Anita T. Layton
- Robert R. & Katherine B. Penn Professor of Mathematics
- Professor in the Department of Mathematics
- Professor of Biomedical Engineering (Secondary)
- Professor in Medicine (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.
Layton, AT. "Mathematical modeling of urea transport in the kidney." Sub-cellular biochemistry 73 (January 2014): 31-43. (Review) Full Text
Li, Y, Williams, SA, and Layton, AT. "A hybrid immersed interface method for driven stokes flow in an elastic tube." Numerical Mathematics 6.4 (November 1, 2013): 600-616. Full Text
Layton, AT, and Bankir, L. "Impacts of Active Urea Secretion into Pars Recta on Urine Concentration and Urea Excretion Rate." Physiol Rep 1.3 (September 10, 2013). Full Text
Ryu, H, and Layton, AT. "Effect of tubular inhomogeneities on feedback-mediated dynamics of a model of a thick ascending limb." Math Med Biol 30.3 (September 2013): 191-212. Full Text
Haer-Wigman, L, Linthorst, GE, Sands, JM, Klein, JD, Thai, TL, Verhoeven, AJ, van Zwieten, R, Folman, C, Jansweijer, MC, Knegt, LC, de Ru, MH, Groothoff, JW, Ludwig, M, Layton, AT, and Bokenkamp, A. "DUPLICATION OF THE UREA TRANSPORTER B GENE (KIDD BLOOD GROUP) IN A KINDRED WITH FAMILIAL AZOTEMIA." VOX SANGUINIS 105 (June 2013): 30-31.
Nieves-González, A, Clausen, C, Layton, AT, Layton, HE, and Moore, LC. "Transport efficiency and workload distribution in a mathematical model of the thick ascending limb." Am J Physiol Renal Physiol 304.6 (March 15, 2013): F653-F664. Full Text
Leiderman, K, Bouzarth, EL, Cortez, R, and Layton, AT. "A regularization method for the numerical solution of periodic Stokes flow." Journal of Computational Physics 236.1 (2013): 187-202. Full Text
Sgouralis, I, and Layton, AT. "Control and modulation of fluid flow in the rat kidney (Submitted)." BULLETIN OF MATHEMATICAL BIOLOGY (November 2012). (Academic Article)