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

Abstract

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 ${\Delta R_2}^{\ast }\propto {\left(\Delta \chi \right)}^{\beta }$ . 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 β 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 $B_0\le$ 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 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.

Keywords: BOLD fMRI; contrast agents; microvascular network; modeling; perfusion MRI.