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.

Recent 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)