# 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.

Layton, AT, Vallon, V, and Edwards, A. "A computational model for simulating solute transport and oxygen consumption along the nephrons." *American Journal of Physiology Renal Physiology* 311.6 (December 2016): F1378-F1390.
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Sgouralis, I, Kett, MM, Ow, CPC, Abdelkader, A, Layton, AT, Gardiner, BS, Smith, DW, Lankadeva, YR, and Evans, RG. "Bladder urine oxygen tension for assessing renal medullary oxygenation in rabbits: experimental and modeling studies." *American Journal of Physiology. Regulatory, Integrative and Comparative Physiology* 311.3 (September 2016): R532-R544.
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Layton, AT. "Recent advances in renal hypoxia: insights from bench experiments and computer simulations." *American Journal of Physiology Renal Physiology* 311.1 (July 2016): F162-F165. (Review)
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Layton, AT, Vallon, V, and Edwards, A. "Predicted consequences of diabetes and SGLT inhibition on transport and oxygen consumption along a rat nephron." *American Journal of Physiology. Renal Physiology* 310.11 (June 2016): F1269-F1283.
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Liu, R, and Layton, AT. "Modeling the effects of positive and negative feedback in kidney blood flow control." *Mathematical biosciences* 276 (June 2016): 8-18.
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Chen, Y, Fry, BC, and Layton, AT. "Modeling Glucose Metabolism in the Kidney." *Bulletin of Mathematical Biology* 78.6 (June 2016): 1318-1336.
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Nganguia, H, Young, Y-N, Layton, AT, Lai, M-C, and Hu, W-F. "Electrohydrodynamics of a viscous drop with inertia." *Physical review. E* 93.5 (May 23, 2016): 053114-.
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Sgouralis, I, Maroulas, V, and Layton, AT. "Transfer Function Analysis of Dynamic Blood Flow Control in the Rat Kidney." *Bulletin of Mathematical Biology* 78.5 (May 12, 2016): 923-960.
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Herschlag, G, Liu, JG, and Layton, AT. "Fluid extraction across pumping and permeable walls in the viscous limit." *Physics of Fluids* 28.4 (April 1, 2016).
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Sgouralis, I, and Layton, AT. "Conduction of feedback-mediated signal in a computational model of coupled nephrons." *Mathematical Medicine and Biology : a Journal of the Ima* 33.1 (March 2016): 87-106.
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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.