# 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)

**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

##### Computational Mathematics

##### 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.

Herschlag, G, Liu, J-G, and Layton, AT. "An Exact Solution for Stokes Flow in a Channel with Arbitrarily Large Wall Permeability." *SIAM Journal on Applied Mathematics* 75.5 (January 2015): 2246-2267.
Full Text

Fry, BC, and Layton, AT. "Oxygen transport in a cross section of the rat inner medulla: impact of heterogeneous distribution of nephrons and vessels." *Mathematical biosciences* 258 (December 2014): 68-76.
Full Text

Pannabecker, TL, and Layton, AT. "Targeted delivery of solutes and oxygen in the renal medulla: role of microvessel architecture." *American journal of physiology. Renal physiology* 307.6 (September 2014): F649-F655. (Review)
Full Text

Fry, BC, Edwards, A, Sgouralis, I, and Layton, AT. "Impact of renal medullary three-dimensional architecture on oxygen transport." *American journal of physiology. Renal physiology* 307.3 (August 2014): F263-F272.
Full Text

Edwards, A, Castrop, H, Laghmani, K, Vallon, V, and Layton, AT. "Effects of NKCC2 isoform regulation on NaCl transport in thick ascending limb and macula densa: a modeling study." *American journal of physiology. Renal physiology* 307.2 (July 2014): F137-F146.
Full Text

Sgouralis, I, and Layton, AT. "Theoretical assessment of renal autoregulatory mechanisms." *American journal of physiology. Renal physiology* 306.11 (June 2014): F1357-F1371.
Full Text

Moss, R, and Layton, AT. "Dominant factors that govern pressure natriuresis in diuresis and antidiuresis: a mathematical model." *American journal of physiology. Renal physiology* 306.9 (May 2014): F952-F969.
Full Text

Ryu, H, and Layton, AT. "Tubular fluid flow and distal NaCl delivery mediated by tubuloglomerular feedback in the rat kidney." *J Math Biol* 68.4 (March 2014): 1023-1049.
Full Text

Edwards, A, and Layton, AT. "Calcium dynamics underlying the myogenic response of the renal afferent arteriole." *Am J Physiol Renal Physiol* 306.1 (January 1, 2014): F34-F48.
Full Text

Ryu, H, and Layton, AT. "Tubular fluid flow and distal NaCl delivery mediated by tubuloglomerular feedback in the rat kidney." *Journal of Mathematical Biology* 68.4 (January 1, 2014): 1023-1049.
Full Text