Harold Layton, Professor

Contact Info:

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

Teaching (Fall 2008):

• MATH 196S.01, SEM MATHEMATICAL MODEL Synopsis

  Physics 119, TuTh 11:40 AM-12:55 PM

Office Hours:

Tuesdays, 4:10 -- 5:00; Fridays, 3:00--4:00; and 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. 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)
2. Jeff M. Sands and Harold E. Layton, The Urine Concentrating Mechanism and Urea Transporters, in The Kidney: Physiology and Pathophysiology, 4th Edition, edited by Robert J. Alpern and Steven C. Hebert (2007), pp. 1143–1178, Elsevier, New York
3. Mariano Marcano, Anita T. Layton, and Harold E. Layton, An optimization algorithm for a distributed-loop model of an avian urine concentrating mechanism, The Bulletin of Mathematical Biology 68(7): 1625-1660, 2006 (October, 2006)
4. Anita T. Layton, Leon C. Moore, Harold E. Layton, Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats, American Journal of Physiology-Renal Physiology 291 (Renal Physiology 60): F79-F97, 2006 (July, 2006)
5. S. Randall Thomas, Anita T. Layton, Harold E. Layton, and Leon C. Moore, Kidney modelling: status and perspectives, Proceedings of the IEEE 94(4): 740-752, 2006. (April, 2006)

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.