акустика / gan_ws_acoustical_imaging_techniques_and_applications_for_en

echo frame is recorded. The movement of echoes is tracked to measure the displacement field. The gelatine block moves in three dimension, so the object boundaries have to be controlled to keep as much of the motion as possible in the imaging plane. Then the movement of ultrasound echoes faithfully represents that of the tissue scattering. The displacements depicted by arrows in Figure 10.25(b) were found using finite-element simulation software on a coarse grid. The vertical component of displacement which is also along the axis of the ultrasound beam is obtained from a finely sampled grid and concentrated into greyscale to give the vertical (axial) displacement image in Figure 10.25(a). The derivation of displacement gives the strain image in Figure 10.25(d). Strain is preferred over displacement for imaging because of higher image contrast (Figure 10.25(c) compared with Figure 10.25(d)). The phantom was build by Insana [57] and the imaging experiment described was performed [57], over a subregion surrounding the stiff inclusion [57]. The result is given in Figure 10.25(e).

The central dark region in strain indicates a region of low deformation and high stiffness. However, regions at the top and bottom appear dark because Insana [57] did not let those surfaces slip during compression to show the effects of boundaries. Strain images can be interpreted as the inverse of Young’s modulus (stiffness) via equation (10.7), only when the applied stress is constant throughout, which it was not in Figure 10.25.

Figure 10.24(c) illustrates how displacement δx (x) and strain εxx (x) develop along the x-axis (the notation is described below). The surface near the fingertips is displaced downward by the amount δ0. If the stiffness of the elastic tissue was constant, we would observe a linear displacement curve (dotted line) and the assorted strain, given by the derivative εxx (x) = dδx/dx, would be constant ε0. However, this medium is heterogeneous. Because stiff objects deform less than their surroundings, regions above and below deform more to keep the total deformation at δ0. Taking the derivative, we find lower strain in the inclusion and enhanced strain immediately surrounding the inclusion. Contrast enhancement is also seen in the modelled and measured strain image of Figure 10.25 on a bright region surrounding the stiff inclusion.

10.7.3Choice of Force Stimulus and Imaging Modality

The nature of the stimulating mechanical force determines which mechanical and geometrical properties of the tissue contribute to image contrast. Stimuli may be generalized as static as the example given above or dynamic. Static methods employ forces that are suddenly applied and held constant during imaging or allowed to slowly vary in time with respect to the temporal sampling of the imaging system, for example the frame rate.

In Figure 10.25, strain is imaged. However, strain may also be combined with stress estimates through constitutive equations [58] to display a modulus [59] and thereby minimize boundary effects. The advantages of modulus imaging must be compared with the extra computation time and any change in image quality or interpretation that affects diagnosis.

Studies on elasticity imaging started with static methods. These involved measurements of deformations from slowly moving endogenous sources like pulsable blood flow [60, 61]. Later methods measured deformations from exogenous sources such as compression plates for in vivo breast imaging [53] and balloons for in vivo vascular [62] and prostate [63] imaging.

The principal limitation of static strain imaging is the strong influence of boundaries on image contrast (e.g. Figure 10.25(d)). Advantages include the use of current image systems

and the simplicity of the calculation that allows high frame rates (commensurate with colourflow imaging) with spatial resolution approaching the intrinsic resolution of the host imaging modality.

For dynamic methods, tissues are stimulated with low-frequency (100 Hz) shear wave vibrations. As surface vibrations travel into the body, ultrasound pulses are introduced and echoes are recorded. The first methods measured the amplitude [64] and phase [65] of the low-frequency vibration from the Doppler modulation frequency of the ultrasound pulses to estimate resolution parameter of muscle and other soft tissues. The approach became more practical for clinical investigation of tumour imaging when colour Doppler systems were adapted to image vibration [66].

Shear waves are attenuated in tissues much more than compressional waves (ultrasound pulses), so it can be difficult to stimulate tissues mechanically deep in body. Continuum wave (CW) shear vibrations allow repeat measurements and temporal averaging when the imaging signals are weak. Yet some of the CW vibrational energy can be reflected from boundaries and form standing waves that interfere with image clarity.

MR elastography can provide distinct advantage over current ultrasound imaging technique [67]. As in dynamic ultrasound approaches, an applicator is coupled to the skin surface to introduce low-frequency shear waves into the body. MR signals are used to measure displacement distribution from travelling shear waves in the tissue volume. Displacement waves describe the wave speed from which shear modulus images are quickly computed (refer to equation (10.16)).

MR methods have also been proposed to image strain from static deformation [68]. The principal advantage over ultrasound is that MR provides finely sampled data from a tissue volume. Volume acquisition reduces signal loss from tissues moving out of the field and it allows for a more complete estimation of the strain tensor [69]. Current disadvantages (compared with ultrasound) include lower temporal resolution and higher imaging costs. With the commercialization of 2D ultrasound array enables the acquisition of volumetric ultrasound data. Also phased array MR techniques are promising to improve MR temporal resolution. So the advantage and disadvantage of each modality vary as technology develops.

Very high frame rate ultrasound techniques (>1000 fps) have been shown capable of imaging shear wave propagation in real time [70]. The advantage of this approach is the possibility of using shear wave pulses that locally stimulate tissues. Localization of the stimulus eliminates boundary effects and makes it possible to separate the influence of material elastic anisotropy from object shape, then increasing the feature space for diagnosis. Acoustic radiation force impulse (ARFI) methods [71, 72] use the radiation force generated by a high-intensity compression wave pulse at its focus to stimulate tissues with a force ‘impulse’ in both time and space. Then conventional broadband imaging pulses scan the medium to record the movement. Like static methods for mechanical stimulators, the elastic modulus of the medium contributes to the object contrast. Unlike static methods, viscous effects also play a major role in contrast, and the isolated ‘push’ from the radiation force of the high-intensity pulse reduces boundary effects significantly. The downside of very high frame rate and ARFI approach is that specialized equipment is needed, and in the ARFI approach, the use of high-intensity pulses raises concern about risks to the transducer and patients.

Vibro-acoustic imaging [73] is another imaging modality for locating calcified tissues in vascular plaques and tumours. Two-co-axial CW ultrasound beams tuned to slightly different transmission frequencies generate a harmonic radiation force that oscillates tissues at the

difference frequency near the focus. If stiff tissues like calcification are in the stimulated region, they radiate sound emerges at the difference frequency, which is in the audible frequency range. Spatial resolution depends on the co-axial pulse volume stimulating the tissue and image contrast depends on the mechanical properties of the tissues. Sensitivity and noise are effects on the ability of audible sound to travel out of the body to be detected by a microphone with a high signal to ambient noise data. Because low-intensity beams stimulate the tissues, bio-effects are not a major concern. However, it is challenging to design transducers that deliver a highly local radiation force that can be scanned electronically at real-time frame rate.

Another modality ultrasound strain rate imaging sometime called tissue Doppler imaging has been used for functional myocardial assessment [74].

10.7.4Physics of Elasticity Imaging

The basic equations used in elasticity imaging are (1) the constitutive equation that relates stress to strain, (2) the acoustic wave equation incorporating the theory of elasticity and (3) the equation describing the displacement of tissues by a mechanical stimulus. The linear theory of elasticity is used. The underlying assumptions are that tissues are a deformable continuum and that local displacements are small, for example (∂ δx/∂ x)n is negligible for n > 1. The second assumption may seem difficult to achieve considering that strain contrast increases with the amount of applied deformations. However, if the image data are acquired at a high frame rate while the forces are applied, the instantaneous displacements between frames can be accumulated [75], thus satisfying the assumption for estimation purposes while still enhancing image contrast.

To design elasticity imaging experiments and correctly interpret the results, it is critically important to understand how the stress loading of tissues and the measurement of displacement or strain determine which material properties influence the elasticity image. Equation (10.7) is a very simple constitutive equation that applies to infinitesimal deformation of 1D, elastic, isotropic medium where the strains vary linearly with stress. Although none of these assumption are strictly true in practice [58], they may be reasonable to assume for some experimental conditions.

We next extend the medium to three dimensions, leaving other assumptions in place. Since the elements of equation (10.7) are tensors and the general linear relation is [76]

The stress σ and strain ε tensors are second order (3 × 3 matrices) and symmetric if we avoid translation and rotation of the tissues from the applied force. Indices i jkl are variables for the coordinate labels (x, y, z). For example, σxy refers to the stress on a Cartesian surface with unit normal given by the x-axis where the force is oriented along the y-axis, that is a shear stress. Cauchy’s infinitesimal stress tensors [58] are found from derivation of the displacement vector

that characterize the medium. As σ and ε are symmetric, it can be shown that C has at most 21 unique components even if the medium is fully anisotropic.

Using directional cosines to define the isotropic axes of symmetry for all three tensors in equation (10.8), we find there are only two unique terms: Cxxxx = λ + 2G and Cxxyy = λ, where λ and G are Lame’ constants described in the following text.

where tr (ε) = εxx + εyy + εzz is the trace of the strain matrix that quantifies how much the volume of the medium changes due to the applied stress and δi j is the Kronecker delta. Equation (10.9) is Navier’s equation for an isotropic Hookean elastic solid [58].

Strain may be separated into two parts:

εi j = εi j + εi j , where εi j = 13 tr (ε) δi j is the mean dilation or contraction of the volume and εi j is the deviation of the deformation about the mean value. This decomposition allows the diagonal stresses of equation (10.9) to be written as

where κ = λ + 2 G3 . κ is the bulk modulus which describes how the medium volume changes under stress. G is the shear modulus that quantifies how the medium shape changes under the same stress. κ and G are fundamental properties of the medium, although the convention separation of strain into volumetric and shape components in Equation (10.10) is only valid for infinitesimal deformation. The numerical constants in Equation (10.9) and (10.10) develop because of traditional definition relating the bulk modulus to isotropic pressure, p = −κtr(ε), and the shear modulus to the amount of shear deformations γ = 2εxy, namely, σxy = Gγ .

Next, we illustrate the concept of derived moduli. Referring to the static strain experiment of Figure 10.25, where a compressional stress is applied to the top surface of a gelatine phantom along the x-axis, that is σxx. The stress and strain matrices for this experiment are

Note that strain components in the yz-plane are equal. The convenient derived quantities are Young’s modulus, E = σxx/εxx and Poisson’s ratio μ = −εyy/εxx. Isotropic media have two independent fundamental moduli and so two derived quantities are needed to characterize the medium for this experiment. Substituting equation (10.11) into equation (10.9),

Solving for σxx and εxx, we can relate Young’s modulus and Poisson’s ratio to the fundamental

The effects of boundaries are very important for static deformation because they modify equation (10.11). The fact that we did not let the top and bottom surface in Figure 10.25(b) slide during compression or restrict movement of the lateral boundaries had major influences on the stresses and strains near the periphery. If we could measure the full stress and strain tensors for each location, we could propose convenient derived quantities for imaging that could be directly related to κ and G.

Material properties that affect compressional (longitudinal) wave propagation can also be identified with these equations. As compressional plane waves propagate along the x-axis,

tissues compress and stretch in highand low-pressure regions along the x-axis. The stress and strain matrices for these conditions are

Derived quantities for this experiment are the wave modulus M = σxx/εxx = κ + 4G/3 and stress ratio

for ultrasonic elasticity imaging. This implies that sound propagation and tissue deformation depend on different material properties of the tissue. Although sound propagation depends on the bulk modulus, deformation depends on the shear modulus. If they were not independent, then deformation could alter the echo signals and ultrasound could not be able to accurately track tissue motion.

We consider only linear elastic and isotropic solids and small amplitude sound waves, where equation (10.9) is obeyed. The mechanical properties of solids are characterized by these parameters κ , G and mass density ρ. In regions where these values are spatially homogeneous and the effects of gravity can be ignored, then the displacement vector δ can be given as

Sound wave will propagate in solids both as compressed wave (longitudinal wave) and shear wave (transverse wave).

10.7.4.1Compressional Wave Propagation

It was shown in previous section that local pressure in compressed waves is given by a symmetric stress tensor. Consequently, the curl of the displacement vector, × δ, is zero [77] so that 2δ = ( · δ ). Substituting this identity into equation (10.15), κ + 43G ( · δ ) = ρ ∂d2t2δ , which gives

where cc = ((κ + 4G/3)/ρ )1/2 is the speed of the compressed wave.

Sometime the response of the medium to a stimulus may also be written as pressure wave [77].

10.7.4.2Shear Wave Propagation

Shear waves are central to dynamic elasticity imaging procedure. They produce no dilation or contraction of the medium, so the divergence of displacement, · δ is zero and

236 Acoustical Imaging: Techniques and Applications for Engineers

where cs = (G/ρ )1/2 is the shear wave velocity. Here, we notice that κ G so that cc cs. The large speed difference allow use of ultrasound imaging to observe travelling shear waves in dynamic elasticity imaging [70–72].

10.7.5Image Formation Algorithm

Here, we discuss the basics of image formation specifically for static ultrasound strain imaging. Imaging strategies are based on models of signal formation which requires an understanding of how tissue properties create the imaging signals and how stress stimuli deform the tissue properties. Common features of imaging algorithm are given in the following text.

10.7.5.1Modelling Object Structure and their Echo Signal

Let f j (x) be the scattering function that describes [78] the spatial distribution of structures interacting with an ultrasound pulse to produce detectable scattered waves during acquisition of the jth ultrasound echo frame. This is a natural representation because tissue scattering is a continuous function of 3D position x. For computer modelling purposes, however, it is convenient to sample f j (x) and rearrange the values into a column vector f j by lexicographical reordering.

Scatter movement is observed by examining the source tissue region during two or more instances in time. Object function present during the sequential acquisition of echo frames are related by displacement vectors δ j (x) that describe the movement of scatterers at each location. In the continuous representation, we have

f j+1 = f j x + δ j+1 (x) , and in the discretere presentation f j+1 = Q j+1 f j + erj+1,

where Q is a square matrix of displacements in the tissue region occurring between frames. The vector erj+1 represents registration errors caused by sampling the continuous function.

Scanning the object with a linear imaging system represented by the operator matrix H, we

where e j = Herj + eαj and eαj is a vector of acquisition errors, for example quantization and amplifier noises. The imaging system does not depend on when the data as acquired or the amount of deformation and therefore has no subscript. The vectors g are the RF echo signals recorded by the ultrasound scanner, not the B-mode image data. The objective in elasticity imaging is to estimate Q which contains the spatial distribution of displacements δ j+1 (x); essentially, the map of arrows seen in Figure 10.25(b).

10.7.5.2Estimating Displacements

To estimate Q, we seek a transformation of g j , given by the operator matrix D that produces the following statement:

The first line of equation (10.19) requires the finding of a matrix D that displaces the echoes of frame j so they match and highly correlated with the echoes of frame j + 1. The second line of equation (10.19) shows that this works perfectly (except for noise) only when the deformation and imaging operators commute, that is we can find a matrix D = Q only when DH = HQ. Unfortunately, this is not true in general as can be shown as follows: Consider that H is a blurring matrix where the rows are impulse responses (point spread function) of the imaging system. Deformed tissue structure of size below the spatial resolution of the image system are not faithfully represented in the echo signal, so there is no deformation matrix H that can be applied to the echo signal g j that allows the right-side equality in the second line of equation (10.19) to be true. Equation (10.19) can be exact (except for noise) only when H equals the identity matrix, that is, when we use a perfect ultrasound imaging system where the shift-invariant impulse response is a Dirac delta function.

Assuming that equation (10.19) is reasonably accurate, displacements are estimated from RF echo frames using constrained optimization. Specifically, we seek to define a matrix D that minimizes the objective function [77]:

where || · || is the norm of the vector, α is a constant and r is a roughness penalty vector and a function of displacement [79]. The purpose is to find a displacement matrix D that minimizes the first term on the right side of equation (10.20) and yet is subject to the constraint that the solution must be spatially smooth, the second term. When we find D that minimizes the

ˆ

objective function, we will use it as the estimate D.

The simplest algorithm that follows this strategy is to simply cross-correlate subsections of g j and g j+1 to find the average local displacements [53, 57, 71, 72]. For small displacements that remain in the scan plane, numerous correlation-based techniques can be unbiased, precise (satisfying the maximum likelihood criterion) and computationly efficient.

To demonstrate the merit of regularization, that is using the smoothness penalty term in equation (10.20) by setting α > 0, consider the phantom images in Figure 10.26. This is a flow phantom that has a stiff, solid central region and a soft flow channel that cuts diagonally across. The 7 MHz B-mode image in Figure 10.26(a) shows both structures as low scattering (hypoecho). The correlation-based strain image in Figure 10.26(b) from Ref. [7] shows the central region to be stiff (low strain) and the flow channel to be soft (high stiffness) as expected, although there is plenty of noise particularly near the softer regions than deform to a greater extent. This strain noise is caused by the low RF echo SNR in the flow channel, by echo decorrelation from motion smaller than the imaging pulse volume, and by same out of plane scatterer movement. α was increased in equation (10.20) as described in Ref. [34], which constrained the space of possible displacement solution to those that were spatially

Figure 10.26 Images of an ultrasonic phantom with a stiff circular inclusion and a soft flow channel. The strain image in (b) was obtained from equation (10.19) without regularization, that is, α = 0, using the correlation algorithm described in Ref. [7]. The strain image in (c) was also obtained from equation (10.19) but with regularization, α > 0, and using the optical flow algorithm described in Ref. [34] (Insana [48] © John Wiley & Sons)

smooth. The physics of tissue-like material deformation show that very rapid oscillation in displacement was nonphysical. The regularization term excludes solutions to the objective function in equation (10.20) that are nonphysical. So the fast spatial fluctuation in strain are treated as noise and eliminated. Regularization should not be used in imaging situation that are not well understood because prior knowledge is too incomplete to restrict the solution space without incurring bias errors. Regularization compromises the spatial resolution of strain estimates to a degree (shown by the flow channel in Figure 10.26(c) which is wider than in Figure 10.26(a) or (b)) but for many situation, the noise improvement makes it worth the effort.

Ultrasound elasticity imaging is also known as advanced ultrasound imaging and it helps to eliminate unnecessary cases of biopsis. Further improvements on the equation of motion by incorporate nonlinear effects will give more features of imaging and provide more valuable information.

10.7.6Some Examples of Commercial Systems

10.7.6.1ACUSON S2000TM Ultrasound System and ACUSON AntaresTM Ultrasound System

eSie Touch Elasticity Imaging

These systems have the capability of eSieTouchTM elasticity imaging. This was first shown by Siemens Medical Solutions at the ECR 2007 (European Congress of Radiology) in Vienna, Austria. The software for this diagnostic advance is offered with the 5.0 release of the Acuson Antares ultrasound system, premium edition.

This application generates an elastogram which provides additional information about mechanical properties, for example the stiffness for breast lesion. This Siemens method offers a significant improvement of the acquisition of the data in most cases, the heart beat and the breathing of the patient will provide a sufficient ultrasound to generate the elastogram. Elasticity imaging illustrates the relative stiffness of tissue compared to its surroundings. As tissue undergoes pathologic changes, its relative stiffness will change. The stiffness of the tissue as well as its size compared to the B-mode image provides further insight into potential pathology.

eSieTouch elasticity imaging uses gentle compression to provide a high-resolution elastogram depicting relative tissue stiffness. This imaging method forms the elastogram by computing relative tissue deformation globally and displaying the information within a user defined region of interest. Axial detection pulses are continuously transmitted throughout the field of view to provide information about the state of tissues deformation along one axial line at a specific point in time. Using this technique, stiff and soft tissue may be differentiated even when the tissues appear isoechoic in the B-mode examination.

The unique features of eSie Touch Elasticity Imaging are as follows:

(a)Quality factor: It provides real-time qualitative feedback to assist images in optimizing their acquisition technique. The real-time numerical elastogram quality score provides additional information for selecting optimal images for review. The quality factor is available exclusively on the ACUSON S2000TM ultrasound system.

(b)Elastographic maps: High-resolution elastographic images may be visualized using a variety of greyscale and colour maps.

(c)Shadow measurements: Measurement calipers are automatically applied to both images in a side-by-side display for comparison of elastography.

(d)Transducer support: eSie Touch imaging is supported on linear endocavity and curved array transducers.

While ultrasound examinations do not eliminate biopsies in general, there is hope that this new method may greatly reduce the number unnecessary breast biopsies. A biopsy is not only an uncomfortable invasion procedure but also often requires a long waiting tune for the results. Estimates by experts show that approximately 75% of all biopsies are negative. As a result, elasticity imaging offers a huge potential to improve patient care and lower costs at the same time.

Virtual Touch Tissue Imaging

The ACUSON S2000 ultrasound system has the capability of Virtual Touch tissue imaging. The Virtual Touch applications are the first commercially available implementation of ARFI technology. Virtual Touch applications include Virtual Touch tissue imaging and Virtual Touch tissue qualification. This imaging method implements ARFI technology for evaluation of decay tissues not accessible by superficial compression. Elastography Virtual Touch imaging provides a qualitative greyscale map (elastogram) of relative stiffness for a user-defined region of interest. Using this method, stiff tissue may be differentiated from soft tissue even if appearing isoechoic using conventional ultrasound imaging.

A Virtual Touch image is acquired through a series of acoustic push pulse/detection pulse sequences. The process may be summed up into three basic steps:

1.Baseline image is acquired.

2.Acoustic push pulse is transmitted to compression tissues.

3.Detection pulses are used to track the amount of compression.

This process is repeated throughout the region of interest. The resultant image is displayed side-by-side to the corresponding B-mode image for comparison.

The benefits of Virtual Touch imaging technology as compared with other elastography techniques are as follows:

(a)No manual compression

(b)Superior image quality

(c)Decreased interoperator variability

(d)Deep tissue imaging

Virtual Touch Tissue Quantification Technology

The Virtual Touch tissue quantification technologies available on the ACUSON S2000 ultrasound system Virtual Touch Tissue Quantification is the first and only quantitative assessment of tissue stiffness through measurement of shear wave speed. Shear waves are generated by displacement of tissue and attenuate approximately 10 000 times more rapidly than conventional ultrasound waves (or compressional waves). The ACUSON S2000TM ultrasound system provides the sensitivity needed to detect and measure shear wave speed.

Virtual Touch qualification uses an acoustic push pulse followed by detection pulses to calculate shear wave speed:

1.Anatomical location for measurement defined by region of intensity (ROI) placement.

2.Acoustic push pulse applied adjacent to ROI.

3.Tracking beams (sensitive to greater than 1/100 the wavelength of sound) are applied adjacent to the acoustic push pulse.

4.Time between the generation of the shear wave and the passing of shear wave peak at an adjacent location is utilized to compute the shear wave velocity.

In general, shear wave speed increases with tissue stiffness.

The benefits of Virtual Quantification are as follows:

(a)Quantitative technology

(b)Reproducible

(c)Provides indication of tissue stiffness

Details of Virtual Touch Tissues Imaging and Quantification

There are three steps in the Virtual Touch software acquisition process. Firstly, a baseline B-mode sonographic reference image is obtained. Secondly, a short (approximately 100 μs acoustic ‘push’ pulse is transmitted through tissue. As this pulse travels through the region of