Harold Layton

  • Professor of Mathematics
External address: 221 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2809

Research Areas and Keywords

Biological Modeling
renal modeling

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.

Education & Training
  • Ph.D., Duke University 1986

  • M.S., University of Kentucky at Lexington 1980

  • B.A., Asbury College 1979

Oldson, DR, Moore, LC, and Layton, HE. "Effect of sustained flow perturbations on stability and compensation of tubuloglomerular feedback." American Journal of Physiology - Renal Physiology 285.5 54-5 (2003): F972-F989.

Marcano-Velázquez, M, and Layton, HE. "An inverse algorithm for a mathematical model of an avian urine concentrating mechanism." Bulletin of Mathematical Biology 65.4 (2003): 665-691. Full Text

Smith, KM, Moore, LC, and Layton, HE. "Advective transport of nitric oxide in a mathematical model of the afferent arteriole." American Journal of Physiology - Renal Physiology 284.5 53-5 (2003): F1080-F1096.

Layton, AT, and Layton, HE. "A numerical method for renal models that represent tubules with abrupt changes in membrane properties." Journal of Mathematical Biology 45.6 (2002): 549-567. Full Text

Layton, AT, and Layton, HE. "A semi-lagrangian semi-implicit numerical method for models of the urine concentrating mechanism." SIAM Journal on Scientific Computing 23.5 (2002): 1526-1548. Full Text

Layton, HE, Davies, JM, Casotti, G, and Braun, EJ. "Mathematical model of an avian urine concentrating mechanism." Am J Physiol Renal Physiol 279.6 (December 2000): F1139-F1160.

Layton, HE, Pitman, EB, and Moore, LC. "Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery." Am J Physiol Renal Physiol 278.2 (February 2000): F287-F301.

Layton, HE, Davies, JM, Casotti, G, and Braun, EJ. "Mathematical model of an avian urine concentrating mechanism." American Journal of Physiology - Renal Physiology 279.6 48-6 (2000): F1139-F1160.

Layton, HE, Pitman, EB, and Moore, LC. "Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery." American Journal of Physiology - Renal Physiology 278.2 47-2 (2000): F287-F301.

Arthurs, KM, Moore, LC, Peskin, CS, Pitman, EB, and Layton, HE. "Modeling arteriolar flow and mass transport using the immersed boundary method." Journal of Computational Physics 147.2 (1998): 402-440. Full Text

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