Anita T. Layton
Professor in the Department of Mathematics
My main research interest is the application of mathematics to biological systems, specifically, mathematical modeling of renal physiology. Current projects involve (1) the development of mathematical models of the mammalian kidney and the application of these models to investigate the mechanism by which some mammals (and birds) can produce a urine that has a much higher osmolality than that of blood plasma; (2) the study of the origin of the irregular oscillations exhibited by the tubuloglomerular feedback (TGF) system, which regulates fluid delivery into renal tubules, in hypertensive rats; (3) the investigation of the interactions of the TGF system and the urine concentrating mechanism; (4) the development of a dynamic epithelial transport model of the proximal tubule and the incorporation of that model into a TGF framework.
Multiscale numerical methods.
I develop multiscale numerical methods---multi-implicit Picard integral deferred correction methods---for the integration of partial differential equations arising in physical systems with dynamics that involve two or more processes with widely-differing characteristic time scales (e.g., combustion, transport of air pollutants, etc.). These methods avoid the solution of nonlinear coupled equations, and allow processes to decoupled (like in operating-splitting methods) while generating arbitrarily high-order solutions.
Numerical methods for immersed boundary problems.
I develop numerical methods to simulate fluid motion driven by forces singularly supported along a boundary immersed in an incompressible fluid.
Appointments and Affiliations
- Professor in the Department of Mathematics
- Research Professor of Mathematics
- Professor of Biomedical Engineering
- Professor in Medicine
- Bass Fellow
- Office Location: 213 Physics Bldg, Durham, NC 27708
- Office Phone: (919) 660-6971
- Email Address: firstname.lastname@example.org
- Ph.D. University of Toronto (Canada), 2001
- M.S. University of Toronto (Canada), 1996
- B.A. Duke University, 1994
- B.S. Duke University, 1994
The application of mathematics to biological systems, specifically, mathematical modeling of renal physiology.
Awards, Honors, and Distinctions
- Bass Fellow. Duke University. 2013
- FOCUS 195FS: Special Topics in Focus
- MATH 161FS: Introduction to Mathematical Modeling in Biology
- MATH 393: Research Independent Study
- MATH 493: Research Independent Study
In the News
- Anita Layton: A Model of STEM Versatility (Jan 3, 2018 | Duke Research Blog)
- Can Math Keep Us Healthy and Safe? (Apr 29, 2015)
- Bringing Scholarship to the Classroom (Nov 19, 2013)
- Layton, AT; Vallon, V; Edwards, A, A computational model for simulating solute transport and oxygen consumption along the nephrons., American Journal of Physiology. Renal Physiology, vol 311 no. 6 (2016), pp. F1378-F1390 [10.1152/ajprenal.00293.2016] [abs].
- Layton, AT; Laghmani, K; Vallon, V; Edwards, A, Solute transport and oxygen consumption along the nephrons: effects of Na+ transport inhibitors., American Journal of Physiology. Renal Physiology, vol 311 no. 6 (2016), pp. F1217-F1229 [10.1152/ajprenal.00294.2016] [abs].
- Sgouralis, I; Kett, MM; Ow, CPC; Abdelkader, A; Layton, AT; Gardiner, BS; Smith, DW; Lankadeva, YR; Evans, RG, Bladder urine oxygen tension for assessing renal medullary oxygenation in rabbits: experimental and modeling studies., American Journal of Physiology Regulatory Integrative and Comparative Physiology, vol 311 no. 3 (2016), pp. R532-R544 [10.1152/ajpregu.00195.2016] [abs].