Curriculum Vitae

Harold Layton

Box 90320, Durham, NC 27708-0320 (919) 660-2809 (office)
(email)
Areas of Research

Mathematical Physiology

Areas of Interest

Mathematical models of renal hemodynamics
Mathematical models of the urine concentrating mechanism
Numerical methods for models of renal systems
Countercurrent systems in animals

Areas of Experience

Modeling countercurrent systems
Renal modeling
Numerical methods for renal models
Computational biofluiddynamics

Professional Experience / Employment History

Duke University
Professor, Department of Mathematics, July 01, 2001 - present
Associate Professor, Department of Mathematics, July 01, 1995 - June 30, 2001
Assistant Professor, Department of Mathematics, September 01, 1988 - June 30, 1995
Visiting Positions
Visiting Member: Courant Institute of the Mathematical Sciences, New York University, 1986 - 1988
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''

Professional Service

Chair
Chair, Department of Mathematics, Duke University, July 1, 2010 - present  
DGS
Director of Graduate Studies in Mathematics, Duke University, July 1, 2008 - June 30, 2009  
DUS
Director of Undergraduate Studies in Mathematics, Duke Unviersity, July 01, 1996 - June 30, 1999  
Dept Officer
Department Chair, 2009 - 2015  
Chair, Department of Mathematics, 1 July 2009--??, January 2010  
Selected Recent Invited Talks

Harmonics and Heterodyning in Renal Hemodynamics, Medical College of Wisconsin, April 18, 2012  
Dynamics of Tubuloglomerular Feedback, Vanderbilt University, Nashville Tennessee, May 20, 2009  
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. Layton, AT; Layton, HE, A computational model of epithelial solute and water transport along a human nephron., Plos Computational Biology, vol. 15 no. 2 (February, 2019), pp. e1006108
  2. Li, Q; McDonough, AA; Layton, HE; Layton, AT, Functional implications of sexual dimorphism of transporter patterns along the rat proximal tubule: modeling and analysis., American Journal of Physiology. Renal Physiology, vol. 315 no. 3 (September, 2018), pp. F692-F700
  3. Sands, JM; Layton, HE, Advances in understanding the urine-concentrating mechanism., Annual Review of Physiology, vol. 76 (January, 2014), pp. 387-409, ISSN 0066-4278
  4. Sands, JM; Mount, DB; Layton, HE, The physiology of water homeostasis, in Core Concepts in the Disorders of Fluid, Electrolytes and Acid-Base Balance (November, 2013), pp. 1-28, Springer US, ISBN 1461437695
  5. Sands, JM; Layton, HE, The Urine Concentrating Mechanism and Urea Transporters, vol. 1 (August, 2013), pp. 1463-1510, Elsevier
  6. Nieves-González, 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. F653-F664
  7. Jeff M. Sands, David B. Mount, and Harold E. Layton, The physiology of water homeostasis, in Core Concepts in the Disorders of Fluids, Electrolytes, and Acid-Base Balance, edited by David B. Mount, Ajay Singh, and Mo Sayegh (August, 2012), Springer
  8. Dantzler, WH; Layton, AT; Layton, HE; Pannabecker, TL, Urine concentrating mechanism in the inner medulla: function of the thin limbs of Henle’s loops, Clinical Journal of the American Society of Nephrology., vol. 9 no. 10 (August, 2012), pp. 1781-1789
  9. Layton, AT; Moore, LC; Layton, HE, Signal transduction in a compliant thick ascending limb., American Journal of Physiology. Renal Physiology, vol. 302 no. 9 (May, 2012), pp. F1188-F1202
  10. Nieves-Gonzalez, A; Clausen, C; Layton, AT; Layton, HE; Moore, LC, Efficiency and workload distribution in a mathematical model of the thick ascending limb, American Journal of Physiology Renal Physiology (2012)
  11. Nieves-Gonzalez, A; Clausen, C; Marcano, M; Layton, AT; Layton, HE; Moore, LC, Fluid dilution and efficiency of Na+ transport in a mathematical model of a thick ascending limb cell, American Journal of Physiology Renal Physiology, vol. 304 no. 6 (2012), pp. F634-F652
  12. 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. F1047-F1056
  13. Anita T. Layton and Harold E. Layton, Countercurrent multiplication may not explain the axial osmolality gradient in the outer medulla of the rat kidney, American Journal of Physiology--Renal Physiology 301: F1047-F1056 (November, 2011)
  14. Dantzler, WH; Pannabecker, TL; Layton, AT; Layton, HE, Urine concentrating mechanism in the inner medulla of the mammalian kidney: role of three-dimensional architecture., Acta Physiologica, vol. 202 no. 3 (July, 2011), pp. 361-378, ISSN 1748-1716
  15. Layton, AT; Bowen, M; Wen, A; Layton, HE, Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs., Mathematical Biosciences, vol. 230 no. 2 (April, 2011), pp. 115-127
  16. Chen, J; Sgouralis, I; Moore, LC; Layton, HE; Layton, AT, A mathematical model of the myogenic response to systolic pressure in the afferent arteriole., American Journal of Physiology. Renal Physiology, vol. 300 no. 3 (March, 2011), pp. F669-F681
  17. Anita T. Layton, Matthew Bowen, Amy Wen, and Harold E. Layton, Feedback-mediated dynamics in a model of coupled nephrons with compliant thick ascending limbs, Mathematical Biosciences Vol. 230: 115-127 (April 2011)
  18. Jeff M. Sands and Harold E. Layton, The urine concentrating mechanism and urea transporters, in Seldin and Giebische's The Kidney: Physiology and Pathophysiology, 5th Edition, edited by Robert Alphern, Orson Moe, & Michaeal Caplan (October, 2012), Elsevier/Academic Press
  19. Mariano Marcano, Anita T. Layton, and Harold E. Layton, Maximum urine concentrating capability for transport parameters and urine flow within prescribed ranges, Bulletin of Mathematical Biology 72:314-339, 2010 (April, 2010)
  20. Layton, AT; Pannabecker, TL; Dantzler, WH; Layton, HE, Functional implications of the three-dimensional architecture of the rat renal inner medulla., American Journal of Physiology. Renal Physiology, vol. 298 no. 4 (April, 2010), pp. F973-F987
  21. Layton, AT; Pannabecker, TL; Dantzler, WH; Layton, HE, Hyperfiltration and inner stripe hypertrophy may explain findings by Gamble and coworkers., American Journal of Physiology. Renal Physiology, vol. 298 no. 4 (April, 2010), pp. F962-F972
  22. Marcano, M; Layton, AT; Layton, HE, Maximum urine concentrating capability in a mathematical model of the inner medulla of the rat kidney., Bulletin of Mathematical Biology, vol. 72 no. 2 (February, 2010), pp. 314-339, ISSN 0092-8240
  23. Jeff M. Sands, Harold E. Layton, and Robert A. Fenton, Urine concentration and dilution, in Brenner and Rector's THE KIDNEY, 9th Edition, edited by Alan S. L. Yu (September 3, 2009), Saunders
  24. Layton, AT; Layton, HE; Dantzler, WH; Pannabecker, TL, The mammalian urine concentrating mechanism: hypotheses and uncertainties., Physiology (Bethesda, Md.), vol. 24 (August, 2009), pp. 250-256, ISSN 1548-9213
  25. Sands, JM; Layton, HE, The physiology of urinary concentration: an update., Seminars in Nephrology, vol. 29 no. 3 (May, 2009), pp. 178-195, ISSN 0270-9295
  26. Layton, AT; Moore, LC; Layton, HE, Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons., Bulletin of Mathematical Biology, vol. 71 no. 3 (April, 2009), pp. 515-555
  27. Sands, JM; Layton, HE, The Urine Concentrating Mechanism and Urea Transporters, in The Kidney: Physiology and Pathophysiology, 4th Edition, edited by Robert J. Alpern and Steven C. Hebert (December, 2008), pp. 1143-1178, Elsevier, New York
  28. Pannabecker, TL; Dantzler, WH; Layton, HE; Layton, AT, Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla., American Journal of Physiology. Renal Physiology, vol. 295 no. 5 (November, 2008), pp. F1271-F1285, ISSN 0363-6127
  29. Budu-Grajdeanu, P; Moore, LC; Layton, HE, Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop., Mathematical Biosciences, vol. 209 no. 2 (October, 2007), pp. 564-592, ISSN 0025-5564
  30. Budu-Grajdeanu, P; Moore, LC; Layton, HE, Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop. Mathematical Biosciences 209(2): 564-592, 2007, Mathematical Biosciences (October, 2007)
  31. Marcano, M; Layton, AT; Layton, HE, An optimization algorithm for a distributed-loop model of an avian urine concentrating mechanism., Bulletin of Mathematical Biology, vol. 68 no. 7 (October, 2006), pp. 1625-1660, ISSN 0092-8240
  32. Layton, AT; Moore, LC; Layton, HE, Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats., American Journal of Physiology. Renal Physiology, vol. 291 no. 1 (July, 2006), pp. F79-F97, ISSN 1931-857X
  33. Thomas, SR; Layton, AT; Layton, HE; Moore, LC, Kidney modeling: Status and perspectives, Proceedings of the Ieee, vol. 94 no. 4 (January, 2006), pp. 740-752, Institute of Electrical and Electronics Engineers (IEEE), ISSN 0018-9219
  34. Layton, AT; Layton, HE, 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, vol. 289 no. 6 (December, 2005), pp. F1346-F1366, ISSN 1931-857X
  35. Layton, AT; Layton, HE, 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, vol. 289 no. 6 (December, 2005), pp. F1367-F1381, ISSN 1931-857X
  36. Bruce Pitman, E; Zaritski, RM; Kesseler, KJ; Moore, LC; Layton, HE, Feedback-mediated dynamics in two coupled nephrons., Bulletin of Mathematical Biology, vol. 66 no. 6 , pp. 1463-1492
  37. Layton, AT; Pannabecker, TL; Dantzler, WH; Layton, HE, Two modes for concentrating urine in rat inner medulla., American Journal of Physiology. Renal Physiology, vol. 287 no. 4 , pp. F816-F839
  38. Oldson, DR; Moore, LC; Layton, HE, Effect of sustained flow perturbations on stability and compensation of tubuloglomerular feedback., American Journal of Physiology. Renal Physiology, vol. 285 no. 5 (November, 2003), pp. F972-F989
  39. Layton, AT; Layton, HE, A region-based model framework for the rat urine concentrating mechanism., Bulletin of Mathematical Biology, vol. 65 no. 5 (September, 2003), pp. 859-901
  40. Marcano-Velázquez, M; Layton, HE, An inverse algorithm for a mathematical model of an avian urine concentrating mechanism., Bulletin of Mathematical Biology, vol. 65 no. 4 (July, 2003), pp. 665-691
  41. Layton, AT; Layton, HE, An efficient numerical method for distributed-loop models of the urine concentrating mechanism., Mathematical Biosciences, vol. 181 no. 2 (February, 2003), pp. 111-132
  42. Smith, KM; Moore, LC; Layton, HE, Advective transport of nitric oxide in a mathematical model of the afferent arteriole, American Journal of Physiology Renal Physiology, vol. 284 no. 5 53-5 (2003), pp. F1080-F1096
  43. Layton, AT; Layton, HE, A semi-lagrangian semi-implicit numerical method for models of the urine concentrating mechanism, Siam Journal on Scientific Computing, vol. 23 no. 5 (December, 2002), pp. 1526-1548, Society for Industrial & Applied Mathematics (SIAM), ISSN 1064-8275
  44. Layton, AT; Layton, HE, A numerical method for renal models that represent tubules with abrupt changes in membrane properties., Journal of Mathematical Biology, vol. 45 no. 6 (December, 2002), pp. 549-567, ISSN 0303-6812
  45. Layton, HE; Davies, JM; Casotti, G; Braun, EJ, Mathematical model of an avian urine concentrating mechanism., American Journal of Physiology. Renal Physiology, vol. 279 no. 6 (December, 2000), pp. F1139-F1160, ISSN 0363-6127
  46. Layton, HE; Pitman, EB; Moore, LC, Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery., American Journal of Physiology. Renal Physiology, vol. 278 no. 2 (February, 2000), pp. F287-F301, ISSN 0363-6127
  47. Arthurs, KM; Moore, LC; Peskin, CS; Pitman, EB; Layton, HE, Modeling arteriolar flow and mass transport using the immersed boundary method, Journal of Computational Physics, vol. 147 no. 2 (December, 1998), pp. 402-440, Elsevier BV
  48. Layton, HE; Pitman, EB; Moore, LC, Potential natriuretic effects of limit-cycle oscillations mediated by tubuloglomerular feedback, Faseb Journal, vol. 12 no. 4 (1998), pp. A108, ISSN 0892-6638
  49. Pitman, EB; Zaritski, R; Moore, LC; Layton, HE, TGF-mediated bifurcation in two coupled nephrons, Faseb Journal, vol. 11 no. 3 (December, 1997), pp. A85, ISSN 0892-6638
  50. Arthurs, KM; Moore, LC; Pitman, EB; Layton, HE, Flow regulation in afferent arterioles following vascular injury, Faseb Journal, vol. 11 no. 3 (December, 1997), pp. A82, ISSN 0892-6638
  51. Layton, HE; Casotti, G; Davies, JM; Braun, EJ, Mathematical model of avian urine concentrating mechanism, Faseb Journal, vol. 11 no. 3 (December, 1997), pp. A9, ISSN 0892-6638
  52. Layton, HE; Pitman, EB; Moore, LC, Spectral properties of the tubuloglomerular feedback system, American Journal of Physiology Renal Physiology, vol. 273 no. 4 42-4 (1997), pp. F635-F649, ISSN 0363-6127
  53. Pitman, EB; Layton, HE, Mass conservation in a dynamic numerical method for a model of the urine concentrating mechanism, Zamm Zeitschrift Für Angewandte Mathematik Und Mechanik, vol. 76 no. SUPPL. 4 (December, 1996), pp. 45-48, ISSN 0044-2267
  54. Layton, HE; Pitman, EB; Moore, LC, Spectral properties of the TGF pathway, Zamm Zeitschrift Für Angewandte Mathematik Und Mechanik, vol. 76 no. SUPPL. 4 (December, 1996), pp. 33-35, ISSN 0044-2267
  55. Layton, HE; Pitman, EB; Moore, LC, Spectral properties of the thick ascending limb, Faseb Journal, vol. 10 no. 3 (December, 1996), pp. A547, ISSN 0892-6638
  56. Layton, HE; Knepper, MA; Chou, CL, Permeability criteria for effective function of passive countercurrent multiplier., The American Journal of Physiology, vol. 270 no. 1 Pt 2 (January, 1996), pp. F9-20, ISSN 0002-9513
  57. Layton, HE; Pitman, EB; Knepper, MA, Dynamic numerical method for models of the urine concentrating mechanism, Siam Journal on Applied Mathematics, vol. 55 no. 5 (January, 1995), pp. 1390-1418, Society for Industrial & Applied Mathematics (SIAM)
  58. Layton, HE; Pitman, EB; Moore, LC, Instantaneous and steady-state gains in the tubuloglomerular feedback system., The American Journal of Physiology, vol. 268 no. 1 Pt 2 (January, 1995), pp. F163-F174
  59. Pitman, EB; Layton, HE; Moore, LC, Numerical simulation of propagating concentration profiles in renal tubules., Bulletin of Mathematical Biology, vol. 56 no. 3 (May, 1994), pp. 567-586, ISSN 0092-8240
  60. Layton, HE; Pitman, EB, A dynamic numerical method for models of renal tubules., Bulletin of Mathematical Biology, vol. 56 no. 3 (May, 1994), pp. 547-565, ISSN 0092-8240
  61. Layton, HE; Davies, JM, Distributed solute and water reabsorption in a central core model of the renal medulla., Mathematical Biosciences, vol. 116 no. 2 (August, 1993), pp. 169-196, ISSN 0025-5564
  62. Chou, CL; Knepper, MA; Layton, HE, Urinary concentrating mechanism: the role of the inner medulla., Seminars in Nephrology, vol. 13 no. 2 (March, 1993), pp. 168-181
  63. Knepper, MA; Chou, CL; Layton, HE, How is urine concentrated by the renal inner medulla?, Contributions to Nephrology, vol. 102 (January, 1993), pp. 144-160
  64. Layton, HE; Pitman, EB; Moore, LC, Bifurcation analysis of TGF-mediated oscillations in SNGFR., The American Journal of Physiology, vol. 261 no. 5 Pt 2 (November, 1991), pp. F904-F919
  65. Layton, HE; Pitman, EB, Oscillations in a simple model of tubuloglomerular feedback, Annual International Conference of the Ieee Engineering in Medicine and Biology Proceedings no. pt 3 (December, 1990), pp. 987-988
  66. Layton, HE, Urea transport in a distributed loop model of the urine-concentrating mechanism., The American Journal of Physiology, vol. 258 no. 4 Pt 2 (April, 1990), pp. F1110-F1124
  67. Layton, HE, Distributed loops of Henle in a central core model of the renal medulla: Where should the solute come out?, Mathematical and Computer Modelling, vol. 14 no. C (January, 1990), pp. 533-537, Elsevier BV, ISSN 0895-7177
  68. Pitman, EB; Layton, HE, Tubuloglomerular feedback in a dynamic nephron, Communications on Pure and Applied Mathematics, vol. 42 no. 6 (January, 1989), pp. 759-787
  69. Layton, HE, Energy advantage of counter-current oxygen transfer in fish gills, Journal of Theoretical Biology, vol. 125 no. 3 (April, 1987), pp. 307-316, Elsevier BV, ISSN 0022-5193
  70. Layton, HE, Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism, Mathematical Biosciences, vol. 84 no. 2 (January, 1987), pp. 197-210, Elsevier BV, ISSN 0025-5564
  71. Layton, HE, Distribution of Henle's loops may enhance urine concentrating capability., Biophysical Journal, vol. 49 no. 5 (May, 1986), pp. 1033-1040
  72. Layton, HE, Nephron distribution enhances concentrating capability, Federation Proceedings, vol. 44 no. 6 (January, 1985), pp. No.-8773
  73. 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.
  74. 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.
  75. 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.
  76. 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.
  77. 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.
  78. 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.
  79. 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.
  80. 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.
  81. 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.
  82. 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.)
  83. 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.
  84. Layton, H. E., Concentrating urine in the inner medulla of the kidney, Comments on Theoretical Biology 1(3): 179-196, 1989.
  85. Layton, H. E., Energy advantage of counter-current oxygen exchange in fish gills, Journal of Theoretical Biology 125: 307-316, 1987.
Last modified: 2022/08/02