Citations

The response of an embedded sphere in a viscoelastic medium excited by acoustic radiation force has been studied in both the time- and frequency-domains. This model is important because it can be used to characterize the viscoelastic properties of the medium by fitting the response to the theoretical model. The Kelvin–Voigt model has been used exclusively in these models. An extension to the previously reported models is described so that any viscoelastic rheological model can be used. This theoretical development describes the generalized embedded sphere response both in the time and frequency domains. Comparing the results from derivations in both domains showed very good agreement with a median absolute error (MAE) ranging from 0.0044 to 0.0072. Good agreement is demonstrated with finite element model simulations and the theory with a MAE of 0.006. Lastly, results for characterization of gelatin and rubber materials with the new theory are shown where the MAE values were used to determine which rheological model best describes the measured responses.

Characterization of viscoelastic soft tissues and materials has been a subject of active research for the past two decades. Techniques involving measuring the motion of embedded spheres in viscoelastic media have been employed to measure the viscoelastic material properties of the media surrounding the sphere. The published work using this technique has been restricted to using the Kelvin–Voigt model, which has worked for gelatin-based materials. We report an extension of this method using different viscoelastic rheological models such as the Maxwell, generalized Maxwell, Zener, and Kelvin–Voigt fractional derivative models. We performed experiments using a focused 3-MHz transducer to produce radiation force and a 7.5-MHz pulse-echo transducer to measure the sphere motion. Two phantoms were tested; one made of gelatin and another made of rubber with stainless steel spheres embedded in the materials. The response was fitted with the generalized theoretical model to find the material properties over bandwidths of 25–3000 Hz. The median absolute errors ranged from 0.0036–0.0421 and 0.0365–0.0879 for the gelatin and rubber phantoms, respectively. This generalized method offers added flexibility to characterize different types of viscoelastic materials using the most appropriate rheological model. [Work supported in part by NIH Grant nos. EB002167 and DK082408.]

Multiple methods have been proposed to characterize the viscoelastic material properties of soft tissues to differentiate normal from pathological tissue. Shearwave dispersion ultrasound vibrometry is a method that uses the dispersion of the shear wave velocity to characterize tissue shear elasticity and viscosity. It has recently been shown [M. W. Urban and J. F. Greenleaf, Phys. Med. Biol. 54, 5919–5933 (2009)] that the Kramers–Kronig relationships can be applied to shear wave measurements in ex vivo skeletal muscle over a frequency bandwidth of 100–600 Hz. We will describe this process where shear wave attenuation is modeled using a power law, and the shear wave velocity dispersion is predicted by applying the Kramers–Kronig relationships. In this study, we apply this method to shear wave propagation measurements made in different soft tissues such as ex vivo porcine skeletal muscle and kidney and in vivo porcine liver. The shear wave velocity predictions using the Kramers–Kronig relationships agree with the velocity measurements. The mean square error for these tissues ranged from 0.0024–0.0625 m2/s2. The Kramers–Kronig relationships can be used in shear wave propagation measurements in different types of soft tissues. [This work was supported in part by NIH Grants Nos. EB002167 and DK082408.]

Vibro-acoustography (VA) is an imaging method based on ultrasound radiation force. In this method, a two dimensional image is formed by scanning two co-focused ultrasound beams with slightly different frequencies over the object (biological tissue) in a C-scan format and recording resulting sound that is emitted from the focal region at the difference frequency. As in other ultrasound-based imaging modalities, it is important to study the thermal safety of the technique. This paper addresses tissue heating due to a VA scan using a concentric confocal transducer. The three dimensional ultrasound intensity field calculated by Field II is used with the bio-heat equation to estimate tissue heating. Results calculated with thermal conduction and with blood perfusion, with conduction and without perfusion, and without conduction and without perfusion are compared. Maximum temperature rise occurs in the transducer near field during VA scans. Heating during one VA scan is below 0.05 °C for soft tissue with attenuation coefficient of 0.3, 0.5, or 0.7 dB/cm MHz. It is concluded that temperature rise in tissue is not significant. [Work supported by NIH Grants CA 91956, CA 127235, and CA121579. Some of the techniques are patented by Mayo Clinic and the some of the authors (M.F. and J.F.G.).]

Considerable interest in the elastic properties of soft tissue has increased in medicine due to their clinical relevance for monitoring various diseases as well as a biomarker for cancer. A recent emerging field is the use of acoustic radiation force for imaging and estimating the elastic properties of tissue. Newly developed imaging modalities include shear wave elasticity imaging, supersonic shear wave imaging, acoustic radiation force impulse imaging, and vibro-acoustography. In these new methods, the shear wave is used to estimate the elasticity of tissue. We have developed a novel surface wave method for noninvasively estimating the elasticity of tissue [X. Zhang et al., J. Acoust. Soc. Am., 122, 2522-2525 (2007)]. In this method, a localized ultrasound radiation force is remotely and noninvasively applied inside the tissue. The surface wave speed is used to estimate the elasticity of tissue. This method has been further developed and applied to estimate the viscoelasticity of animal myocardium tissue. In this abstract, we report our recent results of in vitro studies on animal myocardium tissue. Both the surface wave and shear wave are measured and analyzed. Noninvasive characterization of viscoelastic properties of myocardium tissue may be a very important tool for assessing heart function.

Harmonic or pulsed radiation pressure and subsequent measurement of the tissue response can be used to accurately quantitatively measure fundamental material properties of tissue. The measurement of shear wave dispersion can be used to estimate elastic shear moduli of tissue using an appropriate model. Fundamental model free properties such as complex modulus can also be measured. Ultrasound radiation pressure is used to induce free propagating shear waves. The measurable properties of the shear waves such as speed are sensitive to only the local material properties of the tissue under certain circumstances. A model relating the shear wave speed as a function of frequency is related to the elastic and viscous moduli within small regions of tissue according to, for instance, the Voigt model. Shear and elastic moduli in tissue are measured with high accuracy and precision given appropriate models of wave propagation within the geometry of the tissue. Complex modulus in liver of live pig and other tissues have been made. Careful use of shear wave propagation and subsequent measurements can provide fundamental quantitative measurements of tissue mechanical properties if models are accurate. An application of this method is the noninvasive measurement of liver stiffness as a surrogate for fibrosis.

The propagation speed of shear waves is related to frequency and the complex stiffness (shear elasticity and viscosity) of the medium. A method is presented to solve for shear elasticity and viscosity of a homogeneous medium by measuring shear wave speed dispersion. Harmonic radiation force, introduced by modulating the energy density of incident ultrasound, is used to generate cylindrical shear waves of various frequencies in a homogeneous medium. The speed of shear waves is measured from phase shift detected over the distance propagated. Measurements of shear wave speed at multiple frequencies are fit with the theoretical model to solve for the complex stiffness of the medium. Experiments in gelatin phantoms show promising results validated by an independent method. Practical considerations and challenges in possible medical applications are discussed.

A quantitative model is presented for a sphere vibrated by two ultrasound beams of frequency ω1 and ω2. Due to the interference of two sound beams, the radiation force has a dynamic component of frequency ω2−ω1. The radiation impedance and mechanical impedance of the sphere are then used to compute the vibration speed of the sphere. Vibration speed versus vibration frequency is measured by laser vibrometer on several spheres, both in water and in gel phantom. These experimental results are used to verify the model. This method can be used to estimate the material properties of the medium (e.g., shear modulus) surrounding the sphere.