- Professor of Mathematics
Research Areas and Keywords
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.
Layton, HE, and Davies, JM. "Distributed solute and water reabsorption in a central core model of the renal medulla." Mathematical Biosciences 116.2 (1993): 169-196. Full Text
Layton, HE, Pitman, EB, and Moore, LC. "Bifurcation analysis of TGF-mediated oscillations in SNGFR." American Journal of Physiology - Renal Fluid and Electrolyte Physiology 261.5 30-5 (1991): F904-F919.
Layton, HE. "Distributed loops of Henle in a central core model of the renal medulla: Where should the solute come out?." Mathematical and Computer Modelling 14.C (1990): 533-537.
Layton, HE, and Pitman, EB. "Oscillations in a simple model of tubuloglomerular feedback." Proceedings of the Annual Conference on Engineering in Medicine and Biology pt 3 (1990): 987-988.
Layton, HE. "Urea transport in a distributed loop model of the urine-concentrating mechanism." American Journal of Physiology - Renal Fluid and Electrolyte Physiology 258.4 27-4 (1990): F1110-F1124.
Layton, HE. "Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism." Mathematical Biosciences 84.2 (1987): 197-210.
Layton, HE. "Energy advantage of counter-current oxygen transfer in fish gills." Journal of Theoretical Biology 125.3 (1987): 307-316.
Layton, HE. "Distribution of Henle's loops may enhance urine concentrating capability." Biophysical Journal 49.5 (1986): 1033-1040. Full Text
Layton, HE. "Nephron distribution enhances concentrating capability." Federation Proceedings 44.6 (1985): No.-8773.