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PubMed1994

Externally driven countercurrent multiplication in a mathematical model of the urinary concentrating mechanism of the renal inner medulla.

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.

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PubMedDate not supplied

Countercurrent extraction of sparingly soluble gases for membrane introduction mass spectrometry.

Membrane introduction mass spectrometry has been applied to inert gas measurements in blood and tissue, but gases with low blood solubility are associated with reduced sensitivity. Countercurrent extraction of inert gases from a blood sample into a water carrier phase has the potential to extract most of the gas sample while avoiding dependence of signal on blood solubility. We present the design of a membrane countercurrent exchange (CCE) device coupled with a conventional direct insertion membrane probe to measure partial pressure of low solubility inert gases in aqueous samples. A mathematical model of steady-state membrane CCB predicts that countercurrent extraction with appropriate selection of carrier and sample flow rates can provide a mass spectrometer signal nearly independent of variations in solubility over a specified range, while retaining a linear response to changes in gas partial pressure over several orders of magnitude. Experimental data are presented for sulfur hexafluoride and krypton in water samples. Optimal performance is dependent on adequate equilibration between the sample and carrier streams, and the large resistance to diffusion in the aqueous phase for insoluble gases presents a substantial challenge to the application of this principle.

Animals↗