In this study, we develop a computational model to simulate the in vitro biochemical degradation of articular cartilage explants sourced from the femoropatellar grooves of bovine calves. Cartilage explants were incubated in culture medium with and without the inflammatory cytokine IL-1α. The spatio-temporal evolution of the cartilage explant's extracellular matrix components is modelled. Key variables in the model include chondrocytes, aggrecan, collagen, aggrecanase, collagenase and IL-1α. The model is first calibrated for aggrecan homeostasis of cartilage in vivo, then for data on (explant) controls, and finally for data on the IL-1α driven proteolysis of aggrecan and collagen over a 4-week period. The model was found to fit the experimental data best when: (i) chondrocytes continue to synthesize aggrecan during the cytokine challenge, (ii) a one to two day delay is introduced between the addition of IL-1α to the culture medium and subsequent aggrecanolysis, (iii) collagen degradation does not commence until the total concentration of aggrecan (i.e. both intact and degraded aggrecan) at any specific location within the explant becomes ≤ 1.5 mg/ml and (iv) degraded aggrecan formed due to the IL-1α induced proteolysis of intact aggrecan protects the collagen network while collagen degrades in a two-step process which, together, significantly modulate the collagen network degradation. Under simulated in vivo conditions, the model predicts increased aggrecan turnover rates in the presence of synovial IL-1α, consistent with experimental observations. Such models may help to infer the course of events in vivo following traumatic joint injury, and may also prove useful in quantitatively evaluating the efficiency of various therapeutic molecules that could be employed to avoid or modify the course of cartilage disease states.

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 (µPo) were within ±1 SE of the mean value observed experimentally. The predicted [Formula: see text] or µPo 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 µPo The model parameters analyzed were as follows: ) the major determinants of renal oxygen delivery ([Formula: see text]) (arterial blood Po, hemoglobin concentration, and renal blood flow); ) the major determinants of renal oxygen consumption (V̇o) [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 µPo to the major the determinants of [Formula: see text] and V̇o 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.

No abstract

Renal arterial-to-venous (AV) oxygen shunting limits oxygen delivery to renal tissue. To better understand how oxygen in arterial blood can bypass renal tissue, we quantified the radial geometry of AV pairs and how it differs according to arterial diameter and anatomic location. We then estimated diffusion of oxygen in the vicinity of arteries of typical geometry using a computational model. The kidneys of six rats were perfusion fixed, and the vasculature was filled with silicone rubber (Microfil). A single section was chosen from each kidney, and all arteries (n = 1,628) were identified. Intrarenal arteries were largely divisible into two "types," characterized by the presence or absence of a close physical relationship with a paired vein. Arteries with a close physical relationship with a paired vein were more likely to have a larger rather than smaller diameter, and more likely to be in the inner-cortex than the mid- or outer cortex. Computational simulations indicated that direct diffusion of oxygen from an artery to a paired vein can only occur when the two vessels have a close physical relationship. However, even in the absence of this close relationship oxygen can diffuse from an artery to periarteriolar capillaries and venules. Thus AV oxygen shunting in the proximal preglomerular circulation is dominated by direct diffusion of oxygen to a paired vein. In the distal preglomerular circulation, it may be sustained by diffusion of oxygen from arteries to capillaries and venules close to the artery wall, which is subsequently transported to renal veins by convection.

To assess the physiological significance of arterial-to-venous (AV) oxygen shunting, we generated a new pseudo-three-dimensional computational model of oxygen diffusion from intrarenal arteries to cortical tissue and veins. The model combines the 11 branching levels (known as "Strahler" orders) of the preglomerular renal vasculature in the rat, with an analysis of an extensive data set obtained using light microscopy to estimate oxygen mass transfer coefficients for each Strahler order. Furthermore, the AV shunting model is now set within a global oxygen transport model that includes transport from arteries, glomeruli, peritubular capillaries, and veins to tissue. While a number of lines of evidence suggest AV shunting is significant, most importantly, our AV oxygen shunting model predicts AV shunting is small under normal physiological conditions (~0.9% of total renal oxygen delivery; range 0.4-1.4%), but increases during renal ischemia, glomerular hyperfiltration (~2.1% of total renal oxygen delivery; range 0.84-3.36%), and some cardiovascular disease states (~3.0% of total renal oxygen delivery; range 1.2-4.8%). Under normal physiological conditions, blood Po is predicted to fall by ~16 mmHg from the root of the renal artery to glomerular entry, with AV oxygen shunting contributing ~40% and oxygen diffusion from arteries to tissue contributing ~60% of this decline. Arterial Po is predicted to fall most rapidly from Strahler , under normal physiological conditions. We conclude that AV oxygen shunting normally has only a small impact on renal oxygenation, but may exacerbate renal hypoxia during renal ischemia, hyperfiltration, and some cardiovascular disease states.