15.1 Vibration Amplitude Sonoelastography: Early Results

Vibration amplitude sonoelastography entails the application of a continuous low‐frequency vibration (40–1000 Hz) to excite internal shear waves within the tissue of interest [1, 2]. A disruption in the normal vibration patterns will result if a stiff inhomogeneity is present in soft tissue surroundings. A real‐time vibration image can be created by Doppler detection algorithms. Modal patterns can be created in certain organs with regular boundaries. The shear wave speed of sound in the tissue of these organs can be ascertained with the information revealed by these patterns [3].

Figure 15.1 reproduces the first vibration‐amplitude sonoelastography image [1, 2], which marked the emergence of elastography imaging from the previous studies of tissue motion. The vibration within a sponge and saline phantom containing a harder area (the dark region) is depicted by this low resolution image. Range‐gated Doppler was used to calculate the vibration amplitude of the interior of the phantom as it was vibrated from below. By 1990, a modified color Doppler instrument was used by the University of Rochester group to create real‐time vibration‐amplitude sonoelastography images. In these images, vibration above a certain threshold (in the 2 µm range) produced a saturated color (Figure 15.2).

Measurements of tissue elastic constants, finite‐element modeling results, and phantom and ex vivo tissue sonoelastography were later reported [5–7]. Thus, by the end of 1990, the working elements of vibration elastography (sonoelastography and sonoelasticity were other names used at the time) were in place, including real‐time imaging techniques and stress‐strain analysis of tissues such as prostate, with finite‐element models and experimental images demonstrating conclusively that small regions of elevated Young's modulus could be imaged and detected using conventional Doppler‐imaging scanners.

15.2 Sonoelastic Theory

Along with the useful finite‐element approach of Lerner et al. [5] and Parker et al. [7], there were important theoretical questions to be answered by analytical or numerical techniques. How did vibration fields behave in the presence of elastic inhomogeneities? What is the image contrast of lesions in a vibration field, and how does the contrast depend on the choice of parameters? How do we optimally detect sinusoidal vibration patterns and image them using Doppler or related techniques? These important issues were addressed in a series of papers through the 1990s. One foundational result was published in 1992 under the title: “Sonoelasticity of Organs, Shear Waves Ring a Bell” [3]. This paper demonstrated experimental proofs that vibrational eigenmodes could in fact be created in whole organs, including the liver and kidneys, where extended surfaces create reflections of sinusoidal steady‐state shear waves. Lesions would produce a localized perturbation of the eigenmode pattern, and the background Young's modulus could be calculated from the patterns at discrete eigenfrequencies. Thus, both quantitative and relative imaging contrast detection tasks could be completed with vibration elastography in a clinical setting, in vivo, by 1992. A later review of eigenmodes and a strategy for using multiple frequencies simultaneously (called “chords”) was given in Taylor et al. [8].

Furthermore, a vibration‐amplitude analytical model was created [9, 10]. This model used a sonoelastic Born approximation to solve the wave equations in an inhomogeneous, isotropic medium. The total shear wave field inside the medium can be expressed as

(15.1)

where is the homogeneous or incident field, and is the field scattered by the inhomogeneity. They satisfy, respectively

(15.2)

(15.3)

where is a function of the properties of inhomogeneity and is the wavenumber of shear wave propagation at a frequency . The theory accurately describes how a hard or soft lesion appear as disturbances in a vibration pattern. Figure 15.3 summarizes the theoretical and experimental trends.

Signal processing estimators were also developed in the study of vibration amplitude sonoelastography. Huang et al. suggested a method to estimate a quantity denoted , which is proportional to the vibration amplitude of the target, from the spectral spread [11]. They found a simple correlation between and the Doppler spectral spread

(15.4)

where is the vibration frequency of the vibrating target. This is an uncomplicated and very useful property of the Bessel Doppler function. The effect of noise, sampling, and nonlinearity on the estimation was also considered. In their later work, they studied real‐time estimators of vibration amplitude, phase, and frequency that could be used for a variety of vibration sonoelastography techniques [12].

Finally, an overall theoretical approach that places vibration sonoelastography on a biomechanical spectrum with other techniques including compression elastography, magnetic resonance elastography (MRE), and the use of impulsive radiation force excitations, is found in “A Unified View of Imaging the Elastic Properties of Tissues” [13]. This perspective is highlighted in Chapter of this book.

15.3 Vibration Phase Gradient Sonoelastography

In parallel to the early work at the University of Rochester, a vibration phase gradient approach to sonoelastography was developed by Sato and collaborators at the University of Tokyo [14]. They mapped the amplitude and the phase of low frequency wave propagation inside tissue. From this mapping, they were able to derive wave‐propagation velocity and dispersion properties, which are directly linked to the elastic and viscous characteristics of tissue.

The phase‐modulated (PM) Doppler spectrum of the signal returned from sinusoidally oscillating objects approximates that of a pure‐tone frequency modulation (FM) process, as given in Eq. (15.2). This similarity indicates that the tissue vibration amplitude and phase of tissue motion may be estimated from the ratios of adjacent harmonics. The amplitude ratio between contiguous Bessel bands of the spectral signal is

(15.5)

where is the amplitude at the i‐th harmonic, is the unknown amplitude of vibration in the tissue, and is an i‐th order Bessel function. can be estimated from the experimental data if is calculated as a function of beforehand. The phase of the vibration was calculated from the quadrature signals.

The display of wave propagation as a moving image is permitted by constructing phase and amplitude maps (Figure 15.4) as a function of time. The use of a minimum squared error algorithm to estimate the direction of wave propagation and to calculate phase and amplitude gradients in this direction allows images of amplitude and phase to be computed offline. By assuming that the shear viscosity effect is negligible at low frequencies, Sato's group obtained preliminary in vivo results [14].

Sato's technique was used and refined by Levinson [15], who developed a more general model of tissue viscoelasticity and a linear recursive filtering algorithm based on cubic B‐spline functions. Levinson took the Fourier transform of the wave equation and derived the frequency‐domain displacement equation for a linear, homogeneous, isotropic viscoelastic material. From this, equations that relate the shear modulus of elasticity and viscosity to the wave number and the attenuation coefficient of the wave can be derived.

Levinson et al. [15] conducted a series of experiments on the quadriceps muscle group in human thighs. It was assumed that shear waves predominate and that viscosity at low frequencies is negligible. Phase gradient images of the subjects' thighs under conditions of active muscle contraction enabled the calculation of Young's modulus of elasticity. The tension applied to the muscle was controlled using a pulley device. The measured vibration propagation speed and the calculated values of Young's modulus increased with the increasing degrees of contraction needed to counteract the applied load.

15.4 Crawling Waves

A fascinating extension of vibration sonoelastography is the use of an interference pattern formed by two parallel shear wave sources. The interference patterns reveal the underlying local elastic modulus of the tissue. The term “crawling waves” comes from the useful fact that by implementing a slight frequency difference, typically on the order of 0.1 Hz, between the two parallel sources, the interference pattern will move across the imaging plane at a speed controlled by the sources [16]. Thus, the crawling waves are readily visualized by conventional Doppler imaging scanners at typical Doppler frame rates; there is no need for ultrafast scanning. Other advantages of crawling waves include: (1) the region of interest excited between the two sources is large; (2) most of the energy in the crawling waves is aligned in the Doppler (axial) direction; and (3) a number of analysis or estimation schemes can be applied in a straightforward manner to derive the quantitative estimate of local shear wave velocity and Young's modulus. Crawling waves can also be implemented by a number of techniques including mechanical line sources, surface applicators, or radiation force excitations of parallel beams.

The use of crawling waves was first described in 2004 by Wu et al. at the University of Rochester [16]. It was shown that crawling waves could be used to accurately derive the Young's modulus of materials and to delineate stiff inclusions [17–20]. Estimators of shear wave speed and Young's modulus and the shear wave attenuation are derived by Hoyt et al. [21–23] and McLaughlin et al. [24].

Implementation into scanning probes can be accomplished by utilizing radiation force excitation along parallel beams [25–27], or by utilizing a pair of miniature vibration sources [28].

15.5 Clinical Results

The initial applications of amplitude sonoelastography were to characterize average tissue properties using eigenmode information [3, 29] and to identify stiff lesions by the amplitude contrast effect. In particular, the demonstration of improved detectability of prostate cancer was published in Radiology in 1995 [30]. This work was then adapted to in vivo and 3D studies of the prostate [8, 19, 31–34], and it was demonstrated that the sensitivity and specificity of prostate cancer detection could be markedly improved using sonoelasticity. Separately, it was shown that the definition and volumetric measurement of thermal lesions in tissue could be greatly improved by sonoelastography [35–38].

Applications of crawling waves include the ex vivo prostate [39–41], in vivo muscle [42], and ex vivo liver [20]. An example from ex vivo prostate is given in Figures 15.5a and 15.5b.

Other applications of crawling waves include quantification of the elastic properties of muscle [42, 43], thyroid [44], and fatty livers [45–48].

15.6 Conclusion

There are a number of key advantages to “sonoelastography” imaging and crawling waves imaging. First, in sinusoidal steady‐state shear wave excitation, the amplitude contrast effect (of stiff lesions) can be seen with any Doppler imaging platform; it is not necessary to have any synchronization system or specialized platform [49]. Second, by proper choice of shear wave frequency, entire organs can be covered with shear waves, providing large ROIs for analysis [3]. This fact has been used to great advantage in MRE, as well. Finally, the crawling waves approach provides data that can be analyzed with a number of simple local estimators, while producing comparable resolution and accuracy to the very best shear wave tracking approaches using radiation force excitations [50]. In addition, the crawling waves patterns can be produced simply by external transducers [18, 28] or by an alternating pair of radiation force beams, one on the right and on the left of the ROI [51, 52]. Thus these techniques are widely applicable and efficacious for studies of tissue elastography in the breast, liver, thyroid, muscle, and other soft tissues.

Acknowledgments

This work was supported by the Hajim School of Engineering and Applied Sciences at the University of Rochester, and by National Institutes of Health grants R01 AG016317 and R01 AG029804.

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