Original contribution
Two-Dimensional Sonoelastographic Shear Velocity Imaging

https://doi.org/10.1016/j.ultrasmedbio.2007.07.011Get rights and content

Abstract

We introduce a novel 2-D sonoelastographic technique for estimating local shear velocities from propagating shear wave interference patterns (termed crawling waves) in this paper. A relationship between the local crawling wave spatial phase derivatives and local shear wave velocity is derived, with phase derivatives estimated using a 2-D autocorrelation technique. Comparisons were made between the 2-D sonoelastographic shear velocity estimation technique and its computationally simpler 1-D precursor. In general, the 2-D sonoelastographic shear velocity estimator outperformed the 1-D–based technique in terms of accuracy and estimator noise minimization. For both approaches, increasing the estimator kernel size reduces noise levels but lowers spatial resolution. Homogeneous elastic phantom results demonstrate the ability of sonoelastographic shear velocity imaging to quantify the true underlying shear velocity distributions as verified using time-of-flight measurements. Results also indicate that increasing the estimator kernel size increases the transition zone length about boundaries in heterogeneous elastic mediums and may complicate accurate quantification of smaller elastically contrasting lesions. Furthermore, analysis of contrast-to-noise ratio (CNR) values for sonoelastograms obtained in heterogeneous elastic phantoms reveal that the 2-D sonoelastographic shear velocity estimation technique outperforms the 1-D version for a given kernel size in terms of image noise minimization and contrast enhancement. Experimental results from an embedded porcine liver specimen with a radiofrequency ablation (RFA) lesion demonstrates that the 2-D sonoelastographic shear velocity estimation technique minimizes image noise artifacts and yields a consistent lesion boundary when compared with gross pathology. Volume measurements of the RFA lesion obtained from shear velocity sonoelastograms was comparable to that obtained by fluid displacement of the dissected lesion as illustrated by 3-D volume reconstructions. Overall, 2-D sonoelastographic shear velocity imaging was shown to be a promising new approach to characterizing the shear velocity distribution of elastic materials. (E-mail: [email protected])

Introduction

Palpation is a routine physical examination whereby physicians qualitatively assess the elastic properties of soft tissue. During palpation, stiff masses that are discrete and differ from the surrounding tissue are considered suspicious for malignancy. Although these discrete masses may dislocate or feel fixed within the tissue, subtle findings are much more difficult to interpret. Specifically, in many tumor cases, despite the difference in stiffness, the small size of a pathological lesion or its deep location impedes detection and evaluation by palpation. In addition, lesions may or may not exhibit physical properties that allow detection using conventional medical imaging modalities such as computed tomography, magnetic resonance or ultrasound.

For more than two decades, the development of ultrasound-based imaging techniques for depicting the elastic properties of biological tissues has been the focal point of an international research endeavor (Gao et al 1996, Ophir et al 1999, Greenleaf et al 2003). The universal goal of these initiatives revolves around mapping some tissue mechanical property in an anatomically meaningful manner to describe valuable clinical information. Because changes in tissue stiffness are typically indicative of an abnormal pathological process (Anderson and Kissane 1977), imaging parameters related to tissue elasticity may finally provide a reliable gateway for differentiating normal from abnormal tissues.

Vibrational sonoelastography is a tissue elasticity imaging technique that estimates the amplitude response of tissues under harmonic mechanical excitation using ultrasonic Doppler techniques (Lerner et al. 1988). Because of a mathematical relationship between particle vibrational response and received Doppler spectral variance (Huang et al. 1990), low-frequency (50–500 Hz) and low-amplitude (20–100 μm) shear waves propagating in tissue can be visualized using sonoelastography to detect regions of abnormal stiffness (Parker et al. 1998).

Recently, it was shown that interfering shear waves produce slowly propagating interference patterns with an apparent velocity much less than (but proportional to) the underlying true shear velocity (Wu et al. 2004). Termed crawling waves, they are generated using a pair of mechanical sources vibrating at slightly offset frequencies or by continuously phase shifting one of the source excitation signals. The resultant shear wave interference patterns can be visualized in real-time using sonoelastographic imaging techniques. In general, crawling wave images describe shear wave propagation patterns and allow local estimation of shear velocity distributions (Wu et al. 2006; McLaughlin et al 2006; Hoyt et al. 2006). Assuming that the local shear velocity values are proportional to the square root of the shear modulus, spatial mapping of either parameter allows production of quantitative tissue elasticity images.

A real-time sonoelastographic technique for estimating local shear velocities from crawling wave images was introduced by Hoyt et al. (2006). Specifically, a relationship between crawling wave phase derivatives and local shear wave velocity was derived, with phase derivatives estimated using an autocorrelation-based technique. However, this method computes local shear velocities using a 1-D kernel and estimator and is conducted independent of shear wave displacement data in neighboring depth regions. Despite promising initial results using this shear velocity imaging technique, a more accurate and robust estimator may be realized by utilizing a 2-D shear velocity estimation algorithm. In this paper, a 2-D sonoelastographic shear velocity imaging technique is introduced. Performance of this novel tissue elasticity imaging modality is compared in simulation and experiments to results obtained using its 1-D precursor, followed by a conclusion.

Section snippets

Elastic properties of soft tissue

We begin by considering the wave motion equation for a linear and isotropic medium in terms of the displacements as:E2(1+v)2u¯+E2(1+v)(12v)u¯=ρ2u¯t2, where E, v, ρ, u¯ and t are the Young’s modulus, Poisson’s ratio, mass density, displacement vector and time variable, respectively. As described by Landau and Lifshitz (1986), eqn (1) can be decomposed into two decoupled motion equations: one governing longitudinal wave motion and the other governing shear wave motion. In a homogeneous

Methods

To evaluate shear velocity estimation techniques, sonoelastographic simulation programs were implemented using MATLAB 7.0 (Mathworks, Inc., Natick, MA, USA). The first model assumes plane wave conditions and that the instantaneous shear wave interference patterns (i.e., shear wave displacement vector) propagating in a locally homogeneous and isotropic medium can be described by eqn (5). The shear wave signal-to-noise ratio (SNR) was implemented by superimposing 25 dB of Gaussian noise onto the

Methods

Crawling wave datasets were collected from two homogeneous elasticity phantoms with differing shear moduli. The true shear velocities in these phantoms were determined using shear wave time-of-flight measurements. Shear velocity sonoelastograms were generated using the local 1-D and 2-D shear velocity estimation techniques described in the Theory section. From sequences of shear velocity sonoelastograms equating to one full cycle of shear wave motion (deduced from the underlying crawling wave

Conclusions

In this paper, a novel 2-D sonoelastographic technique for estimating local shear velocities from propagating shear wave interference patterns (termed crawling waves) is introduced. A relationship between the local crawling wave spatial phase derivatives and local shear wave velocity is derived with phase derivatives estimated using a 2-D autocorrelation technique. Comparisons were made between the 2-D sonoelastographic shear velocity estimation technique and its computationally simpler 1-D

Acknowledgements

We are grateful for helpful suggestions from Drs. Deborah J. Rubens, John Strang, Zhe Wu and Man Zhang, and for the loan of equipment and expertise from General Electric (GE) Medical Systems. This work was supported by NIH Grant 5 R01 AG16317-05.

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