School of Computer Science and Software Engineering, The Univ. of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia.
Am J Physiol Renal Physiol. 2012 Sep;303(5):F605-18. doi: 10.1152/ajprenal.00186.2012. Epub 2012 Jun 6.
To understand how geometric factors affect arterial-to-venous (AV) oxygen shunting, a mathematical model of diffusive oxygen transport in the renal cortex was developed. Preglomerular vascular geometry was investigated using light microscopy (providing vein shape, AV separation, and capillary density near arteries) and published micro-computed tomography (CT) data (providing vessel size and AV separation; Nordsletten DA, Blackett S, Bentley MD, Ritman EL, Smith NP. IUPS Physiome Project. http://www.physiome.org.nz/publications/nordsletten_blackett_ritman_bentley_smith_2005/folder_contents). A "U-shaped" relationship was observed between the arterial radius and the distance between the arterial and venous lumens. Veins were found to partially wrap around the artery more consistently for larger rather than smaller arteries. Intrarenal arteries were surrounded by an area of fibrous tissue, lacking capillaries, the thickness of which increased from ∼5 μm for the smallest arteries (<16-μm diameter) to ∼20 μm for the largest arteries (>200-μm diameter). Capillary density was greater near smaller arteries than larger arteries. No capillaries were observed between wrapped AV vessel pairs. The computational model comprised a single AV pair in cross section. Geometric parameters critical in renal oxygen transport were altered according to variations observed by CT and light microscopy. Lumen separation and wrapping of the vein around the artery were found to be the critical geometric factors determining the amount of oxygen shunted between AV pairs. AV oxygen shunting increases both as lumen separation decreases and as the degree of wrapping increases. The model also predicts that capillaries not only deliver oxygen, but can also remove oxygen from the cortical parenchyma close to an AV pair. Thus the presence of oxygen sinks (capillaries or tubules) near arteries would reduce the effectiveness of AV oxygen shunting. Collectively, these data suggest that AV oxygen shunting would be favored in larger vessels common to the cortical and medullary circulations (i.e., arcuate and proximal interlobular arteries) rather than the smaller vessels specific to the cortical circulation (distal interlobular arteries and afferent arterioles).
为了理解几何因素如何影响动静脉（AV）氧分流，我们建立了肾皮质内弥散氧传输的数学模型。使用体视学显微镜（提供静脉形状、AV 分离和动脉附近的毛细血管密度）和已发表的微计算机断层扫描（CT）数据（提供血管大小和 AV 分离；Nordsletten DA、Blackett S、Bentley MD、Ritman EL、Smith NP。IUPS Physiome Project。http://www.physiome.org.nz/publications/nordsletten_blackett_ritman_bentley_smith_2005/folder_contents）研究了肾小球前血管的几何形状。观察到动脉半径与动脉和静脉腔之间的距离之间存在“U 形”关系。对于较大的动脉，静脉更一致地部分环绕动脉，而不是较小的动脉。肾内动脉被一层缺乏毛细血管的纤维组织包围，其厚度从最小的动脉（<16-μm 直径）的约 5μm 增加到最大的动脉（>200-μm 直径）的约 20μm。毛细血管密度在较小的动脉附近大于较大的动脉。在缠绕的 AV 血管对之间没有观察到毛细血管。计算模型由单个 AV 对的横截面组成。根据 CT 和体视学观察到的变化，改变了对肾氧传输至关重要的几何参数。发现管腔分离和静脉环绕动脉的缠绕是决定 AV 对之间氧分流量的关键几何因素。随着管腔分离减小和缠绕程度增加，AV 氧分流增加。该模型还预测，毛细血管不仅输送氧气，还可以从靠近 AV 对的皮质实质中去除氧气。因此，动脉附近存在氧气汇（毛细血管或小管）会降低 AV 氧分流的效果。总的来说，这些数据表明，AV 氧分流将有利于皮质和髓质循环共有的较大血管（即，弓形和近侧小叶间动脉），而不是仅存在于皮质循环中的较小血管（远侧小叶间动脉和入球小动脉）。
