Duke University
Department of Mathematics

Harold Layton: Research

Area of Expertise: Mathematical biology, especially renal models

Research Summary: 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 involve small systems of semilinear hyperbolic partial differential equations (PDEs) with time-delays, 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. To study the fluid dynamics in the afferent arteriole, low Reynolds number flow (Re ~ 0.1) is simulated in a two-dimensional elastic-contractile tube. The tubular walls are included by means of the immersed boundary method. Current work is directed to quantifying the regulatory role of the vasodilator nitric oxide.

Selected Publications:

  1. H. E. Layton. Distribution of Henle's loops may enhance urine concentrating capability. Biophysical Journal, 49: 1033-1040, 1986.

  2. H. E. Layton, E. Bruce Pitman and Leon C. Moore. Bifurcation analysis of TGF-mediated oscillations in SNGFR. American Journal of Physiology 261 ( Renal Fluid Electrolyte Physiology 30): F904-F919, 1991.

  3. H. E. Layton, 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, 1995.

  4. H. E. Layton, Mark A. Knepper and Chung-Lin Chou. Permeability criteria for effective function of countercurrent multiplier. American Journal of Physiology 270 (Renal Fluid Electrolyte Physiology 39): F9-F20, 1996.

  5. H. E. Layton, E. Bruce Pitman, and Leon C. Moore. Nonlinear filter properties of the thick ascending limb. American Journal of Physiology 273 (Renal Physiology 42): F625-F634, 1997.

  6. H. E. Layton, E. Bruce Pitman, and Leon C. Moore. Spectral properties of the tubuloglomerular feedback system. American Journal of Physiology 273 (Renal Physiology 42): F635-F649, 1997.

  7. Kayne M. Arthurs, 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): 402--440, 1998.

  8. H. E. Layton, E. Bruce Pitman, and Leon C. Moore. Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery. American Journal of Physiology 278 (Renal Physiology 47): F287-F301, 2000.

  9. H. E. Layton, John M. Davies, Giovanni Casotti, and Eldon J. Braun. Mathematical model of an avian urine concentrating mechanism. American Journal of Physiology-Renal Physiology 279 (Renal Physiology 48): F1139-F1160, 2000.

    All Research Publications

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    Last modified: 17 September 2004