Influence of tibial slope on the forces in anterior cruciate ligament




anterior cruciate ligament, finite elements method, tibial slope, mathematical modeling


Today, a number of factors have been identified that theoretically increase the risk of anterior cruciate ligament (ACL) graft rupture. An increased posterior tibial slope is considered one of the potential risk factor. Objective: to investigate the influence
of posterior tibial slope angle on the loading forces in the ACL. Methods: the research was made in the program complex for the design and calculation of building structures LIRA-SAPR 2013 R5. The main aim of our study was to determine the loading forces in the ACL according to various angles α (0°, 5°, 10°, 15°). For maximum simplification of the model, the joint was depicted as two planes that correspond to the cross-sections of femoral
and tibial bones at the level of ligaments attachment. Two variants of loading were assumed: 1) the movement of the femoral fragment in the horizontal plane in the direction «forward-backward » was set, the displacement amount was 10 mm; 2) when the conditions of the 1-st task were fulfilled, vertical (axial) movement of the femur was also determined in the direction of physiological loading, with value of 5 mm. Results: with an increase of angles α, loading forces in ACL also increase both in calculations with no vertical displacement and with its account. The smallest forces were obtained at the angle α = 0°.
The greatest forces were obtained in the model with a slope angle α = 15°: 6.1 kN for the first type of calculation, which is 6.83, 4.27 and 1.84 % more than at α = 0°, 5°, 10°, respectively; 5.9 kN for the second type, by 14.56, 9.26 and 4.24 %, respectively. With increase of posterior slope angle, the differences in loading forces obtained in the first and second types of calculations are reduced. Conclusions: in all angles of posterior tibial slope (0°, 5°, 10°, 15°), the increase in loading forces didn’t exceed 15 %. The forces are higher in the model without axial displacement. The proposed mathematical model is quite effective in studying the loading in ACL, however, it is necessary to expand the modifiable components of this model to approach the biomechanics of the human knee. 

Author Biographies

Sergiy Krasnoperov

Zaporizhzhia State Medical University. Ukraine

PhD in Traumatology and Orthopaedics

Maksim Golovakha

Zaporizhzhia State Medical University. Ukraine

MD, Prof. in Traumatology and Orthopaedics

Sergiy Panchenko

SHEI «Pridneprovsk State Academy of Civil Engineering and Architecture». Dniepr. Ukraine


Bisson, L. J., & Gurske-DePerio, J. (2010). Axial and sagittal knee geometry as a risk factor for noncontact anterior cruciate ligament tear: a case-control study. Arthroscopy: The Journal of Arthroscopic & Related Surgery, 26 (7), 901–906. doi:10.1016/j.arthro.2009.12.012

Brandon, M. L., Haynes, P. T., Bonamo, J. R., Flynn, M. I., Barrett, G. R., & Sherman, M. F. (2006). The association between posterior-inferior tibial slope and anterior cruciate ligament insufficiency. Arthroscopy: The Journal of Arthroscopic & Related Surgery, 22 (8), 894–899. doi:10.1016/j.arthro.2006.04.098

Dejour, H., & Bonnin, M. (1994). Tibial translation after anterior cruciate ligament rupture. Two radiological tests compared. The Journal of Bone and Joint Surgery. British volume, 76-B (5), 745–749. doi:10.1302/0301-620x.76b5.8083263

Fening, S., Kovacic, J., Kambic, H., McLean, S., Scott, J., & Miniaci, A. (2008). The effects of modified posterior tibial slope on anterior cruciate ligament strain and knee kinematics – a human cadaveric study. Journal of Knee Surgery, 21 (03), 205–211. doi:10.1055/s-0030-1247820

Giffin, J. R., Vogrin, T. M., Zantop, T., Woo, S. L., & Harner, C. D. (2004). Effects of increasing tibial slope on the biomechanics of the knee. The American Journal of Sports Medicine, 32(2), 376-382. doi:10.1177/0363546503258880

Hashemi, J., Chandrashekar, N., Mansouri, H., Gill, B., Slauterbeck, J. R., Schutt, R. C., … Beynnon, B. D. (2010). Shallow medial tibial plateau and steep medial and lateral tibial slopes: new risk factors for anterior cruciate ligament injuries. The American Journal of Sports Medicine, 38 (1), 54–62. doi:10.1177/0363546509349055

Hohmann, E., Bryant, A., Reaburn, P., & Tetsworth, K. (2011). Is there a correlation between posterior tibial slope and non-contact anterior cruciate ligament injuries? Knee Surgery, Sports Traumatology, Arthroscopy, 19 (S1), 109–114. doi:10.1007/s00167-011-1547-4

Matsuda, S., Miura, H., Nagamine, R., Urabe, K., Ikenoue, T., Okazaki, K., & Iwamoto, Y. (1999). Posterior tibial slope in the normal and varus knee. The American Journal of Knee Surgery, 12 (3), 165–168.

Stijak, L., Herzog, R. F., & Schai, P. (2008). Is there an influence of the tibial slope of the lateral condyle on the ACL lesion? Knee Surgery, Sports Traumatology, Arthroscopy, 16 (2), 112–117. doi:10.1007/s00167-007-0438-1

Todd, M. S., Lalliss, S., Garcia, E., DeBerardino, T. M., & Cameron, K. L. (2010). The relationship between posterior tibial slope and anterior cruciate ligament injuries. The American Journal of Sports Medicine, 38 (1), 63–67. doi:10.1177/0363546509343198

Woo, S. L., Hollis, J. M., Adams, D. J., Lyon, R. M., & Takai, S. (1991). Tensile properties of the human femur-anterior cruciate ligament-tibia complex. The American Journal of Sports Medicine, 19 (3), 217–225. doi:10.1177/036354659101900303

Zeng, C., Cheng, L., Wei, J., Gao, S., Yang, T., Luo, W., … Lei, G. (2012). The influence of the tibial plateau slopes on injury of the anterior cruciate ligament: a meta-analysis. Knee Surgery, Sports Traumatology, Arthroscopy, 22 (1), 53–65. doi:10.1007/s00167-012-2277-y