A Mathematical Model of the Rat Kidney: Ammonia Transport

Abstract

Ammonia generated within the kidney is partitioned into a urinary fraction (the key buffer for net acid excretion), and an aliquot delivered to the systemic circulation. The physiology of this partitioning has yet to be examined in a kidney model, and that is undertaken in this work. This involves explicit representation of the cortical labyrinth, so that cortical interstitial solute concentrations are computed, rather than assigned. A detailed representation of cortical vasculature has been avoided by making the assumption that solute concentrations within interstitium and peritubular capillaries are likely to be identical, and that there is little to no modification of venous composition as blood flows to the renal vein. The model medullary ray has also been revised to include a segment of proximal straight tubule, which supplies ammonia to this region. The principal finding of this work is that cortical labyrinth interstitial ammonia concentration is likely to be several-fold higher than systemic arterial ammonia. This elevation of interstitial ammonia enhances ammonia secretion in both PCT and DCT, with uptake by Na,K-ATPases of both segments. Model prediction of urinary ammonia excretion is concordant with measured values, but at the expense of greater ammoniagenesis, with high rates of renal venous ammonia flux. This derives from a limited capability of the model medulla to replicate the high interstitial ammonia concentrations that are required to drive collecting duct ammonia secretion. Thus, renal medullary ammonia trapping appears key to diverting ammonia from renal vein to urine, but capturing the underlying physiology remains a challenge.