
Harold Layton, Professor of Mathematics and CNCS: Center for nonlinear and complex systems
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 timedelays,
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:
Teaching (Fall 2016):
 MATH 477S.01, MATH MODELING WITH WRITING
Synopsis
 Physics 299, TuTh 11:45 AM01:00 PM
 Education:
Ph.D.  Duke University  1986 
M.S.  University of Kentucky at Lexington  1980 
B.A.  Asbury College  1979 
 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 timedelays,
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 (1996/091998/08)
 Recent Publications
(More Publications)
 Sands, JM; Layton, HE, Advances in understanding the urineconcentrating mechanism.,
Annual Review of Physiology, vol. 76
(January, 2014),
pp. 387409, ISSN 00664278 [doi] [abs]
 Sands, JM; Mount, DB; Layton, HE, The physiology of water homeostasis,
in Core Concepts in the Disorders of Fluid, Electrolytes and AcidBase Balance
(November, 2013),
pp. 128, ISBN 9781461437703 [doi] [abs]
 NievesGonzález, A; Clausen, C; Layton, AT; Layton, HE; Moore, LC, Transport efficiency and workload distribution in a mathematical model of the thick ascending limb.,
American journal of physiology. Renal physiology, vol. 304 no. 6
(March, 2013),
pp. F653F664 [23097466], [doi] [abs]
 Sands, JM; Layton, HE, The Urine Concentrating Mechanism and Urea Transporters,
Seldin and Geibisch's The Kidney, vol. 1
(2013),
pp. 14631510 [doi]
 Layton, AT; Layton, HE, Countercurrent multiplication may not explain the axial osmolality gradient in the outer medulla of the rat kidney.,
American journal of physiology. Renal physiology, vol. 301 no. 5
(November, 2011),
pp. F1047F1056 [21753076], [doi] [abs]
