The signal-to-noise ratio of nuclear magnetic resonance surface coils and application to a lossy dielectric cylinder model. I. Theory

Surface coils are used in magnetic resonance imaging (MRI) for their high signal-to-noise ratio (S/N) when placed near the-region to be imaged. However, their optimization for high field MRI systems is hampered by the lack of understanding of the electromagnetic effects taking place at high frequencies when a coil is placed near the human body. The aim of this work was to calculate the S/N of surface coils using complete solutions to Maxwell's equations and also to study the high frequency effects and parameters determining the S/N. Here the authors present a general approach to the computation of the S/N of surface coils using the reciprocity principal and the complex Poynting vector for arbitrary coil and body geometries. This approach is then applied to the case of the human body modeled as an infinitely long homogeneous dielectric cylinder exhibiting both conductive and dielectric losses. The S/N of a coil of unspecified geometry facing the cylinder is derived using a dyadic Green's function. Complete solutions for the fields of a dipolar source arbitrarily located in the cylinder are first derived, and applying the reciprocity principle, the authors deduce the fields created at the dipole position by a coil excited with a unit radiofrequency current. These yield the expressions for the power dissipated in the cylinder, for its reciprocal the noise picked up by the coil, and also for the signal received. Any coil geometry and any coil or source position can be evaluated with this infinite cylinder model. It is valid at all frequencies and for any tissue parameter. The general approach to the computation of the S/N of MRI coils can be applied to other body geometries as well.<
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