Anita T. Layton

Anita T. Layton
  • Professor in the Department of Mathematics
External address: 213 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-6971

Research Areas and Keywords

Biological Modeling
mathematical biology, mathematical physiology, mathematical modeling, kidney physiology, renal hemodynamics, diabetes, multiscale modeling, fluid-structure interactions, computational fluid dynamics, numerical partial differential equations, feedback control, systems biology
Computational Mathematics
mathematical biology, mathematical physiology, mathematical modeling, kidney physiology, renal hemodynamics, diabetes, multiscale modeling, fluid-structure interactions, computational fluid dynamics, numerical partial differential equations, feedback control, systems biology
PDE & Dynamical Systems
mathematical biology, mathematical physiology, mathematical modeling, kidney physiology, renal hemodynamics, diabetes, multiscale modeling, fluid-structure interactions, computational fluid dynamics, numerical partial differential equations, feedback control, systems biology

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.

Wang, J, and Layton, A. "New numerical methods for Burgers' equation based on semi-Lagrangian and modified equation approaches." Applied Numerical Mathematics 60.6 (2010): 645-657. Full Text

Layton, AT. "Feedback-mediated dynamics in a model of a compliant thick ascending limb." Math Biosci 228.185-194 (2010). (Academic Article)

Marcano, M, Layton, AT, and Layton, HE. "Maximum urine concentrating capability in a mathematical model of the inner medulla of the rat kidney." Bulletin of Mathematical Biology 72.2 (2010): 314-339. Full Text

Layton, AT, and Edwards, A. "Tubuloglomerular feedback signal transduction in a short loop of henle." Bull Math Biol 72.1 (January 2010): 34-62. Full Text

Marcano, M, Layton, AT, and Layton, HE. "Maximum urine concentrating capability for transport parameters and urine flow within prescribed ranges." Bull. Math. Biol. 7.2 (2010): 314-339. (Academic Article)

Layton, AT, Toyama, Y, Yang, G-Q, Edwards, GS, Kiehart, DP, and Venakides, S. "Drosophila morphogenesis: tissue force laws and the modeling of dorsal closure." HFSP J 3.6 (December 2009): 441-460. Full Text

Layton, AT, Layton, HE, Dantzler, WH, and Pannabecker, TL. "The mammalian urine concentrating mechanism: hypotheses and uncertainties." Physiology (Bethesda) 24 (August 2009): 250-256. (Review) Full Text

Layton, AT, Moore, LC, and Layton, HE. "Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons." Bull Math Biol 71.3 (April 2009): 515-555. Full Text

Edwards, A, Chen, J, and Layton, AT. "Impact of Rat Outer Medullary Architecture on Oxygen Distribution." FASEB JOURNAL 23 (April 2009).

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