Mechanobiological tortuosity of blood vessels with stress-modulated growth and remodeling

The stability of blood vessels is essential for maintaining their functions, while severe blood vessel tortuosity leads to various clinical complications. The growth and remodeling of blood vessels, which are regulated by mechanical and biochemical cues, cause residual stresses that affect vessel stability. In this paper, we combine theory and simulations to study the mechanobiological behavior of blood vessels with stress-modulated growth and remodeling. Effects of the volumetric growth of the matrix and the turnover and reorientation of collagen fibers are accounted for. Linear stability analysis is first carried out to investigate the mechanobiological stability of blood vessels. By developing a finite element method that incorporates stress-modulated growth and remodeling, we validate the theoretical solution of the critical state and further capture the postbuckling evolution of blood vessels. Our results show that an increased internal pressure can lead to the thickening of the vessel wall, which stabilizes the blood vessels mechanically, whereas the effect of internal pressure on the mechanobiological buckling is nonmonotonic. Compared to the mechanical instability, the mechanobiological buckling results in a larger mode number and a shorter wavelength, as usually observed in varicose veins. Vessels during postbuckling may exhibit non-uniform wall thicknesses, in consistency with the experimental observation on tortuous aortas. These findings highlight the crucial role of mechanical remodeling in tissue morphogenesis and could deepen the understanding of mechanobiological mechanisms underlying the formation and development of blood vessel tortuosity.