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

Budu-Grajdeanu, P, Moore, LC, and Layton, HE. "Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop." Math Biosci 209.2 (October 2007): 564-592. Full Text

Layton, AT, Moore, LC, and Layton, HE. "Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats." Am J Physiol Renal Physiol 291.1 (July 2006): F79-F97. Full Text

Thomas, SR, Layton, AT, Layton, HE, and Moore, LC. "Kidney modeling: Status and perspectives." Proceedings of the IEEE 94.4 (2006): 740-752. Full Text

Marcano, M, Layton, AT, and Layton, HE. "An optimization algorithm for a distributed-loop model of an avian urine concentrating mechanism." Bulletin of Mathematical Biology 68.7 (2006): 1625-1660. Full Text

Layton, AT, Pannabecker, TL, Dantzler, WH, and Layton, HE. "Two modes for concentrating urine in rat inner medulla." American Journal of Physiology - Renal Physiology 287.4 56-4 (2004): F816-F839. Full Text

Pitman, EB, Zaritski, RM, Kesseler, KJ, Moore, LC, and Layton, HE. "Feedback-mediated dynamics in two coupled nephrons." Bulletin of Mathematical Biology 66.6 (2004): 1463-1492. Full Text

Layton, AT, and Layton, HE. "An efficient numerical method for distributed-loop models of the urine concentrating mechanism." Mathematical Biosciences 181.2 (2003): 111-132. Full Text

Layton, AT, and Layton, HE. "A region-based model framework for the rat urine concentrating mechanism." Bulletin of Mathematical Biology 65.5 (2003): 859-901. Full Text