유한 요소 법을 이용한 노화에 따른 요추의 피질 골과해면 골 간의 하중 분담 비율
Load Sharing Ratios Between the Cortex and Centrum in a Lumbar Vertebral Body with aging using Finite Element Method
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
This research was aimed to analyze load sharing ratios between cortical shell and trabecular bone of a degraded lumbar vertebra with aging, and also evaluate elastic moduli assigned into an FE model, using finite element method. For the better analysis of trabecular bone, effective elastic moduli, that is, nominal elastic moduli divided by the volumetric porosities was used. The elastic moduli of the cortical shell suitable for the trabecular bone were obtained from the equations on the basis of idealized stress-strain relations, including areal porosities. To minimize numerical errors, p-element was used. Using eight parameters that refer to some published papers, the geometry of L3 with a removed posterior part. After the constant compressive displacement was applied, the load sharing ratios were obtained by using both every elastic strain energy and every vertical force between two bones in each 8-volume. As results, 1) according to an increase in age from 20-year to 80-year, load sharing ratios of trabecular bone decreased from 55% to 49%; 2) the maximal ratios of each bone were occurred in the mid-plane of centrums and the endplate of cortical shells, respectively; 3) effective elastic moduli assigned into a porous centrum /cortex were found to be adequate; 4) for load sharing ratios, the difference of two methods showed that the total ratios were almost same within less than 1% but the partial ratios at every depth were more or less different each other.
Abstract
This research was aimed to analyze load sharing ratios between cortical shell and trabecular bone of a degraded lumbar vertebra with aging, and also evaluate elastic moduli assigned into an FE model, using finite element method. For the better analysis of trabecular bone, effective elastic moduli, that is, nominal elastic moduli divided by the volumetric porosities was used. The elastic moduli of the cortical shell suitable for the trabecular bone were obtained from the equations on the basis of idealized stress-strain relations, including areal porosities. To minimize numerical errors, p-element was used. Using eight parameters that refer to some published papers, the geometry of L3 with a removed posterior part. After the constant compressive displacement was applied, the load sharing ratios were obtained by using both every elastic strain energy and every vertical force between two bones in each 8-volume. As results, 1) according to an increase in age from 20-year to 80-year, load sharing ratios of trabecular bone decreased from 55% to 49%; 2) the maximal ratios of each bone were occurred in the mid-plane of centrums and the endplate of cortical shells, respectively; 3) effective elastic moduli assigned into a porous centrum /cortex were found to be adequate; 4) for load sharing ratios, the difference of two methods showed that the total ratios were almost same within less than 1% but the partial ratios at every depth were more or less different each other.
참고문헌 (51)
- W. J. Whitehouse, "The scanning electron microscope in studies of trabecular bone from a human vertebral body", J Anat, 108(Pt 3), pp.481~496 (1971)
- L. Mosekilde, "Sex differences in age-related loss of vertebral trabecular bone mass and structure--biomechanical consequences", Bone, 10(6), pp.425~432 (1989)
- S. F. Evans, "Vertebral morphometry in women aged 50-81years", Bone Miner, 21(1), pp.29~40 (1993)
- L. Mosekilde, "Normal vertebral body size and compressive strength : relations to age and to vertebral and iliac trabecular bone compressive strength", Bone, 7(3), pp.207~212 (1986)
- A. Vesterby, "Biologically meaningful determinants of the in vitro strength of lumbar vertebrae", Bone, 12(3), pp.219~244 (1991)
- L. Mosekilde, "Normal age-related changes in bone mass, structure, and strength--consequences of the remodeling process", Acta Obstet Gynecol Scand, 72, pp.409~410 (1993)
- S. D. Rockoff, "The relative contribution of trabecular and cortical bone to the strength of human lumbar vertebrae", Calcif Tissue Res, 3(2), pp.163~175 (1969)
- 임종완, "새로운 방식의 나사형 인공디스크 고정체 해석", 의공학회지, 31(1), pp.56~66 (2010), 대한의용생체공학회
- M. D. Smith, "Load-bearing capacity of corticocancellous bone grafts in the spine", J Bone Joint Surg Am, 75(8), pp.1206~1213 (1993)
- R. B. Martin, "Porosity and specific surface of bone", Crit Rev Biomed Eng, 10(3), pp.179~222 (1984)
- M. Hongo, "Surface strain distribution on thoracic and lumbar vertebrae under axial compression. The role in burst fractures", Spine(Phila Pa 1976), 24(12), pp.1197~1202 (1999)
- F. E. Masri, "Apparent Young’s modulus of vertebral corticocancellous bone specimens", Comput Methods Biomech Biomed Engin, 15(1), pp.23~28 (2012)
- A. Shirazi-Adl, "On the fibre composite material models of disc annulus--comparison of predicted stresses", J Biomech, 22(4), pp.357~365 (1989)
- M. Dreischarf, "Comparison of eight published static finite element models of the intact lumbar spine : predictive power of models improves when combined together", J Biomech, 47(8), pp.1757~1766 (2014)
- D. R. Carter, "The compressive behavior of bone as a two-phase porous structure", J Bone Joint Surg Am, 59(7), pp.954~962 (1977)
- O. Lindahl, "Mechanical properties of dried defatted spongy bone", Acta Orthop Scand, 47(1), pp.11~19 (1976)
- L. Mosekilde, "Biomechanical competence of vertebral trabecular bone in relation to ash density and age in normal individuals", Bone, 8(2), pp.79~85 (1987)
- T. M. Keaveny, "Systematic and random errors in compression testing of trabecular bone", J Orthop Res, 15(1), pp.101~110 (1997)
- D. L. Kopperdahl, "Yield strain behavior of trabecular bone", J Biomech, 31(7), pp.601~608 (1998)
- Y. N. Yeni, "Finite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions", J Biomech, 34(12), pp.1649~1654 (2001)
- E. F. Morgan, "Nonlinear behavior of trabecular bone at small strains", J Biomech Eng, 123(1), pp.1~9 (2001)
- B. Helgason, "Mathematical relationships between bone density and mechanical properties : a literature review", Clin Biomech(Bristol, Avon), 23(2), pp.135~146 (2008)
- N. Yoganandan, "Functional biomechanics of the thoracolumbar vertebral cortex", Clin Biomech(Bristol, Avon), 3(1), pp.11~18 (1988)
- R. J. McBroom, "Prediction of vertebral body compressive fracture using quantitative computed tomography", J Bone Joint Surg Am, 67(8), pp.1206~1214 (1985)
- K. G. Faulkner, "Effect of bone distribution on vertebral strength : assessment with patient-specific nonlinear finite element analysis", Radiology, 179(3), pp.669~674 (1991)
- M. J. Silva, "Load sharing between the shell and centrum in the lumbar vertebral body", Spine(Phila Pa 1976), 22(2), pp.140~150 (1997)
- D. W. Overaker, "Finite element analysis of vertebral body mechanics with a nonlinear microstructural model for the trabecular core", J Biomech Eng, 121(5), pp.542~550 (1999)
- K. D. Cao, "Load sharing within a human lumbar vertebral body using the finite element method", Spine (Phila Pa 1976), 26(12), pp.E253~E260 (2001)
- S. J. Hollister, "A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress", J Biomech, 27(4), pp.433~444 (1994)
- L. Mosekilde, "Sex differences in age-related changes in vertebral body size, density and biomechanical competence in normal individuals", Bone, 11(2), pp.67~73 (1990)
- W. Frobin, "Precision measurement of disc height, vertebral height and sagittal plane displacement from lateral radiographic views of the lumbar spine", Clin Biomech (Bristol, Avon), 12(suppl 1), pp.S1~S63 (1997)
- F. Lavaste, "Three-dimensional geometrical and mechanical modelling of the lumbar spine", J Biomech, 25(10), pp.1153~1164 (1992)
- S. A. Feik, "Age-related changes in cortical porosity of the midshaft of the human femur", J Anat, 191(Pt 3), pp.407~416 (1997)
- N. L. Fazzalari, "Antero-postero differences in cortical thickness and cortical porosity of T12 to L5 vertebral bodies", Joint Bone Spine, 73(3), pp.293~297 (2006)
- S. J. Edmondston, "Ex vivo estimation of thoracolumbar vertebral body compressive strength : the relative contributions of bone densitometry and vertebral morphometry", Osteoporos Int, 7(2), pp.142~148 (1997)
- C. H. Turner, "The elastic properties of trabecular and cortical bone tissues are similar : results from two microscopic measurement techniques", J Biomech, 32(4), pp.437~441 (1999)
- M. J. Silva, "Direct and computed tomography thickness measurements of the human, lumbar vertebral shell and endplate", Bone, 15(4), pp.409~414 (1994)
- M. E. Roy, "Mechanical and morphological variation of the human lumbar vertebral cortical and trabecular bone", J Biomed Mater Res, 44(2), pp.191~197 (1999)
- C. E. Hoffler, "Heterogeneity of bone lamellar-level elastic moduli", Bone, 26(6), pp.603~609 (2000)
- J. Mizrahi, "Finite-element stress analysis of the normal and osteoporotic lumbar vertebral body", Spine(Phila Pa 1976), 18(14), pp.2088~2096 (1993)
- K. D. Bouzakis, "Loading simulation of lumbar spine vertebrae during a compression test using the finite elements method and trabecular bone strength properties, determined by means of nanoindentations", J Musculoskelet Neuronal Interact, 4(2), pp.152~158 (2004)
- S. Mora, "Age-related changes in cortical and cancellous vertebral bone density in girls : assessment with quantitative CT", AJR Am J Roentgenol, 162(2), pp.405~409 (1994)
- L. Mosekilde, "The predictive value of quantitative computed tomography for vertebral body compressive strength and ash density", Bone, 10(6), pp.465~470 (1989)
- W. A. Kalender, "The European Spine Phantom--a tool for standardization and quality control in spinal bone mineral measurements by DXA and QCT", Eur J Radiol, 20(2), pp.83~92 (1995)
- S. Prevrhal, "Accuracy limits for the determination of cortical width and density : the influence of object size and CT imaging parameters", Phys Med Biol, 44(3), pp.751~764 (1999)
- R. B. Mazess, "Errors in measuring trabecular bone by computed tomography due to marrow and bone composition", Calcif Tissue Int, 35(2), pp.148~152 (1983)
- C. Bergot, "Measurement of anisotropic vertebral trabecular bone loss during aging by quantitative image analysis", Calcif Tissue Int, 43(3), pp.143~149 (1988)
- H. Ritzel, "The thickness of human vertebral cortical bone and its changes in aging and osteoporosis : a histomorphometric analysis of the complete spinal column from thirty-seven autopsy specimens", J Bone Miner Res, 12(1), pp.89~95 (1997)
- W. T. Edwards, "Structural features and thickness of the vertebral cortex in the thoracolumbar spine", Spine(Phila Pa 1976), 26(2), pp.218~225 (2001)
- S. H. Zhou, "Geometrical dimensions of the lower lumbar vertebrae--analysis of data from digitised CT images", Eur Spine J, 9(3), pp.242~248 (2000)
- T. N. Hangartner, "Evaluation of cortical bone by computed tomography", J Bone Miner Res, 11(10), pp.1518~1525 (1996)