Nuclear-magnetic-resonance measurements of the proton-spin relaxation for water in biological cells are known to exhibit a multiexponential decay. A theory, based on the diffusion equation using the bulk diffusivity of water, is developed to explain this phenomenon. It is shown that multiexponential decay arises simply as a consequence of an eigenvalue problem associated with the size and shape of the cell and that this multiexponential decay can only be observed for samples whose size is of the order of a biological cell. As an example, the theory is applied to a previously published data for rat gastronemius cells. Excellent agreement is obtained, and furthermore, the size of the cell is calculated by fitting the theory to the experiment.

• Received 29 September 1978

DOI:https://doi.org/10.1103/PhysRevA.19.2446