**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.

Office Location: | 213 |

Office Phone: | (919) 660-6971 |

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 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

Scientific computing

Multiscale numerical methods

Fluid-structure 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 GTP-Binding Protein • cdc42 GTP-Binding 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 • Hydrogen-Ion 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 • Myosin-Light-Chain Kinase • Nephrons • Neural Conduction • Neurons, Afferent • Nonlinear Dynamics • Numerical Analysis, Computer-Assisted • 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 • Sodium-Potassium-Exchanging ATPase • Stokes flow • Symporters • Systole • Transport Vesicles • Urea • Urine • Vasodilation • Vasomotor System • Water

**Current Ph.D. 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 Nieves-Gonzales (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**- 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. 2512-2533 [doi] [abs] - Burt, T; Noveck, RJ; MacLeod, DB; Layton, AT; Rowland, M; Lappin, G,
*Intra-Target 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. 337-350 [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. 313-333 [doi] [abs] - Chen, Y; Sullivan, JC; Edwards, A; Layton, AT,
*Sex-specific 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. F174-F183 [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. F199-F209 [doi] [abs]

- Edwards, A; Layton, AT,

**Recent Grant Support***Unraveling Kidney Physiology, Pathophysiology & Therapeutics: A Modeling Approach*, National Institutes of Health, 1R01-DK106102-01A1, 2016/05-2020/04.*Collaborative Research: NIGMS: Comparitive Study of Desert and non-Desert Rodent Kidneys*, National Science Foundation, DMS-1263995, 2013/09-2018/08.*Collaborative Research: NIGMS: Comparitive Study of Desert and non-Desert Rodent Kidneys*, National Science Foundation, DMS-1263995, 2013/09-2018/08.*Collaborative Research: Comparative Study of Desert and Non-desert Rodent Kidneys*, National Science Foundation, 2013/09-2017/08.*EMSW21-RTG:*, National Science Foundation, DMS-0943760, 2010/09-2017/08.*Modeling Solute Transport and Urine Concentrating Mechanism in the Rat Kidney*, National Institutes of Health, 2010/08-2016/07.