A constrained reconstruction technique of hyperelasticity parameters for breast cancer assessment

Evaluating the effect of tissue stimulation at different frequencies on breast lesion classification based on nonlinear features using a novel radio frequency time series approach

Objective

Radio Frequency Time Series (RF TS) is a cutting-edge ultrasound approach in tissue typing. The RF TS does not provide dynamic insights into the propagation medium; when the tissue and probe are fixed. We previously proposed the innovative RFTSDP method in which the RF data are recorded while stimulating the tissue. Applying stimulation can unveil the mechanical characteristics of the tissue in RF echo.

Materials and methods

In this study, an apparatus was developed to induce vibrations at different frequencies to the medium. Data were collected from four PVA phantoms simulating the nonlinear behaviors of healthy, fibroadenoma, cyst, and cancerous breast tissues. Raw focused, raw, and beamformed ultrafast data were collected under conditions of no stimulation, constant force, and various vibrational stimulations using the Supersonic Imagine Aixplorer clinical/research ultrasound imaging system. Time domain (TD), spectral, and nonlinear features were extracted from each RF TS. Support Vector Machine (SVM), Random Forest, and Decision Tree algorithms were employed for classification.

Results

The optimal outcome was achieved using the SVM classifier considering 19 features extracted from beamformed ultrafast data recorded while applying vibration at the frequency of 65 Hz. The classification accuracy, specificity, and precision were 98.44 ± 0.20 %, 99.49 ± 0.01 %, and 98.53 ± 0.04 %, respectively. Applying RFTSDP, a notable 24.45 % improvement in accuracy was observed compared to the case of fixed probe assessing the recorded raw focused data.

Conclusions

External vibration at an appropriate frequency, as applied in RFTSDP, incorporates beneficial information about the medium and its dynamic characteristics into the RF TS, which can improve tissue characterization.

On the soft tissue ultrasound elastography using FEM based inversion approach

Elastography is a medical imaging modality that enables visualization of tissue stiffness. It involves quasi-static or harmonic mechanical stimulation of the tissue to generate a displacement field which is used as input in an inversion algorithm to reconstruct tissue elastic modulus. This paper considers quasi-static stimulation and presents a novel inversion technique for elastic modulus reconstruction. The technique follows an inverse finite element framework. Reconstructed elastic modulus maps produced in this technique do not depend on the initial guess, while it is computationally less involved than iterative reconstruction approaches. The method was first evaluated using simulated data (in-silico) where modulus reconstruction's sensitivity to displacement noise and elastic modulus was assessed. To demonstrate the method's performance, displacement fields of two tissue mimicking phantoms determined using three different motion tracking techniques were used as input to the developed elastography method to reconstruct the distribution of relative elastic modulus of the inclusion to background tissue. In the next stage, the relative elastic modulus of three clinical cases pertaining to liver cancer patient were determined. The obtained results demonstrate reasonably high elastic modulus reconstruction accuracy in comparison with similar direct methods. Also it is associated with reduced computational cost in comparison with iterative techniques, which suffer from convergence and uniqueness issues, following the same formulation concept. Moreover, in comparison with other methods which need initial guess, the presented method does not require initial guess while it is easy to understand and implement.

Fabrication of SEBS Block Copolymer-Based Ultrasound Phantom Containing Mimic Tumors for Ultrasound-Guided Needle Biopsy Training

The creation of various phantoms is important in medical education, especially for intern physicians who need to practice their skills. Ultrasound phantoms are particularly useful for training in ultrasound-guided needle biopsy. SEBS, or poly(styrene-ethylene-butylene-styrene), is a thermoplastic elastomer that can be used with mineral oil to make ultrasound phantoms and a tumor-like structure. SEBS block copolymer-based phantoms are inexpensive, non-toxic and shelf-stable, and are easy to modulate. Most importantly, such ultrasound phantoms have acoustic and mechanical properties similar to those of human soft tissues. The quality of ultrasound images of phantoms and mimic tumors is excellent and can be maintained even after several biopsy needle punctures, making them excellent ultrasound phantoms for physician practice as needed.

Nonlinear Elasticity Assessment with Optical Coherence Elastography for High-Selectivity Differentiation of Breast Cancer Tissues

Soft biological tissues, breast cancer tissues in particular, often manifest pronounced nonlinear elasticity, i.e., strong dependence of their Young’s modulus on the applied stress. We showed that compression optical coherence elastography (C-OCE) is a promising tool enabling the evaluation of nonlinear properties in addition to the conventionally discussed Young’s modulus in order to improve diagnostic accuracy of elastographic examination of tumorous tissues. The aim of this study was to reveal and quantify variations in stiffness for various breast tissue components depending on the applied pressure. We discussed nonlinear elastic properties of different breast cancer samples excised from 50 patients during breast-conserving surgery. Significant differences were found among various subtypes of tumorous and nontumorous breast tissues in terms of the initial Young’s modulus (estimated for stress < 1 kPa) and the nonlinearity parameter determining the rate of stiffness increase with increasing stress. However, Young’s modulus alone or the nonlinearity parameter alone may be insufficient to differentiate some malignant breast tissue subtypes from benign. For instance, benign fibrous stroma and fibrous stroma with isolated individual cancer cells or small agglomerates of cancer cells do not yet exhibit significant difference in the Young’s modulus. Nevertheless, they can be clearly singled out by their nonlinearity parameter, which is the main novelty of the proposed OCE-based discrimination of various breast tissue subtypes. This ability of OCE is very important for finding a clean resection boundary. Overall, morphological segmentation of OCE images accounting for both linear and nonlinear elastic parameters strongly enhances the correspondence with the histological slices and radically improves the diagnostic possibilities of C-OCE for a reliable clinical outcome.

Mechanical properties of whole-body soft human tissues: a review

The mechanical properties of soft tissues play a key role in studying human injuries and their mitigation strategies. While such properties are indispensable for computational modelling of biological systems, they serve as important references in loading and failure experiments, and also for the development of tissue simulants. To date, experimental studies have measured the mechanical properties of peripheral tissues (e.g. skin)in-vivoand limited internal tissuesex-vivoin cadavers (e.g. brain and the heart). The lack of knowledge on a majority of human tissues inhibit their study for applications ranging from surgical planning, ballistic testing, implantable medical device development, and the assessment of traumatic injuries. The purpose of this work is to overcome such challenges through an extensive review of the literature reporting the mechanical properties of whole-body soft tissues from head to toe. Specifically, the available linear mechanical properties of all human tissues were compiled. Non-linear biomechanical models were also introduced, and the soft human tissues characterized using such models were summarized. The literature gaps identified from this work will help future biomechanical studies on soft human tissue characterization and the development of accurate medical models for the study and mitigation of injuries.

Measurement of the hyperelastic properties of 72 normal homogeneous and heterogeneous ex vivo breast tissue samples

The mechanical properties of normal soft tissues, including breast tissue, have been of interest to the biomedical research community as there are many clinical and industrial applications that can benefit from quantitative information characterizing such properties. For instance, computer assisted surgery planning, elastography for breast cancer diagnosis, and bra design can all involve biomechanical modeling of the breast to predict its deformation or stress distribution. It is known that most biological soft tissues, including breast tissue, exhibit nonlinear mechanical response over large strains. As such, it is necessary to model such tissues as hyperelastic. In this work, we used indentation testing to estimate the hyperelastic parameters of 4 models (3rd order Ogden, 5-term polynomial, Veronda-Westman and Yeoh) estimated from 72 healthy ex vivo breast tissue samples covering adipose, fibroglandular, and mixed tissue. All estimated parameter sets were confirmed to represent stable material using Drucker's stability criterion. We observed that all three tissue types were statistically similar solidifying the use of homogenous breast modelling over large strain simulation.

An Improved Region-Growing Motion Tracking Method Using More Prior Information for 3-D Ultrasound Elastography

Three-dimensional (3-D) ultrasound elastography can provide 3-D tissue stiffness information that may be used during clinical diagnoses. In the framework of strain elastography, motion tracking plays an important role. In this study, an improved 3-D region-growing motion tracking (RGMT) algorithm based on a concept of exterior boundary points was developed. In principle, the proposed method first determines displacement at some seed points by strictly checking the local correlation and continuity in the neighborhood of those seeds. Subsequent displacement estimation is then conducted from these initial seeds to obtain displacements associated with other locations. This RGMT algorithm is designed to use more known information-including displacements and correlation values of all known-displacement neighboring points-to estimate the displacement of an unknown-displacement point, whereas previous RGMT methods employed information from only one such point. The algorithm was tested on 3-D ultrasound volumetric data acquired from a simulation, a tissue-mimicking phantom, and five human subjects. Motion-compensated cross correlations (MCCCs), strain contrast, and displacement Laplacian values (representing smoothness of an estimated displacement field) were calculated and used to evaluate the merits of the proposed RGMT method. Compared with a previously published RGMT method, the results show that the proposed RGMT method can provide smaller displacement errors and smoother displacements and improve strain contrast while maintaining reasonably high MCCC values, indicating good motion tracking quality. The proposed method is also computationally more efficient. In summary, our preliminary results demonstrated that the proposed RGMT algorithm is capable of obtaining high-quality 3-D strain elastographic data using modified clinical equipment.

Deformable Registration for Longitudinal Breast MRI Screening

MRI screening of high-risk patients for breast cancer provides very high sensitivity, but with a high recall rate and negative biopsies. Comparing the current exam to prior exams reduces the number of follow-up procedures requested by radiologists. Such comparison, however, can be challenging due to the highly deformable nature of breast tissues. Automated co-registration of multiple scans has the potential to aid diagnosis by providing 3D images for side-by-side comparison and also for use in CAD systems. Although many deformable registration techniques exist, they generally have a large number of parameters that need to be optimized and validated for each new application. Here, we propose a framework for such optimization and also identify the optimal input parameter set for registration of 3D T₁-weighted MRI of breast using Elastix, a widely used and freely available registration tool. A numerical simulation study was first conducted to model the breast tissue and its deformation through finite element (FE) modeling. This model generated the ground truth for evaluating the registration accuracy by providing the deformation of each voxel in the breast volume. An exhaustive search was performed over various values of 7 registration parameters (4050 different combinations of parameters were assessed) and the optimum parameter set was determined. This study showed that there was a large variation in the registration accuracy of different parameter sets ranging from 0.29 mm to 2.50 mm in median registration error and 3.71 mm to 8.90 mm in 95 percentile of the registration error. Mean registration errors of 0.32 mm, 0.29 mm, and 0.30 mm and 95 percentile errors of 3.71 mm, 5.02 mm, and 4.70 mm were obtained by the three best parameter sets. The optimal parameter set was applied to consecutive breast MRI scans of 13 patients. A radiologist identified 113 landmark pairs (~ 11 per patient) which were used to assess registration accuracy. The results demonstrated that using the optimal registration parameter set, a registration accuracy (in mm) of 3.4 [1.8 6.8] was achieved.

An Iterative Method for Estimating Nonlinear Elastic Constants of Tumor in Soft Tissue from Approximate Displacement Measurements

Objectives

Various elastography techniques have been proffered based on linear or nonlinear constitutive models with the aim of detecting and classifying pathologies in soft tissues accurately and noninvasively. Biological soft tissues demonstrate behaviors which conform to nonlinear constitutive models, in particular the hyperelastic ones. In this paper, we represent the results of our steps towards implementing ultrasound elastography to extract hyperelastic constants of a tumor inside soft tissue.

Methods

Hyperelastic parameters of the unknown tissue have been estimated by applying the iterative method founded on the relation between stress, strain, and the parameters of a hyperelastic model after (a) simulating the medium's response to a sinusoidal load and extracting the tissue displacement fields in some instants and (b) estimating the tissue displacement fields from the recorded/simulated ultrasound radio frequency signals and images using the cross correlation-based technique.

Results

Our results indicate that hyperelastic parameters of an unidentified tissue could be precisely estimated even in the conditions where there is no prior knowledge of the tissue, or the displacement fields have been approximately calculated using the data recorded by a clinical ultrasound system.

Conclusions

The accurate estimation of nonlinear elastic constants yields to the correct cognizance of pathologies in soft tissues.

Efficient Sensitivity Based Reconstruction Technique to Accomplish Breast Hyperelastic Elastography

Hyperelastic models have been acknowledged as constitutive equations which reliably model the nonlinear behaviors observed from soft tissues under various loading conditions. Among them, the Mooney-Rivlin, Yeoh, and polynomial models have been proved capable of accurately modeling responses of breast tissues to applied compressions. Hyperelastic elastography technique takes advantage of the disparities between hyperelastic parameters of varied tissues and the change in hyperelastic parameters in pathological processes. The precise reconstruction of hyperelastic parameters of a completely unknown pathology in the breast in a noninvasive and nondestructive way using the ultrasound elastography has been scrutinized in this paper. In the ultrasound elastography, tissue displacement field is extracted from radio frequency signals or images recorded using the ultrasound medical imaging system; hence the exact displacement field might not be obtained. Our results indicate that the parameters estimated by manipulating the iterative sensitivity-matrix based method converge to tissue's real hyperelastic parameters providing appropriate parameters are assigned to the hypothetical hyperelastic and regularization parameters. Iterative methods have therefore been proposed to compute proper hypothetical hyperelastic and regularization parameters. Accurate estimates of hyperelastic parameters of obscure breast pathology have been achieved even from imprecise measurements of displacements induced in the tissue by the ramp excitation.

A model study of 3-dimensional localization of breast tumors using piezoelectric fingers of different probe sizes

Mammography is the only Food and Drug Administration approved breast cancer screening method. The drawback of the tumor image in a mammogram is the lack of tumor depth information as it is only a 2-dimensional projection of a 3-dimensional (3D) tumor. In this work, we investigated 3D tumor imaging by assessing tumor depth information using a set of piezoelectric fingers (PEFs) with different probe sizes which were known to be capable of eliciting tissue elastic responses to different depths and tested it on model tumor tissues consisted of gelatin with suspended clay inclusions. The locations of the top and bottom surfaces of an inclusion were resolved by solving a simple spring model using the elastic measurements of the PEFs of different probe sizes as the input. The lateral sizes of an inclusion were determined as the full width at half maximum of the Gaussian fit to the measured lateral tumor elastic modulus profile. The obtained lateral inclusion sizes were in close agreement with the actual values, and the deduced depth profiles of an inclusion also agreed with the actual depth profiles so long as the bottom surface of the inclusion was within the depth sensitivity of the PEF with the largest probe size. This work offers a simple non-invasive method to predict the extent of a tumor in all 3 dimensions. The method is also non-radioactive.

BIOMECHANICAL MODELING AND SIMULATION OF SUBCUTANEOUS ADIPOSE TISSUE BASED ON LINEAR ELASTIC AND HYPERELASTIC MODEL

The biomechanical modeling and simulation of human tissue are the basic part of virtual surgery system. As an important human soft tissue, the biomechanical modeling and simulation method of subcutaneous adipose tissue are urgent problems to be solved in virtual surgery system. In this paper, biomechanical modeling and simulation of subcutaneous adipose tissue were completed based on linear elastic and hyperelastic finite element model. First, the deformation process of subcutaneous adipose tissue was divided into two stages: Initial loading stage and later loading stage. Furthermore, the linear elastic model at initial loading stage and the nonlinear elastic model at later loading stage were established, respectively. Then, the biomechanical model of subcutaneous adipose tissue was solved based on the finite element method. Finally, the linear finite element calculation was included in nonlinear finite element calculations, and finite element simulation program of the subcutaneous adipose tissue was compiled in Visual Studio environment. The accuracy of the model was verified by comparing the simulation results with the experimental results. The efficiency of finite element simulation program of the linear and nonlinear hybrid model is evaluated by comparing the simulation time with the single linear model and the hyperelastic model.

Computational study to investigate effect of tonometer geometry and patient-specific variability on radial artery tonometry

Tonometry-based devices are valuable method for vascular function assessment and for measurement of blood pressure. However current design and calibration methods rely on simple models, neglecting key geometrical features, and anthropometric and property variability among patients. Understanding impact of these influences on tonometer measurement is thus essential for improving outcomes of current devices, and for proposing improved design. Towards this goal, we present a realistic computational model for tissue-device interaction using complete wrist section with hyperelastic material and frictional contact. Three different tonometry geometries were considered including a new design, and patient-specific influences incorporated via anthropometric and age-dependent tissue stiffness variations. The results indicated that the new design showed stable surface contact stress with minimum influence of the parameters analyzed. The computational predictions were validated with experimental data from a prototype based on the new design. Finally, we showed that the underlying mechanics of vascular unloading in tonometry to be fundamentally different from that of oscillatory method. Due to directional loading in tonometry, pulse amplitude maxima was observed to occur at a significantly lower compression level (around 31%) than previously reported, which can impact blood pressure calibration approaches based on maximum pulse pressure recordings.

Stable phantom materials for ultrasound and optical imaging

Phantoms mimicking the specific properties of biological tissues are essential to fully characterize medical devices. Water-based materials are commonly used to manufacture phantoms for ultrasound and optical imaging techniques. However, these materials have disadvantages, such as easy degradation and low temporal stability. In this study, we propose an oil-based new tissue-mimicking material for ultrasound and optical imaging, with the advantage of presenting low temporal degradation. A styrene-ethylene/butylene-styrene (SEBS) copolymer in mineral oil samples was made varying the SEBS concentration between 5%-15%, and low-density polyethylene (LDPE) between 0%-9%. Acoustic properties, such as the speed of sound and the attenuation coefficient, were obtained using frequencies ranging from 1-10 MHz, and were consistent with that of soft tissues. These properties were controlled varying SEBS and LDPE concentration. To characterize the optical properties of the samples, the diffuse reflectance and transmittance were measured. Scattering and absorption coefficients ranging from 400 nm-1200 nm were calculated for each compound. SEBS gels are a translucent material presenting low optical absorption and scattering coefficients in the visible region of the spectrum, but the presence of LDPE increased the turbidity. Adding LDPE increased the absorption and scattering of the phantom materials. Ultrasound and photoacoustic images of a heterogeneous phantom made of LDPE/SEBS containing a spherical inclusion were obtained. Annatto dye was added to the inclusion to enhance the optical absorbance. The results suggest that copolymer gels are promising for ultrasound and optical imaging, making them also potentially useful for photoacoustic imaging.

Development of array piezoelectric fingers towards in vivo breast tumor detection

We have investigated the development of a handheld 4 × 1 piezoelectric finger (PEF) array breast tumor detector system towards in vivo patient testing, particularly, on how the duration of the DC applied voltage, the depression depth of the handheld unit, and breast density affect the PEF detection sensitivity on 40 patients. The tests were blinded and carried out in four phases: with DC voltage durations 5, 3, 2, to 0.8 s corresponding to scanning a quadrant, a half, a whole breast, and both breasts within 30 min, respectively. The results showed that PEF detection sensitivity was unaffected by shortening the applied voltage duration from 5 to 0.8 s nor was it affected by increasing the depression depth from 2 to 6 mm. Over the 40 patients, PEF detected 46 of the 48 lesions (46/48)-with the smallest lesion detected being 5 mm in size. Of 28 patients (some have more than one lesion) with mammography records, PEF detected 31/33 of all lesions (94%) and 14/15 of malignant lesions (93%), while mammography detected 30/33 of all lesions (91%) and 12/15 of malignant lesions (80%), indicating that PEF could detect malignant lesions not detectable by mammography without significantly increasing false positives. PEF's detection sensitivity is also shown to be independent of breast density, suggesting that PEF could be a potential tool for detecting breast cancer in young women and women with dense breasts.

A SENSITIVITY ANALYSIS FOR BREAST DISPLACEMENT BY VARYING MATERIAL PROPERTIES

In the quasi-static ultrasound breast elastography, the simulated displacement greatly influence the results. The breast modeling requires certain mechanical parameters for generating the simulated displacements. However, there are wide ranges of data in the existing literature for the breast mechanical parameters. Therefore, the sensitivity analysis of displacement to the changes of mechanical parameters worths a particular attention.

In this paper we construct a three-dimensional (3D) breast model using magnetic resonance images. The constitutive equations corresponding to both linear elastic and hyperelastic (nonlinear) mechanical behaviors are considered. Then, two series of finite element analysis are performed in order to investigate how the changes of mechanical parameters of the fat and fibroglandular tissues may influence the displacement. The obtained results demonstrate that the displacement are generally less sensitive in the hyperelastic modeling (to the changes of material properties) than they are in the linear elastic modeling. Furthermore, the breast deformation is more influenced by the changes of material properties of fat part than the fibroglandular part.

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function – a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

Characterization of the nonlinear elastic properties of soft tissues using the supersonic shear imaging (SSI) technique: inverse method, ex vivo and in vivo experiments

Dynamic elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which are important for the disease diagnosis, e.g., the detection of breast and thyroid cancer and liver fibrosis. This paper investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described via the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach is established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g., the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and the experiments conducted on the phantom and pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method for measuring the in vivo nonlinear elastic properties of soft tissues. Generalization of the inverse analysis to other material models and the implication of the results reported here for clinical diagnosis have been discussed.

A novel fast full inversion based breast ultrasound elastography technique

Cancer detection and classification have been the focus of many imaging and therapeutic research studies. Elastography is a non-invasive technique to visualize suspicious soft tissue areas where tissue stiffness is used as image contrast mechanism. In this study, a breast ultrasound elastography system including software and hardware is proposed. Unlike current elastography systems that image the tissue strain and present it as an approximation to relative tissue stiffness, this system is capable of imaging the breast absolute Young's modulus in fast fashion. To improve the quality of elastography images, a novel system consisting of two load cells has been attached to the ultrasound probe. The load cells measure the breast surface forces to be used for calculating the tissue stress distribution throughout the breast. To facilitate fast imaging, this stress calculation is conducted by an accelerated finite element method. Acquired tissue displacements and surface force data are used as input to the proposed Young's modulus reconstruction technique. Numerical and tissue mimicking phantom studies were conducted for validating the proposed system. These studies indicated that fast imaging of breast tissue absolute Young's modulus using the proposed ultrasound elastography system is feasible. The tissue mimicking phantom study indicated that the system is capable of providing reliable absolute Young's modulus values for both normal tissue and tumour as the maximum Young's modulus reconstruction error was less than 6%. This demonstrates that the proposed system has a good potential to be used for clinical breast cancer assessment.

A nonlinear elasticity phantom containing spherical inclusions

The strain image contrast of some in vivo breast lesions changes with increasing applied load. This change is attributed to differences in the nonlinear elastic properties of the constituent tissues suggesting some potential to help classify breast diseases by their nonlinear elastic properties. A phantom with inclusions and long-term stability is desired to serve as a test bed for nonlinear elasticity imaging method development, testing, etc. This study reports a phantom designed to investigate nonlinear elastic properties with ultrasound elastographic techniques. The phantom contains four spherical inclusions and was manufactured from a mixture of gelatin, agar and oil. The phantom background and each of the inclusions have distinct Young's modulus and nonlinear mechanical behavior. This phantom was subjected to large deformations (up to 20%) while scanning with ultrasound, and changes in strain image contrast and contrast-to-noise ratio between inclusion and background, as a function of applied deformation, were investigated. The changes in contrast over a large deformation range predicted by the finite element analysis (FEA) were consistent with those experimentally observed. Therefore, the paper reports a procedure for making phantoms with predictable nonlinear behavior, based on independent measurements of the constituent materials, and shows that the resulting strain images (e.g., strain contrast) agree with that predicted with nonlinear FEA.

Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis

We reconstruct the in vivo spatial distribution of linear and nonlinear elastic parameters in ten patients with benign (five) and malignant (five) tumors. The mechanical behavior of breast tissue is represented by a modified Veronda-Westmann model with one linear and one nonlinear elastic parameter. The spatial distribution of these elastic parameters is determined by solving an inverse problem within the region of interest (ROI). This inverse problem solution requires the knowledge of the displacement fields at small and large strains. The displacement fields are measured using a free-hand ultrasound strain imaging technique wherein, a linear array ultrasound transducer is positioned on the breast and radio frequency echo signals are recorded within the ROI while the tissue is slowly deformed with the transducer. Incremental displacement fields are determined from successive radio-frequency frames by employing cross-correlation techniques. The rectangular regions of interest were subjectively selected to obtain low noise displacement estimates and therefore were variables that ranged from 346 to 849.6 mm2 . It is observed that malignant tumors stiffen at a faster rate than benign tumors and based on this criterion nine out of ten tumors were correctly classified as being either benign or malignant.