Viscoelastic properties of soft gels: comparison of magnetic resonance elastography and dynamic shear testing in the shear wave regime

Okamoto, Ruth J.; Clayton, Erik H.; Bayly, Philip V.

doi:10.1088/0031-9155/56/19/014

Cited by 85 publications

(103 citation statements)

References 42 publications

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“…Bessel functions form the basis of the analytical solution. Following Okamoto [20], we simulated the u 3 wave field; however, to highlight the importance of distortion-based inversion, we add to this solution harmonic rigid body motion at the fundamental frequency (Fig. 1).…”

Section: Viscoelastic Parameter Estimationmentioning

confidence: 99%

“…We use both a closed-form analytical wave field and experimental data from a gelatin-based tissue analog [20] to demonstrate our distortion-based LFE approach on viscoelastic isotropic media. Wave propagation in a transversely isotropic material is simulated by the finite element (FE) model and used to verify the extension of our LFE method to anisotropic materials.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mechanical Properties of Viscoelastic Media by Local Frequency Estimation of Divergence-Free Wave Fields

Clayton¹,

Okamoto

Bayly

2013

Journal of Biomechanical Engineering

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Magnetic resonance elastography (MRE) is an imaging modality with which mechanical properties can be noninvasively measured in living tissue. Magnetic resonance elastography relies on the fact that the elastic shear modulus determines the phase velocity and, hence the wavelength, of shear waves which are visualized by motion-sensitive MR imaging. Local frequency estimation (LFE) has been used to extract the local wavenumber from displacement wave fields recorded by MRE. LFE -based inversion is attractive because it allows material parameters to be estimated without explicitly invoking the equations governing wave propagation, thus obviating the need to numerically compute the Laplacian. Nevertheless, studies using LFE have not explicitly addressed three important issues: (1) tissue viscoelasticity; (2) the effects of longitudinal waves and rigid body motion on estimates of shear modulus; and (3) mechanical anisotropy. In the current study we extend the LFE technique to (1) estimate the (complex) viscoelastic shear modulus in lossy media; (2) eliminate the effects of longitudinal waves and rigid body motion; and (3) determine two distinct shear moduli in anisotropic media. The extended LFE approach is demonstrated by analyzing experimental data from a previouslycharacterized, isotropic, viscoelastic, gelatin phantom and simulated data from a computer model of anisotropic (transversely isotropic) soft material.

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Section: Viscoelastic Parameter Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mechanical Properties of Viscoelastic Media by Local Frequency Estimation of Divergence-Free Wave Fields

Clayton¹,

Okamoto

Bayly

2013

Journal of Biomechanical Engineering

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“…The samples were placed on a custom-built dynamic shear testing system (see Fig. 2), which was previously described [30]. The lower surface of the sample underwent small amplitude ($0.03 mm) horizontal oscillations created by a voice coil driving a flexure.…”

Section: Dynamic Shearmentioning

confidence: 99%

“…Control gels were also tested in two orientations by rotating the sample 90 deg after the first test. Contact was determined by lowering the top plate using a digital micrometer until oscillatory forces were observed in both the left and right force transducers [30]. The voice coil was excited using a "chirp," which swept through frequencies from 0 to 200 Hz in 15 s. A data acquisition and control system (Siglab 20-22, Spectral Dynamics, San Jose, CA) averaged data from three The vertical and horizontal lines indicate the dominant fiber directions of the aligned gel.…”

Section: Dynamic Shearmentioning

confidence: 99%

Elastic Characterization of Transversely Isotropic Soft Materials by Dynamic Shear and Asymmetric Indentation

Namani

Feng

Okamoto

et al. 2012

Journal of Biomechanical Engineering

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The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B ¼ 11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20-40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08 6 0. 42 kPa (mean 6 std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58 6 0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.

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“…In the MRE method, the organs were vibrated to generate transverse waves and the stiffness of the organs was quantitatively calculated from the resulting wave patterns (Muthupillai, et al, 1996). MRE measurements have also been conducted on the stiffness of soft matters and validation of the MRE procedures was discussed (Hamhaber, et al, 2003;Atay, et al, 2008;Mariappan, et al, 2009Mariappan, et al, , 2010Perreard, et al, 2010;Okamoto, et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic modulus of agarose gels by magnetic resonance elastography using Micro-MRI

Suzuki

Tadano

Goto

et al. 2015

Mechanical Engineering Journal

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This study aimed to apply magnetic resonance elastography (MRE) using micro-magnetic resonance imaging (micro-MRI) system for the measurements of viscoelastic modulus in soft matters. The rectangular specimens of 90 × 70 × 50 mm were made of agarose gel with five kinds of stiffness by changing concentrations. The specimens were oscillated with longitudinal waves transmitted by an elastic-bar from a vibration generator in a micro-MRI system. Since the viscoelastic properties depend on the excitation frequency and amplitude, the experimental conditions were selected in the range of 50-250 Hz and 0.1-0.5 mm. The viscoelastic modulus was expressed as storage shear modulus G′ and loss shear modulus G″. As a result, G′ increased with the frequency and amplitude, and the difference of G′ between hard and soft gels was obtained. The viscoelastic modulus of agarose gels was measured using the MRE system under the excitation conditions. Furthermore, double-layer specimens composed of 0.6 and 2.0 wt% gels were examined as an application of the MRE system. The difference of wave pattern between the hard and soft parts was observed. The values of G′ in the soft parts of the double-layer specimens corresponded to the value of the single-layer specimen, but the values of G′ in the hard parts were varied. and Klatt et al. (2010) have also measured the viscoelastic modulus of livers in vivo.The authors developed an MRE system consisting of a micro-magnetic resonance imaging (micro-MRI) with 0.3 T, a bar-type transmitter, and a vibration generator, which allowed the excitation frequency of 50-250 Hz and the amplitude of 0.1-0.5 mm (Tadano, et al., 2012). The bar-type transmitter and the vibration generator were used to generate strong excitation. In that study, it was confirmed that the distribution of displacement was obtained within the agarose gel of 1.2 wt% concentration under the excitation conditions. Furthermore, to decrease the error of viscoelastic modulus, the authors proposed a calculation method for the MRE measurements under the low magnetic field based on the integration of the displacement (Jiang and Nakamura, 2011). It is necessary to apply the MRE instrument and the calculation method to the measurements of viscoelastic modulus of soft matters and to discuss the availability of the system. Therefore, the present study aimed to investigate the effect of the excitation frequency of 50-250 Hz and the amplitude of 0.1-0.5 mm on the viscoelastic modulus of agarose gels with five kinds of stiffness by using the MRE system. Furthermore, the distributions of the displacement and viscoelastic modulus in the specimens consisting of hard and soft gel parts were investigated as an application of the MRE system. Three kinds of the double-layer specimen were examined in the study. MethodsWhen a specimen was excited with a sine wave in the MRI, local displacements in the specimen under a gradient magnetic field were calculated from the phase shift of MR signal (Muthupillai, et al., 1996;Manduca, et al., 2001). A complex...

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Viscoelastic properties of soft gels: comparison of magnetic resonance elastography and dynamic shear testing in the shear wave regime

Cited by 85 publications

References 42 publications

Mechanical Properties of Viscoelastic Media by Local Frequency Estimation of Divergence-Free Wave Fields

Mechanical Properties of Viscoelastic Media by Local Frequency Estimation of Divergence-Free Wave Fields

Elastic Characterization of Transversely Isotropic Soft Materials by Dynamic Shear and Asymmetric Indentation

Viscoelastic modulus of agarose gels by magnetic resonance elastography using Micro-MRI

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