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J Biomech. 2017 Jun 14;58:227-231. doi: 10.1016/j.jbiomech.2017.04.021. Epub 2017 May 5.

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

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Department of Biomedical Engineering, Yale University, United States; Department of Aerospace Engineering & Engineering Mechanics, University of Texas at Austin, United States. Electronic address:
LMS, École Polytechnique, CNRS, Université Paris-Saclay, France; Inria, Université Paris-Saclay, France.
Department of Biomedical Engineering, Yale University, United States.


Continued advances in computational power and methods have enabled image-based biomechanical modeling to become an important tool in basic science, diagnostic and therapeutic medicine, and medical device design. One of the many challenges of this approach, however, is identification of a stress-free reference configuration based on in vivo images of loaded and often prestrained 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 because it is easy to implement, convergences reasonably fast, and can be coupled to nearly any finite element package. By means of several practical examples, however, 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.


Aitken’s delta-squared process; Fixed-point methods; Image-based biomechanical modeling; Inverse methods; Stress-free reference configuration

[Indexed for MEDLINE]

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