Research Papers

Estimation of Local Bone Loads for the Volume of Interest

[+] Author and Article Information
Jung Jin Kim

The Cho Chun Shik Graduate
School for Green Transportation,
Korea Advanced Institute of Science and
373-1, Guseong-dong,
Yuseong-gu, Daejon 305-701, South Korea
e-mail: kjj4537@kaist.ac.kr

Youkyung Kim

The Cho Chun Shik Graduate
School for Green Transportation,
Korea Advanced Institute of
Science and Technology,
373-1, Guseong-dong,
Yuseong-gu, Daejon 305-701, South Korea
e-mail: swantom30@naver.com

In Gwun Jang

The Cho Chun Shik Graduate
School for Green Transportation,
Korea Advanced Institute of Science and
373-1, Guseong-dong,
Yuseong-gu, Daejon 305-701, South Korea
e-mail: igjang@kaist.edu

1Corresponding author.

Manuscript received September 17, 2015; final manuscript received April 13, 2016; published online June 7, 2016. Assoc. Editor: David Corr.

J Biomech Eng 138(7), 071004 (Jun 07, 2016) (8 pages) Paper No: BIO-15-1458; doi: 10.1115/1.4033478 History: Received September 17, 2015; Revised April 13, 2016

Computational bone remodeling simulations have recently received significant attention with the aid of state-of-the-art high-resolution imaging modalities. They have been performed using localized finite element (FE) models rather than full FE models due to the excessive computational costs of full FE models. However, these localized bone remodeling simulations remain to be investigated in more depth. In particular, applying simplified loading conditions (e.g., uniform and unidirectional loads) to localized FE models have a severe limitation in a reliable subject-specific assessment. In order to effectively determine the physiological local bone loads for the volume of interest (VOI), this paper proposes a novel method of estimating the local loads when the global musculoskeletal loads are given. The proposed method is verified for the three VOI in a proximal femur in terms of force equilibrium, displacement field, and strain energy density (SED) distribution. The effect of the global load deviation on the local load estimation is also investigated by perturbing a hip joint contact force (HCF) in the femoral head. Deviation in force magnitude exhibits the greatest absolute changes in a SED distribution due to its own greatest deviation, whereas angular deviation perpendicular to a HCF provides the greatest relative change. With further in vivo force measurements and high-resolution clinical imaging modalities, the proposed method will contribute to the development of reliable patient-specific localized FE models, which can provide enhanced computational efficiency for iterative computing processes such as bone remodeling simulations.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Cowin, S. C. , and Hegedus, D. H. , 1976, “ Bone Remodeling I: Theory of Adaptive Elasticity,” J. Elast., 6(3), pp. 313–326. [CrossRef]
Carter, D. R. , Orr, T. E. , and Fyhrie, D. P. , 1989, “ Relationships Between Loading History and Femoral Cancellous Bone Architecture,” J. Biomech., 22(3), pp. 231–244. [CrossRef] [PubMed]
Huiskes, R. , Ruimerman, R. , van Lenthe, G. H. , and Janssen, J. D. , 2000, “ Effects of Mechanical Forces on Maintenance and Adaptation of Form in Trabecular Bone,” Nature, 405(6787), pp. 704–706. [CrossRef] [PubMed]
Adachi, T. , Tsubota, K. , Tomita, Y. , and Hollister, S. J. , 2001, “ Trabecular Surface Remodeling Simulation for Cancellous Bone Using Microstructural Voxel Finite Element Models,” ASME J. Biomech. Eng., 123(5), p. 403. [CrossRef]
Ruimerman, R. , Hilbers, P. , Van Rietbergen, B. , and Huiskes, R. , 2005, “ A Theoretical Framework for Strain-Related Trabecular Bone Maintenance and Adaptation,” J. Biomech., 38(4), pp. 931–941. [CrossRef] [PubMed]
Jang, I. G. , and Kim, I. Y. , 2010, “ Application of Design Space Optimization to Bone Remodeling Simulation of Trabecular Architecture in Human Proximal Femur for Higher Computational Efficiency,” Finite Elem. Anal. Des., 46(4), pp. 311–319. [CrossRef]
Jang, I. G. , and Kim, I. Y. , 2010, “ Computational Study on the Effect of Loading Alteration Caused by Disc Degeneration on the Trabecular Architecture in Human Lumbar Spine,” J. Biomech., 43(3), pp. 492–499. [CrossRef] [PubMed]
Schulte, F. A. , Lambers, F. M. , Webster, D. J. , Kuhn, G. , and Müller, R. , 2011, “ In Vivo Validation of a Computational Bone Adaptation Model Using Open-Loop Control and Time-Lapsed Micro-Computed Tomography,” Bone, 49(6), pp. 1166–1172. [CrossRef] [PubMed]
Christen, P. , Ito, K. , dos Santos, A. A. , Müller, R. , and Bert van Rietbergen , 2013, “ Validation of a Bone Loading Estimation Algorithm for Patient-Specific Bone Remodelling Simulations,” J. Biomech., 46(5), pp. 941–948. [CrossRef] [PubMed]
Levchuk, A. , Zwahlen, A. , Weigt, C. , Lambers, F. M. , Badilatti, S. D. , Schulte, F. A. , Kuhn, G. , and Müller, R. , 2014, “ The Clinical Biomechanics Award 2012—Presented by the European Society of Biomechanics: Large Scale Simulations of Trabecular Bone Adaptation to Loading and Treatment,” Clin. Biomech., 29(4), pp. 355–362. [CrossRef]
Christen, P. , Ito, K. , Müller, R. , Rubin, M. R. , Dempster, D. W. , Bilezikian, J. P. , and van Rietbergen, B. , 2012, “ Patient-Specific Bone Modelling and Remodelling Simulation of Hypoparathyroidism Based on Human Iliac Crest Biopsies,” J. Biomech., 45(14), pp. 2411–2416. [CrossRef] [PubMed]
Liu, X. S. , Huang, A. H. , Zhang, X. H. , Sajda, P. , Ji, B. , and Guo, X. E. , 2008, “ Dynamic Simulation of Three Dimensional Architectural and Mechanical Alterations in Human Trabecular Bone During Menopause,” Bone, 43(2), pp. 292–301. [CrossRef] [PubMed]
Müller, R. , 2005, “ Long-Term Prediction of Three-Dimensional Bone Architecture in Simulations of Pre-, Peri- and Post-Menopausal Microstructural Bone Remodeling,” Osteoporos. Int., 16(S02), pp. S25–S35. [CrossRef] [PubMed]
Wang, H. , Ji, B. , Liu, X. S. , Guo, X. E. , Huang, Y. , and Hwang, K.-C. , 2012, “ Analysis of Microstructural and Mechanical Alterations of Trabecular Bone in a Simulated Three-Dimensional Remodeling Process,” J. Biomech., 45(14), pp. 2417–2425. [CrossRef] [PubMed]
Tsubota, K. I. , Suzuki, Y. , Yamada, T. , Hojo, M. , Makinouchi, A. , and Adachi, T. , 2009, “ Computer Simulation of Trabecular Remodeling in Human Proximal Femur Using Large-Scale Voxel FE Models: Approach to Understanding Wolff's Law,” J. Biomech., 42(8), pp. 1088–1094. [CrossRef] [PubMed]
Boyle, C. , and Kim, I. Y. , 2011, “ Three-Dimensional Micro-Level Computational Study of Wolff's Law Via Trabecular Bone Remodeling in the Human Proximal Femur Using Design Space Topology Optimization,” J. Biomech., 44(5), pp. 935–942. [CrossRef] [PubMed]
Fischer, K. J. , Jacobs, C. R. , and Carter, D. R. , 1995, “ Computational Method for Determination of Bone and Joint Loads Using Bone Density Distributions,” J. Biomech., 28(9), pp. 1127–1135. [CrossRef] [PubMed]
Fischer, K. J. , Jacobs, C. R. , Levenston, M. E. , Cody, D. D. , and Carter, D. R. , 1998, “ Bone Load Estimation for the Proximal Femur Using Single Energy Quantitative CT Data,” Comput. Methods Biomech. Biomed. Engin., 1(3), pp. 233–245. [CrossRef] [PubMed]
Fischer, K. J. , Jacobs, C. R. , Levenston, M. E. , Cody, D. D. , and Carter, D. R. , 1999, “ Proximal Femoral Density Patterns are Consistent With Bicentric Joint Loads,” Comput. Methods Biomech. Biomed. Eng., 2(4), pp. 271–283. [CrossRef]
Fischer, K. J. , Eckstein, F. , and Becker, C. , 1999, “ Density-Based Load Estimation Predicts Altered Femoral Load Directions for Coxa Vara and Coxa Valga,” J. Musculoskelet. Res., 3(2), pp. 83–92. [CrossRef]
Christen, P. , Van Rietbergen, B. , Lambers, F. M. , Müller, R. , and Ito, K. , 2012, “ Bone Morphology Allows Estimation of Loading History in a Murine Model of Bone Adaptation,” Biomech. Model. Mechanobiol., 11(3–4), pp. 483–492. [CrossRef] [PubMed]
Christen, P. , Ito, K. , Knippels, I. , Müller, R. , van Lenthe, G. H. , and van Rietbergen, B. , 2013, “ Subject-Specific Bone Loading Estimation in the Human Distal Radius,” J. Biomech., 46(4), pp. 759–766. [CrossRef] [PubMed]
Campoli, G. , Weinans, H. , and Zadpoor, A. A. , 2012, “ Computational Load Estimation of the Femur,” J. Mech. Behav. Biomed. Mater., 10, pp. 108–119. [CrossRef] [PubMed]
Zadpoor, A. A. , Campoli, G. , and Weinans, H. , 2013, “ Neural Network Prediction of Load From the Morphology of Trabecular Bone,” Appl. Math. Model., 37(7), pp. 5260–5276. [CrossRef]
Zadpoor, A. A. , 2013, “ Open Forward and Inverse Problems in Theoretical Modeling of Bone Tissue Adaptation,” J. Mech. Behav. Biomed. Mater., 27, pp. 249–261. [CrossRef] [PubMed]
Bergmann, G. , Deuretzbacher, G. , Heller, M. , Graichen, F. , Rohlmann, A. , Strauss, J. , and Duda, G. N. , 2001, “ Hip Contact Forces and Gait Patterns From Routine Activities,” J. Biomech., 34(7), pp. 859–871. [CrossRef] [PubMed]
Lloyd, D. G. , and Besier, T. F. , 2003, “ An EMG-Driven Musculoskeletal Model to Estimate Muscle Forces and Knee Joint Moments In Vivo,” J. Biomech., 36(6), pp. 765–776. [CrossRef] [PubMed]
Jinha, A. , Ait-Haddou, R. , and Herzog, W. , 2006, “ Predictions of Co-Contraction Depend Critically on Degrees-of-Freedom in the Musculoskeletal Model,” J. Biomech., 39(6), pp. 1145–1152. [CrossRef] [PubMed]
Kim, H. J. , Fernandez, J. W. , Akbarshahi, M. , Walter, J. P. , Fregly, B. J. , and Pandy, M. G. , 2009, “ Evaluation of Predicted Knee-Joint Muscle Forces During Gait Using an Instrumented Knee Implant,” J. Orthop. Res., 27(10), pp. 1326–1331. [CrossRef] [PubMed]
Phillips, A. T. M. , Villette, C. C. , and Modenese, L. , 2015, “ Femoral Bone Mesoscale Structural Architecture Prediction Using Musculoskeletal and Finite Element Modelling,” Int. Biomech., 2(1), pp. 43–61. [CrossRef]
Cook, R. D. , Malkus, D. S. , Plesha, M. E. , and Witt, R. J. W. , 2002, Concept and Applications of Finite Element Analysis, Wiley, New York.
Morgan, E. F. , Bayraktar, H. H. , and Keaveny, T. M. , 2003, “ Trabecular Bone Modulus–Density Relationships Depend on Anatomic Site,” J. Biomech., 36(7), pp. 897–904. [CrossRef] [PubMed]
Snyder, S. M. , and Schneider, E. , 1991, “ Estimation of Mechanical Properties of Cortical Bone by Computed Tomography,” J. Orthop. Res., 9(3), pp. 422–431. [CrossRef] [PubMed]
Heller, M. O. , Bergmann, G. , Kassi, J. P. , Claes, L. , Haas, N. P. , and Duda, G. N. , 2005, “ Determination of Muscle Loading at the Hip Joint for Use in Pre-Clinical Testing,” J. Biomech., 38(5), pp. 1155–1163. [CrossRef] [PubMed]
Verhulp, E. , van Rietbergen, B. , and Huiskes, R. , 2008, “ Load Distribution in the Healthy and Osteoporotic Human Proximal Femur During a Fall to the Side,” Bone, 42(1), pp. 30–35. [CrossRef] [PubMed]
Adachi, T. , Osako, Y. , Tanaka, M. , Hojo, M. , and Hollister, S. J. , 2006, “ Framework for Optimal Design of Porous Scaffold Microstructure by Computational Simulation of Bone Regeneration,” Biomaterials, 27(21), pp. 3964–3972. [CrossRef] [PubMed]
Shefelbine, S. J. , Augat, P. , Claes, L. , and Simon, U. , 2005, “ Trabecular Bone Fracture Healing Simulation With Finite Element Analysis and Fuzzy Logic,” J. Biomech., 38(12), pp. 2440–2450. [CrossRef] [PubMed]
Kim, J. J. , and Jang, I. G. , “ Image Resolution Enhancement for Healthy Weight-Bearing Bones Based on Topology Optimization,” J. Biomech., (submitted).
Magland, J. F. , Zhang, N. , Rajapakse, C. S. , and Wehrli, F. W. , 2012, “ Computationally-Optimized Bone Mechanical Modeling From High-Resolution Structural Images,” PLoS One, 7(4), p. e35525. [CrossRef] [PubMed]
Bruyneel, M. , and Duysinx, P. , 2005, “ Note on Topology Optimization of Continuum Structures Including Self-Weight,” Struct. Multidiscip. Optim., 29(4), pp. 245–256. [CrossRef]
Jang, I. G. , and Kim, I. Y. , 2008, “ Computational Study of Wolff's Law With Trabecular Architecture in the Human Proximal Femur Using Topology Optimization,” J. Biomech., 41(11), pp. 2353–2361. [CrossRef] [PubMed]
Beck, T. J. , Ruff, C. B. , Scott, W. W. , Plato, C. C. , Tobin, J. D. , and Quan, C. A. , 1992, “ Sex Differences in Geometry of the Femoral Neck With Aging: A Structural Analysis of Bone Mineral Data,” Calcif. Tissue Int., 50(1), pp. 24–29. [CrossRef] [PubMed]
Heller, M. , Bergmann, G. , Deuretzbacher, G. , Dürselen, L. , Pohl, M. , Claes, L. , Haas, N. , and Duda, G. , 2001, “ Musculo-Skeletal Loading Conditions at the Hip During Walking and Stair Climbing,” J. Biomech., 34(7), pp. 883–893. [CrossRef] [PubMed]
Stansfield, B. W. , Nicol, A. C. , Paul, J. P. , Kelly, I. G. , Graichen, F. , and Bergmann, G. , 2003, “ Direct Comparison of Calculated Hip Joint Contact Forces With Those Measured Using Instrumented Implants. An Evaluation of a Three-Dimensional Mathematical Model of the Lower Limb,” J. Biomech., 36(7), pp. 929–936. [CrossRef] [PubMed]
Martelli, S. , Taddei, F. , Cappello, A. , Van Sint Jan, S. , Leardini, A. , and Viceconti, M. , 2011, “ Effect of Sub-Optimal Neuromotor Control on the Hip Joint Load During Level Walking,” J. Biomech., 44(9), pp. 1716–1721. [CrossRef] [PubMed]
Modenese, L. , Gopalakrishnan, A. , and Phillips, A. T. M. , 2013, “ Application of a Falsification Strategy to a Musculoskeletal Model of the Lower Limb and Accuracy of the Predicted Hip Contact Force Vector,” J. Biomech., 46(6), pp. 1193–1200. [CrossRef] [PubMed]
Modenese, L. , Phillips, A. T. M. , and Bull, A. M. J. , 2011, “ An Open Source Lower Limb Model: Hip Joint Validation,” J. Biomech., 44(12), pp. 2185–2193. [CrossRef] [PubMed]
Zhao, C. , Hobbs, B. E. , Mühlhaus, H. B. , and Ord, A. , 1999, “ A Consistent Point-Searching Algorithm for Solution Interpolation in Unstructured Meshes Consisting of 4-Node Bilinear Quadrilateral Elements,” Int. J. Numer. Methods Eng., 45(10), pp. 1509–1526. [CrossRef]
Dohrmann, C. R. , Key, S. W. , and Heinstein, M. W. , 2000, “ A Method for Connecting Dissimilar Finite Element Meshes in Two Dimensions,” Int. J. Numer. Methods Eng., 48(5), pp. 655–678. [CrossRef]
Verhulp, E. , van Rietbergen, B. , and Huiskes, R. , 2006, “ Comparison of Micro-Level and Continuum-Level Voxel Models of the Proximal Femur,” J. Biomech., 39(16), pp. 2951–2957. [CrossRef] [PubMed]
Lee, Y. H. , Kim, Y. , Kim, J. J. , and Jang, I. G. , 2015, “ Homeostasis-Based Aging Model for Trabecular Changes and Its Correlation With Age-Matched Bone Mineral Densities and Radiographs,” Eur. J. Radiol., 84(11), pp. 2261–2268. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Schematic procedure of local bone load estimation: (a) Step 1: a full FE model with the predetermined global loads. The red dotted box represents the VOI, (b) Step 2: a local FE model for the VOI. The cut boundary displacement obtained in Step 1 is imposed on the boundary of the local model, and (c) Step 3: a local FE model with the estimated local loads.

Grahic Jump Location
Fig. 2

Locations of the three volumes of interest in the proximal femur: (a) femoral head, (b) femoral neck, and (c) intertrochanter. Note that white and black colors correspond to the maximum and minimum BMDs, respectively.

Grahic Jump Location
Fig. 3

SED contour plots of the VOIs. Left and middle columns represent a full model with the given global loads and a local model with the estimated local loads, respectively. Right column illustrates the discrepancy of SEDs between full and local models.

Grahic Jump Location
Fig. 5

Estimated local loads on the three cut planes of the VOI in the femoral head

Grahic Jump Location
Fig. 4

Discrepancy of SED distributions of a local model for the femoral head according to the deviation of the HCF: (a)(absolute  change )=|(data  of a perturbed  load)-(data  ofthe original  load)|; (b) (relative  change)=|(data  of aperturbedload)-(data   of the original  load)/(perturbedload)-(originalload)|



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In