Harold Layton, Professor and Chair

Contact Info:

Office Location:	221 Physics
Office Phone:	(919) 660-2809
Email Address:
Web Page:	http://www.math.duke.edu/~layton

Office Hours:

Summer 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:

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.

Curriculum Vitae

Current Ph.D. Students   (Former Students)

Postdocs Mentored

• 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)

1. Anita T. Layton, Leon C. Moore, Harold E. Layton, Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons, Bulletin of Mathematical Biology. 71(3):515-555, 2009. (April, 2009)
2. Jeff M. Sands and Harold E. Layton, The physiology of urinary concentration: an update, Seminars in Nephrology, 29 (2): 178-195, 2009. (May, 2009)
3. Thomas L. Pannabecker, William H. Dantzler, Harold E. Layton, and Anita T. Layton, Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla, American Journal of Physiology--Renal Physiology, 295: F1271 - F1285, 2008 (November, 2008)
4. Mariano Marcano, Anita T. Layton, and Harold E. Layton, Maximum urine concentrating capability for transport parameters and urine flow within prescribed ranges (Accepted, 2009)
5. Paula Budu-Grajdeanu, Leon C. Moore, Harold E. Layton., Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop. Mathematical Biosciences 209(2): 564-592., Mathematical Biosciences (October, 2007)

Recent Grant Support

• Mathematical Models of Renal Dynamics, NIH, 2006/03-2010/02.      
• Conference on Applications of Analysis to Mathematical Biology, Arts & Sciences Committee on Faculty Research, 2006/11-2007/09.