A pseudo-three-dimensional model for quantification of oxygen diffusion from preglomerular arteries to renal tissue and renal venous blood

Anemia and Hypoxia Impact on Chronic Kidney Disease Onset and Progression: Review and Updates

Chronic kidney disease (CKD) is caused by hypoxia in the renal tissue, leading to inflammation and increased migration of pathogenic cells. Studies showed that leukocytes directly sense hypoxia and respond by initiating gene transcription, encoding the 2-integrin adhesion molecules. Moreover, other mechanisms participate in hypoxia, including anemia. CKD-associated anemia is common, which induces and worsens hypoxia, contributing to CKD progression. Anemia correction can slow CKD progression, but it should be cautiously approached. In this comprehensive review, the underlying pathophysiology mechanisms and the impact of renal tissue hypoxia and anemia in CKD onset and progression will be reviewed and discussed in detail. Searching for the latest updates in PubMed Central, Medline, PubMed database, Google Scholar, and Google search engines were conducted for original studies, including cross-sectional studies, cohort studies, clinical trials, and review articles using different keywords, phrases, and texts such as "CKD progression, anemia in CKD, CKD, anemia effect on CKD progression, anemia effect on CKD progression, and hypoxia and CKD progression". Kidney tissue hypoxia and anemia have an impact on CKD onset and progression. Hypoxia causes nephron cell death, enhancing fibrosis by increasing interstitium protein deposition, inflammatory cell activation, and apoptosis. Severe anemia correction improves life quality and may delay CKD progression. Detection and avoidance of the risk factors of hypoxia prevent recurrent acute kidney injury (AKI) and reduce the CKD rate. A better understanding of kidney hypoxia would prevent AKI and CKD and lead to new therapeutic strategies.

Functional implications of microvascular heterogeneity for oxygen uptake and utilization

In the vascular system, an extensive network structure provides convective and diffusive transport of oxygen to tissue. In the microcirculation, parameters describing network structure, blood flow, and oxygen transport are highly heterogeneous. This heterogeneity can strongly affect oxygen supply and organ function, including reduced oxygen uptake in the lung and decreased oxygen delivery to tissue. The causes of heterogeneity can be classified as extrinsic or intrinsic. Extrinsic heterogeneity refers to variations in oxygen demand in the systemic circulation or oxygen supply in the lungs. Intrinsic heterogeneity refers to structural heterogeneity due to stochastic growth of blood vessels and variability in flow pathways due to geometric constraints, and resulting variations in blood flow and hematocrit. Mechanisms have evolved to compensate for heterogeneity and thereby improve oxygen uptake in the lung and delivery to tissue. These mechanisms, which involve long-term structural adaptation and short-term flow regulation, depend on upstream responses conducted along vessel walls, and work to redistribute flow and maintain blood and tissue oxygenation. Mathematically, the variance of a functional quantity such as oxygen delivery that depends on two or more heterogeneous variables can be reduced if one of the underlying variables is controlled by an appropriate compensatory mechanism. Ineffective regulatory mechanisms can result in poor oxygen delivery even in the presence of adequate overall tissue perfusion. Restoration of endothelial function, and specifically conducted responses, should be considered when addressing tissue hypoxemia and organ failure in clinical settings.

Predicting oxygen tension along the ureter

Continuous measurement of bladder urine oxygen tension (Po₂) is a method to potentially detect renal medullary hypoxia in patients at risk of acute kidney injury (AKI). To assess its practicality, we developed a computational model of the peristaltic movement of a urine bolus along the ureter and the oxygen exchange between the bolus and ureter wall. This model quantifies the changes in urine Po₂ as urine transits from the renal pelvis to the bladder. The model parameters were calibrated using experimental data in rabbits, such that most of the model predictions are within ±1 SE of the reported mean in the experiment, with the average percent difference being 7.0%. Based on parametric experiments performed using a model scaled to the geometric dimensions of a human ureter, we found that bladder urine Po₂ is strongly dependent on the bolus volume (i.e., bolus volume-to-surface area ratio), especially at a volume less than its physiological (baseline) volume (<0.2 mL). For the model assumptions, changes in peristaltic frequency resulted in a minimal change in bladder urine Po₂ (<1 mmHg). The model also predicted that there exists a family of linear relationships between the bladder-urine Po₂ and pelvic urine Po₂ for different input conditions. We conclude that it may technically be possible to predict renal medullary Po₂ based on the measurement of bladder urine Po₂, provided that there are accurate real-time measurements of model input parameters.NEW & NOTEWORTHY Measurement of bladder urine oxygen tension has been proposed as a new method to potentially detect the risk of acute kidney injury in patients. A computational model of oxygen exchange between urine bolus and ureteral tissue shows that it may be technically possible to determine the risk of acute kidney injury based on the measurement of bladder urine oxygen tension, provided that the measurement data are properly interpreted via a computational model.

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.

Effects of impaired microvascular flow regulation on metabolism-perfusion matching and organ function

Impaired tissue oxygen delivery is a major cause of organ damage and failure in critically ill patients, which can occur even when systemic parameters, including cardiac output and arterial hemoglobin saturation, are close to normal. This review addresses oxygen transport mechanisms at the microcirculatory scale, and how hypoxia may occur in spite of adequate convective oxygen supply. The structure of the microcirculation is intrinsically heterogeneous, with wide variations in vessel diameters and flow pathway lengths, and consequently also in blood flow rates and oxygen levels. The dynamic processes of structural adaptation and flow regulation continually adjust microvessel diameters to compensate for heterogeneity, redistributing flow according to metabolic needs to ensure adequate tissue oxygenation. A key role in flow regulation is played by conducted responses, which are generated and propagated by endothelial cells and signal upstream arterioles to dilate in response to local hypoxia. Several pathophysiological conditions can impair local flow regulation, causing hypoxia and tissue damage leading to organ failure. Therapeutic measures targeted to systemic parameters may not address or may even worsen tissue oxygenation at the microvascular level. Restoration of tissue oxygenation in critically ill patients may depend on restoration of endothelial cell function, including conducted responses.

Renal microvascular oxygen tension during hyperoxia and acute hemodilution assessed by phosphorescence quenching and excitation with blue and red light

PURPOSE

The kidney plays a central physiologic role as an oxygen sensor. Nevertheless, the direct mechanism by which this occurs is incompletely understood. We measured renal microvascular partial pressure of oxygen (P_kO₂) to determine the impact of clinically relevant conditions that acutely change P_kO₂ including hyperoxia and hemodilution.

METHODS

We utilized two-wavelength excitation (red and blue spectrum) of the intravascular phosphorescent oxygen sensitive probe Oxyphor PdG4 to measure renal tissue PO₂ in anesthetized rats (2% isoflurane, n = 6) under two conditions of altered arterial blood oxygen content (C_aO₂): 1) hyperoxia (fractional inspired oxygen 21%, 30%, and 50%) and 2) acute hemodilutional anemia (baseline, 25% and 50% acute hemodilution). The mean arterial blood pressure (MAP), rectal temperature, arterial blood gases (ABGs), and chemistry (radiometer) were measured under each condition. Blue and red light enabled measurement of P_kO₂ in the superficial renal cortex and deeper cortical and medullary tissue, respectively.

RESULTS

P_kO₂ was higher in the superficial renal cortex (~ 60 mmHg, blue light) relative to the deeper renal cortex and outer medulla (~ 45 mmHg, red light). Hyperoxia resulted in a proportional increase in P_kO₂ values while hemodilution decreased microvascular P_kO₂ in a linear manner in both superficial and deeper regions of the kidney. In both cases (blue and red light), P_kO₂ correlated with C_aO₂ but not with MAP.

CONCLUSION

The observed linear relationship between C_aO₂ and P_kO₂ shows the biological function of the kidney as a quantitative sensor of anemic hypoxia and hyperoxia. A better understanding of the impact of changes in P_kO₂ may inform clinical practices to improve renal oxygen delivery and prevent acute kidney injury.

Oxygenation of the Transplanted Kidney

Although kidney oxygen tensions are heterogenous, and mostly below renal vein level, the nephron is highly dependent on aerobic metabolism for active tubular transport. This renders the kidney particularly susceptible to hypoxia, which is considered a main characteristic and driver of acute and chronic kidney injury, albeit the evidence supporting this assumption is not entirely conclusive. Kidney transplants are exposed to several conditions that may interfere with the balance between oxygen supply and consumption, and enhance hypoxia and hypoxic injury. These include conditions leading to and resulting from brain death of kidney donors, ischemia and reperfusion during organ donation, storage and transplantation, postoperative vascular complications, vasoconstriction induced by immunosuppression, and impaired perfusion resulting from interstitial edema, inflammation, and fibrosis. Acute graft injury, the immediate consequence of hypoxia and reperfusion, results in delayed graft function and increased risk of chronic graft failure. Although current strategies to alleviate hypoxic/ischemic graft injury focus on limiting injury (eg, by reducing cold and warm ischemia times), experimental evidence suggests that preconditioning through local or remote ischemia, or activation of the hypoxia-inducible factor pathway, can decrease hypoxic injury. In combination with ex vivo machine perfusion such approaches hold significant promise for improving transplantation outcomes.

A cardiovascular model for renal perfusion during cardiopulmonary bypass surgery

Acute kidney injury (AKI) is a major complication following cardiac surgery requiring cardiopulmonary bypass (CPB). It is likely that poor renal perfusion contributes to the occurrence of AKI, via renal hypoxia, so it is imperative to maintain optimal renal perfusion during CPB. We have developed a straightforward cardiovascular perfusion model with parameter values calibrated against experimental and/or clinical data from several independent studies of CPB in humans and animals. Following model development and calibration, we performed a one-at-a-time parametric study to investigate the response of renal perfusion to several variables during CPB, namely pump flow (denoted CO for 'cardiac output'), renal vascular resistance, and non-renal vascular resistance. From the parametric study, we have found that all three parameters had a similarly strong influence on renal perfusion. We simulated three potential strategies for maintaining optimum renal perfusion during CPB and tested their effectiveness. The strategies were: (1) increasing the pump flow; (2) administrating noradrenaline (vasopressor); and (3) administrating fenoldopam (renal vasodilator). Simulations have revealed that administration of fenoldopam is likely to be the most effective of the three strategies. Other findings from our simulations are that increasing pump flow is less effective when central venous pressure is elevated. Further, renal autoregulation is likely inoperative during CPB, as evidenced by an unchanging renal vascular resistance with increasing CO and blood pressure. The cardiac-renal perfusion model developed in this study can be linked with other kidney models to simulate the changes in renal oxygenation during CPB.

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.

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.

Analysis of the critical determinants of renal medullary oxygenation

We have previously developed a three-dimensional computational model of oxygen transport in the renal medulla. In the present study, we used this model to quantify the sensitivity of renal medullary oxygenation to four of its major known determinants: medullary blood flow (MBF), medullary oxygen consumption rate (V̇o2,M), hemoglobin (Hb) concentration in the blood, and renal perfusion pressure. We also examined medullary oxygenation under special conditions of hydropenia, extracellular fluid volume expansion by infusion of isotonic saline, and hemodilution during cardiopulmonary bypass. Under baseline (normal) conditions, the average medullary tissue Po2 predicted for the whole renal medulla was ~30 mmHg. The periphery of the interbundle region in the outer medulla was identified as the most hypoxic region in the renal medulla, which demonstrates that the model prediction is qualitatively accurate. Medullary oxygenation was most sensitive to changes in renal perfusion pressure followed by Hb, MBF, and V̇o2,M, in that order. The medullary oxygenation also became sensitized by prohypoxic changes in other parameters, leading to a greater fall in medullary tissue Po2 when multiple parameters changed simultaneously. Hydropenia did not induce a significant change in medullary oxygenation compared with the baseline state, while volume expansion resulted in a large increase in inner medulla tissue Po2 (by ~15 mmHg). Under conditions of cardiopulmonary bypass, the renal medulla became severely hypoxic, due to hemodilution, with one-third of the outer stripe of outer medulla tissue having a Po2 of <5 mmHg.

A model of oxygen transport in the rat renal medulla

The renal medulla is prone to hypoxia. Medullary hypoxia is postulated to be a leading cause of acute kidney injury, so there is considerable interest in predicting the oxygen tension in the medulla. Therefore we have developed a computational model for blood and oxygen transport within a physiologically normal rat renal medulla, using a multilevel modeling approach. For the top-level model we use the theory of porous media and advection-dispersion transport through a realistic three-dimensional representation of the medulla’s gross anatomy to describe blood flow and oxygen transport throughout the renal medulla. For the lower-level models, we employ two-dimensional reaction-diffusion models describing the distribution of oxygen through tissue surrounding the vasculature. Steady-state model predictions at the two levels are satisfied simultaneously, through iteration between the levels. The computational model was validated by simulating eight sets of experimental data regarding renal oxygenation in rats (using 4 sets of control groups and 4 sets of treatment groups, described in 4 independent publications). Predicted medullary tissue oxygen tension or microvascular oxygen tension for control groups and for treatment groups that underwent moderate perturbation in hemodynamic and renal functions is within ±2 SE values observed experimentally. Diffusive shunting between descending and ascending vasa recta is predicted to be only 3% of the oxygen delivered. The validation tests confirm that the computational model is robust and capable of capturing the behavior of renal medullary oxygenation in both normal and early-stage pathological states in the rat.

Heterogeneity of renal cortical oxygenation: seeing is believing

The limited spatial and temporal resolution of available methods for quantifying renal tissue oxygen tension is a major impediment to identification of the roles of renal hypoxia in kidney diseases. Intravital phosphorescence lifetime imaging microscopy allows cellular oxygen tension in the renal cortex of live animals to be resolved to the level of individual tubular cross-sections. This paves the way for future investigations of the spatial relationships between cellular hypoxia and pathophysiological events in kidney disease.

Three-dimensional morphometric analysis of the renal vasculature

Vascular topology and morphology are critical in the regulation of blood flow and the transport of small solutes, including oxygen, carbon dioxide, nitric oxide, and hydrogen sulfide. Renal vascular morphology is particularly challenging, since many arterial walls are partially wrapped by the walls of veins. In the absence of a precise characterization of three-dimensional branching vascular geometry, accurate computational modeling of the intrarenal transport of small diffusible molecules is impossible. An enormous manual effort was required to achieve a relatively precise characterization of rat renal vascular geometry, highlighting the need for an automated method for analysis of branched vasculature morphology to allow characterization of the renal vascular geometry of other species, including humans. We present a semisupervised method for three-dimensional morphometric analysis of renal vasculature images generated by computed tomography. We derive quantitative vascular attributes important to mass transport between arteries, veins, and the renal tissue and present methods for their computation for a three-dimensional vascular geometry. To validate the algorithm, we compare automated vascular estimates with subjective manual measurements for a portion of rabbit kidney. Although increased image resolution can improve outcomes, our results demonstrate that the method can quantify the morphological characteristics of artery-vein pairs, comparing favorably with manual measurements. Similar to the rat, we show that rabbit artery-vein pairs become less intimate along the course of the renal vasculature, but the total wrapped mass transfer coefficient increases and then decreases. This new method will facilitate new quantitative physiological models describing the transport of small molecules within the kidney.

Renal haemodynamics and oxygenation during and after cardiac surgery and cardiopulmonary bypass

Acute kidney injury (AKI) is a common complication following cardiac surgery performed on cardiopulmonary bypass (CPB) and has important implications for prognosis. The aetiology of cardiac surgery-associated AKI is complex, but renal hypoxia, particularly in the medulla, is thought to play at least some role. There is strong evidence from studies in experimental animals, clinical observations and computational models that medullary ischaemia and hypoxia occur during CPB. There are no validated methods to monitor or improve renal oxygenation during CPB, and thus possibly decrease the risk of AKI. Attempts to reduce the incidence of AKI by early transfusion to ameliorate intra-operative anaemia, refinement of protocols for cooling and rewarming on bypass, optimization of pump flow and arterial pressure, or the use of pulsatile flow, have not been successful to date. This may in part reflect the complexity of renal oxygenation, which may limit the effectiveness of individual interventions. We propose a multi-disciplinary pathway for translation comprising three components. Firstly, large-animal models of CPB to continuously monitor both whole kidney and regional kidney perfusion and oxygenation. Secondly, computational models to obtain information that can be used to interpret the data and develop rational interventions. Thirdly, clinically feasible non-invasive methods to continuously monitor renal oxygenation in the operating theatre and to identify patients at risk of AKI. In this review, we outline the recent progress on each of these fronts.

Micro-computed tomographic analysis of the radial geometry of intrarenal artery-vein pairs in rats and rabbits: Comparison with light microscopy

We assessed the utility of synchrotron-radiation micro-computed tomography (micro-CT) for quantification of the radial geometry of the renal cortical vasculature. The kidneys of nine rats and six rabbits were perfusion fixed and the renal circulation filled with Microfil. In order to assess shrinkage of Microfil, rat kidneys were imaged at the Australian Synchrotron immediately upon tissue preparation and then post fixed in paraformaldehyde and reimaged 24 hours later. The Microfil shrank only 2-5% over the 24 hour period. All subsequent micro-CT imaging was completed within 24 hours of sample preparation. After micro-CT imaging, the kidneys were processed for histological analysis. In both rat and rabbit kidneys, vascular structures identified in histological sections could be identified in two-dimensional (2D) micro-CT images from the original kidney. Vascular morphology was similar in the two sets of images. Radial geometry quantified by manual analysis of 2D images from micro-CT was consistent with corresponding data generated by light microscopy. However, due to limited spatial resolution when imaging a whole organ using contrast-enhanced micro-CT, only arteries ≥100 and ≥60 μm in diameter, for the rat and rabbit respectively, could be assessed. We conclude that it is feasible and valid to use micro-CT to quantify vascular geometry of the renal cortical circulation in both the rat and rabbit. However, a combination of light microscopic and micro-CT approaches are required to evaluate the spatial relationships between intrarenal arteries and veins over an extensive range of vessel size.

Accounting for oxygen in the renal cortex: a computational study of factors that predispose the cortex to hypoxia

We develop a pseudo-three-dimensional model of oxygen transport for the renal cortex of the rat, incorporating both the axial and radial geometry of the preglomerular circulation and quantitative information regarding the surface areas and transport from the vasculature and renal corpuscles. The computational model was validated by simulating four sets of published experimental studies of renal oxygenation in rats. Under the control conditions, the predicted cortical tissue oxygen tension ([Formula: see text]) or microvascular oxygen tension (µPo2) were within ±1 SE of the mean value observed experimentally. The predicted [Formula: see text] or µPo2 in response to ischemia-reperfusion injury, acute hemodilution, blockade of nitric oxide synthase, or uncoupling mitochondrial respiration, were within ±2 SE observed experimentally. We performed a sensitivity analysis of the key model parameters to assess their individual or combined impact on the predicted [Formula: see text] and µPo2. The model parameters analyzed were as follows: 1) the major determinants of renal oxygen delivery ([Formula: see text]) (arterial blood Po2, hemoglobin concentration, and renal blood flow); 2) the major determinants of renal oxygen consumption (V̇o2) [glomerular filtration rate (GFR) and the efficiency of oxygen utilization for sodium reabsorption (β)]; and 3) peritubular capillary surface area (PCSA). Reductions in PCSA by 50% were found to profoundly increase the sensitivity of [Formula: see text] and µPo2 to the major the determinants of [Formula: see text] and V̇o2. The increasing likelihood of hypoxia with decreasing PCSA provides a potential explanation for the increased risk of acute kidney injury in some experimental animals and for patients with chronic kidney disease.