Extravascular contribution of blood oxygenation level‐dependent signal changes: A numerical analysis based on a vascular network model

In this study, the extravascular (EV) contribution to blood oxygenation level-dependent (BOLD) signal changes was evaluated, based on a numerical analysis of the nondimensional Bloch-Torrey equation for a vascular network model of randomly oriented paramagnetic vessels. From a statistical point of view, the susceptibility-induced EV BOLD signal changes for both gradient- and spin-echoes are shown to be proportional to cerebral blood volume (CBV). These changes can be expressed by a function of two nondimensional parameters: one represents the characteristic phase change of the signal induced by the deoxyhemoglobin-containing vessels, and the other represents a diffusion effect relative to the vessel radius. The numerical results showed excellent agreement with the analytical solutions obtained previously for the regimes of small and large diffusion effects. Based on the numerical results for gradient- and spin-echoes, it is possible to show the dependence of the EV BOLD contribution on the echo time, the static magnetic field strength, and the stimulation-induced CBV change. This dependence can be demonstrated for vessels of small, intermediate, and large radii, which correspond respectively to the slow, intermediate, and fast diffusion regimes. A more realistic functional MRI (fMRI) simulation which includes an intravascular (IV) contribution is presented, with emphasis on the field strength dependence of the BOLD signal changes.