Department of Medical Biophysics, University of Western Ontario, London, Canada.
Math Biosci. 2011 Jul;232(1):1-10. doi: 10.1016/j.mbs.2011.03.010. Epub 2011 Apr 1.
We present a theoretical model for steady-state radial and longitudinal oxygen transport in arterioles containing flowing blood (plasma and red blood cells) and surrounded by living tissue. This model combines a detailed description of convective and diffusive oxygen transport inside the arteriole with a novel boundary condition at the arteriolar lumen surface, and the results provide new mass transfer coefficients for computing arteriolar O(2) losses based on far-field tissue O(2) tension and in the presence of spatially distributed capillaries. A numerical procedure is introduced for calculating O(2) diffusion from an arteriole to a continuous capillary-tissue matrix immediately adjacent to the arteriole. The tissue O(2) consumption rate is assumed to be constant and capillaries act as either O(2) sources or sinks depending on the local O(2) environment. Using the model, O(2) saturation (SO(2)) and tension (PO(2)) are determined for the intraluminal region of the arteriole, as well as for the extraluminal region in the neighbouring tissue. Our model gives results that are consistent with available experimental data and previous intraluminal transport models, including appreciable radial decreases in intraluminal PO(2) for all vessel diameters considered (12-100 μm) and slower longitudinal decreases in PO(2) for larger vessels than for smaller ones, and predicts substantially less diffusion of O(2) from arteriolar blood than do models with PO(2) specified at the edge of the lumen. The dependence of the new mass transfer coefficients on vessel diameter, SO(2) and far-field PO(2) is calculated allowing their application to a wide range of physiological situations. This novel arteriolar O(2) transport model will be a vital component of future integrated models of microvascular regulation of O(2) supply to capillary beds and the tissue regions they support.
我们提出了一个用于稳态径向和纵向氧气在含有流动血液（血浆和红细胞）的动脉和周围活体组织中传输的理论模型。该模型结合了对动脉内的对流和扩散氧传输的详细描述以及在动脉管腔表面的新边界条件，其结果提供了新的传质系数，用于根据远场组织氧张力和存在空间分布的毛细血管来计算动脉氧损失。引入了一种数值程序，用于计算从动脉扩散到紧邻动脉的连续毛细血管-组织基质的氧扩散。假设组织耗氧量保持恒定，并且毛细血管根据局部氧环境充当氧源或汇。使用该模型，确定了动脉管腔内区域以及相邻组织外腔区域的氧饱和度（SO2）和张力（PO2）。我们的模型给出的结果与可用的实验数据和先前的管内传输模型一致，包括考虑到所有血管直径（12-100μm）时管内 PO2 的明显径向降低以及较大血管的 PO2 的纵向降低速度比较小血管慢，并且与在管腔边缘指定 PO2 的模型相比，预测从动脉血液中扩散的 O2 要少得多。新传质系数对血管直径、SO2 和远场 PO2 的依赖性的计算允许将其应用于广泛的生理情况。这种新型的动脉氧传输模型将成为未来微血管对毛细血管床和它们所支持的组织区域的氧供应调节的综合模型的重要组成部分。
