A Density-Dependent Target Stimulus for Inverse Bone (Re)modeling with Homogenized Finite Element Models

Overview

Journal Ann Biomed Eng

Specialty Biomedical Engineering

Date 2022 Nov 23

PMID 36418745

Authors

Sebastian Bachmann

Dieter H Pahr

Alexander Synek

Affiliations

Soon will be listed here.

Abstract

Inverse bone (re)modeling (IBR) can infer physiological loading conditions from the bone microstructure. IBR scales unit loads, imposed on finite element (FE) models of a bone, such that the trabecular microstructure is homogeneously loaded and the difference to a target stimulus is minimized. Micro-FE (µFE) analyses are typically used to model the microstructure, but computationally more efficient, homogenized FE (hFE) models, where the microstructure is replaced by an equivalent continuum, could be used instead. However, also the target stimulus has to be translated from the tissue to the continuum level. In this study, a new continuum-level target stimulus relating relative bone density and strain energy density is proposed. It was applied using different types of hFE models to predict the physiological loading of 21 distal radii sections, which was subsequently compared to µFE-based IBR. The hFE models were able to correctly identify the dominant load direction and showed a high correlation of the predicted forces, but mean magnitude errors ranged from - 14.7 to 26.6% even for the best models. While µFE-based IBR can still be regarded as a gold standard, hFE-based IBR enables faster predictions, the usage of more sophisticated boundary conditions, and the usage of clinical images.

Citing Articles

Advancing 3D Dental Implant Finite Element Analysis: Incorporating Biomimetic Trabecular Bone with Varied Pore Sizes in Voronoi Lattices.

Alemayehu D, Todoh M, Huang S J Funct Biomater. 2024; 15(4).

PMID: 38667551 PMC: 11051206. DOI: 10.3390/jfb15040094.

References

Badilatti S, Christen P, Ferguson S, Muller R . Computational modeling of long-term effects of prophylactic vertebroplasty on bone adaptation. Proc Inst Mech Eng H. 2017; 231(5):423-431. DOI: 10.1177/0954411916683222. View

Bergmann G, Bender A, Dymke J, Duda G, Damm P . Standardized Loads Acting in Hip Implants. PLoS One. 2016; 11(5):e0155612. PMC: 4873223. DOI: 10.1371/journal.pone.0155612. View

Bergmann G, Bender A, Graichen F, Dymke J, Rohlmann A, Trepczynski A . Standardized loads acting in knee implants. PLoS One. 2014; 9(1):e86035. PMC: 3900456. DOI: 10.1371/journal.pone.0086035. View

Bona M, Martin L, Fischer K . A contact algorithm for density-based load estimation. J Biomech. 2006; 39(4):636-44. DOI: 10.1016/j.jbiomech.2005.01.006. View

Bona M, Martin L, Fischer K . Density-based load estimation using two-dimensional finite element models: a parametric study. Comput Methods Biomech Biomed Engin. 2006; 9(4):221-9. DOI: 10.1080/10255840600792451. View

Campoli G, Weinans H, Zadpoor A . Computational load estimation of the femur. J Mech Behav Biomed Mater. 2012; 10:108-19. DOI: 10.1016/j.jmbbm.2012.02.011. View

Christen P, Ito K, Ellouz R, Boutroy S, Sornay-Rendu E, Chapurlat R . Bone remodelling in humans is load-driven but not lazy. Nat Commun. 2014; 5:4855. DOI: 10.1038/ncomms5855. View

Christen P, Ito K, Galis F, van Rietbergen B . Determination of hip-joint loading patterns of living and extinct mammals using an inverse Wolff's law approach. Biomech Model Mechanobiol. 2014; 14(2):427-32. DOI: 10.1007/s10237-014-0602-8. View

Christen P, Ito K, Knippels I, Muller R, van Lenthe G, van Rietbergen B . Subject-specific bone loading estimation in the human distal radius. J Biomech. 2012; 46(4):759-66. DOI: 10.1016/j.jbiomech.2012.11.016. View

10.

Christen P, van Rietbergen B, Lambers F, Muller R, Ito K . Bone morphology allows estimation of loading history in a murine model of bone adaptation. Biomech Model Mechanobiol. 2011; 11(3-4):483-92. DOI: 10.1007/s10237-011-0327-x. View

11.

Christen P, Schulte F, Zwahlen A, van Rietbergen B, Boutroy S, Melton 3rd L . Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm. J R Soc Interface. 2016; 13(114):20150991. PMC: 4759804. DOI: 10.1098/rsif.2015.0991. View

12.

Daszkiewicz K, Maquer G, Zysset P . The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements. Biomech Model Mechanobiol. 2016; 16(3):731-742. DOI: 10.1007/s10237-016-0849-3. View

13.

Erdemir A, McLean S, Herzog W, van den Bogert A . Model-based estimation of muscle forces exerted during movements. Clin Biomech (Bristol). 2006; 22(2):131-54. DOI: 10.1016/j.clinbiomech.2006.09.005. View

14.

Fischer K, Jacobs C, Carter D . Computational method for determination of bone and joint loads using bone density distributions. J Biomech. 1995; 28(9):1127-35. DOI: 10.1016/0021-9290(94)00182-4. View

15.

Fischer K, Jacobs C, Levenston M, Carter D . Different loads can produce similar bone density distributions. Bone. 1996; 19(2):127-35. DOI: 10.1016/8756-3282(96)00140-8. View

16.

Fischer K, Jacobs C, Levenston M, Cody D, Carter D . Bone Load Estimation for the Proximal Femur Using Single Energy Quantitative CT Data. Comput Methods Biomech Biomed Engin. 2001; 1(3):233-245. DOI: 10.1080/01495739808936704. View

17.

Fischer K, Jacobs C, Levenston M, Cody D, Carter D . Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads. Comput Methods Biomech Biomed Engin. 2001; 2(4):271-283. DOI: 10.1080/10255849908907992. View

18.

Gibson L . The mechanical behaviour of cancellous bone. J Biomech. 1985; 18(5):317-28. DOI: 10.1016/0021-9290(85)90287-8. View

19.

Gross T, Pahr D, Zysset P . Morphology-elasticity relationships using decreasing fabric information of human trabecular bone from three major anatomical locations. Biomech Model Mechanobiol. 2012; 12(4):793-800. DOI: 10.1007/s10237-012-0443-2. View

20.

Hosseini H, Dunki A, Fabech J, Stauber M, Vilayphiou N, Pahr D . Fast estimation of Colles' fracture load of the distal section of the radius by homogenized finite element analysis based on HR-pQCT. Bone. 2017; 97:65-75. DOI: 10.1016/j.bone.2017.01.003. View