Modeling transport in the kidney: investigating function and dysfunction

A review of feto-placental vasculature flow modelling

The placenta provides the vital nutrients and removal of waste products required for fetal growth and development. Understanding and quantifying the differences in structure and function between a normally functioning placenta compared to an abnormal placenta is vital to provide insights into the aetiology and treatment options for fetal growth restriction and other placental disorders. Computational modelling of blood flow in the placenta allows a new understanding of the placental circulation to be obtained. This structured review discusses multiple recent methods for placental vascular model development including analysis of the appearance of the placental vasculature and how placental haemodynamics may be simulated at multiple length scales.

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.

Wet-tip versus dry-tip regimes of osmotically driven fluid flow

The secretion of osmolytes into a lumen and thereby caused osmotic water inflow can drive fluid flows in organs without a mechanical pump. Such fluids include saliva, sweat, pancreatic juice and bile. The effects of elevated fluid pressure and the associated mechanical limitations of organ function remain largely unknown since fluid pressure is difficult to measure inside tiny secretory channels in vivo. We consider the pressure profile of the coupled osmolyte-flow problem in a secretory channel with a closed tip and an open outlet. Importantly, the entire lateral boundary acts as a dynamic fluid source, the strength of which self-organizes through feedback from the emergent pressure solution itself. We derive analytical solutions and compare them to numerical simulations of the problem in three-dimensional space. The theoretical results reveal a phase boundary in a four-dimensional parameter space separating the commonly considered regime with steady flow all along the channel, here termed “wet-tip” regime, from a “dry-tip” regime suffering ceased flow downstream from the closed tip. We propose a relation between the predicted phase boundary and the onset of cholestasis, a pathological liver condition with reduced bile outflow. The phase boundary also sets an intrinsic length scale for the channel which could act as a length sensor during organ growth.

A Glucose-Dependent Pharmacokinetic/ Pharmacodynamic Model of ACE Inhibition in Kidney Cells

Diabetic kidney disease (DKD) is a major cause of renal failure. Podocytes are terminally differentiated renal epithelial cells that are key targets of damage due to DKD. Podocytes express a glucose-stimulated local renin-angiotensin system (RAS) that produces angiotensin II (ANG II). Local RAS differs from systemic RAS, which has been studied widely. Hyperglycemia increases the production of ANG II by podocyte cells, leading to podocyte injury. Angiotensin-converting enzyme (ACE) is involved in the production of ANG II, and ACE inhibitors are drugs used to suppress elevated ANG II concentration. As systemic RAS differs from the local RAS in podocytes, ACE inhibitor drugs should act differently in local versus systemic contexts. Experimental and computational studies have considered the pharmacokinetics (PK) and pharmacodynamics (PD) of ACE inhibition of the systemic RAS. Here, a PK/PD model for ACE inhibition is developed for the local RAS in podocytes. The model takes constant or dynamic subject-specific glucose concentration input to predict the ANG II concentration and the corresponding effects of drug doses locally and systemically. The model is developed for normal and impaired renal function in combination with different glucose conditions, thus enabling the study of various pathophysiological conditions. Parameter uncertainty is also analyzed. Such a model can improve the study of the effects of drugs at the cellular level and can aid in development of therapeutic approaches to slow the progression of DKD.

Physical Processes in Polymeric Filters Used for Dialysis

The key physical processes in polymeric filters used for the blood purification include transport across the capillary wall and the interaction of blood cells with the polymer membrane surface. Theoretical modeling of membrane transport is an important tool which provides researchers with a quantification of the complex phenomena involved in dialysis. In the paper, we present a dense review of the most successful theoretical approaches to the description of transport across the polymeric membrane wall as well as the cell⁻polymer surface interaction, and refer to the corresponding experimental methods while studying these phenomena in dialyzing filters.

Modeling the Effects of Multiple Myeloma on Kidney Function

Multiple myeloma (MM), a plasma cell cancer, is associated with many health challenges, including damage to the kidney by tubulointerstitial fibrosis. We develop a mathematical model which captures the qualitative behavior of the cell and protein populations involved. Specifically, we model the interaction between cells in the proximal tubule of the kidney, free light chains, renal fibroblasts, and myeloma cells. We analyze the model for steady-state solutions to find a mathematically and biologically relevant stable steady-state solution. This foundational model provides a representation of dynamics between key populations in tubulointerstitial fibrosis that demonstrates how these populations interact to affect patient prognosis in patients with MM and renal impairment.

Combination ART-Induced Oxidative/Nitrosative Stress, Neurogenic Inflammation and Cardiac Dysfunction in HIV-1 Transgenic (Tg) Rats: Protection by Mg

Chronic effects of a combination antiretroviral therapy (cART = tenofovir/emtricitatine + atazanavir/ritonavir) on systemic and cardiac oxidative stress/injury in HIV-1 transgenic (Tg) rats and protection by Mg-supplementation were assessed. cART (low doses) elicited no significant effects in normal rats, but induced time-dependent oxidative/nitrosative stresses: 2.64-fold increased plasma 8-isoprostane, 2.0-fold higher RBC oxidized glutathione (GSSG), 3.2-fold increased plasma 3-nitrotyrosine (NT), and 3-fold elevated basal neutrophil superoxide activity in Tg rats. Increased NT staining occurred within cART-treated HIV-Tg hearts, and significant decreases in cardiac systolic and diastolic contractile function occurred at 12 and 18 weeks. HIV-1 expression alone caused modest levels of oxidative stress and cardiac dysfunction. Significantly, cART caused up to 24% decreases in circulating Mg in HIV-1-Tg rats, associated with elevated renal NT staining, increased creatinine and urea levels, and elevated plasma substance P levels. Strikingly, Mg-supplementation (6-fold) suppressed all oxidative/nitrosative stress indices in the blood, heart and kidney and substantially attenuated contractile dysfunction (>75%) of cART-treated Tg rats. In conclusion, cART caused significant renal and cardiac oxidative/nitrosative stress/injury in Tg-rats, leading to renal Mg wasting and hypomagnesemia, triggering substance P-dependent neurogenic inflammation and cardiac dysfunction. These events were effectively attenuated by Mg-supplementation likely due to its substance P-suppressing and Mg’s intrinsic anti-peroxidative/anti-calcium properties.

Diffusive shunting of gases and other molecules in the renal vasculature: physiological and evolutionary significance

Countercurrent systems have evolved in a variety of biological systems that allow transfer of heat, gases, and solutes. For example, in the renal medulla, the countercurrent arrangement of vascular and tubular elements facilitates the trapping of urea and other solutes in the inner medulla, which in turn enables the formation of concentrated urine. Arteries and veins in the cortex are also arranged in a countercurrent fashion, as are descending and ascending vasa recta in the medulla. For countercurrent diffusion to occur, barriers to diffusion must be small. This appears to be characteristic of larger vessels in the renal cortex. There must also be gradients in the concentration of molecules between afferent and efferent vessels, with the transport of molecules possible in either direction. Such gradients exist for oxygen in both the cortex and medulla, but there is little evidence that large gradients exist for other molecules such as carbon dioxide, nitric oxide, superoxide, hydrogen sulfide, and ammonia. There is some experimental evidence for arterial-to-venous (AV) oxygen shunting. Mathematical models also provide evidence for oxygen shunting in both the cortex and medulla. However, the quantitative significance of AV oxygen shunting remains a matter of controversy. Thus, whereas the countercurrent arrangement of vasa recta in the medulla appears to have evolved as a consequence of the evolution of Henle’s loop, the evolutionary significance of the intimate countercurrent arrangement of blood vessels in the renal cortex remains an enigma.

A model of calcium transport along the rat nephron

We developed a mathematical model of calcium (Ca2+) transport along the rat nephron to investigate the factors that promote hypercalciuria. The model is an extension of the flat medullary model of Hervy and Thomas ( Am J Physiol Renal Physiol 284: F65–F81, 2003). It explicitly represents all the nephron segments beyond the proximal tubules and distinguishes between superficial and deep nephrons. It solves dynamic conservation equations to determine NaCl, urea, and Ca2+ concentration profiles in tubules, vasa recta, and the interstitium. Calcium is known to be reabsorbed passively in the thick ascending limbs and actively in the distal convoluted (DCT) and connecting (CNT) tubules. Our model predicts that the passive diffusion of Ca2+ from the vasa recta and loops of Henle generates a significant axial Ca2+ concentration gradient in the medullary interstitium. In the base case, the urinary Ca2+ concentration and fractional excretion are predicted as 2.7 mM and 0.32%, respectively. Urinary Ca2+ excretion is found to be strongly modulated by water and NaCl reabsorption along the nephron. Our simulations also suggest that Ca2+ molar flow and concentration profiles differ significantly between superficial and deep nephrons, such that the latter deliver less Ca2+ to the collecting duct. Finally, our results suggest that the DCT and CNT can act to counteract upstream variations in Ca2+ transport but not always sufficiently to prevent hypercalciuria.

Estimation of single-kidney glomerular filtration rate without exogenous contrast agent

PURPOSE

Measurement of single-kidney filtration fraction and glomerular filtration rate (GFR) without exogenous contrast is clinically important to assess renal function and pathophysiology, especially for patients with comprised renal function. The objective of this study is to develop a novel MR-based tool for noninvasive quantification of renal function using conventional MR arterial spin labeling water as endogenous tracer.

THEORY AND METHODS

The regional differentiation of the arterial spin labeling water between the glomerular capsular space and the renal parenchyma was characterized and measured according to their MR relaxation properties (T1ρ or T2 ), and applied to the estimation of filtration fraction and single-kidney GFR. The proposed approach was tested to quantify GFR in healthy volunteers at baseline and after a protein-loading challenge.

RESULTS

Biexponential decay of the cortical arterial spin labeling water MR signal was observed. The major component decays the same as parenchyma water; the minor component decays much slower as expected from glomerular ultra-filtrates. The mean single-kidney GFR was estimated to be 49 ± 9 mL/min at baseline and increased by 28% after a protein-loading challenge.

CONCLUSION

We developed an arterial spin labeling-based MR imaging method that allows us to estimate renal filtration fraction and singe-kidney GFR without use of exogenous contrast.

Development of a physiologically based computational kidney model to describe the renal excretion of hydrophilic agents in rats

A physiologically based kidney model was developed to analyze the renal excretion and kidney exposure of hydrophilic agents, in particular contrast media, in rats. In order to study the influence of osmolality and viscosity changes, the model mechanistically represents urine concentration by water reabsorption in different segments of kidney tubules and viscosity dependent tubular fluid flow. The model was established using experimental data on the physiological steady state without administration of any contrast media or drugs. These data included the sodium and urea concentration gradient along the cortico-medullary axis, water reabsorption, urine flow, and sodium as well as urea urine concentrations for a normal hydration state. The model was evaluated by predicting the effects of mannitol and contrast media administration and comparing to experimental data on cortico-medullary concentration gradients, urine flow, urine viscosity, hydrostatic tubular pressures and single nephron glomerular filtration rate. Finally the model was used to analyze and compare typical examples of ionic and non-ionic monomeric as well as non-ionic dimeric contrast media with respect to their osmolality and viscosity. With the computational kidney model, urine flow depended mainly on osmolality, while osmolality and viscosity were important determinants for tubular hydrostatic pressure and kidney exposure. The low diuretic effect of dimeric contrast media in combination with their high intrinsic viscosity resulted in a high viscosity within the tubular fluid. In comparison to monomeric contrast media, this led to a higher increase in tubular pressure, to a reduction in glomerular filtration rate and tubular flow and to an increase in kidney exposure. The presented kidney model can be implemented into whole body physiologically based pharmacokinetic models and extended in order to simulate the renal excretion of lipophilic drugs which may also undergo active secretion and reabsorption.

Earlier recognition of nephrotoxicity using novel biomarkers of acute kidney injury

CONTEXT

A broad range of drugs and chemicals are capable of evoking acute kidney injury, which is conventionally determined by rising serum creatinine concentrations. However there are important limitations to this approach, and there has been interest in alternative biomarkers that might provide a more sensitive and rapid means of detecting acute kidney injury. Most of the available clinical data have thus far been ascertained in patients requiring critical care or with acute sepsis. However, if a sensitive indicator of acute kidney injury were developed, then this could provide a significantly improved means of detecting the effects of acute drug or toxin exposure.

OBJECTIVE

To review the available data concerning potential biomarkers of acute kidney injury and to assess their relative strengths and weaknesses in comparison to existing methods based on serum creatinine concentrations. A large number of possible biomarkers have been proposed. Evidence for individual biomarkers is reviewed with a particular emphasis on those with potential application in clinical toxicology. Where available, comparative data are presented.

METHODS

There were 236 papers identified using Medline, Embase, and Google Scholar databases, of which 52 were considered directly relevant. CREATININE: Creatinine is subject to glomerular filtration and, to a lesser extent tubular secretion. Serum concentrations are an insensitive marker of acute kidney injury, and the speed of an increase from baseline depends on the magnitude of the acute injury and pre-existing kidney functional reserve. A wide range of inter-individual concentrations means that single time-point determinations are difficult to interpret, and acute kidney injury may not manifest as a detectable increase in serum creatinine concentrations until at least 24-48 h after the primary insult. KIDNEY ENZYMES: Enzymes are often localised to specific anatomical locations, and acute injury may cause a detectable increase in urinary activity due to up-regulated activity or leakage due to cell membrane disruption. Key examples include gamma-glutamyl transpeptidase (GGT), glutathione-S-transferase (GST), and N-acetyl-glucosaminidase (NAG), which are found predominantly in the proximal tubule and urinary enzyme activity increases after acute exposure to heavy metals and other nephrotoxins. NEUTROPHIL GELATINASE-ASSOCIATED LIPOCALIN: Neutrophil gelatinase-associated lipocalin (NGAL) is expressed by renal tubular epithelium, and a rise in urinary concentrations may provide an indicator of acute renal injury caused by any one of a broad range of provoking factors that is detectable before a rise in serum creatinine concentrations. CYSTATIN C: Serum and urinary cystatin C concentrations are closely related to kidney function and, for example, in acute tubular necrosis allow better prediction of the need for renal replacement therapy than serum creatinine concentrations. KIDNEY INJURY MOLECULE 1: Kidney injury molecule 1 (KIM-1) is expressed in the proximal tubule in the setting of acute ischaemia. For example, urinary KIM-1 concentrations becomes detectable within 24 h of acute tubular necrosis. Urinary KIM-1 expression may be detected after exposure to a variety of nephrotoxic agents, even when serum creatinine concentrations do not increase, and this has been accepted by regulatory authorities as a sensitive biomarker of acute kidney injury during early drug development.

CONCLUSIONS

Novel biomarkers appear capable of offering a more sensitive means of detecting acute kidney injury than existing approaches. Certain of these allow discrimination between the various mechanisms and anatomical site of acute injury. Ultimately, clinical assessment might incorporate a panel of different biomarkers, each informing on the integrated aspects of glomerular, tubular and interstitial function. Presence of biomarkers may in some cases detect mild or transient renal dysfunction that is presently undetected, and the clinical relevance needs further exploration. Whilst many potentially useful biomarkers have been proposed, comparatively few clinical data exist to support their validity in routine practice. Further prospective clinical studies are required to examine the validity of biomarkers after acute drug or toxin exposure, and to establish whether they might offer improved clinical outcomes in the setting of clinical toxicology.

2-DE based proteomic analysis of Saccharomyces cerevisiae wild and K+ transport-affected mutant (trk1,2) strains at the growth exponential and stationary phases

By using a 2-DE based workflow, the proteome of wild and potassium transport mutant trk1,2 under optimal growth potassium concentration (50mM) has been analyzed. At the exponential and stationary phases, both strains showed similar growth, morphology potassium content, and Vmax of rubidium transport, the only difference found being the Km values for this potassium analogue transport, higher for the mutant (20mM) than for the wild (3-6mM) cells. Proteins were buffer-extracted, precipitated, solubilized, quantified, and subjected to 2-DE analysis in the 5-8 pH range. More differences in protein content (37-64mgg(-1) cell dry weight) and number of resolved spots (178-307) were found between growth phases than between strains. In all, 164 spots showed no differences between samples and a total of 105 were considered to be differential after ANOVA test. 171 proteins, corresponding to 71 unique gene products have been identified, this set being dominated by cytosolic species and glycolitic enzymes. The ranking of the more abundant spots revealed no differences between samples and indicated fermentative metabolism, and active cell wall biosynthesis, redox homeostasis, biosynthesis of amino acids, coenzymes, nucleotides, and RNA, and protein turnover, apart from cell division and growth. PCA analysis allowed the separation of growth phases (PC1 and 2) and strains at the stationary phase (PC3 and 4), but not at the exponential one. These results are also supported by clustering analysis. As a general tendency, a number of spots newly appeared at the stationary phase in wild type, and to a lesser extent, in the mutant. These up-accumulated spots corresponded to glycolitic enzymes, indicating a more active glucose catabolism, accompanied by an accumulation of methylglyoxal detoxification, and redox-homeostasis enzymes. Also, more extensive proteolysis was observed at the stationary phase with this resulting in an accumulation of low Mr protein species.