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E 1. Riggs BL, Melton U. The worldwide problemof osteoporosis:Insights afforded by epidemiology, Bone 1995, 17:
505 – 511.
2. Larijani B, Hossein-Nezhad A, Mojtahedi A, Pajouhi M, Bastanhagh MH, Soltani A, Mirfezi SZ, and Dashti R. Normative data of bone mineral density in healthy population of Tehran, Iran: Across sectional study. BMC Musculoskelet Disord 2005; 6:38.
3. Whealan KM, Kwak SD, Tedrow JR, Inoue K, Snyder BD. Non-invasive imaging predicts failure load of the spine with simulated osteolytic defects. J Bone Joint Surg Am 2000; 82:1240-51.
4. Singer K, Edmondstone S, Day R, Breidahl P, Price R. Prediction of thoracic and lumbar vertebral body compressive strength: correlations with bone mineral density and vertebral region. Bone 1995; 17: 167-74.
5. Brickmann P, Biggemann M, Hilweg D. Prediction of the compressive strength of human lumbar vertebrae. Spine 1989; 14: 606-10.
6. Edmondson SJ, Singer KP, Day RE, Price RI, Breidahl PD. Ex vivo estimation of thoracolumbar vertebral body compressive strength: the relative contributions of bone densitometry and vertebral morphometry. Osteoporos Int 1997; 7: 142-8.
7. Ebbesen EN, Thomson JS, Beck-Nielson H, Nepper-Rasmussen HJ, Mosekilde L. Vertebral bone density evaluated by dual-energy X-ray absorbtiometry and quantitative computed tomography in vitro. Bone 1998; 23: 283-90.
8. Cody DD, Gross GJ, Hou FJ, Spencer HJ, Goldstein SA, Fyhrie DP. Femoral strength is better predicted by finite element models than QCT and DXA. J Biomech 1999; 32: 1013-1020.
9. Keyak J.H, Rossi S.A, Jones K.A, Les C.M, Skinner H.B. Prediction of fracture location in the proximal femur using finite element model. Med Eng Phys 2001; 23: 657-664.
10. Liebschner MAK, Kopperdahl DL, Rosenberg WS, Keaveny TM. Finite element modeling of the human thoracolumbar spine. Spine 2003; 28: 559-65.
11. Crawford RP, Cann CE, Keaveny TM. Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography. Bone 2003; 33: 744-50.
12. Buckley JM, Loo K, Motherway J. Comparison of quantitative computed tomography-based measures in predicting vertebral compressive strength. Bone 2007; 40: 767-74.
13. Kopperdahl DL, Morgan EF, Keaveny TM. Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone. J Orthop Res 2002; 20: 801-805.
14. Morgan EF, Keaveny TM. Dependance of yield strain of human trabecular bone on anatomic site. J Biomech 2001; 34: 569-77.