Tissue-blood exchange of extravascular longitudinal magnetization with account of intracompartmental diffusion

The joint effect of both extravascular water diffusion and transcapillary water exchange on the longitudinal magnetisation is evaluated theoretically for tissues with sparse capillary networks (e.g., the brain and myocardium). The spatio-temporal profile of the extravascular longitudinal magnetisation is calculated for the limiting case of a high blood concentration of paramagnetic tracer resulting in negligible intravascular magnetisation, hence in a net flux of magnetisation from the extravascular tissue to its contained blood. A related parameter, termed the effective extravascular depolarised volume, is derived that quantifies the ensuing attenuation of the NMR signal and affords a taxonomy of exchange regimes. It is found that the spatio-temporal pattern of magnetisation decay may deviate strongly from that predicted by chemical exchange models when the rate of transcapillary exchange is limited by slow diffusive transport in the extravascular tissue but reproduces known results in the case of fast extravascular diffusion.