Ursino M, Di Giammarco P, Belardinelli E
IEEE Trans Biomed Eng. 1989 Feb;36(2):183-91. doi: 10.1109/10.16465.
This paper proposes a mathematical model which describes the production and diffusion of vasoactive chemical factors involved in oxygen-dependent cerebral blood flow (CBF) regulation in the rat. Partial differential equations describing the relations between input and output variables have been replaced with simpler ordinary differential equations by using mathematical approximations of the hyperbolic functions in the Laplace transform domain. This model is composed of two submodels. In the first, oxygen transport from capillary blood to cerebral tissue is analyzed to link changes in mean tissue oxygen pressure with CBF and arterial oxygen concentration changes. The second submodel presents equations describing the production of vasoactive metabolites by cerebral parenchyma, due to a lack of oxygen, and their diffusion towards pial perivascular space. These equations have been used to simulate the time dynamics of mean tissue PO2, perivascular adenosine concentration, and perivascular pH to changes in CBF. The present simulation points out that the time delay introduced by diffusion processes is negligible if compared with the other time constants of the system under study. In a subsequent work the same equations will be included in a model of the cerebral vascular bed to clarify the metabolite role in CBF regulation.
本文提出了一个数学模型，该模型描述了参与大鼠氧依赖性脑血流量（CBF）调节的血管活性化学因子的产生和扩散。通过在拉普拉斯变换域中使用双曲函数的数学近似，将描述输入和输出变量之间关系的偏微分方程替换为更简单的常微分方程。该模型由两个子模型组成。在第一个子模型中，分析了从毛细血管血液到脑组织的氧输送，以将平均组织氧压的变化与CBF和动脉氧浓度变化联系起来。第二个子模型给出了描述脑实质因缺氧产生血管活性代谢物及其向软脑膜血管周围间隙扩散的方程。这些方程已被用于模拟平均组织PO2、血管周围腺苷浓度和血管周围pH值随CBF变化的时间动态。目前的模拟指出，与所研究系统的其他时间常数相比，扩散过程引入的时间延迟可以忽略不计。在后续工作中，相同的方程将被纳入脑血管床模型，以阐明代谢物在CBF调节中的作用。
