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Math @ Duke
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Harold Layton, Professor and Chair
 - Contact Info:
- Office Hours:
- By appointment
- Education:
- A.B., mathematics, summa cum laude, Asbury college, 1979
M.S., physics, University of Kentucky, 1980 Ph.D., mathematics, Duke University, 1986
- Specialties:
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Applied Math
- Research Interests: Mathematical Physiology
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.
- Areas of Interest:
- Mathematical models of renal hemodynamics
Mathematical models of the urine concentrating mechanism Numerical methods for models of renal systems Countercurrent systems in animals
- Curriculum Vitae
- Current Ph.D. Students
(Former Students)
- Postdocs Mentored
- Amal El Moghraby (July 01, 2008 - May 31, 2009)
- Paula Budu (September 14, 2002 - August 31, 2005)
- Monica M. Romeo (September 1, 2001 - May 31, 2004)
- Kayne Marie Arthurs (1996/09-1998/08)
- Recent Publications
(More Publications)
- Jing Chen, Ioannis Sgouralis, Leon C. Moore, Harold E. Layton, and Anita T. Layton, A mathematical model of the myogenic response to systolic pressure in the afferent arteriole,
American Journal of Physiology--Renal Physiology
(Accepted, December, 2010)
- Anita T. Layton, Matthew Bowen, Amy Wen, and Harold E. Layton, Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs,
Mathematical Biosciences
(Submitted, December, 2010)
- Anita T. Layton, Leon C. Moore, and Harold E. Layton, Tubuloglomerular feedback signal ransduction in models of the thick ascending limb,
American Journal of Physiology--Renal Physiology
(Submitted, December, 2010)
- Anita T. Layton and Harold E. Layton, Countercurrent multiplication may not explain the axial osmolality gradient,
American Journal of Physiology--Renal Physiology
(Submitted, October, 2010)
- Jeff M. Sands and Harold E. Layton, The urine concentrating mechanism and urea transporters,
in The Kidney: Physiology and Pathophysiology, 5th Edition, edited by Robert Alphern, Orson Moe, & Michaeal Caplan
(Accepted, September, 2010), Elsevier/Academic Press
- Recent Grant Support
- EMSW21-RTG: Enhanced Training and Recruitment in Mathematical Biology, National Science Foundation, DMS-0943760, 2010/09-2014/08.
- Mathematical Models of Renal Dynamics, NIH, 2006/03-2011/02.
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dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
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