Introduction to Mathematical Modeling of Blood Flow Control in the Kidney

Besides its best known role in the excretion of metabolic wastes and toxins, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, acid-base species, blood volume, and blood pressure. To properly fulfill its functions, it is crucial for the kidney to exercise hemodynamic control. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. In particular, we consider mathematical models that simulate renal blood flow regulation by means of key autoregulatory mechanisms: 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 diseases.