Arterial blood stealing as a mechanism of negative BOLD response: From the steady-flow with nonlinear phase separation to a windkessel-based model.

Blood Oxygen Level Dependent (BOLD) signal indirectly characterizes neuronal activity by measuring hemodynamic and metabolic changes in the nearby microvasculature. A deeper understanding of how localized changes in electrical, metabolic and hemodynamic factors translate into a BOLD signal is crucial for the interpretation of functional brain imaging techniques. While positive BOLD responses (PBR) are widely considered to be linked with neuronal activation, the origins of negative BOLD responses (NBR) have remained largely unknown. As NBRs are sometimes observed in close proximity of regions with PBR, a blood "stealing" effect, i.e., redirection of blood from a passive periphery to the area with high neuronal activity, has been postulated. In this study, we used the Hagen-Poiseuille equation to model hemodynamics in an idealized microvascular network that account for the particulate nature of blood and nonlinearities arising from the red blood cell (RBC) distribution (i.e., the Fåhraeus, Fåhraeus-Lindqvist and the phase separation effects). Using this detailed model, we evaluate determinants driving this "stealing" effect in a microvascular network with geometric parameters within physiological ranges. Model simulations predict that during localized cerebral blood flow (CBF) increases due to neuronal activation-hyperemic response, blood from surrounding vessels is reallocated towards the activated region. This stealing effect depended on the resistance of the microvasculature and the uneven distribution of RBCs at vessel bifurcations. A parsimonious model consisting of two-connected windkessel regions sharing a supplying artery was proposed to simulate the stealing effect with a minimum number of parameters. Comparison with the detailed model showed that the parsimonious model can reproduce the observed response for hematocrit values within the physiological range for different species. Our novel parsimonious model promise to be of use for statistical inference (top-down analysis) from direct blood flow measurements (e.g., arterial spin labeling and laser Doppler/Speckle flowmetry), and when combined with theoretical models for oxygen extraction/diffusion will help account for some types of NBRs.