MATHEMATICAL MODELS OF RENAL DYNAMICS

Duke University, Durham NC

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Abstract

DESCRIPTION (Adapted from the Applicant's Abstract): This proposal is for the continuation of research projects that use the technique of mathematical modeling to gain a more complete understanding of 2 regulatory mechanisms found in the kidney: the tubuloglomerular feedback (TGF) mechanism and the urine concentrating mechanism. Mathematical models of renal tubules and micro-vessels will be used to investigate the following hypotheses: (I) regular, sustained TGF-mediated oscillations in tubular flow differentially regulate sodium and water delivery to the distal tubule and enhance sodium excretion; and the emergence of TGF-mediated oscillations is mediated and regulated through its integration with other intrarenal control mechanisms, notably the renin-angiotensin-aldosterone system; (II) under appropriate conditions, irregular TGF-mediated oscillations emerge from excitation of multiple oscillatory modes and tend to enhance sodium and water delivery to the distal tubule and sodium excretion; and (III) tubular heterogeneity in renal tubules (notably, the large fraction of thin limbs of loops of Henle that exhibit alternating subsegments of differing morphological and functional type) have an important functional role in the urine concentrating mechanism of the renal inner medulla. The principal mathematical methods that will be employed in these studies are explicit analysis and numerical methods for solving differential equations. The TGF system, which includes functional aspects of the afferent arteriole and the juxtaglomerular apparatus, is a critical regulatory mechanism for renal blood flow and nephron load. A more complete understanding of this system would enrich our understanding of blood pressure control and renal electrolyte management which are deranged in several important renal diseases, including hypertension and diabetes. The nature of the inner medullary urine concentrating mechanism remains an unsolved mystery of normal renal function. Many disorders of whole-body water balance result from inappropriate or deranged regulation of the urine concentrating mechanism.