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The magnetic field penetration, phase shift and power deposition in planar and cylindrical models of biological tissue exposed to a sinusoidal time-dependent magnetic field have been investigated theoretically over the frequency range 1 to 100 MHz. The results are based on measurements of the relative permittivity and resistivity dispersions of a variety of freshly excised rat tissue at 37 and 25 degrees C, and are analysed in terms of their implications for human body nuclear magnetic resonance (NMR) imaging. The results indicate that at NMR operating frequencies much greater than about 30 MHz, magnetic field amplitude and phase variations experienced by the nuclei may cause serious distortions in an image of a human torso. The maximum power deposition envisaged during an NMR imaging experiment on a human torso is likely to be comparable to existing long-term safe exposure levels, and will depend ultimately on the imaging technique and NMR frequency employed.