The Spencer's Curve: Clinical Implications of a Classic Hemodynamic Model

Merrill P Spencer and John M Reid applied the Hagen-Poiseuille law, continuity principle, and cerebrovascular resistance to describe a theoretical model of the relationship between the flow velocity, flow volume, and decreasing size of the residual vessel lumen. The model was plotted in a graph that became widely known as the Spencer's curve. Although derived for a smooth and axis-symmetric arterial stenosis of a short length in a segment with no bifurcations being perfused at stable arterial pressures and viscosity, this model represents a milestone in understanding cerebral hemodynamics with long-lasting practical and research implications. This review summarizes several hemodynamic principles that determine velocity and flow volume changes, explains how the model aids interpretation of cerebrovascular ultrasound studies, and describes its impact on clinical practice and research.