Treffer: Meshless Computing Method for Simulating Bone Remodeling Process.
Title:
Meshless Computing Method for Simulating Bone Remodeling Process.
Authors:
Qin P; School of Mechanical Engineering, Yanshan University, Qinhuangdao, China., Chen J; School of Mechanical Engineering, Yanshan University, Qinhuangdao, China., Huang H; School of Mechanical Engineering, Yanshan University, Qinhuangdao, China.; Suzhou GYZ Electronic Technology Co. Ltd, Suzhou, China., Zhang L; School of Mechanical Engineering, Yanshan University, Qinhuangdao, China., Liu C; School of Mechanical Engineering, Yanshan University, Qinhuangdao, China.
Source:
International journal for numerical methods in biomedical engineering [Int J Numer Method Biomed Eng] 2026 Jan; Vol. 42 (1), pp. e70134.
Publication Type:
Journal Article
Language:
English
Journal Info:
Publisher: Wiley Country of Publication: England NLM ID: 101530293 Publication Model: Print Cited Medium: Internet ISSN: 2040-7947 (Electronic) Linking ISSN: 20407939 NLM ISO Abbreviation: Int J Numer Method Biomed Eng Subsets: MEDLINE
Imprint Name(s):
Original Publication: [Oxford, UK] : Wiley
MeSH Terms:
References:
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E. de Margerie, J. P. Robin, D. Verrier, J. Cubo, R. Groscolas, and J. Castanet, “Assessing a Relationship Between Bone Microstructure and Growth Rate: A Fluorescent Labelling Study in the King Penguin Chick (Aptenodytes Patagonicus),” Journal of Experimental Biology 207, no. 5 (2004): 869–879, https://doi.org/10.1242/jeb.00841.
B. Ning, T. Mustafy, I. Londono, C. Laporte, and I. Villemure, “Impact Loading Intensifies Cortical Bone (Re)modeling and Alters Longitudinal Bone Growth of Pubertal Rats,” Biomechanics and Modeling in Mechanobiology 22 (2023): 1145–1162, https://doi.org/10.1007/s10237‐023‐01706‐5.
F. Rinaldo, D. R. G. S. Silva, S. Estela, et al., “Biology of Bone Tissue: Structure, Function, and Factors That Influence Bone Cells,” BioMed Research International 2015 (2015): 421746, https://doi.org/10.1155/2015/421746.
J. Winkler, A. Abisoye‐Ogunniyan, K. J. Metcalf, and Z. Werb, “Concepts of Extracellular Matrix Remodelling in Tumour Progression and Metastasis,” Nature Communications 11, no. 1 (2020): 5120, https://doi.org/10.1038/s41467‐020‐18794‐x.
C. G. Vossou, G. S. Savva, and C. G. Provatidis, “The Influence of Different Bone Remodeling Equations on a 2‐D Vertebra Model in the Final Bone Density Distribution,” IEEE International Conference on BioInformatics and BioEngineering, Athens, Greece 8, no. 8 (2008): 1–6, https://doi.org/10.1109/BIBE.2008.4696765.
T. D. Rachner, S. Khosla, and L. C. Hofbauer, “Osteoporosis: Now and the Future,” Lancet 377, no. 9773 (2011): 1276–1287, https://doi.org/10.1016/S0140‐6736(10)62349‐5.
M. M. A. Peyroteo, J. Belinha, L. M. J. S. Dinis, and R. M. N. Jorge, “Bone Remodeling: An Improved Spatiotemporal Mathematical Model,” Archive of Applied Mechanics 90 (2020): 635–649, https://doi.org/10.1007/s00419‐019‐01631‐z.
B. Langdahl, S. Ferrari, and D. W. Dempster, “Bone Modeling and Remodeling: Potential as Therapeutic Targets for the Treatment of Osteoporosis,” Therapeutic Advances in Musculoskeletal Disease 8, no. 6 (2016): 225–235, https://doi.org/10.1177/1759720X16670154.
J. Belinha, M. C. Manzanares‐Céspedes, and A. M. G. Completo, The Computational Mechanics of Bone Tissue (Springer International Publishing, 2020), 138–167.
M. G. Araújo and J. Lindhe, “Dimensional Ridge Alterations Following Tooth Extraction: An Experimental Study in the Dog,” Journal of Clinical Periodontology 32, no. 2 (2005): 212–218, https://doi.org/10.1111/j.1600‐051X.2005.00642.x.
X. Feng and J. M. McDonald, “Disorders of Bone Remodeling,” Annual Review of Pathology: Mechanisms of Disease 6, no. 1 (2011): 121–145, https://doi.org/10.1146/annurev‐pathol‐011110‐130203.
P. Pivonka, B. S. Gardiner, C. R. Dunstan, et al., “Model Structure and Control of Bone Remodeling: A Theoretical Study,” Bone 43, no. 2 (2008): 249–263, https://doi.org/10.1016/j.bone.2008.03.025.
R. Hambli, “Connecting Mechanics and Bone Cell Activities in the Bone Remodeling Process: An Integrated Finite Element Modeling,” Frontiers in Bioengineering and Biotechnology 2 (2014): 6, https://doi.org/10.3389/fbioe.2014.00006.
M. I. Pastrama, S. Scheiner, P. Pivonka, and C. Hellmich, “A Mathematical Multiscale Model of Bone Remodeling, Accounting for Pore Space‐Specific Mechanosensation,” Bone 107 (2018): 208–221, https://doi.org/10.1016/j.bone.2017.11.009.
S. Scheiner, P. Pivonka, and C. Hellmich, “Poromicromechanics Reveals That Physiological Bone Strains Induce Osteocyte‐Stimulating Lacunar Pressure,” Biomechanics and Modeling in Mechanobiology 15 (2016): 9–28, https://doi.org/10.1007/s10237‐015‐0704‐y.
P. Pivonka, P. R. Buenzli, S. Scheiner, C. Hellmich, and C. R. Dunstan, “The Influence of Bone Surface Availability in Bone Remodelling—A Mathematical Model Including Coupled Geometrical and Biomechanical Regulations of Bone Cells,” Engineering Structures 47 (2013): 134–147, https://doi.org/10.1016/j.engstruct.2012.09.006.
C. Lerebours, P. R. Buenzli, S. Scheiner, and P. Pivonka, “A Multiscale Mechanobiological Model of Bone Remodelling Predicts Site‐Specific Bone Loss in the Femur During Osteoporosis and Mechanical Disuse,” Biomechanics and Modeling in Mechanobiology 15 (2016): 43–67, https://doi.org/10.1007/s10237‐015‐0705‐x.
N. Bonfoh, E. Novinyo, and P. Lipinski, “Modeling of Bone Adaptative Behavior Based on Cells Activities,” Biomechanics and Modeling in Mechanobiology 10 (2011): 789–798, https://doi.org/10.1007/s10237‐010‐0274‐y.
M. Doblaré and J. M. Garcıa, “Anisotropic Bone Remodelling Model Based on a Continuum Damage‐Repair Theory,” Journal of Biomechanics 35, no. 1 (2002): 1–17, https://doi.org/10.1016/S0021‐9290(01)00178‐6.
Y. He and J. M. Zhang, “The Development and Application of Meshless Method,” Applied Mechanics and Materials 444 (2014): 214–218, https://doi.org/10.4028/www.scientific.net/AMM.444‐445.214.
K. Miller, G. R. Joldes, G. Bourantas, et al., “Biomechanical Modeling and Computer Simulation of the Brain During Neurosurgery,” International Journal for Numerical Methods in Biomedical Engineering 35, no. 10 (2019): e3250, https://doi.org/10.1002/cnm.3250.
Y. Marechal, B. Ramdane, and D. P. Botelho, “Computational Performances of Natural Element and Finite Element Methods,” IEEE Transactions on Magnetics 50, no. 2 (2014): 405–408, https://doi.org/10.1109/tmag.2013.2285259.
M. Dehghan and A. Ghesmati, “Numerical Simulation of Two‐Dimensional Sine‐Gordon Solitons via a Local Weak Meshless Technique Based on the Radial Point Interpolation Method (RPIM),” Computer Physics Communications 181, no. 4 (2010): 772–786, https://doi.org/10.1016/j.cpc.2009.12.010.
L. P. Faverani, V. A. R. Barão, G. Ramalho‐Ferreira, et al., “The Influence of Bone Quality on the Biomechanical Behavior of Full‐Arch Implant‐Supported Fixed Prostheses,” Materials Science and Engineering: C 37 (2014): 164–170, https://doi.org/10.1016/j.msec.2014.01.013.
X. T. Chen, Y. J. Zhu, Y. W. Liu, et al., “Metal Trabecular Bone Reconstruction System Better Improves Clinical Efficacy and Biomechanical Repair of Osteonecrosis of the Femoral Head Than Free Vascularized Fibular Graft: A Case–Control Study,” Journal of Cellular Physiology 234, no. 11 (2019): 20957–20968, https://doi.org/10.1002/jcp.28700.
X. S. Liu, P. Sajda, P. K. Saha, F. W. Wehrli, and X. E. Guo, “Quantification of the Roles of Trabecular Microarchitecture and Trabecular Type in Determining the Elastic Modulus of Human Trabecular Bone,” Journal of Bone and Mineral Research 21, no. 10 (2006): 1608–1617, https://doi.org/10.1359/jbmr.060716.
P. Zioupos, R. B. Cook, and J. R. Hutchinson, “Some Basic Relationships Between Density Values in Cancellous and Cortical Bone,” Journal of Biomechanics 41, no. 9 (2008): 1961–1968, https://doi.org/10.1016/j.jbiomech.2008.03.025.
B. P. Ayati, C. M. Edwards, G. F. Webb, et al., “A Mathematical Model of Bone Remodeling Dynamics for Normal Bone Cell Populations and Myeloma Bone Disease,” Biology Direct 5 (2010): 1–17, https://doi.org/10.1186/1745‐6150‐5‐28.
S. V. Komarova, R. J. Smith, S. J. Dixon, S. M. Sims, and L. M. Wahl, “Mathematical Model Predicts a Critical Role for Osteoclast Autocrine Regulation in the Control of Bone Remodeling,” Bone 33, no. 2 (2003): 206–215, https://doi.org/10.1016/S8756‐3282(03)00157‐1.
M. Peyroteo, J. Belinha, S. Vinga, et al., “A Model for Bone Remodeling: Cellular Dynamics and Mechanical Loading,” in 2017 IEEE 5th Portuguese Meeting on Bioengineering (ENBENG) (IEEE, 2017), 1–4, https://doi.org/10.1109/ENBENG.2017.7889454.
E. de Margerie, J. P. Robin, D. Verrier, J. Cubo, R. Groscolas, and J. Castanet, “Assessing a Relationship Between Bone Microstructure and Growth Rate: A Fluorescent Labelling Study in the King Penguin Chick (Aptenodytes Patagonicus),” Journal of Experimental Biology 207, no. 5 (2004): 869–879, https://doi.org/10.1242/jeb.00841.
B. Ning, T. Mustafy, I. Londono, C. Laporte, and I. Villemure, “Impact Loading Intensifies Cortical Bone (Re)modeling and Alters Longitudinal Bone Growth of Pubertal Rats,” Biomechanics and Modeling in Mechanobiology 22 (2023): 1145–1162, https://doi.org/10.1007/s10237‐023‐01706‐5.
F. Rinaldo, D. R. G. S. Silva, S. Estela, et al., “Biology of Bone Tissue: Structure, Function, and Factors That Influence Bone Cells,” BioMed Research International 2015 (2015): 421746, https://doi.org/10.1155/2015/421746.
J. Winkler, A. Abisoye‐Ogunniyan, K. J. Metcalf, and Z. Werb, “Concepts of Extracellular Matrix Remodelling in Tumour Progression and Metastasis,” Nature Communications 11, no. 1 (2020): 5120, https://doi.org/10.1038/s41467‐020‐18794‐x.
C. G. Vossou, G. S. Savva, and C. G. Provatidis, “The Influence of Different Bone Remodeling Equations on a 2‐D Vertebra Model in the Final Bone Density Distribution,” IEEE International Conference on BioInformatics and BioEngineering, Athens, Greece 8, no. 8 (2008): 1–6, https://doi.org/10.1109/BIBE.2008.4696765.
T. D. Rachner, S. Khosla, and L. C. Hofbauer, “Osteoporosis: Now and the Future,” Lancet 377, no. 9773 (2011): 1276–1287, https://doi.org/10.1016/S0140‐6736(10)62349‐5.
M. M. A. Peyroteo, J. Belinha, L. M. J. S. Dinis, and R. M. N. Jorge, “Bone Remodeling: An Improved Spatiotemporal Mathematical Model,” Archive of Applied Mechanics 90 (2020): 635–649, https://doi.org/10.1007/s00419‐019‐01631‐z.
B. Langdahl, S. Ferrari, and D. W. Dempster, “Bone Modeling and Remodeling: Potential as Therapeutic Targets for the Treatment of Osteoporosis,” Therapeutic Advances in Musculoskeletal Disease 8, no. 6 (2016): 225–235, https://doi.org/10.1177/1759720X16670154.
J. Belinha, M. C. Manzanares‐Céspedes, and A. M. G. Completo, The Computational Mechanics of Bone Tissue (Springer International Publishing, 2020), 138–167.
M. G. Araújo and J. Lindhe, “Dimensional Ridge Alterations Following Tooth Extraction: An Experimental Study in the Dog,” Journal of Clinical Periodontology 32, no. 2 (2005): 212–218, https://doi.org/10.1111/j.1600‐051X.2005.00642.x.
X. Feng and J. M. McDonald, “Disorders of Bone Remodeling,” Annual Review of Pathology: Mechanisms of Disease 6, no. 1 (2011): 121–145, https://doi.org/10.1146/annurev‐pathol‐011110‐130203.
P. Pivonka, B. S. Gardiner, C. R. Dunstan, et al., “Model Structure and Control of Bone Remodeling: A Theoretical Study,” Bone 43, no. 2 (2008): 249–263, https://doi.org/10.1016/j.bone.2008.03.025.
R. Hambli, “Connecting Mechanics and Bone Cell Activities in the Bone Remodeling Process: An Integrated Finite Element Modeling,” Frontiers in Bioengineering and Biotechnology 2 (2014): 6, https://doi.org/10.3389/fbioe.2014.00006.
M. I. Pastrama, S. Scheiner, P. Pivonka, and C. Hellmich, “A Mathematical Multiscale Model of Bone Remodeling, Accounting for Pore Space‐Specific Mechanosensation,” Bone 107 (2018): 208–221, https://doi.org/10.1016/j.bone.2017.11.009.
S. Scheiner, P. Pivonka, and C. Hellmich, “Poromicromechanics Reveals That Physiological Bone Strains Induce Osteocyte‐Stimulating Lacunar Pressure,” Biomechanics and Modeling in Mechanobiology 15 (2016): 9–28, https://doi.org/10.1007/s10237‐015‐0704‐y.
P. Pivonka, P. R. Buenzli, S. Scheiner, C. Hellmich, and C. R. Dunstan, “The Influence of Bone Surface Availability in Bone Remodelling—A Mathematical Model Including Coupled Geometrical and Biomechanical Regulations of Bone Cells,” Engineering Structures 47 (2013): 134–147, https://doi.org/10.1016/j.engstruct.2012.09.006.
C. Lerebours, P. R. Buenzli, S. Scheiner, and P. Pivonka, “A Multiscale Mechanobiological Model of Bone Remodelling Predicts Site‐Specific Bone Loss in the Femur During Osteoporosis and Mechanical Disuse,” Biomechanics and Modeling in Mechanobiology 15 (2016): 43–67, https://doi.org/10.1007/s10237‐015‐0705‐x.
N. Bonfoh, E. Novinyo, and P. Lipinski, “Modeling of Bone Adaptative Behavior Based on Cells Activities,” Biomechanics and Modeling in Mechanobiology 10 (2011): 789–798, https://doi.org/10.1007/s10237‐010‐0274‐y.
M. Doblaré and J. M. Garcıa, “Anisotropic Bone Remodelling Model Based on a Continuum Damage‐Repair Theory,” Journal of Biomechanics 35, no. 1 (2002): 1–17, https://doi.org/10.1016/S0021‐9290(01)00178‐6.
Y. He and J. M. Zhang, “The Development and Application of Meshless Method,” Applied Mechanics and Materials 444 (2014): 214–218, https://doi.org/10.4028/www.scientific.net/AMM.444‐445.214.
K. Miller, G. R. Joldes, G. Bourantas, et al., “Biomechanical Modeling and Computer Simulation of the Brain During Neurosurgery,” International Journal for Numerical Methods in Biomedical Engineering 35, no. 10 (2019): e3250, https://doi.org/10.1002/cnm.3250.
Y. Marechal, B. Ramdane, and D. P. Botelho, “Computational Performances of Natural Element and Finite Element Methods,” IEEE Transactions on Magnetics 50, no. 2 (2014): 405–408, https://doi.org/10.1109/tmag.2013.2285259.
M. Dehghan and A. Ghesmati, “Numerical Simulation of Two‐Dimensional Sine‐Gordon Solitons via a Local Weak Meshless Technique Based on the Radial Point Interpolation Method (RPIM),” Computer Physics Communications 181, no. 4 (2010): 772–786, https://doi.org/10.1016/j.cpc.2009.12.010.
L. P. Faverani, V. A. R. Barão, G. Ramalho‐Ferreira, et al., “The Influence of Bone Quality on the Biomechanical Behavior of Full‐Arch Implant‐Supported Fixed Prostheses,” Materials Science and Engineering: C 37 (2014): 164–170, https://doi.org/10.1016/j.msec.2014.01.013.
X. T. Chen, Y. J. Zhu, Y. W. Liu, et al., “Metal Trabecular Bone Reconstruction System Better Improves Clinical Efficacy and Biomechanical Repair of Osteonecrosis of the Femoral Head Than Free Vascularized Fibular Graft: A Case–Control Study,” Journal of Cellular Physiology 234, no. 11 (2019): 20957–20968, https://doi.org/10.1002/jcp.28700.
X. S. Liu, P. Sajda, P. K. Saha, F. W. Wehrli, and X. E. Guo, “Quantification of the Roles of Trabecular Microarchitecture and Trabecular Type in Determining the Elastic Modulus of Human Trabecular Bone,” Journal of Bone and Mineral Research 21, no. 10 (2006): 1608–1617, https://doi.org/10.1359/jbmr.060716.
P. Zioupos, R. B. Cook, and J. R. Hutchinson, “Some Basic Relationships Between Density Values in Cancellous and Cortical Bone,” Journal of Biomechanics 41, no. 9 (2008): 1961–1968, https://doi.org/10.1016/j.jbiomech.2008.03.025.
B. P. Ayati, C. M. Edwards, G. F. Webb, et al., “A Mathematical Model of Bone Remodeling Dynamics for Normal Bone Cell Populations and Myeloma Bone Disease,” Biology Direct 5 (2010): 1–17, https://doi.org/10.1186/1745‐6150‐5‐28.
S. V. Komarova, R. J. Smith, S. J. Dixon, S. M. Sims, and L. M. Wahl, “Mathematical Model Predicts a Critical Role for Osteoclast Autocrine Regulation in the Control of Bone Remodeling,” Bone 33, no. 2 (2003): 206–215, https://doi.org/10.1016/S8756‐3282(03)00157‐1.
M. Peyroteo, J. Belinha, S. Vinga, et al., “A Model for Bone Remodeling: Cellular Dynamics and Mechanical Loading,” in 2017 IEEE 5th Portuguese Meeting on Bioengineering (ENBENG) (IEEE, 2017), 1–4, https://doi.org/10.1109/ENBENG.2017.7889454.
Contributed Indexing:
Keywords: RPIM; biological process simulation; bone remodeling process; mechanical model calculation; meshless computing method
Entry Date(s):
Date Created: 20260109 Date Completed: 20260109 Latest Revision: 20260109
Update Code:
20260109
DOI:
10.1002/cnm.70134
PMID:
41511172
Database:
MEDLINE
Weitere Informationen
Bone remodeling refers to the physiological behavior of bone tissue changes with changes in the biomechanical environment. Researches of bone remodeling process are significant for bone tissue engineering. The use of numerical simulation technology is an important means to analyze the bone remodeling process. The research of computational methods can deeply reveal the growth law of bone tissue under external load and environmental effects. This work aims to develop the computational model using a meshless method, and simulate an evolution of the porous structure of trabecular bone. The main research objectives include: (1) proposing a novel bone remodeling model based on the radial point interpolation method (RPIM), which integrates the mechanical and biological aspects of bone remodeling; (2) analyzing the theoretical foundations of the meshless method, including the mechanical model driven by strain energy stimulation and the biological model regulated by cell growth, death, and proliferation. This work and the presented cases are limited to two-dimensional areas. The results demonstrate that the proposed bone remodeling model can reflect the bone remodeling process and reflect the dynamic changes inside the bone throughout its life cycle. The developed computational algorithm is highly efficient, and can form the porous structure of trabecular bone through image fitting.
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