# 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.

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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Li, Y, Williams, SA, and Layton, AT. "A hybrid immersed interface method for driven stokes flow in an elastic tube." *Numerical Mathematics* 6.4 (November 1, 2013): 600-616.
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Layton, AT, and Bankir, L. "Impacts of Active Urea Secretion into Pars Recta on Urine Concentration and Urea Excretion Rate." *Physiol Rep* 1.3 (September 10, 2013).
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Ryu, H, and Layton, AT. "Effect of tubular inhomogeneities on feedback-mediated dynamics of a model of a thick ascending limb." *Math Med Biol* 30.3 (September 2013): 191-212.
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Layton, AT. "Mathematical modeling of kidney transport." *Wiley Interdiscip Rev Syst Biol Med* 5.5 (September 2013): 557-573. (Review)
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Haer-Wigman, L, Linthorst, GE, Sands, JM, Klein, JD, Thai, TL, Verhoeven, AJ, van Zwieten, R, Folman, C, Jansweijer, MC, Knegt, LC, de Ru, MH, Groothoff, JW, Ludwig, M, Layton, AT, and Bokenkamp, A. "DUPLICATION OF THE UREA TRANSPORTER B GENE (KIDD BLOOD GROUP) IN A KINDRED WITH FAMILIAL AZOTEMIA." *VOX SANGUINIS* 105 (June 2013): 30-31.

Nieves-González, A, Clausen, C, Layton, AT, Layton, HE, and Moore, LC. "Transport efficiency and workload distribution in a mathematical model of the thick ascending limb." *Am J Physiol Renal Physiol* 304.6 (March 15, 2013): F653-F664.
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Leiderman, K, Bouzarth, EL, Cortez, R, and Layton, AT. "A regularization method for the numerical solution of periodic Stokes flow." *Journal of Computational Physics* 236.1 (2013): 187-202.
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Sgouralis, I, and Layton, AT. "Control and modulation of fluid flow in the rat kidney (Submitted)." *BULLETIN OF MATHEMATICAL BIOLOGY* (November 2012). (Academic Article)