# Anita T. Layton

- Robert R. & Katherine B. Penn Professor of Mathematics
- Professor in the Department of Mathematics
- Professor of Biomedical Engineering (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.

Lei, T, Zhou, L, Layton, AT, Zhou, H, Zhao, X, Bankir, L, and Yang, B. "Role of thin descending limb urea transport in renal urea handling and the urine concentrating mechanism." *American Journal of Physiology - Renal Physiology* 301.6 (2011): F1251-F1259.
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Edwards, A, and Layton, AT. "Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide." *Am J Physiol Renal Physiol* 301.F979-F996 (2011). (Academic Article)

Bouzarth, EL, Layton, AT, and Young, Y-N. "Modeling a semi-flexible filament in cellular Stokes flow using regularized Stokeslets." *International Journal for Numerical Methods in Biomedical Engineering* 27.12 (2011): 2021-2034.
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Edwards, A, and Layton, AT. "Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide." *American Journal of Physiology - Renal Physiology* 301.5 (2011): F979-F996.
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Layton, AT. "Feedback-mediated dynamics in a model of a compliant thick ascending limb." *Math Biosci* 228.2 (December 2010): 185-194.
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Chen, J, Edwards, A, and Layton, AT. "Effects of pH and medullary blood flow on oxygen transport and sodium reabsorption in the rat outer medulla." *Am J Physiol Renal Physiol* 298.6 (June 2010): F1369-F1383.
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Gilbert, RL, Pannabecker, TL, and Layton, AT. "Role of interstitial nodal spaces in the urine concentrating mechanism of the rat kidney." *FASEB JOURNAL* 24 (April 2010).

Sgouralis, I, and Layton, AT. "Interactions between Tubuloglomerular Feedback and the Myogenic Mechanism of the Afferent Arteriole." *FASEB JOURNAL* 24 (April 2010).

Ryu, H, and Layton, AT. "Tubular Fluid Oscillations Mediated by Tubuloglomerular Feedback in a Short Loop of Henle." *FASEB JOURNAL* 24 (April 2010).

Edwards, A, and Layton, AT. "Impact of nitric oxide-mediated vasodilation on outer medullary NaCl transport and oxygenation." *FASEB JOURNAL* 24 (April 2010).