The purpose of this study was to obtain normative data using magnetic resonance elastography (MRE) to: [a] obtain estimates of the shear modulus of human cerebral tissue in vivo, and [b] assess a possible age dependence of the shear modulus of cerebral tissue in healthy adult volunteers. MR elastography studies were performed on tissue-simulating gelatin phantoms and 25 healthy adult volunteers. The data were analyzed using spatio-temporal filters and a local frequency estimating algorithm. Statistical analysis was performed using a paired t-test. The mean shear stiffness of cerebral white matter was 13.6 kPa (95% CI 12.3 to 14.8 kPa); while that of gray matter was lower at 5.22 kPa (95% CI 4.76 to 5.66 kPa). The difference was statistically significant (p < 0.0001).

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While the contractile properties of skeletal muscle have been studied extensively, relatively little is known about the elastic properties of muscle in vivo. Magnetic resonance elastography (MRE) is a phase contrast-based method for observing shear waves propagating in a material to determine its stiffness. In this work, MRE is applied to skeletal muscle under load to quantify the change in stiffness with loading. A mathematical model of muscle is developed that predicts a linear relationship between shear stiffness and muscle load. The MRE technique was applied to bovine muscle specimens (N 10) and human biceps brachii in vivo (N 5). Muscle stiffness increased linearly for both passive tension (14.5 1.77 kPa/kg) and active tension, in which the increase in stiffness was dependent upon muscle size, as predicted by the model. A means of noninvasively assessing the viscoelastic properties of skeletal muscle in vivo may provide a useful method for studying muscle biomechan-ics in health and disease. J. Magn. Reson. Imaging 2001;13:269-276.

The effect of three types of "quartic" anisotropy energy (i.e. , in the M term of the magnetic Ginzburg-Landau free energy} on the polarization of the "spiral magnetic" state of Blount and Varma is studied near the onset temperature. For a quartic anisotropy with uniaxial symmetry, we find continuous polarization transitions from circular to elliptical and then to linear as the strength of a uni-easy-axis anisotropy is increased. (No transition is found for the uni-hard-axis ease.) If the quartic anisotropy has cubic symmetry, we find a discontinuous transition directly between circular and linear, without going through an elliptic stage, when the sign of the anisotropy energy is to favor the cubic axes. (The polarization stays circular at all strengths of the anisotropy energy if the sign of the latter is to favor the body diagonals.) Finally, we model the anisotropy in primitive tetragonal ErRh484 with a quadratic anisotropy giving a hard c axis, plus a quartic anisotropy in the basal plane with a square symmetry. A first-order polarization transition directly between circular and linear is also obtained for this case, when the quartic anisotropy favors the principal axes in the basal plane. This last case studied provides a plausible explanation for the linear polarization observed in the coexistence state of ErRh484.