Dependence of the MR signal on the magnetic susceptibility of blood studied with models based on real microvascular networks

PURPOSE: The primary goal of this study was to estimate the value of β , the exponent in the power law relating changes of the transverse relaxation rate and intra-extravascular local magnetic susceptibility differences as ΔR2∗∝(Δχ)β . The secondary objective was to evaluate any differences that might exist in the value of β obtained using a deoxyhemoglobin-weighted Δχ distribution versus a constant Δχ distribution assumed in earlier computations. The third objective was to estimate the value of β that is relevant for methods based on susceptibility contrast agents with a concentration of Δχ higher than that used for BOLD fMRI calculations. METHODS: Our recently developed model of real microvascular anatomical networks is used to extend the original simplified Monte-Carlo simulations to compute β from the first principles. RESULTS: Our results show that β=1 for most BOLD fMRI measurements of real vascular networks, as opposed to earlier predictions of β=1 .5 using uniform Δχ distributions. For perfusion or fMRI methods based on contrast agents, which generate larger values for Δχ , β=1 for B0≤ 9.4 T, whereas at 14 T β can drop below 1 and the variation across subjects is large, indicating that a lower concentration of contrast agent with a lower value of Δχ is desired for experiments at high B0 . CONCLUSION: These results improve our understanding of the relationship between R2* and the underlying microvascular properties. The findings will help to infer the cerebral metabolic rate of oxygen and cerebral blood volume from BOLD and perfusion MRI, respectively.