Jen J F, Stephenson J L
Department of Physiology and Biophysics, Cornell University Medical College, New York, NY 10021.
Bull Math Biol. 1994 May;56(3):491-514. doi: 10.1007/BF02460468.
Substitution of measured permeabilities into mathematical models of the concentrating mechanism of the renal inner medulla yields less than the known urine osmolalities. To gain a better understanding of the mechanism we analyse a model in which a force of unspecified origin [expressed as fraction, epsilon, of entering descending thin limb (DTL) concentration] drives fluid from DTL to interstitial vascular space (CORE), thus concentrating the solution in DTL. When flow in the DTL reverses at the hairpin bend of the loop of Henle, the high solute permeability of ascending thin limb (ATL) permits solute to diffuse into the CORE thus permitting epsilon to be multiplied many-fold. Behavior of the model is described by two non-linear differential equations. In the limit for infinite salt permeability of ATL the two equations reduce to a single equation that is formally identical with that for the Hargitay and Kuhn multiplier, which assumes fluid transport directly from DTL to ATL (Z. Electrochem. Angew. Phys. Chem. 55, 539, 1951). Solutions of the equations describing the model with parameters taken from perfused thin limbs show that urine osmolalities of the order of 5000 mosm L-1 can be generated by forces of the order of 20 mosm L-1. It seems probable that mammals including desert rodents use some variant of this basic mechanism for inner medullary concentration.
将测得的渗透率代入肾内髓质浓缩机制的数学模型中，得到的结果低于已知的尿渗透压。为了更好地理解该机制，我们分析了一个模型，其中一个来源不明的力（表示为进入降支细段（DTL）浓度的分数ε）将液体从DTL驱动到间质血管空间（CORE），从而使DTL中的溶液浓缩。当DTL中的液体在亨利袢的发夹弯处反向流动时，升支细段（ATL）的高溶质渗透率允许溶质扩散到CORE中，从而使ε能够增加许多倍。该模型的行为由两个非线性微分方程描述。在ATL的盐渗透率为无限大的极限情况下，这两个方程简化为一个与Hargitay和Kuhn乘数的方程形式相同的方程，该乘数假设液体直接从DTL运输到ATL（《电化学与应用物理化学杂志》55, 539, 1951）。用取自灌注细段的参数描述该模型的方程的解表明，大约20 mosm L-1的力可以产生大约5000 mosm L-1的尿渗透压。包括沙漠啮齿动物在内的哺乳动物似乎很可能使用这种内髓质浓缩基本机制的某种变体。
