# 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.

Budu-Grajdeanu, P, Moore, LC, and Layton, HE. "Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop." *Math Biosci* 209.2 (October 2007): 564-592.
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Layton, AT, Moore, LC, and Layton, HE. "Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats." *Am J Physiol Renal Physiol* 291.1 (July 2006): F79-F97.
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Thomas, SR, Layton, AT, Layton, HE, and Moore, LC. "Kidney modeling: Status and perspectives." *Proceedings of the IEEE* 94.4 (2006): 740-752.
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Marcano, M, Layton, AT, and Layton, HE. "An optimization algorithm for a distributed-loop model of an avian urine concentrating mechanism." *Bulletin of Mathematical Biology* 68.7 (2006): 1625-1660.
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Layton, AT, and Layton, HE. "A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results." *Am J Physiol Renal Physiol* 289.6 (December 2005): F1346-F1366.
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Layton, AT, and Layton, HE. "A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. II. Parameter sensitivity and tubular inhomogeneity." *Am J Physiol Renal Physiol* 289.6 (December 2005): F1367-F1381.
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Layton, AT, Pannabecker, TL, Dantzler, WH, and Layton, HE. "Two modes for concentrating urine in rat inner medulla." *American Journal of Physiology - Renal Physiology* 287.4 56-4 (2004): F816-F839.
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Pitman, EB, Zaritski, RM, Kesseler, KJ, Moore, LC, and Layton, HE. "Feedback-mediated dynamics in two coupled nephrons." *Bulletin of Mathematical Biology* 66.6 (2004): 1463-1492.
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Layton, AT, and Layton, HE. "An efficient numerical method for distributed-loop models of the urine concentrating mechanism." *Mathematical Biosciences* 181.2 (2003): 111-132.
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Layton, AT, and Layton, HE. "A region-based model framework for the rat urine concentrating mechanism." *Bulletin of Mathematical Biology* 65.5 (2003): 859-901.
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