Externally driven countercurrent multiplication in a mathematical model of the urinary concentrating mechanism of the renal inner medulla
| Autor: | J. Frank Jen, John L. Stephenson |
|---|---|
| Rok vydání: | 1994 |
| Předmět: |
Cell Membrane Permeability
Differential equation General Mathematics Immunology Countercurrent multiplication Biological Transport Active Natriuresis Models Biological General Biochemistry Genetics and Molecular Biology Kidney Concentrating Ability Body Water Species Specificity Cricetinae Loop of Henle medicine Renal medulla Animals Countercurrent Distribution General Environmental Science Pharmacology Physics Kidney Medulla Osmotic concentration General Neuroscience Osmolar Concentration Anatomy Mechanics Fluid transport medicine.anatomical_structure Computational Theory and Mathematics Flow (mathematics) Permeability (electromagnetism) Rabbits General Agricultural and Biological Sciences |
| Zdroj: | Bulletin of Mathematical Biology. 56:491-514 |
| ISSN: | 0092-8240 |
| Popis: | 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, ɛ , 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 ɛ 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. |
| Databáze: | OpenAIRE |
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