Mathematical modeling of renal hemodynamics in physiology and pathophysiology

•Hemodynamic control is essential to the maintenance of proper kidney functions.•We describe mathematical models developed to study renal autoregulation.•Models have been applied to understand kidney functions in health and disease.

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.