Visualization and quantification of breast cancer biomechanical properties with magnetic resonance elastography

Mechanical transient-based magnetic resonance elastography

Magnetic resonance elastography (MRE) is a technique for quantifying material properties by measuring cyclic displacements of propagating shear waves. As an alternative to dynamic harmonic wave MRE or quasi-steady-state methods, the idea of using a transient impulse for mechanical excitation is introduced. Two processing methods to calculate shear stiffness from transient data were developed. The techniques were tested in phantom studies, and the transient results were found to be comparable to the harmonic wave results. Transient wave based analysis was applied to the brains of six healthy volunteers in order to assess the method in areas of complex wave patterns and geometry. The results demonstrated the feasibility of measuring brain stiffness in vivo using a transient mechanical excitation. Transient and harmonic methods both measure white matter (approximately 12 kPa) to be stiffer than gray matter ( approximately 8 kPa). There were some anatomic differences between harmonic and transient MRE, specifically where the transient results better depicted the deeper structures of the brain.

A unified view of imaging the elastic properties of tissue

A number of different approaches have been developed to estimate and image the elastic properties of tissue. The biomechanical properties of tissues are vitally linked to function and pathology, but cannot be directly assessed by conventional ultrasound, MRI, CT, or nuclear imaging. Research developments have introduced new approaches, using either MRI or ultrasound to image the tissue response to some stimulus. A wide range of stimuli has been evaluated, including heat, water jets, vibration shear waves, compression, and quasistatic compression, using single or multiple steps or low-frequency (<10 Hz) cyclic excitation. These may seem to be greatly dissimilar, and appear to produce distinctly different types of information and images. However, our purpose in this tutorial is to review the major classes of excitation stimuli, and then to demonstrate that they produce responses that fall within a common spectrum of elastic behavior. Within this spectrum, the major classes of excitation include step compression, cyclic quasistatic compression, harmonic shear wave excitation, and transient shear wave excitation. The information they reveal about the unknown elastic distribution within an imaging region of interest are shown to be fundamentally related because the tissue responses are governed by the same equation. Examples use simple geometry to emphasize the common nature of the approaches.

Assessment of vulnerable plaque composition by matching the deformation of a parametric plaque model to measured plaque deformation

Intravascular ultrasound (IVUS) elastography visualizes local radial strain of arteries in so-called elastograms to detect rupture-prone plaques. However, due to the unknown arterial stress distribution these elastograms cannot be directly interpreted as a morphology and material composition image. To overcome this limitation we have developed a method that reconstructs a Young's modulus image from an elastogram. This method is especially suited for thin-cap fibroatheromas (TCFAs), i.e., plaques with a media region containing a lipid pool covered by a cap. Reconstruction is done by a minimization algorithm that matches the strain image output, calculated with a parametric finite element model (PFEM) representation of a TCFA, to an elastogram by iteratively updating the PFEM geometry and material parameters. These geometry parameters delineate the TCFA media, lipid pool and cap regions by circles. The material parameter for each region is a Young's modulus, EM, EL, and EC, respectively. The method was successfully tested on computer-simulated TCFAs (n = 2), one defined by circles, the other by tracing TCFA histology, and additionally on a physical phantom (n = 1) having a stiff wall (measured EM = 16.8 kPa) with an eccentric soft region (measured EL = 4.2 kPa). Finally, it was applied on human coronary plaques in vitro (n = 1) and in vivo (n = 1). The corresponding simulated and measured elastograms of these plaques showed radial strain values from 0% up to 2% at a pressure differential of 20, 20, 1, 20, and 1 mmHg respectively. The used/reconstructed Young's moduli [kPa] were for the circular plaque EL = 50/66, EM = 1500/1484, EC = 2000/2047, for the traced plaque EL = 25/1, EM = 1000/1148, EC = 1500/1491, for the phantom EL = 4.2/4 kPa, EM = 16.8/16, for the in vitro plaque EL = n.a./29, EM = n.a./647, EC = n.a./1784 kPa and for the in vivo plaque EL = n.a./2, EM = n.a./188, Ec = n.a./188 kPa.

Imaging the shear modulus of the heel fat pads

BACKGROUND

Steady state, dynamic MR elastography provides quantitative images of the shear modulus of tissues in vivo. MR elastography was evaluated for its ability to characterize the mechanical properties of the weight bearing plantar soft tissues in vivo.

METHODS

MR elastography was used to image the heel fat pad and surrounding soft tissues when the subject applied a low pressure on the foot and again when the subject applied high pressure. The placement of the foot was identical for both sets of images.

FINDINGS

The results agree well with expected trends. The shear modulus of the tissue under the calcaneus increased from 8 kPa to 12 kPa with increasing pressure while that of peripheral tissues remained constant at 8 kPa which is similar to the shear modulus of fat in breast tissue.

INTERPRETATION

Preliminary results from the steady state MR elastography methods being developed to measure the shear modulus of plantar soft tissues are promising. MR elastography is sufficiently accurate to observe the change in shear modulus with changes in applied pressure and is capable of characterizing the mechanical properties of the plantar soft tissues. Detailed anatomic information can be combined with co-registered mechanical properties. MR elastography could play a significant role in understanding the weight bearing functions of the plantar soft tissues and in evaluating those structures for improved diagnosis and assessment of disease progression.

Estimation of material elastic moduli in elastography: a local method, and an investigation of Poisson's ratio sensitivity

The local material stiffness of tissues is a well-known indicator of pathology, with locally stiffer tissue related to the possible presence of an abnormal growth in otherwise compliant tissue. Elastography is a non-invasive technique for measuring displacement distributions in loaded tissues within a medical imaging context. From these measured displacement fields, estimated for local strain have been made using well-studied techniques, but the calculation of elastic modulus has been difficult. In this study we show a method for estimating local tissue elastic modulus that gives numerically stable and robust results in test cases, and that is numerically efficient. The method assumes the tissue is isotropic and it requires an independent estimate of tissue Poisson's ratio, but the method reaches a stable result when the estimated Poisson's ratio is in error, and the resulting estimates are not very sensitive to the assumed value.

Imaging articular cartilage under compression?cartilage elastography

We constructed a device to compress small samples of articular cartilage while the samples were imaged in a 1.5 T imager. With the use of a piezoelectric piston, the device compressed 1-cm-diameter cylindrical samples of articular cartilage (200 microm) at a rate of 2 Hz. Simultaneously, we imaged the samples with a displacement-sensitive stimulated-echo acquisition mode (STEAM) sequence. We validated the technique using tissue that mimicked silicone samples. We compared the results from the same cartilage samples before and after they were degraded by digestion in trypsin. The extent of degradation was visualized from T(1)-weighted images of the samples after they were soaked in 0.5 mmolar of GdDTPA. The resulting elastographic images show compression and differential strain in directions both parallel and perpendicular to the surface of the cartilage. The static elastographic images that depict compression made before digestion and after 5 and 15 hr of trypsin digestion show that the elastic modulus of the samples decreased with a spatial variation consistent with the enzymatic digestion as revealed by the T(1) images. We believe this technique will be useful in studies of the mechanical properties of articular cartilage and other tissues, and may in the future be extended to the clinical setting.

MRI-based technique for determining nonuniform deformations throughout the volume of articular cartilage explants

Articular cartilage is critical to the normal function of diarthrodial joints. Despite the importance of the tissue and the prevalence of cartilage degeneration (e.g., osteoarthritis), the technology required to noninvasively describe nonuniform deformations throughout the volume of the tissue has not been available until recently. The objectives of the work reported in this paper were to 1) describe a noninvasive technique (termed the cartilage deformation by tag registration (CDTR) technique) to determine nonuniform deformations in articular cartilage explants with the use of specialized MRI tagging and image processing methods, 2) evaluate the strain error of the CDTR technique using a custom MRI-compatible phantom material, and 3) demonstrate the applicability of the CDTR technique to articular cartilage by determining 3D strain fields throughout the volume of a bovine articular cartilage explant. A custom MRI pulse sequence was designed to tag and image articular cartilage explants at 7 Tesla in undeformed and deformed states during the application of multiple load cycles. The custom pulse sequence incorporated the "delays alternating with nutations for tailored excitation" (DANTE) pulse sequence to apply tags. This was followed by a "fast spin echo" (FSE) pulse sequence to create images of the tags. The error analysis using the phantom material indicated that deformations can be determined with an error, defined as the strain precision, better than 0.83% strain. When this technique was applied to a single articular cartilage explant loaded in unconfined compression, hetereogeneous deformations throughout the volume of the tissue were evident. This technique potentially can be applied to determine normal cartilage deformations, analyze degenerated cartilage, and evaluate cartilage surgical repair and treatment methodologies. In addition, this technique may be applied to other soft tissues that can be appropriately imaged by MR.

Viscoelastic imaging of breast tumor microenvironment with ultrasound

Imaging systems are most effective for detection and classification when they exploit contrast mechanisms specific to particular disease processes. A common example is mammography, where the contrast depends on local changes in cell density and the presence of microcalcifications. Unfortunately the specificity for classifying malignant breast disease is relatively low for many current diagnostic techniques. This paper describes a new ultrasonic technique for imaging the viscoelastic properties of breast tissue. The mechanical properties of glandular breast tissue, like most biopolymers, react to mechanical stimuli in a manner specific to the microenvironment of the tissue. Elastic properties allow noninvasive imaging of desmoplasia while viscous properties describe metabolism-dependent features such as pH. These ultrasonic methods are providing new tools for studying disease mechanisms as well as improving diagnosis.

The tension mounts: mechanics meets morphogenesis and malignancy

The tissue microenvironment regulates mammary gland development and tissue homeostasis through soluble, insoluble and cellular cues that operate within the three dimensional architecture of the gland. Disruption of these critical cues and loss of tissue architecture characterize breast tumors. The developing and lactating mammary gland are also subject to a plethora of tensional forces that shape the morphology of the gland and orchestrate its functionally differentiated state. Moreover, malignant transformation of the breast is associated with dramatic changes in gland tension that include elevated compression forces, high tensional resistance stresses and increased extracellular matrix stiffness. Chronically increased mammary gland tension may influence tumor growth, perturb tissue morphogenesis, facilitate tumor invasion, and alter tumor survival and treatment responsiveness. Because mammary tissue differentiation is compromised by high mechanical force and transformed cells exhibit altered mechanoresponsiveness, malignant transformation of the breast may be functionally linked to perturbed tensional-homeostasis. Accordingly, it will be important to define the role of tensional force in mammary gland development and tumorigenesis. Additionally, it will be critical to identify the key molecular elements regulating tensional-homeostasis of the mammary gland and thereafter to characterize their associated mechanotransduction pathways.

A method to measure the hyperelastic parameters ofex vivobreast tissue samples

Over the past decade, there has been increasing interest in modelling soft tissue deformation. This topic has several biomedical applications ranging from medical imaging to robotic assisted telesurgery. In these applications, tissue deformation can be very large due to low tissue stiffness and lack of physical constraints. As a result, deformation modelling of such organs often requires a treatment, which reflects nonlinear behaviour. While computational techniques such as nonlinear finite element methods are well developed, the required intrinsic nonlinear mechanical parameters of soft tissues that are critical to develop reliable tissue deformation models are not well known. To address this issue, we developed a system to measure the hyperelastic parameters of small ex vivo tissue samples. This measurement technique consists of indenting an unconfined small block of tissue using a computer controlled loading system while measuring the resulting indentation force. The nonlinear tissue force-displacement response is used to calculate the hyperelastic parameters via an appropriate inversion technique. This technique is based on a nonlinear least squares formulation that uses a nonlinear finite element model as the direct problem solver. The features of the system are demonstrated with two samples of breast tissue and typical hyperelastic results are presented.

Modality independent elastography (MIE): a new approach to elasticity imaging

The correlation between tissue stiffness and health is an accepted form of organ disease assessment. As a result, there has been a significant amount of interest in developing methods to image elasticity parameters (i.e., elastography). The modality independent elastography (MIE) method combines a nonlinear optimization framework, computer models of soft-tissue deformation, and standard measures of image similarity to reconstruct elastic property distributions within soft tissue. In this paper, simulation results demonstrate successful elasticity image reconstructions in breast cross-sectional images acquired from magnetic resonance (MR) imaging. Results from phantom experiments illustrate its modality independence by reconstructing elasticity images of the same phantom in both MR and computed tomographic imaging units. Additional results regarding the performance of a new multigrid strategy to MIE and the implementation of a parallel architecture are also presented.

On the feasibility of elastic wave visualization within polymeric solids using magnetic resonance elastography

In this paper, the feasibility of extending previously described magnetic resonance elastography (MRE) dynamic displacement (and associated elasticity) measurement techniques, currently used successfully in tissue, to solid materials which have much higher shear rigidity and much lower nuclear spin densities, is considered. Based on these considerations, the MRE technique is modified in a straightforward manner and used to directly visualize shear wave displacements within two polymeric materials, one of which is relatively stiff.

Evaluation of the adjoint equation based algorithm for elasticity imaging

Recently a new adjoint equation based iterative method was proposed for evaluating the spatial distribution of the elastic modulus of tissue based on the knowledge of its displacement field under a deformation. In this method the original problem was reformulated as a minimization problem, and a gradient-based optimization algorithm was used to solve it. Significant computational savings were realized by utilizing the solution of the adjoint elasticity equations in calculating the gradient. In this paper, we examine the performance of this method with regard to measures which we believe will impact its eventual clinical use. In particular, we evaluate its abilities to (1) resolve geometrically the complex regions of elevated stiffness; (2) to handle noise levels inherent in typical instrumentation; and (3) to generate three-dimensional elasticity images. For our tests we utilize both synthetic and experimental displacement data, and consider both qualitative and quantitative measures of performance. We conclude that the method is robust and accurate, and a good candidate for clinical application because of its computational speed and efficiency.

High-resolution determination of soft tissue deformations using MRI and first-order texture correlation

Mechanical factors such as deformation and strain are thought to play important roles in the maintenance, repair, and degeneration of soft tissues. Determination of soft tissue static deformation has traditionally only been possible at a tissue's surface, utilizing external markers or instrumentation. Texture correlation is a displacement field measurement technique which relies on unique image patterns within a pair of digital images to track displacement. The technique has recently been applied to MR images, indicating the possibility of high-resolution displacement and strain field determination within the mid-substance of soft tissues. However, the utility of MR texture correlation analysis may vary amongst tissue types depending on their underlying structure, composition, and contrast mechanism, which give rise to variations in texture with MRI. In this study, we investigate the utility of a texture correlation algorithm with first-order displacement mapping terms for use with MR images, and suggest a novel index of image "roughness" as a way to decrease errors associated with the use of texture correlation for intra-tissue strain measurement with MRI. We find that a first-order algorithm can significantly reduce strain measurement error, and that an image "roughness" index correlates with displacement measurement error for a variety of imaging conditions and tissue types.

Shear stiffness estimation using intravoxel phase dispersion in magnetic resonance elastography

Dynamic MR elastography (MRE) is a phase-contrast technique in which the periodic shear motion of an object is encoded as variations in the phase of the reconstructed images. An alternative MRE method is presented whereby waves are depicted as intensity variations in the magnitude images due to intravoxel phase dispersion (IVPD). A theoretical framework is developed to model how the IVPD magnitude data are related to the underlying shear wave motion, and how they can be used to estimate shear stiffness. The results are shown in a series of phantom experiments to demonstrate that IVPD MRE complements phase-contrast MRE.

Ultrasound elastography based on multiscale estimations of regularized displacement fields

Elasticity imaging is based on the measurements of local tissue deformation. The approach to ultrasound elasticity imaging presented in this paper relies on the estimation of dense displacement fields by a coarse-to-fine minimization of an energy function that combines constraints of conservation of echo amplitude and displacement field continuity. The multiscale optimization scheme presents several characteristics aimed at improving and accelerating the convergence of the minimization process. This includes the nonregularized initialization at the coarsest resolution and the use of adaptive configuration spaces. Parameters of the energy model and optimization were adjusted using data obtained from a tissue-like phantom material. Elasticity images from normal in vivo breast tissue were subsequently obtained with these parameters. Introducing a smoothness constraint into motion field estimation helped solve ambiguities due to incoherent motion, leading to elastograms less degraded by decorrelation noise than the ones obtained from correlation-based techniques.

Magnetic resonance elastography and diffusion-weighted imaging of the sol/gel phase transition in agarose

The dynamics of the sol/gel phase transition in agarose was analyzed with magnetic resonance elastography (MRE) and diffusion-weighted imaging, providing complementary information on a microstructural as well as on a macroscopic spatial scale. In thermal equilibrium, the diffusion coefficient of agarose is linearly correlated with temperature, independent of the sol/gel phase transition. In larger agarose samples, the transition from the sol to the gel state was characterized by a complex position and temperature dependency of both MRE shear wave patterns and apparent diffusion coefficients (ADC). The position dependency of the temperature was experimentally found to be qualitatively similar to the behavior of the ADC maps. The dynamics of the temperature could be described with a simplified model that described the heat exchange between sol and gel compartments. The experiments supported the approach to derive temperature maps from the ADC maps by a linear relationship. The spatially resolved dynamics of the temperature maps were therefore employed to determine the elasticities. For this reason, experimental MRE data were simulated using a model of coupled harmonic oscillators. The calculated images agreed well with the experimentally observed MRE wave patterns.

Evaluation of renal parenchymal disease in a rat model with magnetic resonance elastography

Alterations in the mechanical properties or "hardness" of tissues allow physicians to detect disease by palpation. Recently, attempts have been made to quantitate and image these tissue properties with the use of magnetic resonance elastography (MRE). This technique has been validated in ex vivo specimens, including kidney, breast, and prostate. In this study, in vivo MRE imaging of rat renal cortex is demonstrated and validated with a disease model that will facilitate further studies. Normal rats and rats with nephrocalcinosis induced with either 2 or 4 weeks of ethylene glycol exposure were studied with MRE. Histology in the diseased rats documented the presence of nephrocalcinosis. MRE measurements and images of shear stiffness were highly reproducible in individual rats. The shear stiffness of the renal cortex in normal rats was 3.87 kPa (95% CI 2.84-4.90 kPa). The shear stiffness increased to 5.02 kPa (95% CI 3.34-6.70 kPa) after 2 weeks of exposure, and to 6.49 kPa (95% CI 4.84-8.14 kPa) after 4 weeks of exposure (P = 0.0302, alpha < 0.05). MRE is capable of detecting alterations in the tissue mechanical properties of kidneys in vivo. It is a promising noninvasive technique that might have pathologic and prognostic significance.

Shear-wave generation using acoustic radiation force: in vivo and ex vivo results

Acoustic radiation force impulse (ARFI) imaging involves the mechanical excitation of tissue using localized, impulsive radiation force. This results in shear-wave propagation away from the region of excitation. Using a single diagnostic transducer on a modified commercial ultrasound (US) scanner with conventional beam-forming architecture, repeated excitations with multiple look directions facilitate imaging shear-wave propagation. Direct inversion methods are then applied to estimate the associated Young's modulus. Shear-wave images are generated in tissue-mimicking phantoms, ex vivo human breast tissue and in vivo in the human abdomen. Mean Young's modulus values of between 3.8 and 5.6 kPa, 11.7 kPa and 14.0 kPa were estimated for fat, fibroadenoma and skin, respectively. Reasonable agreement is demonstrated between structures in matched B-mode and reconstructed modulus images. Although the relatively small magnitude of the displacement data presents some challenges, the reconstructions suggest the clinical feasibility of radiation force induced shear-wave imaging.

Elastographic measurement of the area and volume of thermal lesions resulting from radiofrequency ablation: pathologic correlation

OBJECTIVE

Elastography is a promising tool for visualizing the zone of necrosis in liver tissue resulting from radiofrequency tumor ablation. Because heat-ablated tissues are stiffer than normal untreated tissue, elastography may prove useful for following up patients who undergo radiofrequency ablative therapy. We sought to report the initial evaluations of the reliability of elastography for delineating thermal lesion boundaries in liver tissue by comparing lesion dimensions determined by elastography with the findings at whole-mount pathology.

MATERIALS AND METHODS

Radiofrequency ablation was performed in vitro on liver tissue specimens encased in gelatin phantoms. The imaging plane for elastography was perpendicular to the axis of the radiofrequency electrode so that the ablated region was around the center of the plane. To obtain three-dimensional visualization of thermal lesions, we reconstructed the lesions from multiple elastograms by linearly translating the elastographic scanning plane. Pathology photographs were obtained in the same image plane used for elastography by slicing through the gelatin and tissue phantom using external markers. We used digitized gross pathology photographs obtained at a specified slice thickness to compute the areas and volumes of the lesions. These measurements were then compared to the measurements obtained from the elastograms.

RESULTS

In a sample of 40 thermal lesions, we obtained a correlation between in vitro elastographic and pathologic measurements of r = 0.9371 (p < 0.00001) for area estimates and r = 0.979 (p < 0.00001) for volume estimates.

CONCLUSION

We found excellent correlation between the measurements of the dimensions, areas, and volumes of thermal lesions that were based on elastographic images and the measurements that were based on digitized pathologic images. When compared with digitized pathologic measurements, elastographic measurements showed a tendency to slightly underestimate both the areas and volumes of lesions. Nevertheless, elastography is a reliable technique for delineating thermal lesions resulting from radiofrequency ablation.

Analytic modeling of breast elastography

The elastic moduli of tumors change during their pathological evolution. Elastographic imaging has potential for detecting and characterizing cancers by mapping the stiffness distribution in tissues. In this paper a micromechanics-based analytical method was developed to detect the location, size, and elastic modulus of a tumor mass embedded in a symmetric two-dimensional breast tissue. A closed-form solution for the strain elastograms (forward problem) was derived. A computational algorithm for the inverse problem was developed for the detection, localization, and characterization of a heterogeneous mass embedded in a breast tissue. Numerical examples were presented to evaluate the proposed method's performance. The detectability of a tumor mass was estimated with respect to lesion location, size, and modulus contrast ratio. It was shown that the micromechanics theory provides a powerful tool for the diagnosis of breast cancer.

Electromagnetic actuator for generating variably oriented shear waves in MR elastography

Magnetic resonance elastography (MRE) is a recently developed technique for determining the mechanical properties of biological tissue. In dynamic MRE, electromagnetic units (actuators) are widely used to generate shear waves in tissue. These actuators exploit the interaction between the static magnetic field B(0) and an annular coil supplied with alternating currents. Therefore, coil movements are restricted to selected orientations to B(0). Conventional actuators transfer this movement collinearly to B(0) into the tissue. In this study, an electromagnetic actuator was introduced that overcomes this limitation. It is demonstrated that different directions of mechanical excitation can be generated and monitored by MRE. Different spatial components of the propagation of the shear waves were determined using agarose phantoms. The technique allows maximum contrast for MRE images of objects with anisotropic strain components such as muscle tissue.

Thresholds for detecting and characterizing focal lesions using steady-state MR elastography

An objective contrast-detail analysis was performed in this study to assess the low contrast detectability of a clinical prototype harmonic magnetic resonance elastographic imaging system. Elastographic imaging was performed on gelatin phantoms containing spherical inclusions of varying size and modulus contrast. The results demonstrate that lesions as small as 5 mm can be detected with a minimum modulus contrast of 14 dB. However, the shear modulus of such small lesions was not accurately recovered. In general, the shear modulus of larger focal lesions was accurately (i.e., within 25% of the true value) recovered. The minimum modulus contrast needed to detect focal lesions was observed to decrease with increasing lesion size.

Menstrual-cycle dependence of breast parenchyma elasticity: estimation with magnetic resonance elastography of breast tissue during the menstrual cycle

RATIONALE AND OBJECTIVES

Magnetic resonance elastography (MRE) is a promising diagnostic method that produces images with a contrast proportional to the elasticity of the tissue. This study investigated using MRE the dependence of breast tissue elasticity from the menstrual cycle of healthy volunteers.

METHODS

Five volunteers (age 26-36) without breast disease and contraceptive medication were examined once weekly over 2 menstrual cycles. Examinations were performed with a 1.5 T magnet (ACS-NT, Philips Medical Systems, Best, The Netherlands). Low-frequency mechanical waves (65 Hz) were transmitted into the tissue by an oscillator. By means of a motion-sensitive spin-echo sequence, mechanical waves were displayed within the phase of the MR image and phase images were used to reconstruct the local distribution of elasticity. The elasticity of fibroglandular tissue and adipose breast tissue was analyzed individually, and the median and mean values of elasticity over the menstrual cycle were determined.

RESULTS

All volunteers presented a repeating pattern concerning the elasticity over the 2 cycles. After 5 days of the onset of menses, the median value of elasticity for fibroglandular adipose tissue declined significantly by -29% (P = 0.010). After the second week of the cycle, fibroglandular tissue showed again an increase in elasticity (P = 0.028). The highest median values of elasticity were obtained during days 11 to 23 with an increase of up to 35%. For adipose tissue, only a slight and not significant variation of elasticity during the menstrual cycle was determined.

CONCLUSION

MRE is able to measure a dependence of tissue elasticity on the menstrual cycle.

Detecting stiff masses using strain-encoded (SENC) imaging

A method is proposed for detecting stiff masses using strain-encoded (SENC) magnetic resonance imaging (MRI). An object of interest is compressed to produce local strain distribution that depends on local elasticity, where intensities correlate with the local through-imaging-plane strain component. Because the strain is lower inside a stiff mass than in the surrounding soft tissue, an intensity contrast in the resulting images would enable direct detection of the mass without postprocessing. The technique was validated by a phantom experiment in which a gel phantom with a stiff region was used. The advantages of the proposed method include short imaging time and uncomplicated postprocessing. However, in its current form the technique does not measure elasticity.

A new approach to elastography using mutual information and finite elements

Historically, increased mechanical stiffness during tissue palpation exams has been associated with assessing organ health as well as with detecting the growth of a potentially life-threatening cell mass. As such, techniques to image elasticity parameters (i.e., elastography) have recently become of great interest to scientists. In this work, a new method of elastography will be introduced within the context of mammographic imaging. The elastography method proposed represents a non-rigid iterative image registration algorithm that varies material properties within a finite element model to improve registration. More specifically, regional measures of image similarity are used within an objective function minimization framework to reconstruct elasticity images of tissue stiffness. Numerical simulations illustrate: (1) the encoding of stiffness information within the context of a regional image similarity criterion, (2) the methodology for an iterative elastographic imaging framework and (3) elasticity reconstruction simulations. The real strength in this approach is that images from any modality (e.g., magnetic resonance, computed tomography, ultrasound. etc) that have sufficient anatomically-based intensity heterogeneity and remain consistent from a pre- to a post-deformed state could be used in this paradigm.

Validation of nonrigid image registration using finite-element methods: application to breast MR images

This paper presents a novel method for validation of nonrigid medical image registration. This method is based on the simulation of physically plausible, biomechanical tissue deformations using finite-element methods. Applying a range of displacements to finite-element models of different patient anatomies generates model solutions which simulate gold standard deformations. From these solutions, deformed images are generated with a range of deformations typical of those likely to occur in vivo. The registration accuracy with respect to the finite-element simulations is quantified by co-registering the deformed images with the original images and comparing the recovered voxel displacements with the biomechanically simulated ones. The functionality of the validation method is demonstrated for a previously described nonrigid image registration technique based on free-form deformations using B-splines and normalized mutual information as a voxel similarity measure, with an application to contrast-enhanced magnetic resonance mammography image pairs. The exemplar nonrigid registration technique is shown to be of subvoxel accuracy on average for this particular application. The validation method presented here is an important step toward more generic simulations of biomechanically plausible tissue deformations and quantification of tissue motion recovery using nonrigid image registration. It will provide a basis for improving and comparing different nonrigid registration techniques for a diversity of medical applications, such as intrasubject tissue deformation or motion correction in the brain, liver or heart.

Tissue-mimicking oil-in-gelatin dispersions for use in heterogeneous elastography phantoms

A ten-month study is presented of materials for use in heterogeneous elastography phantoms. The materials consist of gelatin with or without a suspension of microscopic safflower oil droplets. The highest volume percent of oil in the materials is 50%. Thimerosal acts as a preservative. The greater the safflower oil concentration, the lower the Young's modulus. Elastographic data for heterogeneous phantoms, in which the only variable is safflower oil concentration, demonstrate stability of inclusion geometry and elastic strain contrast. Young's modulus ratios (elastic contrasts) producible in a heterogeneous phantom are as high as 2.7. The phantoms are particularly useful for ultrasound elastography. They can also be employed in MR elastography, although the highest achievable ratio of longitudinal to transverse relaxation times is considerably less than is the case for soft tissues.

Initial in vivo experience with steady-state subzone-based MR elastography of the human breast

PURPOSE

To describe initial in vivo experiences with a subzone-based, steady-state MR elastography (MRE) method. This sparse collection of in vivo results is intended to shed light on some of the strengths and weaknesses of existing clinical MRE approaches and to indicate important areas of future research.

MATERIALS AND METHODS

Elastic property reconstruction results are compared with data compiled from the limited existing body of published studies in breast elasticity. Mechanical parameter distributions are also investigated in terms of their implications for the nature of biological soft tissue. Additionally, a derivation of the statistical variance of the elastic parameter reconstruction is given and the resulting confidence intervals (CIs) for different parameter solutions are examined.

RESULTS

By comparison with existing estimates of the elastic properties of breast tissue, the subzone-based, steady-state MRE method is seen to produce reasonable estimates for the mechanical properties of in vivo tissue.

CONCLUSION

MRE shows potential as an effective way to determine the elastic properties of breast tissue, and may be of significant clinical interest.

Comparison of quantitative shear wave MR-elastography with mechanical compression tests

The mechanical properties of in vivo soft tissue are generally determined by palpation, ultrasound measurements (US), and magnetic resonance elastography (MRE). While it has been shown that US and MRE are capable of quantitatively measuring soft tissue elasticity, there is still some uncertainty about the reliability of quantitative MRE measurements. For this reason it was decided to determine in vitro how MRE measurements correspond with other quantitative methods of measuring characteristic elasticity values. This article presents the results of experiments with tissue-like agar-agar gel phantoms in which the wavelength of strain waves was measured by shear wave MR elastography and the resultant shear modulus was compared with results from mechanical compression tests with small gel specimens. The shear moduli of nine homogeneous gels with various agar-agar concentrations were investigated. The elasticity range of the gels covered the elasticity range of typical soft tissues. The systematic comparison between shear wave MRE and compression tests showed good agreement between the two measurement techniques.

Quantitative elasticity imaging: what can and cannot be inferred from strain images

We examine the inverse problem associated with quantitative elastic modulus imaging: given the equilibrium strain field in a 2D incompressible elastic material, determine the elastic stiffness (shear modulus). We show analytically that a direct formulation of the inverse problem has no unique solution unless stiffness information is known a priori on a sufficient portion of the boundary. This implies that relative stiffness images constructed on the assumption of constant boundary stiffness are in error, unless the stiffness is truly constant on the boundary. We show further that using displacement boundary conditions in the forward incompressible elasticity problem leads to a nonunique inverse problem. Indeed, we give examples in which exactly the same strain field results from different elastic modulus distributions under displacement boundary conditions. We also show that knowing the stress on the boundary can, in certain configurations, lead to a well-posed inverse problem for the elastic stiffness. These results indicate what data must be taken if the elastic modulus is to be reconstructed reliably and quantitatively from a strain image.

MR elastography of breast cancer: preliminary results

OBJECTIVE

Motivated by the long-recognized value of palpation in detecting breast cancer, we tested the feasibility of a technique for quantitatively evaluating the mechanical properties of breast tissues on the basis of direct MR imaging visualization of acoustic waves.

SUBJECTS AND METHODS

The prototypic elasticity imaging technique consists of a device for generating acoustic shear waves in tissue, an MR imaging-based method for imaging the propagation of these waves, and an algorithm for processing the wave images to generate quantitative images depicting tissue stiffness. After tests with tissue-simulating phantom materials and breast cancer specimens, we used the prototypic breast MR elastography technique to image six healthy women and six patients with known breast cancer.

RESULTS

Acoustic shear waves were clearly visualized in phantoms, breast cancer specimens, healthy volunteers, and patients with breast cancer. The elastograms of the tumor specimens showed focal areas of high shear stiffness. MR elastograms of healthy volunteers revealed moderately heterogeneous mechanical properties, with the shear stiffness of fibroglandular tissue measuring slightly higher than that of adipose tissue. The elastograms of patients with breast cancer showed focal areas of high shear stiffness corresponding to the locations of the known tumors. The mean shear stiffness of breast carcinoma was 418% higher than the mean value of surrounding breast tissues.

CONCLUSION

The results confirm the hypothesis that the prototypic breast MR elastographic technique can quantitatively depict the elastic properties of breast tissues in vivo and reveal high shear elasticity in known breast tumors. Further research is needed to evaluate the potential applications of MR elastography, such as detecting breast carcinoma and characterizing suspicious breast lesions.

Parametric analysis of breast MRI

Parametric analysis of breast MRI provides unique mapping of pathophysiological characteristics that cannot be obtained by standard conventional MRI. We describe in this review methods based on intrinsic contrast and tissue elasticity as well as methods that use external paramagnetic contrast agents and follow the time evolution of contrast. Processing of the raw data, frequently with new mathematical models and algorithms, yielded calculated parametric images that may help improve the noninvasive detection and diagnosis of breast cancer.

Acoustic radiation force impulse imaging of in vivo vastus medialis muscle under varying isometric load

Acoustic Radiation Force Impulse (ARFI) imaging is a method for characterizing local variations in tissue mechanical properties. In this method, a single ultrasonic transducer array is used to both apply temporally short localized radiation forces within tissue and to track the resulting displacements through time. Images of tissue displacement immediately after force cessation, maximum tissue displacement, the time it takes for the tissue to reach its maximum displacement, and the recovery time constant of the tissue are generated from the ARFI data sets. The information in each of these images demonstrates good agreement with matched B-mode images. The study presented here was designed to evaluate the relationship between changes in these ARFI parameters with known tissue mechanical properties in vivo. Utilizing a modified Siemens Elegra scanner with a 75L40 transducer array, ARFI images of vastus medialis muscle were generated in three of the authors under four levels of activation (0, 5.7, 14.5, and 23.3 N-m). Four ARFI datasets were acquired for each loading condition. The observed trends were that displacement magnitude, the time it took for the tissue to reach its maximum displacement, and recovery time constant decreased with increasing load (i.e., increasing muscle stiffness). Significant differences were observed between load levels and subjects for all parameters (p<0.01). The results indicate that ARFI imaging may be capable of quantifying tissue stiffness in real-time measurements, although further investigation is required.

[Illustration of elasticity differences using MR-elastography]

Differences of elasticity in tissue phantoms with inclusions of different elasticity were mapped by means of MR elastography (MRE). This new magnetic resonance imaging technique is based on the phase shift of the MR signal by switching a motion sensitizing magnetic field gradient simultaneously with the coupling of a shear wave. Wave patterns showing snapshots of the shear wave that propagates through the investigated substance were depicted in tomographic phase images. It was investigated wether a visualization of differences in elasticity of soft tissues was possible on the basis of differences in the wavelength. For this purpose, tissue phantoms with cylindrical inclusions were produced from agar gels, with agar concentrations between 1.0 and 1.5%. The diameters of the inclusions were of the order of a few centimetres. For diameters as small as 4 cm, there were still distinct differences in the wavelength between the matrix and the inclusion. The results of our study suggest that this technique has the potential for future application as an additional imaging method for tumor detection.

MR validation of soft tissue mimicing phantom deformation as modeled by nonlinear finite element analysis

A study of the applicability of nonlinear finite element analysis (FEA) to predict soft tissue deformation was validated with phase contrast magnetic resonance velocity imaging. A phantom of varying stiffness was placed in a special purpose, computer controlled MR compatible compression apparatus which provided precise, time varying compression with surface deformations on the order of 11%. The resulting motion was measured with MR velocity images acquired throughout the cycle of compression. The phantom geometry was modeled with a finite element mesh and the mechanical properties of the phantom material were measured and incorporated in the FEA model. The motion as calculated by the FEA model was compared to the motion measured with MRI and the results were found to vary with the material's Poisson's ratio and the coefficient of friction. A minimum difference was reached when the Poisson's ratio and coefficient of friction were set to 0.485 and 0.3, respectively. Under these conditions, the root mean square difference was found to be 14.4%.

A signal/noise analysis of quasi-static MR elastography

In quasi-static magnetic resonance elastography, strain images of a tissue or material undergoing deformation are produced. In this paper, the signal/noise (S/N) ratio [SNR] of elastographic strain images, as measured by a phase-contrast technique, is analyzed. Experiments are conducted to illustrate how diffusion-mediated signal attenuation limits maximum strain SNR in small displacement cases, while the imaging point-spread function limits large displacement cases. A simple theoretical treatment agrees well with experiments and shows how an optimal displacement encoding moment can be predicted for a given experimental set of parameters to achieve a maximum strain SNR. A further experiment demonstrates how the limitation on strain SNR posed by the imaging point-spread function may potentially be overcome.

A constrained modulus reconstruction technique for breast cancer assessment

A reconstruction technique for breast tissue elasticity modulus is described. This technique assumes that the geometry of normal and suspicious tissues is available from a contrast-enhanced magnetic resonance image. Furthermore, it is assumed that the modulus is constant throughout each tissue volume. The technique, which uses quasi-static strain data, is iterative where each iteration involves modulus updating followed by stress calculation. Breast mechanical stimulation is assumed to be done by two compressional rigid plates. As a result, stress is calculated using the finite element method based on the well-controlled boundary conditions of the compression plates. Using the calculated stress and the measured strain, modulus updating is done element-by-element based on Hooke's law. Breast tissue modulus reconstruction using simulated data and phantom modulus reconstruction using experimental data indicate that the technique is robust.

Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion

Magnetic resonance elastography (MRE) is an important new method used to measure the elasticity or stiffness of tissues in vivo. While there are many possible applications of MRE, breast cancer detection and classification is currently the most common. Several groups have been developing methods based on MR and ultrasound (US). MR or US is used to estimate the displacements produced by either quasi-static compression or dynamic vibration of the tissue. An important advantage of MRE is the possibility of measuring displacements accurately in all three directions. The central problem in most versions of MRE is recovering elasticity information from the measured displacements. In previous work, we have presented simulation results in two and three dimensions that were promising. In this article, accurate reconstructions of elasticity images from 3D, steady-state experimental data are reported. These results are significant because they demonstrate that the process is truly three-dimensional even for relatively simple geometries and phantoms. Further, they show that the integration of displacement data acquisition and elastic property reconstruction has been successfully achieved in the experimental setting. This process involves acquiring volumetric MR phase images with prescribed phase offsets between the induced mechanical motion and the motion-encoding gradients, converting this information into a corresponding 3D displacement field and estimating the concomitant 3D elastic property distribution through model-based image reconstruction. Fully 3D displacement fields and resulting elasticity images are presented for single and multiple inclusion gel phantoms.

Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation

New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.

Three-dimensional subzone-based reconstruction algorithm for MR elastography

Accurate characterization of harmonic tissue motion for realistic tissue geometries and property distributions requires knowledge of the full three-dimensional displacement field because of the asymmetric nature of both the boundaries of the tissue domain and the location of internal mechanical heterogeneities. The implications of this for magnetic resonance elastography (MRE) are twofold. First, for MRE methods which require the measurement of a harmonic displacement field within the tissue region of interest, the presence of 3D motion effects reduces or eliminates the possibility that simpler, lower-dimensional motion field images will capture the true dynamics of the entire stimulated tissue. Second, MRE techniques that exploit model-based elastic property reconstruction methods will not be able to accurately match the observed displacements unless they are capable of accounting for 3D motion effects. These two factors are of key importance for MRE techniques based on linear elasticity models to reconstruct mechanical tissue property distributions in biological samples. This article demonstrates that 3D motion effects are present even in regular, symmetric phantom geometries and presents the development of a 3D reconstruction algorithm capable of discerning elastic property distributions in the presence of such effects. The algorithm allows for the accurate determination of tissue mechanical properties at resolutions equal to that of the MR displacement image in complex, asymmetric biological tissue geometries. Simulation studies in a realistic 3D breast geometry indicate that the process can accurately detect 1-cm diameter hard inclusions with 2.5x elasticity contrast to the surrounding tissue.

Two-dimensional MR elastography with linear inversion reconstruction: methodology and noise analysis

A methodology for imposing approximate plane strain conditions in magnetic resonance elastography through physical constraint is described. Under plane strain conditions, data acquisition and analysis may be conducted in two dimensions, which reduces imaging and reconstruction time significantly compared with three-dimensional analysis. Simulations and experiments are performed to illustrate the constraint concept. A signal/noise analysis of a two-dimensional linear inversion technique for relative elastic modulus is undertaken, and modifications to the numerical method are described which can reduce the SNR requirements by a factor of two to four. Experimentally measured data are reconstructed to illustrate the performance of the method.