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Pré-Publication, Document De Travail Année : 2011

Analysis of a simplified model of the urine concentration mechanism

Résumé

We study a non linear stationary system describing the transport of solutes dissolved in a fluid circulating in a counter-current tubular architecture, which constitutes a simplified model of a kidney nephron. We prove that for every Lipschitz and monotonic nonlinearity (which stems from active transport across the ascending limb), the dynamic system, a PDE which we study through contraction properties, relaxes toward the unique stationary state. A study of the linearized stationary operator enables us, using eigenelements, to further show that under certain conditions regarding the nonlinearity, the relaxation is exponential. We also describe a finite-volume scheme which allows us to efficiently approach the numerical solution to the stationary system. Finally, we apply this numerical method to illustrate how the counter-current arrangement of tubes enhances the axial concentration gradient, thereby favoring the production of highly concentrated urine.
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Dates et versions

hal-00605109 , version 1 (30-06-2011)
hal-00605109 , version 2 (03-03-2013)

Identifiants

  • HAL Id : hal-00605109 , version 1

Citer

Magali Tournus, Aurélie Edwards, Nicolas Seguin, Benoît Perthame. Analysis of a simplified model of the urine concentration mechanism. 2011. ⟨hal-00605109v1⟩
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