Quantitative theory for the transverse relaxation time of blood water

An integrative model is proposed to describe the dependence of the transverse relaxation rate of blood water protons (R_2blood = 1/T_2blood) on hematocrit fraction and oxygenation fraction (Y). This unified model takes into account (a) the diamagnetic effects of albumin, hemoglobin and the cell membrane; (b) the paramagnetic effect of hemoglobin; (c) the effect of compartmental exchange between plasma and erythrocytes under both fast and slow exchange conditions that vary depending on field strength and compartmental relaxation rates and (d) the effect of diffusion through field gradients near the erythrocyte membrane. To validate the model, whole-blood and lysed-blood R₂ data acquired previously using Carr-Purcell-Meiboom-Gill measurements as a function of inter-echo spacing τ_cp at magnetic fields of 3.0, 7.0, 9.4 and 11.7 T were fitted to determine the lifetimes (field-independent physiological constants) for water diffusion and exchange, as well as several physical constants, some of which are field-independent (magnetic susceptibilities) and some are field-dependent (relaxation rates for water protons in solutions of albumin and oxygenated and deoxygenated hemoglobin, ie, blood plasma and erythrocytes, respectively). This combined exchange-diffusion model allowed excellent fitting of the curve of the τ_cp-dependent relaxation rate dispersion at all four fields using a single average erythrocyte water lifetime, τ_ery = 9.1 ± 1.4 ms, and an averaged diffusional correlation time, τ_D = 3.15 ± 0.43 ms. Using this model and the determined physiological time constants and relaxation parameters, blood T₂ values published by multiple groups based on measurements at magnetic field strengths of 1.5 T and higher could be predicted correctly within error. Establishment of this theory is a fundamental step for quantitative modeling of the BOLD effect underlying functional MRI.