Analytic expressions for the ultimate intrinsic signal-to-noise ratio and ultimate intrinsic specific absorption rate in MRI

The ultimate intrinsic signal-to-noise ratio is the highest possible signal-to-noise ratio, and the ultimate intrinsic specific absorption rate provides the lowest limit of the specific absorption rate for a given flip angle distribution. Analytic expressions for ultimate intrinsic signal-to-noise ratio and ultimate intrinsic specific absorption rate are obtained for arbitrary sample geometries. These expressions are valid when the distance between the point of interest and the sample surface is smaller than the wavelength, and the sample is homogeneous. The dependence on the sample permittivity, conductivity, temperature, size, and the static magnetic field strength is given in analytic form, which enables the easy evaluation of the change in signal-to-noise ratio and specific absorption rate when the sample is scaled in size or when any of its geometrical or electrical parameters is altered. Furthermore, it is shown that signal-to-noise ratio and specific absorption rate are independent of the permeability of the sample. As a practical case and a solution example, a uniform, circular cylindrically shaped sample is studied.