Constrained multi-objective Bayesian optimization of novel growth-adaptive auxetic vascular grafts
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Current paediatric vascular grafts lack growth potential, necessitating high-risk re-interventions in adulthood. This work leverages the unique property of negative Poisson’s ratio of auxetic metamaterials in a novel growth-adaptive paediatric vascular graft (primarily for the Fontan procedure). The auxetic structure enables simultaneous controlled axial expansion (AE) and radial expansion (RE) using minimally invasive balloon catheterization. We demonstrate a constrained multi-objective Bayesian optimization framework to optimize a ‘double arrowhead’ auxetic structure. Clinical requirements are an initial diameter of 16mm, RE of 70-100%, and AE of 0-75% [1]. Ideally, both expansions are maximized for accommodating somatic growth. Expansion is evaluated using finite element analysis (FEA) with controlled 70% RE. The material model simulates L605 CoCr with elastoplasticity using a nonlinear isotropic hardening model. The optimization involves four geometric parameters related to strut angle, length, and thickness, an output constraint of 70% RE, and two conflicting objectives: maximize AE and minimize the peak von Mises stresses (for further potential RE). To navigate the design space during optimization while minimizing computationally expensive FEA evaluations, we employ Gaussian Process (GP) surrogate models. The exponential kernel is used to define covariance functions. The GPs are initially fitted to forty simulated designs (generated by Latin hypercube sampling) and are dynamically updated during optimization. New samples are generated by optimizing the expected constrained hypervolume improvement function [2,3]. The surrogate models show high predictive accuracy (R2>88%). The optimized design has an initial diameter of 16mm and 32% AE at 70% RE, satisfying clinical requirements. Compared to a baseline design, a reduced AE with improved peak stresses is observed, and further RE to 90% was possible. The study emphasizes the trade-off between optimizing radial versus axial expansion. The framework facilitates patient-specific optimization of growth-adaptive auxetic vascular grafts. Future work will incorporate axial flexibility and fatigue in the optimization. REFERENCES [1] Hut, T et al. Interdisciplinary cardiovascular and thoracic surgery, 37(5). (2023) [2] Emmerich, M. et al. Rapport technique, Leiden University, 34, 7-3. (2008). [3] Gardner, J. R. et al. ICML (Vol. 2014, pp. 937-945). (2014).
