Math @ Duke
Anita T Layton, Robert R. and Katherine B. Penn Professor
- Contact Info:
Teaching (Fall 2015):
- MATH 161FS.01, MATHEMATICAL MODELS IN BIOLOGY
- Physics 227, TuTh 10:05 AM-11:20 AM
- FOCUS 195FS.26, SPECIAL TOPICS IN FOCUS
- East Union 01, M 06:00 PM-07:30 PM
|PhD||University of Toronto||2001|
|MS||University of Toronto||1996|
- Research Interests: Mathematical physiology; Multiscale numerical methods; Numerical methods for immersed boundary problems.
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.
- Areas of Interest:
- Mathematical physiology
Multiscale numerical methods
- Curriculum Vitae
- Current Ph.D. 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 Nieves-Gonzales (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
- 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
- Luke Xie, Anita Layton, Nian Wang, Peder Larson, Jeff Zhang, Vivian Lee, Chunlei Liu, and G. Allan Johnson, Dynamic contrast-enhanced quantitative susceptibility mapping at ultrashort echo time for evaluating renal function,
Am J Physiol Renal Physiol, submitted
- Anita T. Layton, Mathematical physiology,
in Princeton Companion to Applied Mathematics, edited by Nicholas J. Higham
(2015), ISBN 978-0691150390
- 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
- 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
- Recent Grant Support
- Collaborative Research: Comparative Study of Desert and Non-desert Rodent Kidneys, National Science Foundation, 2013/09-2017/08.
- Modeling Solute Transport and Urine Concentrating Mechanism in the Rat Kidney, National Institutes of Health, 2010/08-2015/07.
- EMSW21-RTG: Enhanced Training and Recruitment in Mathematical Biology,, National Science Foundation, 2010/07-2015/07.
- EMSW21-RTG: Enhanced Training and Recruitment in Mathematical Biology, National Science Foundation, DMS-0943760, 2010/09-2014/08.
- Mathematical Model of Vascular and Tubular Transport in the Rat Outer Medulla, National Institutes of Health, 2009/07-2013/06.
Duke University, Box 90320
Durham, NC 27708-0320