Perturbation of homogeneous magnetic fields by isolated single and confocal spheroids. Implications for NMR spectroscopy of cells

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Abstract
Analytical expressions for the magnetic potential and the magnetic field strength vector in cells modelled as isolated confocal prolate and oblate spheroids have been derived. The important results which emerged from the analysis are that the magnetic field in the central spheroid, in a series of confocal spheroids, is always uniform; but its magnitude depends upon the orientation of the spheroids relative to the external field. Therefore, the NMR line-shape derived from an internal solute in a population of sparsely distributed spheroids, with random orientation of the members, is a superposition of Lorentzians; the resulting ‘complicated’ line shape may often appear to be Gaussian. This spectral phenomenon is at least part of the explanation for the non-Lorentzian character of NMR line-shapes in the spectra of many biological samples. Quantitative analysis of the NMR line-shape of an appropriate intracellular solute can in principal yield the orientational distribution of a dilute suspension of cells of uniform size and shape.