Compressibility and constitutive equation of arterial wall in radial compression experiments

A large number of papers treat the tensile properties of arterial wall, but few treat compressive properties. Almost everybody assumes incompressibility; few have measured the vessel wall fluid extrusion due to compressive loading. In this work, uniaxial compressive force is applied directly on rabbit thoracic artery in the radial direction to study its constitutive equation under compressive stresses. The resulting stress-strain curves show that the wall material becomes increasingly stiffer at larger compressive strain, quite similar to the behavior in tension. A pseudo-strain energy function of the exponential type which has been applied successfully on the tension side is used to identify the material constants on the compression side. The material constants are identified in two ways: with and without the assumption of incompressibility. To determine the compressibility of the wall, the fluid extrusion accompanying this type of loading is measured, and is found to be in the range of 0.50-1.26% of the undeformed tissue volume per 10 kPa compressive stress loading in the radial direction. At compressive stresses higher than 30 kPa, the percentage of fluid extrusion per unit compressive stress decreases. At this degree of fluid extrusion the tissue is only slightly compressible (or nearly incompressible). However, the use of incompressibility assumption in the stress-strain relationship results in a set of material constants which is very different from that derived without that assumption.