# 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.

Bass Fellow. Duke University. July 2013

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 2017

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

Bioinformatics and Computational Biology Training Program awarded by National Institutes of Health (Mentor). 2005 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. "A new microscope for the kidney: mathematics." *American journal of physiology. Renal physiology* 312.4 (April 2017): F671-F672.
Full Text

Jiang, T, Li, Y, Layton, AT, Wang, W, Sun, Y, Li, M, Zhou, H, and Yang, B. "Generation and phenotypic analysis of mice lacking all urea transporters." *Kidney international* 91.2 (February 2017): 338-351.
Full Text

Layton, AT, Laghmani, K, Vallon, V, and Edwards, A. "Solute transport and oxygen consumption along the nephrons: effects of Na+ transport inhibitors." *American journal of physiology. Renal physiology* 311.6 (December 2016): F1217-F1229.
Full Text

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.
Full Text

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.
Full Text

Sgouralis, I, Evans, RG, and Layton, AT. "Renal medullary and urinary oxygen tension during cardiopulmonary bypass in the rat." *Mathematical medicine and biology : a journal of the IMA* (June 8, 2016).

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

## 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, AT, Rouse, DC, Chin, BB, Hawk, TC, Weitzel, DH, Cohen-Wolkowiez, M, Chow, S, and Noveck, RJ. "INTRA-ARTERIAL MICRODOSING (IAM), A NOVEL DRUG DEVELOPMENT APPROACH, PROOF OF CONCEPT IN RATS." August 2015.

Layton, AT. "Impacts of Facilitated Urea Transporters on the Urine-Concentrating Mechanism in the Rat Kidney." 2014. Full Text

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

Olson, SD, and Layton, AT. "Simulating Biofluid-Structure Interactions with an Immersed Boundary Framework - A Review." 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

Spring Breakthrough is a risk-free opportunity for first- and second-year students to explore their intellectual interests. For five days during spring break (March 12-16, 2017), they can participate in a mini-seminar designed to be intellectually... read more »

Q. How can math be used to keep us healthy and safe? We have all sorts of data at our fingertips – on healthcare trials and treatments, crime statistics, and weather patterns for example. But how do we use the data to make the best and most ethical... read more »