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.

**Keywords:**- Absorption, Algorithms, Animals, Arterioles, Biological Clocks, Biological Transport, Active, Blood Pressure, Blood Vessels, Body Water, Calcium, Calcium Channels, Capillary Permeability, Cell Membrane Permeability, Cell Size, Compliance, Computer Simulation, Diet, Diffusion, Feedback, Feedback, Physiological, Glomerular Filtration Rate, Hemodynamics, Homeostasis, Humans, Hydrodynamics, Hypertrophy, Ion Transport, Kidney, Kidney Concentrating Ability, Kidney Diseases, Kidney Glomerulus, Kidney Medulla, Kidney Tubules, Kidney Tubules, Collecting, Loop of Henle, Mathematics, Membrane Potentials, Mice, Models, Animal, Models, Biological, Models, Statistical, Models, Theoretical, Muscle, Smooth, Vascular, Nephrons, Nonlinear Dynamics, Osmolar Concentration, Periodicity, Permeability, Potassium, Rats, Rats, Inbred SHR, Signal Transduction, Sodium, Sodium Chloride, Systole, Urea, Urine

**Areas of Interest:**Mathematical models of renal hemodynamics

Mathematical models of the urine concentrating mechanism

Numerical methods for models of renal systems

Countercurrent systems in animals

**Recent Publications**- Li, Q; McDonough, AA; Layton, HE; Layton, AT,
*Functional implications of sexual dimorphism of transporter patterns along the rat proximal tubule: modeling and analysis.*, American Journal of Physiology. Renal Physiology, vol. 315 no. 3 (September, 2018), pp. F692-F700 [doi] [abs] - Sands, JM; Layton, HE,
*Advances in understanding the urine-concentrating mechanism.*, Annual Review of Physiology, vol. 76 (January, 2014), pp. 387-409, ISSN 0066-4278 [doi] [abs] - Sands, JM; Mount, DB; Layton, HE,
*The physiology of water homeostasis*, in Core Concepts in the Disorders of Fluid, Electrolytes and Acid-Base Balance (November, 2013), pp. 1-28, ISBN 9781461437703 [doi] [abs] - Nieves-González, A; Clausen, C; Layton, AT; Layton, HE; Moore, LC,
*Transport efficiency and workload distribution in a mathematical model of the thick ascending limb.*, American Journal of Physiology. Renal Physiology, vol. 304 no. 6 (March, 2013), pp. F653-F664 [23097466], [doi] [abs] - Sands, JM; Layton, HE,
*The Urine Concentrating Mechanism and Urea Transporters*, Seldin and Geibisch's The Kidney, vol. 1 (2013), pp. 1463-1510 [doi]

- Li, Q; McDonough, AA; Layton, HE; Layton, AT,