Axisymmetric diffraction of a cylindrical transverse wave by a viscoelastic spherical inclusion

Schwartz, Benjamin L.; Liu, Yifei; Royston, Thomas J.; Magin, Richard L.

doi:10.1016/j.jsv.2015.11.023

Cited by 11 publications

(8 citation statements)

References 32 publications

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“…Boumdary effects likely play a role in distorting the wave from the ideal, but in the heterogenous phantom there are two opportunities for miss characterizing the shear moduli inputs, namely the embedding gel and the spherical heterogeneity. Adjusting, for instance,

J m μ_{2}

, when solving the forward problem to better match the experimental data will change the entire linear profile as the displacement of each region depends on the shear moduli of both regions [21]. …”

Section: Discussionmentioning

confidence: 99%

Mechanical analysis of an axially symmetric cylindrical phantom with a spherical heterogeneity for MR elastography

2016

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Cylindrical homogenous phantoms for magnetic resonance (MR) elastography in biomedical research provide one way to validate an imaging systems performance, but the simplified geometry and boundary conditions can cloak complexity arising at tissue interfaces. In an effort to develop a more realistic gel tissue phantom for MRE, we have constructed a heterogenous gel phantom (a sphere centrally embedded in a cylinder). The actuation comes from the phantom container, with the mechanical waves propagating toward the center, focusing the energy thus allowing for the visualization of high-frequency waves that would otherwise be damped. The phantom was imaged and its stiffness determined using a 9.4 T horizontal MRI with a custom build piezo-elastic MRE actuator. The phantom was vibrated at three frequencies, 250, 500, and 750 Hz. The resulting shear wave images were first used to reconstruct material stiffness maps for thin (1 mm) axial slices at each frequency, from which the complex shear moduli μ were estimated, and then compared with forward modeling using a recently developed theoretical model who took μ as inputs. The overall accuracy of the measurement process was assessed by comparing theory with experiment for selected values of the shear modulus (real and imaginary parts). Close agreement is shown between the experimentally obtained and theoretically predicted wave fields.

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J m μ_{2}

Section: Discussionmentioning

confidence: 99%

Mechanical analysis of an axially symmetric cylindrical phantom with a spherical heterogeneity for MR elastography

2016

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“…42 More recently, exact theoretical solutions have been developed and validated for specific experimental configurations for elastography measurements of isotropic materials in a test tube or other cylindrically-shaped container. [43][44][45][46] These are useful in assessing the quality of numerical inversion algorithms that can then be applied to more complex geometries, including in vivo, where the theoretical solution is not possible.…”

Section: A Background and Motivationmentioning

confidence: 99%

“…Measurable shear wave motion can thus be established throughout the entire specimen. Validation of a theoretical solution for an isotropic homogeneous viscoelastic material 43 has been followed by validation of theoretical solutions for nonhomogeneous, but still axisymmetric, composite test materials comprised of concentric annular regions 44 or a spherical region 45 of differing material properties.…”

Section: A Background and Motivationmentioning

confidence: 99%

“…This type of vibratory excitation has been used in previous studies to create a shear wave field within an excised biological specimen or tissue phantom material placed within a cylindrical test tube. 11,[43][44][45][46][48][49][50] The tube itself is harmonically driven along its axis. The inner wall of the test tube serves as the nonhomogeneous displacement boundary condition applied to the material within it.…”

Section: B Converging Shear Waves In a Finite Cylindrical Regionmentioning

confidence: 99%

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Analytical solution for converging elliptic shear wave in a bounded transverse isotropic viscoelastic material with nonhomogeneous outer boundary

Guidetti

Royston

2018

The Journal of the Acoustical Society of America

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Dynamic elastography methods—based on optical, ultrasonic, or magnetic resonance imaging—are being developed for quantitatively mapping the shear viscoelastic properties of biological tissues, which are often altered by disease and injury. These diagnostic imaging methods involve analysis of shear wave motion in order to estimate or reconstruct the tissue's shear viscoelastic properties. Most reconstruction methods to date have assumed isotropic tissue properties. However, application to tissues like skeletal muscle and brain white matter with aligned fibrous structure resulting in local transverse isotropic mechanical properties would benefit from analysis that takes into consideration anisotropy. A theoretical approach is developed for the elliptic shear wave pattern observed in transverse isotropic materials subjected to axisymmetric excitation creating radially converging shear waves normal to the fiber axis. This approach, utilizing Mathieu functions, is enabled via a transformation to an elliptic coordinate system with isotropic properties and a ratio of minor and major axes matching the ratio of shear wavelengths perpendicular and parallel to the plane of isotropy in the transverse isotropic material. The approach is validated via numerical finite element analysis case studies. This strategy of coordinate transformation to equivalent isotropic systems could aid in analysis of other anisotropic tissue structures.

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“…Dwivedi et al [7] solved a similar configuration as [6] in 1D for a viscoelastic soil. More recently, Schwartz et al [8] proposed an analytical solution to the axisymmetric scattering of a cylindrical incident wave from a spherical inclusion within a viscoelastic isotropic medium in the frequency domain by applying a multi-pole expansion technique.…”

Section: Introductionmentioning

confidence: 99%

Transient Response of a Fluid-Filled, Thick-Walled Spherical Shell Embedded in an Elastic Medium

Bahari

Lefeuve-Mesgouez

Mesgouez³

et al. 2016

E3S Web Conf.

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Abstract. The paper addresses the problem of transient elastodynamics analysis of a thick-walled, fluid-filled spherical shell embedded in an elastic medium with an analytical approach. This configuration is investigated at first step for a full-space case. Di↵erent constitutive relations for the elastic medium, shell material and filling fluid can be considered, as well as di↵erent excitation sources (including S/P wave or plane/spherical incident wave at di↵erent locations). With mapmaking visualisation, the wave propagation phenomena can be described and better understood. The methodology is going to be applied to analysis of the tunnels or other shell like structures under the e↵ect of nearby underground explosion.

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Axisymmetric diffraction of a cylindrical transverse wave by a viscoelastic spherical inclusion

Cited by 11 publications

References 32 publications

Mechanical analysis of an axially symmetric cylindrical phantom with a spherical heterogeneity for MR elastography

Mechanical analysis of an axially symmetric cylindrical phantom with a spherical heterogeneity for MR elastography

Analytical solution for converging elliptic shear wave in a bounded transverse isotropic viscoelastic material with nonhomogeneous outer boundary

Transient Response of a Fluid-Filled, Thick-Walled Spherical Shell Embedded in an Elastic Medium

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