Impacts of nitric oxide and superoxide on renal medullary oxygen transport and urine concentration

A comparative modeling study of the mitochondrial function of the proximal tubule and thick ascending limb cells in the rat kidney

To reabsorb >99% of the glomerular filtrate, the metabolic demand of the kidney is high. Interestingly, renal blood flow distribution exhibits marked inhomogeneity, with typical tissue oxygen tension (Po2) of 50-60 mmHg in the well-perfused cortex and 10-20 mmHg in the inner medulla. Cellular fluid composition and acidity also varies substantially. To understand how different renal epithelial cells adapt to their local environment, we have developed and applied computational models of mitochondrial function of proximal convoluted tubule cell (baseline Po2 = 50 mmHg, cytoplasmic pH = 7.20) and medullary thick ascending limb (mTAL) cell (baseline Po2 = 10 mmHg, cytoplasmic pH = 6.85). The models predict key cellular quantities, including ATP generation, P/O (phosphate/oxygen) ratio, proton motive force, electrical potential gradient, oxygen consumption, the redox state of key electron carriers, and ATP consumption. Model simulations predict that close to their respective baseline conditions, the proximal tubule and mTAL mitochondria exhibit qualitatively similar behaviors. Nonetheless, because the mTAL mitochondrion has adapted to a much lower Po2, it can sustain a sufficiently high ATP production at Po2 as low as 4-5 mmHg, whereas the proximal tubule mitochondria would not. Also, because the mTAL cytosol is already acidic under baseline conditions, the proton motive force (pmf) exhibits higher sensitivity to further acidification. Among the different pathways that lead to oxidative phosphorylation impairment, the models predict that both the proximal tubule and mTAL mitochondria are most sensitive to reductions in Complex III activity.NEW & NOTEWORTHY Tissue fluid composition varies substantially within the mammalian kidney. The renal cortex is well perfused and pH neutral, whereas some medullary regions are hypoxic and acidic. How do these environments affect the mitochondrial function of proximal convoluted tubule and medullary thick ascending limb cells, which reside in the cortex and medulla, respectively? This computational modeling study demonstrates that these mitochondria can adapt to their contrasting environments and exhibit different sensitivities to perturbations to local environments.

Sex differences in circadian regulation of kidney function of the mouse

Kidney function is regulated by the circadian clock. Not only do glomerular filtration rate and urinary excretion oscillate during the day, but the expressions of several renal transporter proteins also exhibit circadian rhythms. Interestingly, the circadian regulation of these transporters appears to be sexually dimorphic. Thus, the goal of the present study was to investigate the mechanisms by which the kidney function of the mouse is modulated by sex and time of day. To accomplish this, we developed the first computational models of epithelial water and solute transport along the mouse nephrons that represent the effects of sex and the circadian clock on renal hemodynamics and transporter activity. We conducted simulations to study how the circadian control of renal transport genes affects overall kidney function and how that process differs between male and female mice. Simulation results predicted that tubular transport differs substantially among segments, with relative variations in water and Na+ reabsorption along the proximal tubules and thick ascending limb tracking that of glomerular filtration rate. In contrast, relative variations in distal segment transport were much larger, with Na+ reabsorption almost doubling during the active phase. Oscillations in Na+ transport drive K+ transport variations in the opposite direction. Model simulations of basic helix-loop-helix ARNT like 1 (BMAL1) knockout mice predicted a significant reduction in net Na+ reabsorption along the distal segments in both sexes, but more so in males than in females. This can be attributed to the reduction of mean epithelial Na+ channel activity in males only, a sex-specific effect that may lead to a reduction in blood pressure in BMAL1-null males.NEW & NOTEWORTHY How does the circadian control of renal transport genes affect overall kidney function, and how does that process differ between male and female mice? How does the differential circadian regulation of the expression levels of key transporter genes impact the transport processes along different nephron segments during the day? And how do those effects differ between males and females? We built computational models of mouse kidney function to answer these questions.

Sex and species differences in epithelial transport in rat and mouse kidneys: Modeling and analysis

The goal of this study was to investigate the functional implications of sex and species differences in the pattern of transporters along nephrons in the rat and mouse kidney, as reported by Veiras et al. (J Am Soc Nephrol 28: 3504–3517, 2017). To do so, we developed the first sex-specific computational models of epithelial water and solute transport along the nephrons from male and female mouse kidneys, and conducted simulations along with our published rat models. These models account for the sex differences in the abundance of apical and basolateral transporters, glomerular filtration rate, and tubular dimensions. Model simulations predict that 73% and 57% of filtered Na+ is reabsorbed by the proximal tubules of male and female rat kidneys, respectively. Due to their smaller transport area and lower NHE3 activity, the proximal tubules in the mouse kidney reabsorb a significantly smaller fraction of the filtered Na+, at 53% in male and only 34% in female. The lower proximal fractional Na+ reabsorption in female kidneys of both rat and mouse is due primarily to their smaller transport area, lower Na+/H+ exchanger activity, and lower claudin-2 abundance, culminating in significantly larger fractional delivery of water and Na+ to the downstream nephron segments in female kidneys. Conversely, the female distal nephron exhibits a higher abundance of key Na+ transporters, including Na+-Cl− cotransporters in both species, epithelial Na+ channels for the female rat, and Na+-K+-Cl−cotransporters for the female mouse. The higher abundance of transporters accounts for the enhanced water and Na+ transport along the female rat and mouse distal nephrons, relative to the respective male, resulting in similar urine excretion between the sexes. Model simulations indicate that the sex and species differences in renal transporter patterns may partially explain the experimental observation that, in response to a saline load, the diuretic and natriuretic responses were more rapid in female rats than males, but no significant sex difference was found in mice. These computational models can serve as a valuable tool for analyzing findings from experimental studies conducted in rats and mice, especially those involving genetic modifications.

Animal models of hypertension: The status of nitric oxide and oxidative stress and the role of the renal medulla

Hypertension significantly contributes to overall morbidity and mortality worldwide, and animal models of hypertension provide important tools to verify the physiological and molecular mechanisms underlying the development of the disease. A review of the most important models available would provide an insight into the appropriate targets to be addressed in the treatment of different forms of human hypertension. In the animal models discussed a special attention is given to the status and pathophysiological role of nitric oxide and its interaction with reactive oxygen species and oxidative stress. Another focus of the review are the processes running in the renal medulla which are still insufficiently explored. Deficient nitric oxide synthesis and its reduced bioavailability are important determinants of hypertension since NO is recognized as a major control factor of vascular tone homeostasis. For decades perfusion of the renal medulla has also been regarded as one of the blood pressure control factors and, noteworthily, the renal medulla belongs to the tissues with the highest NO content. The list of most often applied animal hypertension models reviewed here includes variants of salt-induced hypertension, the models with genetic background: such as spontaneously hypertensive rats (SHR) and Dahl salt sensitive (SS/SR) rats, Goldblatt 2K-1C hypertensive rats, and also the pharmacologically-plus-dietary salt-induced model known as DOCA-salt hypertension.

Urinary Thioredoxin as a Biomarker of Renal Redox Dysregulation and a Companion Diagnostic to Identify Responders to Redox-Modulating Therapeutics

Significance: The development and progression of renal diseases, including acute kidney injury (AKI) and chronic kidney disease (CKD), are the result of heterogeneous pathophysiology that reflects a range of environmental factors and, in a lesser extent, genetic mutations. The pathophysiology specific to most kidney diseases is not currently identified; therefore, these diseases are diagnosed based on non-pathological factors. For that reason, pathophysiology-based companion diagnostics for selection of pathophysiology-targeted treatments have not been available, which impedes personalized medicine in kidney disease. Recent Advances: Pathophysiology-targeted therapeutic agents are now being developed for the treatment of redox dysregulation. Redox modulation therapeutics, including bardoxolone methyl, suppresses the onset and progression of AKI and CKD. On the other hand, pathophysiology-targeted diagnostics for renal redox dysregulation are also being developed. Urinary thioredoxin (TXN) is a biomarker that can be used to diagnose tubular redox dysregulation. AKI causes oxidation and urinary excretion of TXN, which depletes TXN from the tubules, resulting in tubular redox dysregulation. Urinary TXN is selectively elevated at the onset of AKI and correlates with the progression of CKD in diabetic nephropathy. Critical Issues: Diagnostic methods should provide information about molecular mechanisms that aid in the selection of appropriate therapies to improve the prognosis of kidney disease. Future Directions: A specific diagnostic method enabling detection of redox dysregulation based on pathological molecular mechanisms is much needed and could provide the first step toward personalized medicine in kidney disease. Urinary TXN is a candidate for a companion diagnostic method to identify responders to redox-modulating therapeutics. Antioxid. Redox Signal. 36, 1051-1065.

Sex-Specific Computational Models of Kidney Function in Patients With Diabetes

The kidney plays an essential role in homeostasis, accomplished through the regulation of pH, electrolytes and fluids, by the building blocks of the kidney, the nephrons. One of the important markers of the proper functioning of a kidney is the glomerular filtration rate. Diabetes is characterized by an enlargement of the glomerular and tubular size of the kidney, affecting the afferent and efferent arteriole resistance and hemodynamics, ultimately leading to chronic kidney disease. We postulate that the diabetes-induced changes in kidney may exhibit significant sex differences as the distribution of renal transporters along the nephron may be markedly different between women and men, as recently shown in rodents. The goals of this study are to (i) analyze how kidney function is altered in male and female patients with diabetes, and (ii) assess the renal effects, in women and men, of an anti-hyperglycemic therapy that inhibits the sodium-glucose cotransporter 2 (SGLT2) in the proximal convoluted tubules. To accomplish these goals, we have developed computational models of kidney function, separate for male and female patients with diabetes. The simulation results indicate that diabetes enhances Na⁺ transport, especially along the proximal tubules and thick ascending limbs, to similar extents in male and female patients, which can be explained by the diabetes-induced increase in glomerular filtration rate. Additionally, we conducted simulations to study the effects of diabetes and SGLT2 inhibition on solute and water transport along the nephrons. Model simulations also suggest that SGLT2 inhibition raises luminal [Cl^–] at the macula densa, twice as much in males as in females, and could indicate activation of the tubuloglomerular feedback signal. By inducing osmotic diuresis in the proximal tubules, SGLT2 inhibition reduces paracellular transport, eventually leading to diuresis and natriuresis. Those effects on urinary excretion are blunted in women, in part due to their higher distal transport capacity.

Using a Human Circulation Mathematical Model to Simulate the Effects of Hemodialysis and Therapeutic Hypothermia

Background: We developed a hemodynamic mathematical model of human circulation coupled to a virtual hemodialyzer. The model was used to explore mechanisms underlying our clinical observations involving hemodialysis. Methods: The model consists of whole body human circulation, baroreflex feedback control, and a hemodialyzer. Four model populations encompassing baseline, dialysed, therapeutic hypothermia treated, and simultaneous dialysed with hypothermia were generated. In all populations atrial fibrillation and renal failure as co-morbidities, and exercise as a treatment were simulated. Clinically relevant measurables were used to quantify the effects of each in silico experiment. Sensitivity analysis was used to uncover the most relevant parameters. Results: Relative to baseline, the modelled dialysis increased the population mean diastolic blood pressure by 5%, large vessel wall shear stress by 6%, and heart rate by 20%. Therapeutic hypothermia increased systolic blood pressure by 3%, reduced large vessel shear stress by 15%, and did not affect heart rate. Therapeutic hypothermia reduced wall shear stress by 15% in the aorta and 6% in the kidneys, suggesting a potential anti-inflammatory benefit. Therapeutic hypothermia reduced cardiac output under atrial fibrillation by 12% and under renal failure by 20%. Therapeutic hypothermia and exercise did not affect dialyser function, but increased water removal by approximately 40%. Conclusions: This study illuminates some mechanisms of the action of therapeutic hypothermia. It also suggests clinical measurables that may be used as surrogates to diagnose underlying diseases such as atrial fibrillation.

Sex differences in solute and water handling in the human kidney: Modeling and functional implications

The kidneys maintain homeostasis by controlling the amount of water and electrolytes in the blood. That function is accomplished by the nephrons, which transform glomerular filtrate into urine by a transport process mediated by membrane transporters. We postulate that the distribution of renal transporters along the nephron is markedly different between men and women, as recently shown in rodents. We hypothesize that the larger abundance of a renal Na+ transport in the proximal tubules in females may also better prepare them for the fluid retention adaptations required during pregnancy and lactation. Also, kidneys play a key role in blood pressure regulation, and a popular class of anti-hypertensive medications and angiotensin converting enzymes (ACE) inhibitors have been reported to be less effective in women. Model simulations suggest that the blunted natriuretic and diuretic effects of ACE inhibition in women can be attributed, in part, to their higher distal baseline transport capacity.

A Computational Model of Kidney Function in a Patient with Diabetes

At the onset of diabetes, the kidney grows large and the glomerular filtration rate becomes abnormally high. These structural and hemodynamics changes affect kidney function and may contribute to the development of chronic kidney disease. The goal of this study is to analyze how kidney function is altered in patients with diabetes and the renal effects of an anti-hyperglyceamic therapy that inhibits the sodium-glucose cotransporter 2 (SGLT2) in the proximal convoluted tubules. To accomplish that goal, we have developed a computational model of kidney function in a patient with diabetes and conducted simulations to study the effects of diabetes and SGLT2 inhibition on solute and water transport along the nephrons. Simulation results indicate that diabetes-induced hyperfiltration and tubular hypertrophy enhances Na+ transport, especially along the proximal tubules and thick ascending limbs. These simulations suggest that SGLT2 inhibition may attenuate glomerular hyperfiltration by limiting Na+-glucose transport, raising luminal [Cl-] at the macula densa, restoring the tubuloglomerular feedback signal, thereby reducing single-nephron glomerular filtration rate.

Association between urine pH and risk of contrast-associated acute kidney injury among patients after emergency percutaneous coronary intervention: a V-shape relationship?

Aim

We investigated whether perioperative urine pH was associated with contrast-associated acute kidney injury (CA-AKI) in patients undergoing emergency percutaneous coronary intervention (PCI).

Methods

The study enrolled 1109 consecutive patients undergoing emergency PCI. Patients were divided into three groups based on perioperative urine pH (5.0–6.0, 6.5– 7.0, 7.5–8.5). The primary endpoint was the development of CA-AKI, defined as an absolute increase ≥ 0.3 mg/dL or a relative increase ≥ 50% from baseline serum creatinine within 48 h after contrast medium exposure.

Results

Overall, 181 patients (16.3%) developed contrast-associated acute kidney injury. The incidences of CA-AKI in patients with urine pH 5.0–6.0, 6.5–7.0, and 7.5–8.5 were 19.7%, 9.8%, and 23.3%, respectively. After adjustment for potential confounding factors, perioperative urine pH 5.0–6.0 and 7.5–8.5 remained independently associated with CA-AKI [odds ratio (OR)1.86, 95% confidence interval (CI) 1.25–2.82, P = 0.003; OR 2.70, 95% CI 1.5–4.68, P < 0.001, respectively]. The association was consistent in subgroups of patients stratified by several CA-AKI risk predictors. However, the risk of CA-AKI associated with urine pH 7.5–8.5 was stronger in patients with worse renal function (estimated glomerular filtration rate (eGFR) < 60 mL/min/1.73m²) (HR 5.587, 95% CI 1.178–30.599 vs. HR 2.487, 95% CI 1.331–4.579; overall interaction P < 0.05).

Conclusion

The urine pH and CA-AKI may underlie the V-shape relationship.

Sex differences in solute transport along the nephrons: effects of Na+ transport inhibition

Each day, ~1.7 kg of NaCl and 180 liters of water are reabsorbed by nephron segments in humans, with urinary excretion fine tuned to meet homeostatic requirements. These tasks are coordinated by a spectrum of renal Na⁺ transporters and channels. The goal of the present study was to investigate the extent to which inhibitors of transepithelial Na⁺ transport (T_Na) along the nephron alter urinary solute excretion and how those effects may vary between male and female subjects. To accomplish that goal, we developed sex-specific multinephron models that represent detailed transcellular and paracellular transport processes along the nephrons of male and female rat kidneys. We simulated inhibition of Na⁺/H⁺ exchanger 3 (NHE3), bumetanide-sensitive Na⁺-K⁺-2Cl^- cotransporter (NKCC2), Na⁺-Cl^- cotransporter (NCC), and amiloride-sensitive epithelial Na⁺ channel (ENaC). NHE3 inhibition simulations predicted a substantially reduced proximal tubule T_Na, and NKCC2 inhibition substantially reduced thick ascending limb T_Na. Both gave rise to diuresis, natriuresis, and kaliuresis, with those effects stronger in female rats. While NCC inhibition was predicted to have only minor impact on renal T_Na, it nonetheless had a notable effect of enhancing excretion of Na⁺, K⁺, and Cl^-, particularly in female rats. Inhibition of ENaC was predicted to have opposite effects on the excretion of Na⁺ (increased) and K⁺ (decreased) and to have only a minor impact on whole kidney T_Na. Unlike inhibition of other transporters, ENaC inhibition induced stronger natriuresis and diuresis in male rats than female rats. Overall, model predictions agreed well with measured changes in Na⁺ and K⁺ excretion in response to diuretics and Na⁺ transporter mutations.

iTRAQ-Based Comparative Proteomics Analysis of Urolithiasis Rats Induced by Ethylene Glycol

Nephrolithiasis is a frequent chronic urological condition with a high prevalence and recurrence rate. Proteomics studies on urolithiasis rat models are highly important in characterizing the pathophysiology of kidney stones and identifying potential approaches for preventing and treating kidney stones. The isobaric tags for relative and absolute quantification (iTRAQ) were performed to identify differentially expressed proteins (DEPs) in the kidney between urolithiasis rats and control rats. The results showed that 127 DEPs (85 upregulated and 42 downregulated) were identified in urolithiasis and control rats. The functions of DEPs were predicted by Gene Ontology (GO) analysis, Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis, and protein-protein interaction (PPI) network analysis. The expression of four upregulated proteins (Tagln, Akr1c9, Spp1, and Fbn1) and four downregulated proteins (Hbb, Epb42, Hmgcs2, and Ca1) were validated by parallel reaction monitoring (PRM). Proteomics studies of ethylene glycol-induced urolithiasis rat models using iTRAQ and PRM helped to elucidate the molecular mechanism governing nephrolithiasis and to identify candidate proteins for the treatment of kidney stones.

Renal oxygenation: From data to insight

Computational models have made a major contribution to the field of physiology. As the complexity of our understanding of biological systems expands, the need for computational methods only increases. But collaboration between experimental physiologists and computational modellers (ie theoretical physiologists) is not easy. One of the major challenges is to break down the barriers created by differences in vocabulary and approach between the two disciplines. In this review, we have two major aims. Firstly, we wish to contribute to the effort to break down these barriers and so encourage more interdisciplinary collaboration. So, we begin with a "primer" on the ways in which computational models can help us understand physiology and pathophysiology. Second, we aim to provide an update of recent efforts in one specific area of physiology, renal oxygenation. This work is shedding new light on the causes and consequences of renal hypoxia. But as importantly, computational modelling is providing direction for experimental physiologists working in the field of renal oxygenation by: (a) generating new hypotheses that can be tested in experimental studies, (b) allowing experiments that are technically unfeasible to be simulated in silico, or variables that cannot be measured experimentally to be estimated, and (c) providing a means by which the quality of experimental data can be assessed. Critically, based on our experience, we strongly believe that experimental and theoretical physiology should not be seen as separate exercises. Rather, they should be integrated to permit an iterative process between modelling and experimentation.

Functional implications of the sex differences in transporter abundance along the rat nephron: modeling and analysis

The goal of the present study was to investigate the functional implications of sexual dimorphism in the pattern of transporters along the rodent nephron as reported by Veiras et al. (J Am Soc Nephrol 28: 3504-3517, 2017). To do so, we developed sex-specific computational models of water and solute transport along the superficial nephrons from male and female rat kidneys. The models account for the sex differences in the abundance of apical and basolateral transporters, single nephron glomerular filtration rate, and tubular dimensions. Model simulations predict that ~70% and 60% of filtered Na⁺ is reabsorbed by the proximal tubule of male and female rat kidneys, respectively. The lower fractional Na⁺ reabsorption in female kidneys is due primarily to their smaller transport area, lower Na⁺/H⁺ exchanger activity, and lower claudin-2 abundance, culminating in significantly larger fractional delivery of water and Na⁺ to the downstream nephron segments in female kidneys. Conversely, the female distal nephron exhibits a higher abundance of key Na⁺ transporters, including Na⁺-K⁺-Cl^- cotransporters, Na⁺-Cl^- cotransporters, and epithelial Na⁺ channels. The higher abundance of transporters accounts for the enhanced water and Na⁺ transport along the female, relative to male, distal nephron, resulting in similar urine excretion between the sexes. Consequently, in response to a saline load, the Na⁺ load delivered distally is greater in female rats than male rats, overwhelming transport capacity and resulting in higher natriuresis in female rats.

Solute and water transport along an inner medullary collecting duct undergoing peristaltic contractions

The mechanism by which solutes accumulate in the inner medulla of the mammalian kidney has remained incompletely understood. That persistent mystery has led to hypotheses based on the peristaltic contractions of the pelvic wall smooth muscles. It has been demonstrated the peristaltic contractions propel fluid down the collecting duct in boluses. In antidiuresis, boluses are sufficiently short that collecting ducts may be collapsed most of the time. In this study, we investigated the mechanism by which about half of the bolus volume is reabsorbed into the collecting duct cells despite the short contact time. To accomplish this, we developed a dynamic mathematical model of solute and water transport along a collecting duct of a rat papilla undergoing peristaltic contractions. The model predicts that, given preexisting axial concentration gradients along the loops of Henle, ∼40% of the bolus volume is reabsorbed as the bolus flows down the inner medullary collecting duct. Additionally, simulation results suggest that while the contraction-induced luminal hydrostatic pressure facilitates water extraction from the bolus, that pressure is not necessary to concentrate the bolus. Also, neither the negative interstitial pressure generated during the relaxation phase nor the concentrating effect of hyaluronic acid has a significant effect on bolus concentration. Taken together, these findings indicate that the high collecting duct apical water permeability allows a substantial amount of water to be extracted from the bolus, despite its short transit time. However, the potential role of the peristaltic waves in the urine-concentrating mechanism remains to be revealed.

Optimizing SGLT inhibitor treatment for diabetes with chronic kidney diseases

Diabetes induces glomerular hyperfiltration, affects kidney function, and may lead to chronic kidney diseases. A novel therapeutic treatment for diabetic patients targets the sodium-glucose cotransporter isoform 2 (SGLT2) in the kidney. SGLT2 inhibitors enhance urinary glucose, [Formula: see text] and fluid excretion and lower hyperglycemia in diabetes by inhibiting [Formula: see text] and glucose reabsorption along the proximal convoluted tubule. A goal of this study is to predict the effects of SGLT2 inhibitors in diabetic patients with and without chronic kidney diseases. To that end, we applied computational rat kidney models to assess how SGLT2 inhibition affects renal solute transport and metabolism when nephron population are normal or reduced (the latter simulates chronic kidney disease). The model predicts that SGLT2 inhibition induces glucosuria and natriuresis, with those effects enhanced in a remnant kidney. The model also predicts that the [Formula: see text] transport load and thus oxygen consumption of the S3 segment are increased under SGLT2 inhibition, a consequence that may increase the risk of hypoxia for that segment. To protect the vulnerable S3 segment, we explore dual SGLT2/SGLT1 inhibition and seek to determine the optimal combination that would yield sufficient urinary glucose excretion while limiting the metabolic load on the S3 segment. The model predicts that the optimal combination of SGLT2/SGLT1 inhibition lowers the oxygen requirements of key tubular segments, but decreases urine flow and [Formula: see text] excretion; the latter effect may limit the cardiovascular protection of the treatment.

Renal medullary and urinary oxygen tension during cardiopulmonary bypass in the rat

Renal hypoxia could result from a mismatch in renal oxygen supply and demand, particularly in the renal medulla. Medullary hypoxic damage is believed to give rise to acute kidney injury, which is a prevalent complication of cardiac surgery performed on cardiopulmonary bypass (CPB). To determine the mechanisms that could lead to medullary hypoxia during CPB in the rat kidney, we developed a mathematical model which incorporates (i) autoregulation of renal blood flow and glomerular filtration rate, (ii) detailed oxygen transport and utilization in the renal medulla and (iii) oxygen transport along the ureter. Within the outer medulla, the lowest interstitial tissue P$_{\rm O2}$, which is an indicator of renal hypoxia, is predicted near the thick ascending limbs. Interstitial tissue P$_{\rm O2}$ exhibits a general decrease along the inner medullary axis, but urine P$_{\rm O2}$ increases significantly along the ureter. Thus, bladder urinary P$_{\rm O2}$ is predicted to be substantially higher than medullary P$_{\rm O2}$. The model is used to identify the phase of cardiac surgery performed on CPB that is associated with the highest risk for hypoxic kidney injury. Simulation results indicate that the outer medulla's vulnerability to hypoxic injury depends, in part, on the extent to which medullary blood flow is autoregulated. With imperfect medullary blood flow autoregulation, the model predicts that the rewarming phase of CPB, in which medullary blood flow is low but medullary oxygen consumption remains high, is the phase in which the kidney is most likely to suffer hypoxic injury.

Modeling glucose metabolism and lactate production in the kidney

The metabolism of glucose provides most of the ATP required for energy-dependent transport processes. In the inner medulla of the mammalian kidney, limited blood flow and O2 supply yield low oxygen tension; therefore, a substantial fraction of the glucose metabolism in that region is anaerobic. Lactate is considered to be a waste product of anaerobic glycolysis, which yields two lactate molecules for each glucose molecule consumed, thereby likely leading to the production and accumulation of a significant amount of lactate in the inner medulla. To gain insights into the transport and metabolic processes in the kidney, we have developed a detailed mathematical model of the renal medulla of the rat kidney. The model represents the radial organization of the renal tubules and vessels, which centers around the vascular bundles in the outer medulla and around clusters of collecting ducts in the inner medulla. Model simulations yield significant radial gradients in interstitial fluid oxygen tension and glucose and lactate concentrations in the outer medulla and upper inner medulla. In the deep inner medulla, interstitial fluid concentrations become much more homogeneous, as the radial organization of tubules and vessels is not distinguishable. Using this model, we have identified parameters concerning glucose transport and basal metabolism, as well as lactate production via anaerobic glycolysis, that yield predicted blood glucose and lactate concentrations consistent with experimental measurements in the papillary tip. In addition, simulations indicate that the radial organization of the rat kidney may affect lactate buildup in the inner medulla.

Sex-specific computational models of the spontaneously hypertensive rat kidneys: factors affecting nitric oxide bioavailability

The goals of this study were to 1) develop a computational model of solute transport and oxygenation in the kidney of the female spontaneously hypertensive rat (SHR), and 2) apply that model to investigate sex differences in nitric oxide (NO) levels in SHR and their effects on medullary oxygenation and oxidative stress. To accomplish these goals, we first measured NO synthase (NOS) 1 and NOS3 protein expression levels in total renal microvessels of male and female SHR. We found that the expression of both NOS1 and NOS3 is higher in the renal vasculature of females compared with males. To predict the implications of that finding on medullary oxygenation and oxidative stress levels, we developed a detailed computational model of the female SHR kidney. The model was based on a published male kidney model and represents solute transport and the biochemical reactions among O₂, NO, and superoxide ([Formula: see text]) in the renal medulla. Model simulations conducted using both male and female SHR kidney models predicted significant radial gradients in interstitial fluid oxygen tension (Po₂) and NO and [Formula: see text] concentration in the outer medulla and upper inner medulla. The models also predicted that increases in endothelial NO-generating capacity, even when limited to specific vascular segments, may substantially raise medullary NO and Po₂ levels. Other potential sex differences in SHR, including [Formula: see text] production rate, are predicted to significantly impact oxidative stress levels, but effects on NO concentration and Po₂ are limited.

Modeling Glucose Metabolism in the Kidney

The mammalian kidney consumes a large amount of energy to support the reabsorptive work it needs to excrete metabolic wastes and to maintain homeostasis. Part of that energy is supplied via the metabolism of glucose. To gain insights into the transport and metabolic processes in the kidney, we have developed a detailed model of the renal medulla of the rat kidney. The model represents water and solute flows, transmural fluxes, and biochemical reactions in the luminal fluid of the nephrons and vessels. In particular, the model simulates the metabolism of oxygen and glucose. Using that model, we have identified parameters concerning glucose transport and basal metabolism that yield predicted blood glucose concentrations that are consistent with experimental measurements. The model predicts substantial axial gradients in blood glucose levels along various medullary structures. Furthermore, the model predicts that in the inner medulla, owing to the relatively limited blood flow and low tissue oxygen tension, anaerobic metabolism of glucose dominates.

Impact of nitric-oxide-mediated vasodilation and oxidative stress on renal medullary oxygenation: a modeling study

The goal of this study was to investigate the effects of nitric oxide (NO)-mediated vasodilation in preventing medullary hypoxia, as well as the likely pathways by which superoxide (O2(-)) conversely enhances medullary hypoxia. To do so, we expanded a previously developed mathematical model of solute transport in the renal medulla that accounts for the reciprocal interactions among oxygen (O2), NO, and O2(-) to include the vasoactive effects of NO on medullary descending vasa recta. The model represents the radial organization of the vessels and tubules, centered around vascular bundles in the outer medulla and collecting ducts in the inner medulla. Model simulations suggest that NO helps to prevent medullary hypoxia both by inducing vasodilation of the descending vasa recta (thus increasing O2 supply) and by reducing the active sodium transport rate (thus reducing O2 consumption). That is, the vasodilative properties of NO significantly contribute to maintaining sufficient medullary oxygenation. The model further predicts that a reduction in tubular transport efficiency (i.e., the ratio of active sodium transport per O2 consumption) is the main factor by which increased O2(-) levels lead to hypoxia, whereas hyperfiltration is not a likely pathway to medullary hypoxia due to oxidative stress. Finally, our results suggest that further increasing the radial separation between vessels and tubules would reduce the diffusion of NO towards descending vasa recta in the inner medulla, thereby diminishing its vasoactive effects therein and reducing O2 delivery to the papillary tip.

Recent advances in renal hemodynamics: insights from bench experiments and computer simulations

It has been long known that the kidney plays an essential role in the control of body fluids and blood pressure and that impairment of renal function may lead to the development of diseases such as hypertension (Guyton AC, Coleman TG, Granger Annu Rev Physiol 34: 13-46, 1972). In this review, we highlight recent advances in our understanding of renal hemodynamics, obtained from experimental and theoretical studies. Some of these studies were published in response to a recent Call for Papers of this journal: Renal Hemodynamics: Integrating with the Nephron and Beyond.