# 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.

Pitman, EB, and Layton, HE. "Mass conservation in a dynamic numerical method for a model of the urine concentrating mechanism." *ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik* 76.SUPPL. 4 (1996): 45-48.

Layton, HE, Knepper, MA, and Chou, C-L. "Permeability criteria for effective function of passive countercurrent multiplier." *American Journal of Physiology* 270.1 PART 2 (1996): F9-F20.

Layton, HE, Knepper, MA, and Chou, CL. "Permeability criteria for effective function of passive countercurrent multiplier." *Am J Physiol* 270.1 Pt 2 (January 1996): F9-20.
Full Text

Layton, HE, Pitman, EB, and Moore, LC. "Instantaneous and steady-state gains in the tubuloglomerular feedback system." *American Journal of Physiology - Renal Fluid and Electrolyte Physiology* 268.1 37-1 (1995): F163-F174.

Layton, HE, Pitman, EB, and Knepper, MA. "Dynamic numerical method for models of the urine concentrating mechanism." *SIAM Journal on Applied Mathematics* 55.5 (1995): 1390-1418.

Layton, HE, and Pitman, EB. "A dynamic numerical method for models of renal tubules." *Bulletin of Mathematical Biology* 56.3 (1994): 547-565.
Full Text

Layton, HE, Pitman, EB, and Moore, LC. "Instantaneous and steady-state gains in the tubuloglomerular feedback system." *American Journal of Physiology - Renal Physiology* 268.1 (1994): F163-F174.

Pitman, EB, Layton, HE, and Moore, LC. "Numerical simulation of propagating concentration profiles in renal tubules." *Bulletin of Mathematical Biology* 56.3 (1994): 567-586.
Full Text

Chou, C-L, Knepper, MA, and Layton, HE. "Urinary concentrating mechanism: The role of the inner medulla." *Seminars in Nephrology* 13.2 (1993): 168-181.

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