# 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.

Layton, HE, Pitman, EB, and Moore, LC. "Potential natriuretic effects of limit-cycle oscillations mediated by tubuloglomerular feedback." *FASEB Journal* 12.4 (1998): A108-.

Layton, HE, Pitman, EB, and Moore, LC. "Nonlinear filter properties of the thick ascending limb." *Am J Physiol* 273.4 Pt 2 (October 1997): F625-F634.

Layton, HE, Pitman, EB, and Moore, LC. "Spectral properties of the tubuloglomerular feedback system." *The American journal of physiology* 273.4 Pt 2 (October 1997): F635-F649.

Layton, HE, Pitman, EB, and Moore, LC. "Spectral properties of the tubuloglomerular feedback system." *American Journal of Physiology - Renal Physiology* 273.4 42-4 (1997): F635-F649.

Arthurs, KM, Moore, LC, Pitman, EB, and Layton, HE. "Flow regulation in afferent arterioles following vascular injury." *FASEB Journal* 11.3 (1997): A82-.

Pitman, EB, Zaritski, R, Moore, LC, and Layton, HE. "TGF-mediated bifurcation in two coupled nephrons." *FASEB Journal* 11.3 (1997): A85-.

Layton, HE, Pitman, EB, and Moore, LC. "Nonlinear filter properties of the thick ascending limb." *American Journal of Physiology - Renal Physiology* 273.4 42-4 (1997): F625-F634.

Layton, HE, Casotti, G, Davies, JM, and Braun, EJ. "Mathematical model of avian urine concentrating mechanism." *FASEB Journal* 11.3 (1997): A9-.

Layton, HE, Pitman, EB, and Moore, LC. "Spectral properties of the TGF pathway." *ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik* 76.SUPPL. 4 (1996): 33-35.

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.