Anita T. Layton
- Robert R. & Katherine B. Penn Professor of Mathematics
- Professor in the Department of Mathematics
- Professor of Biomedical Engineering (Secondary)
Research Areas and Keywords
PDE & Dynamical Systems
Mathematical physiology. My main research interest is the application of mathematics to biological systems, specifically, mathematical modeling of renal physiology. Current projects involve (1) the development of mathematical models of the mammalian kidney and the application of these models to investigate the mechanism by which some mammals (and birds) can produce a urine that has a much higher osmolality than that of blood plasma; (2) the study of the origin of the irregular oscillations exhibited by the tubuloglomerular feedback (TGF) system, which regulates fluid delivery into renal tubules, in hypertensive rats; (3) the investigation of the interactions of the TGF system and the urine concentrating mechanism; (4) the development of a dynamic epithelial transport model of the proximal tubule and the incorporation of that model into a TGF framework.
Multiscale numerical methods. I develop multiscale numerical methods---multi-implicit Picard integral deferred correction methods---for the integration of partial differential equations arising in physical systems with dynamics that involve two or more processes with widely-differing characteristic time scales (e.g., combustion, transport of air pollutants, etc.). These methods avoid the solution of nonlinear coupled equations, and allow processes to decoupled (like in operating-splitting methods) while generating arbitrarily high-order solutions.
Numerical methods for immersed boundary problems. I develop numerical methods to simulate fluid motion driven by forces singularly supported along a boundary immersed in an incompressible fluid.
Edwards, A, and Layton, AT. "Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide." Am J Physiol Renal Physiol 301.F979-F996 (2011). (Academic Article)
Bouzarth, EL, Layton, AT, and Young, Y-N. "Modeling a semi-flexible filament in cellular Stokes flow using regularized Stokeslets." International Journal for Numerical Methods in Biomedical Engineering 27.12 (2011): 2021-2034. Full Text
Edwards, A, and Layton, AT. "Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide." American Journal of Physiology - Renal Physiology 301.5 (2011): F979-F996. Full Text
Layton, AT, Savage, NS, Howell, AS, Carroll, SY, Drubin, DG, and Lew, DJ. "Modeling vesicle traffic reveals unexpected consequences for Cdc42p-mediated polarity establishment." Curr Biol 21 (2011): 1-11. (Academic Article)
Layton, AT. "Feedback-mediated dynamics in a model of a compliant thick ascending limb." Math Biosci 228.2 (December 2010): 185-194. Full Text
Chen, J, Edwards, A, and Layton, AT. "Effects of pH and medullary blood flow on oxygen transport and sodium reabsorption in the rat outer medulla." Am J Physiol Renal Physiol 298.6 (June 2010): F1369-F1383. Full Text
Edwards, A, and Layton, AT. "Impact of nitric oxide-mediated vasodilation on outer medullary NaCl transport and oxygenation." FASEB JOURNAL 24 (April 2010).
Layton, HE, Chen, J, Moore, LC, and Layton, AT. "A mathematical model of the afferent arteriolar smooth muscle cell." FASEB JOURNAL 24 (April 2010).
Nieves-Gonzalez, A, Moore, LC, Clausen, C, Marcano, M, Layton, HE, and Layton, AT. "Efficiency of sodium transport in the thick ascending limb." FASEB JOURNAL 24 (April 2010).
Layton, AT, Pannabecker, TL, Dantzler, WH, and Layton, HE. "Functional implications of the three-dimensional architecture of the rat renal inner medulla." Am J Physiol Renal Physiol 298.4 (April 2010): F973-F987. Full Text