An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling

Manuel K. Rausch (1) , Martin Genet (2) , Jay D. Humphrey (1)

1 Department of Biomedical Engineering [Yale University]
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine

Continuing advances in computational power and methods have enabled image-based biomechanical modeling to become a crucial tool in basic science, diagnostic and therapeutic medicine, and medical device design. One of the many challenges of this approach, however, is the identification of a stress-free reference configuration based on in vivo images of loaded and often prestressed or residually stressed soft tissues and organs. Fortunately, iterative methods have been proposed to solve this inverse problem, among them Sellier’s method. This method is particularly appealing for it is easy to implement, convergences reasonably fast, and can be coupled to nearly any finite element package. However, by means of several practical examples, we demonstrate that in its original formulation Sellier’s method is not optimally fast and may not converge for problems with large deformations. Fortunately, we can also show that a simple, inexpensive augmentation of Sellier’s method based on Aitken’s delta-squared process can not only ensure convergence but also significantly accelerate the method.

Mots clés: Inverse Methods; Fixed-Point Methods; Aitken’s Delta-Squared Process; Stress-free Reference Configuration; Soft Tissue Mechanics

Domaines: Biomécanique [physics.med-ph]; Ingénierie, finance et science [cs.CE]

Manuel K. Rausch, Martin Genet, Jay D. Humphrey. An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling. Journal of Biomechanics, 2017, 58, pp.227 - 231. ⟨10.1016/j.jbiomech.2017.04.021⟩. ⟨hal-01571436⟩