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 beta , the exponent in the power law relating changes of the transverse relaxation rate and intra-extravascular local magnetic susceptibility differences as Delta R-2* alpha(Delta chi)(beta) . The secondary objective was to evaluate any differences that might exist in the value of beta obtained using a deoxyhemoglobin-weighted Delta chi distribution versus a constant Delta chi distribution assumed in earlier computations. The third objective was to estimate the value of beta that is relevant for methods based on susceptibility contrast agents with a concentration of Delta chi 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 beta from the first principles. Results: Our results show that beta=1 for most BOLD fMRI measurements of real vascular networks, as opposed to earlier predictions of beta=1 .5 using uniform Delta chi distributions. For perfusion or fMRI methods based on contrast agents, which generate larger values for Delta chi , beta=1 for B-0 <= 9.4 T, whereas at 14 T beta can drop below 1 and the variation across subjects is large, indicating that a lower concentration of contrast agent with a lower value of Delta chi is desired for experiments at high B-0 . Conclusion: These results improve our understanding of the relationship between R-2(*) 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.