Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Math HOME

.......................

Faculty

.......................

Publications of Harold Layton    :recent first  combined  bibtex listing:

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  [author's comments]

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 [doi]  [abs]
  2. 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 [doi]  [abs]
  3. 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.
  4. 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 [21190949], [doi]  [abs]
  5. 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.
  6. 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 [doi]  [abs]
  7. 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.
  8. 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 [15914776], [doi]  [abs]
  9. 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 [15914775], [doi]  [abs]
  10. 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 [doi]  [abs]
  11. 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 [doi]  [abs]
  12. 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 [doi]  [abs]
  13. 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 [doi]  [abs]
  14. 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 [doi]  [abs]
  15. 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 [doi]  [abs]
  16. 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 [doi]  [abs]
  17. 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 [doi]  [abs]
  18. Layton, H. E., Concentrating urine in the inner medulla of the kidney, Comments on Theoretical Biology 1(3): 179-196, 1989.
  19. 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.
  20. 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.)
  21. 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)
  22. 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 [21753076], [doi]  [abs]
  23. 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.
  24. 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 [doi]  [abs]
  25. 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 [doi]  [abs]
  26. Layton, HE, Distribution of Henle's loops may enhance urine concentrating capability., Biophysical Journal, vol. 49 no. 5 (May, 1986), pp. 1033-1040 [doi]  [abs]
  27. 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.
  28. 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) [doi]  [abs]
  29. 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 [doi]  [abs]
  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. 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 [17499314], [doi]  [abs]
  32. 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)
  33. Layton, H. E., Energy advantage of counter-current oxygen exchange in fish gills, Journal of Theoretical Biology 125: 307-316, 1987.
  34. 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 [doi]  [abs]
  35. 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 [doi]  [abs]
  36. 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)
  37. 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 [21329704], [doi]  [abs]
  38. 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 [doi]  [abs]
  39. 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  [abs]
  40. 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 [doi]  [abs]
  41. 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 [doi]  [abs]
  42. 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 [20053796], [doi]  [abs]
  43. 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.
  44. 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 [doi]
  45. 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 [20042460], [doi]  [abs]
  46. 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 [doi]  [abs]
  47. 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 [doi]  [abs]
  48. 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 [doi]  [abs]
  49. 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  [abs]
  50. 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 [doi]  [abs]
  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  [abs]
  52. 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.
  53. 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)
  54. 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 [doi]  [abs]
  55. 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 [doi]  [abs]
  56. 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 [16204416], [doi]  [abs]
  57. 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 [19205808], [doi]  [abs]
  58. Layton, HE, Nephron distribution enhances concentrating capability, Federation Proceedings, vol. 44 no. 6 (January, 1985), pp. No.-8773
  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 [doi]  [abs]
  60. 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  [abs]
  61. 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 [doi]  [abs]
  62. 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  [abs]
  63. 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 [doi]  [abs]
  64. 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 [22262482], [doi]  [abs]
  65. 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  [abs]
  66. 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  [abs]
  67. 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 [doi]  [abs]
  68. 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  [abs]
  69. 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 [19675356], [doi]  [abs]
  70. 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 [doi]  [abs]
  71. 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
  72. 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 [doi]  [abs]
  73. 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 [doi]
  74. 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
  75. Sands, JM; Layton, HE, The Urine Concentrating Mechanism and Urea Transporters, vol. 1 (August, 2013), pp. 1463-1510, Elsevier [doi]
  76. 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 [23097466], [doi]  [abs]
  77. 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 [doi]  [abs]
  78. 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 [doi]  [abs]
  79. 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 [doi]  [abs]
  80. 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.
  81. 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
  82. 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.
  83. 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 [doi]  [abs]
  84. 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 [doi]  [abs]
  85. 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

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
Mathematics Home | Arts & Sciences | Duke University