Rheological Basis of Magnetic Resonance Elastography

Abstract

Magnetic resonance elastography (MRE) has been invented to measure the elastic properties of the living body on the basis of magnetic resonance imaging. From the viewpoint of medical practice, MRE is regarded as a palpation method. MRE has the advantage over other types of elastography in that the stiffness in all areas of the living body including deep areas inaccessible to the physician’s hand can be measured quantitatively in principle. Hence, by MRE, a complete viscoelastic map of the living body can be obtained. This advantage indicates that MRE is a powerful tool for determining the viscoelastic structures of nonuniform gels beyond the field of medicine. Unfortunately, the present MRE devices cannot perfectly realize the potential ability of the idea of MRE. Further improvements of the instruments for the MRE system and of the analysis algorithm for measured MRE data are necessary. Toward the construction of an ideal MRE system, we are trying to introduce the concept of rheology in MRE and to develop a purely theoretical approach to MRE. We consider what kind of physical quantity is actually measured and what kind of principle connects the measured quantities and the viscoelastic properties of the living body. The amplitude of a steady transverse wave excited in the living body is measured by MRE. The viscoelastic properties of the living body are described in terms of the Voigt model. The relationship between the viscoelastic parameters and the amplitude of the transverse wave is shown. The reconstruction formula of the map of the viscoelastic parameters from the data of the measured quantity is derived. The theoretical base of transverse wave excitation by a longitudinal wave, which enables us to measure the rigidity in deep areas practically, is also developed. A method of measuring the stiffness of a uniaxial system is introduced.