Generalized response of a sphere embedded in a viscoelastic medium excited by an ultrasonic radiation force

Abstract

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.

Measurement of the acoustic radiation force on a sphere embedded in a soft solid

“…In order to preserve the obtained mesoscopic structure after insonification, it has been proposed to work in photocurable resins [18] or in yield-stress fluids [19]. However, while the acoustic radiation force is well characterized in simple inviscid fluids, the effect of viscosity on F rad is still under debate [20][21][22][23][24][25] and only a few studies have been devoted to the general case of viscoelastic media [26][27][28][29][30]. It is thus of growing interest to characterize the acoustic radiation force in complex, soft materials.…”

“…Here, we propose a different approach: assuming that the rheology of the gel is known, we measure the acoustic radiation force through the steady-state displacement δr max of a spherical intruder exposed to much longer insonification. Indeed, assuming a no-slip boundary condition at the sphere surface, F rad is related to δr max by [27,29] F rad = 6πG 0 aδr max ,…”

Viscoelastic tissue mimicking phantom validation study with shear wave elasticity imaging and viscoelastic spectroscopy

“…In this study, SWE measurements were limited to 400 Hz due to shear wave attenuation and low signal-tonoise ratio. The KVFD storage, G s (ω), and loss, G l (ω), modulus are described by [19]:…”

The dynamic deformation of a layered viscoelastic medium under surface excitation

“…In incompressible medium Young’s modulus E j , is three times its shear modulus, ${\mu }_1^j$, i.e., $E_j=3{\mu }_1^j$ for each layer. It has been demonstrated that this model adequately describes tissue and tissue-mimicking phantom behavior under short acoustic radiation force (Aglyamov et al, 2007, Urban and Nenadic, 2011, Yoon et al, 2012, Yoon et al, 2013, Yoon et al, 2011). We assume that shear stress applied on the tissue surface is zero, i.e.…”