# Anita T. Layton

- Research Professor of Mathematics
- 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

**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 2020

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

Layton, A. T., and L. A. Miller. *Preface*. Vol. 8, 2017, pp. v–vi.

Layton, A. T., and L. A. Miller. *Erratum: Women in Mathematical Biology (Association for Women in Mathematics Series, 2017, 8, 10.1007/978-3-319-60304-9)*. Vol. 8, 2017. *Scopus*, doi:10.1007/978-3-319-60304-9_13.
Full Text

Fields, B., and K. Page. *Preface*. Vol. 2015-June, 2015.

Ahmed, Sameed, and Anita T. Layton. “Sex-specific computational models for blood pressure regulation in the rat.” *American Journal of Physiology. Renal Physiology*, vol. 318, no. 4, Apr. 2020, pp. F888–900. *Epmc*, doi:10.1152/ajprenal.00376.2019.
Full Text

Edwards, Aurélie, et al. “A model of mitochondrial O2 consumption and ATP generation in rat proximal tubule cells.” *American Journal of Physiology. Renal Physiology*, vol. 318, no. 1, Jan. 2020, pp. F248–59. *Epmc*, doi:10.1152/ajprenal.00330.2019.
Full Text

Hu, Rui, et al. “Functional implications of the sex differences in transporter abundance along the rat nephron: modeling and analysis.” *American Journal of Physiology. Renal Physiology*, vol. 317, no. 6, Dec. 2019, pp. F1462–74. *Epmc*, doi:10.1152/ajprenal.00352.2019.
Full Text

Layton, Anita T. “Solute and water transport along an inner medullary collecting duct undergoing peristaltic contractions.” *American Journal of Physiology. Renal Physiology*, vol. 317, no. 3, Sept. 2019, pp. F735–42. *Epmc*, doi:10.1152/ajprenal.00265.2019.
Full Text

Layton, A. T. “Multiscale models of kidney function and diseases.” *Current Opinion in Biomedical Engineering*, vol. 11, Sept. 2019, pp. 1–8. *Scopus*, doi:10.1016/j.cobme.2019.09.006.
Full Text

Sadria, Mehrshad, et al. “Network centrality analysis of eye-gaze data in autism spectrum disorder.” *Computers in Biology and Medicine*, vol. 111, Aug. 2019, p. 103332. *Epmc*, doi:10.1016/j.compbiomed.2019.103332.
Full Text

Ahmed, Sameed, et al. “Understanding sex differences in long-term blood pressure regulation: insights from experimental studies and computational modeling.” *American Journal of Physiology. Heart and Circulatory Physiology*, vol. 316, no. 5, May 2019, pp. H1113–23. *Epmc*, doi:10.1152/ajpheart.00035.2019.
Full Text

Fattah, Hadi, et al. “How Do Kidneys Adapt to a Deficit or Loss in Nephron Number?” *Physiology (Bethesda, Md.)*, vol. 34, no. 3, May 2019, pp. 189–97. *Epmc*, doi:10.1152/physiol.00052.2018.
Full Text

Layton, Anita T. “Optimizing SGLT inhibitor treatment for diabetes with chronic kidney diseases.” *Biological Cybernetics*, vol. 113, no. 1–2, Apr. 2019, pp. 139–48. *Epmc*, doi:10.1007/s00422-018-0765-y.
Full Text

Layton, Anita T., and Harold E. Layton. “A computational model of epithelial solute and water transport along a human nephron.” *Plos Computational Biology*, vol. 15, no. 2, Feb. 2019, p. e1006108. *Epmc*, doi:10.1371/journal.pcbi.1006108.
Full Text

## Pages

Layton, A. T., and A. Edwards. *Introduction to Mathematical Modeling of Blood Flow Control in the Kidney*. Vol. 8, 2017, pp. 63–73. *Scopus*, doi:10.1007/978-3-319-60304-9_4.
Full Text

Ciocanel, M. V., et al. *Modeling Autoregulation of the Afferent Arteriole of the Rat Kidney*. Vol. 8, 2017, pp. 75–100. *Scopus*, doi:10.1007/978-3-319-60304-9_5.
Full Text

Sgouralis, I., and A. T. Layton. *Modeling Blood Flow and Oxygenation in a Diabetic Rat Kidney*. Vol. 8, 2017, pp. 101–13. *Scopus*, doi:10.1007/978-3-319-60304-9_6.
Full Text

Layton, A. T. *Tracking the Distribution of a Solute Bolus in the Rat Kidney*. Vol. 8, 2017, pp. 115–36. *Scopus*, doi:10.1007/978-3-319-60304-9_7.
Full Text

Burt, Tal, et al. “Intraarterial Microdosing: A Novel Drug Development Approach, Proof-of-Concept PET Study in Rats.” *J Nucl Med*, vol. 56, no. 11, 2015, pp. 1793–99. *Pubmed*, doi:10.2967/jnumed.115.160986.
Full Text

Burt, T., et al. “Intra-Arterial Microdosing (IAM), a novel Drug development approach, proof of concept in Rats.” *Clinical Therapeutics*, vol. 37, no. 8, Elsevier BV, 2015, pp. e40–41. *Crossref*, doi:10.1016/j.clinthera.2015.05.122.
Full Text

Layton, Anita. *Impacts of Facilitated Urea Transporters on the Urine-Concentrating Mechanism in the Rat Kidney*. American Mathematical Society, 2014, pp. 191–208. *Crossref*, doi:10.1090/conm/628/12518.
Full Text

Ryu, Hwayeon, and Anita Layton. *Feedback-Mediated Dynamics in a Model of Coupled Nephrons with Compliant Short Loop of Henle*. American Mathematical Society, 2014, pp. 209–38. *Crossref*, doi:10.1090/conm/628/12542.
Full Text

Olson, Sarah, and Anita Layton. *Simulating Biofluid-Structure Interactions with an Immersed Boundary Framework – A Review*. American Mathematical Society, 2014, pp. 1–36. *Crossref*, doi:10.1090/conm/628/12545.
Full Text

Gilbert, Rebecca L., et al. “Role of interstitial nodal spaces in the urine concentrating mechanism of the rat kidney.” *Faseb Journal*, vol. 26, FEDERATION AMER SOC EXP BIOL, 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 »