# 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.

Sgouralis, I, and Layton, AT. "Mathematical modeling of renal hemodynamics in physiology and pathophysiology." *Mathematical Biosciences* 264 (June 2015): 8-20.
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Layton, AT, Vallon, V, and Edwards, A. "Modeling oxygen consumption in the proximal tubule: effects of NHE and SGLT2 inhibition." *American Journal of Physiology. Renal Physiology* 308.12 (June 2015): F1343-F1357.
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Fry, BC, Edwards, A, and Layton, AT. "Impacts of nitric oxide and superoxide on renal medullary oxygen transport and urine concentration." *American journal of physiology. Renal physiology* 308.9 (May 2015): F967-F980.
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Layton, AT. "Recent advances in renal hemodynamics: insights from bench experiments and computer simulations." *American journal of physiology. Renal physiology* 308.9 (May 2015): F951-F955. (Review)
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Ford Versypt, AN, Makrides, E, Arciero, JC, Ellwein, L, and Layton, AT. "Bifurcation study of blood flow control in the kidney." *Mathematical Biosciences* 263 (May 2015): 169-179.
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Sgouralis, I, Evans, RG, Gardiner, BS, Smith, JA, Fry, BC, and Layton, AT. "Renal hemodynamics, function, and oxygenation during cardiac surgery performed on cardiopulmonary bypass: a modeling study." *Physiological reports* 3.1 (January 19, 2015).
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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.
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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.
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Dantzler, WH, Layton, AT, Layton, HE, and Pannabecker, TL. "Urine-concentrating mechanism in the inner medulla: function of the thin limbs of the loops of Henle." *Clinical Journal of the American Society of Nephrology : Cjasn* 9.10 (October 2014): 1781-1789.
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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)
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