Math @ Duke

Books
 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: SpringerVerlag, 2002
[author's comments]
Papers Published
 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 AcidBase Balance, edited by David B. Mount, Ajay Singh, and Mo Sayegh
(August, 2012), Springer
 Anita T. Layton, Leon C. Moore, and Harold E. Layton, Signal transduction in a compliant thick ascending limb,
American Journal of PhysiologyRenal Physiology 302:F1188F1202
(May, 2012)
 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 PhysiologyRenal Physiology 301: F1047F1056
(November, 2011)
 Jing Chen, Ioannis Sgouralis, Leon C. Moore, Harold E. Layton, and Anita T. Layton, A mathematical model of the myogenic response to systolic pressure in the afferent arteriole,
American Journal of PhysiologyRenal Physiology 300: F669F681
(March, 2011)
 Anita T. Layton, Matthew Bowen, Amy Wen, and Harold E. Layton, Feedbackmediated dynamics in a model of coupled nephrons with compliant thick ascending limbs,
Mathematical Biosciences Vol. 230: 115127
(April 2011)
 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
 Anita T. Layton, Thomas L. Pannabecker, William H. Dantzler, and Harold E. Layton, Hyperfiltration and innerstripe hypertrophy may explain findings by Gamble and coworkers,
American Journal of PhysiologyRenal Physiology 298: F962F972, 2010
(April, 2010)
 Anita T. Layton, Thomas L. Pannabecker, William H. Dantzler, and Harold E. Layton, Functional implications of the threedimensional architecture of the rat renal inner medulla,
American Journal of PhysiologyRenal Physiology 298: F951F961, 2010
(April, 2010)
 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 72:314339, 2010
(April, 2010)
 William H. Dantzler, Thomas L. Pannabecker, Anita T. Layton, and Harold E. Layton, Urine concentrating mechanism in the inner medulla of the mammalian kidney: Role of threedimensional architecture,
Acta Physiologica 202(3): 361378
(March, 2011)
 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
 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):515555, 2009.
(April, 2009)
 Anita T. Layton, Harold E. Layton, William H. Dantzler, and Thomas L.. Pannabecker, The Mammalian Urine Concentrating Mechanism: Hypotheses and Uncertainties,
Physiology 24: 250256, 2009
(2009)
 Jeff M. Sands and Harold E. Layton, The physiology of urinary concentration: an update,
Seminars in Nephrology, 29 (2): 178195, 2009.
(May, 2009)
 Thomas L. Pannabecker, William H. Dantzler, Harold E. Layton, and Anita T. Layton, Role of threedimensional architecture in the urine concentrating mechanism of the rat renal inner medulla,
American Journal of PhysiologyRenal Physiology, 295: F1271  F1285, 2008
(November, 2008)
 Paula BuduGrajdeanu, 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): 564592, 2007,
Mathematical Biosciences
(October, 2007)
 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
 Mariano Marcano, Anita T. Layton, and Harold E. Layton, An optimization algorithm for a distributedloop model of an avian urine concentrating mechanism,
The Bulletin of Mathematical Biology 68(7): 16251660, 2006
(October, 2006)
 Anita T. Layton, Leon C. Moore, Harold E. Layton, Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats,
American Journal of PhysiologyRenal Physiology 291 (Renal Physiology 60): F79F97, 2006
(July, 2006)
 S. Randall Thomas, Anita T. Layton, Harold E. Layton, and Leon C. Moore, Kidney modelling: status and perspectives,
Proceedings of the IEEE 94(4): 740752, 2006.
(April, 2006)
 Anita T. Layton and Harold E. Layton, A regionbased mathematical model of the urine concentrating mechanism in the rat outer medulla: I. Formulation and basecase results,
American Journal of PhysiologyRenal Physiology 289 (Renal Physiology 58): F1346F1366, 2005
(December, 2005)
 Anita T. Layton and Harold E. Layton, A regionbased mathematical model of the urine concentrating mechanism in the rat outer medulla: II. Parameter sensitivity and tubular inhomogeneity,
American Journal of PhysiologyRenal Physiology 289 (Renal Physiology 58) : F1367  F1381, 2005
(December, 2005)
 E. Bruce Pitman, Roman M. Zaritski, Kevin J. Kesseler, Leon C. Moore, and Harold E. Layton, Feedbackmediated dynamics in two coupled nephrons,
Bulletin of Mathematical Biology, 66(6): 14631492, 2004
 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): F816F839, 2004
 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: F972F989, 2003
 MarcanoVelazquez, M., and Harold E. Layton, An inverse algorithm for a mathematical model of an avian urine concentrating mechanism,
Bulletin of Mathematical Biology 65: 665691, 2003
 Layton, Anita T., and Harold E. Layton, An efficient numerical method for distributedloop models of the urine concentrating mechanism,
Mathematical Biosciences 181(2): 111132, 2003
 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 PhysiologyRenal Physiology 284 (Renal Physiology 53): F1080F1096, 2003
 Layton, Anita T., and Harold E. Layton, A regionbased model framework for the rat urine concentrating mechanism,
Bulletin of Mathematical Biology, 65: 859901, 2003
 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): 549567, 2002.
 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: SpringerVerlag, pp. 345364, 2002.
 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, SpringerVerlag, pp. 233272, 2002.
 Layton, Anita T., and Harold E. Layton, A semiLagrangian semiimplicit numerical method for models of the urine concentrating mechanism,
SIAM Journal on Scientific Computing, 23(5): 15261548, 2002.
 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. 5562.
 Layton, H.E., John M. Davies, Giovanni Casotti, and Eldon J. Braun, Mathematical model of an avian urine concentrating mechanism,
American Journal of PhysiologyRenal Physiology 279 (Renal Physiology 48): F1139F1160, 2000.
 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. 11751216.
 Layton, H. E., E. Bruce Pitman, and Leon C. Moore, Limitcycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery,
American Journal of Physiology 278 (Renal Physiology 47): F287F301, 2000.
 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): 402440, 1998.
 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): F635F649, 1997.
 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): F625F634, 1997.
 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): 4548, 1996.
 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): 3335, 1996.
 Layton, H. E., Mark A. Knepper, and ChungLin Chou, Permeability criteria for effective function of passive countercurrent multiplier,
American Journal of Physiology 270 (Renal Fluid Electrolyte Physiology 39): F9F20, 1996.
 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): 13901418, October, 1995.
 Layton, H. E., E. Bruce Pitman, and Leon C. Moore, Instantaneous and steadystate gains in the tubuloglomerular feedback system,
American Journal of Physiology 268 (Renal Fluid Electrolyte Physiology 37): F163F174, 1995.
 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): 567586, 1994.
 Layton, H. E., and E. Bruce Pitman, A dynamic numerical method for models of renal tubules,
Bulletin of Mathematical Biology 56(3): 547556, 1994.
 Layton, H. E., and John M. Davies, Distributed solute and water reabsorption in a central core model of the renal medulla,
Mathematical Biosciences 116: 169196, 1993.
 Chou, ChungLin, Mark A. Knepper, and H. E. Layton, Urinary concentrating mechanism: role of the inner medulla,
Seminars in Nephrology 13(2): 168181, 1993.
 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 AMSIMSSIAM Joint Research Conference, July 1991, Edited by Angela Cheer and C. P. van Dam, appearing as Contemporary Mathematics (American Mathematical Society) 141: 317336, 1993.
 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. 144160, S. Karger, Basel, 1993.
 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. 119156. (This chapter is an abridgment of the 1992 chapter by the same authors.)
 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. 16491692.
 Layton, H. E., E. Bruce Pitman, and Leon C. Moore, Bifurcation analysis of TGFmediated oscillations in SNGFR,
American Journal of Physiology 259 (Renal Fluid Electrolyte Physiology 30): F904F919, 1991.
 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: 533537, 1990.
 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): 987988, 1990.
 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): F1110F1124, 1990.
 Layton, H. E., Concentrating urine in the inner medulla of the kidney,
Comments on Theoretical Biology 1(3): 179196, 1989.
 Pitman, E. Bruce, and H. E. Layton, Tubuloglomerular feedback in a dynamic nephron,
Communications on Pure and Applied Mathematics 42: 759787, 1989.
 Layton, H. E., Energy advantage of countercurrent oxygen exchange in fish gills,
Journal of Theoretical Biology 125: 307316, 1987.
 Layton, H. E., Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism,
Mathematical Biosciences 84: 197210, 1987.
 Layton, H. E., Distribution of Henle's loops may enhance urine concentrating capability,
Biophysical Journal 49: 10331040, 1986.
Papers Accepted
 William H. Dantzler, Anita T. Layton, Harold E. Layton, and Thomas L. Pannabecker, Urine concentrating mechanism in the inner medulla: function of the thin limbs of Henle’s loops,
Clinical Journal of the American Society of Nephrology.
(August, 2012)
 Aniel NievesGonzalez, Chris Clausen, Mariano Marcano, Anita T. Layton, Harold E. Layton, and Leon C. Moore, Fluid dilution and efficiency of Na+ transport in a mathematical model of a thick ascending limb cell,
American Journal of PhysiologyRenal Physiology
(2012)
 Aniel NievesGonzalez, Chris Clausen, Anita T. Layton, Harold E. Layton, and Leon C. Moore, Efficiency and workload distribution in a mathematical model of the thick ascending limb,
American Journal of PhysiologyRenal Physiology
(2012)


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Mathematics Department
Duke University, Box 90320
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