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


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