Harold Layton

  • Professor of Mathematics
External address: 221 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2809

Research Areas and Keywords

Biological Modeling
renal modeling

Professor Layton is modeling renal function at the level of the nephron (the functional unit of the kidney) and at the level of nephron populations. In particular, he is studying tubuloglomerular feedback (TGF), the urine concentrating mechanism, and the hemodynamics of the afferent arteriole. Dynamic models for TGF and the afferent arteriole involve small systems of semilinear hyperbolic partial differential equations (PDEs) with time-delays, and coupled ODES, which are solved numerically for cases of physiological interest, or which are linearized for qualitative analytical investigation. Dynamic models for the concentrating mechanism involve large systems of coupled hyperbolic PDEs that describe tubular convection and epithelial transport. Numerical solutions of these PDEs help to integrate and interpret quantities determined by physiologists in many separate experiments.

Education & Training
  • Ph.D., Duke University 1986

  • M.S., University of Kentucky at Lexington 1980

  • B.A., Asbury College 1979

Selected Grants

(89-0415) Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990 to 1994

(92-0214) Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990 to 1994

(93-0256) Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990 to 1994

(94-0209) Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990 to 1994

(91-0222) Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990

Pages

Dantzler, WH, Pannabecker, TL, Layton, AT, and Layton, HE. "Urine concentrating mechanism in the inner medulla of the mammalian kidney: role of three-dimensional architecture." Acta physiologica (Oxford, England) 202.3 (2011): 361-378. Full Text

Layton, AT, Pannabecker, TL, Dantzler, WH, and Layton, HE. "Functional implications of the three-dimensional architecture of the rat renal inner medulla." Am J Physiol Renal Physiol 298.4 (April 2010): F973-F987. Full Text

Layton, AT, Pannabecker, TL, Dantzler, WH, and Layton, HE. "Hyperfiltration and inner stripe hypertrophy may explain findings by Gamble and coworkers." Am J Physiol Renal Physiol 298.4 (April 2010): F962-F972. Full Text

Marcano, M, Layton, AT, and Layton, HE. "Maximum urine concentrating capability in a mathematical model of the inner medulla of the rat kidney." Bulletin of Mathematical Biology 72.2 (2010): 314-339. Full Text

Layton, AT, Layton, HE, Dantzler, WH, and Pannabecker, TL. "The mammalian urine concentrating mechanism: hypotheses and uncertainties." Physiology (Bethesda) 24 (August 2009): 250-256. (Review) Full Text

Layton, AT, Moore, LC, and Layton, HE. "Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons." Bull Math Biol 71.3 (April 2009): 515-555. Full Text

Sands, JM, and Layton, HE. "The Physiology of Urinary Concentration: An Update." Seminars in Nephrology 29.3 (2009): 178-195. Full Text

Pannabecker, TL, Dantzler, WH, Layton, HE, and Layton, AT. "Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla." American Journal of Physiology - Renal Physiology 295.5 (2008): F1271-F1285. Full Text

Sands, JM, and Layton, HE. "The Urine Concentrating Mechanism and Urea Transporters." Seldin and Giebisch's The Kidney (2008): 1143-1178. Full Text

Budu-Grajdeanu, P, Moore, LC, and Layton, HE. "Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop. Mathematical Biosciences 209(2): 564-592, 2007." Mathematical Biosciences (October 2007). (Academic Article)

Pages