Growth-driven mechanical buckling as a mechanism of age-related tortuosity in human cerebral arteries

Human cerebral arteries become increasingly, sometimes abnormally, winding with age, but the mechanical basis of this change remains incompletely understood. To examine how arterial bends form and what sets their spacing, we modeled a cerebral artery as a slender elastic vessel supported by surrounding tissue. The distance between its ends remains constant, and the vessel can bend only in a plane tangent to the brain surface. As its natural length increases, axial compression builds until the vessel buckles. Bending partly relieves the compression, and the resulting waves grow in amplitude as elongation continues. Arterial bending stiffness and tissue support determine the wavelength, which is much larger than and proportional to vessel diameter, with comparatively weak dependence on other parameters. Numerical simulations captured a pre-buckling phase, rapid amplification of waves, and slow post-buckling growth during continued elongation. We evaluated these predictions using three-dimensional centerlines of cerebral arteries reconstructed from magnetic resonance angiography in healthy adults. Older age was associated with greater arterial length and excess-length ratio. For arterial waves oriented mostly parallel to the brain surface, wavelength increased with vessel diameter. Both this relationship and the observed wavelength-to-diameter ratio were consistent with model predictions. However, wave amplitude was not significantly associated with age. Overall, the modeling and imaging results support growth-driven buckling and post-buckling deformation under spatial constraint as a plausible mechanical explanation for age-related cerebral arterial tortuosity. This framework links vascular aging to growth-driven instability and pattern formation, with potential applications to diseased arteries beyond the brain.