Modeling Transport and Flow Regulatory Mechanisms of the Kidney

Quantitative renal magnetic resonance imaging: magnetic resonance urography

The goal of functional renal imaging is to identify and quantitate irreversible renal damage and nephron loss, as well as potentially reversible hemodynamic changes. MR urography has evolved into a comprehensive evaluation of the urinary tract that combines anatomical imaging with functional evaluation in a single test without ionizing radiation. Quantitative functional MR imaging is based on dynamic contrast-enhanced MR acquisitions that provide progressive, visible enhancement of the renal parenchyma and urinary tract. The signal changes related to perfusion, concentration and excretion of the contrast agent can be evaluated using both quantitative and qualitative measures. Functional evaluation with MR has continued to improve as a result of significant technical advances allowing for faster image acquisition as well as the development of new tracer kinetic models of renal function. The most common indications for MR urography in children are the evaluation of congenital anomalies of the kidney and urinary tract including hydronephrosis and renal malformations, and the identification of ectopic ureters in children with incontinence. In this paper, we review the underlying acquisition schemes and techniques used to generate quantitative functional parameters including the differential renal function (DRF), asymmetry index, mean transit time (MTT), signal intensity versus time curves as well as the calculation of individual kidney glomerular filtration rate (GFR). Visual inspection and semi-quantitative assessment using the renal transit time (RTT) and calyceal transit times (CTT) are fundamental to accurate diagnosis and are used as a basis for the interpretation of the quantitative data. The importance of visual assessment of the images cannot be overstated when analyzing the quantitative measures of renal function.

Pulsatile flow through idealized renal tubules: Fluid-structure interaction and dynamic pathologies

Kidney tubules are lined with flow-sensing structures, yet information about the flow itself is not easily obtained. We aim to generate a multiscale biomechanical model for analyzing fluid flow and fluid-structure interactions within an elastic kidney tubule when the driving pressure is pulsatile. We developed a two-dimensional macroscopic mathematical model of a single fluid-filled tubule corresponding to a distal nephron segment and determined both flow dynamics and wall strains over a range of driving frequencies and wall compliances using finite-element analysis. The results presented here demonstrate good agreement with available analytical solutions and form a foundation for future inclusion of elastohydrodynamic coupling by neighboring tubules. Overall, we are interested in exploring the idea of dynamic pathology to better understand the progression of chronic kidney diseases such as Polycystic Kidney Disease.

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.

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.

The Kidney in Bardet-Biedl Syndrome: Possible Pathogenesis of Urine Concentrating Defect

BACKGROUND

The ciliopathies are a growing number of disorders caused by mutations in genes involved in the function of the primary cilium. Bardet-Biedl syndrome (BBS) belongs to this group of disorders. In this setting, kidney dysfunction is highly variable, and urine concentrating defect, a common feature of multiple ciliopathies, has been described as the most frequent defect. Here we review the mechanism of urine concentration and describe the possible mechanism underling this defect in ciliopathies and especially BBS, based on the current body of literature.

SUMMARY

Active Na⁺ absorption along the thick ascending limb of the loop of Henle (TAL) is critical for generating the corticomedullary osmotic gradient, and the countercurrent anatomical arrangement of the 2 branches of the loop of Henle enhances this gradient. The vasa recta, paralleling the loop of Henle, operate into the countercurrent mechanism, minimizing washout of solutes from the interstitium. Final water reabsorption is mediated by the aquaporin 2 (AQP2) water channels along the distal nephron, and it is under hormonal control. Several studies demonstrated that hyposthenuria in BBS patients relies on kidney resistance to desmopressin, suggesting a renal origin. We recently showed that the majority of hyposthenuric BBS patients have also a defect regarding maximal urine dilution. Independent studies showed that BBS10 deficiency caused AQP2 mistrafficking in vitro; accordingly, we demonstrated impaired urinary AQP2 excretion in BBS patients with combined concentrating and diluting defect. Whether receptor signaling pathways or downstream events cause AQP2 deregulation is still unclear. In addition, reduced urinary uromodulin excretion in BBS patients opens the possibility that TAL dysfunction may also play a pathogenic role.

KEY MESSAGE

Impaired water handling in BBS is associated with AQP2 mistrafficking. The potential role of additional factors, such as the dissipation of the medullary osmotic gradient due to TAL dysfunction and/or structural anomalies, remains to be elucidated.

Nephron morphometry in mice and rats using tomographic microscopy

The aim was to quantify the glomerular capillary surface area, the segmental tubular radius, length, and area of single nephrons in mouse and rat kidneys. Multiple 2.5-µm-thick serial Epon sections were obtained from three mouse and three rat kidneys for three-dimensional reconstruction of the nephron tubules. Micrographs were aligned for each kidney, and 359 nephrons were traced and their segments localized. Thirty mouse and thirty rat nephrons were selected for further investigation. The luminal radius of each segment was determined by two methods. The luminal surface area was estimated from the radius and length of each segment. High-resolution micrographs were recorded for five rat glomeruli, and the capillary surface area determined. The capillary volume and surface area were corrected for glomerular shrinkage. A positive correlation was found between glomerular capillary area and proximal tubule area. The thickest part of the nephron, i.e., the proximal tubule, was followed by the thinnest part of the nephron, i.e., the descending thin limb, and the diameters of the seven identified nephron segments share the same rank in the two species. The radius and length measurements from mouse and rat nephrons generally share the same pattern; rat tubular radius-to-mouse tubular radius ratio ≈ 1.47, and rat tubular length-to-mouse tubular length ratio ≈ 2.29, suggesting relatively longer tubules in the rat. The detailed tables of mouse and rat glomerular capillary area and segmental radius, length, and area values may be used to enhance understanding of the associated physiology, including existing steady-state models of the urine-concentrating mechanism.

Non-rigid landmark-based large-scale image registration in 3-D reconstruction of mouse and rat kidney nephrons

BACKGROUND

Serial histological sections are suffering from mechanical distortions that disturb the reconstruction of 3-D objects. We have corrected such artifacts with a non-rigid landmark-based method that respects the original geometry in the tissue block. The method is exemplified on a large scale in the registration of semi-thin serial sections of the mouse and rat kidneys, and has been tested on FFPE-sections.

AIM

In this study of mouse and rat kidneys, we have measured and characterized the deformations introduced in the preparation of 2.5-μm-thick Epon sections and then eliminated them by a landmark-based non-rigid transformation (NRT).

METHODS

We obtained 2.5-μm-thick serial Epon sections from three mouse kidneys and three rat kidneys for 3-D reconstruction of the nephron tubules. First, the images from 3000 serial mouse and 13,000 serial rat sections underwent a classic rigid registration (CRR), and the distortions were measured and indexed. The section images underwent a further NRT in order to compensate for the deformations. The NRT used is a classic interactive landmark-based approach. The quality of the NRT was verified by comparing the geometry of the transformed images with corresponding block images.

RESULTS

After CRR, the 2.5-μm-thick sections had a linear deformation of up to 2%, the tubular lengths were overestimated with up to 1.5×, and it was most difficult to trace the tubules from section to section. After the additional NRT, the geometry of the images reflected the original geometry in the block, the tubular lengths were no longer overestimated, and the NRT highly facilitated the tracing of the tubular system.

CONCLUSIONS

NRT has facilitated the tracing of the tubular system in kidneys, a tracing, which would otherwise have been most difficult to perform. NRT has yielded substantial new knowledge to segmental and spatial nephron organization in the mouse and rat kidneys.