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.

血氧水平依赖性 (BOLD) 信号通过测量附近微脉管系统的血流动力学和代谢变化来间接表征神经元活动。更深入地了解电、代谢和血流动力学因素的局部变化如何转化为 BOLD 信号对于解释功能性脑成像技术至关重要。虽然阳性 BOLD 反应（PBR）被广泛认为与神经元激活有关，但阴性 BOLD 反应（NBR）的起源仍然很大程度上未知。由于有时在 PBR 区域附近观察到 NBR，因此推测存在血液“窃取”效应，即将血液从被动外周重定向到神经元活动较高的区域。在本研究中，我们使用 Hagen-Poiseuille 方程对理想化微血管网络中的血流动力学进行建模，该网络解释了血液的颗粒性质以及红细胞 (RBC) 分布（即 Fåhraeus、Fåhraeus-Lindqvist 和相分离效应）。使用这个详细的模型，我们评估了几何参数在生理范围内的微血管网络中驱动这种“窃取”效应的决定因素。模型模拟预测，在神经元激活（充血反应）导致局部脑血流量（CBF）增加期间，周围血管的血液会重新分配到激活区域。这种窃取效应取决于微血管的阻力和血管分叉处红细胞的不均匀分布。提出了一种由共享供应动脉的两个连接的风管区域组成的简约模型，以用最少的参数来模拟窃取效果。 与详细模型的比较表明，简约模型可以在不同物种的生理范围内再现观察到的血细胞比容值的响应。我们新颖的简约模型有望用于直接血流测量（例如动脉自旋标记和激光多普勒/散斑流量计）的统计推断（自上而下的分析），并且与氧气提取/扩散的理论模型相结合将有助于考虑某些类型的 NBR。