Research Interests for Anita T. Layton
Research Interests: Mathematical physiology; Multiscale numerical methods; Numerical methods for immersed boundary problems.
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 methodsmultiimplicit Picard integral deferred correction methodsfor the integration of partial differential equations arising in physical systems with dynamics that involve two or more processes with widelydiffering 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 operatingsplitting methods) while generating arbitrarily highorder 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.  Keywords:
 Absorption, Actin Cytoskeleton, Algorithms, Animals, Aquaporin 1, Arterioles, Biological Clocks, Biological Transport, Biological Transport, Active, Blood Pressure, Blood Vessels, Body Water, Calcium, Calcium Channels, Calibration, Calmodulin, Capillary Permeability, cdc42 GTPBinding Protein, cdc42 GTPBinding Protein, Saccharomyces cerevisiae, Cell Membrane Permeability, Cell Polarity, Cell Size, Chlorides, Compliance, Computer Simulation, Diet, Diffusion, Electric Stimulation, Endocytosis, Endothelium, Vascular, Energy Metabolism, Enzyme Activation, Exocytosis, Feedback, Feedback, Physiological, Fluorescence Recovery After Photobleaching, Gap Junctions, Glomerular Filtration Rate, Hemodynamics, Homeostasis, Humans, Hyaluronic Acid, Hydrodynamics, HydrogenIon Concentration, Hydrostatic Pressure, Hypertrophy, Immunohistochemistry, Ion Transport, Kidney, Kidney Concentrating Ability, Kidney Diseases, Kidney Glomerulus, Kidney Medulla, Kidney Tubules, Kidney Tubules, Collecting, Kidney Tubules, Proximal, Kinetics, Loop of Henle, Male, Mathematics, Membrane Potentials, Membrane Transport Proteins, Mice, Microvessels, Models, Animal, Models, Biological, Models, Statistical, Models, Theoretical, Muscle Contraction, Muscle Relaxation, Muscle, Smooth, Vascular, MyosinLightChain Kinase, Nephrons, Neural Conduction, Neurons, Afferent, Nonlinear Dynamics, Numerical Analysis, ComputerAssisted, Osmolar Concentration, Oxygen, Oxygen Consumption, Oxyhemoglobins, Periodicity, Permeability, Potassium, Pressure, Protein Binding, Protein Isoforms, Protein Transport, Quail, Rats, Rats, Inbred SHR, Rats, Wistar, Renal Circulation, Saccharomyces cerevisiae, Saccharomyces cerevisiae Proteins, Septins, Signal Transduction, SNARE Proteins, Sodium, Sodium Chloride, SodiumPotassiumExchanging ATPase, Stokes flow, Symporters, Systole, Transport Vesicles, Urea, Urine, Vasodilation, Vasomotor System, Water
 Areas of Interest:
Mathematical physiology Scientific computing Multiscale numerical methods Fluidstructure interactions
 Recent Publications
 Fattah, H; Layton, A; Vallon, V, How Do Kidneys Adapt to a Deficit or Loss in Nephron Number?,
Physiology (Bethesda, Md.), vol. 34 no. 3
(May, 2019),
pp. 189197 [doi] [abs]
 Layton, AT, Optimizing SGLT inhibitor treatment for diabetes with chronic kidney diseases.,
Biological Cybernetics, vol. 113 no. 12
(April, 2019),
pp. 139148 [doi] [abs]
 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]
 Layton, AT; Sullivan, JC, Recent advances in sex differences in kidney function.,
American Journal of Physiology. Renal Physiology, vol. 316 no. 2
(February, 2019),
pp. F328F331 [doi]
 Leete, J; Layton, AT, Sexspecific longterm blood pressure regulation: Modeling and analysis.,
Computers in Biology and Medicine, vol. 104
(January, 2019),
pp. 139148 [doi] [abs]
