# 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.

Dantzler, WH, Layton, AT, Layton, HE, and Pannabecker, TL. "Urine concentrating mechanism in the inner medulla: function of the thin limbs of Henle’s loops (Accepted)." *Clinical Journal of the American Society of Nephrology.* (August 2012). (Academic Article)

Sgouralis, I, and Layton, AT. "Autoregulation and conduction of vasomotor responses in a mathematical model of the rat afferent arteriole." *Am J Physiol Renal Physiol* 303.2 (July 15, 2012): F229-F239.
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Layton, AT, Moore, LC, and Layton, HE. "Signal transduction in a compliant thick ascending limb." *Am J Physiol Renal Physiol* 302.9 (May 1, 2012): F1188-F1202.
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Savage, NS, Layton, AT, and Lew, DJ. "Mechanistic mathematical model of polarity in yeast." *Mol Biol Cell* 23.10 (May 2012): 1998-2013.
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Layton, AT, Gilbert, RL, and Pannabecker, TL. "Isolated interstitial nodal spaces may facilitate preferential solute and fluid mixing in the rat renal inner medulla." *Am J Physiol Renal Physiol* 302.7 (April 1, 2012): F830-F839.
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Layton, AT, Dantzler, WH, and Pannabecker, TL. "Urine concentrating mechanism: impact of vascular and tubular architecture and a proposed descending limb urea-Na+ cotransporter." *Am J Physiol Renal Physiol* 302.5 (March 1, 2012): F591-F605.
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Layton, AT, Pham, P, and Ryu, H. "Signal transduction in a compliant short loop of Henle." *Int J Numer Method Biomed Eng* 28.3 (March 2012): 369-383.
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Layton, AT, and Wei, G. "Interface methods for biological and biomedical problems." *International Journal for Numerical Methods in Biomedical Engineering* 28.3 (2012): 289-290.
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Hou, G, Wang, J, and Layton, A. "Numerical methods for fluid-structure interaction - A review." *Communications in Computational Physics* 12.2 (2012): 337-377.
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Witelski, T, Ambrose, D, Bertozzi, A, Layton, A, Li, Z, and Minion, M. "Preface: Special issue on fluid dynamics, analysis and numerics." *Discrete and Continuous Dynamical Systems - Series B* 17.4 (2012): i-ii.
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