A computational model for simulating solute transport and oxygen consumption along the nephrons

Transcriptomics of SGLT2-positive early proximal tubule segments in mice: response to type 1 diabetes, SGLT1/2 inhibition, or GLP1 receptor agonism

SGLT2 inhibitors (SGLT2i) and GLP1 receptor (GLP1R) agonists have kidney protective effects. To better understand their molecular effects, RNA sequencing was performed in SGLT2-positive proximal tubule segments isolated by immunostaining-guided laser capture microdissection. Male adult DBA wild-type (WT) and littermate diabetic Akita mice ± Sglt1 knockout (Sglt1-KO) were given vehicle or SGLT2i dapagliflozin (dapa; 10 mg/kg diet) for 2 wk, and other Akita mice received GLP1R agonist semaglutide [sema; 3 nmol/(kg body wt·day), sc]. Dapa (254 ± 11 mg/dL) and Sglt1-KO (367 ± 11 mg/dL) but not sema (407 ± 44 mg/dL) significantly reduced hyperglycemia in Akita mice (480 ± 33 mg/dL). The 20,748 detected annotated protein-coding genes included robust enrichment of S1-segment marker genes. Akita showed 198 (∼1%) differentially expressed genes versus WT (DEGs; adjusted P ≤ 0.1), including downregulation of anionic transport, unsaturated fatty acid, and carboxylic acid metabolism. Dapa changed only two genes in WT but restored 43% of DEGs in Akita, including upregulation of the lipid metabolic pathway, carboxylic acid metabolism, and organic anion transport. In Akita, sema restored ∼10% of DEGs, and Sglt1-KO and dapa were synergistic (restored ∼61%), possibly involving additive blood glucose effects (193 ± 15 mg/dL). Targeted analysis of transporters and channels (t test, P < 0.05) revealed that ∼10% of 526 detectable transporters and channels were downregulated by Akita, with ∼60% restored by dapa. Dapa, dapa + Sglt1-KO, and sema also altered Akita-insensitive genes. Among DEGs in Akita, ∼30% were unresponsive to any treatment, indicating potential new targets. In conclusion, SGLT2i restored transcription for multiple metabolic pathways and transporters in SGLT2-positive proximal tubule segments in diabetic mice, with a smaller effect also observed for GLP1R agonism.NEW & NOTEWORTHY SGLT2 inhibitors and GLP1 receptor agonists have kidney protective effects. By combining immunostaining-guided laser capture microdissection and RNA sequencing, the study established how the gene expression profile changes in SGLT2-positive proximal tubule cells in response to type 1 Akita diabetes and to pharmacological intervention by SGLT2 inhibition or GLP1R agonism and genetic deletion of SGLT1. The data also indicate genes unresponsive to those treatments that may include new therapeutical candidates.

Focus on oliguria during renal replacement therapy

Oliguria is a clinical symptom characterized by decreased urine output, which can occur at any stage of acute kidney injury and also during renal replacement therapy. In some cases, oliguria may resolve with adjustment of blood purification dose or fluid management, while in others, it may suggest a need for further evaluation and intervention. It is important to determine the underlying cause of oliguria during renal replacement therapy and to develop an appropriate treatment plan. This review looks into the mechanisms of urine production to investigate the mechanism of oliguria during renal replacement therapy from two aspects: diminished glomerular filtration rate and tubular abnormalities. The above conditions all implying a renal oxygen supply-demand imbalance, which is the signal of worsening kidney injury. It also proposes a viable clinical pathway for the treatment and management of patients with acute kidney injury receiving renal replacement therapy.

Paradoxes in magnesium transport in type 1 Bartter's syndrome and Gitelman's syndrome: a modeling analysis

Type 1 Bartter's syndrome and Gitelman's syndrome are characterized by mutations in two key renal Na+ transporters, Na-K-2Cl cotransporter (NKCC2) and Na-Cl cotransporter (NCC). Since these two transporters play an important role in regulating magnesium (Mg2+) and calcium (Ca2+) transport in the kidney, significant alterations in the transport of these two electrolytes are observed in type 1 Bartter's syndrome and Gitelman's syndrome. In this study, we used our sex-specific computational models of renal electrolyte transport in rats to understand the complex compensatory mechanisms, in terms of alterations in tubular dimensions and ion transporter activities, that lead to Mg2+ and Ca2+ preservation or wasting in these two genetic disorders. Given the sexual dimorphism in renal transporter patterns, we also assessed how the magnitude of these alterations may differ between males and females. Model simulations showed that in type 1 Bartter's syndrome, nephron adaptations prevent salt wasting and favor Mg2+ preservation but not Ca2+, whereas in Gitelman's syndrome, those adaptations favor Ca2+ preservation over Mg2+. In addition, our models predicted that the compensatory alterations in tubular dimensions and ion transporter activities are stronger in females than in males.NEW & NOTEWORTHY Although changes in Ca2+ excretion in type 1 Bartter's syndrome and Gitelman's syndrome are well understood, Mg2+ excretion displays an interesting paradox. This computational modeling study provides insights into how renal adaptations in these two disorders impact Ca2+ and Mg2+ transport along different nephron segments. Model simulations showed that nephron adaptations favor Mg2+ preservation over Ca2+ in Bartter's syndrome and Ca2+ preservation over Mg2+ in Gitelman's syndrome and are stronger in females than in males.

Reframing acute kidney injury as a pathophysiological continuum of disrupted renal excretory function

Surrogate measures of glomerular filtration rate (GFR) continue to serve as pivotal determinants of the incidence, severity, and management of acute kidney injury (AKI), as well as the primary reference point underpinning knowledge of its pathophysiology. However, several clinically important deficits in aspects of renal excretory function during AKI other than GFR decline, including acid-base regulation, electrolyte and water balance, and urinary concentrating capacity, can evade detection when diagnostic criteria are built around purely GFR-based assessments. The use of putative markers of tubular injury to detect "sub-clinical" AKI has been proposed to expand the definition and diagnostic criteria for AKI, but their diagnostic performance is curtailed by ambiguity with respect to their biological meaning and context specificity. Efforts to devise new holistic assessments of overall renal functional compromise in AKI would foster the capacity to better personalize patient care by replacing biomarker threshold-based diagnostic criteria with a shift to assessment of compromise along a pathophysiological continuum. The term AKI refers to a syndrome of sudden renal deterioration, the severity of which is classified by precise diagnostic criteria that have unquestionable utility in patient management as well as blatant limitations. Particularly, the absence of an explicit pathophysiological definition of AKI curtails further scientific development and clinical handling, entrapping the field within its present narrow GFR-based view. A refreshed approach based on a more holistic consideration of renal functional impairment in AKI as the basis for a new diagnostic concept that reaches beyond the boundaries imposed by the current GFR threshold-based classification of AKI, capturing broader aspects of pathogenesis, could enhance AKI prevention strategies and improve AKI patient outcome and prognosis.

Sex and circadian regulation of metabolic demands in the rat kidney: A modeling analysis

Renal hemodynamics, renal transporter expression levels, and urine excretion exhibit circadian variations. Disruption of these diurnal patterns is associated with the pathophysiology of hypertension and chronic kidney disease. Renal hemodynamics determines oxygen delivery, whereas renal transport and metabolism determines oxygen consumption; the balance between them yields renal oxygenation which also demonstrates 24-h periodicity. Another notable modulator of kidney function is sex, which has impacts on renal hemodynamics and transport function that are regulated by as well as independent of the circadian clock. The goal of this study was to investigate the diurnal and sexual variations in renal oxygen consumption and oxygenation. For this purpose, we developed computational models of rat kidney function that represent sexual dimorphism and circadian variation in renal hemodynamics and transporter activities. Model simulations predicted substantial differences in tubular Na+ transport and oxygen consumption among different nephron segments. We also simulated the effect of loop diuretics, which are used in the treatment of renal hypoxia, on medullary oxygen tension. Our model predicted a significantly higher effect of loop diuretics on medullary oxygenation in female rats compared to male rats and when administered during the active phase.

Predicting sex differences in the effects of diuretics in renal epithelial transport during angiotensin II-induced hypertension

Chronic angiotensin II (ANG II) infusion is an experimental model that induces hypertension in rodents. The natriuresis, diuresis, and blood pressure responses differ between males and females. This is perhaps not unexpected, given the rodent kidney, which plays a key role in blood pressure regulation, exhibits marked sex differences. Under normotensive conditions, compared with males, the female rat nephron exhibits lower Na+/H+ exchanger 3 (NHE3) activity along the proximal tubule but higher Na+ transporter activities along the distal segments. ANG II infusion-induced hypertension induces a pressure natriuretic response that reduces NHE3 activity and shifts Na+ transport capacity downstream. The goals of this study were to apply a computational model of epithelial transport along a rat nephron 1) to understand how a 14-day ANG II infusion impacts segmental electrolyte transport in male and female rat nephrons and 2) to identify and explain any sex differences in the effects of loop diuretics, thiazide diuretics, and K+-sparing diuretics. Model simulations suggest that the NHE3 downregulation in the proximal tubule is a major contributor to natriuresis and diuresis in hypertension, with the effects stronger in males. All three diuretics are predicted to induce stronger natriuretic and diuretic effects under hypertension compared with normotension, with relative increases in sodium excretion higher in hypertensive females than in males. The stronger natriuretic responses can be explained by the downstream shift of Na+ transport load in hypertension and by the larger distal transport load in females, both of which limit the ability of the distal segments to further elevate their Na+ transport.NEW & NOTEWORTHY Sex differences in the prevalence of hypertension are found in human and animal models. The kidney, which regulates blood pressure, exhibits sex differences in morphology, hemodynamics, and membrane transporter distributions. This computational modeling study provides insights into how the sexually dimorphic responses to a 14-day angiotensin II infusion differentially impact segmental electrolyte transport in rats. Simulations of diuretic administration explain how the natriuretic and diuretic effects differ between normotension and hypertension and between the sexes.

How the kidney regulates magnesium: a modelling study

The kidneys are crucial for maintaining Mg2+ homeostasis. Along the proximal tubule and thick ascending limb, Mg2+ is reabsorbed paracellularly, while along the distal convoluted tubule (DCT), Mg2+ is reabsorbed transcellularly via transient receptor potential melastatin 6 (TRPM6). TRPM6 and other renal transporter expressions are regulated by sex hormones. To investigate renal Mg2 handling, we have developed sex-specific computational models of electrolyte transport along rat superficial nephron. Model simulations indicated that along the proximal tubule and thick ascending limb, Mg2+ and Na+ transport occur parallelly, but they are dissociated along the DCT. In addition, our models predicted higher paracellular Mg2+ permeability in females to attain similar cortical thick ascending limb fractional Mg2+ reabsorption in both sexes. Furthermore, DCT fractional Mg2+ reabsorption is higher in females than in males, allowing females to better fine-tune Mg2+ excretion. We validated our models by simulating the administration of three classes of diuretics. The model predicted significantly increased, marginally increased and significantly decreased Mg2+ excretions for loop, thiazide and K-sparing diuretics, respectively, aligning with experimental findings. The models can be used to conduct in silico studies on kidney adaptations to Mg2+ homeostasis alterations during conditions such as pregnancy, diabetes and chronic kidney disease.

Mitochondrial Dysfunction in Kidney Tubulopathies

Mitochondria play a key role in kidney physiology and pathology. They produce ATP to fuel energy-demanding water and solute reabsorption processes along the nephron. Moreover, mitochondria contribute to cellular health by the regulation of autophagy, (oxidative) stress responses, and apoptosis. Mitochondrial abundance is particularly high in cortical segments, including proximal and distal convoluted tubules. Dysfunction of the mitochondria has been described for tubulopathies such as Fanconi, Gitelman, and Bartter-like syndromes and renal tubular acidosis. In addition, mitochondrial cytopathies often affect renal (tubular) tissues, such as in Kearns-Sayre and Leigh syndromes. Nevertheless, the mechanisms by which mitochondrial dysfunction results in renal tubular diseases are only scarcely being explored. This review provides an overview of mitochondrial dysfunction in the development and progression of kidney tubulopathies. Furthermore, it emphasizes the need for further mechanistic investigations to identify links between mitochondrial function and renal electrolyte reabsorption.

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.

Angiotensin II hypertension along the female rat tubule: predicted impact on coupled transport of Na+ and K. Am J Physiol Renal Physiol 2023;325:F733-F749. [PMID: 37823196 PMCID: PMC10878725 DOI: 10.1152/ajprenal.00232.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Chronic infusion of subpressor level of angiotensin II (ANG II) increases the abundance of Na+ transporters along the distal nephron, balanced by suppression of Na+ transporters along the proximal tubule and medullary thick ascending limb (defined as "proximal nephron"), which impacts K+ handling along the entire renal tubule. The objective of this study was to quantitatively assess the impact of chronic ANG II on the renal handling of Na+ and K+ in female rats, using a computational model of the female rat renal tubule. Our results indicate that the downregulation of proximal nephron Na+ reabsorption (TNa), which occurs in response to ANG II-triggered hypertension, involves changes in both transporter abundance and trafficking. Our model suggests that substantial (∼30%) downregulation of active NHE3 in proximal tubule (PT) microvilli is needed to reestablish the Na+ balance at 2 wk of ANG II infusion. The 35% decrease in SGLT2, a known NHE3 regulator, may contribute to this downregulation. Both depression of proximal nephron TNa and stimulation of distal ENaC raise urinary K+ excretion in ANG II-treated females, while K+ loss is slightly mitigated by cortical NKCC2 and NCC upregulation. Our model predicts that K+ excretion may be more significantly limited during ANG II infusion by ROMK inhibition in the distal nephron and/or KCC3 upregulation in the PT, which remain open questions for experimental validation. In summary, our analysis indicates that ANG II hypertension triggers a series of events from distal TNa stimulation followed by compensatory reduction in proximal nephron TNa and accompanying adjustments to limit excessive K+ secretion.NEW & NOTEWORTHY We used a computational model of the renal tubule to assess the impact of 2-wk angiotensin II (ANG II) infusion on the handling of Na+ and K+ in female rats. ANG II strongly stimulates distal Na+ reabsorption and K+ secretion. Simulations indicate that substantial downregulation of proximal tubule NHE3 is needed to reestablish Na+ balance at 2 wk. Proximal adaptations challenge K+ homeostasis, and regulation of distal NCC and specific K+ channels likely limit urinary K+ losses.

Coupling of renal sodium and calcium transport: a modeling analysis of transporter inhibition and sex differences

Ca2+ transport along the nephron occurs via specific transcellular and paracellular pathways and is coupled to the transport of other electrolytes. Notably, Na+ transport establishes an electrochemical gradient to drive Ca2+ reabsorption. Hence, alterations in renal Na+ handling, under pathophysiological conditions or pharmacological manipulations, can have major effects on Ca2+ transport. An important class of pharmacological agent is diuretics, which are commonly prescribed for the management of blood pressure and fluid balance. The pharmacological targets of diuretics generally directly facilitate Na+ transport but also indirectly affect renal Ca2+ handling. To better understand the underlying mechanisms, we developed a computational model of electrolyte transport along the superficial nephron in the kidney of a male and female rat. Sex differences in renal Ca2+ handling are represented. Model simulations predicted in the female rat nephron lower Ca2+ reabsorption in the proximal tubule and thick ascending limb, but higher reabsorption in the late distal convoluted tubule and connecting tubule, compared with the male nephron. The male rat kidney model yielded a higher urinary Ca2+ excretion than the female model, consistent with animal experiments. Model results indicated that along the proximal tubule and thick ascending limb, Ca2+ and Na+ transport occurred in parallel, but those processes were dissociated in the distal convoluted tubule. Additionally, we conducted simulations of inhibition of channels and transporters that play a major role in Na+ and Ca2+ transport. Simulation results revealed alterations in transepithelial Ca2+ transport, with differential effects among nephron segments and between the sexes.NEW & NOTEWORTHY The kidney plays an important role in the maintenance of whole body Ca2+ balance by regulating Ca2+ reabsorption and excretion. This computational modeling study provides insights into how Ca2+ transport along the nephron is coupled to Na+. Model results indicated that along the proximal tubule and thick ascending limb, Ca2+ and Na+ transport occur in parallel, but those processes were dissociated in the distal convoluted tubule. Simulations also revealed sex-specific responses to different pharmacological manipulations.

Influence of administration time and sex on natriuretic, diuretic, and kaliuretic effects of diuretics

Sex differences in renal function and blood pressure have been widely described across many species. Blood pressure dips during sleep and peaks in the early morning. Similarly, glomerular filtration rate, filtered electrolyte loads, urine volume, and urinary excretion all exhibit notable diurnal rhythms, which reflect, in part, the regulation of renal transporter proteins by circadian clock genes. That regulation is sexually dimorphic; as such, sex and time of day are not two independent regulators of kidney function and blood pressure. The objective of the present study was to assess the effect of sex and administration time on the natriuretic and diuretic effects of loop, thiazide, and K⁺-sparing diuretics, which are common treatments for hypertension. Loop diuretics inhibit Na⁺-K⁺-2Cl^- cotransporters on the apical membrane of the thick ascending limb, thiazide diuretics inhibit Na⁺-Cl^- cotransporters on the distal convoluted tubule, and K⁺-sparing diuretics inhibit epithelial Na⁺ channels on the connecting tubule and collecting duct. We simulated Na⁺ transporter inhibition using sex- and time-of-day-specific computational models of mouse kidney function. The simulation results highlighted significant sex and time-of-day differences in the drug response. Loop diuretics induced larger natriuretic and diuretic effects during the active phase. The natriuretic and diuretic effects of thiazide diuretics exhibited sex and time-of-day differences, whereas these effects of K⁺-sparing diuretics exhibited a significant time-of-day difference in females only. The kaliuretic effect depended on the type of diuretics and time of administration. The present computational models can be a useful tool in chronotherapy, to tailor drug administration time to match the body's diurnal rhythms to optimize the drug effect.NEW & NOTEWORTHY Sex influences cardiovascular disease, and the timing of onset of acute cardiovascular events exhibits circadian rhythms. Kidney function also exhibits sex differences and circadian rhythms. How do the natriuretic and diuretic effects of diuretics, a common treatment for hypertension that targets the kidneys, differ between the sexes? And how do these effects vary during the day? To answer these questions, we conducted computer simulations to assess the effects of loop, thiazide, and K⁺-sparing diuretics.

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.

Numerical simulation of the vascular structure dependence of blood flow in the kidney

A numerical simulation was performed to clarify renal blood flow determination by the vascular structures. Large and small vessels were modeled as symmetric and asymmetric branching vessels, respectively, with simple geometries to parameterize the vascular structures. Modeling individual vessels as straight pipes, Murray's law was used to determine the vessel diameters. Blood flow in the vascular structure was calculated by network analysis based on Hagen-Poiseuille's law. Blood flow simulations for a vascular network segment demonstrated that blood flow rate and pressure vary within the same-generation vessels because of an asymmetric vessel branch while they generally tend to decrease with vessel diameter; thus, the standard deviation of flow rate relative to the mean (relative standard deviation [RSD]) increased from 0.4 to 1.0 when the number of the daughter vessels increased from 3 to 10. Blood flow simulations for an entire vascular network of a kidney showed that the vessel number and branching style, rather than Strahler order, are major parameters in successfully reproducing renal blood flow measured in published experiments. The entire vascular network could generate variation in the physiological flow rate in afferent arterioles at 0.2-0.38 in RSD, which is at least compatible with 0.16 by diameter variation within the same-generation vessels.

Numerical Modeling and Simulation of Blood Flow in a Rat Kidney: Coupling of the Myogenic Response and the Vascular Structure

A numerical simulation was carried out to investigate the blood flow behavior (i.e., flow rate and pressure) and coupling of a renal vascular network and the myogenic response to various conditions. A vascular segment and an entire kidney vascular network were modeled by assuming one single vessel as a straight pipe whose diameter was determined by Murray’s law. The myogenic response was tested on individual AA (afferent artery)–GC (glomerular capillaries)–EA (efferent artery) systems, thereby regulating blood flow throughout the vascular network. Blood flow in the vascular structure was calculated by network analysis based on Hagen–Poiseuille’s law to various boundary conditions. Simulation results demonstrated that, in the vascular segment, the inlet pressure Pinlet and the vascular structure act together on the myogenic response of each individual AA–GC–EA subsystem, such that the early-branching subsystems in the vascular network reached the well-regulated state first, with an interval of the inlet as Pinlet = 10.5–21.0 kPa, whereas the one that branched last exhibited a later interval with Pinlet = 13.0–24.0 kPa. In the entire vascular network, in contrast to the Pinlet interval (13.0–20.0 kPa) of the unified well-regulated state for all AA–GC–EA subsystems of the symmetric model, the asymmetric model exhibited the differences among subsystems with Pinlet ranging from 12.0–17.0 to 16.0–20.0 kPa, eventually achieving a well-regulated state of 13.0–18.5 kPa for the entire kidney. Furthermore, when Pinlet continued to rise (e.g., 21.0 kPa) beyond the vasoconstriction range of the myogenic response, high glomerular pressure was also related to vascular structure, where PGC of early-branching subsystems was 9.0 kPa and of late-branching one was 7.5 kPa. These findings demonstrate how the myogenic response regulates renal blood flow in vascular network system that comprises a large number of vessel elements.

Determining risk factors for triple whammy acute kidney injury

Concurrent use of a diuretic, a renin-angiotensin system (RAS) inhibitor, and a non-steroidal anti-inflammatory drug (NSAID) significantly increases the risk of acute kidney injury (AKI). This phenomenon is known as "triple whammy". Diuretics and RAS inhibitors, such as an angiotensin converting enzyme (ACE) inhibitor or angiotensin receptor blocker, are often prescribed in tandem for the treatment of hypertension, whereas some NSAIDs, such as ibuprofen, are available over the counter. As such, concurrent treatment with all three drugs is common. The goals of this study are to better understand the mechanisms underlying the development of triple whammy AKI and to identify physiological factors that may increase an individual's susceptibility. To accomplish these goals, we utilize sex-specific computational models of long-term blood pressure regulation. These models include variables describing the heart and circulation, kidney function, sodium and water reabsorption in the nephron and the RAS and are parameterized separately for men and women. Hypertension is modeled as overactive renal sympathetic nervous activity. Model simulations suggest that low water intake, the myogenic response, and drug sensitivity may predispose patients with hypertension to develop triple whammy-induced AKI. Triple treatment involving an ACE inhibitor, furosemide, and NSAID results in blood pressure levels similar to double treatment with ACEI and furosemide. Additionally, the male and female hypertensive models act similarly in most situations, except for the ACE inhibitor and NSAID double treatment.

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.

Adaptive Changes in single-nephron GFR, Tubular Morphology, and Transport in a Pregnant Rat Nephron: Modeling and Analysis

Normal pregnancy is characterized by massive increases in plasma volume and electrolyte retention. Given that the kidneys regulate homeostasis of electrolytes and volume, the organ undergoes major adaptations in morphology, hemodynamics, and transport to achieve the volume and electrolyte retention required in pregnancy. These adaptations are complex, sometimes counterintuitive, and not fully understood. In addition, the demands of the developing fetus and placenta change throughout the pregnancy. For example, during late pregnancy, K⁺ retention and thus enhanced renal K⁺ reabsorption is required despite many kaliuretic factors. The goal of this study is to unravel how known adaptive changes along the nephrons contribute to the ability of the kidney to meet volume and electrolyte requirements in mid- and late pregnancy. We developed computational models of solute and water transport in the superficial nephron of the kidney of a rat in mid- and late pregnancy. The mid-pregnant and late-pregnant rat superficial nephron models predict that morphological adaptations and increased activity of the sodium hydrogen exchanger 3 (NHE3) and epithelial sodium channel (ENaC) are essential for enhanced Na⁺ reabsorption observed during pregnancy. Model simulations showed that for sufficient K⁺ reabsorption, increased H ⁺-K ⁺-ATPase activity and decreased K⁺ secretion along the distal segments is required in both mid- and late-pregnancy. Furthermore, certain known sex differences in renal transporter pattern (e.g., the higher NHE3 protein abundance but lower activity in the proximal tubules of virgin female rats compared to male) may serve to better prepare the female for the increased transport demand in pregnancy.

An in silico validation framework for quantitative DCE-MRI techniques based on a dynamic digital phantom

Quantitative evaluation of an image processing method to perform as designed is central to both its utility and its ability to guide the data acquisition process. Unfortunately, these tasks can be quite challenging due to the difficulty of experimentally obtaining the "ground truth" data to which the output of a given processing method must be compared. One way to address this issue is via "digital phantoms", which are numerical models that provide known biophysical properties of a particular object of interest.  In this contribution, we propose an in silico validation framework for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) acquisition and analysis methods that employs a novel dynamic digital phantom. The phantom provides a spatiotemporally-resolved representation of blood-interstitial flow and contrast agent delivery, where the former is solved by a 1D-3D coupled computational fluid dynamic system, and the latter described by an advection-diffusion equation. Furthermore, we establish a virtual simulator which takes as input the digital phantom, and produces realistic DCE-MRI data with controllable acquisition parameters. We assess the performance of a simulated standard-of-care acquisition (Protocol A) by its ability to generate contrast-enhanced MR images that separate vasculature from surrounding tissue, as measured by the contrast-to-noise ratio (CNR). We find that the CNR significantly decreases as the spatial resolution (SRA, where the subscript indicates Protocol A) or signal-to-noise ratio (SNRA) decreases. Specifically, with an SNRA / SRA = 75 dB / 30 μm, the median CNR is 77.30, whereas an SNRA / SRA = 5 dB / 300 μm reduces the CNR to 6.40. Additionally, we assess the performance of simulated ultra-fast acquisition (Protocol B) by its ability to generate DCE-MR images that capture contrast agent pharmacokinetics, as measured by error in the signal-enhancement ratio (SER) compared to ground truth (PESER). We find that PESER significantly decreases the as temporal resolution (TRB) increases. Similar results are reported for the effects of spatial resolution and signal-to-noise ratio on PESER. For example, with an SNRB / SRB / TRB = 5 dB / 300 μm / 10 s, the median PESER is 21.00%, whereas an SNRB / SRB / TRB = 75 dB / 60 μm / 1 s, yields a median PESER of 0.90%. These results indicate that our in silico framework can generate virtual MR images that capture effects of acquisition parameters on the ability of generated images to capture morphological or pharmacokinetic features. This validation framework is not only useful for investigations of perfusion-based MRI techniques, but also for the systematic evaluation and optimization new MRI acquisition, reconstruction, and image processing techniques.

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.

The furosemide stress test and computational modeling identify renal damage sites associated with predisposition to acute kidney injury in rats

Acute kidney injury (AKI) diagnosis relies on plasma creatinine concentration (Cr_pl), a relatively insensitive, surrogate biomarker of glomerular filtration rate that increases only after significant damage befalls. However, damage in different renal structures may occur without increments in Cr_pl, a condition known as subclinical AKI. Thus, detection of alterations in other aspects of renal function different from glomerular filtration rate must be included in an integral diagnosis of AKI. With this aim, we adapted to and validated in rats (for preclinical research) the furosemide stress test (FST), a tubular function test hitherto performed only in humans. We also tested its sensitivity in detecting subclinical tubular alterations. In particular, we predisposed rats to AKI with 3 mg/kg cisplatin and subsequently subjected them to a triggering insult (ie, 50 mg/kg/d gentamicin for 6 days) that had no effect on nonpredisposed animals but caused an overt AKI in predisposed rats. The FST was performed immediately before adding the triggering insult. Predisposed animals showed a reduced response to the FST (namely, reduced furosemide-induced diuresis and K⁺ excretion), whereas nonpredisposed animals showed no alteration, compared to the controls. Computational modeling of epithelial transport of solutes and water along the nephrons applied to experimental data suggested that proximal tubule transport was only minimally reduced, the sodium-chloride symporter was upregulated by 50%, and the renal outer medullary potassium channel was downregulated by 85% in predisposed animals. In conclusion, serial coupling of the FST and computational modeling may be used to detect and localize subclinical tubular alterations.

A mathematical model of the rat kidney. III. Ammonia transport

Ammonia generated within the kidney is partitioned into a urinary fraction (the key buffer for net acid excretion) and an aliquot delivered to the systemic circulation. The physiology of this partitioning has yet to be examined in a kidney model, and that was undertaken in this work. This involves explicit representation of the cortical labyrinth, so that cortical interstitial solute concentrations are computed rather than assigned. A detailed representation of cortical vasculature has been avoided by making the assumption that solute concentrations within the interstitium and peritubular capillaries are likely to be identical and that there is little to no modification of venous composition as blood flows to the renal vein. The model medullary ray has also been revised to include a segment of proximal straight tubule, which supplies ammonia to this region. The principal finding of this work is that cortical labyrinth interstitial ammonia concentration is likely to be several fold higher than systemic arterial ammonia. This elevation of interstitial ammonia enhances ammonia secretion in both the proximal convoluted tubule and distal convoluted tubule, with uptake by Na⁺-K⁺-ATPases of both segments. Model prediction of urinary ammonia excretion was concordant with measured values, but at the expense of greater ammoniagenesis, with high rates of renal venous ammonia flux. This derives from a limited capability of the model medulla to replicate the high interstitial ammonia concentrations that are required to drive collecting duct ammonia secretion. Thus, renal medullary ammonia trapping appears key to diverting ammonia from the renal vein to urine, but capturing the underlying physiology remains a challenge.NEW & NOTEWORTHY This is the first mathematical model to estimate solute concentrations within the kidney cortex. The model predicts cortical ammonia to be several fold greater than in the systemic circulation. This higher concentration drives ammonia secretion in proximal and distal tubules. The model reveals a gap in our understanding of how ammonia generated within the cortex is channeled efficiently into the final urine.

Relative Hypoxia and Early Diabetic Kidney Disease in Type 1 Diabetes

The objective of this study was to compare the ratio of renal oxygen availability (RO₂) to glomerular filtration rate (GFR), a measure of relative renal hypoxia, in adolescents with and without type 1 diabetes (T1D) and relate the ratio to albuminuria, renal plasma flow (RPF), fat mass, and insulin sensitivity (M/I). RO₂ was estimated by blood oxygen level-dependent MRI; fat mass was estimated by DXA; GFR and RPF were estimated by iohexol and p-aminohippurate clearance; albuminuria was estimated by urine albumin-to-creatinine ratio (UACR); and M/I was estimated from steady-state glucose infusion rate/insulin (mg/kg/min) by hyperglycemic clamp in 50 adolescents with T1D (age 16.1 ± 3.0 years, HbA_1c 8.6 ± 1.2%) and 20 control patients of similar BMI (age 16.1 ± 2.9 years, HbA_1c 5.2 ± 0.2%). The RO₂:GFR (ms/mL/min) was calculated as RO₂ (T2*, ms) divided by GFR (mL/min). Whole-kidney RO₂:GFR was 25% lower in adolescents with T1D versus control patients (P < 0.0001). In adolescents with T1D, lower whole-kidney RO₂:GFR was associated with higher UACR (r = -0.31, P = 0.03), RPF (r = -0.52, P = 0.0009), and fat mass (r = -0.33, P = 0.02). Lower medullary RO₂:GFR was associated with lower M/I (r = 0.31, P = 0.03). In conclusion, adolescents with T1D exhibited relative renal hypoxia that was associated with albuminuria and with increased RPF, fat mass, and insulin resistance. These data suggest a potential role of renal hypoxia in the development of diabetic kidney disease.

Role of sodium-glucose cotransporter 2 inhibition to mitigate diabetic kidney disease risk in type 1 diabetes

Diabetic kidney disease (DKD) is a common complication of type 1 diabetes (T1D) and a major risk factor for premature death from cardiovascular disease (CVD). Current treatments, such as control of hyperglycaemia and hypertension, are beneficial, but only partially protect against DKD. Finding new, safe and effective therapies to halt nephropathy progression has proven to be challenging. Sodium-glucose cotransporter 2 (SGLT2) inhibitors have demonstrated, in addition to glycaemic lowering, impressive protection against DKD and CVD progression in people with type 2 diabetes. Although these beneficial cardiorenal effects may also apply to people with T1D, supporting data are lacking. Furthermore, the increased rates of euglycaemic diabetic ketoacidosis may limit the use of this class in people with T1D. In this review we highlight the pathophysiology of DKD in T1D and the unmet need that exists. We further detail the beneficial and adverse effects of SGLT2 inhibitors based on their mechanism of action. Finally, we balance the effects in people with T1D and indicate future lines of research.

Cardiac and renal function interactions in heart failure with reduced ejection fraction: A mathematical modeling analysis

Congestive heart failure is characterized by suppressed cardiac output and arterial filling pressure, leading to renal retention of salt and water, contributing to further volume overload. Mathematical modeling provides a means to investigate the integrated function and dysfunction of heart and kidney in heart failure. This study updates our previously reported integrated model of cardiac and renal functions to account for the fluid exchange between the blood and interstitium across the capillary membrane, allowing the simulation of edema. A state of heart failure with reduced ejection fraction (HF-rEF) was then produced by altering cardiac parameters reflecting cardiac injury and cardiovascular disease, including heart contractility, myocyte hypertrophy, arterial stiffness, and systemic resistance. After matching baseline characteristics of the SOLVD clinical study, parameters governing rates of cardiac remodeling were calibrated to describe the progression of cardiac hemodynamic variables observed over one year in the placebo arm of the SOLVD clinical study. The model was then validated by reproducing improvements in cardiac function in the enalapril arm of SOLVD. The model was then applied to prospectively predict the response to the sodium-glucose co-transporter 2 (SGLT2) inhibitor dapagliflozin, which has been shown to reduce heart failure events in HF-rEF patients in the recent DAPAHF clinical trial by incompletely understood mechanisms. The simulations predict that dapagliflozin slows cardiac remodeling by reducing preload on the heart, and relieves congestion by clearing interstitial fluid without excessively reducing blood volume. This provides a quantitative mechanistic explanation for the observed benefits of SGLT2i in HF-rEF. The model also provides a tool for further investigation of heart failure drug therapies.

The New Biology of Diabetic Kidney Disease-Mechanisms and Therapeutic Implications

Diabetic kidney disease remains the most common cause of end-stage kidney disease in the world. Despite reductions in incidence rates of myocardial infarction and stroke in people with diabetes over the past 3 decades, the risk of diabetic kidney disease has remained unchanged, and may even be increasing in younger individuals afflicted with this disease. Accordingly, changes in public health policy have to be implemented to address the root causes of diabetic kidney disease, including the rise of obesity and diabetes, in addition to the use of safe and effective pharmacological agents to prevent cardiorenal complications in people with diabetes. The aim of this article is to review the mechanisms of pathogenesis and therapies that are either in clinical practice or that are emerging in clinical development programs for potential use to treat diabetic kidney disease.

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.

Inhibition of oxygen-sensing prolyl hydroxylases increases lipid accumulation in human primary tubular epithelial cells without inducing ER stress

The role of the hypoxia-inducible transcription factor (HIF) pathway in renal lipid metabolism is largely unknown. As HIF stabilizing prolyl hydroxylase (PHD) inhibitors are currently investigated in clinical trials for the treatment of renal anemia, we studied the effects of genetic deletion and pharmacological inhibition of PHDs on renal lipid metabolism in transgenic mice and human primary tubular epithelial cells (hPTEC). Tubular cell-specific deletion of HIF prolyl hydroxylase 2 (Phd2) increased the size of Oil Red-stained lipid droplets in mice. In hPTEC, the PHD inhibitors (PHDi) DMOG and ICA augmented lipid accumulation, which was visualized by Oil Red staining and assessed by microscopy and an infrared imaging system. PHDi-induced lipid accumulation required the exogenous availability of fatty acids and was observed in both proximal and distal hPTEC. PHDi treatment was not associated with structural features of cytotoxicity in contrast to treatment with the immunosuppressant cyclosporine A (CsA). PHDi and CsA differentially upregulated the expression of the lipid droplet-associated genes PLIN2, PLIN4 and HILPDA. Both PHDi and CsA activated AMP-activated protein kinase (AMPK) indicating the initiation of a metabolic stress response. However, only CsA triggered endoplasmic reticulum (ER) stress as determined by the increased mRNA expression of multiple ER stress markers but CsA-induced ER stress was not linked to lipid accumulation. Our data raise the possibility that PHD inhibition may protect tubular cells from toxic free fatty acids by trapping them as triacylglycerides in lipid droplets. This mechanism might contribute to the renoprotective effects of PHDi in experimental kidney diseases.

Claudins in Renal Physiology and Pathology

Claudins are integral proteins expressed at the tight junctions of epithelial and endothelial cells. In the mammalian kidney, every tubular segment express a specific set of claudins that give to that segment unique properties regarding permeability and selectivity of the paracellular pathway. So far, 3 claudins (10b, 16 and 19) have been causally traced to rare human syndromes: variants of CLDN10b cause HELIX syndrome and variants of CLDN16 or CLDN19 cause familial hypomagnesemia with hypercalciuria and nephrocalcinosis. The review summarizes our current knowledge on the physiology of mammalian tight junctions and paracellular ion transport, as well as on the role of the 3 above-mentioned claudins in health and disease. Claudin 14, although not having been causally linked to any rare renal disease, is also considered, because available evidence suggests that it may interact with claudin 16. Some single-nucleotide polymorphisms of CLDN14 are associated with urinary calcium excretion and/or kidney stones. For each claudin considered, the pattern of expression, the function and the human syndrome caused by pathogenic variants are described.

Sex-specific computational models for blood pressure regulation in the rat

In the past decades, substantial effort has been devoted to the development of computational models of the cardiovascular system. Some of these models simulate blood pressure regulation in humans and include components of the circulatory, renal, and neurohormonal systems. Although such human models are intended to have clinical value in that they can be used to assess the effects and reveal mechanisms of hypertensive therapeutic treatments, rodent models would be more useful in assisting the interpretation of animal experiments. Also, despite well-known sexual dimorphism in blood pressure regulation, almost all published models are gender neutral. Given these observations, the goal of this project is to develop the first computational models of blood pressure regulation for male and female rats. The resulting sex-specific models represent the interplay among cardiovascular function, renal hemodynamics, and kidney function in the rat; they also include the actions of the renal sympathetic nerve activity and the renin-angiotensin-aldosterone system as well as physiological sex differences. We explore mechanisms responsible for blood pressure and renal autoregulation and notable sexual dimorphism. Model simulations suggest that fluid and sodium handling in the kidney of female rats, which differs significantly from males, may contribute to their observed lower salt sensitivity as compared with males. Additionally, model simulations highlight sodium handling in the kidney and renal sympathetic nerve activity sensitivity as key players in the increased resistance of females to angiotensin II-induced hypertension as compared with males.

On the role of the epithelium in a model of sodium exchange in renal tubules

In this study we present a mathematical model describing the transport of sodium in a fluid circulating in a counter-current tubular architecture, which constitutes a simplified model of Henle's loop in a kidney nephron. The model explicitly takes into account the epithelial layer at the interface between the tubular lumen and the surrounding interstitium. In a specific range of parameters, we show that explicitly accounting for transport across the apical and basolateral membranes of epithelial cells, instead of assuming a single barrier, affects the axial concentration gradient, an essential determinant of the urinary concentrating capacity. We present the solution related to the stationary system, and we perform numerical simulations to understand the physiological behaviour of the system. We prove that when time grows large, our dynamic model converges towards the stationary system at an exponential rate. In order to prove rigorously this global asymptotic stability result, we study eigen-problems of an auxiliary linear operator and its dual.

A model of mitochondrial O2 consumption and ATP generation in rat proximal tubule cells

Oxygen tension in the kidney is mostly determined by O2 consumption (Qo2), which is, in turn, closely linked to tubular Na+ reabsorption. The objective of the present study was to develop a model of mitochondrial function in the proximal tubule (PT) cells of the rat renal cortex to gain more insight into the coupling between Qo2, ATP formation (GATP), ATP hydrolysis (QATP), and Na+ transport in the PT. The present model correctly predicts in vitro and in vivo measurements of Qo2, GATP, and ATP and Pi concentrations in PT cells. Our simulations suggest that O2 levels are not rate limiting in the proximal convoluted tubule, absent large metabolic perturbations. The model predicts that the rate of ATP hydrolysis and cytoplasmic pH each substantially regulate the GATP-to-Qo2 ratio, a key determinant of the number of Na+ moles actively reabsorbed per mole of O2 consumed. An isolated increase in QATP or in cytoplasmic pH raises the GATP-to-Qo2 ratio. Thus, variations in Na+ reabsorption and pH along the PT may, per se, generate axial heterogeneities in the efficiency of mitochondrial metabolism and Na+ transport. Our results also indicate that the GATP-to-Qo2 ratio is strongly impacted not only by H+ leak permeability, which reflects mitochondrial uncoupling, but also by K+ leak pathways. Simulations suggest that the negative impact of increased uncoupling in the diabetic kidney on mitochondrial metabolic efficiency is partly counterbalanced by increased rates of Na+ transport and ATP consumption. This model provides a framework to investigate the role of mitochondrial dysfunction in acute and chronic renal diseases.

A Computer Model of Oxygen Dynamics in the Cortex of the Rat Kidney at the Cell-Tissue Level

The renal cortex drives renal function. Hypoxia/reoxygenation are primary factors in ischemia-reperfusion (IR) injuries, but renal oxygenation per se is complex and awaits full elucidation. Few mathematical models address this issue: none captures cortical tissue heterogeneity. Using agent-based modeling, we develop the first model of cortical oxygenation at the cell-tissue level (RCM), based on first principles and careful bibliographical analysis. Entirely parameterized with Rat data, RCM is a morphometrically equivalent 2D-slice of cortical tissue, featuring peritubular capillaries (PTC), tubules and interstitium. It implements hemoglobin/O2 binding-release, oxygen diffusion, and consumption, as well as capillary and tubular flows. Inputs are renal blood flow RBF and PO2 feeds; output is average tissue PO2 (tPO2). After verification and sensitivity analysis, RCM was validated at steady-state (tPO2 37.7 ± 2.2 vs. 36.9 ± 6 mmHg) and under transients (ischemic oxygen half-time: 4.5 ± 2.5 vs. 2.3 ± 0.5 s in situ). Simulations confirm that PO2 is largely independent of RBF, except at low values. They suggest that, at least in the proximal tubule, the luminal flow dominantly contributes to oxygen delivery, while the contribution of capillaries increases under partial ischemia. Before addressing IR-induced injuries, upcoming developments include ATP production, adaptation to minutes-hours scale, and segmental and regional specification.

Mathematical models for kidney function focusing on clinical interest

We give an overview of mathematical models of renal physiology and anatomy with the clinician in mind. Beyond the past focus on issues of local transport mechanisms along the nephron and the urine concentrating mechanism, recent models have brought insight into difficult problems such as renal ischemia (oxygen and CO₂ diffusion in the medulla) or calcium and potassium homeostasis. They have also provided revealing 3D reconstructions of the full trajectories of families of nephrons and collecting ducts through cortex and medulla. The recent appearance of sophisticated whole-kidney models representing nephrons and their associated renal vasculature promises more realistic simulation of renal pathologies and pharmacological treatments in the foreseeable future.

Impact of angiotensin II-mediated stimulation of sodium transporters in the nephron assessed by computational modeling

Angiotensin II (ANG II) raises blood pressure partly by stimulating tubular Na⁺ reabsorption. The effects of ANG II on tubular Na⁺ transporters (i.e., channels, pumps, cotransporters, and exchangers) vary between short-term and long-term exposure. To better understand the physiological impact, we used a computational model of transport along the rat nephron to predict the effects of short- and long-term ANG II-induced transporter activation on Na⁺ and K⁺ reabsorption/secretion, and to compare measured and calculated excretion rates. Three days of ANG II infusion at 200 ng·kg^-1·min^-1 is nonpressor, yet stimulates transporter accumulation. The increase in abundance of Na⁺/H⁺ exchanger 3 (NHE3) or activated Na⁺-K⁺-2Cl^- cotransporter-2 (NKCC2-P) predicted significant reductions in urinary Na⁺ excretion, yet there was no observed change in urine Na⁺. The lack of antinatriuresis, despite Na⁺ transporter accumulation, was supported by Li⁺ and creatinine clearance measurements, leading to the conclusion that 3-day nonpressor ANG II increases transporter abundance without proportional activation. Fourteen days of ANG II infusion at 400 ng·kg^-1·min^-1 raises blood pressure and increases Na⁺ transporter abundance along the distal nephron; proximal tubule and medullary loop transporters are decreased and urine Na⁺ and volume output are increased, evidence for pressure natriuresis. Simulations indicate that decreases in NHE3 and NKCC2-P contribute significantly to reducing Na⁺ reabsorption along the nephron and to pressure natriuresis. Our results also suggest that differential regulation of medullary (decrease) and cortical (increase) NKCC2-P is important to preserve K⁺ while minimizing Na⁺ retention during ANG II infusion. Lastly, our model indicates that accumulation of active Na⁺-Cl^- cotransporter counteracts epithelial Na⁺ channel-induced urinary K⁺ loss.

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.

How Do Kidneys Adapt to a Deficit or Loss in Nephron Number?

A deficit or loss in the number of nephrons, the functional unit of the kidney, can induce compensatory growth and hyperfunction of remaining nephrons. An increase in single nephron glomerular filtration rate (SNGFR) aims to compensate but may be deleterious in the long term. The increase in SNGFR is determined by the dynamics of nephron loss, total remaining GFR, the body's excretory demand, and the functional capacity to sustain single nephron hyperfunction.

Renal tubular solute transport and oxygen consumption: insights from computational models

PURPOSE OF REVIEW

To maintain electrolyte homeostasis, the kidneys reabsorb more than 99% of the filtered Na under physiological conditions, resulting in less than 1% of the filtered Na excreted in urine. In contrast, due to distal tubular secretion, urinary K output may exceed filtered load. This review focuses on a relatively new methodology for investigating renal epithelial transport, computational modelling and highlights recent insights regarding renal Na and K transport and O2 consumption under pathophysiological conditions, with a focus on nephrectomy.

RECENT FINDINGS

Recent modelling studies investigated the extent to which the adaptive response to nephrectomy, which includes elevation in single-nephron glomerular filtration rate and tubular transport capacity, may achieve balance but increases O2 consumption per nephron. Simulation results pointed to potential mechanisms in a hemi-nephrectomized rat that may attenuate the natriuresis response under K load, or that may augment the natriuretic, diuretic and kaliuretic effects of sodium glucose cotransporter 2 inhibition.

SUMMARY

Computational models provide a systemic approach for investigating system perturbations, such as those induced by drug administration or genetic alterations. Thus, computational models can be a great asset in data interpretation concerning (but not limited to) renal tubular transport and metabolism.

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.

Understanding sex differences in long-term blood pressure regulation: insights from experimental studies and computational modeling

Sex differences in blood pressure and the prevalence of hypertension are found in humans and animal models. Moreover, there has been a recent explosion of data concerning sex differences in nitric oxide, the renin-angiotensin-aldosterone system, inflammation, and kidney function. These data have the potential to reveal the mechanisms underlying male-female differences in blood pressure control. To elucidate the interactions among the multitude of physiological processes involved, one may apply computational models. In this review, we describe published computational models that represent key players in blood pressure regulation, and highlight sex-specific models and their findings.

A computational model of epithelial solute and water transport along a human nephron

We have developed the first computational model of solute and water transport from Bowman space to the papillary tip of the nephron of a human kidney. The nephron is represented as a tubule lined by a layer of epithelial cells, with apical and basolateral transporters that vary according to cell type. The model is formulated for steady state, and consists of a large system of coupled ordinary differential equations and algebraic equations. Model solution describes luminal fluid flow, hydrostatic pressure, luminal fluid solute concentrations, cytosolic solute concentrations, epithelial membrane potential, and transcellular and paracellular fluxes. We found that if we assume that the transporter density and permeabilities are taken to be the same between the human and rat nephrons (with the exception of a glucose transporter along the proximal tubule and the H⁺-pump along the collecting duct), the model yields segmental deliveries and urinary excretion of volume and key solutes that are consistent with human data. The model predicted that the human nephron exhibits glomerulotubular balance, such that proximal tubular Na⁺ reabsorption varies proportionally to the single-nephron glomerular filtration rate. To simulate the action of a novel diabetic treatment, we inhibited the Na⁺-glucose cotransporter 2 (SGLT2) along the proximal convoluted tubule. Simulation results predicted that the segment’s Na⁺ reabsorption decreased significantly, resulting in natriuresis and osmotic diuresis.

In addition to its well-known function of waste removal from the body, the kidney is also responsible for the critical regulation of the body’s salt, potassium, acid content, and blood pressure. The kidneys perform these life-sustaining task by filtering and returning to blood stream about 200 quarts of blood every 24 hours. What isn’t returned to blood stream is excreted as urine. The production of urine involves highly complex steps of secretion and reabsorption. To study these processes without employing invasive experimental procedures, we developed the first computational model of the human nephron (which is the functional unit of a kidney). The model contains detailed representation of the transport processes that take place in the epithelial cells that form the walls of the nephron. Using that model, we conducted simulations to predict how much filtered solutes and and water is transported along each individual and functionally distinct nephron segment. We conducted these simulations under normal physiological conditions, and under pharmacological conditions. The nephron model can be used as an essential component in an integrated model of kidney function in humans.

3D simulation of solutes concentration in urinary concentration mechanism in rat renal medulla

In this work, a mathematical model was developed to simulate the urinary concentration mechanism. A 3-D geometry was derived based on the detail physiological pictures of rat kidney. The approximate region of each tubule was obtained from the volume distribution of structures based on Walter Pfaller's monograph and Layton's region-based model. Mass and momentum balances were applied to solve for the change in solutes concentration and osmolality. The osmolality of short and long descending nephrons at the end of the outer medulla was obtained to be 530 mOsmol/kgH2O and 802 mOsmol/kgH2O, respectively, which were in acceptable agreement with experimental data. The fluid osmolality of the short and long ascending nephrons was also compatible with experimental data. The osmolality of CD fluid at the end of the inner medulla was determined to be 1198 mOsmol/kgH2O which was close the experimental data (1216 ± 118). Finally, the impact of the position of each tubule on the fluid osmolality and solutes concentration were obvious in the results; for example, short descending limb a1, which is the closest tubule to the collecting duct, had the highest urea concentration in all tubules. This reflects the important effect of the 3D modeling on the precise analysis of urinary concentration mechanism.

Sex-specific long-term blood pressure regulation: Modeling and analysis

Hypertension is a global health challenge: it affects one billion people worldwide and is estimated to account for >60% of all cases or types of cardiovascular disease. In part because sex differences in blood pressure regulation mechanisms are not sufficiently well understood, fewer hypertensive women achieve blood pressure control compared to men, even though compliance and treatment rates are generally higher in women. Thus, the objective of this study is to identify which factors contribute to the sexual dimorphism in response to anti-hypertensive therapies targeting the renin angiotensin system (RAS). To accomplish that goal, we develop sex-specific blood pressure regulation models. Sex differences in the RAS, baseline adosterone level, and the reactivity of renal sympathetic nervous activity (RSNA) are represented. A novel aspect of the model is the representation of sex-specific vasodilatory effect of the bound angiotensin II type two receptor (AT2R-bound Ang II) on renal vascular resistance. Model simulations suggest that sex differences in RSNA are the largest cause of female resistance to developing hypertension due to the direct influence of RSNA on afferent arteriole resistance. Furthermore, the model predicts that the sex-specific vasodilatory effects of AT2R-bound Ang II on renal vascular resistance may explain the higher effectiveness of angiotensin receptor blockers in treating hypertensive women (but not men), compared to angiotensin converting enzyme inhibitors.

Functional implications of sexual dimorphism of transporter patterns along the rat proximal tubule: modeling and analysis

The goal of this study is to investigate the functional implications of the sexual dimorphism in transporter patterns along the proximal tubule. To do so, we have developed sex-specific computational models of solute and water transport in the proximal convoluted tubule of the rat kidney. The models account for the sex differences in expression levels of the apical and basolateral transporters, in single-nephron glomerular filtration rate, and in tubular dimensions. Model simulations predict that 70.6 and 38.7% of the filtered volume is reabsorbed by the proximal tubule of the male and female rat kidneys, respectively. The lower fractional volume reabsorption in females can be attributed to their smaller transport area and lower aquaporin-1 expression level. The latter also results in a larger contribution of the paracellular pathway to water transport. Correspondingly similar fractions (70.9 and 39.2%) of the filtered Na+ are reabsorbed by the male and female proximal tubule models, respectively. The lower fractional Na+ reabsorption in females is due primarily to their smaller transport area and lower Na+/H+ exchanger isoform 3 and claudin-2 expression levels. Notably, unlike most Na+ transporters, whose expression levels are lower in females, Na+-glucose cotransporter 2 (SGLT2) expression levels are 2.5-fold higher in females. Model simulations suggest that the higher SGLT2 expression in females may compensate for their lower tubular transport area to achieve a hyperglycemic tolerance similar to that of males.

A Multicellular Vascular Model of the Renal Myogenic Response

The myogenic response is a key autoregulatory mechanism in the mammalian kidney. Triggered by blood pressure perturbations, it is well established that the myogenic response is initiated in the renal afferent arteriole and mediated by alterations in muscle tone and vascular diameter that counterbalance hemodynamic perturbations. The entire process involves several subcellular, cellular, and vascular mechanisms whose interactions remain poorly understood. Here, we model and investigate the myogenic response of a multicellular segment of an afferent arteriole. Extending existing work, we focus on providing an accurate—but still computationally tractable—representation of the coupling among the involved levels. For individual muscle cells, we include detailed Ca2+ signaling, transmembrane transport of ions, kinetics of myosin light chain phosphorylation, and contraction mechanics. Intercellular interactions are mediated by gap junctions between muscle or endothelial cells. Additional interactions are mediated by hemodynamics. Simulations of time-independent pressure changes reveal regular vasoresponses throughout the model segment and stabilization of a physiological range of blood pressures (80–180 mmHg) in agreement with other modeling and experimental studies that assess steady autoregulation. Simulations of time-dependent perturbations reveal irregular vasoresponses and complex dynamics that may contribute to the complexity of dynamic autoregulation observed in vivo. The ability of the developed model to represent the myogenic response in a multiscale and realistic fashion, under feasible computational load, suggests that it can be incorporated as a key component into larger models of integrated renal hemodynamic regulation.