Adaptive Algorithms for Optimal Hip Implant Positioning. Issue 1 (15th March 2018)

• Record Type: Journal Article
• Authors: Moldenhauer, Marian; Weiser, Martin; Zachow, Stefan
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 17:Issue 1(2017)
• Page Start: 203
• Page End: 204
• Publication Date: 2018-03-15
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201710071
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: In an aging society where the number of joint replacements rises, it is important to also increase the longevity of implants. In particular hip implants have a lifetime of at most 15 years. This derives primarily from pain due to implant migration, wear, inflammation, and dislocation, which is affected by the positioning of the implant during the surgery. Current joint replacement practice uses 2D software tools and relies on the experience of surgeons. Especially the 2D tools fail to take the patients' natural range of motion as well as stress distribution in the 3D joint induced by different daily motions into account. Optimizing the hip joint implant position for all possible parametrized motions under the constraint of a contact problem is prohibitively expensive as there are too many motions and every position change demands a recalculation of the contact problem. For the reduction of the computational effort, we use adaptive refinement on the parameter domain coupled with the interpolation method of Kriging. A coarse initial grid is to be locally refined using goal‐oriented error estimation, reducing locally high variances. This approach will be combined with multi‐grid optimization such that numerical errors are reduced. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)