# Anita T. Layton

- Professor in the Department of Mathematics
- Professor of Biomedical Engineering (Secondary)
- Professor in Medicine (Secondary)
- Bass Fellow

**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.

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.
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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.
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Sgouralis, I, and Layton, AT. "Theoretical assessment of renal autoregulatory mechanisms." *American Journal of Physiology. Renal Physiology* 306.11 (June 2014): F1357-F1371.
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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.
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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.
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Edwards, A, and Layton, AT. "Calcium dynamics underlying the myogenic response of the renal afferent arteriole." *American Journal of Physiology. Renal Physiology* 306.1 (January 2014): F34-F48.
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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.
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Li, Y, Sgouralis, I, and Layton, AT. "Computing viscous flow in an elastic tube." *Numerical Mathematics* 7.4 (January 1, 2014): 555-574.
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Layton, AT. "Mathematical modeling of urea transport in the kidney." *Sub-cellular biochemistry* 73 (January 2014): 31-43. (Review)
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Sgouralis, I, and Layton, AT. "Control and modulation of fluid flow in the rat kidney." *Bulletin of Mathematical Biology* 75.12 (December 2013): 2551-2574.
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