CNCS Center for Nonlinear and Complex Systems
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Harold Layton, Professor of Mathematics and CNCS: Center for nonlinear and complex systems

Harold Layton

Professor Layton is modeling renal function at the level of the nephron (the functional unit of the kidney) and at the level of nephron populations. In particular, he is studying tubuloglomerular feedback (TGF), the urine concentrating mechanism, and the hemodynamics of the afferent arteriole. Dynamic models for TGF and the afferent arteriole involve small systems of semilinear hyperbolic partial differential equations (PDEs) with time-delays, and coupled ODES, which are solved numerically for cases of physiological interest, or which are linearized for qualitative analytical investigation. Dynamic models for the concentrating mechanism involve large systems of coupled hyperbolic PDEs that describe tubular convection and epithelial transport. Numerical solutions of these PDEs help to integrate and interpret quantities determined by physiologists in many separate experiments.

Contact Info:
Office Location:  221 Physics Bldg, Durham, NC 27708
Office Phone:  (919) 660-2809
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~layton

Teaching (Fall 2016):

  • MATH 477S.01, MATH MODELING WITH WRITING Synopsis
    Physics 299, TuTh 11:45 AM-01:00 PM
Education:

Ph.D.Duke University1986
M.S.University of Kentucky at Lexington1980
B.A.Asbury College1979
Specialties:

Applied Math
Research Interests: Mathematical Physiology

Professor Layton is modeling renal function at the level of the nephron (the functional unit of the kidney) and at the level of nephron populations. In particular, he is studying tubuloglomerular feedback (TGF), the urine concentrating mechanism, and the hemodynamics of the afferent arteriole. Dynamic models for TGF and the afferent arteriole involve small systems of semilinear hyperbolic partial differential equations (PDEs) with time-delays, and coupled ODES, which are solved numerically for cases of physiological interest, or which are linearized for qualitative analytical investigation. Dynamic models for the concentrating mechanism involve large systems of coupled hyperbolic PDEs that describe tubular convection and epithelial transport. Numerical solutions of these PDEs help to integrate and interpret quantities determined by physiologists in many separate experiments.

Keywords:

Absorption • Algorithms • Animals • Arterioles • Biological Clocks • Biological Transport, Active • Blood Pressure • Blood Vessels • Body Water • Calcium • Calcium Channels • Capillary Permeability • Cell Membrane Permeability • Cell Size • Compliance • Computer Simulation • Diet • Diffusion • Feedback • Feedback, Physiological • Glomerular Filtration Rate • Hemodynamics • Homeostasis • Humans • Hydrodynamics • Hypertrophy • Ion Transport • Kidney • Kidney Concentrating Ability • Kidney Diseases • Kidney Glomerulus • Kidney Medulla • Kidney Tubules • Kidney Tubules, Collecting • Loop of Henle • Mathematics • Membrane Potentials • Mice • Models, Animal • Models, Biological • Models, Statistical • Models, Theoretical • Muscle, Smooth, Vascular • Nephrons • Nonlinear Dynamics • Osmolar Concentration • Periodicity • Permeability • Potassium • Rats • Rats, Inbred SHR • Signal Transduction • Sodium • Sodium Chloride • Systole • Urea • Urine

Curriculum Vitae
Current Ph.D. Students   (Former Students)

    Postdocs Mentored

    • Amal El Moghraby (July 01, 2008 - May 31, 2009)  
    • Paula Budu (September 14, 2002 - August 31, 2005)  
    • Monica M. Romeo (September 1, 2001 - May 31, 2004)  
    • Kayne Marie Arthurs (1996/09-1998/08)  
    Recent Publications   (More Publications)

    1. JM Sands and HE Layton, Advances in understanding the urine-concentrating mechanism., Annual review of physiology, vol. 76 (January, 2014), pp. 387-409, ISSN 0066-4278 [doi]  [abs]
    2. JM Sands, DB Mount and HE Layton, The physiology of water homeostasis, in Core Concepts in the Disorders of Fluid, Electrolytes and Acid-Base Balance, scopus (November, 2013), pp. 1-28, ISBN 1461437695 [doi]  [abs]
    3. A Nieves-Gonz├ílez, C Clausen, AT Layton, HE Layton and LC Moore, Transport efficiency and workload distribution in a mathematical model of the thick ascending limb., Am J Physiol Renal Physiol, vol. 304 no. 6 (March, 2013), pp. F653-F664 [23097466], [doi]  [abs]
    4. JM Sands and HE Layton, The Urine Concentrating Mechanism and Urea Transporters, Seldin and Geibisch's The Kidney, vol. 1 (2013), pp. 1463-1510 [doi]
    5. AT Layton and HE Layton, Countercurrent multiplication may not explain the axial osmolality gradient in the outer medulla of the rat kidney., Am J Physiol Renal Physiol, vol. 301 no. 5 (November, 2011), pp. F1047-F1056 [21753076], [doi]  [abs]