Theory of fast field-cycling NMR relaxometry of liquid systems undergoing chemical exchange

The time evolution of the nuclear magnetisation of chemically exchanging systems in liquids is calculated for the pre-polarised fast field-cycling sequence of nuclear magnetic resonance (NMR) relaxometry. The obtained parameter expressions of the magnetisation allow one to derive the longitudinal relaxation rates and the residence times of the exchanging sites from the experiment. In the particular cases of slow and fast exchange, approximations leading to simple analytic expressions are derived. The theory takes account of the delay time necessary to ensure that the field for acquiring the signal is stable enough after its rapid jump from its relaxation value. The domains of mono-exponential or bi-exponential relaxation of the magnetisation are displayed in a concise way through 3D and 2D logarithmic plots of the population ratio of the exchanging sites and of their intrinsic relaxation times. The influence of the acquisition delay on the fitted values of the populations, residence times, and intrinsic relaxation times of the sites is emphasised in the case of the bi-exponential water proton relaxation observed in a tumour tissue.