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

Abstract

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...

Viscoelastic shear properties of in vivo thigh muscles measured by MR elastography

“…In the literature, multiple phantoms have been created with different compositions: agarose, 24 bovine, 25 Wirosil, 26 Plastisol, 27 zerdine hydrogel, 28 and copolymer-in-oil. 29 Multifrequency MRE tests can provide the viscoelastic properties of phantoms, 30 which are usually then validated using other mechanical techniques, such as rheometers. 31 The main objective of this study was to measure the elasticity (G 0 ) and viscosity (G 00 ) parameters of individual passive thigh muscles (gracilis: Gr, semimembranosus: SM, semitendinosus: ST and biceps: BC) using multifrequency MRE and rheological models (Voigt, Maxwell, Zener, springpot).…”

“…In the literature, multiple phantoms have been created with different compositions: agarose, bovine, Wirosil, Plastisol, zerdine hydrogel, and copolymer‐in‐oil . Multifrequency MRE tests can provide the viscoelastic properties of phantoms, which are usually then validated using other mechanical techniques, such as rheometers …”

Convergence of Levenberg–Marquardt method for the inverse problem with an interior measurement

“…In this section we will numerically test the performance of our Levenberg-Marquad method. The set up for this numerical test is based on our MRE experiments done in Hokkaido University [19].…”

“…In this section we will numerically test the performance of our Levenberg-Marquad method. The set up for this numerical test is based on our MRE experiments done in Hokkaido University [19]. Concerning the spacial resolution of our 0.3 T micro-MRI, which is 1 mm, and the typical size of our two layered agarose gel phantom, which is 120×120 grids of a 120 mm × 120 mm rectangular domain Ω (see Figure 4.1), we consider the following boundary value problem as a special case of (1.1):…”

“…The above u and g in (1.1) are the component of the displacement vector of time harmonic vibration in Ω and at ∂Ω, respectively. Especially the diplacement g at ∂Ω is given by a probe attached at some part of ∂Ω connected with a bar made of glass fiber-reinforced plastic (GFRP) which propagates the vibration excited by the vibration system of MRI (see [19]). Away from the place the probe is attached we should have to give Neumann boundary condition.…”