Research Interests for Anita T Layton

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.

Areas of Interest:

Mathematical physiology
Scientific computing
Multiscale numerical methods
Fluid-structure interactions

Recent Publications

1. Anita T. Layton, Leon C. Moore, and Harold E. Layton, Signal transduction in a compliant thick ascending limb, Am. J. Physiol. Renal Physiol., in press (Accepted, 2012)
2. Anita T. Layton and Guowei Wei, Editorial: Interface methods for biological and biomedical problems, Int J Numer Methods Biomed Eng, in press (Accepted, 2012)
3. Anita T. Layton and Guo-Wei Wei (editors), Interface Methods for Biological and Biomedical Problems, Int J Numer Methods Biomed Eng, in press (2012)
4. Thoma Witelski, David Ambrose, Andrea Bertozzi, Anita Layton, and Zhilin Li (editors), Fluid Dynamics, Analysis and Numerics, Special issue of Discrete and Continuous Dynamical Systems - Series B (2012)
5. Aurélie Edwards and Anita T. Layton, Impact of nitric oxide-mediated vasodilation on outer medullary NaCl transport and oxygenation, Am J Physiol Renal Physiol, submitted (Submitted, 2012)