Curriculum Vitae

Harold Layton

Department of Mathematics
Duke University
Box 90320
Durham, NC 27708 		(919) 660-2809 (office)
(email)
Education

A.B., mathematics, summa cum laude, Asbury college, 1979
M.S., physics, University of Kentucky, 1980
Ph.D., mathematics, Duke University, 1986

Areas of Research

Mathematical Physiology

Areas of Experience

Countercurrent Systems
Renal Modeling
Numerical Methods for Renal Models
Computational Biofluiddynamics

Major Grant Support

National Science Foundation: Mathematical Sciences Postdoctoral Research Fellow, 1986-1988, ``Mathematical Models of Kidney Function''
National Institutes of Health: First Independent Research Support and Transition Award, 1990-1994, ``Mathematical Models of Renal Dynamics''
National Institutes of Health: Regular Research (R01) Grant, 1995-2000, ``Mathematical Models of Renal Dynamics''
National Science Foundation: Group Infrastructure Grant, 1997-2000, ``Applications of Mathematics to Physiology'' (Michael C. Reed, principal investigator; H. E. Layton and J. JosephBlum, co-principal investigators)
National Institutes of Health: Regular Research (R01) Grant, 2000-2005, ``Mathematical Models of Renal Dynamics''
National Institutes of Health: Regular Research (R01) Grant, 2006-2010, ``Mathematical Models of Renal Dynamics''

Recent Grant Support

Professional Service

Director of Graduate Studies, July 01, 2008 - present  
Graduate Affairs Committee, January -- March 2008  
Reviewed papers for applied math/math biology/physiology journals, December 2008  
Selected Recent Invited Talks

The urine concentrating mechanism: insights from mathematical modeling, San Diego, CA, April 07, 2008  
The Urine concentrating mechanism of the inner medulla: functional significance of reconstructions based on new immunohistochemical data, San Diego, 15 December 2005  
The Urine Concentrating Mechanism of the Rat Kidney Inner Medulla, Emory University School of Medicine, Renal Division, May 18, 2004  
Irregular Oscillations in Nephron Flow Mediated by Tubuloglomerular Feedback, AMS Southeastern Sectional Meeting, University of North Carolina, Chapel Hill, North Carolina, 2003/10/24  
Spectral Complexity in TGF Limit-cycle Oscillations, Nephrons and Numbers: The Past and Furture of Renal Systems Physiology (a symposium in honor of Donald Marsh), San Deigo, California, 11 April 2003  
Formation of Concentrated Urine by Birds and Mammals, Seminar, Department of Physiology, McGill University, Montreal, Canada, 24 May 2002  
Oscillations in Nephron Flow Mediated by Tubuloglomerular Feedback, Centre for Nonlinear Dynamics, McGill University, Montreal, Canada, 23 May 2002  
Oscillations Mediated by Tubuloglomerular Feedback: Physiological Role and Pathophysiology, Special Session on Applications of Mathematics to Human Physiology and Medicine, at the 2001 National Meeting of the American Mathematical Society, New Orleans, LA, 12 January 2001  
Irregular Oscillations in Kidney Nephron Flow May Be Mediated by Tubuloglomerular Feedback (TGF), Minisymposium ``Mathematical Models for Physiology'' at the 2000 SIAM Annual Meeting, Rio Grande, Peurto Rico, 11 July 2000  
The Dynamic Kidney, Joint Seminar in Mathematics and Physiology, University of Minnesota, Minneapolis, MN, 25 February 1999  
Oscillations in the Tubuloglomerular Feedback System, Minisymposium ``Time Delays in Physiological and Neural System'' at the combined annual meetings of the Society for Industrial and Applied Mathematics and the Society for Mathematical Biology, University of Toronto, Toronto, Canada, 15 July 1998  
Doctoral Theses Directed

Kevin Jay Kesseler, Analysis of Feedback-Mediated Dynamics in Two Coupled Nephrons, (2001 - May 09, 2004)  
Darren Randall Oldson, Flow Perturbations in a Mathematical Model of the Tubuloglomerular Feedback System, (2003)  
Kayne Marie Arthurs, Flow Regulation in the Afferent Arteriole: An Application of the Immersed Boundary Method, (1996)  
Professional Affiliations

American Physiological Society
American Society of Nephrology
Society for Mathematical Biology

Publications

Books

  1. Harold E. Layton and Alan M. Weinstein, editors, Membrane Transport and Renal Physiology, (The IMA Volumes in Mathematics and its Applications, Volume 129) New York: Springer-Verlag, 2002

Papers Published

  1. Anita T. Layton, Leon C. Moore, Harold E. Layton, Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons, Bulletin of Mathematical Biology. 71(3):515-555, 2009. (April, 2009)
  2. Jeff M. Sands and Harold E. Layton, The physiology of urinary concentration: an update, Seminars in Nephrology, 29 (2): 178-195, 2009. (May, 2009)
  3. Thomas L. Pannabecker, William H. Dantzler, Harold E. Layton, and Anita T. Layton, Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla, American Journal of Physiology--Renal Physiology, 295: F1271 - F1285, 2008 (November, 2008)
  4. Paula Budu-Grajdeanu, Leon C. Moore, Harold E. Layton., Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop. Mathematical Biosciences 209(2): 564-592., Mathematical Biosciences (October, 2007)
  5. Jeff M. Sands and Harold E. Layton, The Urine Concentrating Mechanism and Urea Transporters, in The Kidney: Physiology and Pathophysiology, 4th Edition, edited by Robert J. Alpern and Steven C. Hebert (2007), pp. 1143–1178, Elsevier, New York
  6. Mariano Marcano, Anita T. Layton, and Harold E. Layton, An optimization algorithm for a distributed-loop model of an avian urine concentrating mechanism, The Bulletin of Mathematical Biology 68(7): 1625-1660, 2006 (October, 2006)
  7. Anita T. Layton, Leon C. Moore, Harold E. Layton, Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats, American Journal of Physiology-Renal Physiology 291 (Renal Physiology 60): F79-F97, 2006 (July, 2006)
  8. S. Randall Thomas, Anita T. Layton, Harold E. Layton, and Leon C. Moore, Kidney modelling: status and perspectives, Proceedings of the IEEE 94(4): 740-752, 2006. (April, 2006)
  9. Anita T. Layton and Harold E. Layton, A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla: I. Formulation and base-case results, American Journal of Physiology--Renal Physiology 289 (Renal Physiology 58): F1346-F1366, 2005 (December, 2005)
  10. Anita T. Layton and Harold E. Layton, A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla: II. Parameter sensitivity and tubular inhomogeneity, American Journal of Physiology--Renal Physiology 289 (Renal Physiology 58) : F1367 - F1381, 2005 (December, 2005)
  11. E. Bruce Pitman, Roman M. Zaritski, Kevin J. Kesseler, Leon C. Moore, and Harold E. Layton, Feedback-mediated dynamics in two coupled nephrons, Bulletin of Mathematical Biology, 66(6): 1463-1492, 2004
  12. Anita T. Layton, Thomas L. Pannabecker, William H. Dantzler, and Harold E. Layton, Two modes for concentrating urine in rat inner medulla, American Journal of Physiology, Renal Physiology, 287 (Renal Physiology, 56): F816-F839, 2004
  13. Oldson, Darren R., Leon C. Moore, and Harold E. Layton, Effect of sustained flow perturbations on stability and compensation of tubuloglomerular feedback, American Journal of Physiology, Renal Physiology, 285: F972-F989, 2003
  14. Marcano-Velazquez, M., and Harold E. Layton, An inverse algorithm for a mathematical model of an avian urine concentrating mechanism, Bulletin of Mathematical Biology 65: 665-691, 2003
  15. Layton, Anita T., and Harold E. Layton, An efficient numerical method for distributed-loop models of the urine concentrating mechanism, Mathematical Biosciences 181(2): 111-132, 2003
  16. Smith, Kayne M., Leon C. Moore, and Harold E. Layton, Advective transport of nitric oxide in a mathematical model of the afferent arteriole, American Journal of Physiology---Renal Physiology 284 (Renal Physiology 53): F1080-F1096, 2003
  17. Layton, Anita T., and Harold E. Layton, A region-based model framework for the rat urine concentrating mechanism, Bulletin of Mathematical Biology, 65: 859-901, 2003
  18. Layton, Anita T., and Harold E. Layton, A numerical method for renal models that represent abrupt changes in tubular properties, Journal of Mathematical Biology 45(5): 549-567, 2002.
  19. Pitman, E. Bruce, Roman M. Zaritski, Leon C. Moore, and Harold E. Layton, A reduced model for nephron flow dynamics mediated by tubuloglomerular feedback, In: Membrane Transport and Renal Physiology, The IMA Volumes in Mathematics and its Applications, Volume 129, edited by Harold E. Layton and Alan M. Weinstein. New York: Springer-Verlag, pp. 345-364, 2002.
  20. Layton, Harold E., Mathematical models of the mammalian urine concentrating mechanism, In: Membrane Transport and Renal Physiology, The IMA Volumes in Mathematics and Its Applications, Volume 129, edited by Harold E. Layton and Alan M. Weinstein. New York, Springer-Verlag, pp. 233-272, 2002.
  21. Layton, Anita T., and Harold E. Layton, A semi-Lagrangian semi-implicit numerical method for models of the urine concentrating mechanism, SIAM Journal on Scientific Computing, 23(5): 1526-1548, 2002.
  22. Zaritski, Roman M., E. Bruce Pitman, Harold E. Layton and Leon C. Moore, Coupling a tubuloglomerular feedback nephron model with a myogenic afferent arteriole model, In: Computing and Information Technologies (Proceedings of the International Conference on Computing and Information Technologies, Montclair State University, Upper Montclair, NJ, USA, 12 October 2001), edited by George Antoniou and Dorothy Deremer. World Scientific Publishing Co. Pte. Ltd., 2001, p. 55-62.
  23. Layton, H.E., John M. Davies, Giovanni Casotti, and Eldon J. Braun, Mathematical model of an avian urine concentrating mechanism, American Journal of Physiology-Renal Physiology 279 (Renal Physiology 48): F1139-F1160, 2000.
  24. Sands, Jeff M., and Harold E. Layton, Urine concentrating mechanism and its regulation, Chapter 45 in: The Kidney: Physiology and Pathophysiology (third edition), edited by D. W. Seldin and G. Giebisch. Philadelphia: Lippincott Williams & Wilkins, 2000, p. 1175-1216.
  25. Layton, H. E., E. Bruce Pitman, and Leon C. Moore, Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery, American Journal of Physiology 278 (Renal Physiology 47): F287-F301, 2000.
  26. Arthurs, Kayne M., Leon C. Moore, Charles S. Peskin, E. Bruce Pitman, and H. E. Layton, Modeling arteriolar flow and mass transport using the immersed boundary method, Journal of Computational Physics 147 (2): 402-440, 1998.
  27. Layton, H. E., E. Bruce Pitman, and Leon C. Moore, Spectral properties of the tubuloglomerular feedback system, American Journal of Physiology 273 (Renal Physiology 42): F635-F649, 1997.
  28. Layton, H. E., E. Bruce Pitman, and Leon C. Moore, Nonlinear filter properties of the thick ascending limb, American Journal of Physiology 273 (Renal Physiology 42): F625-F634, 1997.
  29. Pitman, E. B., and H. E. Layton, Mass conservation in a dynamic numerical method for a model of the urine concentrating mechanism, Conference proceedings of The Third International Congress on Industrial and Applied Mathematics, appearing in Zeitschrift fuer Angewandte Mathematik und Mechanik 76(S4): 45-48, 1996.
  30. Layton, H. E., L. C. Moore, and E. B. Pitman, Spectral properties of the TGF pathway, Conference proceedings of The Third International Congress on Industrial and Applied Mathematics, appearing in Zeitschrift fuer Angewandte Mathematik und Mechanik 76(S4): 33-35, 1996.
  31. Layton, H. E., Mark A. Knepper, and Chung-Lin Chou, Permeability criteria for effective function of passive countercurrent multiplier, American Journal of Physiology 270 (Renal Fluid Electrolyte Physiology 39): F9-F20, 1996.
  32. Layton, H. E., E. Bruce Pitman, and Mark A. Knepper, A dynamic numerical method for models of the urine concentrating mechanism, SIAM Journal on Applied Mathematics 55(5): 1390-1418, October, 1995.
  33. Layton, H. E., E. Bruce Pitman, and Leon C. Moore, Instantaneous and steady-state gains in the tubuloglomerular feedback system, American Journal of Physiology 268 (Renal Fluid Electrolyte Physiology 37): F163-F174, 1995.
  34. Pitman, E. Bruce, H. E. Layton, and Leon C. Moore, Numerical simulation of propagating concentration profiles in renal tubules, Bulletin of Mathematical Biology 56(3): 567-586, 1994.
  35. Layton, H. E., and E. Bruce Pitman, A dynamic numerical method for models of renal tubules, Bulletin of Mathematical Biology 56(3): 547-556, 1994.
  36. Layton, H. E., and John M. Davies, Distributed solute and water reabsorption in a central core model of the renal medulla, Mathematical Biosciences 116: 169-196, 1993.
  37. Chou, Chung-Lin, Mark A. Knepper, and H. E. Layton, Urinary concentrating mechanism: role of the inner medulla, Seminars in Nephrology 13(2): 168-181, 1993.
  38. Pitman, E. Bruce, H. E. Layton, and Leon C. Moore, Dynamic flow in the nephron: filtered delay in the TGF pathway, in Fluid Dynamics in Biology: Proceedings of the AMS-IMS-SIAM Joint Research Conference, July 1991, Edited by Angela Cheer and C. P. van Dam, appearing as Contemporary Mathematics (American Mathematical Society) 141: 317-336, 1993.
  39. Knepper, M. A., C.-L. Chou, and H. E. Layton, How is urine concentrated by the inner medulla?, In: Moving Points in Nephrology, edited by E. Bourke, N. P. Mallick, and V. E. Pollak, appearing as Contributions to Nephrology, Vol. 102, pp. 144-160, S. Karger, Basel, 1993.
  40. Jamison, Rex L., Dennis R. Roy, and Harold E. Layton, Countercurrent mechanism and its regulation, Chapter 7 in Clinical Disturbances of Water Metabolism, edited by D. W. Seldin and G. Giebisch. New York: Raven Press, 1993, p. 119-156. (This chapter is an abridgment of the 1992 chapter by the same authors.)
  41. Roy, Dennis R., Jr., Harold E. Layton, and Rex L. Jamison, Countercurrent mechanism and its regulation, Chapter 45 in The Kidney: Physiology and Pathophysiology (second edition), edited by D. W. Seldin and G. Giebisch. New York: Raven Press, 1992, p. 1649-1692.
  42. Layton, H. E., E. Bruce Pitman, and Leon C. Moore, Bifurcation analysis of TGF-mediated oscillations in SNGFR, American Journal of Physiology 259 (Renal Fluid Electrolyte Physiology 30): F904-F919, 1991.
  43. Layton, H. E., Distributed loops of Henle in a central core model of the renal medulla: Where should the solute come out?, Proceedings of the Seventh International Conference on Mathematical and Computer Modelling in Science and Technology, Mathematical and Computer Modelling 14: 533-537, 1990.
  44. Layton, H. E., and E. Bruce Pitman, Oscillations in a simple model of tubuloglomerular feedback, Proceedings of the Twelfth Annual International Conference of the Institute of Electrical and Electronics Engineers/Engineering in Medicine and Biology Society 12(3): 987-988, 1990.
  45. Layton, H. E., Urea transport in a distributed loop model of the urine concentrating mechanism, American Journal of Physiology 258 (Renal Fluid Electrolyte Physiology 27): F1110-F1124, 1990.
  46. Layton, H. E., Concentrating urine in the inner medulla of the kidney, Comments on Theoretical Biology 1(3): 179-196, 1989.
  47. Pitman, E. Bruce, and H. E. Layton, Tubuloglomerular feedback in a dynamic nephron, Communications on Pure and Applied Mathematics 42: 759-787, 1989.
  48. Layton, H. E., Energy advantage of counter-current oxygen exchange in fish gills, Journal of Theoretical Biology 125: 307-316, 1987.
  49. Layton, H. E., Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism, Mathematical Biosciences 84: 197-210, 1987.
  50. Layton, H. E., Distribution of Henle's loops may enhance urine concentrating capability, Biophysical Journal 49: 1033-1040, 1986.

Papers Accepted

  1. Mariano Marcano, Anita T. Layton, and Harold E. Layton, Maximum urine concentrating capability for transport parameters and urine flow within prescribed ranges (2009)
Last modified: 2009/07/29