A versatile and experimentally validated finite element model to assess the accuracy of shear wave elastography in a bounded viscoelastic medium

In silico analysis reveals the prospects of renal anisotropy in improving chronic kidney disease detection using ultrasound shear wave elastography

Renal anisotropy is a complex property of the kidney and often poses a challenge in obtaining consistent measurements when using shear wave elastography to detect chronic kidney disease. To circumvent the challenge posed by renal anisotropy in clinical settings, a dimensionless biomarker termed the 'anisotropic ratio' was introduced to establish a correlation between changes in degree of renal anisotropy and progression of chronic kidney disease through an in silico perspective. To achieve this, an efficient model reduction approach was developed to model the anisotropic property of kidneys. Good agreement between the numerical and experimental data were obtained, as percentage errors of less than 5.5% were reported when compared against experimental phantom measurement from the literature. To demonstrate the applicability of the model to clinical measurements, the anisotropic ratio of sheep kidneys was quantified, with both numerical and derived experimental results reporting a value of .667. Analysis of the anisotropic ratio with progression of chronic kidney disease demonstrated that patients with normal kidneys would have a lower anisotropic ratio of .872 as opposed to patients suffering from renal impairment, in which the anisotropic ratio may increase to .904, as determined from this study. The findings demonstrate the potential of the anisotropic ratio in improving the detection of chronic kidney disease using shear wave elastography.

The role of shear viscosity as a biomarker for improving chronic kidney disease detection using shear wave elastography: A computational study using a validated finite element model

The application of ultrasound shear wave elastography for detecting chronic kidney disease, namely renal fibrosis, has been widely studied. A good correlation between tissue Young's modulus and the degree of renal impairment has been established. However, the current limitation of this imaging modality pertains to the linear elastic assumption used in quantifying the stiffness of renal tissue in commercial shear wave elastography systems. As such, when underlying medical conditions such as acquired cystic kidney disease, which may potentially influence the viscous component of renal tissue, is present concurrently with renal fibrosis, the accuracy of the imaging modality in detecting chronic kidney disease may be affected. The findings in this study demonstrate that quantifying the stiffness of linear viscoelastic tissue using an approach similar to those implemented in commercial shear wave elastography systems led to percentage errors as high as 87%. The findings presented indicate that use of shear viscosity to detect changes in renal impairment led to a reduction in percentage error to values as low as 0.3%. For cases in which renal tissue was affected by multiple medical conditions, shear viscosity was found to be a good indicator in gauging the reliability of the Young's modulus (quantified through a shear wave dispersion analysis) in detecting chronic kidney disease. The findings show that percentage error in stiffness quantification can be reduced to as low as 0.6%. The present study demonstrates the potential use of renal shear viscosity as a biomarker to improve the detection of chronic kidney disease.

A New Estimation Scheme for Improving the Performance of Shear Wave Elasticity Imaging

Shear wave velocity (SWV) reconstruction based on time-of-flight (TOF) is widely adopted to realize shear wave elasticity imaging (SWEI). It typically breaks down the reconstruction of a SWV image into many kernels and treats them independently. We hypothesized that information exchange among kernels improves the performance of SWEI. Therefore, we propose the approach of iterative re-weighted least squares based on inter-kernel communication (IKC-IRLS). We also hypothesized that time-to-peak (TTP) is superior to cross-correlation (CC) in visualizing small targets because TTP uses higher shear wave frequencies than CC. To examine the hypotheses, IKC-IRLS was combined with TTP data and compared with four established methods. The five methods were tested by imaging several small-size stiff targets (2.5, 4.0 and 6.4 mm in diameter) using different kernel sizes in the simulation and real experiments. The results indicate that the IKC-IRLS approach can mitigate speckle noise and is robust to TTP outliers. Consequently, the proposed method achieves the highest contrast-to-noise ratio and the lowest mean absolute percentage error of target in almost all tested cases.

Tapering of the interventricular septum can affect ultrasound shear wave elastography: An in vitro and in silico study

Shear wave elastography (SWE) has the potential to determine cardiac tissue stiffness from non-invasive shear wave speed measurements, important, e.g., for predicting heart failure. Previous studies showed that waves traveling in the interventricular septum (IVS) may display Lamb-like dispersive behaviour, introducing a thickness-frequency dependency in the wave speed. However, the IVS tapers across its length, which complicates wave speed estimation by introducing an additional variable to account for. The goal of this work is to assess the impact of tapering thickness on SWE. The investigation is performed by combining in vitro experiments with acoustic radiation force (ARF) and 2D finite element simulations, to isolate the effect of the tapering curve on ARF-induced and natural waves in the heart. The experiments show a 11% deceleration during propagation from the thick to the thin end of an IVS-mimicking tapered phantom plate. The numerical analysis shows that neglecting the thickness variation in the wavenumber-frequency domain can introduce errors of more than 30% in the estimation of the shear modulus, and that the exact tapering curve, rather than the overall thickness reduction, determines the dispersive behaviour of the wave. These results suggest that septal geometry should be accounted for when deriving cardiac stiffness with SWE.

Effects of Loading and Boundary Conditions on the Performance of Ultrasound Compressional Viscoelastography: A Computational Simulation Study to Guide Experimental Design

Most biomaterials and tissues are viscoelastic; thus, evaluating viscoelastic properties is important for numerous biomedical applications. Compressional viscoelastography is an ultrasound imaging technique used for measuring the viscoelastic properties of biomaterials and tissues. It analyzes the creep behavior of a material under an external mechanical compression. The aim of this study is to use finite element analysis to investigate how loading conditions (the distribution of the applied compressional pressure on the surface of the sample) and boundary conditions (the fixation method used to stabilize the sample) can affect the measurement accuracy of compressional viscoelastography. The results show that loading and boundary conditions in computational simulations of compressional viscoelastography can severely affect the measurement accuracy of the viscoelastic properties of materials. The measurement can only be accurate if the compressional pressure is exerted on the entire top surface of the sample, as well as if the bottom of the sample is fixed only along the vertical direction. These findings imply that, in an experimental validation study, the phantom design should take into account that the surface area of the pressure plate must be equal to or larger than that of the top surface of the sample, and the sample should be placed directly on the testing platform without any fixation (such as a sample container). The findings indicate that when applying compressional viscoelastography to real tissues in vivo, consideration should be given to the representative loading and boundary conditions. The findings of the present simulation study will provide a reference for experimental phantom designs regarding loading and boundary conditions, as well as guidance towards validating the experimental results of compressional viscoelastography.

Breast Tumor Diagnosis Using Finite-Element Modeling Based on Clinical in vivo Elastographic Data

OBJECTIVES

This study exploited finite-element modeling (FEM) to simulate breast tissue multicompression during ultrasound elastography to classify breast tumors based on their nonlinear biomechanical properties.

METHODS

Numeric simulations were first calculated by using 3-dimensional (3D) virtual models with an assumed tumor's geometric dimensions but with actual material properties to test and validate the FEM. Further numeric simulations were used to construct 3D models based on in vivo experimental data to verify our models. The models were designed for each individual in vivo case, emphasizing the geometry, position, and biomechanical properties of the breast tissue. At different compression levels, tissue strains were analyzed between the tumors and the background normal tissues to explore their nonlinearity and classify the tumor type. Tumor classification parameters were deduced by using a power-law relationship between the applied compressive forces and strain differences.

RESULTS

Classification parameters were compared between benign and malignant tumors, for which they were found to be statistically significant in classifying the tumor types (P < .05) by both the validation and verification of FEM. We compared the classification parameters between the in vivo and FEM classifications, for which they were found to be strongly correlated (R = 0.875; P < .001), with no statistical differences between their outcomes (P = .909).

CONCLUSIONS

Good agreement between the model outcomes and the in vivo diagnostics was reported. The implemented models were validated and verified. The introduced 3D modeling method may augment elastographic methods to preliminary classify breast tumors at an early stage.

Analysis of multiple shear wave modes in a nonlinear soft solid: Experiments and finite element simulations with a tilted acoustic radiation force

Tissue nonlinearity is conventionally measured in shear wave elastography by studying the change in wave speed caused by the tissue deformation, generally known as the acoustoelastic effect. However, these measurements have mainly focused on the excitation and detection of one specific shear mode, while it is theoretically known that the analysis of multiple wave modes offers more information about tissue material properties that can potentially be used to refine disease diagnosis. This work demonstrated proof of concept using experiments and finite element simulations in a uniaxially stretched phantom by tilting the acoustic radiation force excitation axis with respect to the material's symmetry axis. Using this unique set-up, we were able to visualize two propagating shear wave modes across the stretch direction for stretches larger than 140%. Complementary simulations were performed using material parameters determined from mechanical testing, which enabled us to convert the observed shear wave behavior into a correct representative constitutive law for the phantom material, i.e. the Isihara model. This demonstrates the potential of measuring shear wave propagation in combination with shear wave modeling in complex materials as a non-invasive alternative for mechanical testing.

On the Challenges Associated with Obtaining Reproducible Measurements Using SWEI in the Median Nerve

This work discusses challenges we have encountered in acquiring reproducible measurements of shear wave speed (SWS) in the median nerve and suggests methods for improving reproducibility. First, procedural acquisition challenges are described, including nerve echogenicity, transducer pressure and transmit focal depth. Second, we present an iterative, radon sum-based algorithm that was developed specifically for measuring the SWS in median nerves. SWSs were measured using single track location shear wave elasticity imaging (SWEI) in the median nerves of six healthy volunteers and six patients diagnosed with carpal tunnel syndrome. Unsuccessful measurements were associated with several challenges including reverberation artifacts, low signal-to-noise ratio and temporal window limitations for tracking the velocity wave. To address these challenges, an iterative convergence algorithm was implemented to identify an appropriate temporal processing window that removed the reverberation artifacts while preserving shear wave signals. Algorithmically, it was important to consider the lateral regression kernel size and position and the temporal window. Procedurally, both nerve echogenicity and transducer compression were determined to impact the measured SWS. Shear waves were successfully measured in the median nerve proximal to the carpal tunnel, but SWEI measurements were significantly compromised within the carpal tunnel itself. The velocity-based SWSs were statistically significantly higher than the displacement SWSs (p < 0.0001), demonstrating for the first time dispersion in the median nerve in vivo using SWEI.

Spring-damper equivalents of the fractional, poroelastic, and poroviscoelastic models for elastography

In MR elastography, it is common to use an elastic model for the tissue's response in order to interpret the results properly. More complex models, such as viscoelastic, fractional viscoelastic, poroelastic, or poroviscoelastic ones, are also used. These models appear at first sight to be very different, but here it is shown that they may all be expressed in terms of elementary viscoelastic models. For a medium expressed with fractional models, many elementary spring-damper combinations are added, each of them weighted according to a long-tailed distribution of time constants or relaxation frequencies. This may open up a more physical interpretation of fractional models. The shear-wave component of the poroelastic model is shown to be modeled exactly by a three-component Zener model. The extended poroviscoelastic model is found to be equivalent to what is called a non-standard four-parameter model. Accordingly, the large number of parameters in the porous models can be reduced to the same number as in their viscoelastic equivalents. While the individual displacements from the solid and fluid parts cannot be measured individually, the main use of the poro(visco)elastic models is therefore as a physics-based method for determining parameters in a viscoelastic model.

Robust Phase Velocity Dispersion Estimation of Viscoelastic Materials Used for Medical Applications Based on the Multiple Signal Classification Method

Ultrasound shear wave elastography (SWE) is emerging as a promising imaging modality for the noninvasive evaluation of tissue mechanical properties. One of the ways to explore the viscoelasticity is through analyzing the shear wave velocity dispersion curves. To explore the dispersion, it is necessary to estimate the shear wave velocity at each frequency. An increase of the available spectrum to be used for phase velocity estimation is significant for a tissue dispersion analysis in vivo. A number of available methods suffer because the available spectrum that one can work with is limited. We present an alternative method to the classical 2-D Fourier transform (2D-FT) that uses the multiple signal classification (MUSIC) technique to provide robust estimation of the -space and phase velocity dispersion curves. We compared results from the MUSIC method with the 2D-FT technique twofold: by searching for maximum peaks and gradient-based strategy. We tested this method on digital phantom data created using finite-element methods (FEMs) in viscoelastic media as well as on the experimental phantoms used in the Radiological Society of North America Quantitative Imaging Biomarker Alliance effort for the standardization of shear wave velocity in liver fibrosis applications. In addition, we evaluated the algorithm with different levels of added noise for FEMs. The MUSIC algorithm provided dispersion curves estimation with lower errors than the conventional 2D-FT method. The MUSIC method can be used for the robust evaluation of shear wave velocity dispersion curves in viscoelastic media.

Investigating Shear Wave Physics in a Generic Pediatric Left Ventricular Model via In Vitro Experiments and Finite Element Simulations

Shear wave elastography (SWE) is a potentially valuable tool to noninvasively assess ventricular function in children with cardiac disorders, which could help in the early detection of abnormalities in muscle characteristics. Initial experiments demonstrated the potential of this technique in measuring ventricular stiffness; however, its performance remains to be validated as complicated shear wave (SW) propagation characteristics are expected to arise due to the complex non-homogenous structure of the myocardium. In this work, we investigated the (i) accuracy of different shear modulus estimation techniques (time-of-flight (TOF) method and phase velocity analysis) across myocardial thickness and (ii) effect of the ventricular geometry, surroundings, acoustic loading, and material viscoelasticity on SW physics. A generic pediatric (10-15-year old) left ventricular model was studied numerically and experimentally. For the SWE experiments, a polyvinylalcohol replicate of the cardiac geometry was fabricated and SW acquisitions were performed on different ventricular areas using varying probe orientations. Additionally, the phantom's stiffness was obtained via mechanical tests. The results of the SWE experiments revealed the following trends for stiffness estimation across the phantom's thickness: a slight stiffness overestimation for phase speed analysis and a clear stiffness underestimation for the TOF method for all acquisitions. The computational model provided valuable 3-D insights in the physical factors influencing SW patterns, especially the surroundings (water), interface force, and viscoelasticity. In conclusion, this paper presents a validation study of two commonly used shear modulus estimators for different ventricular locations and the essential role of SW modeling in understanding SW physics in the pediatric myocardium.

Review: Mechanical Characterization of Carotid Arteries and Atherosclerotic Plaques

Cardiovascular disease (CVD) is a leading cause of death and is in the majority of cases due to the formation of atherosclerotic plaques in arteries. Initially, thickening of the inner layer of the arterial wall occurs. Continuation of this process leads to plaque formation. The risk of a plaque to rupture and thus to induce an ischemic event is directly related to its composition. Consequently, characterization of the plaque composition and its proneness to rupture are of crucial importance for risk assessment and treatment strategies. The carotid is an excellent artery to be imaged with ultrasound because of its superficial position. In this review, ultrasound-based methods for characterizing the mechanical properties of the carotid wall and atherosclerotic plaque are discussed. Using conventional echography, the intima media thickness (IMT) can be quantified. There is a wealth of studies describing the relation between IMT and the risk for myocardial infarction and stroke. Also the carotid distensibility can be quantified with ultrasound, providing a surrogate marker for the cross-sectional mechanical properties. Although all these parameters are associated with CVD, they do not easily translate to individual patient risk. Another technique is pulse wave velocity (PWV) assessment, which measures the propagation of the pressure pulse over the arterial bed. PWV has proven to be a marker for global arterial stiffness. Recently, an ultrasound-based method to estimate the local PWV has been introduced, but the clinical effectiveness still needs to be established. Other techniques focus on characterization of plaques. With ultrasound elastography, the strain in the plaque due to the pulsatile pressure can be quantified. This technique was initially developed using intravascular catheters to image coronaries, but recently noninvasive methods were successfully developed. A high correlation between the measured strain and the risk for rupture was established. Acoustic radiation force impulse (ARFI) imaging also provides characterization of local plaque components based on mechanical properties. However, both elastography and ARFI provide an indirect measure of the elastic modulus of tissue. With shear wave imaging, the elastic modulus can be quantified, although the carotid artery is one of the most challenging tissues for this technique due to its size and geometry. Prospective studies still have to establish the predictive value of these techniques for the individual patient. Validation of ultrasound-based mechanical characterization of arteries and plaques remains challenging. Magnetic resonance imaging is often used as the "gold" standard for plaque characterization, but its limited resolution renders only global characterization of the plaque. CT provides information on the vascular tree, the degree of stenosis, and the presence of calcified plaque, while soft plaque characterization remains limited. Histology still is the gold standard, but is available only if tissue is excised. In conclusion, elastographic ultrasound techniques are well suited to characterize the different stages of vascular disease.

Ultrasound Shear Wave Viscoelastography: Model-Independent Quantification of the Complex Shear Modulus

Ultrasound shear wave elastography methods are commonly used for estimation of mechanical properties of soft biological tissues in diagnostic medicine. A limitation of most currently used elastography methods is that they yield only the shear storage modulus ( G^' ) but not the loss modulus ( G^'' ). Therefore, no information on viscosity or loss tangent (tan δ) is provided. In this paper, an ultrasound shear wave viscoelastography method is developed for model-independent quantification of frequency-dependent viscoelastic complex shear modulus of macroscopically homogeneous tissues. Three in vitro tissue-mimicking phantoms and two ex vivo porcine liver samples were evaluated. Shear waves were remotely induced within the samples using several acoustic radiation force pushes to generate a semicylindrical wave field similar to those generated by most clinically used elastography systems. The complex shear modulus was estimated over a broad frequency range (up to 1000 Hz) through the analytical solution of the developed inverse wave propagation problem using the measured shear wave speed and amplitude decay versus propagation distance. The shear storage and loss moduli obtained for the in vitro phantoms were compared with those from a planar shear wave method and the average differences over the whole frequency range studied were smaller than 7% and 15%, respectively. The reliability of the proposed method highlights its potential for viscoelastic tissue characterization, which may improve noninvasive diagnosis.

Characterization of material properties of soft solid thin layers with acoustic radiation force and wave propagation

Evaluation of tissue engineering constructs is performed by a series of different tests. In many cases it is important to match the mechanical properties of these constructs to those of native tissues. However, many mechanical testing methods are destructive in nature which increases cost for evaluation because of the need for additional samples reserved for these assessments. A wave propagation method is proposed for characterizing the shear elasticity of thin layers bounded by a rigid substrate and fluid-loading, similar to the configuration for many tissue engineering applications. An analytic wave propagation model was derived for this configuration and compared against finite element model simulations and numerical solutions from the software package Disperse. The results from the different models found very good agreement. Experiments were performed in tissue-mimicking gelatin phantoms with thicknesses of 1 and 4 mm and found that the wave propagation method could resolve the shear modulus with very good accuracy, no more than 4.10% error. This method could be used in tissue engineering applications to monitor tissue engineering construct maturation with a nondestructive wave propagation method to evaluate the shear modulus of a material.