A model of calcium transport along the rat nephron

Abstract

(Ca 2ϩ ) transport along the rat nephron to investigate the factors that promote hypercalciuria. The model is an extension of the flat medullary model of Hervy and Thomas (Am J Physiol Renal Physiol 284: F65-F81, 2003). It explicitly represents all the nephron segments beyond the proximal tubules and distinguishes between superficial and deep nephrons. It solves dynamic conservation equations to determine NaCl, urea, and Ca 2ϩ concentration profiles in tubules, vasa recta, and the interstitium. Calcium is known to be reabsorbed passively in the thick ascending limbs and actively in the distal convoluted (DCT) and connecting (CNT) tubules. Our model predicts that the passive diffusion of Ca 2ϩ from the vasa recta and loops of Henle generates a significant axial Ca 2ϩ concentration gradient in the medullary interstitium. In the base case, the urinary Ca 2ϩ concentration and fractional excretion are predicted as 2.7 mM and 0.32%, respectively. Urinary Ca 2ϩ excretion is found to be strongly modulated by water and NaCl reabsorption along the nephron. Our simulations also suggest that Ca 2ϩ molar flow and concentration profiles differ significantly between superficial and deep nephrons, such that the latter deliver less Ca 2ϩ to the collecting duct. Finally, our results suggest that the DCT and CNT can act to counteract upstream variations in Ca 2ϩ transport but not always sufficiently to prevent hypercalciuria. calcium; finite volume; kidney; mathematical model; transport CALCIUM (CA 2ϩ ) IS THE MOST abundant cation in the body. It plays an essential role in cardiac, skeletal, and smooth muscle function, and extra-and intracellular Ca 2ϩ concentrations ([Ca 2ϩ ]) must therefore be kept within a narrow range. Calcium homeostasis is maintained by the concerted action of the intestine, the parathyroid glands, and the kidneys. Preserving low Ca 2ϩ concentrations in the urinary filtrate is especially important, since hypercalciuria is one of the major risk factors for the formation of kidney stones. Recent studies on Ca 2ϩ handling by the kidney have focused on the molecular transporters and sensors of Ca 2ϩ (2, 9), but our understanding of Ca 2ϩ transport at the organ level remains limited. Whether there is a corticomedullary interstitial [Ca 2ϩ ] gradient has yet to be determined, and the contribution of each nephron segment to perturbations in the renal Ca 2ϩ balance is not fully understood. To address these questions, we developed a mathematical model of renal Ca 2ϩ transport across all nephron segments below the proximal tubules from the descending limbs of Henle to the inner medullary collecting ducts (IMCD). Our model is based on that of Hervy and Thomas (17), referred to below as the HT model, which describes the transport of water, NaCl, glucose, and lactate in the renal medulla. We modified the HT model to 1) make it dynamic, 2) explicitly represent the distal cortical segments, and 3) incorporate Ca 2ϩ transport. For this purpose, we developed a new finite-volume scheme that is robust and fast.About t...

Regulation of calcium reabsorption along the rat nephron: a modeling study

“…Another reason why the contribution of the CD to Ca 2ϩ transport is difficult to determine experimentally has to do with the heterogeneity of tubular transport capacity. Calcium reabsorption profiles differ significantly between superficial and juxta-medullary nephrons (which merge in the CD system), as previously recognized (1,25) and as confirmed by our recent macroscopic model of Ca 2ϩ transport in different populations of nephrons and vasa recta (54). That model did not explicitly incorporate apical and basolateral transporters, instead it assumed segment-specific Ca 2ϩ permeability values and prescribed the transepithelial voltage along the nephrons.…”

“…We should nevertheless acknowledge some of its limitations. We consider one representative nephron, without distinguishing between superficial and juxta-medullary nephrons, when in fact luminal concentrations at the mTAL inlet are predicted to vary significantly with the length of Henle's loop (33,42,54). Because the model does not take into consideration the complex architecture of the medulla and the role of vasa recta, it assumes fixed interstitial concentration gradients along the corticomedullary axis, following the approach of Weinstein (61); we did, however, abolish these gradients in the furosemide simulations.…”

“…Peritubular and inlet Ca 2ϩ concentrations. We recently built a "macroscopic" model of calcium transport in different populations of nephrons, vasa recta, and the interstitium (54). In contrast with the current model, the macroscopic model did not represent the epithelial barrier at the cellular level, but it computed interstitial concentrations.…”

Three-dimensional reconstruction of the rat nephron

“…In recent years, especially the rat renal medulla has been the subject of intensive comparative structural-functional studies and computer modeling [see e.g., Refs. 15 and 20 and very recently a very comprehensive study on modeling calcium transport in the rat nephron was published (28)]. A prerequisite for conducting these kinds of studies is that the detailed morphology of the kidney is known.…”

A simple derivation of BV bounds for inhomogeneous relaxation systems

“…The problem of interest is to prove the convergence of the microscopic quantities depending on ǫ toward the macroscopic quantities. A problem entering the framework of hyperbolic relaxation is motivated by very simplified models of kidney physiology [18,19,17] and fits the Jin and Xin framework with two major differences, boundary conditions, and spatial dependence of the source term. The type of boundary condition and the spatial dependence constitute the main novelty of the present study.…”