# 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.

Oldson, DR, Moore, LC, and Layton, HE. "Effect of sustained flow perturbations on stability and compensation of tubuloglomerular feedback." *American Journal of Physiology - Renal Physiology* 285.5 54-5 (2003): F972-F989.

Marcano-Velázquez, M, and Layton, HE. "An inverse algorithm for a mathematical model of an avian urine concentrating mechanism." *Bulletin of Mathematical Biology* 65.4 (2003): 665-691.
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Smith, KM, Moore, LC, and Layton, HE. "Advective transport of nitric oxide in a mathematical model of the afferent arteriole." *American Journal of Physiology - Renal Physiology* 284.5 53-5 (2003): F1080-F1096.

Layton, AT, and Layton, HE. "A numerical method for renal models that represent tubules with abrupt changes in membrane properties." *Journal of Mathematical Biology* 45.6 (2002): 549-567.
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Layton, AT, and Layton, HE. "A semi-lagrangian semi-implicit numerical method for models of the urine concentrating mechanism." *SIAM Journal on Scientific Computing* 23.5 (2002): 1526-1548.
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Layton, HE, Davies, JM, Casotti, G, and Braun, EJ. "Mathematical model of an avian urine concentrating mechanism." *Am J Physiol Renal Physiol* 279.6 (December 2000): F1139-F1160.
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Layton, HE, Pitman, EB, and Moore, LC. "Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery." *Am J Physiol Renal Physiol* 278.2 (February 2000): F287-F301.
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Layton, HE, Davies, JM, Casotti, G, and Braun, EJ. "Mathematical model of an avian urine concentrating mechanism." *American Journal of Physiology - Renal Physiology* 279.6 48-6 (2000): F1139-F1160.

Layton, HE, Pitman, EB, and Moore, LC. "Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery." *American Journal of Physiology - Renal Physiology* 278.2 47-2 (2000): F287-F301.

Arthurs, KM, Moore, LC, Peskin, CS, Pitman, EB, and Layton, HE. "Modeling arteriolar flow and mass transport using the immersed boundary method." *Journal of Computational Physics* 147.2 (1998): 402-440.
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