Blood vessel buckling within soft surrounding tissue generates tortuosity.

The stability of blood vessel under lumen pressure load is essential to the maintenance of normal arterial function. Previous mechanical models showed that blood vessels may buckle into a half sine wave but arteries and veins in vivo often demonstrate tortuous paths with multiple waves. The objective of this study was to analyze the buckling of blood vessels under lumen pressure with surrounding tissue support. Blood vessels were modeled as elastic cylindrical vessels within an elastic substrate. Buckling equations were established to determine the critical pressure and the wavelength. These equations and simulation results demonstrated that blood vessels do take higher order mode shapes when buckling inside an elastic substrate while they take the basal mode shape without the substrate. The wave number increases i.e. blood vessels take a higher mode shape, as the stiffness of the substrate increases. These results suggest that mechanical buckling is a possible mechanism for the development of tortuous blood vessels. The current model provides a powerful tool for further studying the tortuosity of arteries and veins.