# 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.

Edwards, A, and Layton, AT. "Nitric oxide and superoxide transport in a cross section of the rat outer medulla. I. Effects of low medullary oxygen tension." *American Journal of Physiology - Renal Physiology* 299.3 (2010): F616-F633.
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Edwards, A, and Layton, AT. "Nitric oxide and superoxide transport in a cross section of the rat outer medulla. II. Reciprocal interactions and tubulovascular cross talk." *American Journal of Physiology - Renal Physiology* 299.3 (2010): F634-F647.
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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.
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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.
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Loreto, M, and Layton, AT. "An optimization study of a mathematical model of the urine concentrating mechanism of the rat kidney." *Math Biosci* 223.1 (January 2010): 66-78.
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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.
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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)
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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.
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Edwards, A, Chen, J, and Layton, AT. "Impact of Rat Outer Medullary Architecture on Oxygen Distribution." *FASEB JOURNAL* 23 (April 2009).