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.