Characterization of transverse isotropy in compressed tissue-mimicking phantoms

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.

Unravelling anisotropic nonlinear shear elasticity in muscles: Towards a non-invasive assessment of stress in living organisms

Acoustoelasticity theory describes propagation of shear waves in uniaxially stressed medium and allows the retrieval of nonlinear elastic coefficients of tissues. In transverse isotropic medium such as muscles the theory leads to 9 different configurations of propagating shear waves (stress axis vs. fibers axis vs. shear wave polarization axis vs. shear wave propagation axis). In this work we propose to use 4 configurations to quantify these nonlinear parameters ex vivo and in vivo. Ex vivo experiments combining ultrasound shear wave elastography and mechanical testing were conducted on iliopsoas pig muscles to quantify three third-order nonlinear coefficients A, H and K that are possibly linked to the architectural structure of muscles. In vivo experiments were performed with human volunteers on biceps brachii during a stretching exercise on an ergometer. A combination of the third order nonlinear elastic parameters was assessed. The knowledge of this nonlinear elastic parameters paves the way to quantify in vivo the local forces produced by muscle during exercise, contraction or movements.

Comparison of ultrasound elastography, magnetic resonance elastography and finite element model to quantify nonlinear shear modulus

Objective. The aim of this study is to validate the estimation of the nonlinear shear modulus (A) from the acoustoelasticity theory with two experimental methods, ultrasound (US) elastography and magnetic resonance elastography (MRE), and a finite element method.Approach. Experiments were performed on agar (2%)-gelatin (8%) phantom considered as homogeneous, elastic and isotropic. Two specific setups were built to ensure a uniaxial stress step by step on the phantom, one for US and a nonmagnetic version for MRE. The stress was controlled identically in both imaging techniques, with a water tank placed on the top of the phantom and filled with increasing masses of water during the experiment. In US, the supersonic shear wave elastography was implemented on an ultrafast US device, driving a 6 MHz linear array to measure shear wave speed. In MRE, a gradient-echo sequence was used in which the three spatial directions of a 40 Hz continuous wave displacement generated with an external driver were encoded successively. Numerically, a finite element method was developed to simulate the propagation of the shear wave in a uniaxially stressed soft medium.Main results. Similar shear moduli were estimated at zero stress using experimental methods,μ0US= 12.3 ± 0.3 kPa andμ0MRE= 11.5 ± 0.7 kPa. Numerical simulations were set with a shear modulus of 12 kPa and the resulting nonlinear shear modulus was found to be -58.1 ± 0.7 kPa. A very good agreement between the finite element model and the experimental models (AUS= -58.9 ± 9.9 kPa andAMRE= -52.8 ± 6.5 kPa) was obtained.Significance. These results show the validity of such nonlinear shear modulus measurement quantification in shear wave elastography. This work paves the way to develop nonlinear elastography technique to get a new biomarker for medical diagnosis.

New Metric to Evaluate Cardiac Anisotropic Mechanics by Directional High-Frequency Ultrasound-Based Transverse Wave Elastography

The evaluation of cardiac anisotropic mechanics is important in the diagnosis of heart disease. However, other representative ultrasound imaging-based metrics, which are capable of quantitatively evaluating anisotropic cardiac mechanics, are insufficient for accurately diagnosing heart disease due to the influence of viscosity and geometry of cardiac tissues. In this study, we propose a new ultrasound imaging-based metric, maximum cosine similarity (MaxCosim), for quantifying anisotropic mechanics of cardiac tissues by evaluating the periodicity of the transverse wave speeds depending on the measurement directions using ultrasound imaging. We developed a high-frequency ultrasound-based directional transverse wave imaging system to measure the transverse wave speed in multiple directions. The ultrasound imaging-based metric was validated by performing experiments on 40 rats randomly assigned to four groups; three doxorubicin (DOX) treatment groups received 10, 15, or 20 mg/kg DOX, while the control group received 0.2 mL/kg saline. In each heart sample, the developed ultrasound imaging system allowed measuring transverse wave speeds in multiple directions, and the new metric was then calculated from 3-D ultrasound transverse wave images to evaluate the degree of anisotropic mechanics of the heart sample. The results of the metric were compared with histopathological changes for validation. A decrease in the MaxCosim value was observed in the DOX treatment groups, with the degree of decrease depending on the dose. These results are consistent with the histopathological features, suggesting that our ultrasound imaging-based metric can quantify the anisotropic mechanics of cardiac tissues and potentially be used for the early diagnosis of heart disease.

Quantitative Estimation of Mechanical Anisotropy Using Acoustic Radiation Force (ARF)-Induced Peak Displacements (PD): In Silico and Experimental Demonstration

Elastic degree of anisotropy (DoA) is a diagnostically relevant biomarker in muscle, kidney, breast, and other organs. Previously, elastic DoA was qualitatively assessed as the ratio of peak displacements (PD) achieved with the long-axis of a spatially asymmetric Acoustic Radiation Force Impulse (ARFI) excitation point spread function (PSF) aligned along versus across the axis of symmetry (AoS) in transversely isotropic materials. However, to better enable longitudinal and cross-sectional analyses, a quantitative measure of elastic DoA is desirable. In this study, qualitative ARFI PD ratios are converted to quantitative DoA, measured as the ratio of longitudinal over transverse shear elastic moduli, using a model empirically derived from Field II and finite element method (FEM) simulations. In silico, the median absolute percent error (MAPE) in ARFI-derived shear moduli ratio (SMR) was 1.75%, and predicted SMRs were robust to variations in transverse shear modulus, Young's moduli ratio, speed of sound, attenuation, density, and ARFI excitation PSF dimension. Further, ARFI-derived SMRs distinguished two materials when the true SMRs of the compared materials differed by as little as 10%. Experimentally, ARFI-derived SMRs linearly correlated with the corresponding ratios measured by Shear Wave Elasticity Imaging (SWEI) in excised pig skeletal muscle ( [Formula: see text], MAPE = 13%) and in pig kidney, in vivo ( [Formula: see text], MAPE = 5.3%). These results demonstrate the feasibility of using the ARFI PD to quantify elastic DoA in biological tissues.

Phase and group velocities for shear wave propagation in an incompressible, hyperelastic material with uniaxial stretch

Objective. Determining elastic properties of materials from observations of shear wave propagation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this study, we derive expressions for the phase velocities of the SH and SV propagation modes as a function of propagation direction in an incompressible, hyperelastic material with uniaxial stretch. Approach. Wave motion is included in the material model by adding incremental, small amplitude motion to the initial, finite deformation. Equations of motion for the SH and SV propagation modes are constructed using the Cauchy stress tensor derived from the strain energy function of the material. Group velocities for the SH and SV propagation modes are derived from the angle-dependent phase velocities. Main results. Sample results are presented for the Arruda–Boyce, Mooney–Rivlin, and Isihara material models using model parameters previously determined in a phantom. Significance. Results for the Mooney–Rivlin and Isihara models demonstrate shear splitting in which the SH and SV propagation modes have unequal group velocities for propagation across the material symmetry axis. In addition, for sufficiently large stretch, the Arruda–Boyce and Isihara material models show cusp structures with triple-valued group velocities for the SV mode at angles of roughly 15° to the material symmetry axis.

The combined importance of finite dimensions, anisotropy, and pre-stress in acoustoelastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties that are altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasistatic tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article, we review how prestress alters both bulk mechanical wave motion and wave motion in one- and two-dimensional waveguides. Key findings are linked to studies on skeletal muscle and the human cornea, as one- and two-dimensional waveguide examples. This study highlights the underappreciated combined acoustoelastic and waveguide challenge to elastography. Can elastography truly determine viscoelastic properties of a material when what it is measuring is affected by both these material properties and unknown prestress and other boundary conditions?

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.

Tractable calculation of the Green's tensor for shear wave propagation in an incompressible, transversely isotropic material

Assessing material properties from observations of shear wave propagation following an acoustic radiation force impulse (ARFI) excitation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this paper, we describe a method to calculate shear wave signals using Green’s tensor methods in an incompressible, transversely isotropic (TI) material characterized by three material parameters. The Green’s tensor is written as the sum of an analytic expression for the SH propagation mode, and an integral expression for the SV propagation mode that can be evaluated by interpolation within precomputed integral functions with an efficiency comparable to the evaluation of a closed-form expression. By using parametrized integral functions, the number of requried numerical integrations is reduced by a factor of 10² − 10⁹ depending on the specific problem under consideration. Results are presented for the case of a point source positioned at the origin and a tall Gaussian source similar to an ARFI excitation. For an experimental configuration with a tilted material symmetry axis, results show that shear wave signals exhibit structures that are sufficiently complex to allow measurement of all three material parameters that characterize an incompressible, TI material.

Which Confounders Have the Largest Impact in Shear Wave Elastography of Muscle and How Can They be Minimized? An Elasticity Phantom, Ex Vivo Porcine Muscle and Volunteer Study Using a Commercially Available System

The goal of the study was to investigate the quantitative impact of region of interest (ROI), software choice, muscle fiber orientation and preload tension on shear wave velocity (SWV). First, SWV was assessed in an isotropic elasticity phantom and ex vivo porcine muscle using a commercially available clinical ultrasound system. Secondly, SWV was acquired in relaxed and stretched calf muscles of healthy volunteers (dorsal extension of the talocrural joint), for both parallel and transverse probe direction to the fibers, as well as for different ROIs and software versions. The effect of intermediate probe-fiber alignments was also analyzed. Finally, the impact of confounding factors on SWV reproducibility was minimized with a second force-controlled volunteer study, in which the calf was isometrically loaded, and fiber orientation and ROI were well-defined. 2046 in vivoSWE images were acquired to analyze SWV reproducibility with different confounder settings. In healthy volunteers, the main variance-contributing factors were in order of importance muscle tension, fiber orientation, horizontal ROI size and insertion depth. Regression analysis showed significantly reduced SWV with increasing insertion depth for each study material. Parallel probe-fiber orientation, muscle stretch and increasing horizontal ROI size led to significantly higher SWV. Based on the results of the study, we provide recommendations to minimize the impact of confounders in musculoskeletal elastography and discuss the main confounding mechanisms and trade-offs between confounding variables. Coefficients of variation can be significantly reduced with a controlled protocol, if the confounders are clinically taken into account.

A comparison of hyperelastic constitutive models applicable to shear wave elastography (SWE) data in tissue-mimicking materials

Shear wave elastography (SWE) techniques have received substantial attention in recent years. Strong experimental data in SWE suggest that shear wave speed changes significantly due to the known acoustoelastic effect (AE). This presents both challenges and opportunities toward in vivo characterization of biological soft tissues. In this work, under the framework of continuum mechanics, we model a tissue-mimicking material as a homogeneous, isotropic, incompressible, hyperelastic material. Our primary objective is to quantitatively and qualitatively compare experimentally measured acoustoelastic data with model-predicted outcomes using multiple strain energy functions. Our analysis indicated that the classic Neo-Hookean and Mooney-Rivlin models are inadequate for modeling the AE in tissue-mimicking materials. However, a subclass of strain energy functions containing both high-order/exponential term(s) and second-order invariant dependence showed good agreement with experimental data. Based on data investigated, we also found that discrepancies may exist between parameters inversely estimated from uniaxial compression and SWE data. Overall, our findings may improve our understanding of clinical SWE results.