Arterial Tube Laws and Wave Speeds

The 1-D theory of flow in the arteries yields an equation for the wave speed in terms of the density of blood and the distensibility of the vessel. By means of this equation there is a duality between the equation for the wave speed and the tube law describing the area of the vessel as a function of pressure. We explore this duality for the equations for wave speed and tube laws that are most commonly used in theoretical arterial hemodynamics. We see that there are qualitative differences between these laws and the experimental data on wave speed in canine arteries measured by Anliker and his colleagues 50 years ago. We suggest an empirical equation for wave speed (and its dual tube law) that fits the experimental data as well as the common expectation that arteries become stiffer as the pressure increases. We conclude with a cautionary historical tale about the differences between the theoretical predictions and the experimental measurements of the speed of sound in air that persisted for more than 200 years.