Study on the Mathematical Relationship between Cerebral Vascular Stent Structural Parameters and Flexibility

Vascular stents play a crucial role in managing vascular pathologies with high mortality and disability rates. New opportunities for cerebrovascular stent design are offered by biodegradable materials. However, current design methodologies rely heavily on empirical trial-and-error. A systematic theoretical framework is still lacking. A closed-form analytical mathematical model, which differs from existing models by targeting the specific flexibility requirement of tortuous cerebrovascular anatomies, is presented in this study. The model is established based on cantilever beam theory, energy conservation and Castigliano's theorem. The model is built to correlate stent structural parameters with mechanical flexibility. Numerical calculation is performed with MATLAB. Validation is conducted via finite element analysis (FEA), with a coefficient of determination R 2 =0.997 for the core parameter strut width (w) and an overall average R 2 of 0.917 for all structural parameters after dimensionless normalization. Key findings are revealed: stent flexibility is inversely proportional to the cube of strut width (w) and thickness (t). A more significant effect on flexibility is exerted by w than t. The transition of cerebrovascular stent design from empirical-driven approaches to theory-guided reasoning is realized by this work.