A computational model for emergent dynamics in the kidney

In this paper, concepts from network automata are adapted and extended to model complex biological systems. Specifically, systems of nephrons , the operational units of the kidney, are modelled and the dynamics of such systems are explored. Nephron behaviour can fluctuate widely and, under certain conditions, become chaotic. However, the behaviour of the whole kidney remains remarkably stable and blood solute levels are maintained under a wide range of conditions even when many nephrons are damaged or lost. A network model is used to investigate the stability of systems of nephrons and interactions between nephrons. More sophisticated dynamics are explored including the observed oscillations in single nephron filtration rates and the development of stable ionic and osmotic gradients in the inner medulla which contribute to the countercurrent exchange mechanism. We have used the model to explore the effects of changes in input parameters including hydrostatic and osmotic pressures and concentrations of ions, such as sodium and chloride. The intrinsic nephron control, tubuloglomerular feedback, is included and the effects of coupling between nephrons are explored in two-, eight- and 72-nephron models.

Single-nephron filtration rate and proximal reabsorption in aging rats

Age-related changes in the function of individual nephrons were investigated by micropuncture experiments measuring single-nephron filtration rates (SNGFR) and proximal reabsorptions in 10-, 20-, and 30-mo-old rats. The animals were female WAG/Rij rats with low incidence of chronic progressive nephropathy, no loss of nephrons, and renal hypertrophy of both kidneys in the oldest animals. Mean SNGFR values per gram kidney weight were 41.4 +/- 1.1, 37.1 +/- 1.5, and 32.2 +/- 1.1 nl.min-1.g kidney wt-1 (n = 41) in the 10-, 20-, and 30-mo-old animals, respectively. This age-related decrease in filtration was no longer apparent when SNGFR values were expressed per nephron (means 24.3 +/- 0.7, 23.7 +/- 0.9, and 24.4 +/- 0.9 nl/min. Individual filtered loads of sodium, potassium, calcium, and magnesium and their absolute reabsorption by the proximal tubule were not different in the three age groups; however, absolute and fractional reabsorptions of phosphate decreased significantly in the 30-mo-old rats. These results indicate that, with the exception of phosphate, individual filtrations and proximal reabsorptions are well maintained in aging rats free of disease. This may be related to the observed renal hypertrophy.

Evaluation of methods of measuring glomerular and nutrient blood flow in rat kidneys

In normal rats, glomerular plasma flow rates (GPF) were estimated from the uptake of microspheres, and single-nephron filtration rates were estimated by Hanssen's technique in order to calculate single-nephron filtration fractions (SNFF) for outer (C1), middle, (C2), and deep (C3) nephrons. With large microspheres (15 micron), SNFF averaged 0.19, 0.41, and 0.63, and with small microspheres (9 micron), SNFF averaged 0.25, 0.48, and 0.42 for areas C1, C2, and C3, respectively. Kidney filtration fractions (FF) averaged 0.36. Because microsphere experiments in normal rats have generally suggested that SNFF-C1 and FF are similar, we conclude that both types of microspheres overestimated outer cortical plasma flow rates, and probably underestimated inner cortical plasma flow rates. In addition, not all of the smaller microspheres were trapped in the glomeruli. Nutrient blood flow rates were estimated from the uptake of 86Rb. Values ranged from 7.3 ml/g per min in the outer cortex to 4.7 ml/g per min in the inner cortex. Because these values are very similar to measurements made by several other techniques, we conclude that 86Rb uptake adequately estimates cortical blood flow. Medullary blood flow estimates, however, increased with time and were probably too high.