Longitudinal Residual Strains in Coronary Arteries

Constitutive formulation is fundamental to the study of vascular mechanics. A robust and accurate constitutive model can aid in the design of tissue engineered grafts or provide insights for growth and remodeling studies. Strains in constitutive model are defined with reference to a stress-free configuration. Therefore, identifying the appropriate stress-free configuration is important and has been the focus of many studies. Fung [1] and Vaishnav and Vossoughi [2] independently presented evidence showing that the traction-free state of a blood vessel is not stress-free due to the presence of residual strains. These residual strains are evident when a vessel ring in the unloaded state opens up into a sector in response to a radial cut. Chuong and Fung [3] proposed quantifying these residual strains by measuring the opening angle of the sector. The opening angle is defined as the angle between two lines which join at the midpoint of the inner wall extending to the tips of the inner wall at the location of the radial cut as shown in Figure 1. This technique has now become the canonical method for measuring residual strains in blood vessels. It is believed that this single radial cut can relieve a majority of the vessel’s residual stress [4].