Microstructural indexes that determine the trabecular bone maximum stress of micro-finite element models

doi:10.12307/2023.207

Abstract

Abstract: BACKGROUND: The mechanical response of trabecular bone under loading can be studied using micro-CT based micro-finite element. It is generally considered that bone volume fraction in animal specimens is the most important index that determines the compressive strength of trabecular bone. However, in the micro-CT based finite element model, the microstructural index leading to stress concentration or determining the maximum stress is not clear.
OBJECTIVE: To investigate the microstructural indexes that affect the maximum stress of trabecular bone micro-finite element model.
METHODS: The microstructural indexes of trabecular bone of 10 normal rats from bilateral femoral metaphysis region of interest were obtained and the differences of trabecular bone in bilateral regions of interest were compared. The 20 trabecular bone finite element models were constructed and loaded. The average stress values of the ranking 5%, 2%, 1% and 0.5% of stress value were taken as the maximum stress value. The reliability of the models was verified according to the stress and effective strain. Finally, with the maximum stress value as the dependent variable and the trabeculae microstructural index as the independent variable, the key factor affecting the maximum stress of trabeculae micro-finite element model was explored by multiple linear stepwise regression method.
RESULTS AND CONCLUSION: There was homogeneity in trabecular bone microstructure of bilateral femoral metaphysis (P > 0.05), and then data were combined. The average number of elements and nodes of 20 trabeculae finite element models was 232 813 and 606 82. The average stress of the ranking 5%, 2%, 1% and 0.5% elements was 31.91, 41.96, 50.86 and 61.23 MPa, respectively, and the average effective strain was 3.28%. The results of multiple linear stepwise regression analysis indicated that the structure model index was the most important factor influencing the maximum stress of trabeculae finite element model (P < 0.001, R2=0.807). It is indicated that the trabecular bone structure model index is the most important bone microstructure index that affects the stress concentration of the trabecular bone micro-finite element model.

Key words: trabecular bone, microstructure, maximum stress, stress concentration, finite element, biomechanics, trabecular bone structure model index

CLC Number:

Zhong Yizheng, Huang Peizhen, Cai Qunbin, Zheng Liqin, He Xingpeng, Dong Hang. Microstructural indexes that determine the trabecular bone maximum stress of micro-finite element models[J]. Chinese Journal of Tissue Engineering Research, 2023, 27(9): 1313-1318.

Figures/Tables 6

References

[1] 李磊, 方诗元. Singh指数在骨质疏松性髋部骨折中的应用研究[J]. 中国骨质疏松杂志,2016,22(6):777-780.
[2] IM GI, PARK PG, MOON SW. The relationship between radiological parameters from plain hip radiographs and bone mineral density in a Korean population. J Bone Miner Metab. 2012;30(5):504-508.
[3] THOMAS CD, MAYHEW PM, POWER J, et al. Femoral neck trabecular bone: loss with aging and role in preventing fracture. J Bone Miner Res. 2009;24(11):1808-1818.
[4] HOLZER G, VON SKRBENSKY G, HOLZER LA, et al. Hip fractures and the contribution of cortical versus trabecular bone to femoral neck strength. J Bone Miner Res. 2009;24(3):468-474.
[5] MARTELLI S, GIORGI M, DALL’ A E, et al. Damage tolerance and toughness of elderly human femora. Acta Biomater. 2021;123:167-177.
[6] OFTADEH R, ENTEZARI V, SPÖRRI G, et al. Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone.J R Soc Interface. 2015;12(106):20150070.
[7] LIU P, LIANG X, LI Z, et al. Decoupled effects of bone mass, microarchitecture and tissue property on the mechanical deterioration of osteoporotic bones. Composites Part B-Engineering. 2019;177.
[8] KNOWLES NK, IPK, FERREIRA LM. The Effect of Material Heterogeneity, Element Type, and Down-Sampling on Trabecular Stiffness in Micro Finite Element Models.Ann Biomed Eng. 2019;47(2):615-623.
[9] SABET FA, JIN O, KORIC S, et al. Nonlinear micro-CT based FE modeling of trabecular bone-Sensitivity of apparent response to tissue constitutive law and bone volume fraction. Int J Numer Method Biomed Eng. 2018;34(4):e2941.
[10] RIEGER R, AUREGAN JC, HOC T. Micro-finite-element method to assess elastic properties of trabecular bone at micro- and macroscopic level. Morphologie. 2018;102(336):12-20.
[11] CORY E, NAZARIAN A, ENTEZARI V, et al. Compressive axial mechanical properties of rat bone as functions of bone volume fraction, apparent density and micro-ct based mineral density. J Biomech. 2010;43(5): 953-960.
[12] YANG H, NAWATHE S, FIELDS AJ, et al. Micromechanics of the human vertebral body for forward flexion. J Biomech. 2012;45(12):2142-2148.
[13] YANG H, XU X, BULLOCK W, et al. Adaptive changes in micromechanical environments of cancellous and cortical bone in response to in vivo loading and disuse. J Biomech. 2019;89:85-94.
[14] DEPALLE B, CHAPURLAT R, WALTER-LE-BERRE H, et al. Finite element dependence of stress evaluation for human trabecular bone. J Mech Behav Biomed Mater. 2013;18:200-212.
[15] 吴宇航,郑利钦,张彪,等. 去势大鼠骨质疏松性骨小梁的压缩断裂仿真[J]. 中国组织工程研究,2020,24(15):2387-2392.
[16] NIKODEM A. Correlations between structural and mechanical properties of human trabecular femur bone. Acta Bioeng Biomech. 2012;14(2):37-46.
[17] GOULET RW, GOLDSTEIN SA, CIARELLI MJ, et al. The relationship between the structural and orthogonal compressive properties of trabecular bone. J Biomech. 1994;27(4):375-389.
[18] MAQUER G, MUSY SN, WANDEL J, et al. Bone volume fraction and fabric anisotropy are better determinants of trabecular bone stiffness than other morphological variables.J Bone Miner Res. 2015;30(6): 1000-1008.
[19] DING M, OVERGAARD S. 3-D microarchitectural properties and rod- and plate-like trabecular morphometric properties of femur head cancellous bones in patients with rheumatoid arthritis, osteoarthritis, and osteoporosis. J Orthop Translat. 2021;28:159-168.
[20] VAN RIETBERGEN B, ODGAARD A, KABEL J, et al. Relationships between bone morphology and bone elastic properties can be accurately quantified using high-resolution computer reconstructions. J Orthop Res. 1998;16(1):23-28.
[21] BARAK MM, BLACK MA. A novel use of 3D printing model demonstrates the effects of deteriorated trabecular bone structure on bone stiffness and strength. J Mech Behav Biomed Mater. 2018;78:455-464.
[22] WANG J, ZHOU B, LIU XS, et al. Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone. Bone. 2015;72:71-80.
[23] 秦国宁,邢飞,卢斌,等. 新鲜正常股骨头组织力学加载下内部空间结构变化[J]. 医用生物力学,2021,36(S1):41.
[24] 赵森,高颜,李太阳,等. 动态加载作用下大鼠尾椎骨应力分布的数值模拟研究[J]. 医用生物力学,2021,36(S1):227.
[25] HAMBLI R. Micro-CT finite element model and experimental validation of trabecular bone damage and fracture. Bone. 2013;56(2):363-374.
[26] KAZUYUKI K, TAKUAKI Y, GORO M, et al. The role of sclerotic changes in the starting mechanisms of collapse: A histomorphometric and FEM study on the femoral head of osteonecrosis. Bone. 2015;81:644-648.
[27] GOFF MG, LAMBERS FM, SORNA RM, et al. Finite element models predict the location of microdamage in cancellous bone following uniaxial loading. J Biomech. 2015;48(15):4142-4148.
[28] 张长灏,孟昊业,汪爱媛,等. 股骨头坏死中松质骨微观力学特性的演变规律[J]. 北京生物医学工程,2021,40(2):123-129.
[29] VIVEEN J, PERILLI E, ZAHROONI S, et al. Three-dimensional cortical and trabecular bone microstructure of the proximal ulna. Arch Orthop Trauma Surg. 2021 Jul 5. doi: 10.1007/s00402-021-04023-7.
[30] ZHOU B, LIU X S, WANG J, et al. Dependence of mechanical properties of trabecular bone on plate-rod microstructure determined by individual trabecula segmentation (ITS). J Biomech. 2014;47(3):702-708.
[31] STEIN E M, KEPLEY A, WALKER M, et al. Skeletal structure in postmenopausal women with osteopenia and fractures is characterized by abnormal trabecular plates and cortical thinning. J Bone Miner Res. 2014,29(5):1101-1109.
[32] WANG J, ZHOU B, PARKINSON I, et al. Trabecular Plate Loss and Deteriorating Elastic Modulus of Femoral Trabecular Bone in Intertrochanteric Hip Fractures. Bone Res. 2013;1(4):346-354.
[33] GREENWOOD C, CLEMENT J, DICKEN A, et al. Age-Related Changes in Femoral Head Trabecular Microarchitecture. Aging Dis. 2018;9(6):976-987.
[34] SALMON PL, OHLSSON C, SHEFELBINE SJ, et al. Structure Model Index Does Not Measure Rods and Plates in Trabecular Bone. Front Endocrinol (Lausanne). 2015;6:162.
[35] FELDER AA, MONZEM S, DE SOUZA R, et al. The plate-to-rod transition in trabecular bone loss is elusive. R Soc Open Sci. 2021;8(6):201401.