Ex vivo bovine liver nonlinear viscoelastic properties: MR elastography and rheological measurements

Knowledge of the nonlinear viscoelastic properties of the liver is important, but the complex tissue behavior outside the linear viscoelastic regime has impeded their characterization, particularly in vivo. Combining static compression with magnetic resonance (MR) elastography has the potential to be a useful imaging method for assessing large deformation mechanical properties of soft tissues in vivo. However, this remains to be verified. Therefore this study aims first to determine whether MR elastography can measure the nonlinear mechanical properties of ex vivo bovine liver tissue under varying levels of uniform and focal preloads (up to 30%), and second to compare MR elastography-derived complex shear modulus with standard rheological measurements.

Nine fresh bovine livers were collected from a local abattoir, and experiments were conducted within 12hr of death. Two cubic samples (∼10 × 10 × 10 cm³) were dissected from each liver and imaged using MR elastography (60 Hz) under 4 levels of uniform and focal preload (1, 10, 20, and 30% of sample width) to investigate the relationship between MR elastography-derived complex shear modulus (G∗) and the maximum principal Right Cauchy Green Strain (C₁₁). Three tissue samples from each of the same 9 livers underwent oscillatory rheometry under the same 4 preloads (1, 10, 20, and 30% strain). MR elastography-derived complex shear modulus (G∗) from the uniform preload was validated against rheometry by fitting the frequency dependence of G∗ with a power-law and extrapolating rheometry-derived G∗ to 60 Hz.

MR elastography-derived G∗ increased with increasing compressive large deformation strain, and followed a power-law curve (G∗ = 1.73 × C₁₁^-0.38, R² = 0.96). Similarly, rheometry-derived G∗ at 1 Hz, increasing from 0.66 ± 1.03 kPa (1% strain) to 1.84 ± 1.65 kPa (30% strain, RM one-way ANOVA, P < 0.001), and the frequency dependence of G∗ followed a power-law with the exponent decreasing from 0.13 to 0.06 with increasing preload. MR elastography-derived G∗ was 1.4-3.1 times higher than the extrapolated rheometry-derived G∗ at 60 Hz, but the strain dependence was consistent between rheometry and MR elastography measurements.

This study demonstrates that MR elastography can detect changes in ex vivo bovine liver complex shear modulus due to either uniform or focal preload and therefore can be a useful technique to characterize nonlinear viscoelastic properties of soft tissue, provided that strains applied to the tissue can be quantified. Although MR elastography could reliably characterize the strain dependence of the ex vivo bovine liver, MR elastography overestimated the complex shear modulus of the tissue compared to rheological measurements, particularly at lower preload (<10%). That is likely to be important in clinical hepatic MR elastography diagnosis studies if preload is not carefully considered. A limitation is the absence of overlapping frequency between rheometry and MR elastography for formal validation.