# 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.

Bass Fellow. Duke University. July 2013

### Selected Grants

Bioinformatics and Computational Biology Training Program awarded by National Institutes of Health (Mentor). 2005 to 2021

Unraveling Kidney Physiology, Pathophysiology & Therapeutics: A Modeling Approach awarded by National Institutes of Health (Principal Investigator). 2016 to 2020

Collaborative Research: NIGMS: Comparitive Study of Desert and non-Desert Rodent Kidneys awarded by National Science Foundation (Principal Investigator). 2013 to 2019

EMSW21-RTG: awarded by National Science Foundation (Co-Principal Investigator). 2010 to 2017

Modeling Solute Transport and Urine Concentrating Mechanism in the Rat Kidney awarded by National Institutes of Health (Principal Investigator). 2010 to 2016

Modeling Fluid Dynamics and Solute Transport in the Kidney awarded by National Science Foundation (Principal Investigator). 2007 to 2012

Workshop on Fluid Motion awarded by National Science Foundation (Principal Investigator). 2010 to 2011

FAN 2010 awarded by National Science Foundation (Co-Principal Investigator). 2010 to 2011

A Conference on Applications of Analysis to Mathematical Biology awarded by National Science Foundation (Principal Investigator). 2007 to 2008

ADVANCE Fellows Award: Mathematical Modeling of Renal Physiology awarded by National Science Foundation (Principal Investigator). 2004 to 2007

Fields, B, and Page, K. "Preface." January 1, 2015.

Layton, AT. "Optimizing SGLT inhibitor treatment for diabetes with chronic kidney diseases." *Biological Cybernetics* 113.1-2 (April 2019): 139-148.
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Layton, AT, and Layton, HE. "A computational model of epithelial solute and water transport along a human nephron." *Plos Computational Biology* 15.2 (February 25, 2019): e1006108-null.
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Layton, AT, and Sullivan, JC. "Recent advances in sex differences in kidney function." *American Journal of Physiology. Renal Physiology* 316.2 (February 2019): F328-F331.
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Leete, J, and Layton, AT. "Sex-specific long-term blood pressure regulation: Modeling and analysis." *Computers in Biology and Medicine* 104 (January 2019): 139-148.
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Wei, N, Gumz, ML, and Layton, AT. "Predicted effect of circadian clock modulation of NHE3 of a proximal tubule cell on sodium transport." *American Journal of Physiology. Renal Physiology* 315.3 (September 2018): F665-F676.
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Li, Q, McDonough, AA, Layton, HE, and Layton, AT. "Functional implications of sexual dimorphism of transporter patterns along the rat proximal tubule: modeling and analysis." *American Journal of Physiology. Renal Physiology* 315.3 (September 2018): F692-F700.
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Layton, AT, and Vallon, V. "Renal tubular solute transport and oxygen consumption: insights from computational models." *Current Opinion in Nephrology and Hypertension* 27.5 (September 2018): 384-389.
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Layton, AT. "Sweet success? SGLT2 inhibitors and diabetes." *American Journal of Physiology. Renal Physiology* 314.6 (June 2018): F1034-F1035.
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Layton, AT, and Vallon, V. "SGLT2 inhibition in a kidney with reduced nephron number: modeling and analysis of solute transport and metabolism." *American Journal of Physiology. Renal Physiology* 314.5 (May 2018): F969-F984.
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Wei, N, and Layton, AT. "Theoretical assessment of the Ca 2 + oscillations in the afferent arteriole smooth muscle cell of the rat kidney." *International Journal of Biomathematics* 11.3 (April 1, 2018).
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## Pages

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." November 2015. Full Text

Burt, T, Wu, H, Layton, A, Rouse, D, Chin, B, Hawk, T, Weitzel, D, Cohen-Wolkowiez, M, Chow, S, and Noveck, R. "Intra-Arterial Microdosing (IAM), a novel Drug development approach, proof of concept in Rats." August 2015. Full Text

Layton, A. "Impacts of Facilitated Urea Transporters on the Urine-Concentrating Mechanism in the Rat Kidney.": American Mathematical Society, 2014. Full Text

Ryu, H, and Layton, A. "Feedback-Mediated Dynamics in a Model of Coupled Nephrons with Compliant Short Loop of Henle.": American Mathematical Society, 2014. Full Text

Olson, S, and Layton, A. "Simulating Biofluid-Structure Interactions with an Immersed Boundary Framework – A Review.": American Mathematical Society, 2014. Full Text

Gilbert, RL, Pannabecker, TL, and Layton, AT. "Role of interstitial nodal spaces in the urine concentrating mechanism of the rat kidney." April 2012.

Pannabecker, TL, Dantzler, WH, and Layton, AT. "Urine Concentrating Mechanism: Impact of Vascular and Tubular Architecture and a Proposed Descending Limb Urea-Na Cotransporter." April 2012.

Edwards, A, and Layton, AT. "Impact of nitric oxide-mediated vasodilation on outer medullary NaCl transport and oxygenation." April 2012.

Ryu, H, and Layton, AT. "Tubular Fluid Oscillations Mediated by Tubuloglomerular Feedback in a Short Loop of Henle." April 2012.

Sgouralis, I, and Layton, AT. "Interactions between Tubuloglomerular Feedback and the Myogenic Mechanism of the Afferent Arteriole." April 2012.

## Pages

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