Linear and nonlinear elasticity imaging of soft tissue in vivo: demonstration of feasibility

A Force-Matched Approach to Large-Strain Nonlinearity in Elasticity Imaging for Breast Lesion Characterization

OBJECTIVE

Ultrasound elasticity imaging is a class of ultrasound techniques with applications that include the detection of malignancy in breast lesions. Although elasticity imaging traditionally assumes linear elasticity, the large strain elastic response of soft tissue is known to be nonlinear. This study evaluates the nonlinear response of breast lesions for the characterization of malignancy using force measurement and force-controlled compression during ultrasound imaging.

METHODS

54 patients were recruited for this study. A custom force-instrumented compression device was used to apply a controlled force during ultrasound imaging. Motion tracking derived strain was averaged over lesion or background ROIs and matched with compression force. The resulting force-matched strain was used for subsequent analysis and curve fitting.

RESULTS

Greater median differences between malignant and benign lesions were observed at higher compressional forces (p-value < 0.05 for compressional forces of 2-6N). Of three candidate functions, a power law function produced the best fit to the force-matched strain. A statistically significant difference in the scaling parameter of the power function between malignant and benign lesions was observed (p-value = 0.025).

CONCLUSIONS

We observed a greater separation in average lesion strain between malignant and benign lesions at large compression forces and demonstrated the characterization of this nonlinear effect using a power law model. Using this model, we were able to differentiate between malignant and benign breast lesions.

SIGNIFICANCE

With further development, the proposed method to utilize the nonlinear elastic response of breast tissue has the potential for improving non-invasive lesion characterization for potential malignancy.

Evaluation of endometrial receptivity by ultrasound elastography to predict pregnancy outcome is a non-invasive and worthwhile method

Up to today, there is no effective, specific and non-invasive evaluation method to assess the endometrial receptivity. This study aimed to establish a non-invasive and effective model with the clinical indicators to evaluate endometrial receptivity. Ultrasound elastography can reflect the overall state of the endometrium. Ultrasonic elastography images from 78 hormonally prepared frozen embryo transfer (FET) patients were assessed in this study. Meanwhile, the clinical indicators reflecting endometrium in the transplantation cycle were collected. The patients were received to transfer only one high-quality blastocyst. A novel code rule that can generate a large number of 0-1 symbols was designed to collect data on different factors. At the same time, a logistic regression model of the machine learning process with an automatic combination of factors was designed for analysis. The logistic regression model was based on age, body mass index, waist-hip ratio, endometrial thickness, perfusion index (PI), resistance index (RI), elastic grade, elastic ratio cutoff value, serum estradiol level and 9 other indicators. The accuracy rate of predicting pregnancy outcome of the logistic regression model was 76.92%. Elastic ultrasound can reflect the endometrial receptivity of patients in FET cycles. We established a prediction model including ultrasound elastography and the model precisely predicted the pregnancy outcome. The predictive accuracy of endometrial receptivity by the predictive model is significantly higher than that of the single clinical indicator. The prediction model by integrating the clinical indicators to evaluate endometrial receptivity may be a non-invasive and worthwhile method for evaluating endometrial receptivity.

Ultrasound shear wave elastography in pediatric stricturing small bowel Crohn disease: correlation with histology and second harmonic imaging microscopy

BACKGROUND

Preclinical animal as well as small exploratory ex vivo and in vivo human studies have suggested that bowel wall shear wave speed (SWS) measurements may be a noninvasive biomarker of intestinal damage.

OBJECTIVE

To evaluate the relationships between bowel wall stiffness, measured using ultrasound shear wave elastography (SWE), and intestinal fibrosis and smooth muscle hypertrophy as determined by (1) histology and (2) second harmonic imaging microscopy (SHIM) in surgically resected ileal strictures from pediatric Crohn disease patients.

MATERIALS AND METHODS

Nineteen pediatric Crohn disease patients with symptomatic ileal strictures underwent research ultrasound examinations before surgical resection between December 2017 and September 2020. Two-dimensional SWE was performed through the area of the most severe stenosis, with measurements obtained from the bowel wall at the 9:00, 12:00 and 3:00 o'clock locations with 0%, 10% and 20% abdominal strain. Overall right lower quadrant stiffness also was documented. Median bowel wall and overall right lower quadrant SWS measurements were correlated with bowel wall histological scores of inflammation, fibrosis and smooth muscle proliferation as well as SHIM collagen signal.

RESULTS

Diagnostic ultrasound SWE imaging was obtained from 18 participants. The median age was 16.8 years. There were negative correlations between histological mucosal active inflammation and both bowel wall SWS with 10% abdominal strain (r=-0.50, P = 0.04) and overall right lower quadrant SWS with 20% abdominal strain (r=-0.69, P = 0.002). There were positive correlations between histological muscularis propria inner layer smooth muscle hypertrophy and both median bowel wall SWS with 10% abdominal strain (r = 0.72, P = 0.002) and overall right lower quadrant SWS with 20% abdominal strain (r = 0.71, P = 0.002). There were no associations between ultrasound stiffness metrics and bowel wall SHIM collagen measurements.

CONCLUSION

Bowel wall and overall right lower quadrant ultrasound stiffness measurements correlate with mucosal active inflammation and muscularis propria smooth muscle hypertrophy in pediatric stricturing ileal Crohn disease, but not with intestinal fibrosis.

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.

A Non-invasive Method to Estimate the Stress-Strain Curve of Soft Tissue Using Ultrasound Elastography

Ultrasound elastography performed under small strain conditions has been intensively studied. However, small deformations may be not sufficiently large to differentiate some abnormal tissues. By combining quasi-static and shear wave elastography, we developed a non-invasive method to estimate the localized stress- strain curve of materials. This method exerts progressive multistep uniaxial compression on the materials, and shear wave measurements were performed at every compression step. This method estimates the 2-D displacements between steps via a 2-D region growing motion tracking method and accumulates these displacements to obtain the large material displacements with respect to the initial configuration. At each step, the shear modulus and stress were calculated according to linear elastic theory. The proposed method was tested on custom-made tissue-mimicking phantoms. Mechanical compression testing was conducted on the samples made of the same material as the phantoms and taken as the reference. The stress-strain curves for the same material from the proposed method and from mechanical testing are in good agreement. The root mean square error (RMSE) and area percentage error (APE) of the stress-strain curve between ultrasound measurement and mechanical testing for soft materials ranged from 0.18 to 0.26 kPa and from 5.6% to 7.8%, respectively. The RMSE and APE for stiff materials ranged from 0.56 to 1.17 kPa and 8.0% to 17.9%. Therefore, our method was able to provide good estimates of the stress-strain curve for tissue-mimicking materials.

Speed of sound and shear wave speed for calf soft tissue composition and nonlinearity assessment

Background

The purpose of this study was threefold: (I) to study the correlation of speed-of-sound (SoS) and shear-wave-speed (SWS) ultrasound (US) in the gastrocnemius muscle, (II) to use reproducible tissue compression to characterize tissue nonlinearity effects, and (III) to compare the potential of SoS and SWS for tissue composition assessment.

Methods

Twenty gastrocnemius muscles of 10 healthy young subjects (age range, 23-34 years, two females and eight males) were prospectively examined with both clinical SWS (GE Logiq E9, in m/s) and a prototype system that measures SoS (in m/s). A reflector was positioned opposite the US probe as a timing reference for SoS, with the muscle in between. Reproducible tissue compression was applied by reducing probe-reflector distance in 5 mm steps. The Ogden hyperelastic model and the acoustoelastic theory were used to characterize SoS and SWS variations with tissue compression and extract novel metrics related to tissue nonlinearity. The body fat percentage (BF%) of the subjects was estimated using bioelectrical impedance analysis.

Results

A weak negative correlation was observed between SWS and SoS (r=-0.28, P=0.002). SWS showed an increasing trend with increasing tissue compression (P=0.10) while SoS values decayed nonlinearly (P<0.001). The acoustoelastic modeling showed a weak correlation for SWS (r=-0.36, P<0.001) but a very strong correlation for SoS (r=0.86, P<0.001), which was used to extract the SoS acoustoelastic parameter. SWS showed higher variability between both calves [intraclass correlation coefficient (ICC) =0.62, P=0.08] than SoS (ICC =0.91, P<0.001). Correlations with BF% were strong and positive for SWS (r=0.60, P<0.001), moderate and negative for SoS (r=-0.43, P=0.05), and moderate positive for SoS acoustoelastic parameter (r=0.48, P=0.03).

Conclusions

SWS and SoS provide independent information about tissue elastic properties. SWS correlated stronger with BF% than SoS, but measurements were less reliable. SoS enabled the extraction of novel metrics related to tissue nonlinearity with potential complementary information.

Repeatability of Linear and Nonlinear Elastic Modulus Maps From Repeat Scans in the Breast

Compression elastography allows the precise measurement of large deformations of soft tissue in vivo. From an image sequence showing tissue undergoing large deformation, an inverse problem for both the linear and nonlinear elastic moduli distributions can be solved. As part of a larger clinical study to evaluate nonlinear elastic modulus maps (NEMs) in breast cancer, we evaluate the repeatability of linear and nonlinear modulus maps from repeat measurements. Within the cohort of subjects scanned to date, 20 had repeat scans. These repeated scans were processed to evaluate NEM repeatability. In vivo data were acquired by a custom-built, digitally controlled, uniaxial compression device with force feedback from the pressure-plate. RF-data were acquired using plane-wave imaging, at a frame-rate of 200 Hz, with a ramp-and-hold compressive force of 8N, applied at 8N/sec. A 2D block-matching algorithm was used to obtain sample-level displacement fields which were then tracked at subsample resolution using 2D cross correlation. Linear and nonlinear elasticity parameters in a modified Veronda-Westmann model of tissue elasticity were estimated using an iterative optimization method. For the repeated scans, B-mode images, strain images, and linear and nonlinear elastic modulus maps are measured and compared. Results indicate that when images are acquired in the same region of tissue and sufficiently high strain is used to recover nonlinearity parameters, then the reconstructed modulus maps are consistent.

Shear Induced Non-Linear Elasticity Imaging: Elastography for Compound Deformations

The goal of non-linear ultrasound elastography is to characterize tissue mechanical properties under finite deformations. Existing methods produce high contrast non-linear elastograms under conditions of pure uni-axial compression, but exhibit bias errors of 10-50% when the applied deformation deviates from the uni-axial condition. Since freehand transducer motion generally does not produce pure uniaxial compression, a motion-agnostic non-linearity estimator is desirable for clinical translation. Here we derive an expression for measurement of the Non-Linear Shear Modulus (NLSM) of tissue subject to combined shear and axial deformations. This method gives consistent nonlinear elasticity estimates irrespective of the type of applied deformation, with a reduced bias in NLSM values to 6-13%. The method combines quasi-static strain imaging with Single-Track Location-Shear Wave Elastography (STL-SWEI) to generate local estimates of axial strain, shear strain, and Shear Wave Speed (SWS). These local values were registered and non-linear elastograms reconstructed with a novel nonlinear shear modulus estimation scheme for general deformations. Results on tissue mimicking phantoms were validated with mechanical measurements and multiphysics simulations for all deformation types with an error in NLSM of 6-13%. Quantitative performance metrics with the new compound-motion tracking strategy reveal a 10-15 dB improvement in Signal-to-Noise Ratio (SNR) for simple shear versus pure compressive deformation for NLSM elastograms of homogeneous phantoms. Similarly, the Contrast-to-Noise Ratio (CNR) of NLSM elastograms of inclusion phantoms improved by 25-30% for simple shear over pure uni-axial compression. Our results show that high fidelity NLSM estimates may be obtained at ~30% lower strain under conditions of shear deformation as opposed axial compression. The reduction in strain required could reduce sonographer effort and improve scan safety.

Application of ultrasound elastography in the evaluation of muscle strength in a healthy population

Background

To investigate the validity of shear wave elastography (SWE) for the evaluation of muscle strength compared with isokinetic muscle testing, and to assess the influence of demographic factors such as height, weight, and body mass index (BMI) on the shear wave velocity (SWV).

Methods

Sixty healthy volunteers were consecutively enrolled. SWE was used to measure the SWV of the right quadriceps femoris in a relaxed position, in a tensive position, and under loads of 1 and 2 kg. Muscle strength parameters including peak torque (PT), PT to body weight ratio (PT/BW), and total work (TW) were evaluated using isokinetic muscle testing. The SWV of the rectus femoris in different positions were compared using the Friedman test and the Kruskal-Wallis test, and the SWV and muscle strength parameters were compared between different genders and age groups using the Mann-Whitney U test. Additionally, Spearman's correlation coefficient was used to evaluate the correlation between SWV and muscle strength, as well as the possible effects of height, weight, and BMI on SWV.

Results

As the load increased, the SWV of the rectus femoris increased (P<0.001). In the relaxed position, there was no significant correlation between the SWV and the results of isokinetic muscle testing. With increasing load, the SWV and the results of isokinetic muscle testing were not significantly correlated (r=-0.256--0.392, P<0.05). In the 1 kg load position, height and weight were not significantly correlated with SWV (r=-0.261--0.393, P<0.05). In the relaxed position, there were no significant differences in the maximum, minimum, or mean SWV of the rectus femoris between different genders and age groups (P>0.05). However, under a 1 kg load, the maximum, minimum, and mean SWV of the females in this study were significantly higher than those of the males (4.49±0.60 vs. 3.98±0.68 m/s; 2.55±0.61 vs. 2.20±0.63 m/s; and 3.51±0.60 vs. 3.06±0.58 m/s; P=0.003, 0.028, and 0.004, respectively). Furthermore, there were significant differences in the maximum and mean velocities between the groups aged 20-34 and 35-60 years (4.11±0.62 vs. 4.47±0.70 m/s; 3.17±0.53 vs. 3.52±0.69 m/s; P=0.045 and 0.044, respectively).

Conclusions

Ultrasound elastography (UE) shows potential for the measurement of muscle strength. The SWV of muscles demonstrate an increasing trend with the increase of impedance. Additionally, age and gender have a significant effect on SWV, while the effects of height, weight, and BMI require further investigation.

A structural-based computational model of tendon-bone insertion tissues

Tendon-to-bone insertion provides a gradual transition from soft tendon to hard bone tissue, functioning to alleviate stress concentrations at the junction of these tissues. Such macroscopic mechanical properties are achieved due to the internal structure in which collagen fibers and mineralization levels are key ingredients. We develop a structural-based model of tendon-to-bone insertion incorporating such details as fiber preferred orientation, fiber directional dispersion, mineralization level, and their inhomogeneous spatial distribution. A python script is developed to alter the tapered tendon-bone transition zone and to provide spatial grading of material properties, which may be rather complex as experiments suggest. A simple linear interpolation between tendon and bone material properties is first used to describe the graded property within the insertion region. Stress distributions are obtained and compared for spatially graded and various piece-wise materials properties. It is observed that spatial grading results in more smooth stress distributions and significantly reduces maximum stresses. The geometry of the tissue model is optimized by minimizing the peak stress to mimic in-vivo tissue remodeling. The in-silico elastic models constructed in this work are verified and modified by comparing to our in-situ biaxial mechanical testing results, thereby serving as translational tools for accurately predicting the material behavior of the tendon-to-bone insertions. This model will be useful for understanding how tendon-to-bone insertion develops during tissue remodeling, as well as for developing orthopedic implants.

C-Elastography: In Vitro Feasibility Phantom Study

C-Elastography (CE) is a new ultrasound technique that locally maps the non-linear elasticity of soft tissue using low-frequency (150-250 Hz) shear waves generated by the acoustic radiation force (ARF). CE is based on a recent finding that the magnitude of the ARF in an isotropic tissue-like solid is related linearly to a third-order modulus of elasticity, C, which is responsible for the coupling between deviatoric and volumetric constitutive behaviors. The main objective of the work described here was to examine the feasibility of using and performance of C-elastography in differentiating and characterizing soft tissue via a pilot study on ex vivo tissue and tissue-mimicking inclusions cast in a gelatin block. In this vein, the CE technique deploys a combination of ultrasound motion sensing and 3-D visco-elastodynamic simulation to estimate the non-linear modulus C. As ultrasound focusing inherently confines the ARF to a small region, CE provides the means for measuring C within O(mm3) volumes. Equipped with such data analysis, we performed in vitro CE experiments on agar-based, xenograft and normal breast tissue samples embedded in a gelatin matrix. The compound C-elastograms indicate marked (and sharp) C-contrast, with average values of 1.9 and 5.6 at push points inside the featured soft and hard inclusions, respectively.

Large-Strain 3-D in Vivo Breast Ultrasound Strain Elastography Using a Multi-compression Strategy and a Whole-Breast Scanning System

Non-linear mechanical properties of breast tissue can be employed to diagnose and differentiate breast tumors. To obtain such non-linear mechanical properties, it is necessary to track tissue motion under large deformation. In this study, a multi-compression strategy was utilized to produce large tissue deformation, and a method to estimate 3-D motion of tissue under large deformation was introduced. Given multiple volumes of ultrasound data, the proposed method first estimates volume-to-volume incremental displacements using a 3-D region-growing motion-tracking method. Then, possible outliers among all incremental displacements are removed to avoid error accumulation. Once large displacement errors have been removed, all incremental displacements are registered together to obtain accumulated displacements under large tissue deformation (e.g., >10%). The proposed method was tested with one set of in vivo tumor-bearing ultrasound data acquired from a human subject. A total of 10 small-strain deformation steps were performed to obtain the final accumulated displacement field, in which the breast lesion and its surrounding were deformed by approximately 6% and 16%, respectively. The contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) of the elasticity images obtained with the proposed method were all higher than those obtained with a 2-D tracking method. Furthermore, in three orthogonal views of accumulated axial strain images, the breast lesion was clearly visible with good correspondence between the axial strain and B-mode images.

Quantitative assessment of cervical softening during pregnancy with shear wave elasticity imaging: an in vivo longitudinal study

We report here the results of a longitudinal study of cervix stiffness during pregnancy. Thirty women, ages ranging from 19 to 37 years, were scanned with ultrasound at five time points beginning at their normal first-trimester screening (8-13 weeks) through term pregnancy (nominally 40 week) using a clinical ultrasound imaging system modified with a special ultrasound transducer and system software. The system estimated the shear wave speed (its square proportional to the shear modulus under idealized conditions) in the cervix. We found a constant fractional reduction (about 4% per week) in shear wave speed with increasing gestational age. We also demonstrated a spatial gradient in shear wave speed along the length of the cervix (softest at the distal end). Results were consistent with our previous ex vivo and in vivo work in women. Shear wave elasticity imaging may be a potentially useful clinical tool for objective assessment of cervical softening in pregnancy.

Accelerating 3-D GPU-based Motion Tracking for Ultrasound Strain Elastography Using Sum-Tables: Analysis and Initial Results

Now, with the availability of 3-D ultrasound data, a lot of research efforts are being devoted to developing 3-D ultrasound strain elastography (USE) systems. Because 3-D motion tracking, a core component in any 3-D USE system, is computationally intensive, a lot of efforts are under way to accelerate 3-D motion tracking. In the literature, the concept of Sum-Table has been used in a serial computing environment to reduce the burden of computing signal correlation, which is the single most computationally intensive component in 3-D motion tracking. In this study, parallel programming using graphics processing units (GPU) is used in conjunction with the concept of Sum-Table to improve the computational efficiency of 3-D motion tracking. To our knowledge, sum-tables have not been used in a GPU environment for 3-D motion tracking. Our main objective here is to investigate the feasibility of using sum-table-based normalized correlation coefficient (ST-NCC) method for the above-mentioned GPU-accelerated 3-D USE. More specifically, two different implementations of ST-NCC methods proposed by Lewis et al. and Luo-Konofagou are compared against each other. During the performance comparison, the conventional method for calculating the normalized correlation coefficient (NCC) was used as the baseline. All three methods were implemented using compute unified device architecture (CUDA; Version 9.0, Nvidia Inc., CA, USA) and tested on a professional GeForce GTX TITAN X card (Nvidia Inc., CA, USA). Using 3-D ultrasound data acquired during a tissue-mimicking phantom experiment, both displacement tracking accuracy and computational efficiency were evaluated for the above-mentioned three different methods. Based on data investigated, we found that under the GPU platform, Lou-Konofaguo method can still improve the computational efficiency (17–46%), as compared to the classic NCC method implemented into the same GPU platform. However, the Lewis method does not improve the computational efficiency in some configuration or improves the computational efficiency at a lower rate (7–23%) under the GPU parallel computing environment. Comparable displacement tracking accuracy was obtained by both methods.

Acoustoelasticity Analysis of Transient Waves for Non-Invasive In Vivo Assessment of Urinary Bladder

A non-invasive method for measurement of the bladder wall nonlinear elastic behavior is presented. The method is based on acoustoelasticity modeling of the elasticity changes in bladder tissue modulus at different volumetric strain levels. At each volume, tissue strain is obtained from the real-time ultrasound images. Using acoustic radiation force, a transient Lamb wave is excited on the bladder wall and instantaneous modulus of shear elasticity is obtained from the 2-D Fourier analysis of the spatial-temporal dispersion maps. Measured elasticity and strain data are then used in an acoustoelasticity formulation to obtain the third order elastic coefficient, referred to as nonlinearity parameter A, and initial resting elasticity μ₀. The method was tested in ex vivo porcine bladder samples (N = 9) before and after treatment with formalin. The estimated nonlinearity parameter, A, was significantly higher in the treated samples compared to intact (p < 0.00062). The proposed method was also applied on 16 patients with neurogenic bladders (10 compliant and 6 non-compliant subjects). The estimated nonlinearity parameter A was significantly higher in the non-compliant cases compared to the compliant (p < 0.0293). These preliminary results promise a new method for non-invasive evaluation of the bladder tissue nonlinearity which may serve as a new diagnostic and prognostic biomarker for management of the patients with neurogenic bladders.

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.

Evaluation of the Effect of Tissue Compression on the Results of Shear Wave Elastography Measurements

Shear wave imaging is considered to be more precise and less operator dependent when compared with strain imaging. It enables quantitative and reproducible data (Young's modulus of the imaged tissue). However, results of shear wave imaging can be affected by a variety of different factors. The aim of this study is to evaluate the effect of the pressure applied by the ultrasound probe during examination on the measured values of Young's modulus. The effect of the tissue compression on the results of the real-time shear wave elastography was evaluated via the gelatine phantom measurements, via the ex vivo experiments with pig liver, and via the in vivo measurements of the thyroid gland stiffness on healthy volunteers. The results of our measurements confirmed that the measured value of Young's modulus increases with the increasing pressure applied on the imaged object. The highest increase was observed during the ex vivo experiments (400%), and the lowest increase was detected in the case of the phantom measurements (8%). A two- to threefold increase in Young's modulus was observed between the minimum and maximum pressure in the case of the in vivo elastography measurements of thyroid gland. The Veronda-Westman theoretical model was used for the description of the tissue nonlinearity. We conclude that tissue compression by the force exerted on the probe can significantly affect the results of the real-time shear wave elastography measurements. Minimum pressure should be used when measuring the absolute value of Young's modulus of superficial organs.

Breast magnetic resonance elastography: a review of clinical work and future perspectives

This review on magnetic resonance elastography (MRE) of the breast provides an overview of available literature and describes current developments in the field of breast MRE, including new transducer technology for data acquisition and multi-frequency-derived power-law behaviour of tissue. Moreover, we discuss the future potential of breast MRE, which goes beyond its original application as an additional tool in differentiating benign from malignant breast lesions. These areas of ongoing and future research include MRE for pre-operative tumour delineation, staging, monitoring and predicting response to treatment, as well as prediction of the metastatic potential of primary tumours.

Stiffness reconstruction methods for MR elastography

Assessment of tissue stiffness is desirable for clinicians and researchers, as it is well established that pathophysiological mechanisms often alter the structural properties of tissue. Magnetic resonance elastography (MRE) provides an avenue for measuring tissue stiffness and has a long history of clinical application, including staging liver fibrosis and stratifying breast cancer malignancy. A vital component of MRE consists of the reconstruction algorithms used to derive stiffness from wave-motion images by solving inverse problems. A large range of reconstruction methods have been presented in the literature, with differing computational expense, required user input, underlying physical assumptions, and techniques for numerical evaluation. These differences, in turn, have led to varying accuracy, robustness, and ease of use. While most reconstruction techniques have been validated against in silico or in vitro phantoms, performance with real data is often more challenging, stressing the robustness and assumptions of these algorithms. This article reviews many current MRE reconstruction methods and discusses the aforementioned differences. The material assumptions underlying the methods are developed and various approaches for noise reduction, regularization, and numerical discretization are discussed. Reconstruction methods are categorized by inversion type, underlying assumptions, and their use in human and animal studies. Future directions, such as alternative material assumptions, are also discussed.

A General Approach to Derive Stress and Elasticity Tensors for Hyperelastic Isotropic and Anisotropic Biomaterials

Hyperelastic models are of particular interest in modeling biomaterials. In order to implement them, one must derive the stress and elasticity tensors from the given potential energy function explicitly. However, it is often cumbersome to do so because researchers in biomechanics may not be well-exposed to systematic approaches to derive the stress and elasticity tensors as it is vaguely addressed in literature. To resolve this, we present a framework of a general approach to derive the stress and elasticity tensors for hyperelastic models. Throughout the derivation we carefully elaborate the differences between formulas used in the displacement-based formulation and the displacement/pressure mixed formulation. Three hyperelastic models, Mooney-Rivlin, Yeoh and Holzapfel-Gasser-Ogden models that span from first-order to higher order and from isotropic to anisotropic materials, are served as examples. These detailed derivations are validated with numerical experiments that demonstrate excellent agreements with analytical and other computational solutions. Following this framework, one could implement with ease any hyperelastic model as user-defined functions in software packages or develop as an original source code from scratch.

Mechanical behavior of surgical meshes for abdominal wall repair: In vivo versus biaxial characterization

Despite the widespread use of synthetic meshes in the surgical treatment of the hernia pathology, the election criteria of a suitable mesh for specific patient continues to be uncertain. Thus, in this work, we propose a methodology to determine in advance potential disadvantages on the use of certain meshes based on the patient-specific abdominal geometry and the mechanical features of the certain meshes. To that purpose, we have first characterized the mechanical behavior of four synthetic meshes through biaxial tests. Secondly, two of these meshes were implanted in several New Zealand rabbits with a total defect previously created on the center of the abdominal wall. After the surgical procedure, specimen were subjected to in vivo pneumoperitoneum tests to determine the immediate post-surgical response of those meshes after implanted in a healthy specimen. Experimental performance was recorded by a stereo rig with the aim of obtaining quantitative information about the pressure-displacement relation of the abdominal wall. Finally, following the procedure presented in prior works (Simón-Allué et al., 2015, 2017), a finite element model was reconstructed from the experimental measurements and tests were computationally reproduced for the healthy and herniated cases. Simulations were compared and validated with the in vivo behavior and results were given along the abdominal wall in terms of displacements, stresses and strain. Mechanical characterization of the meshes revealed Surgipro^TM as the most rigid implant and Neomesh SuperSoft® as the softer, while other two meshes (Neomesh Soft®, Neopore®) remained in between. These two meshes were employed in the experimental study and resulted in similar effect in the abdominal wall cavity and both were close to the healthy case. Simulations confirmed this result while showed potential objections in the case of the other two meshes, due to high values in stresses or elongation that may led to discomfort in real tissue. The use of this methodology on human surgery may provide the surgeons with reliable and useful information to avoid certain meshes on specific-patient treatment.

Application of Acoustoelasticity to Evaluate Nonlinear Modulus in Ex Vivo Kidneys

Currently, dynamic elastography techniques estimate the linear elastic shear modulus of different body tissues. New methods that investigate other properties of soft tissues such as anisotropy, viscosity, and shear nonlinearity would provide more information about the structure and function of the tissue and might provide a better contrast than tissue stiffness and hence provide more effective diagnostic tools for some diseases. It has previously been shown that shear wave velocity in a medium changes due to an applied stress, a phenomenon called acoustoelasticity (AE). Applying a stress to compress a medium while measuring the shear wave velocity versus strain provides data with which the third-order nonlinear shear modulus can be estimated. To evaluate the feasibility of estimating , we evaluated ten ex vivo porcine kidneys embedded in 10% porcine gelatin to mimic the case of a transplanted kidney. Under assumptions of an elastic incompressible medium for AE measurements, the shear modulus was quantified at each compression level and the applied strain was assessed by measuring the change in the thickness of the kidney cortex. Finally, was calculated by applying the AE theory. Our results demonstrated that it is possible to estimate a nonlinear shear modulus by monitoring the changes in strain and due to kidney deformation. The magnitudes of are higher when the compression is performed progressively and when using a plate attached to the transducer. Nevertheless, the values obtained for are similar to those previously reported in the literature for breast tissue.

NADPH oxidase mediates microtubule alterations and diaphragm dysfunction in dystrophic mice

Skeletal muscle from mdx mice is characterized by increased Nox2 ROS, altered microtubule network, increased muscle stiffness, and decreased muscle/respiratory function. While microtubule de-tyrosination has been suggested to increase stiffness and Nox2 ROS production in isolated single myofibers, its role in altering tissue stiffness and muscle function has not been established. Because Nox2 ROS production is upregulated prior to microtubule network alterations and ROS affect microtubule formation, we investigated the role of Nox2 ROS in diaphragm tissue microtubule organization, stiffness and muscle/respiratory function. Eliminating Nox2 ROS prevents microtubule disorganization and reduces fibrosis and muscle stiffness in mdx diaphragm. Fibrosis accounts for the majority of variance in diaphragm stiffness and decreased function, implicating altered extracellular matrix and not microtubule de-tyrosination as a modulator of diaphragm tissue function. Ultimately, inhibiting Nox2 ROS production increased force and respiratory function in dystrophic diaphragm, establishing Nox2 as a potential therapeutic target in Duchenne muscular dystrophy.

Three-dimensional Ultrasound Elasticity Imaging on an Automated Breast Volume Scanning System

Ultrasound elasticity imaging has demonstrated utility in breast imaging, but it is typically performed with handheld transducers and two-dimensional imaging. Two-dimensional (2D) elastography images tissue stiffness of only a plane and hence suffers from errors due to out-of-plane motion, whereas three-dimensional (3D) data acquisition and motion tracking can be used to track out-of-plane motion that is lost in 2D elastography systems. A commercially available automated breast volume scanning system that acquires 3D ultrasound data with precisely controlled elevational movement of the 1D array ultrasound transducer was employed in this study. A hybrid guided 3D motion-tracking algorithm was developed that first estimated the displacements in one plane using a modified quality-guided search method, and then performed an elevational guided-search for displacement estimation in adjacent planes. To assess the performance of the method, 3D radiofrequency echo data were acquired with this system from a phantom and from an in vivo human breast. For both experiments, the axial displacement fields were smooth and high cross-correlation coefficients were obtained in most of the tracking region. The motion-tracking performance of the new method was compared with a correlation-based exhaustive-search method. For all motion-tracking volume pairs, the average motion-compensated cross-correlation values obtained by the guided-search motion-tracking method were equivalent to those by the exhaustive-search method, and the computation time was about a factor of 10 lesser. Therefore, the proposed 3D ultrasound elasticity imaging method was a more efficient approach to produce a high quality of 3D ultrasound strain image.

A GPU-Accelerated 3-D Coupled Subsample Estimation Algorithm for Volumetric Breast Strain Elastography

Our primary objective of this paper was to extend a previously published 2-D coupled subsample tracking algorithm for 3-D speckle tracking in the framework of ultrasound breast strain elastography. In order to overcome heavy computational cost, we investigated the use of a graphic processing unit (GPU) to accelerate the 3-D coupled subsample speckle tracking method. The performance of the proposed GPU implementation was tested using a tissue-mimicking phantom and in vivo breast ultrasound data. The performance of this 3-D subsample tracking algorithm was compared with the conventional 3-D quadratic subsample estimation algorithm. On the basis of these evaluations, we concluded that the GPU implementation of this 3-D subsample estimation algorithm can provide high-quality strain data (i.e., high correlation between the predeformation and the motion-compensated postdeformation radio frequency echo data and high contrast-to-noise ratio strain images), as compared with the conventional 3-D quadratic subsample algorithm. Using the GPU implementation of the 3-D speckle tracking algorithm, volumetric strain data can be achieved relatively fast (approximately 20 s per volume [2.5 cm ×2.5 cm ×2.5 cm]).

An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.

Nonlinear characterization of elasticity using quantitative optical coherence elastography

Optical coherence elastography (OCE) has been used to perform mechanical characterization on biological tissue at the microscopic scale. In this work, we used quantitative optical coherence elastography (qOCE), a novel technology we recently developed, to study the nonlinear elastic behavior of biological tissue. The qOCE system had a fiber-optic probe to exert a compressive force to deform tissue under the tip of the probe. Using the space-division multiplexed optical coherence tomography (OCT) signal detected by a spectral domain OCT engine, we were able to simultaneously quantify the probe deformation that was proportional to the force applied, and to quantify the tissue deformation. In other words, our qOCE system allowed us to establish the relationship between mechanical stimulus and tissue response to characterize the stiffness of biological tissue. Most biological tissues have nonlinear elastic behavior, and the apparent stress-strain relationship characterized by our qOCE system was nonlinear an extended range of strain, for a tissue-mimicking phantom as well as biological tissues. Our experimental results suggested that the quantification of force in OCE was critical for accurate characterization of tissue mechanical properties and the qOCE technique was capable of differentiating biological tissues based on the elasticity of tissue that is generally nonlinear.

Wide-field optical coherence micro-elastography for intraoperative assessment of human breast cancer margins

Incomplete excision of malignant tissue is a major issue in breast-conserving surgery, with typically 20 - 30% of cases requiring a second surgical procedure arising from postoperative detection of an involved margin. We report advances in the development of a new intraoperative tool, optical coherence micro-elastography, for the assessment of tumor margins on the micro-scale. We demonstrate an important step by conducting whole specimen imaging in intraoperative time frames with a wide-field scanning system acquiring mosaicked elastograms with overall dimensions of ~50 × 50 mm, large enough to image an entire face of most lumpectomy specimens. This capability is enabled by a wide-aperture annular actuator with an internal diameter of 65 mm. We demonstrate feasibility by presenting elastograms recorded from freshly excised human breast tissue, including from a mastectomy, lumpectomies and a cavity shaving.

Building a virtual simulation platform for quasistatic breast ultrasound elastography using open source software: A preliminary investigation

PURPOSE

Quasistatic ultrasound elastography (QUE) is being used to augment in vivo characterization of breast lesions. Results from early clinical trials indicated that there was a lack of confidence in image interpretation. Such confidence can only be gained through rigorous imaging tests using complex, heterogeneous but known media. The objective of this study is to build a virtual breast QUE simulation platform in the public domain that can be used not only for innovative QUE research but also for rigorous imaging tests.

METHODS

The main thrust of this work is to streamline biomedical ultrasound simulations by leveraging existing open source software packages including Field II (ultrasound simulator), VTK (geometrical visualization and processing), FEBio [finite element (FE) analysis], and Tetgen (mesh generator). However, integration of these open source packages is nontrivial and requires interdisciplinary knowledge. In the first step, a virtual breast model containing complex anatomical geometries was created through a novel combination of image-based landmark structures and randomly distributed (small) structures. Image-based landmark structures were based on data from the NIH Visible Human Project. Subsequently, an unstructured FE-mesh was created by Tetgen. In the second step, randomly positioned point scatterers were placed within the meshed breast model through an octree-based algorithm to make a virtual breast ultrasound phantom. In the third step, an ultrasound simulator (Field II) was used to interrogate the virtual breast phantom to obtain simulated ultrasound echo data. Of note, tissue deformation generated using a FE-simulator (FEBio) was the basis of deforming the original virtual breast phantom in order to obtain the postdeformation breast phantom for subsequent ultrasound simulations. Using the procedures described above, a full cycle of QUE simulations involving complex and highly heterogeneous virtual breast phantoms can be accomplished for the first time.

RESULTS

Representative examples were used to demonstrate capabilities of this virtual simulation platform. In the first set of three ultrasound simulation examples, three heterogeneous volumes of interest were selected from a virtual breast ultrasound phantom to perform sophisticated ultrasound simulations. These resultant B-mode images realistically represented the underlying complex but known media. In the second set of three QUE examples, advanced applications in QUE were simulated. The first QUE example was to show breast tumors with complex shapes and/or compositions. The resultant strain images showed complex patterns that were normally seen in freehand clinical ultrasound data. The second and third QUE examples demonstrated (deformation-dependent) nonlinear strain imaging and time-dependent strain imaging, respectively.

CONCLUSIONS

The proposed virtual QUE platform was implemented and successfully tested in this study. Through show-case examples, the proposed work has demonstrated its capabilities of creating sophisticated QUE data in a way that cannot be done through the manufacture of physical tissue-mimicking phantoms and other software. This open software architecture will soon be made available in the public domain and can be readily adapted to meet specific needs of different research groups to drive innovations in QUE.

Contrast-Enhanced Quantitative Intravascular Elastography: The Impact of Microvasculature on Model-Based Elastography

Model-based intravascular ultrasound elastography visualizes the stress distribution within vascular tissue-information that clinicians could use to predict the propensity of atherosclerotic plaque rupture. However, there are concerns that clusters of microvessels may reduce the accuracy of the estimated stress distribution. Consequently, we have developed a contrast-enhanced intravascular ultrasound system to investigate how plaque microvasculature affects the performance of model-based elastography. In simulations, diameters of 200, 400 and 800 μm were used, where the latter diameter represented a cluster of microvessels. In phantoms, we used a microvessel with a diameter of 750 μm. Peak stress errors of 3% and 38% were incurred in the fibrous cap when stress recovery was performed with and without a priori information about microvessel geometry. The results indicate that incorporating geometric information about plaque microvasculature obtained with contrast-enhanced ultrasound imaging improves the accuracy of estimates of the stress distribution within the fibrous cap precisely.

Percutaneous real-time sonoelastography as a non-invasive tool for the characterization of solid focal liver lesions: A prospective study

BACKGROUND

Real-time sonoelastography is currently used for the characterization of superficial solid lesions such as thyroid and breast masses. This study evaluates the usefulness of percutaneous sonoelastography for the characterization of solid focal liver lesions.

METHODS

30 out of 43 patients with 38 known liver lesions were included in a prospective, diagnostic study. Qualitative analysis (pattern of deformation, elasticity type of liver tumour) and semi-quantitative measurements (strain ratio, hardness percentage, histogram) were evaluated. Sensitivity, specificity, positive and negative predictive values were calculated and the area under the receiver operating characteristics curve was constructed.

RESULTS

Patterns A and C-D are specific of benign lesions and metastases respectively. The patterns for haemangiomas, focal nodular hyperplasia and metastases were significantly different to each other in terms of strain ratio, hardness percentage and histogram (p<0.05). A statistically significant difference (p<0.001) was observed between the median values of the 3 measured parameters for benign (1.02; 12%; 47) and malignant lesions (1.66; 65%; 20.5) respectively. The area under the receiver operating characteristics curve values for strain ratio, hardness percentage and histogram were 0.88, 0.89, and 0.86 respectively for cut-off values of 1.2, 45, and 30.

CONCLUSIONS

By percutaneous sonoelastography it is possible to differentiate benign versus malignant focal liver lesions, metastases in particular, with good diagnostic performance.

In Vivo Quantification of the Nonlinear Shear Modulus in Breast Lesions: Feasibility Study

Breast cancer detection in the early stages is of great importance since the prognosis, and the treatment depends more on this. Multiple techniques relying on the mechanical properties of soft tissues have been developed to help in early detection. In this study, we implemented a technique that measures the nonlinear shear modulus (NLSM) (μ(NL)) in vivo and showed its utility to detect breast lesions from healthy tissue. The technique relies on the acoustoelasticity theory in quasi-incompressible media. In order to recover μ(NL), static elastography and supersonic shear imaging are combined to subsequently register strain maps and shear modulus maps while the medium is compressed. Then, μ(NL) can be recovered from the relationship between the stress, deduced from strain maps, and the shear modulus. For this study, a series of five nonlinear phantoms were built using biological tissue (pork liver) inclusions immersed in an agar-gelatin gel. Furthermore, 11 in vivo acquisitions were performed to characterize the NLSM of breast tissue. The phantom results showed a very good differentiation of the liver inclusions when measuring μ(NL) with a mean value of -114.1 kPa compared to -34.7 kPa for the gelatin. Meanwhile, values for the shear modulus for the liver and the gelatin were very similar, 3.7 and 3.4 kPa, respectively. In vivo NLSM mean value for the healthy breast tissue was of -95 kPa, while mean values of the benign and the malignant lesions were -619 and -806 kPa with a strong v ariability, respectively. This study shows the potential of the acoustoelasticity theory in quasi-incompressible medium to bring a new parameter for breast cancer diagnosis.

A coupled subsample displacement estimation method for ultrasound-based strain elastography

Obtaining accurate displacement estimates along both axial (parallel to the acoustic beam) and lateral (perpendicular to the beam) directions is an important task for several clinical applications such as shear strain imaging, modulus reconstruction and temperature imaging, where a full description of the two or three-dimensional (2D/3D) deformation field is required. In this study we propose an improved speckle tracking algorithm where axial and lateral motion estimations are simultaneously performed to enhance motion tracking accuracy. More specifically, using conventional ultrasound echo data, this algorithm first finds an iso-contour in the vicinity of the peak correlation between two segments of the pre- and post-deformation ultrasound radiofrequency echo data. The algorithm then attempts to find the center of the iso-contour of the correlation function that corresponds to the unknown (sub-sample) motion vector between these two segments of echo data. This algorithm has been tested using computer-simulated data, studies with a tissue-mimicking phantom, and in vivo breast lesion data. Computer simulation results show that the method improves the accuracy of both lateral and axial tracking. Such improvements are more significant when the deformation is small or along the lateral direction. Results from the tissue-mimicking phantom study are consistent with findings observed in computer simulations. Using in vivo breast lesion data we found that, compared to the 2D quadratic subsample displacement estimation methods, higher quality axial strain and shear strain images (e.g. 18.6% improvement in contrast-to-noise ratio for shear strain images) can be obtained for large deformations (up to 5% frame-to-frame and 15% local strains) in a multi-compression technique. Our initial results demonstrated that this conceptually and computationally simple method could improve the image quality of ultrasound-based strain elastography with current clinical equipment.

Quantitative micro-elastography: imaging of tissue elasticity using compression optical coherence elastography

Probing the mechanical properties of tissue on the microscale could aid in the identification of diseased tissues that are inadequately detected using palpation or current clinical imaging modalities, with potential to guide medical procedures such as the excision of breast tumours. Compression optical coherence elastography (OCE) maps tissue strain with microscale spatial resolution and can delineate microstructural features within breast tissues. However, without a measure of the locally applied stress, strain provides only a qualitative indication of mechanical properties. To overcome this limitation, we present quantitative micro-elastography, which combines compression OCE with a compliant stress sensor to image tissue elasticity. The sensor consists of a layer of translucent silicone with well-characterized stress-strain behaviour. The measured strain in the sensor is used to estimate the two-dimensional stress distribution applied to the sample surface. Elasticity is determined by dividing the stress by the strain in the sample. We show that quantification of elasticity can improve the ability of compression OCE to distinguish between tissues, thereby extending the potential for inter-sample comparison and longitudinal studies of tissue elasticity. We validate the technique using tissue-mimicking phantoms and demonstrate the ability to map elasticity of freshly excised malignant and benign human breast tissues.

A PDE-Based Regularization Algorithm Toward Reducing Speckle Tracking Noise: A Feasibility Study for Ultrasound Breast Elastography

Obtaining accurate ultrasonically estimated displacements along both axial (parallel to the acoustic beam) and lateral (perpendicular to the beam) directions is an important task for various clinical elastography applications (e.g., modulus reconstruction and temperature imaging). In this study, a partial differential equation (PDE)-based regularization algorithm was proposed to enhance motion tracking accuracy. More specifically, the proposed PDE-based algorithm, utilizing two-dimensional (2D) displacement estimates from a conventional elastography system, attempted to iteratively reduce noise contained in the original displacement estimates by mathematical regularization. In this study, tissue incompressibility was the physical constraint used by the above-mentioned mathematical regularization. This proposed algorithm was tested using computer-simulated data, a tissue-mimicking phantom, and in vivo breast lesion data. Computer simulation results demonstrated that the method significantly improved the accuracy of lateral tracking (e.g., a factor of 17 at 0.5% compression). From in vivo breast lesion data investigated, we have found that, as compared with the conventional method, higher quality axial and lateral strain images (e.g., at least 78% improvements among the estimated contrast-to-noise ratios of lateral strain images) were obtained. Our initial results demonstrated that this conceptually and computationally simple method could be useful for improving the image quality of ultrasound elastography with current clinical equipment as a post-processing tool.

The 'sixth sense' of ultrasound: probing nonlinear elasticity with acoustic radiation force

Prompted by a recent finding that the magnitude of the acoustic radiation force (ARF) in isotropic tissue-like solids depends linearly on a particular third-order modulus of elasticity-hereon denoted by C, this study investigates the possibility of estimating C from the amplitude of the ARF-generated shear waves. The featured coefficient of nonlinear elasticity, which captures the incipient nonlinear interaction between the volumetric and deviatoric modes of deformation, has so far received only a limited attention in the context of soft tissues due to the fact that the latter are often approximated as (i) fluid-like when considering ultrasound waves, and (ii) incompressible under static deformations. On establishing the analytical and computational platform for the proposed sensing methodology, the study proceeds with applying the prototype technique toward estimating via ARF the third-order modulus C in a series of tissue-mimicking phantoms. To help validate the concept and its implementation, the germane third-order modulus is independently estimated in each phantom via an established technique known as acoustoelasticity. The C-estimates obtained respectively via acoustoelasticity and the new theory of ARF show a significant degree of consistency. The key features of the new sensing methodology are that: (a) it requires no external deformation of a material other than that produced by the ARF, and (b) it estimates the nonlinear C-modulus locally, over the focal region of an ultrasound beam-where the shear waves are being generated.

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.

Towards clinical prostate ultrasound elastography using full inversion approach

PURPOSE

Various types of cancers including prostate cancer are known to be associated with biological changes that lead to tissue stiffening. Digital rectal examination is based on manually palpating the prostate tissue via the rectum. This test lacks sufficient accuracy required for early diagnosis which is necessary for effective management of prostate cancer. To develop an effective prostate cancer diagnostic technique, the authors propose an imaging technique that maps the distribution of the relative prostate tissue's elasticity modulus. Unlike digital rectal examination, this technique is quantitative, capable of accurately detecting small prostate lesions that cannot be sensed by manual palpation, and its accuracy is independent of the physician's experience.

METHODS

The proposed technique is a quasistatic elastography technique which uses ultrasound imaging to acquire tissue displacements resulting from transrectal ultrasound mechanical stimulation. The system involves a standard ultrasound imaging unit with accessibility to its radiofrequency data. The displacements are used as data for the tissue elasticity reconstruction. This reconstruction does not require tissue segmentation and is based on physics governing tissue mechanics. It is formulated using an inverse problem framework where elastic tissue deformation equations are fully inverted using an iterative scheme where each iteration involves stress calculation followed by elastic modulus updating until convergence is achieved.In silico and tissue mimicking phantom studies were conducted to validate the proposed technique, followed by a clinical pilot study involving two prostate cancer patients with whole-mount histopathology analysis on prostatectomy specimens to confirm a cancer location.

RESULTS

The phantom studies demonstrated robustness and reasonably high accuracy of the proposed method. Obtained Young's modulus ratios indicated reconstruction errors of less than 12%. Reconstructed elastic modulus images of the two clinical cases were compared to whole-mount histopathology slides where cancerous areas were identified. This comparison indicated marked tissue stiffening in the cancer area with reasonably accurate consistency observed between cancerous lesions identified by histopathology and high stiffness areas of the elastography images.

CONCLUSIONS

Results obtained from the phantom and patient studies indicate that the proposed method is reasonably accurate for detecting cancerous lesions. The proposed system does not require any additional hardware attachment for mechanical stimulation or data acquisition while the elasticity reconstruction algorithm can be easily implemented, leading to a low cost system that can be potentially utilized as an effective clinical tool for prostate cancer diagnosis.

Development of an Inverse Approach for the Characterization of In Vivo Mechanical Properties of the Lower Limb Muscles

The purpose of this study was to develop an inverse method, coupling imaging techniques with numerical methods, to identify the muscle mechanical behavior. A finite element model updating (FEMU) was developed in three main interdependent steps. First, a 2D FE modeling, parameterized by a Neo-Hookean behavior (C10 and D), was developed from a segmented thigh muscle 1.5T MRI (magnetic resonance imaging). Thus, a displacement field was simulated for different static loadings (contention, compression, and indentation). Subsequently, the optimal mechanical test was determined from a sensitivity analysis. Second, ultrasound parameters (gain, dynamic, and frequency) were optimized on the thigh muscles in order to apply the digital image correlation (DIC), allowing the measurement of an experimental displacement field. Third, an inverse method was developed to identify the Neo-Hookean parameters (C10 and D) by performing a minimization of the distance between the simulated and measured displacement fields. To replace the experimental data and to quantify the identification error, a numerical example was developed. The result of the sensitivity analysis showed that the compression test was more adapted to identify the Neo-Hookean parameters. Ultrasound images were recorded with a frequency, gain, and dynamic of 9 MHz, 34 dB, 42 dB, respectively. In addition, the experimental noise on displacement field measurement was estimated to be 0.2 mm. The identification performed on the numerical example revealed a low error for the C10 (<3%) and D (<7%) parameters with the experimental noise. This methodology could have an impact in the scientific and medical fields. A better knowledge of the muscle behavior will help to follow treatment and to ensure accurate medical procedures during the use of robotic devices.

3-D visualization and non-linear tissue classification of breast tumors using ultrasound elastography in vivo

The goal of the study described here was to introduce new methods for the classification and visualization of human breast tumors using 3-D ultrasound elastography. A tumor's type, shape and size are key features that can help the physician to decide the sort and extent of necessary treatment. In this work, tumor type, being either benign or malignant, was classified non-invasively for nine volunteer patients. The classification was based on estimating four parameters that reflect the tumor's non-linear biomechanical behavior, under multi-compression levels. Tumor prognosis using non-linear elastography was confirmed with biopsy as a gold standard. Three tissue classification parameters were found to be statistically significant with a p-value < 0.05, whereas the fourth non-linear parameter was highly significant, having a p-value < 0.001. Furthermore, each breast tumor's shape and size were estimated in vivo using 3-D elastography, and were enhanced using interactive segmentation. Segmentation with level sets was used to isolate the stiff tumor from the surrounding soft tissue. Segmentation also provided a reliable means to estimate tumors volumes. Four volumetric strains were investigated: the traditional normal axial strain, the first principal strain, von Mises strain and maximum shear strain. It was noted that these strains can provide varying degrees of boundary enhancement to the stiff tumor in the constructed elastograms. The enhanced boundary improved the performance of the segmentation process. In summary, the proposed methods can be employed as a 3-D non-invasive tool for characterization of breast tumors, and may provide early prognosis with minimal pain, as well as diminish the risk of late-stage breast cancer.

Characterization of biomechanical properties of agar based tissue mimicking phantoms for ultrasound stiffness imaging techniques

Pathological changes of the body have been observed to change the mechanical properties of soft tissue types which can be imaged by ultrasound elastography. Though initial clinical results using ultrasound elastography in detection of tumors are promising, quantification of signal to noise ratio, resolution and strain image patterns are the best achieved under a controlled study using phantoms with similar biomechanical properties of normal and abnormal tissues. The purpose of this work is to characterize the biomechanical properties of agar based tissue mimicking phantoms by varying the agar concentration from 1.7 to 6.6% by weight and identify the optimum property to be used in classification of cancerous tissues. We performed quasi-static uniaxial compression test under a strain rate of 0.5mm/min up to 15% strain and measured Young's modulus of phantom samples which are from 50kPa to 450kPa. Phantoms show nonlinear stress-strain characteristics at finite strain which were characterized using hyperelastic parameters by fitting Neo-Hookean, Mooney Rivlin, Ogden and Veronda Westmann models. We also investigated viscoelastic parameters of the samples by conducting oscillatory shear rheometry at various precompression levels (2-5%). Loss modulus values are always less than storage modulus which represents the behavior of soft tissues. The increase in agar concentration increases the shear modulus of the samples as well as decreases the linear viscoelastic region. The results suggest that dynamic shear modul are more promising than linear and nonlinear elastic modul in differentiation of various classes of abnormal tissues.

Two-dimensional simulations of displacement accumulation incorporating shear strain

Using ultrasound images to track large tissue deformations usually requires breaking up the deformation into steps and then summing the resulting displacement estimates. The accumulated displacement estimation error therefore depends not only on the error in each step but also on the statistical relationships between estimation steps. These relationships have not been thoroughly studied. Building on previous work with one-dimensional (1-D) simulations, the work reported here measured error variance for single-step and accumulated displacement estimates using two-dimensional (2-D) numerical simulations of ultrasound echo signals, subjected to both normal and axial shear strain as well as electronic noise. Previous results from 1-D simulations were confirmed, showing that errors due to electronic noise are negatively correlated between steps and accumulate slowly, while errors due to strain are positively correlated and accumulate quickly. These properties hold for both normal and axial shear strain. An analysis of 2-D kernel size for tissue under normal and axial shear strain was also performed. Under axial shear strain, error variance tends to increase with larger lateral kernel sizes but decrease for larger axial kernel sizes; the opposite relationship holds under normal strain. A combination of these two types of strain limits the practical kernel size in both dimensions.