Background and Purpose: Renal hypoxia is postulated to be a leading cause of acute kidney injury, and the renal medulla is known to be most susceptible to hypoxia. The ability to accurately predict normal and abnormal oxygen states in terms of tissue oxygen tension (PO2) within the renal medulla is highly desirable, as among other uses predicted medullary PO2 can be correlated with local tissue damage. In this study, we have developed a computational model for blood and oxygen transport within the renal medulla to estimate medullary tissue PO2.
Materials and Methods: A multiscale modelling approach was used to model the blood flow and oxygen transport within a realistic 3-D medullary geometry. At the macroscale level, the blood flow in the medullary vasa recta was modelled using a set of three, coupled, 3D porous media models, each representing the blood flow in the descending vasa recta, long ascending vasa recta, and short ascending vasa recta. Another set of three advection-diffusion models, each coupled with a blood flow model, were employed to simultaneously represent the oxygen transport throughout the whole medulla. In addition to the six top-level models, four diffusive oxygen transport models were employed at the microscale level to describe the distribution of oxygen in two spatial dimensions across the renal tissue surrounding the vasculature. Each low-level model represents a single vascular bundle and associated tissue. The low-level models were located in the outer and inner stripes, near the base and near the tip of the inner medulla. The model predictions, based on reported geometry, model parameters, boundary conditions and source-sink terms obtained from the literature on the rat kidney were found by iterating between the macroscale and microscale sub-models until all ten sub-models were satisfied simultaneously.
Results & Discussion: The model predictions were validated by simulating eight sets of published experimental data in rats (four sets of control groups and four sets of treatment groups, reported in four independent papers). These experiments examined the effects of acute hemodilution, acute renal ischemia/reperfusion (IR), and chronic administration (30 days) of dinitrophenol (DNP). For each validation test, model parameters were altered according to experimental observations. Tissue and/or microvascular PO2 predicted by the model was then compared with that observed experimentally.
All model predictions for control groups were within ± 1 standard error of the mean (SEM) value observed experimentally. Most of the model predictions for treatment groups were also within ± 1 SEM, except for later stages in the acute hemodilution experiment, where the model predicted PO2 exceeded the measured PO2 by more than 7 SEM. Deviations from the model predictions are probably due to unidentified external or intra-renal processes, triggered by pathologic processes, but not accounted for in the model or measured in the experiments.
Conclusion: The validation tests confirmed that the proposed renal medullary PO2 model is robust and can accurately capture the behaviour of renal medullary oxygenation in both normal and early pathologic states in the rat.