Professor Layton is modeling renal function at the level of the nephron (the functional unit of the kidney) and at the level of nephron populations. In particular, he is studying tubuloglomerular feedback (TGF), the urine concentrating mechanism, and the hemodynamics of the afferent arteriole. Dynamic models for TGF and the afferent arteriole involve small systems of semilinear hyperbolic partial differential equations (PDEs) with time-delays, and coupled ODES, which are solved numerically for cases of physiological interest, or which are linearized for qualitative analytical investigation. Dynamic models for the concentrating mechanism involve large systems of coupled hyperbolic PDEs that describe tubular convection and epithelial transport. Numerical solutions of these PDEs help to integrate and interpret quantities determined by physiologists in many separate experiments.

Office Location: | 221 Physics Bldg, Durham, NC 27708 |

Office Phone: | (919) 660-2809 |

Email Address: | |

Web Page: | http://www.math.duke.edu/~layton |

**Office Hours:**- By appointment

**Education:**Ph.D. Duke University 1986 M.S. University of Kentucky at Lexington 1980 B.A. Asbury College 1979

**Specialties:**- Applied Math

**Research Interests:***Mathematical Physiology*Professor Layton is modeling renal function at the level of the nephron (the functional unit of the kidney) and at the level of nephron populations. In particular, he is studying tubuloglomerular feedback (TGF), the urine concentrating mechanism, and the hemodynamics of the afferent arteriole. Dynamic models for TGF and the afferent arteriole involve small systems of semilinear hyperbolic partial differential equations (PDEs) with time-delays, and coupled ODES, which are solved numerically for cases of physiological interest, or which are linearized for qualitative analytical investigation. Dynamic models for the concentrating mechanism involve large systems of coupled hyperbolic PDEs that describe tubular convection and epithelial transport. Numerical solutions of these PDEs help to integrate and interpret quantities determined by physiologists in many separate experiments.

**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

**Keywords:**Absorption • Algorithms • Animals • Arterioles • Biological Clocks • Biological Transport, Active • Blood Pressure • Blood Vessels • Body Water • Calcium • Calcium Channels • Capillary Permeability • Cell Membrane Permeability • Cell Size • Compliance • Computer Simulation • Diet • Diffusion • Feedback • Feedback, Physiological • Glomerular Filtration Rate • Hemodynamics • Homeostasis • Humans • Hydrodynamics • Hypertrophy • Ion Transport • Kidney • Kidney Concentrating Ability • Kidney Diseases • Kidney Glomerulus • Kidney Medulla • Kidney Tubules • Kidney Tubules, Collecting • Loop of Henle • Mathematics • Membrane Potentials • Mice • Models, Animal • Models, Biological • Models, Statistical • Models, Theoretical • Muscle, Smooth, Vascular • Nephrons • Nonlinear Dynamics • Osmolar Concentration • Periodicity • Permeability • Potassium • Rats • Rats, Inbred SHR • Signal Transduction • Sodium • Sodium Chloride • Systole • Urea • Urine

**Current Ph.D. Students**

**Postdocs Mentored**- Amal El Moghraby (July 01, 2008 - May 31, 2009)
- Paula Budu (September 14, 2002 - August 31, 2005)
- Monica M. Romeo (September 1, 2001 - May 31, 2004)
- Kayne Marie Arthurs (1996/09-1998/08)

**Recent Publications**- 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] - 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] - 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] - 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] - Sands, JM; Layton, HE,
*The Urine Concentrating Mechanism and Urea Transporters*, vol. 1 (August, 2013), pp. 1463-1510, Elsevier [doi]

- Layton, AT; Layton, HE,

**Recent Grant Support***EMSW21-RTG:*, National Science Foundation, DMS-0943760, 2010/09-2017/08.