# 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.

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.
Full Text

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)
Full Text

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.
Full Text

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.
Full Text

Chen, Y, Fry, BC, and Layton, AT. "Modeling Glucose Metabolism in the Kidney." *Bulletin of mathematical biology* 78.6 (June 2016): 1318-1336.
Full Text

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-.
Full Text

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.
Full Text

Herschlag, G, Liu, J-G, and Layton, AT. "Fluid extraction across pumping and permeable walls in the viscous limit." *Physics of Fluids* 28.4 (April 2016): 041902-041902.
Full Text

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.
Full Text

Fry, BC, Edwards, A, and Layton, AT. "Impact of nitric-oxide-mediated vasodilation and oxidative stress on renal medullary oxygenation: a modeling study." *American journal of physiology. Renal physiology* 310.3 (February 2016): F237-F247.
Full Text

## Pages

Layton, AT. "Role of UTB Urea Transporters in the Urine Concentrating Mechanism of the Rat Kidney." April 2011.

Nieves-Gonzalez, A, Clausen, C, Marcano, M, Layton, HE, Layton, AT, and Moore, LC. "Efficiency of sodium transport in a model of the Thick Ascending Limb (TAL)." April 2011.

Pannabecker, TL, and Layton, AT. "Isolated interstitial nodal spaces facilitate preferential solute and fluid mixing." April 2011.

Layton, AT, Sgouralis, I, Layton, H, and Moore, L. "Propagation of vasoconstrictive responses in a mathematical model of the rat afferent arteriole." April 2011.

Nieves-Gonzalez, A, Clausen, C, Layton, HE, Layton, AT, and Moore, LC. "Dynamical Properties of the Thick Ascending Limb (TAL): A Modeling Study." April 2011.

Marcano, M, Layton, AT, and Layton, HE. "Maximum urine concentrating capability for transport parameters and urine flow within prescribed ranges." April 2007.

Layton, HE, Layton, AT, and Moore, LC. "A mechanism for the generation of harmonics in oscillations mediated by tubuloglomerular feedback." April 2007.

Marcano, M, Layton, AT, and Layton, HE. "Estimation of collecting duct parameters for maximum urine concentrating capability in a mathematical model of the rat inner medulla." March 7, 2006.

Moore, LC, Siu, KL, Layton, AT, Layton, HE, and Chon, KH. "Evidence for multi-stability of the tubuloglomerular feedback system in spontaneously-hypertensive rats (SHR)." March 6, 2006.

Layton, AT, Moore, LC, and Layton, HE. "Dynamics in coupled nephrons may contribute to irregular flow oscillations in spontaneously hypertensive rats." March 6, 2006.