Background

Viscoelastic characterization of liver tissue using MR elastography (MRE) has been getting attention because correlation between viscoelastic parameters (viscosity, η and elasticity, μ) and histological changes in development of chronic liver diseases such as fibrosis and inflammation has been shown. These findings are especially important for distinguishing nonalcoholic fatty liver disease from simple steatosis in clinical liver imaging.^1-3 Multi-frequency MRE and non-linear calculation method has been used as a standard method for estimating viscoelastic parameters of the liver.⁴ However, non-linear calculation method is time consuming and difficult to perform in clinical setting because dedicated post-processing application to calculate viscoelastic parameters has not been commercially available. Therefore, it is important to develop alternative simple post-processing method for promoting viscoelastic analysis of liver diseases using MRE. The purpose of this study is to develop fast and precise method for calculation of viscoelastic parameters using multi-frequency MRE.

Methods

Observed velocity of elastic wave, Y(ω) was determined from perfect elastic body model elasticity, Μ(ω) on single-frequency MR elastogram by following equation: Y(ω) = (Μ(ω)/ρ)^0.5, ω = 2πf. Where f and ρ are frequency of pneumatic driver and density. Theoretical velocity of elastic wave, υ(ω) in Voigt viscoelastic model was determined from following equations: υ(ω) = 1/Re|(ρ/G(ω))^0.5|, G(ω) = μ + iωη, where G(ω) is complex shear module consist from viscosity (η) and elasticity (μ). Re|| means real part of complex number. Then, η and μ were determined by non-linear calculation method such as least square method minimizing cost function J = Σ{Y(ω_n) - υ(ω_n)}²/N (ω_n: n = 1, 2, …N) using multi-frequency MRE.⁴ In Voigt viscoelastic model, squared absolute value for G(ω) with higher and lower angular frequencies (ω_H and ω_L) are given by following equations: |G(ω_H)|² = μ² + ω_H²η², |G(ω_L)|² = μ² + ω_L²η². Solving these equations, η and μ can be linearly approximated by following equations using perfect elastic body model elasticity, Μ(ω) on multi-frequency MR elastograms: η = α[{M(ω_H)² - M(ω_L)²}/(ω_H² - ω_L²)]^0.5, μ = β[{ω_L²|M(ω_H)|² - ω_H²|M(ω_L)|²}/(ω_L² – ω_H²)]^0.5, where α and β are proportional constants. Eventual value for viscoelastic parameters (η and μ) were determined by average of viscoelastic parameters (η_n and μ_n) obtained from all combination of 2 frequencies (ω_Hn and ω_Ln) from given number of frequencies N, (n = 1, 2, … _NC₂). Proportional constants α and β were determined from computer simulation with various η, μ, and f (0 < η < 20 Pas, 0 < μ < 20,000 Pa, 40 < f < 150 Hz). Correlation of obtained viscoelastic parameters and time to calculation were statistically analyzed between linear and non-linear methods by phantom and patients study using 1.5-T MR system. In phantom study, polyvinyl alcohol (PVA)-boric acid hydrogel phantom containing various viscoelastic properties prepared by mixing PVA solution (approximately 10 wt%) and boric acid solution (5, 10, and 20 wt%) was evaluated by multi-frequency MRE (f = 150, 130, 110, 90, 70 Hz). Calculation was repeated at every pixel (80 x 80 pixels) in phantom on MR elastograms filtered by 25 x 25 averaging filter. In patients study, consecutive 19 patients who underwent multi-frequency MRE (f = 80, 60, 40 Hz) for evaluation of chronic liver diseases were included. Calculation was performed using single region of interest (25 x 25 pixels) located in the liver on MR elastograms.

Results

Linear approximation equations for viscosity (η) and elasticity (μ) obtained from computer simulation were as follows: η = 0.68675[{Μ(ω_H)² -Μ(ω_L)²}/(ω_H² – ω_L²)]^0.5, μ = 1.0165[{ω_L²Μ(ω_H)² – ω_H²Μ(ω_L)²}/(ω_L² – ω_H²)]^0.5. In PVA-boric acid hydrogel phantom study, correlation coefficient between viscoelastic parameters calculated by linear and non-linear methods were 0.980 (P < 0.001) for μ and 0.983 (P < 0.001) for η, respectively. Time for calculation was significantly short in linear method (0.42 s) compared to non-linear method (47.14 s) (P < 0.001). In patient study, correlation coefficient between viscoelastic parameters calculated by linear and non-linear methods were 0.932 (P < 0.001) for μ and 0.935 (P < 0.001) for η, respectively.

Discussion

Correlation of viscoelastic parameters between linear and non-linear calculation methods was significantly high in phantom and patients study. Further more, calculation speed by linear method was significantly faster than that by non-linear method. These results assure clinical application of linear calculation method as an alternative to non-linear method that has been regarded as a standard in viscoelastic characterization by multi-frequency MR elastography.⁴

Conclusion

Linear approximation method enables fast and precise calculation of viscoelastic parameters of the liver using multi-frequency MR elastograms. This method will promote clinical application of viscoelastic analysis of liver diseases using MRE.

Acknowledgements

No acknowledgement found.