Elastography for Breast Imaging

Transcription

1 Elastography for Breast Imaging Michael I. Miga, Vanderbilt University, Department of Biomedical Engineering, Nashville, TN Marvin M. Doyley, Dartmouth College, Thayer School of Engineering, Hanover, NH Jeffrey C Bamber, Institute of Cancer Research and Royal Marsden NHS Trust, Sutton, UK John B. Weaver, Dartmouth Hitchcock Medical Center, Lebanon, NH Keith D. Paulsen, Dartmouth College, Thayer School of Engineering, Hanover, NH Jao J. Ou, Vanderbilt University, Department of Biomedical Engineering, Nashville, TN PREFACE 1 INTRODUCTION 1.1 GENERAL INTRODUCTION 1.2 INTRODUCTION TO ULTRASOUND ELASTOGRAPHY (USE) 1.3 INTRODUCTION TO MAGNETIC RESONANCE ELASTOGRAPHY (MRE) 1.4 INTRODUCTION TO MODALITY-INDEPENDENT ELASTOGRAPHY (MIE) 2 ULTRASOUND ELASTOGRAPHY 2.1 INTRODUCTION 2.2 HISTORICAL DEVELOPMENT OF ULTRASONIC ELASTOGRAPHY 2.3 CLINICAL PROTOTYPE FREEHAND ELASTOGRAPHIC IMAGING SYSTEM 2.4 CLINICAL RESULTS 2.5 MODEL-BASED ELASTOGRAPHIC IMAGING 2.6 COMPARTIVE EVALUATION OF STRAIN-BASED AND MODEL-BASED ELASTOGRAPHY

2 3 MAGNETIC RESONANCE ELASTOGRAPHY 3.1 BACKGROUND 3.2 MAGNETIC RESONANCE ELASTOGRAPHY METHODS MECHANICAL ACTUATION ENCODING TISSUE DISPLACEMENTS IMAGE RECONSTRUCTION SYSTEM PERFORMANCE 3.3 RESULTS CLINICAL IMAGES SHEAR MODULUS COMPARISON IN REPRESENTATIVE ABNORMALITIES 3.4 CONCLUSIONS 3.5 ACKNOWLEDGEMENTS 4 MODALITY-INDEPENDENT ELASTOGRAPHY 4.1 BACKGROUND 4.2 MODALITY INDEPENDENT ELASTOGRAPHY METHODS BIOMECHANICAL MODEL MODALITY INDEPENDENT ELASTOGRAPHY 4.3 BREAST AND PHANTOM EXPERIMENTS BREAST EXPERIMENTS PHANTOM EXPERIMENTS RECONSTRUCTION QUALITY EVALUATION 4.4 BREAST AND PHANTOM RESULTS

3 4.4.1 BREAST RESULTS PHANTOM RESULTS 4.5 DISCUSSION 4.6 CONCLUSIONS 4.7 ACKNOWLEDGEMENTS 5 REFERENCES

4 PREFACE This chapter is divided into five major sections. Within the first section, a brief introduction is provided to the field of elastography. The specific listing of the elastography methods within the introduction is not meant to be a complete listing but rather reflects some of the important initial contributions followed by representative references to the use of elastography. To write an inclusive chapter of all the different variants of elastography would be a book in its own right. The content of this chapter does reflect the expertise of the authors. The contribution for the ultrasound elastography section was provided by Marvin M. Doyley of Dartmouth College s Thayer School of Engineering and Jeffrey C. Bamber of the Institute of Cancer Research and Royal Marsden NHS Trust. The contribution for the magnetic resonance elastography section was provided by John B. Weaver of the Dartmouth Hitchcock Medical Center and Keith D. Paulsen of Dartmouth College s Thayer School of Engineering. The contribution for modality independent elastography section was provided by Michael I. Miga and Jao J. Ou of Vanderbilt University s Department of Biomedical Engineering. 1 INTRODUCTION 1.1 GENERAL INTRODUCTION Since their advent, traditional imaging modalities such as X-ray, ultrasound, magnetic resonance have been primarily used to image anatomical structure for breast cancer characterization. However, the sensitivity of mammography with current technology is between 85% and 90% [1]. Therefore, in recent years, many of these imaging methods, ultrasound and MR in particular, have matured to become more functional in nature; i.e. rather than studying morphometric change solely, derivative measurements are being used to look for important biomarkers that detect cancerous tissue. This chapter is focused on the use of tissue elasticity as

5 a contrast mechanism for breast cancer diagnosis and tissue differentiation [2]. Within medical diagnosis, the correlation between the stiffness and health of tissue is an accepted form of organ disease assessment. With respect to breast cancer specifically, the use of palpation by self-exams is still the first line of investigation for breast cancer detection. Indeed, up to 60% of malignancies are first identified through either self-examination or clinical examination [3]. As a result, there has been a significant amount of interest in developing methods to image elasticity parameters with hopes that it can improve early detection. This field of research is largely referred to as elastography. In this chapter, three methods of elastography will be reviewed that use: (1) ultrasound imaging, (2) magnetic resonance imaging, and (3) a modality-independent image processing technique. The purpose of this chapter is to illuminate the initiation and recent developments in the field as well as provide some practical sense of the fidelity of these methods. 1.2 INTRODUCTION TO ULTRASOUND ELASTOGRAPHY (USE) In the late 1980 s, observations within ultrasound (US) images that seemed to correlate deformation and tissue motion with pathology were being reported [4-11]. This early work seemed to suggest that tissue movement could facilitate detection of tissue changes and possibly yield diagnostic discrimination. Building on these observations, Ophir et al. disseminated the first refined realization of an ultrasound elastography framework in a paper that appeared in Ultrasonic Imaging in April of 1991, [12]. Ophir et al. used a cross-correlation analysis of preand post-compression A-line ultrasound pairs to perform axial strain estimates on soft tissue material. The measurements of axial strain coupled with information regarding tissue compression conditions, i.e. applied stress, were used to spatially estimate Young s Modulus [12]. Since its inception, advances to the approach have been made on many different fronts to

6 include: strain estimation methods, image reconstruction, mechanical excitation methods, and novel displacement measurement approaches. As a result of these advances, ultrasound elastography has continued to advance and has been applied to various organs including breast [13-16], prostate [17, 18], intravascular evaluations [19, 20], and thyroid [21]. 1.3 INTRODUCTION TO MAGNETIC RESONANCE ELASTOGRAPHY (MRE) Although techniques in magnetic resonance tagging were being investigated in the late 1980 s [22-24], the realization of magnetic resonance elastography (MRE) was relayed in the September 1995 issue of Science by Muthupillai et al. [25]. In this paper, MR motion-sensitized gradient sequences were used to phase encode the propagation of strain waves in elastic media. One of the most important advances with the MRE framework is its ability to capture displacement in three dimensions. While ultrasound is low-cost and less cumbersome, the resolution of non-axial displacement is still somewhat poorer than axial measurements. The potential for the MRE measurement to be performed in three dimensions at the same resolution as a standard MR image series is very exciting. Subsequent to this investigation, a series of papers were published demonstrating the potential power of MRE in the context of breast, prostate and brain applications [26-33]. As was the case in USE, advances to the approach have been made on many different fronts to include: new imaging sequences, new image reconstruction techniques, and varying implementations of mechanical excitation. 1.4 INTRODUCTION TO MODALITY INDEPENDENT ELASTOGRAPHY (MIE) The previous two elastography methods are derived from using conventional imaging modalities as displacement measurement devices. To generate elasticity contrast, these measurements are further processed using assumptions regarding the mechanical behavior of the

7 material of interest and tissue elasticity information is presented. The method described in this section is more akin to the original intention of medical imaging, i.e. anatomical interrogation. This approach is derived from quantifying morphometric changes within acquired structural images during mechanical excitation. As a result, the method is dependent on image processing techniques but it is not inherently linked to any particular imaging modality. In some respects, this method represents a shift from the methods presented above in that it removes the necessity of having to accurately measure internal tissue deformations. Rather, it uses the information shared between two images at the anatomic structural level to drive its reconstruction. Computational techniques to non-linearly register image data via modeling methods have considerable precedent within the medical image processing community. For example, elastic matching has been a widely used technique to register multi-modality neuroanatomical images since the early 1980 s [34-36]. While similar techniques using speckle tracking have been employed to measure displacement within ultrasound images [37-39], the unique aspect to the approach in this section is that the elastography process becomes solely a function of image similarity and does not require the added processing step of constructing displacement fields. The method has been called modality-independent elastography (MIE) and was first reported in [40, 41]. Subsequent to this initial work, a series of related papers analyzing different similarity metrics, analysis with clinical data, and phantom experiments were reported [42, 43]. Others have also suggested that elastography reconstruction methods could be based on analyzing image pattern [44, 45]. The transition away from a displacement driven reconstruction is perhaps one of the most attractive characteristics of the technique, and the results in this section show its viability as a future clinical screening method.

8 2 ULTRASOUND ELASTOGRAPHY 2.1 INTRODUCTION The observation that malignant tumors are stiffer and immobile compared to surrounding healthy breast tissue [46] have been utilized by clinicians during palpation since the earliest days of medicine. It is important to note that the properties assessed during manual palpation are different from bulk elastic modulus that governs the propagation of longitudinal ultrasonic waves. The elastic properties of soft tissues are dependent on both their molecular composition (fat, collagen, etc), and on the microscopic and macroscopic structural organization of these components. In breast, for example, glandular tissue is firmer than fatty areas. Additionally, the elastic modulus contrast of abnormal tissues with respect to their surrounding normal tissue can be as much as one order of magnitude [2, 47]; however, none of the traditional medical imaging modalities such as Ultrasound (US), Magnetic Resonance Imaging (MRI), X-ray Computed Tomography (CT) or Positron Emission Tomography (PET) can directly measure tissue elasticity. For example, many tumors of the breast are barely visible on standard ultrasound examination, despite being much harder than the surrounding tissue an expected outcome since the interaction with soft tissue is not correlated with tissue elasticity as such. We hypothesized that an imaging system that is capable if imaging tissue elasticity should improve both the detection and characterization breast cancer by taking advantage of the large contrast in modulus of elasticity between abnormal and normal breast tissue, particularly in pre-menopausal women where the efficacy of X-ray mammography is questionable. Although none of the established medical imaging modalities can provide a direct measure of tissue elasticity, most can impart information about the mechanical response of soft tissues to either an external or internal mechanical stimulation, and from this information various

9 mechanical parameters can be inferred. There have been substantial interests during the decade, in developing elasticity imaging or elastography a term that was first coined by [12] to describe their ultrasonic elasticity-imaging approach. A central feature of this imaging technique is the estimation of externally or internally induced internal tissue motion by employing a conventional medical imaging modality, namely diagnostic ultrasound (US). 2.2 HISTORICAL DEVELOPMENT OF ULTRASONIC ELASTOGRAPHY In the mid-1970s, a few investigators began to employ M-mode and static B-mode scanners to assess the compressibility of breast masses by observing the response of echo motion in response to hand-induced transducer motion [48, 49]. This technique provided diagnostic information that was not readily available to water-bath ultrasonic breast imaging technique. Such relative motion assessment was extended in the 1980s to the use of real-time B-mode scanning, to assess so-called dynamic features of tissue motion in response to handinduced transducer motion. This approach continues to be used today but appears to be limited to centers that have a small number of experts; however, it provides the foundation for our freehand approach to elastographic imaging which we regard being a direct extension to the process of evaluating the dynamic features of breast malignancy.

10 Current elastographic imaging techniques can be classified under two board categories depending on the nature of the mechanical stimulation that is employed to induce motion within the phantom or tissue under investigation (i.e. dynamic or quasi-static). Dynamic elasticity imaging or sonoelasticity imaging as the technique is more commonly know [50] visualizes tissue elasticity by inducing low frequency ( 1 khz) shear acoustic waves within the tissue under investigation. A stiff in-homogeneity that is surrounded by relatively soft tissue will create a disturbance in the normal vibration pattern, which can be visualized in real-time by employing color Doppler [50-53]. Although real-time capability of sonoelasticity makes it a very attractive elasticity imaging technique, the images are in general very difficult to interpret owing to the complex nature of modal patterns that are produced. A quasi-static elastography image formation Figure 2.1. The general principle of ultrasonic elastography. Showing the reduction in the strain between two non-overlapping pre and post RF segments.

11 process generally consists of four-steps; first, an ultrasonic radiofrequency (RF) echo frame is acquired from the tissue or phantom under investigation; second, a small motion is induced within the tissue by employing either an external or internal quasi-static mechanical source; third, a second ultrasonic RF echo frame is acquired; fourth, the spatial variation of the ensuing internal tissue motion are estimated by performing cross-correlation analysis on the acquired RF echo frames. Note that the displacement between consecutive pairs of pre and post-deformed RF echo segments are estimated based on the assumption that the speed of sound is constant in soft tissues (i.e ms -1 ). Local tissue strain is subsequently computed, as illustrated in Figure 2.1 from the ratio of the separation between the post-deformed RF echo segments (i.e. (Δt i -Δt i-1 )) to the distance in separation in the pre-deformed RF echo segments (ΔT). The segments are translated along the axis of RF A-line and the calculation is repeated for all depths. This computation is performed for all A-lines pairs to produce a matrix of strain estimates, which are displayed as a grey scale image known as a strain elastogram. The strength of this approach to elastography resides in its simplicity and robustness, but mechanical artifacts and incomplete contrast recovery can impede clinical utility a consequence of interpreting strain images as relative stiffness images (i.e. modulus elastograms) by assuming stress uniformity a conjecture that is applicable only for very special cases [54]. Additionally, the specialized equipment and non-standard approach to ultrasonic examination of the breast limit its clinical usefulness, and hence the likelihood of its rapid acceptance for widespread use. In particular, the constraining devices that are used to reduce undesirable sources of tissue motion, makes it difficult to examine a large proportion of the breast. Consequently, we have developed a freehand approach to elastographic imaging [55-57].

12 2.3 CLINICAL PROTOTYPE FREEHAND ELASTOGRAPHIC IMAGING SYSTEM Figure 2.2 Acoustic footprint extender. The general idea is to employ hand-induced transducer motion as the source of mechanical stimulation, albeit at the cost of introducing additional sources of measurement noise and artifacts, relative to standard elastography (i.e. mechanically induced transducer motion). For example, manual probe motion is expected to result in large transducer displacements, in plane Figure 2.3. Schematic diagram of ICR Freehand elastographic imaging system.

13 and out-of-plane probe motion. To minimize these undesirable feature of probe motion and their consequences, a transducer palpation footprint-extender was employed (Figure 2.2), and a fast data acquisition was developed to allow continuous streaming of radio frequency (RF) echo data at full frame rate (30 fps) from a commercially available ACUSON 128XP ultrasound scanner (Mountain View CA), whilst palpating the breast with the transducer for ~ 2 s (Figure 2.3). Other features incorporated onto the system included incremental echo tracking [56] to allow estimation large internal tissue displacements without excessive decorrelation noise, two dimensional RF cross-correlation tracking algorithm to reduce decorrelation due to lateral transducer motion and lateral strains. Figure 2.4 shows representative examples of a strain elastogram obtained from an elastically inhomogeneous phantom using mechanically induced and hand-induced transducer motion. The signal to noise ratio (SNR e ) of elastograms produced using the hand-held transducer motion is visually lower than those produced using mechanical induced transducer motion; however, it is apparent that quality of free hand elastograms is sufficient to produced clinically useful results.

14 a b Figure 2.4 (a) mechanical and (b) freehand elastogram obtained from a phantom containing a 15 mm diameter inclusion that was approximately three times stiffer than the surrounding background tissue. A theoretical framework known as the strain filter was developed by Varghese and Ophir [54] for characterizing the performance of elastographic imaging systems. We recently extended this concept to allow the computation of strain filters (a plot of elastographic signal to noise ratio as a function of the applied strain) experimentally. Figure 2.5 shows an experimentally derived strain filter obtained from elastically homogenous phantoms computed using hand-induced transducer motion relative to those computed using mechanical deformation system. The bandpass characteristics of the strain filter can clearly be seen in both cases (i.e. the loss of SNR e, both at low strains, due to the dominance of electronic noise and interpolation errors, and at high strains, due to structural decorrelation noise. Performance Measure Freehand elastography Standard elastography Minimum Strain 0.5 % ± % ± 0.05 Maximum Strain 2.2 % ± % ± 0.20 SNR e 9 16 Dynamic range 4.4 ± Table 2.1 Comparison of elastograms produced using a hand-held transducer and mechanically induced transducer motion.

15 a b Figure 2.5 Experimentally derived strain filter produced using (A) mechanically induced and (B) handheld transducer motion. The performance metrics extracted from Figure 2.5 are summarized in Table 2.1, note that the clinical prototype freehand elastographic imaging system compares favorably relative to the standard approach to elastography.

16 2.4 CLINICAL RESULTS Using these methods, elastographic imaging on 70 breast cancer patients has been performed, and demonstrated that freehand elastography can produce images with sufficient spatial and contrast resolution to discriminate between normal and abnormal breast anatomy [58, 59]. For 74% of all lesions the contrast for freehand elastography was equal to or better than conventional ultrasound, and overall lesion visibility was judged to be equal or improved for free hand elastography (FE) in 50 % of the cases. Freehand elastography had an impact on the diagnosis in 24 % of cases and increased the diagnostic confidence in 25%. For 9%, confidence deteriorated, mainly in benign lesions (66%). Additionally, combining FE and diagnostic US increased sensitivity and specificity to 90% and 46% respectively; compared with 84% and 43% for US alone. An example of a sonogram that was obtained from a 73 year old female with a Phylloides tumor (borderline with associated lobular carcinoma) in the upper outer quadrant of her left breast is shown in Figure 2.6a. Phylloides tumors are relatively rare variants of fibroadenoma with a richer stromal component and more cellularity. They grow quickly, developing a macroscopically lobulated internal structure and may reach a large size, visibly altering the breast profile. Sonography generally shows a solid, moderately hypoechoic nodule, with smooth borders and good sound transmission [60]. Inhomogeneous structures may be present because of small internal liquid areas. These appearances are non-specific and sonography is not currently able to distinguish between benign and malignant cases, nor make a differential diagnosis between fibroadenoma and phylloides tumor. Note that the tumor covers most of the field of view, with the capsule of the anterior margin visible close to the top of the image and the posterior margin visible at the bottom left. Within the tumor the appearance is heterogeneous on a large scale, with macroscopic lobules separated by echogenic boundaries that

17 a b c Figure 2.6 (a) Sonographic, (b) elastographic, (c) histologic images of Phylloides breast tumor. are probably fibrous in nature. The freehand elastogram (Figure 2.6b) confirms this appearance but shows it much more clearly with greater contrast than the sonogram. The capsule at the top of the image is seen to be stiffer than either the subcutaneous fat (anterior) or the tumor tissue (inferior). The macroscopic lobules within the tumor are very clearly defined as relatively soft regions separated by stiff septa, which is also consistent with the septa being of a fibrous nature. Within the macroscopic lobules the stiffness appears relatively homogenous, which is consistent with the locally homogeneous and densely cellular structure seen on the histological section in Figure 2.6c. Finally, the small amount of tissue visible posterior to the tumor (bottom left) is seen to be very soft relative to the other structures in the image. This information was not available from the sonogram or any other image.

18 Figure 2.7 shows another example of sonogram and strain elastogram that was obtained from a 58 year-old female with a grade 3 ductal carcinoma (with two foci of ductal carcinoma in situ) in the upper outer quadrant of her left breast. This malignant tumor was an interesting case because it was reported on clinical examination as non-palpable and on X-ray mammography as displaying suspicious microcalcifications but no imagable mass. This tumor was difficult to visualize on sonography but a suspicious ill-defined, irregular hypoechoic region may be seen in Figure 2.7a. The freehand elastogram (Figure 2.7b) showed that this region is stiffer than the surrounding gland and that the boundary of the region of increased stiffness corresponds very closely to the boundary of the hypoechoic region. This tumor also appears to have a heterogeneous internal stiffness, which may correspond to the histological appearance seen Figure 2.7c that dense regions of tumor cells and stroma co-exist with edema and fat deposits. Furthermore, within the general region of increased stiffness one may see two small regions of tissue that are very stiff indeed. The histopathology report, obtained after tumor excision, confirmed that within this carcinoma there exist two focal areas of ductal carcinoma in situ. It was thought that these had probably been the original seed sites from which two cancers had a b c Figure 2.7 (a) Sonographic, (b) elastographic and (c) histological images of an invasive ductal carcinoma in situ.

19 grown and subsequently coalesced into a larger tumor. Note that freehand elastography was the only imaging technique employed that provided this information non-invasively. 2.5 MODEL-BASED ELASTOGRAPHIC IMAGING Images of internal tissue strain represent the response of soft tissues to an external (or internal) mechanical stimulus; therefore, strain alone represents an approximation measure of tissue elasticity. Accurate quantification of tissue elasticity requires knowledge of both the axial strain and the full three-dimensional (3D) stress state vector. At present, stress cannot be measured in vivo; therefore, it is customary to interpret strain elastograms as modulus elastograms based on the assumption of stress uniformity. In practice, the internal stress distribution is seldom uniform because of stress decay and stress concentrations that appears near modulus non-uniformity [12]. Therefore, interpreting strain elastograms as relative modulus elastograms based on the premise of stress uniformity will generally induce mechanical artifacts and reduce the elasticity contrast-transfer efficiency. To address this problem, reconstruction methods have been developed for solving inverse problems an approach to elastography that requires an accurate formulation of the forward elasticity problem that predicts the observed mechanical response (displacement and/or strain) based on some knowledge of the external boundary conditions, and the intrinsic tissue mechanical parameters. Besides reducing image artifacts, this approach to elastography (i.e. model-based elastography) should improve the contrast-transfer efficiency [61, 62], particularly in high contrast media. The inverse elasticity problem was solved by formulating it as a constrained parameter optimization problem where the goal is to minimize an objective function that has the following form Φ(μ) = U m U{μ} 2, where U{μ} represents the axial displacements computed from the modulus distribution {} μ by employing the finite element method, and U m is the ultrasonically

20 a b c Figure 2.8 (a) Sonogram, (b) strain elastogram, and (c) modulus elastogram obtained from a gelatin phantom containing a single cylindrical inclusion measured axial displacements. Minimizing this objective function with respect to modulus variations is a nonlinear process, which is realized through an iterative solution for {} μ based upon an initial guess of the modulus distribution (the trial solution). The resulting matrix solution at the (k+1) iteration has the form {} k μ +1 = {} μ k + J(μ k ) T J(μ k ) + ρ k I 1 J(μ k ) T U m U μ k ( {}), where {} μ is a vector of modulus updates at all coordinates in the reconstruction field of view, and J(μ k ) is the Jacobian or sensitivity matrix. The Hessian matrix, [ J(E k ) T J(E k )], is poorly conditioned, and may be regularized by employing either the Marquardt or Tikhonov regularization method. Figure 2.8 shows example of modulus elastograms recovered from a gelatin phantom that contained a single cylindrical isoechogenic inclusion. The inclusion is not discernible in the sonogram but is highly visible in the strain and modulus elastograms, demonstrating that strain and modulus elastography can convey new information. It is also apparent from this figure that solving the inverse problem reduces mechanical artifacts incurred when strain elastograms are interpreted as modulus elastograms by assuming stress uniformity. Two implementations of this inversion scheme have been realized. One approach computes modulus elastograms based on knowledge of known displacement boundary conditions

21 (DBC); whereas the other computes modulus elastograms based on knowledge of known stress boundary conditions (SBC). The results of a comprehensive evaluation of both implementations of the inversion scheme [63] revealed that the stress on the boundary of the tissue must be specified to reconstruct absolute values of the modulus. Otherwise, the modulus elastogram obtained from known DBC will have to be calibrated using either an external or internal tissue reference of known shear or Young s modulus. Krouskop et al. [2] have shown that among various breast tissues, fat has a consistent and linear modulus over a wide range of applied strain that could be employed as an internal tissue reference. Encouraging computer simulation and phantom studies have been reported; however, this approach to elastographic imaging (i.e., modulus imaging) is challenging owing to the ill-posed nature of the inverse problem. Factors such as model-to-data discrepancy, and measurement noise could compromise the quality and accuracy of ensuing modulus elastograms. Additionally, there is no guarantee of producing unique modulus elastograms when solving the discrete inverse elasticity problem [64] another characteristic trait of ill-posed problems. To minimize these potential problems, we have imposed additional constrains (i.e., a priori information concerning the mechanical properties of the underlying tissue structures, and the variance incurred during displacement estimation) on the image reconstruction problem through the Bayesian framework. Figure 2.9 shows an example of strain and modulus elastograms obtained from a gelatin phantom containing a single 20 mm diameter inclusion with modulus contrast of 20 db. The strain elastogram (left) was computed by spatially differentiating the measured axial displacement using a simple gradient operator. The tumor-like inclusion is discernible at the correct location in the strain elastogram; however, Decorrelation noise (i.e., the dominant noise source incurred in ultrasonic elastography) is apparent in the strain elastogram a consequence of employing large strains (i.e., 3 %) when

22 Figure 2.9 Elastograms obtained from a gelatin phantom that contained a single 20 mm diameter inclusion when elastographic imaging was performed using applied strain of 2 %. Showing, strain elastogram (left) using conventional strain imaging methodology, modulus elastogram computed using the standard least-squares estimation criterion (middle), and modulus elastogram computed within the Bayesian framework. performing elastographic imaging. Decorrelation noise has two effects when model-based elastographic imaging is performed with limited a-priori information (middle); firstly, it could generate spurious modulus estimates; secondly, it may produce erroneous modulus elastograms. However, image reconstruction is more resilient to decorrelation noise when reconstruction performed within the Bayesian framework an expected outcome since imposing further constraints on the image reconstruction process should reduce the likelihood of the reconstruction procedure being trapped in a local minima. This observation is relevant to the proposed research since decorrelation noise associated with in-plane and out off plane catheter motion frequently pose problems in intravascular elastography [65] a problem that could reduce the clinically useful modulus elastograms computed by employing a moderately constrained image reconstruction procedure [61, 63] COMPARTIVE EVALUATION OF STRAIN-BASED AND MODEL-BASED ELASTOGRAPHY Preliminary investigation was conducted to assess the performance of this modulus reconstruction strategy relative to quantitative strain imaging [61].. While the initial investigation pertains only to quantitative strain imaging as described in [12] and the inversion

23 reconstruction approach described in [63] the analysis is applicable to all elastographic-imaging techniques and provides insight into the relative merit of both elastographic imaging approaches. Figure 2.10 shows a representative example of strain and modulus elastograms obtained from a gelatin phantom that contained a single 10 mm diameter inclusion that was approximately three times as stiff as the surrounding tissue matrix. Strain-based modulus elastograms were computed by inverting the low resolution strain elastograms based on the assumption of stress uniformity; whereas, model-based modulus elastograms were computed by solving the inverse problem. Visually, the contrast-to-noise ratio (CNR e ) of the modulus elastogram would appear to be substantial higher than that of strain elastogram; however, the strain elastogram clearly possess superior spatial resolution. The disparity in spatial resolution was foreseen because the performance of the image reconstruction techniques, as previously discussed, was stabilized in the presence of measurement noise by forcing the image reconstruction algorithm to converge to Figure 2.10 Modulus elastograms computed by directly inverting strain elastograms (top panel), and solving the inverse problem (bottom panel). These elastograms were obtained from simulated phantoms containing single 10 mm diameter inclusions whose modulus contrast was progressively increased from 0.8 db to 20 db (going from left to right).

24 a smooth stable solution (i.e. the regularized solution) albeit at the cost of degrading the spatial resolution of the resulting image. It is reasonable to assume that the observed difference in CNR e is due solely to differences in the spatial resolution rather than any intrinsic differences in the contrast resolution of strain and modulus imaging. Consequently, the spatial resolution of the strain elastograms was degraded to that of the modulus elastograms by applying the spatial filter described in [63] recursively to strain elastograms to facilitate an objective comparison of both elastographic imaging techniques. The mean contrast-to-noise ratio (CNR e ) and contrast-transfer efficiency (CTE e ) [62, 66, 67] performance metric are plotted as a function of actual modulus contrast in Figure Note that a fix spatial resolution, the CNR e of both elastographic imaging approach are statistically equivalent; however, at high modulus contrast (Ec > 6 db) the contrasttransfer efficiency (CTE e ) of modulus elastograms computed by employing model-based inversion approach is superior, which confirms the prediction of Ophir and colleagues [54, 66] that solving the inverse problem should substantially improve the elastographic contrast transfer efficiency, particular in high contrast medium.

25 Figure 2.11 The mean CNR e (A) and contrast transfer effeciency (CTE) (B) computed from strainbase (soild-squares) and model-base (open-circles) modulus elastograms. The error-bar represents ± 1 standard deviation computed from 25 independent elastograms at each modulus contrast. Figure 2.12 representative examples of modulus elastograms and modulus images obtained from gelatin phantoms containing foam-reinforced cylindrical inclusion with diameters in the range of 2-25 mm. Strain-based and model-based modulus elastograms were compared to modulus images obtained from independent mechanical measurement with a nano-indentation system as described in [68]. Note that the position and extent of the inclusions were discernible in all images (i.e. elastograms and nano-indenter modulus images); however, small inclusions

26 (a) (b) (c) Figure 2.12 (a) Sonograms, (b) modulus elastograms and (c) modulus images obtained from gelatin phantoms containing cylindrical inclusions with diameters of 2 mm, 10 mm and 20 mm. (i.e. inclusion with diameter < 5 mm) were poorly visualized in the nano-indenter modulus image due to the low spatial resolution of the nano-indenter elastograms. In general there was good visual correlation between the nano-indenter modulus images and modulus elastograms computed by employing the model-based inversion technique, and simply inverting strain elastograms.

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28 3 MAGNETIC RESONANCE ELASTOGRAPHY 3.1 BACKGROUND The primary advantage of MR elastography (MRE) over other elastography methods is that the resolution of the displacement data is equally accurate in all three directions. Ultrasound is less expensive and faster but the through plane resolution is poor which for ultrasound leads to poor estimates of the displacement in that direction. Dynamic MRE methods have been more productive than static MRE methods [69] because the data acquisition is much faster and the mechanical properties produced are not relative values as they are with static methods where the boundary values are not accurately known. Several MRE approaches based on dynamic displacements have emerged which employed different modes of displacement. In all methods, induced tissue motion is measured using phasecontrast imaging [25], which is a powerful MR technique that is capable of sensing extremely small tissue motions (typically on the order of 10 s of microns). The first methods induced propagating waves in the tissue, and the shear modulus were computed directly from local estimates of wavelength [70]. This approach is an elegant one that has produced encouraging in vivo and in vitro results [71-73]. However, it can be difficult to generate coherent wave in complex structures and then the accurate quantification of wavelength is limited by the presence of longitudinal mechanical waves and reflections from internal tissue boundaries. Several second generation reconstruction methods are being explored to remedy those limitations [74, 75]. Alternatively, the steady state approach measures the time varying displacements under harmonic conditions [76, 77] and then reconstructs the spatial variation of shear modulus using either a direct inversion [76] or an iterative, model-based inverse technique [78]. It is a distinct advantage that steady state methods have no special requirements for the induced motion so any

29 vibration pattern will suffice as long as it is in steady state. Another advantage to steady state methods is that the acquisitions are faster because there are no propagation delays that the first two methods require. Initial clinical evidence produced by the dynamic MRE methods currently used on limited numbers of subjects show that it has promise to effectively identify malignant breast tissues. A preliminary clinical evaluation of 15 patients with malignant tumors of the breast, 5 subjects with benign breast lesions and 15 healthy volunteers [79] showed that MRE has the potential for differentiating between benign and malignant tissues. McKnight et al [72] have also reported their clinical experience with MRE on 6 breast cancer patients and 6 healthy volunteers. The elastograms obtained from the healthy subjects revealed moderately heterogeneous mechanical properties with the shear modulus of fibroglandular tissue being slightly higher than that of adipose tissue; whereas the elastograms of women with breast cancer showed focal areas of elevated shear modulus. The mean shear modulus of breast carcinoma was observed to be approximately four times higher than the mean shear modulus of surrounding healthy breast. In addition, MRE has been shown to be sensitive enough to characterize normal breast tissue in a variety of ways and in a variety of situations. Sinkus and colleagues [79] showed that the sensitivity of MRE is sufficient to characterize breast tissue changes during the menstrual cycle [80]. Fibroglandular tissue stiffness decreased 5 days after the onset of menses and increased after the second week of the cycle. No significant variation in the shear modulus of adipose tissue was observed. Kruse et al. [73] described a variety of early tissue characterization results based on the use of local frequency estimation and an assumption of linear elastic wave propagation. These data show frequency and temperature dependence in modulus measurements in kidney and liver samples in vitro, as well as the possible effects of anisotropy on varying

30 measurements in highly ordered skeletal muscle. Additionally, an example of an in vivo breast elasticity image was given that showed a localized area roughly two to three times stiffer than the surrounding fibrous tissues corresponding to a biopsy-proven malignancy. Plewes et al. [81] presented quasi-static strain images from the breast of a healthy volunteer. Elastographic signal to noise ratio of 10 and 16 was reported for fibroglandular and fatty tissue, respectively. However, a basic study of shear wave propagation in excised tissue by Bishop et al. [82] indicated that wave speed exhibits relatively small changes with frequency. 3.2 MAGNETIC RESONANCE ELASTOGRAPHY METHODS MRE systems require three elements to produce an image of the mechanical properties of tissue: a) mechanical activation of the tissue, b) measurements of the resulting displacements and c) reconstruction of the mechanical properties. The type of vibration must be described by the equations used in the reconstruction model to obtain accurate mechanical properties. For example, reflections are problematic for the dynamic methods that use local wavelength estimations of the shear modulus but steady-state methods using the general Stokes equation require the reflections to have reached steady state.

31 3.2.1 MECHANICAL ACTUATION Our current mechanical actuation system integrated with our phased array breast coil is shown in Figure 3.1. The system consists of a vibrating top-plate and stationary back-plate which is fixed to the coil and MR table. The top-plate is pushed across the back-plate by a piezoelectric actuator and returned by a hard gel spring. A dove-tail fitting on the stationary back-plate fits tightly into a grove in the spacers that are used to establish the height and angle of the plate required to accommodate a given breast size. The primary advantages of piezoelectric actuation are that they produce displacements that are linear with applied voltage, the applied Figure 3.1: Breast RF coil with vibrating plate below. The top view (far right) shows the face of the vibrating plate set up for the right breast. Side views (left) show the vibrating plate fixed on spacers to accommodate varying breast sizes.

32 Figure 3.2 Motion in the three directions generated by the shear plate shown in a gel phantom. The motion amplitude, given in the color bar in microns, ranges up to 300 microns. forces generated are large enough and they can be placed in the high magnetic fields generated by MRI in any desired orientation. The maximum mechanical actuation of the plate is currently 240 microns. The design has proven to be simple to use and generates consistent motion successfully. Figure 3.2 shows the kind of motion maps obtained, in this case in a phantom, and Figure 3.3 shows a typical clinical result from an MRE exam on a volunteer with normal (BI- RADS 1) breasts ENCODING TISSUE DISPLACEMENTS Motion is measured using motion encoding gradients (MEGs) between the RF excitation pulse and the signal readout as shown in Figure 3.4. MEGs are applied sequentially in each of three spatial directions and oscillate at the identical frequency as the induced mechanical motion, itself. When a voxel of tissue is being moved sinusoidally, the phase of the MR signal is a cosine function whose amplitude and phase uniquely determine the amplitude and phase of the harmonic vibration.

33 Figure 3.3: MR magnitude (top row) and reconstructed shear modulus images (bottom row) acquired during a clinical breast exam with the RF coil and vibrating plate system in Figure 3.1. Harmonic motion can be represented as: x = x o + A sin(ϕ) where the phase, ϕ, of the motion and the amplitude of the motion, A, completely characterize the vibration. To estimate the amplitude and phase of the displacement in one direction, the MR image phase must be measured at multiple phase offsets between the motion and the MEGs, θ. The phase of the MR image is the phase accumulated by motion during the MEG, ξ m, plus the baseline phase from spurious sources. The motion induced phase is the inner product of the MEG with the motion which is: ξ m (θ) = A cos(ϕ + θ). The simplest way to solve for A and ϕ is to sample ξ(θ) at θ sampled evenly over one cycle and take the Fourier transform of the phase, ξ(θ) [76]. The amplitude of the first fundamental frequency is A and the phase of the first fundamental frequency is ϕ. Each phase offset requires another image acquisition so the imaging times can be longer than desired. Several methods have been suggested to reduce the imaging times.

34 Acquisition with θ 1 Acquisition with θ 2 RF Slice Selection Phase Encoding Frequency Encoding Motion θ 1 θ 2 Figure 3.4: The convensional 3D phase contrast gradient echo pulse sequence used to measure the motion of each voxel in the field-of-view. The phase between the signal driving the mechanical actuation and the MEG is labeled as θ in the figure. Separate acquisitions are made for each value of θ making the acquisition times rather long. The MEG s are also inverted to produce a phase cycled pair of acquisitions. Figure 3.5 Motion measured using Hadamard encoded MEG s (top) and convensional MEGs (bottom). The motion is very similar as expected but the acquisition time is two thirds of a convensional acquisition. Constraining the estimation of motion from the phase using the fact that the magnitude is identical for all measurements reduces imaging times but increases the instability of the motion calculation [83]. However, methods that do not cause such instabilities also exist: i) Hadarmard encoding of the motion, and ii) elimination of the MEGs.

35 RF Slice Selection Phase Encoding Frequency Encoding Motion Figure 3.6: Motion accumulates phase during the frequency encoding gradient just as phase is accumulated during the MEG so the frequency encoding gradient can be used to encode motion as well as position. The phase cycled pair of acquisitions using the frequency encoding gradients is shown. The TR is reduced which reduces the acquisition time by ~2.5 and the TE is reduced which improves the SNR and reduces susceptibility artifacts. However, the sensitivity to motion is also reduced so larger motions are required. There is some interaction between the position encoding and motion encoding but it is minimal for relatively small motion. Figure 3.7: Comparison of motion measured using traditional MEG s and the same motion measured using the frequency encoding gradient. The frequency is identical but the imaging time is roughly half. The SNR is equivalent in the two images. The sensitivity to motion is reduced when using the frequency encoding gradients but the SNR is similar.

36 Hadamard encoding of phase contrast measurements was suggested for 3D velocity measurements in the 1991 [84, 85]. The first MRE paper used the method for encoding the motion in all three directions [25], but recent papers have mostly encoded each direction individually [75]. Hadamard encoding reduces the imaging times by a third by using baseline measurements more efficiently. Normally a MEG is turned on in one direction at a time. For each direction, images are acquired with the gradient on normally and then with the gradient inverted. The phases of the two acquisitions are subtracted to remove the baseline phase caused by a wide variety of spurious effects like eddy currents and any field inhomogeneity. Six acquisitions are required to encode all three directions. Hadamard encoding turns on all three MEGs simultaneously. The signs of the MEGs in all three directions are changed to acquire four independent combinations of the four unknowns: the phase produced by motion in the three directions and the baseline phase. The phase produced by the motion in the three directions must then be solved. The resulting phase estimate is double that obtained by using the same gradients acquired individually, improving the SNR of the phase angles calculated. However, gradient heating limits the SNR improvement to ~1.2 when all three gradients are on simultaneously. Imaging time is reduced from six to four acquisitions for each angle θ. Figure 3.5 shows phantom data acquired using conventional MEGs compared to that acquired using Hadamard encoded MEGs. Currently the MR manufacturer limits the number of images obtained in one acquisition, so we can only acquire 16 slices with Hadamard encoding which is often too few for clinical work. However, the slice number limitation will be eliminated on future systems and Hadamard encoding should become more popular because the SNR is improved and the acquisition time is reduced by a third.

37 Another alternative method of reducing the imaging times is to eliminate the MEGs entirely; or more accurately to use the imaging gradients to record motion as well as position [86]. The frequency encoding gradient is the most productive one to use because it is largest. Figure 3.6 shows the pulse sequence the can be compared to Figure 3.4 which shows the conventional one. The elimination of the MEGs reduces the TE significantly thereby increasing the signal. It also reduces the TR which decreases the imaging time. For 100 Hz motion, the TR and the TE have been reduced by approximately 2.5. Reduction of the TE also decreases the sensitivity to susceptibility artifacts. The drawback is ambiguity in the encoding which produces a convolution like error in the estimated motion. The error only occurs at discontinuities in the motion or the magnitude of the image. Simulations show that for motion which is 2% of a pixel dimension, the magnitude of the error is approximately 6% for full scale discontinuities in either the magnitude or the phase or 12% for both magnitude and phase simultaneously. These errors are very difficult to find experimentally because discontinuities in the motion are rare and difficult to produce.

38 3.2.3 IMAGE RECONSTRUCTION Start Initial Estimate Of Shear Modulus Distribution Divide Image into Subzones Optimize Shear Modulus Distribution on Each Subzone 2 u ρ = 2 t 2 v ρ = 2 t 2 w ρ = 2 t ( λ+ ) ( λ+ ) Δ 2 μ + μ u x Δ 2 μ + μ v x Δ x 2 ( λ+ μ) + μ w No Global Error < Tolerance Yes End Figure 3.8: Flow diagram showing the subzone reconstruction. The method is iterative starting with uniform mechanical properties. The region is subdivided into subzones that are small enough that the Stokes equations can be solved for the subzone. The set of mechanical parameters associated with the motion that most closely matches the measured motion is obtained iteratively. The process is repeated on the subsequent subzones. Then the entire process is repeated till the global error in the motion reaches an acceptable level. In this section, the reconstruction algorithm we employ will be described. We begin by briefly summarizing our subzone approach which has served as the backbone for our development of solutions of alternative mechanical parameters. We then describe extensions to the model in terms of multi-parametric property estimation including the imaging of tissue damping. We have formulated the MRE reconstruction problem as a constrained optimization task whose objective is to minimize the difference between a set of measured displacement fields and those computed by a model description in which the tissue property distribution is parameterized as a set of unknown coefficients representing the observed mechanical behavior. The typical strategy defines a single objective function to be minimized (usually the sum of squared differences between measured and calculated quantities) over the entire domain. In our case, we view the total problem domain (i.e. image field-of-view) as a union of multiple subzones such

39 that the minimization of the sum over the subzones is replaced by the sum of minimizations over the individual subzones. The advantages of the approach are considerable. First, the nonlinear minimization process occurs only over a single subzone at a time. The significant reduction in the size of the inversion problem is important because the least-squares approach scales cubically in the number of parameters to be estimated. Second, it maximizes the utilization of the complete MR displacement data set and the concomitant tissue property resolution that can be achieved. By dividing the problem into subzones, high resolution (e.g. MR voxel level) property maps can be deduced that take full advantage of the high density of tissue measurements which the MRE technique provides. Figure 3.8 shows a flow chart of the subzone inversion technique. The 3D subzone inversion algorithm has been extensively tested and evaluated in both simulation and phantom studies and has been found to be robust to noise in the motion data. The power of the method resides in its stability and to its flexibility. The method provides accurate values of the shear modulus even in the presence of significant noise [87]. For example, lesions as small as 5 mm can be accurately characterized [88]. The flexibility of the method is demonstrated by the wide variety of models which can be employed. Initially the inversion algorithm used the equations of motion for a linearly elastic solid where maps of the shear modulus and of the Lame s constant were found. However, the inversion can be formulated on the basis of a model which is a simple approximation to the Navier s equations of motion that includes the addition of a damping term in the dynamic equilibrium description: G u + ( λ + G) u = α u t + ρ 2 u t 2 (1) where u is the displacement vector, G and λ are the Lame's constants, α is a damping coefficient and ρ is the tissue density. The MR measurements are generated in terms of harmonic magnitude and phase; hence, equation (1) is recast in the frequency domain for the purposes of

40 Figure 3.9: T2 weighted FSE image of the breast with the regions of low damping coefficient outlined in red. The regions all appear to be isolated by fibrous encapsulation. image reconstruction. This is accomplished by the steady-state harmonic conversion u( x, y, z, t)= Re u ( x, y, z)e iωt { } where u is the spatially varying complex-valued displacement vector phasor in which case (1) becomes G u + λ ( + G) u = ( iωα pω 2 )u (2) Using (2), several options have been implemented including (i) the case where tissue density, ρ, is assumed known and assigned a homogeneous value throughout the breast while the shear modulus, G, Lame's constant, λ, and damping coefficient, α, are estimated spatially and (ii) the case where tissue density, ρ, shear modulus, G, and Lame's constant, λ, are estimated spatially while the damping coefficient, α, is set to zero.

41 3.2.4 SYSTEM PERFORMANCE The system performance has been evaluated in several ways. Standard linear system analysis has been applied: high contrast resolution was measured by the MTF and low contrast resolution was measured by noise sensitivity methods. The MTF measures the spatial resolution (high contrast resolution) of the MRE process and was obtained from shear modulus images of a phantom with a cylindrical inclusion that approximated a discontinuity in the shear modulus. There is some melting of the gels when an inclusion is added to a hot background gel so the discontinuity is not perfect but it provides a lower bound on the MTF; i.e., the MTF may be significantly better than that shown. The MTF s were obtained by averaging the conditioned ratio of the Fourier transform of the assumed discontinuity in the shear modulus image, where the position of the discontinuity was found from the magnitude image, with the Fourier transform of the shear modulus. The position of the discontinuity was obtained from the magnitude image. MTF estimation is always limited by noise so we have taken a conservative effective spatial resolution of 0.50 MTF. The MTF s indicate the effective limiting resolution in the shear modulus is ~1 to 3mm when a conservative detection threshold of 0.50 was used. This can be compared to the 0.5 mm limiting resolution in the magnitude image. The combination of noise and spatial resolution limits can be seen in the contrast detail experiments [87]. The limiting resolution for detection and for accurate characterization of the shear modulus are both provided in that reference. Reconstructions are not only spatially accurate in terms of localizing the regions of increased stiffness, but also are quantitatively correct (within 10 15%) in terms of characterizing the shear modulus. Accurate characterization was obtained at 5mm for the lowest contrast inclusion (2:1 relative to the background).

42 3.3 RESULTS CLINICAL IMAGES Figure 3.10: MRE images (magnitude left, shear modulus, right) from a breast with (BI-RAD 1) normal findings. Correlation between the stiffer properties (in red) and the glandular structure is evident Cancer Figure 3.11: An MRE examination of a subject with a malignancy in the upper outer quadrant which correlates well with the tissue that presents the stiffest mechanical properties. Our clinical experience with MRE is based on normal subjects (BI-RADS 1) and a limited number of abnormalities. Two representative examinations are shown in Figures 3.10

43 Figure 3.12: Shear modulus values of all of the abnormalities imaged compared to normal fat and glandular tissue. The carcinoma imaged in a screening venue (was not being treated) is much harder than normal tissues and the fibroadenoma. The neoadjuvant therapy patients are more complicated; carcinoma is always harder than normal tissue but subject 1903 was significantly softer following chemotherapy. Both patients responded to chemotherapy but 1903 was responding more fully during imaging than 1904 was. and Figure 3.10 shows the close correspondence between the fibro-glandular tissue in the center of the breast, appearing dark in the MR magnitude images and the stiffer regions, shown in yellow and red, in the shear modulus images. The fatty zones around the periphery are softer. An exam with breast cancer is illustrated in Figure The malignancy appears in the shear modulus images as the highlighted mass. It was located in the upper outer quadrant on mammography and this position matches well with the stiffest properties in the breast according to the elastograms. The results of all the clinical cases imaged are shown in Figure SHEAR MODULUS COMPARISON IN REPRESENTATIVE ABNORMALITIES The shear modulus values of normal fatty and fibroglandular tissue found using our MRE

44 system has been shown to agree well with the literature [89]. A plot showing the shear modulus values for representative abnormalities is presented in Figure There are not enough cases to draw anything other than broad conclusions. However, all of the shear moduli of carcinomas are stiffer than the fat and fibroglandular tissue in the same patient. The single screening carcinoma is much stiffer than the fat and fibroglandular tissue in any of the normal subjects. The screening carcinoma is also much stiffer than the fibroadenoma. The shear moduli of the neo-adjuvant therapy patients is somewhat more complicated. The regions averaged were taken from the areas of high contrast uptake and the anatomical images. Patient 1903 was imaged on two dates, and the shear modulus of both breast cancers decreased on the second session. The shear moduli of the carcinoma, and of the normal tissues, were much lower than in the screening case, although still stiffer than normal tissues in the same patient. The cancer values were in the range of stiffness present in normal subjects. This patient was well into the second chemotherapy regimen when imaged and none of the treatments showed clinical response. The cancer was open and ulcerative with discharge at times of examination. The left breast had a dramatic response to an alternative therapy after imaging. The lesion in subject 1904 was very difficult to image with mammography and was difficult to palpate because of breast size and density. Nonetheless, the lesion was clearly seen on MRE. The cancer was very stiff in MRE which agrees with the lack of response shown in CT and physical examination. Also, there was substantial residual cancer in the breast on extensive lumpectomy after 4 cycles of treatment on 10/23/ CONCLUSIONS Evidence that MRE will be able to contribute significantly toward earlier detection, with the associated improvement in patient outcomes, continues to accumulate. However, as with any

45 new method there are more relevant clinical and biological questions about where MRE might fit into the diagnostic process than there are answers: Can MRE reduce the number of biopsies as a follow up study for abnormalities found on mammography? Or might it be useful in screening high risk populations? Or might it be useful in following treatment? All are possible applications that should be pursued, especially when the biological causes of increased stiffness are better understood. MRE is poised to allow the biological mechanisms that influent stiffness to be understood. The underlying biological mechanisms that increase the stiffness in cancer are not known [92]; increased tissue pressures and increased amounts of collagen in the extracellular matrix, as well as increased cross linking of that collagen, are all present in cancer and all impact tissue stiffness [91, 92]. Further, the impact of increased stiffness on cancer s etiology is not known; there is evidence that the stiffness of the extracellular matrix influences, or even initiates, the malignant transformation [90]. Understanding what biological mechanisms are reflected by increased stiffness and how increased stiffness influences malignant progression will show us where elastography can contribute clinically toward improving diagnosis and treatment of breast cancer. MRE has a unique role to play in obtaining that understanding because it is robust and quantitative. 3.5 ACKNOWLEDGEMENTS Supported by P01-CA-80139, R01-NS-33900, and R01-DK

46 4 MODALITY-INDEPENDENT ELASTOGRAPHY 4.1 BACKGROUND Model-based methods for non-rigid image registration may provide a potentially new framework for characterizing breast disease. This section recasts the conventional non-rigid image registration problem as a model-constrained constitutive property reconstruction whereby soft tissue mechanical properties are quantified and potentially used to assess breast tissue health. The algorithm used is a non-linear optimization that couples a biomechanical model to an image registration framework such that the mechanical properties (e.g. Young s modulus) of the deforming tissue become the driving parameters for improved image registration. This technique is multi-resolution and is used to quantitatively evaluate the elastic properties in simulation and in a tissue-like phantom with two embedded inclusions. The results demonstrate good localization and quantification of Young s modulus contrast in both simulations and data. A central goal within the field of non-rigid image registration is to provide correspondence between spatial coordinates in one image set (often referred to as the source) to that within a second (often referred to as the target) where the relationship between spatial coordinates is non-linear. The alignment function may be challenged in a variety of ways. For example, intra-modal image data of a subject may be available but non-rigid discrepancies may be present due to physical, mechanical, or acquisition processes as in increased brain atrophy in Alzheimer s [93], deformations due to surgical intervention [94], or distortions by the imaging unit itself [95]. Regardless of the source, of paramount importance within these applications, is to automatically quantify and/or correct for these non-rigid movements using image processing techniques.

47 One way of classifying non-rigid registration methods is by the underpinning numerical technique that non-rigidly deforms the source to the target. In this classification, one possible category would use interpolating/approximating functions such as cubic, or B-splines as the means for the deformation process [96]. A second category would be to base deformations on a physical model grounded within mechanics. Deformation processes described by these techniques use the natural constitutive behaviors associated with biomechanical elastic or fluid models to drive the non-rigid motion [97, 98]. While each category has its strengths and weaknesses, the underpinning motivation is to transform one image set to another by any means within the computational framework possible such that the source and target have maximum correspondence. The work presented in this section takes a different viewpoint of the registration problem within the context of model-based methods. Rather than viewing the model and its parameterization as an alignment with many unconstrained degrees of freedom, this work utilizes a constrained model whereby the constitutive parameters are the only degrees of freedom allowed to achieve a best-fit source-totarget image match. By casting the problem in this manner, the parameters determined take on a functional role that may potentially be used for tissue characterization. Although non-rigid image registration and subsequent model analysis has been used by investigators for the understanding of tissue mechanics (e.g. MR tagging [99], and scar assessment [100]), this section presents a more instrumented depiction of non-rigid registration. In some sense, this outlook represents a new class of algorithm that is focused at diagnostic probing of tissue via model-based image registration. This methodology has been preliminarily tested within breast and dermoscopic applications [40-43].

48 4.2 MODALITY INDEPENDENT ELASTOGRAPHY METHODS BIOMECHANICAL MODEL A central component to model-based inverse problems is the manner in which the continuum is represented. While the constitutive model that best describes the deformation mechanics of tissue is more complex, for this initial work, a linear elastic model has been employed. The partial differential equation that expresses a state of mechanical equilibrium can be written as: σ = 0 (4.1) where σ is the Cartesian stress tensor. The relationship between stress and strain was assumed to be Hookean. Within the experiments presented below, two separate assumptions were made to reduce the dimensionality of the problem from three to two dimensions. For the simulation experiments concerned with performing reconstructions on MR and CT frontal breast image slices, a condition of plane strain was assumed since the out-of-plane strains would be negligible. For the experiments that involved the phantom material, a condition of plane stress was assumed since the phantom geometry was thin and out-of-plane stresses are considered negligible [101]. In plane stress, σ σ τ x y xy = 1 ν 0 εx E ν 1 0 ε 2 y (4.2) ( 1 ν ) 0 0 ( 1 ν) / 2 γ xy describes the constitutive relationship between the Cartesian stress tensor [σ x, σ y, τ xy ] and strain tensor [ε x, ε y, γ xy ]. Similarly, in plane strain,

49 σ σ τ x y xy 1 E( 1 ν) = ν /( 1 ν) ( 1+ ν)( 1 2ν) 0 ν /( 1 ν) ε 0 ε ( 1 2ν) γ 2( 1 ν) x y xy (4.3) These assumptions allow for the simplification of Cauchy s law from 36 stiffness constants to 2 (Young s modulus, E, and Poisson s ratio, ν) and a reduction in the dimensionality, respectively MODALITY INDEPENDENT ELASTOGRAPHY Figure 4.1. Example of K-means region formation using 16 material property regions. The method developed to reconstruct the Young s modulus values within tissue and tissue-like phantoms is called Modality Independent Elastography (MIE) [40-43]. MIE begins by acquiring a source/target image pair that differs due to an applied deformation from a mechanical device. A finite element model is constructed from the source image and boundary conditions are determined (in this case, by inspection of the acquired image data or by careful device construction). After the model has been generated, two discretization processes are performed: (1) the model domain is separated into a prescribed number of regions whereby each has a distinct set of elastic properties that are spatially homogeneous, and (2) the target image domain is separated into a prescribed number of zones. For the remainder of the chapter, regions

50 will refer to the local domains associated with the mechanical properties of the model, while zones will refer to the local domains associated with the target image. For region partitioning, a K-means clustering approach groups element centroids into a user-prescribed number (N) of regions such that the sum of all point-to-region centroid distances is minimized. For this work, the implementation in the MATLAB (MathWorks, Natick, MA Statistics Toolbox Version 5 was used. Figure 4.1 illustrates an example of this approach on the rectangular domain whereby the element centroids have been clustered into 16 separate regions. In the realization of MIE presented here, a multi-resolution strategy has been employed whereby coarser resolutions (i.e. fewer regions) are used at the initiation of the reconstructive process and progressively finer resolutions are employed in subsequent iterations. Previous work used only a single property resolution [41, 43]. In more recent developments, five progressively finer resolutions were used (16, 64, 256, 512, and 800 regions) while the number of image comparison zones ranged between The zones were rectangular in shape and distributed uniformly within the deformed target image. The number of zones was based on previous work that qualitatively studied reconstruction performance with respect to zone size [41]. Briefly stated, the reconstruction algorithm begins by assigning an initial Young s modulus to each of the regions at the first resolution, e.g. 16 regions (Poisson s ratio was held constant at 0.485). Once a material property description is prescribed, the biomechanical finite element model is solved for the tissue displacements. These displacements are then used to deform the source image. This model-deformed source image is then compared to the target image over each individual zone using an image similarity method (correlation coefficient was used in the work presented here) [102]. Other image similarity methods have been used in previous work [41, 43]. Modulus values in the regions are updated based on maximizing the

51 similarity between the model-deformed source image and the target image over all the similarity zones until a tolerance is reached or the desired number of iterations has been completed. Upon reaching a stopping criterion, the material property description is interpolated onto the distribution associated with the next resolution and the optimization steps are repeated. It has been shown in [42] that use of the multi-resolution technique can result in the avoidance of local minima and improved elastography image reconstruction. The parameter optimization framework can be portrayed as the minimization of a least square error objective function: where S( E r T ) φ r r r 2 ( E) = min S( E ) S( ) T E E (4.4) is the similarity value achieved when comparing the target image to itself (i.e. the maximum value for the similarity metric) and S( E r E ) is the similarity between the modeldeformed source and the target image using the current estimate of Young s modulus. Using a Marquardt [103] approach to equation (4.4), it can be written as: { } r r r T T [[J ][J] α[] I ]{ ΔE} = [ J ] S( E ) S( E ) + (4.5) t E

52 Select Resolution N regions Image Data Boundary Conditions Finite Element Model Region & Zone Discretization Go to next resolution Stiffness Parameter Optimization (N Properties Found) Elasticity Image no Final resolution been achieved? yes a Figure 4.2. (a) Flow chart for multi-resolution MIE: a functionalized image registration method, and (b) demonstration of multi-resolution reconstruction of a single inclusion with increasing number of property regions (16, 36, 64, 256, 400 regions). where [ J] is the M x N Jacobian matrix of the form r ( ) SE E J= r where M is the number of zones, E and N is the number of regions ([ I] is the identity matrix). The details of equation (4.5) have been reported previously [40, 41, 43]. In these types of inverse problems, the increase in convergent parameter space afforded by Marquardt s method is particularly important. The regularization parameter α was determined using the methods described in [104]. Figure 4.2a is a flowchart for the multi-resolution approach where equation (4.5) is being iteratively solved within the Stiffness Parameter Optimization process block. Figure 4.2b illustrates an example b

53 of mutli-resolution results with a single-inclusion simulation whereby the initial resolutions provide localization while higher resolutions begin to capture more subtle shape changes. It should be noted that in addition to regularization, spatial averaging and solution relaxation are also employed within the elasticity imaging framework. These operations have been found to improve the stability of the reconstruction algorithm.

54 4.3 BREAST AND PHANTOM EXPERIMENTS Since this method is based on image similarity, the method is independent of any particular imaging modality, as the name suggests. As a result, the method is solely dependent on intensity structural contrast with a given image pair. In order to demonstrate this, three different modalities are present in the experiments below: (1) X-ray computed tomography (CT), (2) magnetic resonance (MR), and (3) optical BREAST EXPERIMENTS Figure 4.3. Images slices of breast tissue extracted from a CT volume (left) and MR volume (right) used in simulation study of the ability of the reconstruction method to utilize disparate image data types. Simulation reconstructions were performed using image slices extracted from breast image volumes obtained from CT and MR scans (see Figure 4.3). Although these were taken from two different patients, the images were selected to be approximately corresponding slices ~2 cm away from the chest wall in the frontal orientation of the standard anatomical position. The simulations were set up in the same manner, using either one or two inclusions of about 1 cm in diameter embedded within the true elasticity distribution and a small compression (~8% strain) in the cranial-caudal direction. The relative stiffness of the inclusions was designated to

55 be 5.7:1 for consistency with the material testing data and also because the value is fairly representative of breast tumor properties [2]. The plane strain model approximation was used in the breast simulation trials, progressing through resolutions of N = 24, 64, 256, and 576 regions using M = 200 zones. The reconstruction method was then run for all four test cases (1 tumor CT, 2 tumors CT, 1 tumor MR, 2 tumors MR) PHANTOM EXPERIMENTS In order to test our inverse problem framework with real data from yet another imaging modality, a two-material phantom membrane model was constructed. The bulk of the phantom was made using Smooth-On Evergreen 10 polyurethane (Smooth-On, 2000 Saint John Street, Easton, PA). Two 1.5cm cylindrical inclusions were placed within the membrane phantom and were made of a stiffer polyurethane material (Evergreen 50). The inclusion material was chosen for its relative stiffness to that of Evergreen 10 and the similarity in color to the Evergreen 10. A permanent marker was used to place a texture pattern on the membrane. Figure 4.4a-b shows the skin phantom used for data collection in this series of experiments with the inclusions designated in Figure 4.6. Membrane data was collected in a pre- and post- stretched state (compare Figure (a) (b) (c) Figure 4.4. Phantom membrane (a) before and (b) after mechanical stretching. (c) is a difference image.

56 Figure 4.5. Example stress-strain curve for the bulk material as measured with a material tester. 4.4a to 4.4b with difference image Figure 4.4c). A commercial webcam (Logitech QuickCam Pro 4000, 960 x 1280 pixel resolution) was rigidly mounted above the membrane and acquired the image pairs. In addition, independent material testing using a compression testing device was performed on each of the phantom materials in separate tests. The stress-strain behavior of each material was modestly non-linear. Figure 4.5 is an example stress-strain curve for the bulk material used in the experiment. Young s modulus values were determined in a piece-wise linear fashion across the entire stress regime. For the strains observed in Figure 4.4a-b, the Young s modulus for the bulk and inclusion material was approximately 147 kpa and 865 kpa, respectively, which gives an inclusion-to-bulk stiffness contrast ratio of 6:1. With respect to model calculations, equation (4.1) was solved using the Galerkin finite element method [105]. The computational domain involved 1255 nodes and 2367 elements (approximate 3 mm element edge length). The mesh domain is shown below in Figure 4.6a.

57 T 1 T 2 2 T 2 1 Boundary conditions for the model were determined manually from the image data and prescribed as boundary displacements. Since Dirichlet type boundary conditions are solely used, the elastic model is only sensitive to Young s modulus contrast. Without applying a boundary stress or designating one material property value within the domain, absolute properties cannot be determined. For comparison between experimentally measured (as performed by material testing) and reconstructed Young s moduli, transects T 1 and T 2 were designated in Figure 4.6b whereby the Young s modulus along the transect was compared to the bulk material s modulus. With the optical images, two specific reconstructions were performed. The first experiment imposed a Young s modulus distribution on the domain shown in Figure 4.6a-b. This description matched the inclusion sizes and locations to those of the physical phantom. The assigned property values reflected a 6:1 Young s modulus ratio between inclusion and bulk material, respectively. The image shown in Figure 4.4a was deformed in simulation with the inclusions present in the model. Beginning with a homogeneous guess at the Young s modulus description, the finite element domain, the source image, and the simulated model-deformed target image, the multi-resolution MIE algorithm was initiated. a Figure 4.6. (a) Finite element domain used in MIE reconstruction, and (b) image domain showing location of inclusions (dotted lines) and transects (T 1, T 2 ) used in analysis. T 1 b

58 The second reconstruction experiment repeated the above steps but the acquired target image shown in Figure 4.4b was used in lieu of the simulated target image. For determining the Young s modulus contrast ratio, it required the determination of the homogeneous value within the reconstruction so as to generate the ratio throughout the image. To accomplish this, the average Young s modulus within the central area of the phantom was used as the value for the bulk material property value RECONSTRUCTION QUALITY EVALUATION The fidelity of the elasticity reconstruction was evaluated on its ability to detect the presence of an inclusion based on classification of the material property distribution, and the retrospective accuracy of localizing the lesions. The elastic properties as a whole were treated as a Gaussian mixture of two classes and separated by a threshold established via the method described in [106]. The likelihood of detecting a lesion in the elasticity image was found using the contrast-to-noise ratio as defined by [87, 107]: 2( μ μ ) CNR = (4.6) σ + σ L 2 L 2 B 2 B where μ and σ 2 are the sample mean and variance of a material property distribution and the subscripts L and B denote the lesion and bulk material classes, respectively. Values of significance for successful detection and localization were set at CNR 2.2 as noted by [87]. The average modulus contrast is found from the ratio of the means of the two material classes, and a peak modulus contrast value is also reported by taking the ratio of two manually selected homogeneous regions of approximately equal area known to be representative of the two materials.

59 4.4 BREAST AND PHANTOM RESULTS BREAST RESULTS Figure 4.7. Reconstructions of simulation trials for the CT breast slice using a single inclusion (left) and two inclusions (right). The true inclusion boundaries are overlaid in each elasticity image. Figure 4.8. Reconstructions of simulation trials for the MR breast slice using a single inclusion (left) and two inclusions (right). The true elasticity distributions are also shown (top row) for comparison.