# Anita T. Layton

- Research Professor 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, Anita T., et al. “Adaptive changes in GFR, tubular morphology, and transport in subtotal nephrectomized kidneys: modeling and analysis..” *American Journal of Physiology. Renal Physiology*, vol. 313, no. 2, Aug. 2017, pp. F199–209. *Epmc*, doi:10.1152/ajprenal.00018.2017.
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Chen, Ying, et al. “Modeling glucose metabolism and lactate production in the kidney..” *Mathematical Biosciences*, vol. 289, July 2017, pp. 116–29. *Epmc*, doi:10.1016/j.mbs.2017.04.008.
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Layton, Anita T. “A new microscope for the kidney: mathematics..” *American Journal of Physiology. Renal Physiology*, vol. 312, no. 4, Apr. 2017, pp. F671–72. *Epmc*, doi:10.1152/ajprenal.00648.2016.
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Jiang, Tao, et al. “Generation and phenotypic analysis of mice lacking all urea transporters..” *Kidney International*, vol. 91, no. 2, Feb. 2017, pp. 338–51. *Epmc*, doi:10.1016/j.kint.2016.09.017.
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Layton, Anita T., et al. “A computational model for simulating solute transport and oxygen consumption along the nephrons..” *American Journal of Physiology. Renal Physiology*, vol. 311, no. 6, Dec. 2016, pp. F1378–90. *Epmc*, doi:10.1152/ajprenal.00293.2016.
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Layton, Anita T., et al. “Solute transport and oxygen consumption along the nephrons: effects of Na+ transport inhibitors..” *American Journal of Physiology. Renal Physiology*, vol. 311, no. 6, Dec. 2016, pp. F1217–29. *Epmc*, doi:10.1152/ajprenal.00294.2016.
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Sgouralis, Ioannis, et al. “Bladder urine oxygen tension for assessing renal medullary oxygenation in rabbits: experimental and modeling studies..” *American Journal of Physiology. Regulatory, Integrative and Comparative Physiology*, vol. 311, no. 3, Sept. 2016, pp. R532–44. *Epmc*, doi:10.1152/ajpregu.00195.2016.
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Layton, Anita T. “Recent advances in renal hypoxia: insights from bench experiments and computer simulations..” *American Journal of Physiology. Renal Physiology*, vol. 311, no. 1, July 2016, pp. F162–65. *Epmc*, doi:10.1152/ajprenal.00228.2016.
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Layton, Anita T., et al. “Predicted consequences of diabetes and SGLT inhibition on transport and oxygen consumption along a rat nephron..” *American Journal of Physiology. Renal Physiology*, vol. 310, no. 11, June 2016, pp. F1269–83. *Epmc*, doi:10.1152/ajprenal.00543.2015.
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Liu, Runjing, and Anita T. Layton. “Modeling the effects of positive and negative feedback in kidney blood flow control..” *Mathematical Biosciences*, vol. 276, June 2016, pp. 8–18. *Epmc*, doi:10.1016/j.mbs.2016.02.007.
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## Pages

Marcano, M., et al. “An optimization algorithm for a model of the urine concentrating mechanism in rat inner medulla.” *Faseb Journal*, vol. 19, no. 4, FEDERATION AMER SOC EXP BIOL, 2005, pp. A150–A150.

Layton, A. T., and H. E. Layton. “A mathematical model of the urine concentrating mechanism of the inner medulla of the chinchilla kidney.” *Faseb Journal*, vol. 19, no. 4, FEDERATION AMER SOC EXP BIOL, 2005, pp. A149–A149.

Layton, A. T., et al. “Effects of structural organization on the urine concentrating mechanism of the rat kidney.” *Faseb Journal*, vol. 18, no. 5, FEDERATION AMER SOC EXP BIOL, 2004, pp. A1021–A1021.

Layton, H. E., and A. T. Layton. “Impaired countercurrent exchange in a mathematical model of a urine concentrating mechanism lacking UT-B urea transporter..” *Journal of the American Society of Nephrology*, vol. 14, LIPPINCOTT WILLIAMS & WILKINS, 2003, pp. 76A-76A.

Layton, A. T., and H. E. Layton. “A method for tracking solute distribution in mathematical models of the urine concentrating mechanism (UCM).” *Faseb Journal*, vol. 17, no. 4, FEDERATION AMER SOC EXP BIOL, 2003, pp. A485–A485.