Characterization of anisotropic elastic properties of the arteries by exponential and polynomial strain energy functions.

Three-dimensional quasi-static mechanical measurements were carried out on cylindrical segments of the dog carotid and iliac arteries for determination of the passive anisotropic elastic properties of the vessel wall. On the basis of passive characteristics of outer diameter vs. intraluminal pressure, and axial extending force vs. intraluminal pressure, picked up at various fixed initial vascular length values, the incremental Young moduli and poisson ratios of the vessel wall were calculated in the 0--33 kPa (0--250 mm Hg) pressure range. The strain energy function of the arteries was approximated by polynomial and exponential models. We found that an exponential energy function with 4-parameters gives more accurate results than the 7- or 12-parameter polynomial functions. According to the results the axial modulus reaches higher values than the tangential and radial moduli at a low tangential stretch level, while at high tangential stretch the tangential modulus is the highest in both carotid and iliac arteries. After elevation of the initial tangential stretch the increase in the tangential modulus is the most pronounced, while the values of radial and axial moduli increased less. A change in the initial axial stretch influences the axial and radial moduli to a similar extent, but has no substantial effect on the value of the tangential modulus. The values of corresponding poisson ratios depend in a similar way on the initial deformation state. The different behaviour of the two Poisson ratios characterizing the mechanical coupling between tangential and axial directions, indicates that the structural coupling between the two main directions is asymmetrical. It is assumed that this property of the passive vascular structure can be explained by the network arrangement of collagen fibres in the vessel wall.