Sara Aristizabal

On Lamb and Rayleigh Wave Convergence in Viscoelastic Tissues

Characterization of the viscoelastic material properties of soft tissue has become an important area of research over the last two decades. Our group has been investigating the feasibility of using a shear wave dispersion ultrasound vibrometry (SDUV) method to excite Lamb waves in organs with plate-like geometry to estimate the viscoelasticity of the medium of interest. The use of Lamb wave dispersion ultrasound vibrometry to quantify the mechanical properties of viscoelastic solids has previously been reported. Two organs, the heart wall and the spleen, can be readily modeled using plate-like geometries. The elasticity of these two organs is important because they change in pathological conditions. Diastolic dysfunction is the inability of the left ventricle (LV) of the heart to supply sufficient stroke volumes into the systemic circulation and is accompanied by the loss of compliance and stiffening of the LV myocardium. It has been shown that there is a correlation between high splenic stiffness in patients with chronic liver disease and strong correlation between spleen and liver stiffness. Here, we investigate the use of the SDUV method to quantify the viscoelasticity of the LV free-wall myocardium and spleen by exciting Rayleigh waves on the organs surface and measuring the wave dispersion (change of wave velocity as a function of frequency) in the frequency range 40–500 Hz. An equation for Rayleigh wave dispersion due to cylindrical excitation was derived by modeling the excised myocardium and spleen with a homogenous Voigt material plate immersed in a nonviscous fluid. Boundary conditions and wave potential functions were solved for the surface wave velocity. Analytical and experimental convergence between the Lamb and Rayleigh waves is reported in a finite element model of a plate in a fluid of similar density, gelatin plate and excised porcine spleen and left-ventricular free-wall myocardium.

Modeling transversely isotropic, viscoelastic, incompressible tissue-like materials with application in ultrasound shear wave elastography.

In this paper, we propose a method to model the shear wave propagation in transversely isotropic, viscoelastic and incompressible media. The targeted application is ultrasound-based shear wave elastography for viscoelasticity measurements in anisotropic tissues such as the kidney and skeletal muscles. The proposed model predicts that if the viscoelastic parameters both across and along fiber directions can be characterized as a Voigt material, then the spatial phase velocity at any angle is also governed by a Voigt material model. Further, with the aid of Taylor expansions, it is shown that the spatial group velocity at any angle is close to a Voigt type for weakly attenuative materials within a certain bandwidth. The model is implemented in a finite element code by a time domain explicit integration scheme and shear wave simulations are conducted. The results of the simulations are analyzed to extract the shear wave elasticity and viscosity for both the spatial phase and group velocities. The estimated values match well with theoretical predictions. The proposed theory is further verified by an ex vivo tissue experiment measured in a porcine skeletal muscle by an ultrasound shear wave elastography method. The applicability of the Taylor expansion to analyze the spatial velocities is also discussed. We demonstrate that the approximations from the Taylor expansions are subject to errors when the viscosities across or along the fiber directions are large or the maximum frequency considered is beyond the bandwidth defined by radii of convergence of the Taylor expansions.

Phase Aberration and Attenuation Effects on Acoustic Radiation Force-Based Shear Wave Generation

Elasticity is measured by shear wave elasticity imaging (SWEI) methods using acoustic radiation force to create the shear waves. Phase aberration and tissue attenuation can hamper the generation of shear waves for in vivo applications. In this study, the effects of phase aberration and attenuation in ultrasound focusing for creating shear waves were explored. This includes the effects of phase shifts and amplitude attenuation on shear wave characteristics such as shear wave amplitude, shear wave speed, shear wave center frequency, and bandwidth. Two samples of swine belly tissue were used to create phase aberration and attenuation experimentally. To explore the phase aberration and attenuation effects individually, tissue experiments were complemented with ultrasound beam simulations using fast object-oriented C++ ultrasound simulator (FOCUS) and shear wave simulations using finite-element-model (FEM) analysis. The ultrasound frequency used to generate shear waves was varied from 3.0 to 4.5 MHz. Results: The measured acoustic pressure and resulting shear wave amplitude decreased approximately 40%-90% with the introduction of the tissue samples. Acoustic intensity and shear wave displacement were correlated for both tissue samples, and the resulting Pearsons correlation coefficients were 0.99 and 0.97. Analysis of shear wave generation with tissue samples (phase aberration and attenuation case), measured phase screen, (only phase aberration case), and FOCUS/FEM model (only attenuation case) showed that tissue attenuation affected the shear wave generation more than tissue aberration. Decreasing the ultrasound frequency helped maintain a focused beam for creation of shear waves in the presence of both phase aberration and attenuation.

Ultrasound-based shear wave evaluation in transverse isotropic tissue mimicking phantoms and muscle

Ultrasound radiation force-based methods often neglect the inherent anisotropy nature of tissue. Measurements were made in four cube-shaped phantoms composed of fibrous or fishing line material embedded in 8% and 14% gelatin concentrations and in pork tenderloin. Measurements were made at different angles relative to the transducer. For the fibrous phantom, the mean and standard deviations of the shear wave speeds for 8% and 14% gelatin along the fibers were (3.60 ± 0.03 and 4.10 ± 0.11 m/s) and across the fibers were (3.18 ± 0.12 and 3.90 ± 0.02 m/s), respectively. For the fishing line material phantom the shear wave speeds for 8% and 14% gelatin along the fibers were (2.86 ± 0.20 and 3.40 ± 0.09 m/s) and across the fibers were (2.44 ± 0.24 and 2.84 ± 0.14 m/s), respectively. For the pork muscle, the shear wave speeds along the fibers at two different locations were (3.83 ± 0.16 and 3.86 ± 0.12 m/s ) and across the fibers were (2.73 ± 0.18 and 2.70 ± 0.16 m/s), respectively. The fibrous gelatin-based phantoms and the fishing line gelatin-based phantoms exhibited anisotropy that resembles that observed in pork muscle.

Effects of phase aberration on acoustic radiation force-based shear wave generation

Tissue elasticity is measured by shear wave elasticity imaging methods using acoustic radiation force to create the shear waves. Reliable tissue elasticity measurements are achieved with strong shear waves. Phase aberration and tissue attenuation can hamper the generation of shear waves for in vivo applications. In this study we explored how phase aberration affects ultrasound focusing for creating shear waves and evaluate the resulting shear wave amplitude and the shear wave velocity. A Verasonics ultrasound system equipped with a linear, a curved linear, and a phased array transducer (L7-4, C4-2 and P4-2) was used. An excised piece of swine belly tissue consisted of the skin, subcutaneous fat, and muscle were placed on top of the elastic phantom to evaluate the shear wave produced when transmitting through the different layers. The ultrasound frequency used for three transducers was varied to evaluate the resulting shear waves with the different tissue layers. Analysis of shear wave production with real tissue layers showed that large fat layers and combinations of skin, fat, and muscle defocused the ultrasound beam most, thereby decreasing the shear wave amplitudes.

Application of acoustoelasticity to evaluate non-linear modulus in ex vivo kidneys

Dynamic elastography techniques estimate the elastic shear modulus in order to evaluate the health of different soft tissues. However, the diagnostic potential of these methods is limited as the knowledge of shear elasticity may not be sufficient to reach a clinical diagnosis. To better understand pathologies, new methods that investigate non-linear tissue mechanical properties have been proposed. It has previously been shown that shear wave speed changes with respect to an applied stress, a phenomenon called acoustoelasticity (AE). Using AE by compressing a medium and measuring the shear wave speed at different compression levels, we can estimate the third order non-linear modulus, A. The goal of this study was to evaluate the feasibility of performing AE in ex vivo kidneys. We evaluated the non-linear characteristics of ten ex vivo porcine kidneys embedded in 10% gelatin. Measurements were performed under three different conditions: a) presence or absence of a plate attached to the transducer, b) progressive or regressive compression and (c) views of the kidney (longitudinal and transverse). The results obtained demonstrated that it is possible to recover the non-linear modulus A by monitoring changes in strain and shear modulus during kidney deformation.

Evaluation of the nonlinear modulus in renal transplant patients using progressive and regressive compression and shear wave measurements

End-stage renal disease (ESRD) is an irreversible deterioration in the renal function in which the body loses its ability to maintain the fluid and metabolic balance. Transplantation is the treatment of choice for patients with ESRD. After transplantation, biopsies are performed to monitor the function of the kidney transplant over time. Due to the invasive nature of biopsies, we are investigating the potential of noninvasive shear wave based methods such as acoustoelasticity (AE) to estimate the nonlinear mechanical properties of tissues. Using AE by compressing a medium and measuring the shear wave speed at different compression levels, we can estimate the third order nonlinear coefficient, A. The goal of this study was to evaluate the feasibility of performing AE using two directions of compression and to evaluate the potential of A as an indicator of the presence of renal fibrosis in the transplanted kidney.

Evaluation of the feasibility of measuring the fourth-order nonlinear parameter D in Ex vivo kidneys

Current elastography techniques can measure mechanical properties of soft tissues by estimating the elastic shear modulus, μ0. Recently, the assessment of tissue nonlinearity using acoustoelasticity (AE) has shown some promising results in differentiating healthy from malignant tissue by estimating a third-order nonlinear coefficient A. To fully characterize the nonlinear properties of the tissue, it may be necessary to develop techniques to also reliably estimate the fourth-order elastic constant D as the combination with the other parameters μ and A could provide diagnostic discriminatory power. This study evaluates the implementation of a three-parameter fit (μ0, A, D) to estimate the nonlinear properties of ex vivo kidneys using the shear modulus, μ vs. strain, ∊ estimates obtained when the phantoms are subjected to compression.

Compressing and shearing the transplanted kidney

Kidney transplantation is one treatment for end-stage renal disease. Transplant rejection is typically evaluated with an invasive biopsy. Noninvasive methods for evaluating renal transplants would be beneficial for frequent evaluation. We propose the use of shear wave elastography (SWE) to evaluate viscoelastic properties in renal transplants. Further, we also use acoustoelasticity to measure the nonlinear modulus of the renal transplants. Acoustoelasticity is the phenomenon where the shear wave velocity (SWV) in a material varies with applied stress and is quantified by a nonlinear modulus, A. By applying pressure with the ultrasound transducer, stress is applied to the kidney under investigation and B-mode imaging was used to measure induced strain and SWE was used to make measurements of SWV. Using relationships involving the measured strain and shear moduli at different compression levels, we can obtain estimates of A. In our ongoing study, we use a General Electric Logiq E9 to perform SWE measurement...

Use of shear wave ultrasound vibrometry for detection of simulated esophageal malignancy in ex vivo porcine esophagi

Esophageal cancer is a malignant neoplasm with poor outcomes. Determination of local disease progression is a major determining factor in treatment modality, radiation dose, radiation field and subsequent surgical therapy. Discrimination of true tumor extent is difficult given the similarity of soft tissues of the malignancy compared to non-malignant tissues using current imaging modalities. A possible method to discriminate between these tissues may be to exploit mechanical properties to diagnostic advantage, as malignant tissues tend to be stiffer relative to normal adjacent tissue. Shear waves propagate faster in stiffer tissues relative to softer tissues. This may be measured by using ultrasound based shear wave vibrometry. In this method, acoustic radiation force is used to create a shear wave in the tissue of interest and ultrafast ultrasound imaging is used to track the propagating wave to measure the wave velocity and estimate the shear moduli. In this study we created simulated malignant lesions (1.5 cm length) using radiofrequency ablation in ex vivo esophageal samples with varied progression (partial thickness n = 4, and full thickness n = 5) and used normal regions of the same esophageal specimen as controls. Shear wave vibrometry was used to measure shear wave group velocity and shear wave phase velocity in the ex vivo specimens. These values were used to estimate shear moduli using an elastic shear wave model and elastic and viscoelastic Lamb wave models. Our results show that the group and phase velocities increase due to both full and mucosal ablation, and that discrimination may be provided by higher order analysis using viscoelastic Lamb wave fitting. This technique may have application for determination of extent of early esophageal malignancy and warrants further investigation using in vivo approaches to determine performance compared to current imaging modalities.