Nonlinear Ultrasound Radiation-Force Elastography

Nonlinear Ultrasound Radiation-Force Elastography

Alexia Giannoula (University of Toronto, Canada) and Richard S.C. Cobbold (University of Toronto, Canada)
DOI: 10.4018/978-1-60566-314-2.ch024
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“Elastography” or “elasticity imaging” can be defined as the science and methodology of estimating the mechanical properties of a medium (including soft tissue). In this chapter, an overview of elastography and its relation to tissue pathology will be presented. The basic principles of the static and dynamic methods will be described with special emphasis on the dynamic methods that rely on the acoustic radiation force of ultrasound. Of interest are the low-frequency narrowband shear waves that can be generated by a modulated radiation force produced by the interference of two continuous-wave (CW) ultrasound beams of slightly different frequencies. The advantages of using narrowband shear waves to estimate the viscoelastic properties of tissue will be discussed. Furthermore, an implementation of the inverse-problem approach will be presented and it will be shown how harmonic maps of the local shear modulus and viscosity can be reconstructed based on both the fundamental and higher-harmonic components of the propagated narrowband shear waves.
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The elasticity of soft tissues depends, to a large extent, on their molecular building blocks (fat, collagen, etc.), and on the microscopic and macroscopic structural organization of these blocks (Fung, 1981). Pathological changes are generally correlated with local changes in tissue stiffness (Figure 1). Many cancers, such as scirrhous carcinoma of the breast, liver metastases, prostatic carcinoma, and thyroid cancer, appear as extremely hard nodules (Anderson, 1984). Other types of breast cancers (e.g. intraductal and papillary carcinoma) are soft (Ariel, 1987). Other diseases involve fatty and/or collagenous deposits, which increase or decrease tissue elasticity. The standard medical practice of soft tissue palpation is based on qualitative assessment of the low-frequency stiffness of tissue and has been used for centuries by physicians to distinguish between normal and diseased tissues. Palpation is sometimes used to assess organs such as the liver, and it is not uncommon for surgeons at the time of laparotomy to palpate tumors that were not detected preoperatively using conventional imaging methods, such as Ultrasound, Computer Tomography (CT), or Magnetic Resonance Imaging (MRI), since none of these modalities currently provides the type of information elicited by palpation.

Figure 1.

(a) Sonogram and (b) elastogram of an in-vivo benign breast tumour (fibroadenoma) and (c) sonogram and (d) elastogram of an in-vivo malignant breast tumour (invasive ductal carcinoma). Note that black indicates stiff and white indicates soft tissue. Adapted version, reprinted from Ultrasonics, 38, Konofagou (2000), pp. 400-404, ©2000, with permission from Elsevier.


In many cases, despite the difference in stiffness, the small size of a pathological lesion and/or its location deep in the body, preclude its detection and evaluation by palpation. In general, the lesion may or may not possess acoustic backscatter properties, which would make it detectable using ultrasound. For example, tumors of the prostate or the breast could be invisible or barely visible in standard ultrasound examinations, yet be much harder than the embedding tissue. Furthermore, diffuse diseases (e.g. cirrhosis of the liver) are known to significantly increase the stiffness of the liver tissue as a whole (Anderson, 1984). However, they may appear normal in conventional B-mode ultrasound examination. Based on the simple concept of palpation and the observation that echogenicity and the stiffness of tissue are generally uncorrelated (Garra, 1997; Ophir, 2001), tissue elastography or elasticity imaging (Ophir, 1991) seeks to provide non-invasive quantitative systems that can measure or image the local mechanical properties of tissue. Such systems could provide new information related to tissue structure and/or pathology (see Figure 1) and could significantly enhance the accuracy of diagnosis, even at early stages of disease.

In conventional (B-mode) ultrasound imaging, the ability to differentiate between various tissues within the body depends on changes in the acoustic properties, which in turn, depend primarily on the bulk (elastic) modulus (Cobbold, 2007). The range of variation of the bulk modulus is very small, i.e., significantly less than an order of magnitude. On the other hand, the shear modulus μl (known as the second Lamé constant), which is defined as the ratio of shear stress to shear strain that is involved in the passage of a transverse wave, may change by many orders of magnitude, depending on the tissue (Cobbold, 2007). This suggests that by imaging one or more characteristics of shear wave propagation, improved sensitivity to localized changes in elastic properties could be achieved, thereby, providing useful diagnostic information (Sarvazyan, 1998).

Key Terms in this Chapter

Acoustic Radiation Force: The force that is exerted when an ultrasound wave hits an obstacle that absorbs, scatters, or reflects energy. This force is in the direction of propagation and is also known as the time-averaged (Langevin) radiation pressure.

Inverse-Problem: It involves the mathematical processes where the values of some parameters, characterizing a system under investigation, must be inferred from the observed (measured) data.

Shear (or Transverse) Wave: Form of wave propagation in a solid medium where the particle movement is at right angles to the direction of propagation.

Elastography (or Elasticity Imaging): The general class of quantitative methods, which aim at measuring or imaging the mechanical properties of a medium, including soft tissue.

Shear Viscosity: A coefficient that characterizes the viscous properties of a fluid and is related to the absorption (loss) of energy (or else, damping) due to the presence of velocity gradients in the fluid. This means that adjacent layers move at differing speeds and as a result, there is a frictional drag force that causes energy to be dissipated.

Narrowband Spectrum: It describes a signal whose frequency spectrum occupies a narrow range of frequencies (as opposed to broadband).

Finite-Amplitude Acoustic Wave: Propagation of an acoustic wave within a medium under conditions where the pressure and density are nonlinearly related. The small-signal approximation that is involved in the linear propagation theory is no longer valid. The pressure is considered sufficiently high that nonlinear effects arise, which cause the generation of higher harmonics.

Shear Modulus: The ratio of the shear stress to the shear strain (or angular deformation), that is related to the passage of a transverse wave (where a shearing motion is involved). It is also known as the second Lamé constant.

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