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

Magnetic resonance elastography (MRE) is used to quantify the viscoelastic shear modulus, G*, of human and animal tissues. Previously, values of G* determined by MRE have been compared to values from mechanical tests performed at lower frequencies. In this study, a novel dynamic shear test (DST) was used to measure G* of a tissue-mimicking material at higher frequencies for direct comparison to MRE. A closed-form solution, including inertial effects, was used to extract G* values from DST data obtained between 20 and 200 Hz. MRE was performed using cylindrical ‘phantoms’ of the same material in an overlapping frequency range of 100–400 Hz. Axial vibrations of a central rod caused radially propagating shear waves in the phantom. Displacement fields were fit to a viscoelastic form of Navier's equation using a total least-squares approach to obtain local estimates of G*. DST estimates of the storage G′ (Re[G*]) and loss modulus G″ (Im[G*]) for the tissue-mimicking material increased with frequency from 0.86 to 0.97 kPa (20–200 Hz, n = 16), while MRE estimates of G′ increased from 1.06 to 1.15 kPa (100–400 Hz, n = 6). The loss factor (Im[G*]/Re[G*]) also increased with frequency for both test methods: 0.06–0.14 (20–200 Hz, DST) and 0.11–0.23 (100–400 Hz, MRE). Close agreement between MRE and DST results at overlapping frequencies indicates that G* can be locally estimated with MRE over a wide frequency range. Low signal-to-noise ratio, long shear wavelengths and boundary effects were found to increase residual fitting error, reinforcing the use of an error metric to assess confidence in local parameter estimates obtained by MRE.