A method to measure the hyperelastic parameters of ex vivo breast 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.     

A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis

Digital tomosynthesis mammography (DTM) is a promising new modality for breast cancer detection. In DTM, projection-view images are acquired at a limited number of angles over a limited angular range and the imaged volume is reconstructed from the two-dimensional projections, thus providing three-dimensional structural information of the breast tissue. In this work, we investigated three representative reconstruction methods for this limited-angle cone-beam tomographic problem, including the backprojection (BP) method, the simultaneous algebraic reconstruction technique (SART) and the maximum likelihood method with the convex algorithm (ML-convex). The SART and ML-convex methods were both initialized with BP results to achieve efficient reconstruction. A second generation GE prototype tomosynthesis mammography system with a stationary digital detector was used for image acquisition. Projection-view images were acquired from 21 angles in 3 degrees increments over a +/- 30 degrees angular range. We used an American College of Radiology phantom and designed three additional phantoms to evaluate the image quality and reconstruction artifacts. In addition to visual comparison of the reconstructed images of different phantom sets, we employed the contrast-to-noise ratio (CNR), a line profile of features, an artifact spread function (ASF), a relative noise power spectrum (NPS), and a line object spread function (LOSF) to quantitatively evaluate the reconstruction results. It was found that for the phantoms with homogeneous background, the BP method resulted in less noisy tomosynthesized images and higher CNR values for masses than the SART and ML-convex methods. However, the two iterative methods provided greater contrast enhancement for both masses and calcification, sharper LOSF, and reduced interplane blurring and artifacts with better ASF behaviors for masses. For a contrast-detail phantom with heterogeneous tissue-mimicking background, the BP method had strong blurring artifacts along the x-ray source motion direction that obscured the contrast-detail objects, while the other two methods can remove the superimposed breast structures and significantly improve object conspicuity. With a properly selected relaxation parameter, the SART method with one iteration can provide tomosynthesized images comparable to those obtained from the ML-convex method with seven iterations, when BP results were used as initialization for both methods.     

Viscoelastic characterization of soft tissue from dynamic finite element models

An iterative solution to the inverse problem of elasticity and viscosity is proposed in this paper. A new dynamic finite element model that is consistent with known rheological models has been derived to account for the viscoelastic changes in soft tissue. The model assumes known lumped masses at the nodes, and comprises two vectors of elasticity and viscosity parameters that depend on the material elasticity and viscosity distribution, respectively. Using this deformation model and the observed dynamic data for harmonic excitation, the inverse problem is solved to reconstruct the viscosity and elasticity in the medium by using a Gauss-Newton-based approach. As in other inverse problems, previous knowledge of the parameters on the boundaries of the medium is necessary to assure uniqueness and convergence and to obtain an accurate map of the viscoelastic properties. The sensitivity of the solutions to noise, model and boundary conditions has been studied through numerical simulations. Experimental results are also presented. The viscosity and elasticity of a gelatin-based phantom with inclusion of known properties have been reconstructed and have been shown to be close to the values obtained using standard rheometry.     

Sparsity regularization in dynamic elastography

We consider the inverse problem of continuum mechanics with the tissue deformation described by a mixed displacement-pressure finite element formulation. The mixed formulation is used to model nearly incompressible materials by simultaneously solving for both elasticity and pressure distributions. To improve numerical conditioning, a common solution to this problem is to use regularization to constrain the solutions of the inverse problem. We present a sparsity regularization technique that uses the discrete cosine transform to transform the elasticity and pressure fields to a sparse domain in which a smaller number of unknowns is required to represent the original field. We evaluate the approach by solving the dynamic elastography problem for synthetic data using such a mixed finite element technique, assuming time harmonic motion, and linear, isotropic and elastic behavior for the tissue. We compare our simulation results to those obtained using the more common Tikhonov regularization. We show that the sparsity regularization is less dependent on boundary conditions, less influenced by noise, requires no parameter tuning and is computationally faster. The algorithm has been tested on magnetic resonance elastography data captured from a CIRS elastography phantom with similar results as the simulation.     

采用径向压缩的超声弹性成像逆问题求解

超声弹性成像在前列腺的应用以及血管弹性成像中,组织压缩的方向是沿径向的.本文利用极坐标下的应力-应变关系,提出一种有限元迭代的方法,进行组织弹性模量分布的重建,即弹性成像逆问题的求解.采用扇形组织模型和环形组织模型两种模型进行了计算机仿真,分别用来模拟超声弹性成像在前列腺中的应用情形和血管弹性成像的情形.仿真结果表明了该方法的可行性.     

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

A quasistatic magnetic resonance elastography (MRE) method for the evaluation of breast cancer is proposed. Using a phase contrast, stimulated echo MRI approach, strain imaging in phantoms and volunteers is presented. First-order assessment of tissue biomechanical properties based on inverse strain mapping is outlined and demonstrated. The accuracy of inverse strain imaging is studied through simulations in a two-dimensional model and in an anthropomorphic, three-dimensional finite-element model of the breast. To improve the accuracy of modulus assessment by elastography, inverse methods are discussed as an extension to strain imaging, and simulations quantify MRE in terms of displacement signal/noise required for robust inversion. A direct inversion strategy providing information on tissue modulus and pressure distribution is described along with a novel iterative method utilizing a priori knowledge of tissue geometry. It is shown that through the judicious choice of information from previous contrast-enhanced MRI breast images, MRE data acquisition requirements can be significantly reduced while maintaining robust modulus reconstruction in the presence of strain noise. An experimental apparatus for clinical breast MRE and preliminary images of a normal volunteer are presented.     

Image guided near-infrared spectroscopy of breast tissue in vivo using boundary element method

We demonstrate quantitative functional imaging using image-guided near-infrared spectroscopy (IG-NIRS) implemented with the boundary element method (BEM) for reconstructing 3-D optical property estimates in breast tissue in vivo. A multimodality MRI-NIR system was used to collect measurements of light reflectance from breast tissue. The BEM was used to model light propagation in 3-D based only on surface discretization in order to reconstruct quantitative values of total hemoglobin (HbT), oxygen saturation, water, and scatter. The technique was validated in experimental measurements from heterogeneous breast-shaped phantoms with known values and applied to a total of seven subjects comprising six healthy individuals and one participant with cancer imaged at two time points during neoadjuvant chemotherapy. Using experimental measurements from a heterogeneous breast phantom, BEM for IG-NIRS produced accurate values for HbT in the inclusion with a <3% error. Healthy breast tissues showed higher HbT and water in fibroglandular tissue than in adipose tissue. In a subject with cancer, the tumor showed higher HbT compared to the background. HbT in the tumor was reduced by 9 μM during treatment. We conclude that 3-D MRI-NIRS with BEM provides quantitative and functional characterization of breast tissue in vivo through measurement of hemoglobin content. The method provides potentially complementary information to DCE-MRI for tumor characterization.     

Optical imaging of breast tumor through temporal log-slope difference mappings

A novel optical temporal log-slope difference mapping approach is proposed for cancerous breast tumor detection. In this method, target tissues are illuminated by near-infrared (700-1000 nm) ultrashort laser pulses from various surface source points, and backscattered time-resolved light signals are collected at the same surface points. By analyzing the log-slopes of decaying signals over all points on the source-detection grid, a log-slope distribution on the surface is obtained. After administration of absorption contrast agents, the presence of cancerous tumors increases the decaying steepness of the transient signals. The mapping of log-slope difference between native tissue and absorption-enhanced cancerous tissue indicates the location and projection of tumors on the detection surface. In this paper, we examine this method in the detection of breast tumors in two model tissue phantoms through computer simulation. The first model has a spherical tumor of 6mm in diameter embedded at the tissue center. The second model is a large tissue phantom embedded with a non-centered spherical tumor 8mm in diameter. Monte Carlo methods were employed to simulate the light transport and signal measurement. It is shown that the tumor in both the tissue models will be accurately projected on the detection surface by the proposed log-slope difference mapping method. The image processing is very fast and does not require any inverse optimization in image reconstruction.     

Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography

We suitably adapt the design of a tissue-equivalent phantom used for photoacoustic imaging to construct phantoms for optical elastography. The elastography phantom we consider should have optical properties such as scattering coefficient, scattering anisotropy factor, and refractive index; mechanical properties such as storage and loss modulus; and acoustic properties such as ultrasound velocity, attenuation coefficient, and acoustic impedance to match healthy and diseased tissues. The phantom is made of poly (vinyl alcohol) (PVA) and its mechanical, optical, and acoustic properties are tailored by physical cross-linking effected through subjecting a suitable mix of PVA stock and water to a number of freeze-thaw cycles and by varying the degree of hydrolysis in the PVA stock. The optical, mechanical, and acoustic properties of the samples prepared are measured by employing different techniques. The measured variations in the values of optical scattering coefficient, scattering anisotropy factor, and refractive index and storage modulus are found to be comparable to those in normal and diseased breast tissues. The acoustic properties such as sound speed, acoustic attenuation coefficient, and density are found to be close to the average values reported in the literature for normal breast tissue.     

Interstitial fluid pressure in soft tissue as a result of an externally applied contact pressure

Manipulation of interstitial fluid pressure (IFP) has a clinical potential when used in conjunction with near-infrared spectroscopy for the detection of breast cancer. In order to better interpret how the applied pressure alters the vascular space and interstitial water volumes in breast tissue, a study on tissue-mimicking, gelatin phantoms was carried out to mimic the translation of external force into internal pressures. A complete set of three-dimensional (3D) pressure maps were obtained for the interior volumes of phantoms as an external force of 10 mmHg was applied, using mixtures of elastic moduli 19 and 33 kPa to simulate adipose and fibroglandular values of breast tissue. Corresponding linear elastic finite element analysis (FEA) cases were formulated. Shear stress, nonlinear mechanical properties, gravity and tissue geometry were all observed to contribute to internal pressure distribution, with surface shear stresses increasing internal pressures near the surface to greater than twice the applied external pressure. Average pressures by depth were predicted by the linear elastic FEA models. FEA models were run for cases mimicking a 93 kPa tumor inclusion within regions of adipose, fibroglandular tissue, and a composite of the two tissue types to illustrate the localized high fluid pressures caused by a tumor when an external force is applied. The conclusion was that external contact forces can generate potentially clinically useful fluid pressure magnitudes in regions of sharp effective elastic modulus gradients, such as tumor boundaries.     

Shear strain imaging using shear deformations

In this article we investigate the generation of shear strain elastograms induced using a lateral shear deformation. Ultrasound simulation and experimental results demonstrate that the shear strain elastograms obtained under shear deformation exhibit significant differences between bound and unbound inclusions in phantoms, when compared to shear strain images induced upon an axial compression. A theoretical model that estimates the decorrelation between pre- and postdeformation radio frequency signals, as a function of extent of shear deformation, is also developed. Signal-to-noise ratios of shear strain elastograms obtained at different shear angles are investigated theoretically and verified using ultrasound simulations on a uniformly elastic phantom. For the simulation and experiment, a two-dimensinal block-matching-based algorithm is used to estimate the axial and lateral displacement. Shear strains are obtained from the displacement vectors using a least-squares strain estimator. Our results indicate that the signal-to-noise ratio (SNR) of shear strain images increases to reach a maximum and saturates, and then decreases with increasing shear angle. Using typical system parameters, the maximum achievable SNR for shear strain elastography is around 8 (18 dB), which is comparable to conventional axial strain elastography induced by axial compression. Shear strain elastograms obtained experimentally using single inclusion tissue-mimicking phantoms with both bound and unbound inclusions (mimicking cancerous masses and benign fibroadenomas, respectively) demonstrate the characteristic differences in the depiction of these inclusions on the shear strain elastograms.     

磁共振成像数据的不规则采集及图像重建软件

开发出了一个基于PC机的软件，用于不规则磁共振成像数据的图像重建。该软件具有临床数据读入、数字图像模型生成、采样轨迹设计、κ空间数据生成、采样密度补偿函数计算、图像重建和图像定量分析等功能。该软件用VC 6编写，可运行在普通配置的微机上。     

The impact of calibration phantom errors on dual-energy digital mammography

Microcalcification is one of the earliest and main indicators of breast cancer. Because dual-energy digital mammography could suppress the contrast between the adipose and glandular tissues of the breast, it is considered a promising technique that will improve the detection of microcalcification. In dual-energy digital mammography, the imaged object is a human breast, while in calibration measurements only the phantoms of breast tissue equivalent materials are available. Consequently, the differences between phantoms and breast tissues will lead to calibration phantom errors. Based on the dual-energy imaging model, formulae of calibration phantom errors are derived in this paper. Then, this type of error is quantitatively analyzed using publicly available data and compared with other types of error. The results demonstrate that the calibration phantom error is large and dominant in dual-energy mammography, seriously decreasing calculation precision. Further investigations on the physical meaning of calibration phantom error reveal that the imaged objects with the same glandular ratio have identical calibration phantom error. Finally, an error correction method is proposed based on our findings.     

Radio-frequency ablation electrode displacement elastography: a phantom study

This article describes the evaluation of a novel method of tissue displacement for use in the elastographic visualization of radio-frequency (rf) ablation-induced lesions. The method involves use of the radio-frequency ablation electrode as a displacement device, which provides localized compression in the region of interest. This displacement mechanism offers the advantage of easy in vivo implementation since problems such as excessive lateral and elevational displacements present when using external compression are reduced with this approach. The method was tested on a single-inclusion tissue-mimicking phantom containing a radio-frequency ablation electrode rigidly attached to the inclusion center. Full-frame rf echo signals were acquired from the phantom before and after electrode displacements ranging from 0.05 to 0.2 mm. One-dimensional cross-correlation analysis between pre- and postcompression signals was used to measure tissue displacements, and strains were determined by computing the gradient of the displacement. The strain contrast, contrast-to-noise ratio, and signal-to-noise ratio were estimated from the resulting strain images. Comparisons are drawn between the elastographically measured dimensions and those known a priori for the single-inclusion phantom. Electrode displacement elastography was found to slightly underestimate the inclusion dimensions. The method was also tested on a second tissue-mimicking phantom and on in vitro rf-ablated lesions in canine liver tissue. The results validate previous in vivo findings that electrode displacement elastography is an effective method for monitoring rf ablation.     

Quantitative analysis of near-infrared tomography: sensitivity to the tissue-simulating precalibration phantom

A near-infrared (NIR) imaging system is evaluated as a diagnostic clinical tool to image total hemoglobin concentration and oxygen saturation within tissue. Calibration of this type of system requires measurement of the response at each detector and source location from a homogeneous tissue-simulating phantom. The effect of using calibration phantoms of varying composition, size, and optical properties is examined to determine how it affects the overall image accuracy. All of the calibration phantoms investigated result in accurate reconstruction of absorbing heterogeneities due to increased blood concentration with less than 4% standard deviation. Images from a patient with a biopsy-confirmed ductal carcinoma are also evaluated and found to be insensitive to the choice of calibration object, with only 1% variation between images generated with different calibration objects. The tumor total hemoglobin contrast is approximately 240% higher than the average total hemoglobin concentration in contralateral breast. Soft calibration phantoms, which mimic the elastic properties of human breast tissue, are also considered and found to diminish positioning errors in the fibers relative to the actual breast exam, thereby reducing the artifacts in the periphery of the reconstructed image.     

超声弹性成像中的逆问题求解方法

超声弹性成像通常只能得到组织在外部压缩作用下的纵向应变分布.超声弹性成像逆问题的求解,即重建组织内部的弹性模量分布,具有重要的意义.本文提出一种利用组织的应力-应变关系和基于有限元分析的迭代计算方法,从组织的纵向应变分布重建出组织的弹性模量分布.对平面应变状态下的均匀组织内含一圆形异物的模型和弹性模量连续过渡的模型分别进行了计算机仿真.结果初步验证了该方法的可行性.     

Nonlinear optical Fourier filtering technique for medical image processing

Real-time nonlinear optical Fourier filtering for medical image processing is demonstrated, exploiting light modulating characteristics of thin films of the biophotonic material bacteriorhodopsin (bR). The nonlinear transmission of bR films for a 442 nm probe beam with a 568 nm control beam and vice versa is experimentally studied in detail. The spatial frequency information carried by the blue probe beam is selectively manipulated in the bR film by changing the position and intensity of the yellow control beam. The feasibility of the technique is first established with different shapes and sizes of phantom objects. The technique is applied to filter out low spatial frequencies corresponding to soft dense breast tissue and displaying only high spatial frequencies corresponding to microcalcifications in clinical screen film mammograms. With the aid of an electrically addressed spatial light modulator (SLM), we successfully adapt the technique for processing digital phantoms and digital mammograms. Unlike conventional optical spatial filtering techniques that use masks, the technique proposed can easily accommodate the changes in size and shape of details in a mammogram.     

Evaluation of x-ray scatter properties in a dedicated cone-beam breast CT scanner

The magnitude of scatter contamination on a first-generation prototype breast computed tomography (CT) scanner was evaluated using the scatter-to-primary ratio (SPR) metric. The SPR was measured and characterized over a wide range of parameters relevant to breast CT imaging, including x-ray beam energy, breast diameter, breast composition, isocenter-to-detector distance, collimated slot thickness, and grid ratio. The results demonstrated that in the absence of scatter reduction techniques, the SPR levels for the average breast (e.g., 14 cm diameter 50/50 composition cylindrical phantom) are quite high (approximately 0.5 at the center of the phantom for 80 kVp in true cone-beam CT geometry), and increases as the diameter of the phantom is increased (to approximately 1.0 at the center of a 18 cm diameter 50/50 phantom). The x-ray beam energy and the phantom compositions had only minimal impact on the measured SPR. When an ideal bowtie filter was used, the SPRs at the central axis of the 14 and 18 cm cylindrical phantoms were reduced while the SPRs at the edge of the phantoms were increased. Lastly, collimation in the vertical direction had a significant impact on the SPRs at the central axis of the phantoms. These high SPR levels might lead to cupping artifacts and increased noise in the reconstructed CT images, and this suggests that efficient scatter rejection and/or correction techniques may be required to improve the quality and accuracy of cone beam CT images.     

Mechanical property assessment of tissue-mimicking phantoms using remote palpation and optical read-out for amplitude of vibration and refractive index modulation

A coherent light beam is used to interrogate the focal region within a tissue-mimicking phantom insonified by an ultrasound transducer. The ultrasound-tagged photons exiting from the object carry with them information on local optical path length fluctuations caused by refractive index variations and medium vibration. Through estimation of the force distribution in the focal region of the ultrasound transducer, and solving the forward elastography problem for amplitude of vibration of tissue particles, we observe that the amplitude is directed along the axis of the transducer. It is shown that the focal region interrogated by photons launched along the transducer axis carries phase fluctuations owing to both refractive index variations and particle vibration, whereas the photons launched perpendicular to the transducer axis carry phase fluctuations arising mainly from the refractive index variations, with only smaller contribution from vibration of particles. Monte-Carlo simulations and experiments done on tissue-mimicking phantoms prove that as the storage modulus of the phantom is increased, the detected modulation depth in autocorrelation is reduced, significantly for axial photons and only marginally for the transverse-directed photons. It is observed that the depth of modulation is reduced to a significantly lower and constant value as the storage modulus of the medium is increased. This constant value is found to be the same for both axial and transverse optical interrogation. This proves that the residual modulation depth is owing to refractive index fluctuations alone, which can be subtracted from the overall measured modulation depth, paving the way for a possible quantitative reconstruction of storage modulus. Moreover, since the transverse-directed photons are not significantly affected by storage modulus variations, for a quantitatively accurate read-out of absorption coefficient variation, the interrogating light should be perpendicular to the focusing ultrasound transducer axis.     

Measurement of guided mode wavenumbers in soft tissue-bone mimicking phantoms using ultrasonic axial transmission

Human soft tissue is an important factor that influences the assessment of human long bones using quantitative ultrasound techniques. To investigate such influence, a series of soft tissue-bone phantoms (a bone-mimicking plate coated with a layer of water, glycerol or silicon rubber) were ultrasonically investigated using a probe with multi-emitter and multi-receiver arrays in an axial transmission configuration. A singular value decomposition signal processing technique was applied to extract the frequency-dependent wavenumbers of several guided modes. The results indicate that the presence of a soft tissue-mimicking layer introduces additional guided modes predicted by a fluid waveguide model. The modes propagating in the bone-mimicking plate covered by the soft-tissue phantom are only slightly modified compared to their counterparts in the free bone-mimicking plate, and they are still predicted by an elastic transverse isotropic two-dimensional waveguide. Altogether these observations suggest that the soft tissue-bone phantoms can be modeled as two independent waveguides. Even in the presence of the overlying soft tissue-mimicking layer, the modes propagating in the bone-mimicking plate can still be extracted and identified. These results suggest that our approach can be applied for the purpose of the characterization of the material and structural properties of cortical bone.