Pathological Growth-Induced Helical Buckling of Blood Vessels

Abstract

Helical vessels are widely observed in many pathological tissues, such as solid tumors, healing wounds, and varicose veins. However, it remains yet unclear how originally healthy and straight vessels transit to helical shapes. Here, we combine theoretical analysis and numerical simulations to investigate the helical buckling of growing vessels embedded in matrix. Based on linear stability analysis, we predict the critical growth strain that induces three-dimensional (3D) helical and two-dimensional (2D) sinusoidal buckling of vessels. This critical growth strain is regulated by the geometry of the vessel and the modulus ratio between the vessel and the matrix. A phase diagram is established to reveal the dependence of helical and sinusoidal modes on the vessel thickness and modulus ratio. Finite element simulations are performed to validate the theoretical prediction of the critical growth strain and further track the postbuckling evolution of growing vessels. The pitch of helix and the long and short axis of projected cross-section of vessels are characterized with increasing growth strain. Our findings elucidate the mechanism underlying abnormal formation of helical vessels, in consistency with the observations in tumors and varicose veins. This study could also inspire mechanics-based technologies for diseases diagnosis.