Oncologic Ultrasound, An Issue of Ultrasound Clinics (eBook)

Vikram S. Dogra (Autor)

eBook Download: PDF | EPUB

2014 | 1. Auflage
100 Seiten
Elsevier Health Sciences (Verlag)
978-0-323-26417-4 (ISBN)

Infos

The detection of tumors in various organ systems remains one of the central applications of ultrasound. This issue of Ultrasound Clinics will consist of 10 articles under the title 'Oncologic Ultrasound” and will feature several articles on elastrography (a developing method for distinguishing tumors from normal tissue), as well as endoscopic ultrasound in oncology, ultrasound guidance in tumor ablation, and ultrasound guided biopsies. The editor, Vikram Dogra, who also serves as consulting editor of the series, has put together an issue that addresses the core clinical concerns of oncologic imaging for the radiologist specializing in ultrasound.

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Elastography

General Principles and Clinical Applications

Marvin M. Doyley, PhD∗[e-mail] and Kevin J. Parker, PhD,     Department of Electrical and Computer Engineering, University of Rochester, Hopeman Engineering Building 343, Box 270126, Rochester, NY 14627, USA

∗Corresponding author.

Elastography visualizes differences in the biomechanical properties of normal and diseased tissues. Elastography was developed in the late 1980s to early 1990s to improve ultrasonic imaging, but the success of ultrasonic elastography has inspired investigators to develop analogs based on MRI and optical coherence tomography. This article focuses on ultrasonic techniques with a brief reference to approaches based on MRI.

Keywords

Elastography

Ultrasonic imaging

Ultrasonic elastography

MRI

Key points

• Like conventional medical imaging modalities, forward and the inverse problems are encountered in elastography.

• Quasistatic elastography visualizes the strain induced within tissue using either an external or internal source.

• Direct and iterative inversion schemes have been developed to make quasistatic elastograms more quantitative.

• Soft tissues display several biomechanical properties, including viscosity and nonlinearity, which may improve the diagnostic value of elastography when visualized alone or in combination with shear modulus. Elastography can characterize the nonlinear behavior of soft tissues and may be used to differentiate between benign and malignant tumors.

Introduction

Elastography visualizes differences in the biomechanical properties of normal and diseased tissues.1–4 Elastography was developed in the late 1980s to early 1990s to improve ultrasonic imaging,5–7 but the success of ultrasonic elastography has inspired investigators to develop analogs based on MRI8–11 and optical coherence tomography.12–14 This article focuses on ultrasonic techniques with a brief reference to approaches based on MRI.

The general principles of elastography can be summarized as follows: (1) perturb the tissue using a quasistatic, harmonic, or transient mechanical source; (2) measure the resulting mechanical response (displacement, strain or amplitude, and phase of vibration); and (3) infer the biomechanical properties of the underlying tissue by applying either a simplified or continuum mechanical model to the measured mechanical response.2,15–18 This article describes (1) the general principles of quasistatic, harmonic, and transient elastography (Fig. 1)—the most popular approaches to elastography—and (2) the physics of elastography—the underlying equations of motion that govern the motion in each approach. Examples of clinical applications of each approach are provided.

Fig. 1 Schematic representation of current approaches to elastographic imaging: quasistatic elastography (left), harmonic elastography (middle), and transient elastography (right).

The physics of elastography

Like conventional medical imaging modalities, forward and the inverse problems are encountered in elastography. The former problems are concerned with predicting the mechanical response of a material with known biomechanical properties and external boundary conditions. Understanding these problems and devising accurate theoretical models to solve them have been an effective strategy in developing and optimizing the performance of ultrasound displacement estimation methods. The latter problems are concerned with estimating biomechanical properties noninvasively using the forward model and knowledge of the mechanical response and external boundary conditions. A comprehensive review of methods developed to solve inverse problems is given in the article by Doyley19; therefore, this section focuses only on the forward problem.

The forward elastography problem can be described by a system of partial differential equations (PDEs) given in compact form20,21:

(1)

where σij is the 3-D stress tensor (ie, a vector of vectors), βi is the deforming force, and ∇ is the del operator. Using the assumption that soft tissues exhibit linear elastic behavior, then the strain tensor (ε) maybe related to the stress tensor (σ) as follows22:

(2)

where the tensor (C) is a rank-four tensor consisting of 21 independent elastic constants.16,20,23 Under the assumption that soft tissues exhibit isotropic mechanical behavior, however, then only 2 independent constants, λ and μ (lambda and shear modulus), are required. The relationship between stress and strain for linear isotropic elastic materials is given by:

(3)

where Θ = ∇ ⋅ u = ε11 + ε22 + ε33 is the compressibility relation, δ is the Kronecker delta, and the components of the strain tensor are defined as:

(4)

Lamé constants (ie, λ and μ) are related to Young modulus (E) and Poisson ratio (v), as follows20,21:

(5)

The stress tensor is eliminated from the equilibrium equations (ie, Equation 2) using Equation 3. The strain components are then expressed in terms of displacements using Equation 4. The resulting equations (ie, the Navier-Stokes equations) are given by:

(6)

where ρ the is density of the material, u is the displacement vector, and t is time. For quasistatic deformations, Equation 6 reduces to:

(7)

For harmonic deformations, the time-independent (steady-state) equations in the frequency domain give10,24:

(8)

where ω is the angular frequency of the sinusoidal excitation. For transient deformations, the wave equation is derived by differentiating Equation 6 with respect to x, y, and z, which gives21:

(9)

where ∇ ⋅ u = Δ, and the velocity of the propagating compressional wave, c1, is given by:

(10)

The wave equation for the propagating shear wave is given by:

(11)

where ζ = ∇ ⋅ u/2 is the rotational vector, and the shear wave velocity, c2, is given by:

(12)

Analytical methods have been used to solve the governing equations for quasistatic, harmonic, and transient elastographic imaging methods25–28 for simple geometries and boundary conditions. Numeric methods—namely, the finite-element method—are used, however, to solve the governing equations for all 3 approaches to elastography on irregular domains and for heterogeneous elasticity distributions.24,29–36

Approaches to elastography

Quasistatic Elastography

Quasistatic elastography visualizes the strain induced within tissue using either an external or internal source. A small motion is induced within the tissue (typically approximately 2% of the axial dimension) with a quasistatic mechanical source. The axial component of the internal tissue displacement is measured by performing cross-correlation analysis on pre- and postdeformed radiofrequency (RF) echo frames6,7,37 and strain is estimated by spatially differentiating the axial displacements. In quasistatic elastography, soft tissues are typically viewed as a series of 1-D springs that are arranged in a simple fashion. For this simple mechanical model, the measured strain (ε) is related to the internal stress (σ) by Hooke’s law:

(13)

where k is the Young modulus (or stiffness) of the tissue. No method can measure the internal stress distribution in vivo; consequently, the internal stress distribution is assumed to be constant (ie, σ ≈ 1); an approximate estimate of Young modulus is computed from the reciprocal of the measured strain. The disadvantage of computing modulus elastograms in this manner is that it does not account for stress decay or stress concentration; consequently, quasistatic elastograms typically contain target-hardening artifacts,31,35 as illustrated in Fig. 2.

Fig. 2 Sonogram (A) and strain (B) elastograms obtained from a phantom containing a single 10-mm diameter inclusion whose modulus contrast was approximately 6.03 dB.

Despite this limitation, several groups have obtained good elastograms in applications where accurate quantification of...

Produkt-Details

• Erscheint lt. Verlag: 23.5.2014
• Sprache: englisch
• Themenwelt: Medizin / Pharmazie ► Gesundheitsfachberufe
• Themenwelt: Medizinische Fachgebiete ► Radiologie / Bildgebende Verfahren ► Radiologie
• Themenwelt: Medizinische Fachgebiete ► Radiologie / Bildgebende Verfahren ► Sonographie / Echokardiographie
• ISBN-10: 0-323-26417-4 / 0323264174
• ISBN-13: 978-0-323-26417-4 / 9780323264174