A Novel Fractal Model to Explain the Rheology of Liver Tissue using MR-Elastography
Sinkus R, Bercoff J, Robert B, Fink M, Tanter M
Laboratoire Ondes et Acoustique
Steady-state mono-chromatic MR-Elastography is used to measure the complex shear modulus G*(w)=Gd(w)+iGl(w) of ex-vivo bovine liver tissue within the frequency interval 40-100Hz. The frequency dependence of the shear wave speed can be explained by the classical Voigt model. However, the model fails to describe the frequency dependence of real and imaginary part separately. In order to account for the observed power-law behavior of Gd(w)~Gl(w)~w^0.75 and the constant ratio Gl(w)/Gd(w)=tan(0.15*pi/2) we propose a rheological model which consists of two fractal networks. The frequency powers of the individual networks resemble what has been established for the cytoplasm (~w^0.75) and the cytoskeleton (~w^0.15).