Harold Layton

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
renal 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.

Education & Training
  • Ph.D., Duke University 1986

  • M.S., University of Kentucky at Lexington 1980

  • B.A., Asbury College 1979

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. Full Text

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. Full Text

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. Full Text

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. Full Text

Layton, HE. "Nephron distribution enhances concentrating capability." Federation Proceedings 44.6 (1985): No.-8773.