IOP PUBLISHING
PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 52 (2007) 2615–2633
doi:10.1088/0031-9155/52/9/019
Visualization of bonding at an inclusion boundary using axial-shear strain elastography: a feasibility study Arun Thitaikumar1,2, Thomas A Krouskop1,3, Brian S Garra4 and Jonathan Ophir1,2 1
Department of Diagnostic and Interventional Imaging, The University of Texas Medical School, Ultrasonics Laboratory, Houston, TX, USA 2 Electrical and Computer Engineering Department, University of Houston, Houston, TX, USA 3 Department of Physical Medicine and Rehabilitation, Baylor College of Medicine, Houston, TX, USA 4 Department of Radiology, University of Vermont college of Medicine, Burlington, VT, USA E-mail:
[email protected]
Received 15 December 2006, in final form 1 March 2007 Published 18 April 2007 Online at stacks.iop.org/PMB/52/2615 Abstract Ultrasound elastography produces strain images of compliant tissues under quasi-static compression. In axial-shear strain elastography, the local axialshear strain resulting from application of quasi-static axial compression to an inhomogeneous material is imaged. The overall hypothesis of this work is that the pattern of axial-shear strain distribution around the inclusion/background interface is completely determined by the bonding at the interface after normalization for inclusion size and applied strain levels, and that it is feasible to extract certain features from the axial-shear strain elastograms to quantify this pattern. The mechanical model used in this study consisted of a single stiff circular inclusion embedded in a homogeneous softer background. First, we performed a parametric study using finite-element analysis (FEA) (no ultrasound involved) to identify possible features that quantify the pattern of axial-shear strain distribution around an inclusion/background interface. Next, the ability to extract these features from axial-shear strain elastograms, estimated from simulated pre- and post-compression noisy RF data, was investigated. Further, the feasibility of extracting these features from in vivo breast data of benign and malignant tumors was also investigated. It is shown using the FEA study that the pattern of axial-shear strain distribution is determined by the degree of bonding at the inclusion/background interface. The results suggest the feasibility of using normalized features that capture the region of positive and negative axial-shear strain area to quantify the pattern of the axial-shear strain distribution. The simulation results showed that it was feasible to extract the features, as identified in the FEA study, from axial-shear strain elastograms. However, an effort must be made to obtain axial-shear strain 0031-9155/07/092615+19$30.00 © 2007 IOP Publishing Ltd Printed in the UK
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elastograms with the highest signal-to-noise ratio (SNRasse) possible, without compromising the resolution. The in vivo results demonstrated the feasibility of producing and extracting features from the axial-shear strain elastograms from breast data. Furthermore, the in vivo axial-shear strain elastograms suggest an additional feature not identified in the simulations that may potentially be used for distinguishing benign from malignant tumors—the proximity of the axial-shear strain regions to the inclusion/background interface identified in the sonogram. (Some figures in this article are in colour only in the electronic version)
Introduction It is known that among breast lesions, malignant tumors are generally more firmly bonded to their surroundings than are benign tumors (Chen et al 1995, Ueno 1986, Konofagou et al 2000). Malignant tumors appear to exhibit a stellate (star-shaped) or spiculated appearance, with tentacles radiating outward from the tumor into the surrounding tissue (Popli 2002). Unlike malignant tumors, benign tumors appear to have a smooth margin and may be more loosely bonded to the surrounding tissue (Fry 1954, Ueno 1986, Moon et al 2002). Figure 1 adapted from Ueno (1986) shows a cartoon of isolated benign and malignant tumors. Conventional ultrasound techniques for distinguishing benign from malignant tumors use criteria such as margin irregularity, shadowing, microlobulation, ellipsoid or wider-than-tall (parallel) orientation along with a thin, echogenic capsule and shape (Stavros et al 1995). In another study, tumor margin was shown to be the most important sonographic feature in differentiating benign from malignant tumors (Chen et al 2004). More detailed reviews of breast cancer differentiation are available in the literature (Sickles 2000, Orel and Schnall 2001). However, the features used in conventional ultrasound techniques do not directly relate to how the tumor may be bonded to the surrounding tissue. Elastography (Ophir et al 1991) is now a well-established technique, which is being commercially introduced for applications in breast diagnosis. It is an imaging technique that applies a quasi-static compression to detect stiffness variations within ultrasonically scanned tissue to create strain elastograms. If certain tissue regions have different stiffness parameters than others, the level of strain in those regions will generally be higher or lower than those in the surrounding material; a stiffer tissue region will generally experience less strain than a softer one. The theoretical and practical basis for elastography is given in Ophir et al (1999). Elastography has been proven to be helpful in detecting tumors in breast and prostate tissues (Garra et al 1997, Hiltawski et al 2001, Lorenz et al 1999). Ophir et al (1996a) have shown that there may exist a size difference between the sonographic and elastographic appearance of malignant breast tumors, where malignant tumors appear bigger in the elastograms than in the sonogram. A number of researchers (Garra et al 1997, Hall et al 2001, Svensson et al 2005, Barr 2006) have used these differences to classify breast tumors as benign or malignant. The difference in size of tumor was tentatively attributed to the presence of desmoplasia in and around malignant tumors, but this remains unproven. Despite some promising results, the difficultly in determining the tumor size, mainly due to poor tumor definition on the sonograms (due to low echogenicity and shadowing artifacts) limits the accuracy of this method in tumor classification.
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Figure 1. Tumor appearances from pathology: (a) benign, (b) malignant (adapted from Ueno (1986)).
Therefore, the key question is: Can additional information about the bonding at the tumor interface be obtained by using elastographic techniques, which might be useful in increasing the accuracy of this classification? The elastic modulus and Poisson’s ratio are the two parameters that describe the response of isotropic, homogeneous, linearly elastic tissues to mechanical loading (Saada 1983). The elastic modulus is defined as the ratio of stress to strain on the loading plane along the loading direction and it contributes to the stiffness of a tissue. Similarly, the ratio of shearing stress to shearing strain defines the constant, G, called the modulus of elasticity in shear or the modulus of rigidity (Timoshenko and Goodier 1970). For homogeneous, isotropic, elastic materials the modulus of rigidity, G, is related to the elastic modulus, E, and Poisson’s ratio, υ as G = E/2(1 + υ); under simplistic assumption of tissue incompressibility (υ ∼ 0.495), 3G ∼ E. Therefore, under such conditions one can determine either modulus, elastic modulus or modulus of rigidity, if the other one is known. When an inhomogeneous material is subjected to a quasi-static axial compression (as in elastography), shear strains, known as pure shear (Timoshenko and Goodier 1970), are generated at the interfaces between the inhomogeneities and the embedding material. The magnitude and distribution of these shear strains depend on the bonding at the interface as well as other factors listed in the following section (Twiss and Moores 1992, Knight et al 2002). It is in this context that imaging of the shear strains appears to be of significance. Whereas axial strains provide information on the tissue stiffness, the shear strains near the interface are related to the bonding at the interface. Thus, we hypothesize that quantifying the pattern of shear strain distribution near the interface may convey information that is directly related to the bonding at the interface after accounting for the effects of other factors. In order to optimally interpret and utilize any image, it is necessary to use an image that is created at the best attainable image quality for a given task. The image quality is usually described in terms of the signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), resolution and dynamic range (Wells 1977, Rangayyan 2005). Recently, we reported the image quality aspects of the shear strain elastograms (Thitaikumar et al 2005, 2006, 2007). In Thitaikumar et al (2005), it was shown that the shear strain component obtained from lateral displacements, i.e. the lateral shear strain, had a poorer SNR when compared to the shear strain component obtained from axial displacements, or the axial-shear strain. This study highlighted the limitations in using the total shear strain as a sum of the axial and lateral shear strain components. The practical impact of this limitation is not yet fully understood. However, in the case of a circularly (or elliptically) symmetric inclusion, which is the likely shape of breast tumors (Stavros et al 1995), it is expected from our preliminary work (unpublished) that the axial-shear strain alone may provide adequate quality information on the bonding at the interface. Therefore, investigation of the image quality in terms of resolution (Thitaikumar et al 2006) and contrast-to-noise ratio (CNRasse) (Thitaikumar et al
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2007) was done only for the axial-shear strain elastograms. It was shown that the resolution along a non-normal direction to that of the ultrasound beam axis was determined by the larger of the beamwidth and the bandwidth. However, for a given ultrasound system, the achievable resolution was limited by the window length but not by the window shift. The CNRasse on the other hand did not improve with increase in the window length or window shift and a trade-off between CNRasse and resolution in axial-shear strain elastography was found only in terms of the system parameters (beamwidth and pitch), but not in terms of the signalprocessing parameters (window length and window shift). In addition, it was shown that the 0.5%–3% applied axial compressive strain range that is optimal in terms of CNRe and SNRe in axial elastography (Srinivasan et al 2003) is also optimal for axial-shear strain elastography. Therefore, throughout this paper we assume that for a given ultrasound system, the chosen signal-processing parameters yielded axial-shear strain elastograms of best attainable image quality, in terms of CNRasse, for a differential strain estimator. It is important to understand how the fundamental mechanical parameters, apart from bonding at the inclusion/background interface, affect the axial-shear strain distribution. This understanding is necessary because it may help in identifying features that can quantify the pattern of axial-shear strain distribution, which may relate to bonding at the interface. This issue needs to be addressed before we can utilize axial-shear strain elastograms effectively to obtain information on the bonding at the interface. Note that the understanding of the action of the fundamental mechanical aspects need not involve ultrasound and signal-processing parameters. Therefore, the first task is to identify the existence of feature(s) that quantify the pattern of axial-shear strain distribution and are sensitive only to bonding at the interface. A logical extension to this is to investigate whether such features can be extracted from axialshear strain elastograms (i.e., those involving ultrasound and signal-processing parameters) in the presence of estimation noise. However, the ultimate assessment of the utility of any image is when it is used in actual settings. Hence, it is necessary to investigate the feasibility to produce in vivo axial-shear strain elastograms and extract from them the features that provide information about bonding at the interface. Further, the potential to utilize the extracted features to classify a tumor as benign or malignant needs to be ultimately assessed. In this paper, we describe the study that was designed to address the issues raised in the previous paragraph. The paper is organized as follows. First, a parametric study consisting of finite-element modeling and analysis (FEM/FEA) to understand the influence of the fundamental mechanical aspects is described. Next, a simulation study (involving ultrasound beam simulation and strain estimation algorithms) to investigate the feasibility of extracting shear strain features from axial-shear strain elastograms is described. Later, a retrospective in vivo study to demonstrate the feasibility to produce and extract features from axial-shear strain elastograms is described. Finally, results from each of the studies are reported. Note that clinical utility of in vivo axial-shear strain elastograms for classifying tumors is not a subject of this paper. Materials and methods FEM and analysis R (Ansys Inc, The modeling was done using the finite-element (FEM) software ANSYS Canonsburg, PA). We considered only a 2D plane strain problem. The geometry consisted of a single stiff circular inclusion embedded in a square homogeneous softer background. The material properties of the inclusion and the background differed only in terms of their Young’s moduli, and both had the same Poisson’s ratio value of 0.495. The dimensions of the
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square background region were set at 40 mm by 40 mm. It is important to note that when an inclusion is embedded to a background, the inclusion/background interface is modeled by default as being firmly bonded in FEM software. Therefore, we introduced contact elements at the interface in order to change the degree of bonding at the interface. One of the attributes of the contact elements is the coefficient of friction, a unitless constant usually between 0 and 1 (Mase 1970), which can be changed to simulate different degrees of bonding at the interface. The lower limit on the coefficient of friction is zero while a firmly bonded inclusion is considered to have infinite friction coefficient. The simulated phantoms were free to move on the sides (i.e., no lateral confinement) and had slip boundary conditions at the bottom (a node at the axis of lateral symmetry was fixed to the bottom of the phantom to avoid rigid body motion). In addition, the node at the center of the inclusion was confined in the lateral direction. This prevented any rigid body rotation of the inclusion. The phantom was subjected to a compressive axial strain and the resulting axial and lateral displacements of each node in the simulated phantom were extracted from the output of the FEA software. Apart from the external boundary conditions, the other mechanical modeling parameters that can be controlled are as follows. 1. 2. 3. 4. 5.
Applied axial compressive strain. Inclusion–background Young’s modulus contrast. Size of the inclusion. Degree of bonding at the interface, modeled using the coefficient of friction. Location and shape of the inclusion.
In this part of the study, we performed a parametric analysis to determine the effect of each of the parameters listed above on the distribution of axial-shear strain, except the last one. The reason for that is as follows. It is always desirable to position the transducer so that the inclusion is at the center of axis of lateral symmetry. Therefore, to study the effect of position is not really required. The shape of the inclusion is still critical. However, considering that most of the breast tumors can be approximated to have a circular symmetric shape (Stavros et al 1995), we did not consider other shapes. Unless otherwise stated, the following values were assigned to the modeling parameters: applied axial strain of 1%, inclusion–background modulus contrast of 2, and the diameter of the inclusion of 10 mm. First, the applied axial strain was changed from 0.5% to 5% and the resulting changes in the axial-shear strain pattern were studied. Next, the effect of Young’s modulus contrast was studied for inclusion/background modulus contrast ranging from 2 to 10. Similarly, the effect of size of the inclusion was studied by changing inclusion diameter from 4 mm to 10 mm. Finally, the effect of degree of bonding was studied by changing the coefficient of friction from 0.001 to 1 and using the additional case of the firmly bonded inclusion. Figure 2 presents an example image of the axial-shear strain for a firmly bonded (corresponding to an infinite coefficient of friction), and a loosely bonded inclusion with a coefficient of friction of 0.01. Observe that apart from symmetry, there are some interesting features. The axial-shear strain inside the inclusion is zero in the case of the firmly bonded inclusion while in the case of the loosely bonded inclusion there exist significant shear strains inside the perimeter of the inclusion. In addition, note that in the case of the loosely bonded inclusion there are two regions outside the inclusion (in any one quadrant) that are of opposite signs, unlike in the firmly bonded inclusion case, where there is only one such region. It must be remembered that we are attempting to identify features that quantify the pattern of axial-shear strain distribution. In reality, we know the amount of applied axial compression; we can estimate the inclusion size from the corresponding sonogram/axial elastogram.
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Figure 2. Axial-shear strain images from FEM of (a) a firmly-bonded and (b) a loosely bonded inclusion. The coefficient of friction was 0.01. The applied axial strain was 2%. The inclusion was twice stiffer than the background in both the cases.
Figure 3. Axial-shear strain images from FEM of loosely bonded inclusion (with a coefficient of friction of 0.01) illustrating the various possible features that can be used to quantify the pattern of axial-shear strain distribution.
Therefore, if we normalize the features with respect to these known quantities, we could derive normalized features that are sensitive only to bonding at the interface for a given modulus contrast. Thus, we have normalized the features for the size of the inclusion and the applied axial strain. Because of symmetry, analysis was done using only one quadrant. The various normalized features are illustrated in figure 3 for a contour threshold set at 25% of applied axial strain. These include the area of positive axial-shear strain region, area of negative axial-shear strain region, difference between the two areas and distance of separation between the positive and negative axial-shear strain regions of the first and second quadrants. The features that describe area metrics have been normalized to the inclusion area and the one that describes the length metric has been normalized by the inclusion radius. The features involving area were obtained by contouring the axial-shear strain magnitude with a threshold. The contour threshold was set as a percentage of the applied axial strain. Thus, features were automatically normalized for the applied axial strain. We evaluated the effect of choice of the contour threshold on the features. As an example, the normalized positive axial-shear
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Figure 4. Effect of the contour threshold on segmentation of the positive axial-shear strain area from the axial-shear strain image. Observe that the smaller threshold favors larger slope compared to larger threshold. Note that the choice of the lower threshold value is noise limited.
strain area obtained for three different contour threshold values at various degrees of bonding is plotted in figure 4. It can be observed that the lower the threshold, the larger the slope of the curve (more sensitive) and the larger the threshold, the smaller the slope (less sensitive). Therefore, lower values for the threshold are preferred. However, choice of lower thresholds is limited by the noise in the image; clearly a conflicting requirement. Thus, we chose an arbitrary threshold value to be 25% of the applied axial strain as a compromise between the two requirements. Note that the features have not been normalized to remove the effect of the modulus contrast. One possible method to do so is as follows. The Young’s modulus contrast can be estimated from the axial elastograms by using the analytic expression relating the strain contrast to modulus contrast (equation (29), Kallel et al (1996)). Even though this expression was developed under the assumption that the inclusion was firmly bonded, we have found (Thitaikumar and Ophir 2006) that under some conditions (and within some reasonable error bounds), it can be extended to the loosely bonded inclusion as well. Further, it was shown in Thitaikumar et al (2007) that the axial-shear strain magnitude increases with increase in modulus contrast at any given applied axial strain. Therefore, with the knowledge of the modulus contrast and applied axial strain, we can adjust the contour threshold to normalize for the modulus contrast. This will make the normalized features sensitive only to bonding at the interface. Simulations The 2D transducer point spread function (PSF) was simulated using a shift-invariant Gaussianmodulated cosine pulse in the axial direction and Gaussian beam profile in the lateral direction. The center frequency was set at 5 MHz while the fractional bandwidth was kept fixed at 50% of the center frequency, and the beamwidth of the Gaussian beam profile in the lateral direction was set to 1 mm. The scanner parameters were chosen to closely correspond to those of the HDI-1000 (ATL-Philips Inc., Bothell, WA) because it was used to obtain in vivo data presented in this paper. The simulations were performed assuming the speed of sound to be 1540 m s−1. The pre-compression RF signal was simulated by convolving the 2D PSF with the scattering function. A normal distribution of scatterer amplitudes was used to model the scattering
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function (Wagner et al 1983, Meunier and Bertrand 1995a, 1995b). The displacement profile calculated from the FEA software, as explained in the previous section, was used to define the post-compression position of the ultrasonic scatterers. The post-compression RF signal was simulated by convolving the displaced point scatterers with the original PSF (C´espedes 1993). The sonographic signal-to-noise ratio (SNRs) was set to 40 dB by adding an appropriate amount of uncorrelated random noise. The RF sampling frequency was set to ten times the R (Mathworks, MA). center frequency. All the simulations were done using MATLAB The simulated pre-compression and temporally stretched post-compression RF signals were segmented and used in an adaptive strain estimation algorithm with lateral correction to estimate the axial displacement (Srinivasan et al 2002a). The local axial-shear strains were estimated as the gradients of the axial displacements in the lateral direction. A crosscorrelation window length of 1 mm and a shift of 20% of the window length were used unless otherwise stated. As explained earlier, we are interested in obtaining information on the bonding at the inclusion/background interface from axial-shear strain elastograms. It is natural to expect that the ability to extract the normalized features from axial-shear strain elastograms depends on its image quality. As a result, it is desirable to use axial-shear strain elastograms with high SNR and high resolution. In order to improve the SNR without compromising the resolution, each of the elastograms considered is an average over 15 independent elastograms. A total of 180 independent realizations of the axial-shear elastograms were simulated. Therefore, the means and error bars in the plots correspond to 12 realizations. In addition, we also simulated elastograms at different resolutions (by changing the center frequency from 3 MHz to 10 MHz with an elemental pitch of λ/2). This was done in order to see the effect of resolution on the ability to extract the normalized features. In vivo study The objective of this study was twofold: first, to investigate the feasibility to produce in vivo axial-shear strain elastograms; second, to evaluate the feasibility to extract normalized features from the axial-shear strain elastograms. The data were acquired at the University of Vermont, by Dr Brian Garra. Data from a total of seven malignant tumors and seven benign tumors are reported in this paper. The pathology of the tumors was confirmed by histological analysis. The data used to create the elastograms were acquired using the HDI-1000 (ATL-Philips Inc, Bothell, WA) scanner. The acquisition protocol involved multi-compression, with a step size of 0.25%. The total compression was 5% and thus each elastogram shown in this paper is a multi-compression average of 20 realizations. The displacements from the pre- and postcompression RF data were estimated using the same algorithm as that used in simulations. However, the axial-shear strain was estimated by extending the staggered strain estimation proposed by Srinivasan et al (2002b) to the lateral direction. As explained earlier, there exists a size difference between tumor appearance in sonograms and elastograms for the case of malignant tumors. Therefore, in order to normalize the features for the size of the lesion, one could estimate the lesion size from either the sonogram or the corresponding axial elastogram. In this study, we have normalized the features using the size from the sonogram. Results FEA The results from FEA are reported in the following manner. The effect of each of the mechanical parameters on the features quantifying the pattern is shown for two different
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Figure 5. Plots showing the effect of applied axial strain on the normalized features extracted from the axial-shear strain image of a firmly bonded inclusion (solid line) and loosely bonded inclusion (--). The normalized features are area of positive axial-shear strain region (×), area of negative axial-shear strain region (∗), difference between the two areas (), and distance of separation between positive and negative axial-shear strain regions (♦).
bonding conditions. The first bonding condition represents a firmly bonded inclusion (infinite coefficient of friction) and the second represents a loosely bonded inclusion with a coefficient of friction of 0.01. The features at any other coefficient of friction are expected to elicit similar behavior as reported for the representative cases. Applied axial strain Figure 5 shows the normalized feature values, which quantify the pattern, at different values of applied axial strain. It is clear from the plots that the normalized features identified do not change with applied axial strain. This suggests that the pattern of axial-shear strain distribution does not depend on applied axial strain. However, note that the values of the normalized features are different for the two different bonding conditions. This issue is addressed later in this section. Inclusion–background Young’s modulus contrast The various normalized features are shown as a function of modulus contrast in figure 6. It can be noticed that the magnitude of the features does depend on the modulus contrast. This is not surprising because we normalized the features only for the applied axial strain and lesion size, which are known, and not for modulus contrast. As mentioned earlier, we can normalize for the modulus contrast by estimating it from the strain contrast observed in the axial elastogram (Thitaikumar and Ophir 2006) and scaling the contour threshold accordingly. Size of the inclusion Figure 7 shows the plot of the normalized features as a function of inclusion size. Clearly, the size of the inclusion does not have any influence on the pattern of the axial-shear strain distribution. This was expected since we normalized the features to account for the size of the inclusion.
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Figure 6. Plots showing the effect of modulus contrast on the normalized features extracted from the axial-shear strain image of a firmly bonded inclusion (solid line) and loosely bonded inclusion (--). The normalized features are area of positive axial-shear strain region (×), area of negative axial-shear strain region (∗), difference between the two areas (), and distance of separation between positive and negative axial-shear strain regions (♦).
Figure 7. Plots showing the effect of inclusion size on the normalized features extracted from the axial-shear strain image of a firmly bonded inclusion (solid line) and loosely bonded inclusion (--). The normalized features are area of positive axial-shear strain region (×), area of negative axial-shear strain region (∗), difference between the two areas (), and distance of separation between positive and negative axial-shear strain regions (♦).
Degree of bonding at the interface, modeled using the coefficient of friction The results clearly indicate that for a given bonding at the interface, and at a given modulus contrast, the other mechanical parameters do not influence the pattern of distribution of the axial-shear strain around the inclusion. Recollect our hypothesis that the changes in the pattern of axial-shear strain distribution are related to the bonding at the interface. Figure 8 shows
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Figure 8. The normalized features from axial-shear strain image as a function of coefficient of friction at the interface. Note that most of the identified features are sensitive to bonding at the interface in the coefficient of friction range of 0.1–1.
the normalized features as a function of bonding at the interface. The degree of bonding was modeled using a coefficient of friction at the interface. As mentioned earlier, a firmly bonded condition has a theoretical infinite coefficient of friction. Therefore, for plotting purposes, we have assigned a coefficient of friction value of 100 to the firmly bonded condition. It is clear from the plots shown in figure 8 that the pattern of axial-shear strain distribution depends on the degree of bonding at the interface. However, note that the features are all not equally sensitive to the degree of bonding over the entire dynamic range of coefficient of friction values. It appears that for coefficient of friction values below 0.1 or above 1, most of the features saturate and are insensitive to the degree of bonding. The feature that quantifies the ‘distance of separation’ is even more restricted in its dynamic range. Clearly, there is a useful dynamic range of the values of degree of bonding, within which we can use the normalized feature values to infer the bonding. This range of values is labeled as the useful region in figure 8. Simulations The normalized features discussed in the FEA were extracted from the simulated axial-shear strain elastograms. Figures 9(a) and (b) show the effects of applied axial strain and inclusion size on the estimated feature values, respectively. It can be observed that the normalized features are not sensitive to these mechanical parameters, as noted in FEA. However, note that as the inclusion size increases, the estimation error decreases, and the values stabilize. This effect may be explained in terms of how the inclusion size compares to the resolution of the system. The larger the inclusion size compared to the resolution of the system, the smaller will be the error in estimating the feature values and vice versa. It was shown using FEA that there existed normalized features that are sensitive to bonding at the interface. However, the axial-shear strain images used in FEA can be treated as an image with very high SNR and resolution, compared to elastographic images. We averaged
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Figure 9. Plots showing the effect of (a) applied axial strain and (b) inclusion size on the normalized features extracted from the axial-shear strain elastogram of a firmly bonded inclusion (solid line) and loosely bonded inclusion (--). The normalized features are area of positive axial-shear strain region (×), area of negative axial-shear strain region (∗), difference between the two areas (), and distance of separation between positive and negative axial-shear strain regions (♦).
15 elastograms to improve the SNRasse, but the resolution is ultimately limited to that of the elastographic system. Figure 10 shows a comparison between the axial-shear strain images from FEA and that estimated from the simulations, at different values of coefficient of friction. It appears that overall the estimated axial-shear strain elastogram closely resembles the image predicted by finite-element analysis. However, we observe in the simulated elastograms a finite region at the interface (sandwiched between like signed axial-shear strain values) that is not visible in the finite-element images. We suspect the reason for this to be the finite resolution of the elastographic system. When the inclusion is loosely bonded, there is a singularity at the interface. This singularity manifests itself in the FEA image, but because of the high resolution it is not prominently visible. Therefore, we can expect the finite region to start to vanish with improvements in resolution. Figure 11 shows the axial-shear strain elastograms for a loosely bonded inclusion (coefficient of friction 0.3) at different resolutions. It is seen that the finite region in fact starts to vanish with improving resolutions. The qualitative observations from figure 10 and 11 are quantified and shown in figure 12. This figure shows plots of each of the normalized features at different coefficients of friction values. It is apparent that the finiteness of the resolution introduces two effects. The feature corresponding to the area of positive axial-shear strain is overestimated while that of negative axial-shear strain is underestimated. This underestimation/overestimation is referred to as ‘bias’ in the plots. Since the feature extraction is a post-processing step, we can estimate the finite region that is sandwiched and offset for the bias. Estimating the sandwiched region is relatively easy as it comprises positive valued pixels between negative valued pixels along a small portion of the interface. Note how closely the plots follow the curve obtained from FEA after correction for bias. Further, note that the feature that quantifies the distance of separation does not suffer from any bias. This is not surprising because it does not include a jump across interface. This feature involves distance measurements and hence has large error bars compared to those metrics that involve measures of area. Moreover, this feature is sensitive only over a restricted range of coefficients of friction compared to the other features. All these reasons may ultimately limit the usefulness of this feature.
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Figure 10. Top row: axial-shear strain images from FEA (‘ideal’); and bottom row: axial-shear elastograms (estimated using US in the presence of noise) at different coefficients of friction. The coefficient of friction for each model is (a) (L to R) 0.01, 0.05, 0.1, 0.3 (b) (L to R) 0.5, 0.7, firmlybonded. The black outlines inside the image represent the contour line at a particular axial-shear strain magnitude threshold.
Preliminary in vivo results Axial-shear strain elastograms corresponding to seven each of pathologically-confirmed benign and malignant breast tumors were analyzed in this study. As an example, sets of axial-shear strain elastograms superimposed on the corresponding sonogram are shown in figures 13 and 14. Only those pixels that had axial-shear strain values greater than 40% of the applied axial strain and corresponding correlation coefficient greater than 0.75 were overlaid on the corresponding sonogram to obtain the composite image. However, for the image shown in figure 14(b) additional processing was done to remove a few pixels far away from the lesion interface that survived these thresholds. Observe that similarly to FEA/simulated
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Figure 11. Simulated axial-shear strain elastograms at different resolutions. The resolution was improved by increasing the center frequency and maintaining a constant transducer elemental pitch of λ/2 and a lateral beam overlap of 70%. The coefficient of friction for this model was 0.3. Observe that the ‘sandwiched region’ (indicated by the arrows) reduces with improving resolution.
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Figure 12. Plots comparing the normalized features as a function of coefficient of friction predicted by FEM (solid line) and estimated from the axial-shear strain elastograms with (--) and without (-··) correction for the bias. (a) Normalized positive strain area, (b) normalized negative area, (c) normalized difference strain area, and (d) normalized distance between positive and negative strain areas outside the inclusion. Observe that the normalized positive area is overestimated while the normalized negative area is underestimated. Moreover, the amount of overestimation/underestimation varies with the coefficient of friction. Note that the normalized distance is not biased.
axial-shear strain elastograms, we note symmetry in the distribution of axial-shear strain just outside the tumor/background interface. Moreover, we also see that the proximity of the axial-
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Figure 13. An example showing the axial-shear strain elastogram (color) superimposed on the corresponding sonogram of (a) cancer and (b) benign lesion. We can observe two features. First, the proximity of the axial-shear strain region (indicated by the green arrow) to the sonographically visible lesion is different for both the cases. Second, the region of the axial-shear strain compared to lesion size is different for both the cases. The second observation is consistent with findings from simulations.
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Figure 14. Another example showing the axial-shear strain elastogram (color) superimposed on the corresponding sonogram of a cancer (left) and benign lesion (right). We can observe the same two features as noted in the previous example in figure 13.
shear strain distribution to the tumor/background interface visible in sonogram is different for benign tumors when compared to malignant tumors. This is akin to the size discrepancy reported in axial elastography (Ophir et al 1996b, Garra et al 1997, Svensson et al 2005). However, because of the ability to overlay axial-shear strain elastograms on the corresponding sonogram, without obstructing the tumor in the sonogram, it may be easier to visualize the proximity discrepancy than size discrepancy using axial elastograms alone. Unlike FEA or simulated elastograms, we do not obtain a symmetric pattern in all the four quadrants around the tumor. Therefore, we chose the quadrants based on availability of the axial-shear strain in them. The area of the axial-shear strain outside the tumor was estimated and normalized with respect to the inclusion area estimated from the corresponding
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Figure 15. Scatter plots of the normalized feature and the proximity measure estimated from axialshear strain elastogram of seven benign and seven malignant tumors. The feature is normalized by the lesion size estimated from the sonogram.
sonogram. Even though 2D FEM/simulated elastograms suggested the possibility of utilizing several normalized features, it is apparent from figures 13 and 14 that when analyzing in vivo elastograms we may not be able to extract all the features that were previously identified, depending on the image quality and/or how well the in vivo tumor mimics the simulation model. Nevertheless, we can still extract the normalized area feature. Ultimately, this feature along with the feature measuring the proximity may provide a way to classify tumors as benign or malignant. As mentioned earlier, proximity may be similar to the size discrepancy reported in axial elastography. Therefore, size discrepancy measured as the ratio of the lesion size in axial elastogram to that in sonogram may be used as a proximity measure. A scatter plot is shown in figure 15 with the normalized area feature in one axis and the proximity measure in the other axis. Observe that the values of the normalized feature from cancer data are larger when compared to benign data. Note that in the scatter plot we can visualize two clusters, one containing features from benign data and the other from malignant data sets. The scatter plot was generated from the features extracted from the axial-shear strain elastograms and the sonogram. The feature selection was semi-automated in the sense that the R ; however, the contouring and segmentation was done automatically by routines in MATLAB regions identified from the automated segmentation were confirmed manually by an observer. Since axial-shear strain elastography is a relatively new modality, we did not have any trained neutral observer at this preliminary stage and therefore one of the authors acted as the observer. Moreover, the objective of this task was not to asses the classification performance using axialshear strain elastograms, but to see if the scatter plots are promising for further investigation on a larger data set by trained neutral observers. Discussion It is shown in this paper that the fundamental mechanical parameter that governs the pattern of axial-shear strain distribution in an inhomogeneous material is the bonding at the inclusion/background interface. This is an important result considering that there is a difference in the way a benign breast tumor is bonded to the surrounding tissue compared to a malignant tumor (Garra et al 1997, Chen et al 1995). Thus, we hypothesize that the ability
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to image the axial-shear strain distribution may provide additional information about the bonding at the interface, which can be used in discriminating between benign and malignant tumors. It is interesting to note that the axial-shear strain distribution that we are interested in is a result of quasi-static axial compression. It was reported earlier that the axial compression strain range that is optimal for axial elastography, in terms of CNRe, also works well for axial-shear strain elastography (Thitaikumar et al 2007). This suggested that we can obtain the axial-shear strain elastograms from the same data used to create the axial elastograms, thus saving acquisition time and cost. The ability to utilize the same data to produce two different elastograms simultaneously provides an additional advantage. The information about the size of the inclusion and inclusion/background modulus contrast can be obtained from axial elastograms. This information is beneficial while normalizing the features obtained from axial-shear strain elastograms. It was reported by Garra et al (2006) that there is a need for additional independent information, along with axial elastograms and sonograms, to improve the performance of breast tumor classification. In this context, we believe that features quantifying the pattern in axial-shear strain elastograms may provide at least some of the additional independent information needed. We have demonstrated in this paper the feasibility of obtaining axial-shear strain elastograms in vivo. However, it must be noted that the data used in this study were not originally acquired for the purpose of producing axial-shear strain elastograms. Since it was observed in Thitaikumar et al (2007) that the data obtained for producing axial elastograms can also be utilized to produce axial-shear strain elastograms, we retrospectively processed the in vivo data already obtained for a previous study on axial elastography. Further, the acquisition involved multi-compression. The effect of different acquisition schemes on the quality of axial-shear strain elastograms has not been studied yet. The data set reported in this manuscript consisted of seven benign and seven malignant breast tumor cases. Even though the size of the data set reported is small, these preliminary data nevertheless appear to show the potential of the axial-shear strain elastography for tumor classification. The authors realize however that as the data set increases, the variety of the axial-shear strain distribution patterns may increase. Therefore, current 2D simulations need to be extended to more realistic 3D simulations in order to better predict the utility of the shear strain elastograms on a larger in vivo data set. It should be noted that the scope of the work reported in this paper is limited to demonstrating the feasibility and not evaluating the utility of axial-shear strain elastograms in breast tumor classification. Conclusions In this paper, we have shown using a parametric study that the pattern of axial-shear strain distribution is determined by the degree of bonding at the inclusion/background interface. This was accomplished by quantifying the pattern using normalized features. We also showed that it is feasible to extract these features from axial-shear strain elastogram. More importantly, the feasibility of producing axial-shear strain elastograms retrospectively from breast lesion data in vivo was also demonstrated. Coincidentally, an additional feature from the in vivo data was identified, the ‘proximity measure’, which had not been identified in the simulation study. This feature, along with the features identified in simulation, may be used to asses the utility of axial-shear strain elastography in distinguishing benign breast tumors from malignant ones. The ‘proximity measure’ may turn out to be correlated to the size discrepancy feature of axial elastography and thus may provide diagnostically similar information. However, because of higher axial-shear strain contrast and the ability to obtain composite images, it may be
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easier to visualize the proximity discrepancy than size discrepancy using axial elastograms alone. Acknowledgments This work was supported in part by NIH program project grant P01-EB02105-12 awarded to the University of Texas Medical School at Houston. The author was also supported in part by the Electrical and Computer Engineering Department, University of Houston through a teaching assistantship. The authors would like to thank the anonymous reviewers for their helpful suggestions. References Barr R G 2006 Clinical applications of a real time elastography technique in breast imaging Proc. 5th Int. Conf. on Ultrasonic Measurement and Imaging of Tissue Elasticity p 112 C´espedes I 1993 Elastography. Imaging of biological tissue elasticity PhD Dissertation University of Houston Chen E J et al 1995 Ultrasound tissue displacement imaging with application to breast cancer Ultrasound Med. Biol. 21 1153–62 Chen S C et al 2004 Analysis of sonographic features for the differentiation of benign and malignant breast tumors of different sizes Ultrasound Obstet. Gynecol. 23 188–93 Fry K E 1954 Benign lesions of the breast CA Cancer J. Clin. 4 160–1 Garra B S et al 1997 Elastography of breast lesions: initial clinical results Radiology 202 79–86 Garra B S et al 2006 Clinical breast elastography: blinded reader performance and strategies for improving reader performance Proc. 5th Int. Conf. on Ultrasonic Measurement and Imaging of Tissue Elasticity p 60 Hall J T et al 2001 In vivo results of real-time free hand elasticity imaging IEEE Ultrason. Symp. pp 7649–53 Hiltawski K K et al 2001 Freehand ultrasound elastography of breast lesions: clinical results Ultrasound Med. Biol. 27 1461–9 Kallel F et al 1996 Fundamental limitations on the contrast-transfer efficiency in elastography: an analytic study Ultrason. Med. Biol. 22 463–70 Knight M G et al 2002 Parametric study of the contact stresses around spherical and cylindrical inclusions Comput. Mater. Sci. 25 115–21 Konofagou E E et al 2000 Shear strain estimation and lesion mobility assessment in elastography Ultrasonics 38 400–404 Lorenz A et al 1999 A new system for the acquisition of ultrasonic multicompression strain images of the human prostate in vivo IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46 1147–54 Mase G E 1970 Schaum’s Outline Series: Continuum Mechanic (New York: McGraw-Hill) Meunier J and Bertrand M 1995a Ultrasonic texture motion analysis: theory and simulation IEEE Trans. Ultrason. Ferroelectr. Freq. Control 14 293–300 Meunier J and Bertrand M 1995b Echographic image mean gray level changes with tissue dynamics: a system-based model study IEEE Trans. Biomed. Eng. 42 403–10 Moon W K et al 2002 US of ductal carcinoma in situ Radiographics 22 269–80 Ophir J et al 1991 Elastography: a method for imaging the elasticity of biological tissues Ultrason. Imaging 13 11–3 Ophir J et al 1996a Elastography: ultrasonic imaging of tissue strain and elastic modulus in vivo Eur. J. Ultrasound 3 49–70 Ophir J et al 1996b Elastography: a method for imaging the elastic properties of tissue in vivo Ultrasonic Tissue Characterization ed M Tanaka et al (Tokyo: Springer) chapter 7, pp 95–123 Ophir J et al 1999 Elastography: ultrasonic estimation and imaging of elastic properties of tissues Proc. Inst. Mech. Eng. (UK) 213 203–33 Orel S G and Schnall M D 2001 MR Imaging of the breast for detection, diagnosis, and staging of breast cancer Radiology 220 13–30 Popli M B 2002 Pictorial essay: sonographic differentiation of solid breast lesions Ind. J. Radiol. Imaging 12 275–9 Rangayyan R M 2005 Biomedical Image Analysis (Boca Raton, FL: CRC Press) Saada S 1983 Elasticity, Theory and Applications (New York: Pergamon) Sickles E A 2000 Breast imaging: from 1965 to the present Radiology 215 1–16 Srinivasan S et al 2002a Analysis of an adaptive strain estimation technique in elastography Ultrason. Imaging 24 109–18
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