This proposal is for the continuation of research projects that use mathematical modeling to gain a more complete understanding of two regulatory mechanisms found in the kidney: the tubuloglomerular feedback (TGF) mechanism and the urine concentrating mechanism. Mathematical models of renal tubules and microvessels, coupled with explicit analysis and methods for solving differential equations, will be used to investigate the following hypotheses: (I) vascular coupling between nephrons increases the propensity for oscillatory dynamics and serves as a regulatory mechanism for increasing NaCI delivery to the distal nephron; (II) irregular TGF-mediated oscillations found in the nephrons of hypertensive rats emerge from multiple oscillatory modes; from lability, in key parameters, that episodically and significantly impacts otherwise regular oscillations; and from coupling between nephrons soaffected; (III) the urine concentrating mechanism of the renal inner medulla arises from passive solute mixing in the interstitium; this mechanism is made effective by specialized axial segmentation in descending limbs of loops of Henle, by a loop of Henle cascade, and by specific three-dimensional relationships among tubules and vessels. Significance. This proposal aims to provide a more complete and quantitative understanding of the means by which blood flow is controlled and regulated within the kidney and of the means by which the kidney can produce urine that is more concentrated than blood plasma (i.e., that contains more solute per unit volume than does blood plasma). This basic research is relevant to public health, because disordered blood flow control by the kidney, and abnormalities of the kidney's urine concentrating capability, are known to cause, contribute to, be a consequence of, or occur along with, a number of important disorders and diseases, including abnormal body water and salt retention or loss, high blood pressure, diabetes, and injury to the kidney.