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
 Layton, H. E., Energy advantage of countercurrent oxygen exchange in fish gills,
Journal of Theoretical Biology 125: 307316, 1987.
 Layton, H. E., Concentrating urine in the inner medulla of the kidney,
Comments on Theoretical Biology 1(3): 179196, 1989.
 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.
 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.)
 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.
 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.
 Chou, ChungLin, Mark A. Knepper, and H. E. Layton, Urinary concentrating mechanism: role of the inner medulla,
Seminars in Nephrology 13(2): 168181, 1993.
 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.
 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.
 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.
 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 numerical method for renal models that represent abrupt changes in tubular properties,
Journal of Mathematical Biology 45(5): 549567, 2002.
 Layton, HE, Nephron distribution enhances concentrating capability,
Federation Proceedings, vol. 44 no. 6
(1985),
pp. No.8773
 Layton, HE, Distribution of Henle's loops may enhance urine concentrating capability,
Biophysical Journal, vol. 49 no. 5
(1986),
pp. 10331040 [doi]
 Layton, HE, Energy advantage of countercurrent oxygen transfer in fish gills,
Journal of Theoretical Biology, vol. 125 no. 3
(1987),
pp. 307316, ISSN 00225193 [abs]
 Layton, HE, Existence and uniqueness of solutions to a mathematical model of the urine concentrating mechanism,
Mathematical Biosciences, vol. 84 no. 2
(1987),
pp. 197210, ISSN 00255564 [abs]
 Pitman, EB; Layton, HE, Tubuloglomerular feedback in a dynamic nephron,
Communications on Pure and Applied Mathematics, vol. 42 no. 6
(September, 1989),
pp. 759787 [doi]
 Layton, HE; Pitman, EB, Oscillations in a simple model of tubuloglomerular feedback,
Proceedings of the Annual Conference on Engineering in Medicine and Biology no. pt 3
(1990),
pp. 987988 [abs]
 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
(1990),
pp. 533537, ISSN 08957177 [abs]
 Layton, HE, Urea transport in a distributed loop model of the urineconcentrating mechanism.,
The American Journal of Physiology, vol. 258 no. 4 Pt 2
(April, 1990),
pp. F1110F1124 [doi] [abs]
 Layton, HE; Pitman, EB; Moore, LC, Bifurcation analysis of TGFmediated oscillations in SNGFR,
American Journal of Physiology  Renal Fluid and Electrolyte Physiology, vol. 261 no. 5 305
(1991),
pp. F904F919 [abs]
 Layton, HE; Davies, JM, Distributed solute and water reabsorption in a central core model of the renal medulla,
Mathematical Biosciences, vol. 116 no. 2
(1993),
pp. 169196, ISSN 00255564 [doi] [abs]
 Knepper, MA; Chou, CL; Layton, HE, How is urine concentrated by the renal inner medulla?,
Contributions to nephrology, vol. 102
(1993),
pp. 144160
 Chou, CL; Knepper, MA; Layton, HE, Urinary concentrating mechanism: The role of the inner medulla,
Seminars in Nephrology, vol. 13 no. 2
(1993),
pp. 168181
 Pitman, EB; Layton, HE; Moore, LC, Numerical simulation of propagating concentration profiles in renal tubules,
Bulletin of Mathematical Biology, vol. 56 no. 3
(1994),
pp. 567586, ISSN 00928240 [doi] [abs]
 Layton, HE; Pitman, EB, A dynamic numerical method for models of renal tubules,
Bulletin of Mathematical Biology, vol. 56 no. 3
(1994),
pp. 547565, ISSN 00928240 [doi] [abs]
 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
(1995),
pp. 13901418 [abs]
 Layton, HE; Pitman, EB; Moore, LC, Instantaneous and steadystate gains in the tubuloglomerular feedback system,
American Journal of Physiology  Renal Fluid and Electrolyte Physiology, vol. 268 no. 1 371
(1995),
pp. F163F174 [abs]
 Layton, HE; Pitman, EB; Moore, LC, Instantaneous and steadystate gains in the tubuloglomerular feedback system.,
The American Journal of Physiology, vol. 268 no. 1 Pt 2
(January, 1995),
pp. F163F174 [doi] [abs]
 Layton, HE; Knepper, MA; Chou, CL, Permeability criteria for effective function of passive countercurrent multiplier,
The American Journal of Physiology, vol. 270 no. 1 PART 2
(1996),
pp. F9F20, ISSN 00029513 [doi] [abs]
 Pitman, EB; Layton, HE, Mass conservation in a dynamic numerical method for a model of the urine concentrating mechanism,
ZammZeitschrift Fuer Angewandte Mathematik Und Mechanik, vol. 76 no. SUPPL. 4
(1996),
pp. 4548, ISSN 00442267 [abs]
 Layton, HE; Pitman, EB; Moore, LC, Spectral properties of the TGF pathway,
ZammZeitschrift Fuer Angewandte Mathematik Und Mechanik, vol. 76 no. SUPPL. 4
(1996),
pp. 3335, ISSN 00442267 [abs]
 Layton, HE; Pitman, EB; Moore, LC, Spectral properties of the thick ascending limb,
Faseb Journal, vol. 10 no. 3
(1996),
pp. A547, ISSN 08926638 [abs]
 Layton, HE; Pitman, EB; Moore, LC, Nonlinear filter properties of the thick ascending limb,
American Journal of Physiology Renal Physiology, vol. 273 no. 4 424
(1997),
pp. F625F634, ISSN 03636127 [abs]
 Pitman, EB; Zaritski, R; Moore, LC; Layton, HE, TGFmediated bifurcation in two coupled nephrons,
Faseb Journal, vol. 11 no. 3
(1997),
pp. A85, ISSN 08926638 [abs]
 Arthurs, KM; Moore, LC; Pitman, EB; Layton, HE, Flow regulation in afferent arterioles following vascular injury,
Faseb Journal, vol. 11 no. 3
(1997),
pp. A82, ISSN 08926638 [abs]
 Layton, HE; Pitman, EB; Moore, LC, Spectral properties of the tubuloglomerular feedback system,
American Journal of Physiology Renal Physiology, vol. 273 no. 4 424
(1997),
pp. F635F649, ISSN 03636127 [abs]
 Layton, HE; Casotti, G; Davies, JM; Braun, EJ, Mathematical model of avian urine concentrating mechanism,
Faseb Journal, vol. 11 no. 3
(1997),
pp. A9, ISSN 08926638 [abs]
 Layton, HE; Pitman, EB; Moore, LC, Potential natriuretic effects of limitcycle oscillations mediated by tubuloglomerular feedback,
Faseb Journal, vol. 12 no. 4
(1998),
pp. A108, ISSN 08926638 [abs]
 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
(1998),
pp. 402440 [doi] [abs]
 Layton, HE; Pitman, EB; Moore, LC, Limitcycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery,
American Journal of Physiology Renal Physiology, vol. 278 no. 2 472
(2000),
pp. F287F301, ISSN 03636127 [doi] [abs]
 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. 6 486
(2000),
pp. F1139F1160, ISSN 03636127 [doi] [abs]
 Layton, AT; Layton, HE, A semilagrangian semiimplicit numerical method for models of the urine concentrating mechanism,
Siam Journal on Scientific Computing, vol. 23 no. 5
(2002),
pp. 15261548, ISSN 10648275 [doi] [abs]
 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
(2002),
pp. 549567, ISSN 03036812 [doi] [abs]
 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. 5 535
(2003),
pp. F1080F1096 [abs]
 MarcanoVelázquez, M; Layton, HE, An inverse algorithm for a mathematical model of an avian urine concentrating mechanism,
Bulletin of Mathematical Biology, vol. 65 no. 4
(2003),
pp. 665691 [doi] [abs]
 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. 5 545
(2003),
pp. F972F989 [abs]
 Layton, AT; Layton, HE, An efficient numerical method for distributedloop models of the urine concentrating mechanism,
Mathematical Biosciences, vol. 181 no. 2
(2003),
pp. 111132 [doi] [abs]
 Layton, AT; Layton, HE, A regionbased model framework for the rat urine concentrating mechanism,
Bulletin of Mathematical Biology, vol. 65 no. 5
(2003),
pp. 859901 [doi] [abs]
 Pitman, EB; Zaritski, RM; Kesseler, KJ; Moore, LC; Layton, HE, Feedbackmediated dynamics in two coupled nephrons,
Bulletin of Mathematical Biology, vol. 66 no. 6
,
pp. 14631492 [doi] [abs]
 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. F816F839 [doi] [abs]
 Layton, AT; Layton, HE, A regionbased mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and basecase results.,
American Journal of Physiology. Renal Physiology, vol. 289 no. 6
(December, 2005),
pp. F1346F1366, ISSN 1931857X [15914776], [doi] [abs]
 Layton, AT; Layton, HE, A regionbased 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. F1367F1381, ISSN 1931857X [15914775], [doi] [abs]
 Thomas, SR; Layton, AT; Layton, HE; Moore, LC, Kidney modeling: Status and perspectives,
Proceedings of the Ieee, vol. 94 no. 4
(April, 2006),
pp. 740752, ISSN 00189219 [doi] [abs]
 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. F79F97, ISSN 1931857X [16204416], [doi] [abs]
 Marcano, M; Layton, AT; Layton, HE, An optimization algorithm for a distributedloop model of an avian urine concentrating mechanism.,
Bulletin of Mathematical Biology, vol. 68 no. 7
(October, 2006),
pp. 16251660, ISSN 00928240 [doi] [abs]
 BuduGrajdeanu, 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. 564592, ISSN 00255564 [17499314], [doi] [abs]
 BuduGrajdeanu, P; Moore, LC; Layton, HE, 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)
 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,
Seldin and Giebisch's The Kidney
(2007),
pp. 11431178, Elsevier, New York [doi]
 Pannabecker, TL; Dantzler, WH; Layton, HE; Layton, AT, Role of threedimensional 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. F1271F1285, ISSN 03636127 [doi] [abs]
 Sands, JM; Layton, HE, The Physiology of Urinary Concentration: An Update,
Seminars in Nephrology, vol. 29 no. 3
(May, 2009),
pp. 178195, ISSN 02709295 [doi] [abs]
 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. 515555 [19205808], [doi] [abs]
 Layton, AT; Layton, HE; Dantzler, WH; Pannabecker, TL, The mammalian urine concentrating mechanism: hypotheses and uncertainties.,
Physiology (Bethesda, Md.), vol. 24
(August, 2009),
pp. 250256, ISSN 15489213 [19675356], [doi] [abs]
 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
 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
(2010),
pp. 314339, ISSN 00928240 [doi] [abs]
 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)
 Layton, AT; Pannabecker, TL; Dantzler, WH; Layton, HE, Functional implications of the threedimensional architecture of the rat renal inner medulla.,
American Journal of Physiology. Renal Physiology, vol. 298 no. 4
(April, 2010),
pp. F973F987 [20053796], [doi] [abs]
 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. F962F972 [20042460], [doi] [abs]
 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, 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)
 Dantzler, WH; Pannabecker, TL; Layton, AT; Layton, HE, Urine concentrating mechanism in the inner medulla of the mammalian kidney: role of threedimensional architecture.,
Acta Physiologica, vol. 202 no. 3
(March, 2011),
pp. 361378, ISSN 17481716 [doi] [abs]
 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. F669F681 [21190949], [doi] [abs]
 Layton, AT; Bowen, M; Wen, A; Layton, HE, Feedbackmediated dynamics in a model of coupled nephrons with compliant thick ascending limbs.,
Mathematical Biosciences, vol. 230 no. 2
(April, 2011),
pp. 115127 [21329704], [doi] [abs]
 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)
 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]
 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. F1188F1202 [22262482], [doi] [abs]
 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
 Sands, JM; Layton, HE, The Urine Concentrating Mechanism and Urea Transporters,
Seldin and Geibisch's The Kidney, vol. 1
(2013),
pp. 14631510 [doi]
 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; 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]
 Sands, JM; Layton, HE, Advances in understanding the urineconcentrating mechanism.,
Annual Review of Physiology, vol. 76
(January, 2014),
pp. 387409, ISSN 00664278 [doi] [abs]
 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. F692F700 [doi] [abs]
Papers Accepted
 NievesGonzalez, 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 PhysiologyRenal Physiology
(2012)
 NievesGonzalez, 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 PhysiologyRenal Physiology
(2012)
 Dantzler, WH; Layton, AT; Layton, HE; Pannabecker, TL, Urineconcentrating mechanism in the inner medulla: function of the thin limbs of the loops of Henle.,
Clinical Journal of the American Society of Nephrology : Cjasn, vol. 9 no. 10
(August, 2012),
pp. 17811789 [doi] [abs]


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ph: 919.660.2800
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Mathematics Department
Duke University, Box 90320
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