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

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.

计算能力和方法的不断进步使基于图像的生物力学建模成为基础科学、诊断和治疗医学以及医疗器械设计中的重要工具。然而，这种方法面临的众多挑战之一是根据加载的且往往是预应变或存在残余应力的软组织和器官的体内图像来确定无应力参考构型。幸运的是，已经有人提出了迭代方法来解决这个逆问题，其中包括塞利耶（Sellier）方法。这种方法特别有吸引力，因为它易于实施，收敛速度相当快，并且可以与几乎任何有限元软件包相结合。然而，通过几个实际例子，我们证明在其原始公式中，塞利耶方法并非最优快速，对于大变形问题可能不会收敛。幸运的是，我们还可以表明，基于艾特肯（Aitken）的德尔塔平方过程对塞利耶方法进行一种简单、低成本的改进，不仅可以确保收敛，还能显著加快该方法的速度。