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.

中文翻译：

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具有应力调节生长和重塑的血管机械生物学弯曲

血管的稳定性对于维持其功能至关重要，而严重的血管迂曲会导致各种临床并发症。血管的生长和重塑受机械和生化信号的调节，会产生影响血管稳定性的残余应力。在本文中，我们结合理论和模拟来研究血管在压力调节生长和重塑过程中的力学生物学行为。考虑了基质体积生长以及胶原纤维的周转和重新定向的影响。首先进行线性稳定性分析来研究血管的机械生物学稳定性。通过开发一种结合了应力调制生长和重塑的有限元方法，我们验证了临界状态的理论解决方案，并进一步捕获了血管的屈曲后演化。我们的结果表明，内压增加会导致血管壁增厚，从而机械地稳定血管，而内压对机械生物学屈曲的影响是非单调的。与机械不稳定性相比，机械生物学屈曲导致更大的模式数和更短的波长，正如在静脉曲张中通常观察到的那样。后屈曲期间的血管可能表现出不均匀的壁厚，这与弯曲主动脉的实验观察结果一致。这些发现强调了机械重塑在组织形态发生中的关键作用，并可以加深对血管迂曲形成和发展背后的机械生物学机制的理解。