This proposal is for mathematical modeling of three features of renal function: (1) the dynamics of tubuloglomerular feedback; (2) the dynamics of the renal papilla; and (3) the structural and functional heterogeneity of the renal medulla. This research will elucidate (1) the origin, character, and long-time behavior of oscillations in pressure, fluid flow, and solute concentrations in the in the tubules of nephrons; (2) the role of papillary peristalsis in intratubular fluid connection, in transtubular water and solute transport, and in the generation and maintenance of the inner medullary concentration gradient; and (3) the importance of distributed loops of Henle, of variation in single nephron glomerular filtration rates as a generation of the medullary concentration gradient. The principal mathematical methods that will be employed in each of the three projects are (1) flux-corrected transport for the solution of systems of hyperbolic partial differential equations; (2) the technique of Charles S. Peskin and David M. McQueen for the solution of the Navier-Stokes equations in a region containing an immersed boundary; and (3) fixed-point iteration and continuation of parameters for the solution of systems of integro-differential equations. The models will be developed in consultation/collaboration with numerical analysts and physiologists. Every effort will be made to ensure the mathematical integrity and physiological applicability of the results. Because many issues in renal physiology remain unresolved and because much new experimental data needing interpretation is being generated, the integrative work proposed here may contribute significantly to the understanding of normal renal function. Such understanding is essential, over the long term, for progress in the analysis and treatment of kidney disease.
| Dantzler, William H; Layton, Anita T; Layton, Harold E et al. (2014) Urine-concentrating mechanism in the inner medulla: function of the thin limbs of the loops of Henle. Clin J Am Soc Nephrol 9:1781-9 |
| Nieves-Gonzalez, Aniel; Clausen, Chris; Layton, Anita T et al. (2013) Transport efficiency and workload distribution in a mathematical model of the thick ascending limb. Am J Physiol Renal Physiol 304:F653-64 |
| Nieves-Gonzalez, Aniel; Clausen, Chris; Marcano, Mariano et al. (2013) Fluid dilution and efficiency of Na(+) transport in a mathematical model of a thick ascending limb cell. Am J Physiol Renal Physiol 304:F634-52 |
| Layton, Anita T; Moore, Leon C; Layton, Harold E (2012) Signal transduction in a compliant thick ascending limb. Am J Physiol Renal Physiol 302:F1188-202 |
| Dantzler, W H; Pannabecker, T L; Layton, A T et al. (2011) Urine concentrating mechanism in the inner medulla of the mammalian kidney: role of three-dimensional architecture. Acta Physiol (Oxf) 202:361-78 |
| Chen, Jing; Sgouralis, Ioannis; Moore, Leon C et al. (2011) A mathematical model of the myogenic response to systolic pressure in the afferent arteriole. Am J Physiol Renal Physiol 300:F669-81 |
| Layton, Anita T; Bowen, Matthew; Wen, Amy et al. (2011) Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs. Math Biosci 230:115-27 |
| Layton, Anita T; Layton, Harold E (2011) Countercurrent multiplication may not explain the axial osmolality gradient in the outer medulla of the rat kidney. Am J Physiol Renal Physiol 301:F1047-56 |
| Layton, Anita T; Pannabecker, Thomas L; Dantzler, William H et al. (2010) Functional implications of the three-dimensional architecture of the rat renal inner medulla. Am J Physiol Renal Physiol 298:F973-87 |
| Layton, Anita T; Pannabecker, Thomas L; Dantzler, William H et al. (2010) Hyperfiltration and inner stripe hypertrophy may explain findings by Gamble and coworkers. Am J Physiol Renal Physiol 298:F962-72 |
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