Anita T. Layton

Anita T. Layton

Robert R. & Katherine B. Penn Professor of Mathematics

Mathematical physiology. 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

  • Robert R. & Katherine B. Penn Professor of Mathematics
  • Professor in the Department of Mathematics
  • Professor of Biomedical Engineering

Contact Information

Education

  • Ph.D. UniversityToronto, 2001
  • M.S. UniversityToronto, 1996
  • B.A. Duke University, 1994
  • B.S. Duke University, 1994

Research Interests

Anita T. Layton's main research interest is the application of mathematics to biological systems, specifically, mathematical modeling of renal physiology.

Awards, Honors, and Distinctions

  • Bass Fellow. Duke University. 2013

Courses Taught

  • FOCUS 195FS: Special Topics in Focus
  • MATH 161FS: Introduction to Mathematical Modeling in Biology
  • MATH 391: Independent Study
  • MATH 393: Research Independent Study
  • MATH 477S: Seminar in Mathematical Modeling with a Focus on Writing
  • MATH 493: Research Independent Study
  • MATH 790-77: Current Research in Mathematical Biology
  • MATH 799: Special Readings

In the News

Representative Publications

  • Layton, AT; Edwards, A, Predicted effects of nitric oxide and superoxide on the vasoactivity of the afferent arteriole., American Journal of Physiology: Renal Physiology, vol 309 no. 8 (2015), pp. F708-F719 [abs].
  • Nganguia, H; Young, Y-N; Layton, AT; Hu, W-F; Lai, M-C, An Immersed Interface Method for Axisymmetric Electrohydrodynamic Simulations in Stokes flow, Communications in computational physics, vol 18 no. 02 (2015), pp. 429-449 [10.4208/cicp.171014.270315a] [abs].
  • Sgouralis, I; Layton, AT, Mathematical modeling of renal hemodynamics in physiology and pathophysiology., Mathematical Biosciences, vol 264 (2015), pp. 8-20 [abs].
  • Layton, AT; Vallon, V; Edwards, A, Modeling oxygen consumption in the proximal tubule: effects of NHE and SGLT2 inhibition., American Journal of Physiology: Renal Physiology, vol 308 no. 12 (2015), pp. F1343-F1357 [abs].
  • Fry, BC; Edwards, A; Layton, AT, Impacts of nitric oxide and superoxide on renal medullary oxygen transport and urine concentration., American Journal of Physiology: Renal Physiology, vol 308 no. 9 (2015), pp. F967-F980 [abs].