Department of Mathematics, Duke University, Durham, NC 27708-0320, USA.
Am J Physiol Renal Physiol. 2010 Apr;298(4):F973-87. doi: 10.1152/ajprenal.00249.2009. Epub 2010 Jan 6.
A new, region-based mathematical model of the urine concentrating mechanism of the rat renal inner medulla (IM) was used to investigate the significance of transport and structural properties revealed in recent studies that employed immunohistochemical methods combined with three-dimensional computerized reconstruction. The model simulates preferential interactions among tubules and vessels by representing two concentric regions. The inner region, which represents a collecting duct (CD) cluster, contains CDs, some ascending thin limbs (ATLs), and some ascending vasa recta; the outer region, which represents the intercluster region, contains descending thin limbs, descending vasa recta, remaining ATLs, and additional ascending vasa recta. In the upper portion of the IM, the model predicts that interstitial Na(+) and urea concentrations (and osmolality) in the CD clusters differ significantly from those in the intercluster regions: model calculations predict that those CD clusters have higher urea concentrations than the intercluster regions, a finding that is consistent with a concentrating mechanism that depends principally on the mixing of NaCl from ATLs and urea from CDs. In the lower IM, the model predicts that limited or nearly zero water permeability in descending thin limb segments will increase concentrating effectiveness by increasing the rate of solute-free water absorption. The model predicts that high urea permeabilities in the upper portions of ATLs and increased contact areas of longest loop bends with CDs both modestly increase concentrating capability. A surprising finding is that the concentrating capability of this region-based model falls short of the capability of a model IM that has radially homogeneous interstitial fluid at each level but is otherwise analogous to the region-based model.
一种新的基于区域的大鼠肾髓质尿液浓缩机制数学模型被用来研究最近结合免疫组织化学方法和三维计算机重建技术的研究中揭示的转运和结构特性的意义。该模型通过表示两个同心区域来模拟小管和血管之间的优先相互作用。内区代表集合管(CD)簇,包含 CD、一些升支细段(ATL)和一些升支直血管;外区代表簇间区,包含降支细段、降支直血管、剩余的 ATL 和额外的升支直血管。在肾髓质的上部,该模型预测 CD 簇中的间质 Na(+)和尿素浓度(和渗透压)与簇间区有显著差异:模型计算预测 CD 簇的尿素浓度高于簇间区,这一发现与主要依赖于 ATL 中的 NaCl 和 CD 中的尿素混合的浓缩机制一致。在肾髓质的下部,降支细段中水通透性有限或几乎为零,通过增加溶质游离水的吸收速率来提高浓缩效率。模型预测,ATL 上部的高尿素通透性和最长环弯曲与 CD 的接触面积增加都适度提高了浓缩能力。一个令人惊讶的发现是,该基于区域的模型的浓缩能力低于具有每个水平径向均匀间质液的模型 IM 的能力,但在其他方面与基于区域的模型类似。