least efficient method, RD.Significance.All results indicated that our proposed Fourier-based method shows promise in reliably and efficiently providing reference values for group SWS in homogeneous bulk media.

Quantitative Shear Wave Speed Assessment for Muscles With the Diagnosis of Taut Bands and/or Myofascial Trigger Points Using Probe Oscillation Shear Wave Elastography: A Pilot Study

OBJECTIVE

To use probe oscillation shear wave elastography (PROSE) with two vibration sources to generate two shear waves in the imaging plane to quantitatively assess the shear wave speeds (SWSs) of muscles with and without the diagnosis of taut bands (TB) and/or myofascial trigger points (MTrPs).

METHODS

Thirty-three patients were scanned with the PROSE technique. Shear waves were generated through continuous vibration of the ultrasound probe, while the shear wave motions were detected using the same probe. SWSs for the sides with and without TBs and/or MTrPs were computed and compared. The pressure pain thresholds (PPTs) were measured as an indicator of maximum pain tolerance of patients. The statistical differences between the SWSs with and without TBs and/or MTrPs with different PPT values were analyzed using the nonparametric Wilcoxon rank-sum test.

RESULTS

The mean SWSs for the sides with TBs and/or MTrPs are faster than that of the contralateral side without TBs and/or MTrPs. A significant difference was observed between mean SWSs with and without TBs and/or MTrPs without any information of PPT, with rank-sum test P <  .005. Additionally, with the information of PPT, a significant difference was observed between mean SWSs for the sides with and without TBs and/or MTrPs, for PPT values between 0 and 50 N/cm2 (P <  .005), but for PPT values between 50 and 90 N/cm2 , it was difficult to differentiate mean SWSs with and without TBs and/or MTrPs.

CONCLUSION

Our preliminary results show that SWSs measured from patients had a significant difference between the mean SWSs with and without TBs and/or MTrPs.

Analyzing acoustoelastic effect of shear wave elastography data for perfused and hydrated soft tissues using a macromolecular network inspired model

Shear wave elastography (SWE) has enhanced our ability to non-invasively make in vivo measurements of tissue elastic properties of animal and human tissues. Recently, researchers have taken advantages of acoustoelasticity in SWE to extract nonlinear elastic properties from soft biological tissues. However, most investigations of the acoustoelastic effects of SWE data (AE-SWE) rely on classic hyperelastic models for rubber-like (dry) materials. In this paper, we focus solely on understanding acoustoelasticity in soft hydrated tissues using SWE data and propose a straightforward approach to modeling the constitutive behavior of soft tissue that has a direct microstructural/macromolecular interpretation. Our approach incorporates two constitutive features relevant to biological tissues into AE-SWE: static dilation of the medium associated with nonstructural components (e.g. tissue hydration and perfusion) and finite extensibility derived from an ideal network of biological filaments. We evaluated the proposed method using data from an in-house tissue-mimicking phantom experiment, and ex vivo and in vivo AE-SWE data available in the SWE literature. In conclusion, predictions made by our approach agreed well with measurements obtained from phantom, ex vivo and in vivo tissue experiments.

A comparison of hyperelastic constitutive models applicable to shear wave elastography (SWE) data in tissue-mimicking materials

Shear wave elastography (SWE) techniques have received substantial attention in recent years. Strong experimental data in SWE suggest that shear wave speed changes significantly due to the known acoustoelastic effect (AE). This presents both challenges and opportunities toward in vivo characterization of biological soft tissues. In this work, under the framework of continuum mechanics, we model a tissue-mimicking material as a homogeneous, isotropic, incompressible, hyperelastic material. Our primary objective is to quantitatively and qualitatively compare experimentally measured acoustoelastic data with model-predicted outcomes using multiple strain energy functions. Our analysis indicated that the classic Neo-Hookean and Mooney-Rivlin models are inadequate for modeling the AE in tissue-mimicking materials. However, a subclass of strain energy functions containing both high-order/exponential term(s) and second-order invariant dependence showed good agreement with experimental data. Based on data investigated, we also found that discrepancies may exist between parameters inversely estimated from uniaxial compression and SWE data. Overall, our findings may improve our understanding of clinical SWE results.