Finite element analysis (FEA) is an advanced computer technique of structural stress analysis developed in engineering mechanics. Because the compressive behavior of vertebral bone shows nonlinear behavior, a nonlinear FEA should be utilized to analyze the clinical vertebral fracture. In this article, a computed tomography-based nonlinear FEA (CT/FEA) to analyze the vertebral bone strength, fracture pattern, and fracture location is introduced. The accuracy of the CT/FEA was validated by performing experimental mechanical testing with human cadaveric specimens. Vertebral bone strength and the minimum principal strain at the vertebral surface were accurately analyzed using the CT/FEA. The experimental fracture pattern and fracture location were also accurately simulated. Optimization of the element size was performed by assessing the accuracy of the CT/FEA, and the optimum element size was assumed to be 2 mm. It is expected that the CT/FEA will be valuable in analyzing vertebral fracture risk and assessing therapeutic effects on osteoporosis.
Imai Kazuhiro. Analysis of Vertebral Bone Strength, Fracture Pattern, and Fracture Location: A Validation Study Using a Computed Tomography-Based Nonlinear Finite Element Analysis[J]. Aging and disease,
2015, 6(3): 180-187.
Figure 1. Finite element models. A whole vertebral body constructed with 1 mm (left), 2 mm (middle), or 3 mm (right) tetrahedral elements from the computed tomography data.
Figure 2. CT/FEA analyzed minimum principal strain versus measured minimum principal strain. Values of CT/FEA analyzed minimum principal strain and those of measured minimum principal strain by mechanical testing were significantly correlated.
Figure 3. The reconstructed micro-CT image and the minimum principal strain distribution analyzed by the CT/FEA. The minimum principal strain distribution constructed with1 mm (left), 2 mm (middle), and 3 mm (right) elements at the mid-sagittal cross section.
Figure 4. The mid-sagittal section of the undecalcified specimen after the mechanical testing. Direct histological observation revealed that the fracture line in the upper part consisted of piled calcified trabecular bone.
Figure 5. The lateral soft X-ray radiogram and the reconstructed micro-CT image after the mechanical testing. Marked radiolucency was recognized at the anterior part of the vertebra.
Figure 6. CT/FEA analysis. Red elements as the failed elements appeared at the anterior part of the vertebra.
Figure 7. The minimum principal strain distribution. CT/FEA analysis with 1 mm (left), 2 mm (middle), and 3 mm (right) elements.
Figure 8. The histological examination of the mid-section of the specimen after the mechanical testing.
There was little continuity of the longitudinal trabecula with less content of the bone marrow at the anterior part.
Brekelmans WA, Poort HW, Slooff TJ (1972). A new method to analyse the mechanical behaviour of skeletal parts. ActaOrthopScand, 43: 301-317.
Huiskes R, Chao EY (1983). A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomech, 16: 385-409.
Faulkner KG, Cann CE, Hasegawa BH (1991). Effect of bone distribution on vertebral strength: assessment with patient-specific nonlinear finite element analysis. Radiology, 179: 669-674.
Silva MJ, Keaveny TM, Hayes WC (1998). Computed tomography-based finite element analysis predicts failure loads and fracture patterns for vertebral sections. J Orthop Res, 16: 300-308.
Martin H, Werner J, Andresen R, Schober HC, Schmitz KP (1998). Noninvasive assessment of stiffness and failure load of human vertebrae from CT-data. Biomed Tech, 43: 82-88.
Liebschner MA, Kopperdahl DL, Rosenberg WS, Keaveny TM (2003). Finite element modeling of the human thoracolumbar spine. Spine, 28: 559-565.
Crawford RP, Cann CE, Keaveny TM (2003). Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography. Bone, 33: 744-750.
Keaveny TM, Wachtel EF, Ford CM, Hayes WC (1994). Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. J Biomech, 27: 1137-1146.
Morgan EF, Keaveny TM (2001). Dependence of yield strain of human trabecular bone on anatomic site. J Biomech, 34: 569-577.
Silva MJ, Wang C, Keaveny TM, Hayes WC (1994). Direct and computed tomography thickness measurements of the human, lumbar vertebral shell and endplate. Bone, 15: 409-414.
Vesterby A, Mosekilde L, Gundersen HJ,et al (1991). Biologically meaningful determinants of the in vitro strength of lumbar vertebrae. Bone, 12: 219-224.
Mosekilde L (1993). Vertebral structure and strength in vivo and in vitro. Calcif Tissue Int, 53: S121-S126.
Dougherty G, Newman D (1999). Measurement of thickness and density of thin structures by computed tomography: a simulation study. Med Phys, 26: 1341-1348.
Prevrhal S, Engelke K, KalenderWA (1999). Accuracy limits for the determination of cortical width and density: the influence of object size and CT imaging parameters. Phys Med Biol, 44: 751-764.
Imai K, Ohnishi I, Bessho M, Nakamura K (2006). Nonlinear finite element model predicts vertebral bone strength and fracture site. Spine, 31: 1789-1794.
Imai K, Ohnishi I, Yamamoto S, Nakamura K (2008). In vivo assessment of lumbar vertebral strength in elderly women using CT-based nonlinear finite element model. Spine, 33: 27-32.
Keyak JH, Rossi SA, Jones KA, Skinner HB (1998). Prediction of femoral fracture load using automated finite element modeling. J Biomech, 31: 125-133.
JensenKS, Mosekilde L (1990). A model of vertebral trabecular bone architecture and its mechanical properties. Bone, 11: 417-423.
Rho JY, Tsui TY, Pharr GM (1997). Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials, 18: 1325-1330.
Hou FJ, Lang SM, Hoshaw SJ, Reimann DA, Fyhrie DP (1998). Human vertebral body apparent and hard tissue stiffness. J Biomech, 31: 1009-1015.
Ladd AJ, Kinney JH, Haupt DL, Goldstein SA (1998). Finite-element modeling of trabecular bone: comparison with mechanical testing and determination of tissue modulus. J Orthop Res, 16: 622-628.
Overaker DW, Langrana NA, Cuitino AM (1999). Finite element analysis of vertebral body mechanics with a nonlinear microstructural model for the trabecular core. J Biomech Eng, 121: 542-550.
Rockoff SD, Sweet E, Bleustein J (1969). The relative contribution of trabecular and cortical bone to the strength of human lumbar vertebrae. Calcif Tissue Res, 3: 163-175.
Ito M (2005). Assessment of bone quality using micro-computed tomography (micro-CT) and synchrotron micro-CT. J Bone Miner Metab, 23: S115-S121.
Matsumoto T, Ohnishi I, Bessho M, Imai K, Ohashi S, Nakamura K (2009). Prediction of vertebral strength under loading conditions occurring in activities of daily living using a computed tomography-based nonlinear finite element method. Spine, 34: 1464-1469.
Imai K, Ohnishi I, Matsumoto T, Yamamoto S, Nakamura K (2009). Assessment of vertebral fracture risk and therapeutic effects of alendronate in postmenopausal women using a quantitative computed tomography-based nonlinear finite element method. OsteoporosInt, 20: 801-810.
Imai K (2011). Vertebral fracture risk and alendronate effects on osteoporosis assessed by a computed tomography-based nonlinear finite element method. J Bone Miner Metab, 29: 645-651.