THEORETICAL ANALYSIS OF SOLUTE & WATER TRANSPORT IN MAMMALIAN KIDNEYS

这项工作的总体目标是综合实验数据。 在膜和分子水平上转化为预测数学 哺乳动物肾脏的模型，对理解两者都很有用 它的正常和病态功能。哺乳动物的肾脏由一个 大量的单位，肾单位，并行运行。每个人 肾单位是一根长约1厘米、10次方厘米的管子。 直径。封闭的一端缠绕着一个特殊的结 毛细血管形成肾小球；开放的末端合并成空的 输尿管，然后是膀胱。尿液形成的第一步 是表达一种蛋白质和无细胞的血液滤液。AS 这种肾小球滤液顺着肾单位流下，它被 对大多数溶质和水的选择性重吸收，以及 选择性地分泌其他溶质以形成最终的尿液。通过 改变最终尿液的成分，尿液的成分 沐浴身体细胞的间质液体维持在 狭窄的界限与生活相容。从实验中分离出 灌流的小管，许多关于输运性质的知识 单个肾小管，以及来自整个动物实验的 人们对肾脏的整体功能有很多了解。缺少的是 将微观功能与整体功能联系起来的连贯理论 功能。我们为此设计的建模的一般方法 错综复杂的系统就是要解描述的微分方程组 单个管内的体积和溶质流动与假设相反 溶质浓度和静水压力值 血管间质间隙。透壁溶质和水通量 为管子计算的，然后代入差分器 空间的方程式。如果这些满足某些指定的要求 宽容，我们有一个解决方案。如果不是，则对假设的 浓度由牛顿型方法计算。该计划是 迭代直到得到满意的解。我们目前的情况 研究正在沿着两个平行的方向向更现实的模型发展 路径：L)融入肾脏解剖的更多细节。这里 我们正在从假设间隙空间的模型转向 径向很好地混合到模型中，在该模型中，径向和 考虑了结构的轴向分布。2)成立为 更多关于经口部运输的细节。我们目前的肾脏模型 描述从管腔到周围的溶质和水的通量 将管壁作为单层膜处理的间隙 并用不可逆的现象学来描述通过它的通量 热力学。在各个细分市场的模型中，此描述具有 取而代之的是一个考虑通过 细胞和细胞内空间。这些详细的管状模型包括 被引入全肾模型。

The overall goal of this work is to synthesize experimental data at the membrane and molelcular level into predictive mathematical models of the mammalian kidney that are useful in understanding both its normal and diseased function. The mammalian kidney consists of a large number of units, the nephrons, operating in parallel. Each nephron is a tube approximately 1 cm long and 10 to the -3 power cm in diameter. The closed end is wrapped around a specialized knot of capillaries to form the glomerulus; the open ends merge to empty into the ureter and thence the bladder. The first step in urine formation is the expression of a protein and cell-free filtrate of blood. As this glomerular filtrate flows down the nephron it is modified by the selective reabsorption of most of the solutes and water and the selective secretion of other solutes to form the final urine. By varying the composition of the final urine, the composition of the interstitial fluid bathing the cells of the body is maintained within the narrow limits compatible with life. From experiments on isolated perfused tubules, a great deal is known about the transport properties of the individual renal tubules, and from whole animal experiments a great deal is known about overall function of the kidney. Lacking is a coherent theory that links microscopic function with overall function. The general method we have devised for modeling this intricate system is to solve the differential equations describing volume and solute flow in the individual tubules against assumed values of solute concentrations and hydrostatic pressure in the vascular interstitial space. Transmural solute and water fluxes computed for the tubes are then substituted into the differential equations for the space. If these are satisfied to some specified tolerance, we have a solution. If not, a correction to the assumed concentrations is computed by a Newton type method. The scheme is iterated until a satisfactory solution is obtained. Our current research is evolving toward more realistic models along two parallel paths: l) Incorporation of more details of the renal anatomy. Here we are moving from models in which the interstitial space is assumed to be radially well mixed toward models in which both the radial and axial distribution of structures are considered. 2) Incorporation of more details of transtubular transport. Our current kidney models describe fluxes of solute and water from tubular lumen to surrounding interstitial space by treating the tubular wall as a single membrane and describing fluxes through it by the phenomenology of irreversible thermodynamics. In models of individual segments this description has been replaced by one that considers the details of transport through cells and intracellular space. These detailed tubular models are being introduced into the whole kidney models.