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, 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.

Layton, HE, Pitman, EB, and Moore, LC. "Spectral properties of the thick ascending limb." FASEB Journal 10.3 (1996): A547-.

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.

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