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Diffusive spin exchange is one of the most important relaxation mechanisms inthe Nuclear Magnetic Resonance (NMR) applications to medicine and biology. Twomodels based on the Bloch-McConnell (B-M) and the Bloch-Torrey (B-T) equationsare commonly used for modelling the physical processes which determine the NMRlineshapes. Qualitative arguments for each of the two methods can be found invarious studies in the literature. However, there is a lack of systematicquantitative investigations of the diffusive exchange spectra calculated withthe two methods for the same physical system or model. In this work exactfrequency-domain transverse magnetization solutions of the B-M and the B-Tequations with boundary conditions for a two-compartment radial diffusiveexchange model are presented. Theoretical spectra and the two correspondingmetrics were computed by varying three different parameters: diffusivepermeability of the separating membrane between the two compartments (P), theradius of the inner spherical compartment (a), and the chemical shift betweenthe two compartments (\Deltaf). In general, the two models predicted differentspectral broadening for the same parameters in agreement with the differentanalytical solutions. However, the numerical analysis of the spectralbroadening demonstrated that the two models converge to the same results in thelimit of large chemical shift on the scale of the exchange rate. The resultswere qualitatively interpreted based on the difference between the two models:the B-M model assumes a single average exchange time constant while the B-Tmodel implies a more realistic continuous distribution of diffusive exchangetimes.

Analysis of theoretical NMR spectra generated by exact solutions of the  Bloch-McConnell and the Bloch-Torrey equations for a two-compartment radial  diffusive exchange model