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

• Published in: Journal of biomechanics Vol. 58; pp. 227 - 231
• Main Authors: Rausch, Manuel K., Genet, Martin, Humphrey, Jay D.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 14.06.2017; Elsevier Limited; Elsevier
• Subjects: Aitken’s delta-squared process; Algorithms; Augmentation; Biomechanical Phenomena; Biomechanics; Blood clots; Blood pressure; Computational Engineering, Finance, and Science; Computer applications; Computer Science; Convergence; Coronary vessels; Deformation; Diagnostic software; Diagnostic systems; Engineering Sciences; Finite Element Analysis; Finite element method; Fixed-point methods; Fluid-structure interaction; Geometry; Image-based biomechanical modeling; Inverse methods; Iterative methods; Mathematical analysis; Mathematical models; Mechanics; Medical devices; Medical equipment; Medicine; Methods; Models, Biological; Optimization; Organs; Physical Medicine and Rehabilitation; Soft tissues; Stress-free reference configuration; Stresses; Inverse methods; Image-based biomechanical modeling; Stress-free reference configuration; Fixed-point methods; Aitken’s delta-squared process; Stress-free Reference Configuration; Aitken’s Delta-Squared Process; Inverse Methods; Soft Tissue Mechanics; Fixed-Point Methods
• ISSN: 0021-9290; 1873-2380; 1873-2380
• DOI: 10.1016/j.jbiomech.2017.04.021

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.