Research Interests for Harold Layton

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

Recent Publications

1. 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)
2. 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)
3. 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)
4. 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)
5. 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