A Nonlinear Thin-Wall Model for Vein Buckling

Tortuous or twisted veins are often seen in the retina, cerebrum, and legs (varicose veins) of one-third of the aged population, but the underlying mechanisms are poorly understood. While the collapse of veins under external pressure has been well documented, the bent buckling of long vein segments has not been studied. The objectives of this study were to develop a biomechanical model of vein buckling under internal pressure and to predict the critical pressure. Veins were modeled as thin-walled nonlinear elastic tubes with the Fung exponential strain energy function. Our results demonstrated that veins buckle due to high blood pressure or low axial tension. High axial tension stabilized veins under internal pressure. Our buckling model estimated the critical pressure accurately compared to the experimental measurements. The buckling equation provides a useful tool for studying the development of tortuous veins.