Surrogate optimization of a lattice foot orthotic.
Derivative-free optimization
Finite element method
Flat foot
Foot orthotics
Homogenization
Surrogate
Journal
Computers in biology and medicine
ISSN: 1879-0534
Titre abrégé: Comput Biol Med
Pays: United States
ID NLM: 1250250
Informations de publication
Date de publication:
03 2023
03 2023
Historique:
received:
05
06
2022
revised:
04
11
2022
accepted:
27
11
2022
pubmed:
17
2
2023
medline:
15
3
2023
entrez:
16
2
2023
Statut:
ppublish
Résumé
Additive manufacturing enables to print patient-specific Foot Orthotics (FOs). In FOs featuring lattice structures, the variation of the cell's dimensions provides a locally variable stiffness to meet the therapeutic needs of each patient. In an optimization problem, however, using explicit Finite Element (FE) simulation of lattice FOs with converged 3D elements is computationally prohibitive. This paper presents a framework to efficiently optimize the cell's dimensions of a honeycomb lattice FO for flat foot condition. We built a surrogate based on shell elements whose mechanical properties were computed by the numerical homogenization technique. The model was submitted to a static pressure distribution of a flat foot and it predicted the displacement field for a given set of geometrical parameters of the honeycomb FO. This FE simulation was considered as a black-box and a derivative-free optimization solver was employed. The cost function was defined based on the difference between the predicted displacement by the model against a therapeutic target displacement. Using the homogenized model as a surrogate significantly accelerated the stiffness optimization of the lattice FO. The homogenized model could predict the displacement field 78 times faster than the explicit model. When 2000 evaluations were required in an optimization problem, the computational time was reduced from 34 days to 10 hours using the homogenized model rather than explicit model. Moreover, in the homogenized model, there was no need to re-create and re-mesh the insole's geometry in each iteration of the optimization. It was only required to update the effective properties. The presented homogenized model can be used as a surrogate within an optimization framework to customize cell's dimensions of honeycomb lattice FO in a computationally efficient manner.
Sections du résumé
BACKGROUND
Additive manufacturing enables to print patient-specific Foot Orthotics (FOs). In FOs featuring lattice structures, the variation of the cell's dimensions provides a locally variable stiffness to meet the therapeutic needs of each patient. In an optimization problem, however, using explicit Finite Element (FE) simulation of lattice FOs with converged 3D elements is computationally prohibitive. This paper presents a framework to efficiently optimize the cell's dimensions of a honeycomb lattice FO for flat foot condition.
METHODS
We built a surrogate based on shell elements whose mechanical properties were computed by the numerical homogenization technique. The model was submitted to a static pressure distribution of a flat foot and it predicted the displacement field for a given set of geometrical parameters of the honeycomb FO. This FE simulation was considered as a black-box and a derivative-free optimization solver was employed. The cost function was defined based on the difference between the predicted displacement by the model against a therapeutic target displacement.
RESULTS
Using the homogenized model as a surrogate significantly accelerated the stiffness optimization of the lattice FO. The homogenized model could predict the displacement field 78 times faster than the explicit model. When 2000 evaluations were required in an optimization problem, the computational time was reduced from 34 days to 10 hours using the homogenized model rather than explicit model. Moreover, in the homogenized model, there was no need to re-create and re-mesh the insole's geometry in each iteration of the optimization. It was only required to update the effective properties.
CONCLUSION
The presented homogenized model can be used as a surrogate within an optimization framework to customize cell's dimensions of honeycomb lattice FO in a computationally efficient manner.
Identifiants
pubmed: 36796183
pii: S0010-4825(22)01084-8
doi: 10.1016/j.compbiomed.2022.106376
pii:
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
106376Informations de copyright
Copyright © 2022 Elsevier Ltd. All rights reserved.
Déclaration de conflit d'intérêts
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.