Kidney Models of Calcium Oxalate Stone Formation

Abstract

This review compares and contrasts three mathematical models used to describe the flow of urine through the renal tubule and the composition of tubular fluid throughout the length of the nephron. From these data the relative supersaturation of tubular fluid with respect to calcium oxalate (CaOx) is calculated at various points along the tubule. This shows that glomerular filtrate is well undersaturated with respect to CaOx and is still undersaturated at the end of the proximal tubule. By the end of the descending limb of the loop of Henle, it is highly supersaturated as a result of water reabsorption and CaOx may nucleate in this region, particularly when the tubular concentration of oxalate is increased. Supersaturation falls slightly by the end of the ascending limb and becomes briefly undersaturated again in the short distal tubule. The final water adjustment in the collecting tubules causes the supersaturation to rise to a very high value by the end of the collecting duct and spontaneous CaOx crystalluria is likely to occur. The review also examines the probability of these crystals growing large enough to be trapped at some point in the nephron within the transit time of tubular fluid from glomerular capsule to ducts of Bellini. All three models agree that, under normal conditions, the likelihood of individual crystals growing large enough to be trapped within the measured urine transit time of 3–4 min is very small. It is concluded that either there has to be aggregation of crystals or some other factor that delays the passage of crystals for them to grow large enough to become lodged at some point in the nephron. Three new hydrodynamic factors are introduced that may lead to delay of crystal passage: (a) fluid drag close to the tubule walls; (b) the drag effect of tubular walls on particles travelling close to the tubule walls, and (c) the effect of gravity on particles travelling in upward-draining sections of tubule. When these factors are introduced into the mathematical model of urine flow and tubular concentration, it is shown that any crystals that form at the end of the descending limb of the loop of Henle and which travel close to the tubular walls may be delayed long enough to grow large enough to become trapped further down the nephron, particularly in upward-draining sections of the nephron. This possibility becomes increasingly significant as urinary oxalate concentration increases. Crystals that nucleate in the late collecting duct, however, are readily passed as small crystals and are at no risk of being trapped in the tubular system. These predictions are used to explain data on the effects of oxalate loading on CaOx crystalluria in stone formers and normal controls. The data are interpreted as showing that if the additional hydrodynamic factors are added to the mathematical model of nephron function, then the ‘free-particle’ model of calcium stone formation is still possible. This possibility will be further enhanced if crystal aggregation also takes place during the period when crystal passage is delayed by these factors.