# 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.

Knepper, MA, Chou, CL, and Layton, HE. "How is urine concentrated by the renal inner medulla?." *Contributions to nephrology* 102 (1993): 144-160.

Layton, HE, and Davies, JM. "Distributed solute and water reabsorption in a central core model of the renal medulla." *Mathematical Biosciences* 116.2 (1993): 169-196.
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Layton, HE, Pitman, EB, and Moore, LC. "Bifurcation analysis of TGF-mediated oscillations in SNGFR." *American Journal of Physiology - Renal Fluid and Electrolyte Physiology* 261.5 30-5 (1991): F904-F919.

Layton, HE. "Urea transport in a distributed loop model of the urine-concentrating mechanism." *The American Journal of Physiology* 258.4 Pt 2 (April 1990): F1110-F1124.
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Layton, HE. "Distributed loops of Henle in a central core model of the renal medulla: Where should the solute come out?." *Mathematical and Computer Modelling* 14.C (1990): 533-537.

Layton, HE, and Pitman, EB. "Oscillations in a simple model of tubuloglomerular feedback." *Proceedings of the Annual Conference on Engineering in Medicine and Biology* pt 3 (1990): 987-988.

Pitman, EB, and Layton, HE. "Tubuloglomerular feedback in a dynamic nephron." *Communications on Pure and Applied Mathematics* 42.6 (September 1989): 759-787.
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Layton, HE. "Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism." *Mathematical Biosciences* 84.2 (1987): 197-210.

Layton, HE. "Energy advantage of counter-current oxygen transfer in fish gills." *Journal of Theoretical Biology* 125.3 (1987): 307-316.

Layton, HE. "Distribution of Henle's loops may enhance urine concentrating capability." *Biophysical Journal* 49.5 (1986): 1033-1040.
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