# 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

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.

### 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.
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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.
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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.
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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.
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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)
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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.
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Sands, JM, and Layton, HE. "The Physiology of Urinary Concentration: An Update." *Seminars in Nephrology* 29.3 (2009): 178-195.
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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.
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Sands, JM, and Layton, HE. "The Urine Concentrating Mechanism and Urea Transporters." *Seldin and Giebisch's The Kidney* (2008): 1143-1178.
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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)