Acoustic Waves in Medical Imaging and Diagnostics

Abstract

Up until about two decades ago acoustic imaging and ultrasound imaging were synonymous. The term “ultrasonography,” or its abbreviated version “sonography” meant an imaging modality based on the use of ultrasonic compressional bulk waves. Since the 1990s numerous acoustic imaging modalities started to emerge based on the use of a different mode of acoustic wave: shear waves. It was demonstrated that imaging with these waves can provide very useful and very different information about the biological tissue being examined. We will discuss physical basis for the differences between these two basic modes of acoustic waves used in medical imaging and analyze the advantages associated with shear acoustic imaging. A comprehensive analysis of the range of acoustic wavelengths, velocities, and frequencies that have been used in different imaging applications will be presented. We will discuss the potential for future shear wave imaging applications.

Introduction

Two decades ago, in the field of medical imaging, the terms “acoustic imaging” and “ultrasonic imaging” were synonymous. The only acoustic waves used for imaging biological structures were ultrasonic compressional (or longitudinal) waves. In the 1990s, a new acoustic imaging technology started to emerge that was based on shear (or transverse) acoustic waves. In the remainder of this paper we will use the term shear wave for the entire family of transverse waves.

The wave speeds of these different kinds of waves are governed by two different types of moduli. The compressional wave speed is related to the bulk modulus of the tissue while the shear wave speed is related to the shear modulus. The compressional wave speed does not vary significantly for biological tissues when compared to the variation of the shear wave velocity in the same tissues. For this reason, elasticity imaging, which is targeted at imaging the shear modulus of tissue, has a wide dynamic range that can be exploited (Sarvazyan et al. 1998).

The purpose of this paper is to explore the differences between imaging with compressional and shear waves. We will explore the ranges of relevant frequencies used in each of the two modalities and the ranges of acoustic wave speeds. We explore how different imaging techniques exploit parameters obtained with the use of shear waves and discuss regions of these parameter spaces that have yet to be explored.

Mechanisms of Contrast in Acoustic Imaging

The wave motion in a medium is governed by the wave equation. For simplicity we will assume a linear, elastic, isotropic, and homogeneous medium (Manduca et al. 2001),

$$\rho \frac{{\partial }^2}{\partial t^2}u(\mathbf{x},t)=(\lambda +\mu )\nabla \left(\nabla ·u(\mathbf{x},t)\right)+\mu \nabla u(\mathbf{x},t),$$ (1)

where ρ is the mass density, λ_L and μ_L are the Lamé parameters, t is time, and x is a spatial vector defined as x = [x, y, z]. A solution of the wave equation is given by

$$u(\mathbf{x},t)=u_0{e}^{i(\omega t-k\mathbf{x})},$$ (2)

where u₀ is the displacement amplitude, ω is the angular frequency, and k is the wavenumber, k = ω/c, where c is the speed of the acoustic wave. As stated above, compressional waves have been used for over 60 years to image the internal structures of the body. Conventional B-mode imaging is based on differences in acoustic impedance of tissue, Z, which is given by

$$Z=\rho c_c,$$ (3)

where c_c is the compressional wave velocity. The compressional wave velocity, c_c, is related to both the Lamé parameters by

$$c_c=\sqrt{\frac{{\lambda }_L+2{\mu }_L}{\rho }}=\sqrt{\frac{E(1-v)}{\rho (1+v)(1-2v)}}.$$ (4)

The above relationship can also be written in terms of the bulk modulus, K, and the shear modulus, μ, where K = λ_L + 2μ_L/3 and μ = μ_L.

$$c_c=\sqrt{\frac{K+4\mu /3}{\rho }}.$$ (5)

It will be shown later that the bulk modulus is typically several orders of magnitude larger than the shear modulus in tissues so the compressional wave velocity is almost solely determined by the bulk modulus of the tissue. The bulk and shear moduli can also be written as (Sarvazyan et al. 2011)

$$K=\frac{E}{(1+v)(1-2v)},$$ (6)

$$\mu =\frac{E}{2(1+v)},$$ (7)

where E is the compressional Young’s modulus assuming a Hookean elastic solid and v is the Poisson’s ratio. In most soft tissues, the Poisson’s ratio is assumed to be very close to 0.5, which is the condition for incompressibility.

Both fundamental components of bulk acoustic impedance of a material, the density and bulk modulus are dependent on the molecular composition of that material. Water is the main molecular component of soft tissue, thus the speed of compressional waves in all soft tissues lie within the range of ±10% of that of water (Goss et al. 1978; Goss et al. 1980; Duck 1990; Sarvazyan and Hill 2004). It is well known that the speed and attenuation of compressional waves in soft tissue are mainly defined by its molecular content rather than structure: disintegration, i.e. mechanical homogenization of tissue, generally does not lead to substantial, immediate change in these acoustical parameters (Pauly and Schwan 1971; Sarvazyan et al. 1987). The speed of compressional waves in liver tissue samples of different levels of structural integrity (intact, ground and highly homogenized) differs less that 0.5% (Sarvazyan et al. 1987). The wave speed in the ground tissue is slightly higher than that in the intact tissue and this small increase is explained by an increase in the level of hydration of some biopolymers released in the ground tissue. Both compressibility and density, which define the compressional wave speed in tissue, are determined by short range intermolecular interactions and water as the major component of soft tissue contributes the most to these bulk properties of tissue. Therefore, the images obtained using compressional waves represent mainly the pattern of water hydrating the molecules composing the tissue (Sarvazyan and Hill 2004). This pertains to imaging of most soft tissues such as liver, kidney, heart, skeletal muscle, which contain 70–75% of water and which are the main target of ultrasonic imaging, but this is not the case for tissues like lung, cartilage and fat which do not have high water content.

This strong association of acoustic tissue properties with that of water becomes evident from the comparison of temperature dependences of compressional wave speed in pure water and soft tissues. The most characteristic acoustical feature of water is a unique nonlinear temperature dependence of sound speed resulting from the temperature-induced changes in the dynamics of hydrogen-bonded clusters. No other fluid or substance has similar dependence. The temperature dependence of compressional wave speed in tissue closely resembles that of pure water (Fig. 1) (Sarvazyan et al. 2005).

Figure 1.

Variation of compressional phase velocity in skeletal muscle and pure water. [© 2004 Elsevier. Reproduced with permission from (Sarvazyan et al. 2005)].

While conventional sonography is mainly based on visualizing the spatial distribution of acoustic impedance, which is defined by short-range molecular interactions in the tissue, the imaging based on the use of shear waves shows quite a different set of macroscopic structural features determined by long-range molecular and cellular interactions (Sarvazyan 2001; Sarvazyan and Hill 2004).

Shear waves have been used over the last two decades to explore the underlying material properties of soft tissues (Sarvazyan et al. 2011). The shear wave speed is dependent on the shear modulus of the material as given by

$$c_s=\sqrt{\frac{\mu }{\rho }}=\sqrt{\frac{E}{2\rho (1+v)}}.$$ (8)

The shear modulus of a material is highly dependent on the tissue architecture and structural makeup. This tissue architecture varies greatly depending on the organ and its state. For example, the liver is largely isotropic and homogenous with an intricate series of blood vessels running through it so that the liver can filter the blood supply. Alternatively, other organs are very specifically arranged. Skeletal muscle can be assumed to be transversely anisotropic. That is, it is arranged into bundles of fibers in a semi-crystalline architecture. In this case, there are different values of the shear modulus along the muscle fibers and perpendicular to the muscle fiber direction (Gennisson et al. 2003; Chen et al. 2009; Urban and Greenleaf 2009; Gennisson et al. 2010; Lee et al. 2012a). Lee, et al., measured the moduli in a material with orthotropic symmetry (Lee et al. 2012a). The shear modulus tensor can be written as

$$M=\left[\begin{array}{cc}{\mu }_{11}& {\mu }_{12}\\ {\mu }_{12}& {\mu }_{22}\end{array}\right]=R\left[\begin{array}{cc}{\mu }_{//}& 0\\ 0& {\mu }_{\perp }\end{array}\right]R^T,$$ (9)

where

$$R=\left[\begin{array}{cc}cos(\theta )& -sin(\theta )\\ sin(\theta )& cos(\theta )\end{array}\right]$$ (10)

μ_// and μ_⊥ are the shear moduli parallel and perpendicular to the muscle fibers, and θ is the angle with respect to the muscle fiber longitudinal direction. Each of the moduli can be calculated using Eq. (8). The value of μ_// is assumed to be the largest eigenvalue found in the material.

Other organs such as the heart and skin consist of different layers. In the case of the heart wall, the layers are oriented at different angles through the thickness (Sosnovik et al. 2001; Couade et al. 2011; Lee et al. 2012b). The dependence of shear wave behavior on these different long-range molecular and cellular characteristics has provided the opportunity to investigate with ultrasound methods some new and fundamental tissue properties.

In contrast to compressional waves, shear waves are polarized which makes them sensitive to tissue anisotropy, an important structural anatomical characteristic that can have diagnostic value. This is illustrated by the shear wave displacements in Fig. 2 in the axial and radial directions, in which the distributions are very different in two orthogonal directions. Therefore, by directing shear waves in different directions it could be possible to characterize tissue anisotropy.

Figure 2.

Shear wave amplitude distributions in axial and radial directions. [© 1998 Elsevier. Partially reproduced with permission from (Sarvazyan et al. 1998)].

There are two other aspects that can cause variation in shear wave velocities. Up until now, we have assumed that soft tissues behave as elastic materials. However, many studies have demonstrated that biological tissues are more appropriately characterized as viscoelastic materials, that is, their deformation will depend on the time course of the stress applied. To incorporate this viscoelasticity, we can define the wavenumber for the shear wave as a complex quantity

$$k=k_r+{ik}_i$$ (11)

where k_r = ω/c_s and k_i = α_s. The shear modulus can alternatively be defined as

$$\mu =\rho \frac{{\omega }^2}{k^2}.$$ (12)

Because k is a complex quantity, the shear modulus also becomes a complex quantity, μ = μ₁ + iμ₂ where μ₁ is known as the elastic or storage modulus and μ₂ is known as the viscous or loss modulus (Vappou et al. 2009).

$${\mu }_1=\rho {\omega }^2\frac{k_r^2-k_i^2}{{\left(k_r^2+k_i^2\right)}^2}$$ (13)

$${\mu }_2=-2\rho {\omega }^2\frac{k_r{k}_i}{{\left(k_r^2+k_i^2\right)}^2}$$ (13)

The relationships for the shear wave speed and attenuation can be written as

$$c_s(\omega )=\sqrt{\frac{2\left({\mu }_1^2+{\omega }^2{\mu }_2^2\right)}{\rho \left({\mu }_1+\sqrt{{\mu }_1^2+{\omega }^2{\mu }_2^2}\right)}},$$ (15)

$${\alpha }_s(\omega )=\sqrt{\frac{\rho {\omega }^2\left(\sqrt{{\mu }_1^2+{\omega }^2{\mu }_2^2}-{\mu }_1\right)}{2\left({\mu }_1^2+{\omega }^2{\mu }_2^2\right)}}.$$ (16)

It is readily evident that due to the viscoelasticity of the tissue, the shear wave speed will vary with frequency, a characteristic called dispersion. This becomes important in the quantitative characterization of soft tissue because the frequency must be known to provide an accurate result.

The second parameter that can affect the shear wave speed is the dimensions of the boundaries of the tissue with respect to the wavelength being used. In this case, where the shear wavelengths are larger than the object, geometric dispersion can result even when the material is elastic. In tissues such as the heart wall, arterial wall, and skin, various modes of guided waves can be generated when the thickness of these tissues are comparable to the shear wavelength. The guided wave speed is a function of both the geometry and the material properties of the tissue. One example in ex vivo arteries demonstrated multiple modes of vibration and guided wave speeds ranging from 5–30 m/s (Bernal et al. 2011). Lamb waves occur in plates which have been used to model the heart wall and cornea. Circumferential and flexural waves occur in cylindrical structures such as the arteries. Surface waves have been employed in the study of skin and lung.

Because the tissue structure and constituents can vary so widely among different soft tissues, the shear wave speed in soft tissues can vary over two orders of magnitude. This variation of the shear wave speed increases in many tissues in the presence of disease. It is well documented that cancerous tissues can be significantly stiffer than normal tissue, particularly in breast and prostate cancer (Rubens et al. 1995; Krouskop et al. 1998; Lorenzen et al. 2002; Kemper et al. 2004; Sinkus et al. 2005a; Hoyt et al. 2008; Tanter et al. 2008). Additionally, disease processes that damage tissue can cause fibrotic replacement of normal tissue in organs like the liver and kidney which in turn increases the stiffness, and thus the shear wave speed, of the organ (Sandrin et al. 2003; Rouviere et al. 2006; Arndt et al. 2010).

The compressional wave speed will also typically increase in these cases but the percent change is much smaller than for the shear wave speed. Diagnostic information can be obtained from the large variations in shear wave speed caused by disease (Sandrin et al. 2003; Rouviere et al. 2006; Tanter et al. 2008). Table 1 tabulates ranges of compressional and shear wave speeds for different types of normal and pathological tissues.

Table 1.

Variation of compressional and shear wave speeds in different tissues

Tissue	Compressional Waves		Shear Waves
	cc, m/s	References	cs, m/s	References
Breast	1450–1570	(Goss et al. 1978; Duck 1990)	1.10–3.46	(Lorenzen et al. 2003; Sinkus et al. 2005b; Sinkus et al. 2007; Tanter et al. 2008; Athanasiou et al. 2010; Bai et al. 2012)
Breast cancer	1437–1584	(Goss et al. 1978; Duck 1990	3.25–9.64	(McKnight et al. 2002; Sinkus et al. 2005b; Sinkus et al. 2007; Tanter et al. 2008; Athanasiou et al. 2010; Evans et al. 2010; Bai et al. 2012; Berg et al. 2012)
Liver	1522–1623	(Goss et al. 1978; Goss et al. 1980; Duck 1990)	0.85–3.01	(Rouviere et al. 2006; Palmeri et al. 2008; Friedrich-Rust et al. 2009; Muller et al. 2009; Asbach et al. 2010; Bavu et al. 2011)
Fibrotic/cirrhotic liver	1535–1581	(Duck 1990)	0.84–5.00	(Sandrin et al. 2003; Huwart et al. 2006; Friedrich-Rust et al. 2009; Muller et al. 2009; Asbach et al. 2010; Castéra et al. 2010; Stebbing et al. 2010; Bavu et al. 2011)
Skeletal muscle	1500–1610	(Goss et al. 1978)	1.56–7.60	(Gennisson et al. 2003; Uffmann et al. 2004; Ringleb et al. 2007; Nordez et al. 2008; Chen et al. 2009; Urban and Greenleaf 2009; Gennisson et al. 2010; Klatt et al. 2010)
Kidney	1558–1562	(Duck 1990)	1.20–3.50	(Arndt et al. 2010; Stock et al. 2010; Amador et al. 2011; Syversveen et al. 2011; Derieppe et al. 2012)
Heart	1528–1602	(Goss et al. 1978; Goss et al. 1980; Duck 1990)	0.83–7.00	(Kanai 2005; Bouchard et al. 2009; Kolipaka et al. 2010; Couade et al. 2011; Nenadic et al. 2011a; Nenadic et al. 2011c; Pernot et al. 2011; Lee et al. 2012b)
Arteries	1559–1660	(Goss et al. 1980; Duck 1990)	2.83–6.09	(Zhang et al. 2005; Luo et al. 2009; Couade et al. 2010; Vappou et al. 2010; Bernal et al. 2011; Luo et al. 2012)
Brain	1460–1580	(Goss et al. 1978; Goss et al. 1980; Duck 1990)	1.02–4.63	(Green et al. 2008; Kruse et al. 2008; Sack et al. 2008; Sack et al. 2009; Mace et al. 2011; Zhang et al. 2011a)
Skin	1498–1540	(Goss et al. 1978)	2.66–5.99	(Zhang et al. 2011b)
Lung	577–1472	(Goss et al. 1978; Duck 1990)	0.90–3.54	(Goss et al. 2006; McGee et al. 2009; Mariappan et al. 2011; Zhang et al. 2011c; Mariappan et al. 2012)
Spleen	1515–1635	(Goss et al. 1978; Goss et al. 1980; Duck 1990)	1.10–2.36	(Talwalkar et al. 2009; Mannelli et al. 2010; Nedredal et al. 2011; Nenadic et al. 2011a)
Cornea	1542–1639	(Goss et al. 1978; Goss et al. 1980; Duck 1990)	1.43–6.80	(Tanter et al. 2009; Litwiller et al. 2010)
Cervix/uterus	1625–1633	(Goss et al. 1978; Duck 1990)	2.01–2.58	(Stewart et al. 2011)
Thrombus	1586–1597	(Duck 1990)	0.33–1.27	(Gennisson et al. 2006)
Tendons	1631–3530	(Goss et al. 1978; Duck 1990)	79.4	(Song 2010)
Cartilage	1520–1665	(Goss et al. 1978; Ling et al. 2007; Nieminen et al. 2007)	39.71–87.83	(Lopez et al. 2007; Lopez et al. 2008)
Bone	1630–4170	(Goss et al. 1978; Goss et al. 1980; Duck 1990)	1420–3541	(Goss et al. 1978)

Examination of Wave Parameters in Acoustic Imaging

To explore where compressional and shear waves can be used for tissue property analysis, it is useful to examine the parameter space governed by the simple equation

$$c=f\lambda ,$$ (17)

where c is the wave speed, f is the frequency of the wave and λ is the wavelength. Figure 3 shows a logarithmic plot of the acoustic wave velocity versus frequency. Three diagonal lines are also drawn that correspond to acoustic wavelengths of 0.1, 1.0, 10.0, and 100 mm. The ability to image a material depends on the wavelength used and the characteristic dimensions of the material. To support wave propagation the dimensions of the tissue should be larger than the wavelength and to resolve a specific feature, the wavelength must be shorter than the dimension of that feature. Therefore the region corresponding to large wavelengths (λ > 100 mm), is defined in Fig. 3 as a “non-wave” region. Secondly, when the wavelength falls below 0.1 mm, very high wave attenuation is present which limits the distance these waves can travel. The desired propagation distance should be comparable to the dimensions of the structures that need to be imaged. Based on the data on attenuation of acoustic waves in biological tissue, it can be estimated that the wavelength cannot be shorter than a few tens of microns and corresponding region in Fig. 3 is defined as “too high attenuation”. Two regions on the vertical axis, corresponding to the compressional and shear wave speeds in biological tissues, are highlighted in blue. The region for the compressional wave speeds range from 1500–1800 m/s and cover a frequency range from 10^5.7–10⁸ Hz. The region where the shear wave velocities range from 0.5–100 m/s and the frequencies vary from 10⁰–10⁶ Hz.

Figure 3.

Acoustic imaging feature space. The ranges of compressional and shear wave speeds are given by c_c and c_s.

The first observation from Fig. 3 is the large ranges of the parameters related to the shear waves as compared to the compressional waves, which again highlights the increased potential for using shear waves to characterize biological tissues. Another advantage is that the shear waves extend to such low frequencies (a few Hertz to tens of Hertz for certain modes of guided waves) which cover characteristic time scales for observing certain structural and functional processes in biological tissues.

Acoustic Wave Imaging Methods

Having defined the parameter space in Fig. 3, it is important that we examine how different investigators have explored this space with different acoustic imaging methods. This analysis will also define which regions have not been investigated to date. We will discuss the potential of future applications related to those heretofore unexplored regions.

Imaging with Compressional Waves

Within the region defined by the compressional waves, B-mode ultrasound imaging is typically performed using frequencies ranging from 1–15 MHz. Echocardiography and abdominal imaging typically is performed with lower frequencies ranging from 1–4 MHz. These lower frequencies are used because the structures of interest are typically 4–15 cm deep and the attenuation at these frequencies is lower. For more superficial applications such as imaging of the breast, thyroid, and vasculature, higher ultrasound frequencies are used ranging from 5–15 MHz. These higher frequencies provide higher spatial resolution, which is typically needed to resolve small structural details. For ophthalmic applications high frequencies are used that range from 10–20 MHz. It is important to note that there are no appreciable gaps in frequency for using compressional waves for diagnostic acoustic imaging.

Imaging with Shear Waves

There a number of methods that have been developed to generate and measure the propagation of shear waves in tissue. These techniques are often defined by how they excite the shear wave as well as how they are measured. A recent review provides a comprehensive overview of these different methods and for which types of applications they have been used (Sarvazyan et al. 2011). We will briefly describe those methods and what frequencies are typically used. The frequencies used are typically determined by the application.

One of the early methods used to generate propagating shear waves in tissue was to use external mechanical actuators. This was performed by Krouskop, et al., by using a mechanical actuator on the quadriceps muscle while measuring the motion with Doppler ultrasound (Krouskop et al. 1987). Similar measurements soon followed in an article by Yamakoshi, et al., in which measurements were made in the human liver (Yamakoshi et al. 1990). Additionally, a method called sonoelasticity imaging was also reported that used vibration to examine soft tissue (Lerner et al. 1990; Parker et al. 1990). The vibration was measured using Doppler ultrasound methods and the wave motion was analyzed using a model based on a Bessel function expansion of the Doppler signals. About a decade after these developments, a related method called sonoelastography imaging was developed that used two mechanical drivers exciting the tissue at slightly different frequencies to create “crawling waves” at the beat frequency of the two drivers (Wu et al. 2004).

Another method that used mechanical actuation is called magnetic resonance elastography (MRE). The resulting shear waves were measured with magnetic resonance imaging (MRI) techniques (Muthupillai et al. 1995). This technique uses harmonic waves at a specific frequency typically ranging from 20–200 Hz, although some applications have been performed at frequencies ranging from 500–9000 Hz (Kruse et al. 2000; Manduca et al. 2001; Lopez et al. 2007; Lopez et al. 2008). A recent publication demonstrated MRE measurements on a viscoelastic silicone rubber over a large bandwidth, 200–7750 Hz (Yasar et al. 2012). One of the unique elements of this study is that three different sample sizes were used in two different MR scanners, and the overlap between these samples and scanners was quite good. MRE applications have been reviewed thoroughly by several authors (Mariappan et al. 2010; Litwiller et al. 2012; Sinkus et al. 2012).

Transient elastography (TE) is a method that was developed to measure the transient shear waves produced by an impulsive mechanical actuation (Sandrin et al. 2002a; Sandrin et al. 2002b). This method was used to make measurements in various types of tissues, but has found widespread use in measuring liver stiffness after being commercialized by EchoSens as a product called FibroScan. In the liver application, the frequency used is typically 50 Hz (Sandrin et al. 2003).

Starting in the mid-1990s, another method was introduced to create shear waves which involved the use of focused ultrasound to produce acoustic radiation force. This approach was derived from studies that started to use ultrasound radiation force to perturb tissue. Sugimoto was one of the first to use radiation force to investigate tissue hardness (Sugimoto et al. 1990). Subsequent developments of methods called vibro-acoustography by Fatemi and Greenleaf (Fatemi and Greenleaf 1998; Fatemi and Greenleaf 1999) and acoustic radiation force impulse imaging by Nightingale, et al., (Nightingale et al. 2001) also used radiation force to stimulate tissue and measure the mechanical response. These contributions served as motivation for later developments of using radiation force to generate shear waves (Sarvazyan et al. 1998; Nightingale et al. 2003).

Chen, et al., used modulated ultrasound to produce harmonic radiation force at frequencies ranging from 100–500 Hz (Chen et al. 2004). This harmonic radiation force produced shear waves at the same frequencies, and the shear waves were measured using a laser vibrometer in gelatin phantoms. These measurements were used to characterize the viscoelastic properties of the phantoms.

Other groups used tonebursts of ultrasound. The length of the pulses used for creating the radiation force typically ranges from 50–1000 μs. For these types of pulses, the tissue reacts as if the excitation is impulsive, so many frequencies can be excited at the same time. Multiple methods have been developed using this impulsive radiation force coupled with ultrasound imaging techniques to measure the propagating shear waves. These methods include Shear Wave Elasticity Imaging (Sarvazyan et al. 1998; Nightingale et al. 2003; Palmeri et al. 2008), Supersonic Shear Imaging (SSI) (Bercoff et al. 2004; Fink and Tanter 2011), Shearwave Dispersion Ultrasound Vibrometry (SDUV) (Chen et al. 2004; Chen et al. 2009; Urban et al. 2012), Spatially Modulated Ultrasound Radiation Force (SMURF) (McAleavey et al. 2007), and sonoelastography using radiation force (Hah et al. 2012; Hazard et al. 2012). These various methods have been applied to many types of tissues. Two of radiation force-based methods, SSI and SWEI, have been commercialized for clinical use on the SuperSonic Imagine Aixplorer as Shear Wave Elastography and on the Siemens Acuson S2000 as Virtual Touch Quantification. The frequency used in these methods typically range from 50–1000 Hz and the shear wave velocities range from 0.5–12 m/s.

Investigation of certain tissues such as the heart, arteries, and cornea with acoustic radiation force produces guided waves (Kanai 2005; Tanter et al. 2009; Couade et al. 2010; Bernal et al. 2011; Nenadic et al. 2011a; Nenadic et al. 2011b; Nenadic et al. 2011c; Brum et al. 2012). These waves are strongly affected by the geometry of the organ, and wave velocities are governed by the material properties and the geometrical structure. Guided wave velocities can range from 1–30 m/s and the frequency range is quite large, 100–7000 Hz.

A few methods have been reported that use endogenous motion of certain organs, typically associated with the beating of the heart. Kanai has made measurements of the waves present in the heart as it beats (Kanai 2005; Kanai 2009). A method called electromechanical imaging has been used to measure the electromechanical waves propagating in the heart wall and the pulse waves propagating in the arterial vasculature (Pernot et al. 2007; Wang et al. 2008; Vappou et al. 2010; Konofagou et al. 2011; Provost et al. 2011). A method that uses passive tomography methods, adapted from the field of seismology, has been reported that uses physiological motion to measure the shear wave velocity in various soft tissues (Benech et al. 2009; Gallot et al. 2011). The frequency range for these methods is quite low because typical heart rates range from 0.8–2.0 Hz.

Lastly, there are methods that perturb the tissue using acoustic radiation force and measure the resulting tissue deformation directly or indirectly. One such method is called vibro-acoustography, which uses two beams of ultrasound with slightly different frequencies to create acoustic radiation force at the difference frequency, Δf, between the two beams (Fatemi and Greenleaf 1998; Fatemi and Greenleaf 1999; Urban et al. 2011). The values for Δf typically range between 40–120 kHz. The beating radiation force stimulates an acoustic response resulting in a propagating compressional wave at Δf. This acoustic wave is measured by a nearby hydrophone. The excitation beam is scanned over an object to create an image. In another method called harmonic motion imaging, modulated ultrasound is used to create a harmonic radiation force at frequencies of 10–200 Hz (Konofagou and Hynynen 2003; Maleke and Konofagou 2008; Konofagou and Maleke 2011). The displacement of the tissue is measured with ultrasound techniques and the excitation beam is scanned over the object to create an image.

Analysis of Acoustic Imaging Feature Space

With this background on the various methods employed to measure the acoustic waves in biological tissues, we can turn to a modified version of Fig. 3 in which we overlay colored sections (Fig. 4) indicating how these various methods cover the spaces occupied by the modalities that use compressional and shear waves to image tissue. Within the imaging space occupied by using compressional waves, the portion occupied by diagnostic B-mode imaging could be subdivided by frequency based on application areas.

Figure 4.

Acoustic imaging feature space with regions depicting methods used for shear and compressional acoustic wave imaging.

Most of the shear wave applications occupy the space in the lower left corner of the speed/frequency space. Methods that use endogenous motion lie in the most extreme part of the space because of the low frequency content present in the physiological motion. One other low frequency effect may be the poroelastic behavior of the tissue that occurs at frequencies much lower than the ones depicted in the feature space of Fig. 3 (Konofagou et al. 2001; Righetti et al. 2004; Righetti et al. 2005; Berry et al. 2006a; Berry et al. 2006b). MRE and the methods that use acoustic radiation force most often operate in the 50–500 Hz bandwidth. The methods that use mechanical excitation are more often limited to lower frequency ranges than methods that use acoustic radiation force. In special applications that involve guided waves, particularly those that explore the viscoelastic and/or geometry based wave speed dispersion, frequencies extend to a few kilohertz.

There exists a substantial lack of data for tissues with very high shear wave speeds. These types of tissue would typically be either cancerous tissues or very fibrotic tissues. Additionally, tissues such as tendons, cartilage, and cancellous and cortical bone would also have very high shear wave speeds (c_s > 20 m/s). In tissue engineering applications, cartilage can be grown and as it matures the elastic modulus increases along a continuum (Huang et al. 2010). In studies that examine the digestion of cartilage to analyze the contributions of the constituents, a wide range of elastic moduli have also been found (Stolz et al. 2004). Although there are not a lot of data in the elasticity imaging community on these types of materials, measurements could potentially be made to quantify the mechanical properties with shear or guided waves.

Measuring the shear wave speed in materials with high shear wave speeds is difficult for two reasons. First, a high shear wave speed inherently implies that the tissue is stiff, so if the same stress that is applied in soft tissues will produce markedly lower displacements in these stiffer tissues. The minimum motion that most ultrasound-based methods can measure is typically 0.1 microns. A second issue is that because the waves move so fast, a very high frame rate must be used to measure the shear waves. The tissue motion must be tracked at several lateral locations through time to make a reliable estimate of the shear wave speed. If the number of spatial locations is limited or the measurement interval is too long, then these fast waves may not be evaluated correctly.

To analyze this problem, a theoretical treatment of shear wave phase velocity estimation was given by Urban, et al. (Urban et al. 2009). The shear wave phase velocity is the velocity at which each frequency component of the shear wave travels. The conclusions of this study were that errors can be decreased with increased shear wave displacement amplitude, increased number of lateral locations used for shear wave estimation, and increased signal-to-noise ratio in received ultrasound echoes. This same theoretical framework could be adapted to examine a time-domain based time-of-flight estimation of the shear wave group velocity. The shear wave group velocity is the velocity at which the wave packet travels.

These two aforementioned problems regarding displacement amplitude and increasing measurement frame rate can be addressed in a few ways. To induce more motion, the radiation force could be increased either by extending the excitation toneburst or by increasing the ultrasound intensity. Both of these approaches may be limited for clinical implementation because these methods must comply with regulatory limits on mechanical index (MI) and spatial-peak temporal average intensities (I_spta) set by the Food and Drug Administration (Herman and Harris 2002). As an alternative to radiation force, mechanical actuation can be used to produce more motion. This may increase the complexity of a particular method because of inaccessibility to the organ of choice or issues relating to alignment of the actuator and measurement device.

To increase the temporal resolution of the measurement, fewer spatial locations can be measured or a single location can be measured with M-mode ultrasound and the excitation can be repeated for every spatial measurement location to synthetically examine the wave propagation. In this case, measurements could be made with frame rates in the kilohertz range. This approach may be prohibitive for the amount of time it might take, particularly to make images. Another technique that has come into practice is to insonify the medium with a plane wave and perform beamforming only in receive (Bercoff et al. 2004). This method can be repeated at very high frame rates (up to 20,000 frames per second), but the signal-to-noise ratio (SNR) is typically poor. Coherent compounding with plane wave insonifications at different angles is one way to reclaim adequate SNR to make reliable shear wave velocity measurements (Montaldo et al. 2009).

Biological tissues that have higher shear wave speed also typically are thin in nature, such as cartilage and cortical bone. To make images of these materials, shorter shear wavelengths are needed, which would require higher frequencies. Waves with these higher frequencies with sufficient motion amplitude may be difficult to excite for reasons discussed above. The use of guided waves of lower frequencies may provide a solution for measuring these types of tissues, but methods have yet to be developed to address this.

Another region that has yet to be explored in detail is the “high attenuation” area where the shear wavelengths are very small. This region has significant importance because it includes shear modulus variations at the microscopic level. It is of significant interest for researchers in this field of elasticity imaging to relate how changes in the microenvironment translate to changes in the shear modulus measured at the macroscopic level. A greater understanding of these relationships could provide scientists and clinicians with useful information for understanding various disease processes including tissue fibrosis and cancer.

Shear Wave Imaging as a “Multiwave” Approach

Mathias Fink, et al., coined the term “multiwave imaging” to describe various methods used in elasticity imaging (Fink and Tanter 2010; Fink and Tanter 2011). This description is particularly pertinent to this discussion of acoustic imaging. In almost all of the methods described, a multiwave approach is taken to generate and/or measure shear waves. When mechanical actuation is used, a pure shear actuator is rarely used. Instead the actuator is typically inducing a compressional wave as well as a shear wave. The compressional wave typically has very low amplitude and travels very fast, so it is rarely reliably measured.

In methods that utilize acoustic radiation force, compressional ultrasound waves of sufficiently high intensity are used to displace the tissue and cause shear waves. Additionally, the motion detection, that is inherently necessary in all of the discussed methods, provides another circumstance of multiwave imaging. Compressional ultrasound waves are used to interrogate the tissue repeatedly to estimate the motion caused by shear wave propagation. In MRE, electromagnetic waves are used to measure the tissue deformation.

Dispersion in Shear Wave Measurements

Many methods use the group velocity of the shear wave for characterizing the material properties of tissue. When the group velocity is used, assumptions are typically made that the material is elastic and that the object is much larger than the shear wavelengths. These assumptions neglect dispersion due to either viscosity or finite geometry of the material. As a result, reporting only the group velocity could lead to bias in measurements if the effects of dispersion are neglected. It is imperative that if only group velocity is documented in studies then the frequency of the wave should also be reported so that the effects of dispersion may be assessed.

As many published reports have documented, soft tissues are inherently viscoelastic. One advantage of using shear waves for characterization of tissue is that the shear wave speeds exhibit dispersion. Multiple groups have examined the dispersion of shear waves in various soft tissues (Yamakoshi et al. 1990; Kruse et al. 2000; Kanai 2005; Klatt et al. 2007; Asbach et al. 2008; Tanter et al. 2008; Chen et al. 2009; Deffieux et al. 2009; Muller et al. 2009; Urban and Greenleaf 2009; Asbach et al. 2010; Couade et al. 2010; Gennisson et al. 2010; Amador et al. 2011; Bernal et al. 2011; Mitri et al. 2011; Nenadic et al. 2011c). Some groups use individual frequencies with mechanical actuation while others use impulsive shear waves generated using acoustic radiation force. The advantage of using acoustic radiation force is that many different frequencies can be excited in one acquisition. These shear waves can have large bandwidth typically ranging from 100–500 Hz, but in some cases up to 1500 Hz (Couade et al. 2010; Bernal et al. 2011). With larger bandwidths, the dispersion of the shear wave velocities can be more fully characterized and used for evaluating the elastic and viscous components of the tissue. Viscosity has been evaluated in a few different studies, but needs more exploration in different tissues to assess its usefulness as a biomarker of tissue health (Huwart et al. 2006; Chen et al. 2009). The large frequency range of the shear wave velocity feature space provides potential for using high bandwidth shear waves for viscoelastic property estimation.

Dispersion has also been used in the context of guided waves in tissues with specific geometries, particularly the heart, arteries and cornea (Kanai 2005; Tanter et al. 2009; Couade et al. 2010; Bernal et al. 2011; Nenadic et al. 2011a; Nenadic et al. 2011b; Nenadic et al. 2011c; Brum et al. 2012). As mentioned above, the dispersion in the measured wave velocities arises because of the tissue viscoelasticity and geometry. Using acoustic radiation force, waves with large bandwidth can be generated that can induce different modes of vibration within the tissue structure. Specific modes of vibration can be used in conjunction with geometrical measurements and a model to sensitively assess the viscoelastic properties of the tissue (Bernal et al. 2011; Nenadic et al. 2011c).

Potential Directions of Future Research Using Shear Waves

As discussed, there remains a broad region of the shear wave feature space that has yet to be explored, particularly for tissues with high shear wave velocities at the upper end of the frequency range.

One feature of shear waves that should be noted is that they are polarized allowing one to use shear waves to study tissue anisotropy. It should be noted that compressional waves are polarized as well, but if we revisit Eq. (5), the compressional modulus and density do not change with direction so the polarization is only due to the shear modulus. For example, in skeletal muscle it was shown that the compressional wave speeds changed as a function of fiber orientation and contraction state, but the change was at most 0.6% (Mol and Breddels 1982). Previously reported studies have taken advantage of this feature to explore the anisotropy present in skeletal and cardiac muscle (Gennisson et al. 2003; Chen et al. 2009; Urban and Greenleaf 2009; Gennisson et al. 2010; Lee et al. 2012b). Another organ that has also been examined in terms of its anisotropy is the kidney. The kidney consists of a network of tubules that are oriented radially. As a result, shear wave measurements made along or perpendicular to this radial orientation produces different results (Amador et al. 2011).

Another area that has only been studied in a preliminary fashion is elastic nonlinearity of soft solids. Nonlinear properties of tissue as it relates to elasticity have not been adequately addressed and may provide another parameter that could serve as a clinically relevant indicator (Catheline et al. 2003; Gennisson et al. 2007; Latorre-Ossa et al. 2012).

Conclusions

Shear acoustic imaging has been developed into a clinical imaging modality over the last two decades. Comparisons and contrasts between imaging with compressional and shear waves were described. Shear wave speeds are sensitive to tissue structure, such as anisotropy. Shear material properties have a large dynamic range, which provides large potential for characterizing different types of tissue, normal or pathological. Additionally, there is a large frequency range over which shear wave measurements can be made providing possibilities to evaluate soft tissue shear wave speed dispersion. This dispersion whether caused by viscoelasticity or geometry or the combination of these two factors can be used to sensitively evaluate material properties of the studied tissue. Some of the regions of the range of shear wave phase velocities have been studied by currently available methods, but there are some regions in this frequency/phase velocity space that have yet to be exploited. Also, parameters such as tissue anisotropy, viscosity, and nonlinearity can be characterized using shear waves. These parameters may serve as interesting biomarkers that could yield important diagnostic information. Shear acoustic imaging is still a young imaging modality that will continue to develop and has substantial potential for characterizing different soft tissues for clinical diagnosis.