Correlation of elastic modulus and x-ray bone density in the area of the ankle joint

Taras Omelchenko, Oleksandr Buryanov, Andrey Lyabakh, Vadim Mazevich, Mykola Shidlovsky, Olga Musienko


Objective: to determine the relationship between the X-ray density and the modulus of elasticity of the bone in the ankle joint, using an empirical method (in a natural experimental study).

Methods: the modulus of elasticity of 10 samples of the tibia cortical bone and 42 — cancellous bone of the distal part of the tibia, fibula and talus was determined. The study of the bone modulus of elasticity was carried out by recording of linear dis­placements at static and quasistatic compression loads. X-ray density in Hounsfield units (HU) was estimated using computer tomography.

Results: it was found that the average radiological density for cancellous tibia bone tissue was 314.8 HU, and the modulus of elasticity was 581.5 MPa. For the fibula the average values of the corresponding indicators were 258.9 HU and 374.7 MPa; for the talus — 255.6 HU and 445.3 MPa, respective­ly. For the cortical tibia shaft, the mean value of the X- ray density was 1 887.7 HU, the modulus of elasticity was 10 002.8 MPa. As a result of the regression analysis, a correlation between the radiological density of the bone and its modulus of elasticity in the ankle joint was established. The revealed dependence for cortical bone is described by the formula E = 6,3 ∙ HU – 1905; and for cancellous — E = 3 ∙ HU – 407.

Conclusions: the use of the obtained formulas allows noninvasive determination of the modulus of elasticity of bone tissue in patients on the basis of the radiographic density in a standard computer tomography scan with sufficient accuracy.


cancellous (trabecular) bone; cortical bone; distal tibia; talus; X-ray density; modulus of elasticity; Jung modulus; Hounsfield unit


Burianov, O. A., Liabakh, A. P., Voloshyn, O. I., Omelchenko, T. M. (2006) Analiz prychyn nezadovilnykh rezultativ likuvannia perelomiv v diliantsi homilkovostupnevoho suhloba. Litopys travmatolohii ta ortopedii, 1–2, 93–96. (in Ukrainian)

Malanchuk, V. O., Kryshchuk, M. H., Kopchak, A. V. (2013) Imitatsiine komp’iuterne modeliuvannia v shchelepno-lytsevii khirurhii. K.: Askaniia. doi: 10.15674/0030-59872013435-40. (in Ukrainian)

Omelchenko, T. N. (2013) Perelomy lodyzhek i bystroprogressiruyushchiy osteoartroz golenostopnogo sustava: profilaktika i lechenie. Ortopediya, travmatologiya i protezirovanie, 4, 35–40. doi: 10.15674/0030-59872013435-40 (in Russian)

Leardini, A., O’Connor, J. J., & Giannini, S. (2014). Biomechanics of the natural, arthritic, and replaced human ankle joint. Journal of Foot and Ankle Research, 7(1). doi:10.1186/1757-1146-7-8

Ciarelli, M. J., Goldstein, S. A., Kuhn, J. L., Cody, D. D., & Brown, M. B. (1991). Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography. Journal of Orthopaedic Research, 9(5), 674–682. doi:10.1002/jor.1100090507

Esses, S. I., Lotz, J. C., & Hayes, W. C. (2009). Biomechanical properties of the proximal femur determined in vitro by single-energy quantitative computed tomography. Journal of Bone and Mineral Research, 4(5), 715–722. doi:10.1002/jbmr.5650040510

Harp, J. H., Aronson, J., & Hollis, M. (1994). Noninvasive Determination of Bone Stiffness for Distraction Osteogenesis by Quantitative Computed Tomography Scans. Clinical Orthopaedics and Related Research,(301), 42-48. doi:10.1097/00003086-199404000-00008

Hobatho, M. C. (1997) Anatomical variation of human cancellous bone mechanical properties in vitro. Studies in Health Technology and Informatics, 40, 157–173.

Hvid, I., Bentzen, S. M., Linde, F., Mosekilde, L., & Pongsoipetch, B. (1989). X-ray quantitative computed tomography: The relations to physical properties of proximal tibial trabecular bone specimens. Journal of Biomechanics, 22(8–9), 837–844. doi:10.1016/0021-9290(89)90067-5

McBroom, R. J., Hayes, W. C., Edwards, W. T., Goldberg, R. P., & White, A. A. (1985). Prediction of vertebral body compressive fracture using quantitative computed tomography. The Journal of Bone & Joint Surgery, 67(8), 1206–1214. doi:10.2106/00004623-198567080-00010

Rho, J., Hobatho, M., & Ashman, R. (1995). Relations of mechanical properties to density and CT numbers in human bone. Medical Engineering & Physics, 17(5), 347–355. doi:10.1016/1350-4533(95)97314-f

Taylor, W., Roland, E., Ploeg, H., Hertig, D., Klabunde, R., Warner, M., … Clift, S. (2002). Determination of orthotropic bone elastic constants using FEA and modal analysis. Journal of Biomechanics, 35(6), 767–773. doi:10.1016/s0021-9290(02)00022-2

Linde, F., Hvid, I., & Madsen, F. (1992). The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens. Journal of Biomechanics, 25(4), 359–368. doi:10.1016/0021-9290(92)90255-y

Linde, F. (1994) Elastic and viscoelastic properties of trabecular bone by a compression testing approach. Danish Medical Bulletin, 1(2), 119–138.

Copyright (c) 2018 Taras Omelchenko, Olexandr Buryanov, Andrij Lyabakh, Vadim Mazevich, Mykola Shidlovsky, Olga Musienko

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