# 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

EMSW21-RTG: awarded by National Science Foundation (Co-Principal Investigator). 2010 to 2017

Modeling Solute Transport and Urine Concentrating Mechanism in the Rat Kidney awarded by National Institutes of Health (Collaborator). 2010 to 2016

Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 2006 to 2010

A Conference on Applications of Analysis to Mathematical Biology awarded by National Science Foundation (Co-Principal Investigator). 2007 to 2008

Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990 to 2005

Mathematical Sciences/GIG: Applications of Mathematics to Physiology awarded by National Science Foundation (Co-Principal Investigator). 1997 to 2001

(96-0846) Mathematical Modes of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990 to 2000

(97-0521) Applications of Mathematics to Physiology awarded by National Science Foundation (Co-Principal Investigator). 1997 to 1999

(94-1029) Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990 to 1999

(97-0855) Mathematical Models of Renal Dynamics awarded by National Institutes of Health (Principal Investigator). 1990 to 1999

## Pages

Sands, JM, Mount, DB, and Layton, HE. "The physiology of water homeostasis." *Core Concepts in the Disorders of Fluid, Electrolytes and Acid-Base Balance.* November 1, 2013. 1-28.
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Li, Q, McDonough, AA, Layton, HE, and Layton, AT. "Functional implications of sexual dimorphism of transporter patterns along the rat proximal tubule: modeling and analysis." *American Journal of Physiology Renal Physiology* 315.3 (September 2018): F692-F700.
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Dantzler, WH, Layton, AT, Layton, HE, and Pannabecker, TL. "Urine-concentrating mechanism in the inner medulla: function of the thin limbs of the loops of Henle." *Clinical Journal of the American Society of Nephrology : Cjasn* 9.10 (October 2014): 1781-1789.
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Sands, JM, and Layton, HE. "Advances in understanding the urine-concentrating mechanism." *Annual review of physiology* 76 (January 2014): 387-409. (Review)
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Nieves-González, A, Clausen, C, Layton, AT, Layton, HE, and Moore, LC. "Transport efficiency and workload distribution in a mathematical model of the thick ascending limb." *American Journal of Physiology. Renal Physiology* 304.6 (March 2013): F653-F664.
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Sands, JM, and Layton, HE. "The Urine Concentrating Mechanism and Urea Transporters." *Seldin and Geibisch's The Kidney* 1 (2013): 1463-1510.
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Layton, AT, Moore, LC, and Layton, HE. "Signal transduction in a compliant thick ascending limb." *American Journal of Physiology. Renal Physiology* 302.9 (May 2012): F1188-F1202.
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Nieves-Gonzalez, A, Clausen, C, Layton, AT, Layton, HE, and Moore, LC. "Efficiency and workload distribution in a mathematical model of the thick ascending limb (Accepted)." *American Journal of Physiology--Renal Physiology* (2012). (Academic Article)

Nieves-Gonzalez, A, Clausen, C, Marcano, M, Layton, AT, Layton, HE, and Moore, LC. "Fluid dilution and efficiency of Na+ transport in a mathematical model of a thick ascending limb cell (Accepted)." *American Journal of Physiology---Renal Physiology* (2012). (Academic Article)

Layton, AT, and Layton, HE. "Countercurrent multiplication may not explain the axial osmolality gradient in the outer medulla of the rat kidney." *American Journal of Physiology. Renal Physiology* 301.5 (November 2011): F1047-F1056.
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Layton, AT, Bowen, M, Wen, A, and Layton, HE. "Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs." *Math Biosci* 230.2 (April 2011): 115-127.
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