Woo J H, Hathout G M
Department of Radiologic Sciences, University of California Los Angeles, UCLA Center for the Health Sciences, Los Angeles, California 90095-1721, USA.
J Cereb Blood Flow Metab. 2001 May;21(5):517-28. doi: 10.1097/00004647-200105000-00006.
The authors revisit a simple mathematical model, presented in previous work, that characterizes the response of cerebral venous oxygenation to changes in blood flow and oxygen consumption. This physiologically based model can qualitatively duplicate the results of several recent empirical studies in which other authors have tested the hypothesis of linearity in the functional magnetic resonance imaging (fMRI) response to task activation, in that the experimentally found nearly linear behavior of the system and also its subtle departures from linearity are both predicted by simulations of the model. The model is simple enough that its equations can be explicitly solved. Moreover, an amended model that incorporates a varying cerebral blood volume parameter is found to have similar if not better consistency with the empirical data; indeed, this "extended" model is shown to be solvable by the same differential equation as the authors' simple one, wherein the volume is fixed as a constant. These investigations lend further indirect support to the blood oxygen level-dependent hypothesis of venous deoxyhemoglobin as the primary mechanism for fMRI signal changes during task activation, as well as for the authors' simple system as a useful physiologic model thereof. Although the authors' mathematical model does not formally represent a linear system with respect to the flow input, its underlying linear character may help partially explain the "nearly" linear behavior of the fMRI response.
作者重新审视了先前工作中提出的一个简单数学模型，该模型描述了脑静脉氧合对血流和氧消耗变化的反应。这个基于生理学的模型能够定性地重现近期其他作者的几项实证研究结果，在这些研究中，作者们检验了功能磁共振成像（fMRI）对任务激活反应的线性假设，即该系统实验发现的近似线性行为及其与线性的细微偏差均由该模型的模拟预测得出。该模型足够简单，其方程可以明确求解。此外，一个纳入了变化的脑血容量参数的修正模型被发现与实证数据具有相似（如果不是更好）的一致性；实际上，这个“扩展”模型被证明可以用与作者的简单模型相同的微分方程求解，其中体积被固定为一个常数。这些研究进一步间接支持了静脉脱氧血红蛋白的血氧水平依赖假设，即其作为任务激活期间fMRI信号变化的主要机制，以及支持作者的简单系统作为其有用的生理模型。尽管作者的数学模型相对于流量输入而言并非形式上的线性系统，但其潜在的线性特征可能有助于部分解释fMRI反应的“近似”线性行为。
