scholarly journals A mathematical model of O2 transport in the rat outer medulla. I. Model formulation and baseline results

2009 ◽  
Vol 297 (2) ◽  
pp. F517-F536 ◽  
Author(s):  
Jing Chen ◽  
Anita T. Layton ◽  
Aurélie Edwards
Keyword(s):  
Mathematical Model ◽  
Structural Organization ◽  
Capillary Flow ◽  
Renal Medulla ◽  
Vascular Bundles ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Vasa Recta ◽  
Complex Structural ◽  
The Impact

The mammalian kidney is particularly vulnerable to hypoperfusion, because the O2 supply to the renal medulla barely exceeds its O2 requirements. In this study, we examined the impact of the complex structural organization of the rat outer medulla (OM) on O2 distribution. We extended the region-based mathematical model of the rat OM developed by Layton and Layton ( Am J Physiol Renal Physiol 289: F1346–F1366, 2005) to incorporate the transport of RBCs, Hb, and O2. We considered basal cellular O2 consumption and O2 consumption for active transport of NaCl across medullary thick ascending limb epithelia. Our model predicts that the structural organization of the OM results in significant Po2 gradients in the axial and radial directions. The segregation of descending vasa recta, the main supply of O2, at the center and immediate periphery of the vascular bundles gives rise to large radial differences in Po2 between regions, limits O2 reabsorption from long descending vasa recta, and helps preserve O2 delivery to the inner medulla. Under baseline conditions, significantly more O2 is transferred radially between regions by capillary flow, i.e., advection, than by diffusion. In agreement with experimental observations, our results suggest that 79% of the O2 supplied to the medulla is consumed in the OM and that medullary thick ascending limbs operate on the brink of hypoxia.

scholarly journals A mathematical model of O2 transport in the rat outer medulla. II. Impact of outer medullary architecture

2009 ◽  
Vol 297 (2) ◽  
pp. F537-F548 ◽  
Author(s):  
Jing Chen ◽  
Aurélie Edwards ◽  
Anita T. Layton
Keyword(s):  
Mathematical Model ◽  
Anaerobic Metabolism ◽  
Critical Level ◽  
Vascular Bundles ◽  
Outer Medulla ◽  
O2 Transport ◽  
Vasa Recta ◽  
Parameter Variations ◽  
Complex Structural ◽  
The Impact

we extended the region-based mathematical model of the urine-concentrating mechanism in the rat outer medulla (OM) developed by Layton and Layton ( Am J Physiol Renal Physiol 289: F1346–F1366, 2005) to examine the impact of the complex structural organization of the OM on O2 transport and distribution. In the present study, we investigated the sensitivity of predicted Po2 profiles to several parameters that characterize the degree of OM regionalization, boundary conditions, structural dimensions, transmural transport properties, and relative positions and distributions of tubules and vessels. Our results suggest that the fraction of O2 supplied to descending vasa recta (DVR) that reaches the inner medulla, i.e., a measure of the axial Po2 gradient in the OM, is insensitive to parameter variations as a result of the sequestration of long DVR in the vascular bundles. In contrast, O2 distribution among the regions surrounding the vascular core strongly depends on the radial positions of medullary thick ascending limbs (mTALs) relative to the vascular core, the degree of regionalization, and the distribution of short DVR along the corticomedullary axis. Moreover, if it is assumed that the mTAL active Na+ transport rate decreases when mTAL Po2 falls below a critical level, O2 availability to mTALs has a significant impact on the concentrating capability of the model OM. The model also predicts that when the OM undergoes hypertrophy, its concentrating capability increases significantly only when anaerobic metabolism supports a substantial fraction of the mTAL active Na+ transport and is otherwise critically reduced by low interstitial and mTAL luminal Po2 in a hypertrophied OM.

A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. II. Parameter sensitivity and tubular inhomogeneity

2005 ◽  
Vol 289 (6) ◽  
pp. F1367-F1381 ◽  
Author(s):  
Anita T. Layton ◽  
Harold E. Layton
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Rat Kidney ◽  
Vascular Bundles ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Model Calculations ◽  
Concentrating Mechanism ◽  
Vasa Recta ◽  
Urine Concentrating Mechanism

In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1346–F1366, 2005), a region-based mathematical model was formulated for the urine concentrating mechanism (UCM) in the outer medulla (OM) of the rat kidney. In the present study, we quantified the sensitivity of that model to several structural assumptions, including the degree of regionalization and the degree of inclusion of short descending limbs (SDLs) in the vascular bundles of the inner stripe (IS). Also, we quantified model sensitivity to several parameters that have not been well characterized in the experimental literature, including boundary conditions, short vasa recta distribution, and ascending vasa recta (AVR) solute permeabilities. These studies indicate that regionalization elevates the osmolality of the fluid delivered into the inner medulla via the collecting ducts; that model predictions are not significantly sensitive to boundary conditions; and that short vasa recta distribution and AVR permeabilities significantly impact concentrating capability. Moreover, we investigated, in the context of the UCM, the functional significance of several aspects of tubular segmentation and heterogeneity: SDL segments in the IS that are likely to be impermeable to water but highly permeable to urea; a prebend segment of SDLs that may be functionally like thick ascending limb (TAL); differing IS and outer stripe Na+ active transport rates in TAL; and potential active urea secretion into the proximal straight tubules. Model calculations predict that these aspects of tubular of segmentation and heterogeneity generally enhance solute cycling or promote effective UCM function.

scholarly journals Impact of renal medullary three-dimensional architecture on oxygen transport

2014 ◽  
Vol 307 (3) ◽  
pp. F263-F272 ◽  
Author(s):  
Brendan C. Fry ◽  
Aurélie Edwards ◽  
Ioannis Sgouralis ◽  
Anita T. Layton
Keyword(s):  
Oxygen Delivery ◽  
Interstitial Fluid ◽  
Collecting Duct ◽  
Rat Kidney ◽  
Three Dimensional ◽  
Fluid Composition ◽  
Vascular Bundles ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
The Impact

We have developed a highly detailed mathematical model of solute transport in the renal medulla of the rat kidney to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies. The model represents the arrangement of tubules around a vascular bundle in the outer medulla and around a collecting duct cluster in the upper inner medulla. Model simulations yield marked gradients in intrabundle and interbundle interstitial fluid oxygen tension (Po2), NaCl concentration, and osmolality in the outer medulla, owing to the vigorous active reabsorption of NaCl by the thick ascending limbs. In the inner medulla, where the thin ascending limbs do not mediate significant active NaCl transport, interstitial fluid composition becomes much more homogeneous with respect to NaCl, urea, and osmolality. Nonetheless, a substantial Po2 gradient remains, owing to the relatively high oxygen demand of the inner medullary collecting ducts. Perhaps more importantly, the model predicts that in the absence of the three-dimensional medullary architecture, oxygen delivery to the inner medulla would drastically decrease, with the terminal inner medulla nearly completely deprived of oxygen. Thus model results suggest that the functional role of the three-dimensional medullary architecture may be to preserve oxygen delivery to the papilla. Additionally, a simulation that represents low medullary blood flow suggests that the separation of thick limbs from the vascular bundles substantially increases the risk of the segments to hypoxic injury. When nephrons and vessels are more homogeneously distributed, luminal Po2 in the thick ascending limb of superficial nephrons increases by 66% in the inner stripe. Furthermore, simulations predict that owing to the Bohr effect, the presumed greater acidity of blood in the interbundle regions, where thick ascending limbs are located, relative to that in the vascular bundles, facilitates the delivery of O2 to support the high metabolic requirements of the thick limbs and raises NaCl reabsorption.

scholarly journals Nitric oxide and superoxide transport in a cross section of the rat outer medulla. I. Effects of low medullary oxygen tension

2010 ◽  
Vol 299 (3) ◽  
pp. F616-F633 ◽  
Author(s):  
Aurélie Edwards ◽  
Anita T. Layton
Keyword(s):  
Nitric Oxide ◽  
Cross Section ◽  
Vascular Bundle ◽  
Fluid Model ◽  
Vascular Bundles ◽  
Concentration Gradients ◽  
Outer Medulla ◽  
Vasa Recta ◽  
The Difference ◽  
The Impact

To examine the impact of the complex radial organization of the rat outer medulla (OM) on the distribution of nitric oxide (NO), superoxide (O2−) and total peroxynitrite (ONOO), we developed a mathematical model that simulates the transport of those species in a cross section of the rat OM. To simulate the preferential interactions among tubules and vessels that arise from their relative radial positions in the OM, we adopted the region-based approach developed by Layton and Layton ( Am J Physiol Renal Physiol 289: F1346–F1366, 2005). In that approach, the structural organization of the OM is represented by means of four concentric regions centered on a vascular bundle. The model predicts the concentrations of NO, O2−, and ONOO in the tubular and vascular lumen, epithelial and endothelial cells, red blood cells (RBCs), and interstitial fluid. Model results suggest that the large gradients in Po2 from the core of the vascular bundle toward its periphery, which stem from the segregation of O2-supplying descending vasa recta (DVR) within the vascular bundles, in turn generate steep radial NO and O2− concentration gradients, since the synthesis of both solutes is O2 dependent. Without the rate-limiting effects of O2, NO concentration would be lowest in the vascular bundle core, that is, the region with the highest density of RBCs, which act as a sink for NO. Our results also suggest that, under basal conditions, the difference in NO concentrations between DVR that reach into the inner medulla and those that turn within the OM should lead to differences in vasodilation and preferentially increase blood flow to the inner medulla.

Vasoconstriction of outer medullary vasa recta by angiotensin II is modulated by prostaglandin E2

1994 ◽  
Vol 266 (6) ◽  
pp. F850-F857 ◽  
Author(s):  
T. L. Pallone
Keyword(s):  
Angiotensin Ii ◽  
Prostaglandin E2 ◽  
Regional Blood Flow ◽  
Renal Medulla ◽  
Hydraulic Pressure ◽  
Vascular Bundles ◽  
Ang Ii ◽  
Vasa Recta ◽  
Anatomical Arrangement

Vasa recta were dissected from outer medullary vascular bundles in the rat and perfused in vitro. Examination by transmission electron microscopy reveals them to be only outer medullary descending vasa recta (OM-DVR). To establish a method for systematic examination of vasoconstriction, OMDVR were perfused at 5 nl/min with collection pressure increased to 5 mmHg. Under these conditions, transmembrane volume flux was found to be near zero, and the transmural hydraulic pressure gradient was found to be < 15 mmHg. Over a concentration range of 10(-12) to 10(-8) M, abluminal application of angiotensin II (ANG II) caused graded focal vasoconstriction of OMDVR that is blocked by saralasin. Luminal application of ANG II over the same concentration range was much less effective. Abluminal application of prostaglandin E2 (PGE2) shifted the vasoconstrictor response of OMDVR to higher ANG II concentrations. PGE2 reversibly dilated OMDVR that had been preconstricted by ANG II. These results demonstrate that OMDVR are vasoactive segments. Their anatomical arrangement suggests that they play a key role in the regulation of total and regional blood flow to the renal medulla.

scholarly journals Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide

2011 ◽  
Vol 301 (5) ◽  
pp. F979-F996 ◽  
Author(s):  
Aurélie Edwards ◽  
Anita T. Layton
Keyword(s):  
Nitric Oxide ◽  
Active Transport ◽  
Collecting Duct ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Nacl Transport ◽  
Complex Interactions ◽  
Medullary Thick Ascending Limb ◽  
The Impact ◽  
Stimulation Of

We expanded our region-based model of water and solute exchanges in the rat outer medulla to incorporate the transport of nitric oxide (NO) and superoxide (O2−) and to examine the impact of NO-O2− interactions on medullary thick ascending limb (mTAL) NaCl reabsorption and oxygen (O2) consumption, under both physiological and pathological conditions. Our results suggest that NaCl transport and the concentrating capacity of the outer medulla are substantially modulated by basal levels of NO and O2−. Moreover, the effect of each solute on NaCl reabsorption cannot be considered in isolation, given the feedback loops resulting from three-way interactions between O2, NO, and O2−. Notwithstanding vasoactive effects, our model predicts that in the absence of O2−-mediated stimulation of NaCl active transport, the outer medullary concentrating capacity (evaluated as the collecting duct fluid osmolality at the outer-inner medullary junction) would be ∼40% lower. Conversely, without NO-induced inhibition of NaCl active transport, the outer medullary concentrating capacity would increase by ∼70%, but only if that anaerobic metabolism can provide up to half the maximal energy requirements of the outer medulla. The model suggests that in addition to scavenging NO, O2− modulates NO levels indirectly via its stimulation of mTAL metabolism, leading to reduction of O2 as a substrate for NO. When O2− levels are raised 10-fold, as in hypertensive animals, mTAL NaCl reabsorption is significantly enhanced, even as the inefficient use of O2 exacerbates hypoxia in the outer medulla. Conversely, an increase in tubular and vascular flows is predicted to substantially reduce mTAL NaCl reabsorption. In conclusion, our model suggests that the complex interactions between NO, O2−, and O2 significantly impact the O2 balance and NaCl reabsorption in the outer medulla.

scholarly journals Inhibition of calcium signaling in descending vasa recta endothelia by ANG II

2000 ◽  
Vol 278 (4) ◽  
pp. H1248-H1255 ◽  
Author(s):  
Thomas L. Pallone ◽  
Erik P. Silldorff ◽  
Zhong Zhang
Keyword(s):  
Collecting Duct ◽  
No Production ◽  
Vascular Bundles ◽  
Thick Ascending Limb ◽  
Ang Ii ◽  
Vasomotor Tone ◽  
Medullary Thick Ascending Limb ◽  
Vasa Recta ◽  
Medullary Collecting Duct ◽  
Peak Phase

The intracellular calcium ([Ca2+]i) response of outer medullary descending vasa recta (OMDVR) endothelia to ANG II was examined in fura 2-loaded vessels. Abluminal ANG II (10− 8 M) caused [Ca2+]i to fall in proportion to the resting [Ca2+]i ( r =0.82) of the endothelium. ANG II (10− 8 M) also inhibited both phases of the [Ca2+]i response generated by bradykinin (BK, 10− 7 M), 835 ± 201 versus 159 ± 30 nM (peak phase) and 169 ± 26 versus 103 ± 14 nM (plateau phase) (means ± SE). Luminal ANG II reduced BK (10− 7 M)-stimulated plateau [Ca2+]i from 180 ± 40 to 134 ± 22 nM without causing vasoconstriction. Abluminal ANG II added to the bath after luminal application further reduced [Ca2+]i to 113 ± 9 nM and constricted the vessels. After thapsigargin (TG) pretreatment, ANG II (10− 8 M) caused [Ca2+]i to fall from 352 ± 149 to 105 ± 37 nM. This effect occurred at a threshold ANG II concentration of 10− 10 M and was maximal at 10− 8 M. ANG II inhibited both the rate of Ca2+ entry into [Ca2+]i-depleted endothelia and the rate of Mn2+ entry into [Ca2+]i-replete endothelia. In contrast, ANG II raised [Ca2+]i in the medullary thick ascending limb and outer medullary collecting duct, increasing [Ca2+]i from baselines of 99 ± 33 and 53 ± 11 to peaks of 200 ± 47 and 65 ± 11 nM, respectively. We conclude that OMDVR endothelia are unlikely to be the source of ANG II-stimulated NO production in the medulla but that interbundle nephrons might release Ca2+-dependent vasodilators to modulate vasomotor tone in vascular bundles.

Renal medullary blood flow: its measurement and physiology

1986 ◽  
Vol 64 (7) ◽  
pp. 873-880 ◽  
Author(s):  
W. A. Cupples
Keyword(s):  
Blood Flow ◽  
Renal Medulla ◽  
Vascular Bundles ◽  
Medullary Blood Flow ◽  
Vasa Recta ◽  
Countercurrent Exchange ◽  
Renal Medullary Blood Flow ◽  
Urinary Concentrating Ability ◽  
Velocity Tracking ◽  
Uptake Method

The vasculature of the mammalian renal medulla is complex, having neither discrete input nor output. There is also efficient countercurrent exchange between ascending and descending vasa recta in the vascular bundles. These considerations have hampered measurement of medullary blood flow since they impose pronounced constraints on methods used to assess flow. Three main strategies have been used: (i) indicator extraction; (ii) erythrocyte velocity tracking; and (iii) indicator dilution. These are discussed with respect to their assumptions, requirements, and limitations. There is a consensus that medullary blood flow is autoregulated, albeit over a narrower pressure range than is total renal blood flow. When normalized to gram tissue weight, medullary blood flow in the dog is similar to that in the rat, on the order of 1 to 1.5 mL∙min−1∙g−1. This is considerably greater than estimated by the radioiodinated albumin uptake method which has severe conceptual and practical problems. From both theoretical and experimental evidence it ssems that urinary concentrating ability is considerably less sensitive to changes in medullary blood flow than is often assumed.

scholarly journals Fluid dilution and efficiency of Na+ transport in a mathematical model of a thick ascending limb cell

2013 ◽  
Vol 304 (6) ◽  
pp. F634-F652 ◽  
Author(s):  
Aniel Nieves-González ◽  
Chris Clausen ◽  
Mariano Marcano ◽  
Anita T. Layton ◽  
Harold E. Layton ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cell Model ◽  
Cell Volume Regulation ◽  
Mass Conservation ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Transport Efficiency ◽  
Nacl Concentration ◽  
Model Equations ◽  
Static Head

Thick ascending limb (TAL) cells are capable of reducing tubular fluid Na+ concentration to as low as ∼25 mM, and yet they are thought to transport Na+ efficiently owing to passive paracellular Na+ absorption. Transport efficiency in the TAL is of particular importance in the outer medulla where O2 availability is limited by low blood flow. We used a mathematical model of a TAL cell to estimate the efficiency of Na+ transport and to examine how tubular dilution and cell volume regulation influence transport efficiency. The TAL cell model represents 13 major solutes and the associated transporters and channels; model equations are based on mass conservation and electroneutrality constraints. We analyzed TAL transport in cells with conditions relevant to the inner stripe of the outer medulla, the cortico-medullary junction, and the distal cortical TAL. At each location Na+ transport efficiency was computed as functions of changes in luminal NaCl concentration ([NaCl]), [K+], [NH4+], junctional Na+ permeability, and apical K+ permeability. Na+ transport efficiency was calculated as the ratio of total net Na+ transport to transcellular Na+ transport. Transport efficiency is predicted to be highest at the cortico-medullary boundary where the transepithelial Na+ gradient is the smallest. Transport efficiency is lowest in the cortex where luminal [NaCl] approaches static head.

Effect of norepinephrine and acetylcholine on outer medullary descending vasa recta

1995 ◽  
Vol 269 (2) ◽  
pp. H710-H716 ◽  
Author(s):  
S. Yang ◽  
E. P. Silldorff ◽  
T. L. Pallone
Keyword(s):  
Nitric Oxide ◽  
Nitric Oxide Synthase ◽  
Regional Blood Flow ◽  
Renal Medulla ◽  
Cholinergic Innervation ◽  
Vascular Bundles ◽  
Nitric Oxide Synthase Inhibitor ◽  
Vasa Recta ◽  
Oxide Synthase

To examine their responsiveness to norepinephrine (NE) and acetylcholine (ACh), outer medullary descending vasa recta (OMDVR) have been dissected from vascular bundles of the rat and perfused in vitro. Abluminal application of NE produced graded vasoconstriction in a concentration range of 10(-9)-10(-6) M. When applied with NE, ACh at concentrations of 10(-8)-10(-5) M dilated NE-preconstricted OMDVR. In contrast, ACh applied in the absence of NE caused vasoconstriction. ACh-induced vasodilation was blocked by addition of the nitric oxide synthase inhibitor N omega-nitro-L-arginine (L-NNA, 2 x 10(-4) M). L-NNA in the absence of ACh enhanced NE-induced vasoconstriction. Supraphysiological (10(-3) M) L-arginine (L-Arg) reversed the effects of L-NNA, and abluminal application of L-NNA alone resulted in OMDVR vasoconstriction. At concentrations of 10(-6)-10(-3) M, abluminal application of L-Arg produced graded vasodilation of NE-constricted OMDVR. These results suggest that adrenergic and cholinergic innervation could influence OMDVR vasomotor tone to modulate total and regional blood flow to the renal medulla. The data also favor a role for the activity of constitutively expressed nitric oxide synthase to modulate OMDVR vasoactivity.

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