A mathematical model of O2 transport in the rat outer medulla. II. Impact of outer medullary architecture

Chen J, Edwards A, Layton AT. A mathematical model of O-2 transport in the rat outer medulla. II. Impact of outer medullary architecture. Am J Physiol Renal Physiol 297: F537-F548, 2009. First published April 29, 2009; doi:10.1152/ajprenal.90497.2008.-In the companion study (Am J Physiol Renal Physiol. First published April 29, 2009; doi: 10.1152/ajprenal.90496.2008), we extended the region-based mathematical model of the urine-concentrating mechanism in the rat outer medulla (OM) developed by Layton and Layton (Am J Physiol Renal Physiol 289: F1346-F1366, 2005) to examine the impact of the complex structural organization of the OM on O-2 transport and distribution. In the present study, we investigated the sensitivity of predicted PO2 profiles to several parameters that characterize the degree of OM regionalization, boundary conditions, structural dimensions, transmural transport properties, and relative positions and distributions of tubules and vessels. Our results suggest that the fraction of O-2 supplied to descending vasa recta (DVR) that reaches the inner medulla, i.e., a measure of the axial PO2 gradient in the OM, is insensitive to parameter variations as a result of the sequestration of long DVR in the vascular bundles. In contrast, O-2 distribution among the regions surrounding the vascular core strongly depends on the radial positions of medullary thick ascending limbs (mTALs) relative to the vascular core, the degree of regionalization, and the distribution of short DVR along the corticomedullary axis. Moreover, if it is assumed that the mTAL active Na+ transport rate decreases when mTAL PO2 falls below a critical level, O-2 availability to mTALs has a significant impact on the concentrating capability of the model OM. The model also predicts that when the OM undergoes hypertrophy, its concentrating capability increases significantly only when anaerobic metabolism supports a substantial fraction of the mTAL active Na+ transport and is otherwise critically reduced by low interstitial and mTAL luminal PO2 in a hypertrophied OM.