Math @ Duke

Anita T Layton, Robert R. and Katherine B. Penn Professor
 Contact Info:
Teaching (Fall 2015):
 MATH 161FS.01, MATHEMATICAL MODELS IN BIOLOGY
Synopsis
 Physics 227, TuTh 10:05 AM11:20 AM
 FOCUS 195FS.26, SPECIAL TOPICS IN FOCUS
Synopsis
 East Union 01, M 06:00 PM07:30 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)
 Postdocs Mentored
 Austin Baird (August 01, 2014  present)
 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)
 Ioannis Sgouralis and Anita T. Layton, Modeling blood flow and oxygenation in a diabetic rat kidney, submitted,
in AWM proceedings for NIMBioS WS for Women in Mathematical Biology
(Submitted, 2015)
 Luke Xie, Anita Layton, Nian Wang, Peder Larson, Jeff Zhang, Vivian Lee, Chunlei Liu, and G. Allan Johnson, Dynamic contrastenhanced quantitative susceptibility mapping at ultrashort echo time for evaluating renal function,
Am J Physiol Renal Physiol, submitted
(Submitted, 2015)
 Anita T. Layton, Mathematical physiology,
in Princeton Companion to Applied Mathematics, edited by Nicholas J. Higham
(2015), ISBN 9780691150390
 Ioannis Sgouralis, Roger Evans, Bruce S. Gardiner, Julian A Smith, Brendan C. Fry, and Anita T. Layton, Renal hemodynamics, function and oxygenation during cardiac surgery performed on cardiopulmonary bypass: A modeling study,
Physiol Report, vol. 3 no. 1
(2015)
 H. Nganguia, Y.N. Young, A.T. Layton, W.F. Hu, and M.C. Lai, An immersed interface method for axisymmetric electrohydrodynamic simulations in Stokes flow,
Comm Comput Phys, in press
(Accepted, 2015)
 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

