Effect of magnetic field gradients induced by microvasculature on NMR measurements of molecular self-diffusion in biological tissues

Presence of induced mesoscopic gradients of magnetic field in magnetically heterogeneous samples affects the measured value of apparent diffusion coefficient. This effect is investigated theoretically in the context of diffusion measurements in perfused biological tissues with blood as the paramagnetic compartment. It is shown that the apparent diffusion coefficient is sensitive to mutual correlations in vessel positions. Neglect of these correlations results in a failure of the commonly used model of microvasculature in which vessels are described as independently placed cylinders. The model is modified to account for intervessel correlations. The results indicate an underestimation of apparent diffusion coefficient in proportion to the magnetic susceptibility of intravascular compartment in agreement with published experimental data. The proportionality coefficient depends on the microvascular architecture. Comparison with experimental data yields a numerical value for a new model parameter that characterises the correlation in mutual positions of blood vessels.