Robertson W G
University College London, Institute of Urology and Nephrology, London, UK.
Nephron Physiol. 2004;98(2):p21-30. doi: 10.1159/000080260.
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.
本综述比较并对比了三种用于描述尿液流经肾小管以及整个肾单位长度内小管液成分的数学模型。根据这些数据，计算了小管液相对于草酸钙（CaOx）在小管不同位置的相对过饱和度。结果表明，肾小球滤过液相对于CaOx的饱和度很低，在近端小管末端仍处于不饱和状态。到髓袢降支末端时，由于水的重吸收，其过饱和度很高，CaOx可能在此区域成核，尤其是当小管中草酸盐浓度升高时。到髓袢升支末端时，过饱和度略有下降，在短的远端小管中又会短暂地变为不饱和。集合小管的最终水调节作用会使过饱和度在集合管末端升至非常高的值，很可能会发生自发性草酸钙结晶尿。该综述还研究了在小管液从肾小球囊到乳头管的转运时间内，这些晶体生长得足够大并在肾单位的某个位置被滞留的可能性。所有三种模型都认为，在正常情况下，单个晶体生长得足够大并在测量的3 - 4分钟尿液转运时间内被滞留的可能性非常小。得出的结论是，要么存在晶体聚集，要么存在其他一些因素延迟晶体的通过，使其生长得足够大从而在肾单位的某个位置滞留。引入了三个新的流体动力学因素，它们可能导致晶体通过延迟：（a）靠近管壁的流体阻力；（b）管壁对靠近管壁移动颗粒的阻力作用；（c）重力对在小管向上引流段移动颗粒产生的影响。当将这些因素引入尿液流动和小管浓度的数学模型时，结果表明，在髓袢降支末端形成且靠近管壁移动的任何晶体可能会被延迟足够长的时间，从而生长得足够大，进而在肾单位更下游的位置被滞留，尤其是在肾单位的向上引流段。随着尿草酸盐浓度的增加，这种可能性变得越来越显著。然而，在集合管后期成核的晶体很容易以小晶体的形式通过，不会有被困在肾小管系统中的风险。这些预测被用于解释关于草酸盐负荷对结石形成者和正常对照者草酸钙结晶尿影响的数据。这些数据被解释为表明，如果将额外的流体动力学因素添加到肾单位功能的数学模型中，那么钙结石形成的“自由颗粒”模型仍然是可能存在的。如果在这些因素延迟晶体通过的期间也发生晶体聚集，这种可能性将进一步增加。
