Theory of susceptibility-induced transverse relaxation in the capillary network in the diffusion narrowing regime

The transverse relaxation effect of deoxyhemoglobin compartmentalization in erythrocytes in the capillary network is investigated using an analytical approach. The capillaries are modeled as long arrays of paramagnetic spheres, simulating the individual red blood cells. Calculations are performed in the diffusion narrowing regime, which holds for the native blood paramagnetism at moderate fields up to about 1.5 T, for the free induction decay, the Hahn spin-echo, and the Carr-Purcell-Meiboom-Gill sequence. The commonly used model of capillaries as homogeneously magnetized cylinders is shown to underestimate the capillary contribution to the susceptibility-induced relaxation rate by up to 55%. This results in a noticeable change in the predicted deoxyhemoglobin concentration needed to cause the variation in the transverse relaxation rate observed in functional MRI and may affect subsequent quantification of physiological parameters derived from the BOLD signal. Furthermore, the model for the individual red blood cells (RBCs) represents a framework for investigating the effects of interspecies and intersubject variations in hematocrit, RBC deoxyhemoglobin concentration, and cell size on the relaxation rate. The results agree within their validity domain with previous Monte Carlo simulations.