# 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.

Xie, L, Layton, AT, Wang, N, Larson, PEZ, Zhang, JL, Lee, VS, Liu, C, and Johnson, GA. "Dynamic contrast-enhanced quantitative susceptibility mapping with ultrashort echo time MRI for evaluating renal function." *American journal of physiology. Renal physiology* 310.2 (January 2016): F174-F182.
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Burt, T, Rouse, DC, Lee, K, Wu, H, Layton, AT, Hawk, TC, Weitzel, DH, Chin, BB, Cohen-Wolkowiez, M, Chow, S-C, and Noveck, RJ. "Intraarterial Microdosing: A Novel Drug Development Approach, Proof-of-Concept PET Study in Rats." *JOURNAL OF NUCLEAR MEDICINE* 56.11 (November 2015): 1793-1799.
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Layton, AT, and Edwards, A. "Predicted effects of nitric oxide and superoxide on the vasoactivity of the afferent arteriole." *American journal of physiology. Renal physiology* 309.8 (October 2015): F708-F719.
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Nganguia, H, Young, Y-N, Layton, AT, Hu, W-F, and Lai, M-C. "An Immersed Interface Method for Axisymmetric Electrohydrodynamic Simulations in Stokes flow." *Communications in Computational Physics* 18.02 (August 2015): 429-449.
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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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## Pages

Marcano, M, Layton, AT, and Layton, HE. "An optimization algorithm for a model of the urine concentrating mechanism in rat inner medulla." March 4, 2005.

Layton, AT, and Layton, HE. "A mathematical model of the urine concentrating mechanism of the inner medulla of the chinchilla kidney." March 4, 2005.

Layton, AT, Pannabecker, TL, Dantzler, WH, and Layton, HE. "Effects of structural organization on the urine concentrating mechanism of the rat kidney." March 24, 2004.

Layton, HE, and Layton, AT. "Impaired countercurrent exchange in a mathematical model of a urine concentrating mechanism lacking UT-B urea transporter." November 2003.

Layton, AT, and Layton, HE. "A method for tracking solute distribution in mathematical models of the urine concentrating mechanism (UCM)." March 14, 2003.