Math @ Duke

Anita T Layton, Robert R. and Katherine B. Penn Associate Professor
 Contact Info:
Teaching (Fall 2014):
 MATH 161FS.01, MATHEMATICAL MODELS IN BIOLOGY
Synopsis
 Physics 227, MW 10:05 AM11:20 AM
 MATH 79077.01, CURR RSRCH MATHEMATICAL BIOL
Synopsis
 Physics 119, W 11:45 AM01:00 PM
 Education:
PhD  University of Toronto  2001 
MS  University of Toronto  1996 
BS  Duke University  1994 
BA  Duke University  1994 
 Specialties:

Applied Math
 Research Interests: Mathematical physiology; Multiscale numerical methods; Numerical methods for immersed boundary problems.
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 methodsmultiimplicit Picard integral deferred correction methodsfor the integration of partial differential equations arising in physical systems with dynamics that involve two or more processes with widelydiffering 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 operatingsplitting methods) while generating arbitrarily highorder 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.
 Areas of Interest:
Mathematical physiology Scientific computing Multiscale numerical methods Fluidstructure interactions
 Curriculum Vitae
 Current Ph.D. Students
(Former Students)
 Hwayeon Ryu
 Ioannis Sgouralis
 Postdocs Mentored
 Brendan Fry (August 01, 2013  July 31, 2016)
 Gregory Herschlag (August 01, 2013  July 31, 2016)
 Rob Moss (October 1, 2012  present)
 Aniel NievesGonzales (January 1, 2011  July 31, 2012)
 Natasha Savage (October 18, 2010  present)
 Karin Leiderman (August 01, 2010  present)
 Jing Chen (March 1, 2009  May 14, 2010)
 Elizabeth L. Bouzarth (August 1, 2008  July 31, 2011)
 Amal El Moghraby (July 1, 2008  May 31, 2009)
 Milagros Loreto (August 01, 2007  August 31, 2008)
 Undergraduate Research Supervised
 Justin Summerville (May 01, 2013  June 30, 2013)
 Alex Wertheim (May 13, 2012  June 30, 2012)
 Scott Cara (May 13, 2012  December 31, 2012)
 Kara Karpman (May 13, 2012  December 31, 2012)
 Angela Wood (May 18, 2011  July 01, 2011)
 Angelica Schwartz (May 18, 2011  July 01, 2011)
 Philip Pham (May 01, 2010  April 30, 2011)
 Peichun Wang (May 1, 2010  April 30, 2010)
 Anne Peterson (May 01, 2010  April 30, 2011)
 Yajing Gao (May, 2008  June, 2008)
 Amy Wen (May, 2008  June, 2008)
 Mark A Hallen (May 01, 2008  April 01, 2009)
Thesis: Expanding the scope of quantitative FRAP analysis
 Recent Publications
(More Publications)
 Aurelie Edwards and Anita T. Layton, Calcium dynamics underlying the myogenic response of the renal afferent arteriole,
Am J Physiol Renal Physiol, vol. 306 no. F34F48
(2014)
 Ioannis Sgouralis and Anita T. Layton, Theoretical assessment of renal autoregulatory mechanisms,
Am J Physiol Renal Physiol, vol. 306
(2014),
pp. F1357F1371
 Robert Moss and Anita T. Layton, Dominant factors that govern pressure natriuresis in diuresis and antidiuresis: a mathematical model,
Am J Physiol Renal Physiol, vol. 306
(2014),
pp. F952F969
 Yi Li, Ioannis Sgouralis, and Anita T. Layton, Computing viscous flow in an elastic tube,
Numer. Math. Theor. Meth. Appl., in press
(Accepted, 2014)
 Hwayeon Ryu and Anita T. Layton, Tubular fluid flow and distal NaCl delivery mediated by tubuloglomerular feedback in the rat kidney,
J Math Biol, vol. 68
(2014),
pp. 10231049
 Recent Grant Support
 Collaborative Research: Comparative Study of Desert and Nondesert Rodent Kidneys, National Science Foundation, 2013/092017/08.
 Modeling Solute Transport and Urine Concentrating Mechanism in the Rat Kidney, National Institutes of Health, 2010/082015/07.
 EMSW21RTG: Enhanced Training and Recruitment in Mathematical Biology,, National Science Foundation, 2010/072015/07.
 EMSW21RTG: Enhanced Training and Recruitment in Mathematical Biology, National Science Foundation, DMS0943760, 2010/092014/08.
 Mathematical Model of Vascular and Tubular Transport in the Rat Outer Medulla, National Institutes of Health, 2009/072013/06.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

