title: Mathematical modeling of renal hemodynamics in physiology and pathophysiology.
abstract: In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease.
authors.affiliation: National Institute for Mathematical and Biological Synthesis, University of Tennessee, United States. Electronic address: sgouralis@nimbios.org.
authors.forename: Ioannis
authors.initials: I
authors.lastname: Sgouralis
authors.affiliation: Department of Mathematics, Duke University, Box 90320, Durham, NC 27708, United States. Electronic address: alayton@math.duke.edu.
authors.forename: Anita T
authors.initials: AT
authors.lastname: Layton
mesh_terms: D006439:Hemodynamics / Q000502:physiology*; D006801:Humans; D007668:Kidney / Q000502:physiology / Q000503:physiopathology*; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D012079:Renal Circulation / Q000502:physiology*
keywords: Blood flow; Glomerular filtration; Kidney; Myogenic response; Nonlinear dynamics; Tubuloglomerular feedback