Anita T. Layton, Robert R. & Katherine B. Penn Professor of Mathematics and Professor of Biomedical Engineering and Professor in Medicine of Medicine, Nephrology
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.  Contact Info:
Office Location:  213  Office Phone:  (919) 6606971  Email Address:    Education:
Ph.D.  University of Toronto (Canada)  2001 
M.S.  University of Toronto (Canada)  1996 
B.S.  Duke University  1994 
B.A.  Duke University  1994 
 Specialties:

Mathematical Biology
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
 Keywords:
Absorption • Actin Cytoskeleton • Algorithms • Animals • Aquaporin 1 • Arterioles • Biological Clocks • Biological Transport • Biological Transport, Active • Blood Pressure • Blood Vessels • Body Water • Calcium • Calcium Channels • Calibration • Calmodulin • Capillary Permeability • cdc42 GTPBinding Protein • cdc42 GTPBinding Protein, Saccharomyces cerevisiae • Cell Membrane Permeability • Cell Polarity • Cell Size • Chlorides • Compliance • Computer Simulation • Diet • Diffusion • Electric Stimulation • Endocytosis • Endothelium, Vascular • Energy Metabolism • Enzyme Activation • Exocytosis • Feedback • Feedback, Physiological • Fluorescence Recovery After Photobleaching • Gap Junctions • Glomerular Filtration Rate • Hemodynamics • Homeostasis • Humans • Hyaluronic Acid • Hydrodynamics • HydrogenIon Concentration • Hydrostatic Pressure • Hypertrophy • Immunohistochemistry • Ion Transport • Kidney • Kidney Concentrating Ability • Kidney Diseases • Kidney Glomerulus • Kidney Medulla • Kidney Tubules • Kidney Tubules, Collecting • Kidney Tubules, Proximal • Kinetics • Loop of Henle • Male • Mathematics • Membrane Potentials • Membrane Transport Proteins • Mice • Microvessels • Models, Animal • Models, Biological • Models, Statistical • Models, Theoretical • Muscle Contraction • Muscle Relaxation • Muscle, Smooth, Vascular • MyosinLightChain Kinase • Nephrons • Neural Conduction • Neurons, Afferent • Nonlinear Dynamics • Numerical Analysis, ComputerAssisted • Osmolar Concentration • Oxygen • Oxygen Consumption • Oxyhemoglobins • Periodicity • Permeability • Potassium • Pressure • Protein Binding • Protein Isoforms • Protein Transport • Quail • Rats • Rats, Inbred SHR • Rats, Wistar • Renal Circulation • Saccharomyces cerevisiae • Saccharomyces cerevisiae Proteins • Septins • Signal Transduction • SNARE Proteins • Sodium • Sodium Chloride • SodiumPotassiumExchanging ATPase • Stokes flow • Symporters • Systole • Transport Vesicles • Urea • Urine • Vasodilation • Vasomotor System • Water
 Curriculum Vitae
 Current Ph.D. Students
(Former Students)
 Postdocs Mentored
 Ying Chen (August 15, 2015  present)
 Lei Li (August 01, 2015  present)
 Austin Baird (August 1, 2014  June 30, 2015)
 Brendan Fry (August 1, 2013  July 31, 2015)
 Gregory Herschlag (August 1, 2013  present)
 Rob Moss (October 1, 2012  July 31, 2014)
 Aniel NievesGonzales (January 1, 2011  July 31, 2012)
 Natasha Savage (October 18, 2010  July 31, 2012)
 Karin Leiderman (August 1, 2010  July 31, 2012)
 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 1, 2007  August 31, 2008)
 Undergraduate Research Supervised
 Ruijing (Bryan) Liu (May 1, 2015  present)
 Dev Dabke (January 1, 2015  present)
 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 1, 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 1, 2008  April 1, 2009)
Thesis: Expanding the scope of quantitative FRAP analysis
 Recent Publications
(More Publications)
 Edwards, A; Layton, AT, Cell Volume Regulation in the Proximal Tubule of Rat Kidney : Proximal Tubule Cell Volume Regulation.,
Bulletin of Mathematical Biology, vol. 79 no. 11
(November, 2017),
pp. 25122533 [doi] [abs]
 Burt, T; Noveck, RJ; MacLeod, DB; Layton, AT; Rowland, M; Lappin, G, IntraTarget Microdosing (ITM): A Novel Drug Development Approach Aimed at Enabling Safer and Earlier Translation of Biological Insights Into Human Testing.,
Clinical and Translational Science, vol. 10 no. 5
(September, 2017),
pp. 337350 [doi]
 Sgouralis, I; Evans, RG; Layton, AT, Renal medullary and urinary oxygen tension during cardiopulmonary bypass in the rat.,
Mathematical Medicine and Biology: A Journal of the IMA, vol. 34 no. 3
(September, Submitted, 2017),
pp. 313333 [doi] [abs]
 Chen, Y; Sullivan, JC; Edwards, A; Layton, AT, Sexspecific computational models of the spontaneously hypertensive rat kidneys: factors affecting nitric oxide bioavailability.,
American Journal of Physiology: Renal Physiology, vol. 313 no. 2
(August, 2017),
pp. F174F183 [doi] [abs]
 Layton, AT; Edwards, A; Vallon, V, Adaptive changes in GFR, tubular morphology, and transport in subtotal nephrectomized kidneys: modeling and analysis.,
American Journal of Physiology: Renal Physiology, vol. 313 no. 2
(August, 2017),
pp. F199F209 [doi] [abs]
 Recent Grant Support
 Unraveling Kidney Physiology, Pathophysiology & Therapeutics: A Modeling Approach, National Institutes of Health, 1R01DK10610201A1, 2016/052020/04.
 Collaborative Research: NIGMS: Comparitive Study of Desert and nonDesert Rodent Kidneys, National Science Foundation, DMS1263995, 2013/092018/08.
 Collaborative Research: NIGMS: Comparitive Study of Desert and nonDesert Rodent Kidneys, National Science Foundation, DMS1263995, 2013/092018/08.
 Collaborative Research: Comparative Study of Desert and Nondesert Rodent Kidneys, National Science Foundation, 2013/092017/08.
 EMSW21RTG:, National Science Foundation, DMS0943760, 2010/092017/08.
 Modeling Solute Transport and Urine Concentrating Mechanism in the Rat Kidney, National Institutes of Health, 2010/082016/07.
