**Published at : ** 10 Jul 2024

**Volume :** **IJtech**
Vol 15, No 4 (2024)

**DOI :** https://doi.org/10.14716/ijtech.v15i4.6883

Mahdieh, L., Lenjannejadian, S., 2024. Mechanical Loading of Anterior Cruciate Ligament in Different Strategies of Stop-Jump Landing.

61

Leili Mahdieh | Faculty of Sport Sciences, University of Isfahan, Hezar Jerib, Isfahan 8174673441, Iran |

Shahram Lenjannejadian | Faculty of Sport Sciences, University of Isfahan, Hezar Jerib, Isfahan 8174673441, Iran |

Abstract

Knee and anterior cruciate ligament (ACL) are
among the most injured parts of the body during sports activities. Therefore,
this study aimed to evaluate knee torque and mechanical stress on ACL under
various conditions of stop-jump landing, as well as identify risk factors for
injury, and propose improved strategies. The stop-jump landing was modeled
using anthropometric and kinematic data. Knee torque was calculated with the
inverse dynamic method, and ACL stress was determined using a Finite Element
Model (FEM). Different landing strategies were simulated, including variations
in knee flexion at initial foot contact, as well as knee and hip angular
displacement. The results showed based on mechanical stress analysis, females
(6.30 MPa) had a higher probability of ACL injury compared to males (4.51 MPa).
Increasing knee flexion at initial contact caused decreased knee torque and
approximately a 7% reduction in ACL stress. Furthermore, increasing knee and
hip angular displacement led to a decrease in knee torque, with a reduction in
ACL stress by 44% and 11% respectively. To reduce the risk of ACL injury, it is
recommended to increase knee flexion at initial contact as well as promote knee
and hip angular displacement during landing.

Biomechanics; Finite element; Knee; Modelling; Stress

Introduction

ACL injury is a common incident in sports activities, and numerous
studies have indicated that the primary cause is non-contact mechanisms *et al.*, 2008)*et al.*, 2017; Tsujii, Nakamura, and Horibe, 2017)

Previous
studies have used various methods to examine the mechanisms of non-contact ACL
injury *et al.*, 2009; Renstrom *et al.*,
2008)*et al.*, 2020)*et al.*, 2021; Söderman
*et al.*, 2020)

Biomechanical modeling is a viable method for obtaining kinetic and
kinematic parameters during movement analysis *et al.*, 2021; Ahmad
*et al.*, 2020)*et al.*, 2021; Taborri *et al.*,
2020)*et al.*, 2020; Kellis and Kouvelioti, 2009)*et al.*, 2021)

Although most previous investigations on sports movements have
been experimental, some also used modeling and simulation methods which are
powerful tools in various engineering studies *et al.*, 2023;
Hamza *et al.*, 2023)*et al.*, 2017;
Peña *et al.*, 2006; Moglo and Shirazi-Adl,
2003)*et al.*, 2009; Beillas *et
al.*, 2004)*et al.*, 2009; Shin, Chaudhari, and Andriacchi
2009; Beillas *et al.*, 2004)*et al.*, 2008)

Experimental Methods

This
study focused on landing phase of the stop-jump movement pattern. To achieve
the objective, two biomechanical models were developed. The first model was a
multi-link dynamic model used to calculate knee joint torque, while the second
model was a finite element model used to analyze stress distribution in ACL.
Using these models, different stop-jump landing strategies were simulated
separately for both males and females. The first strategy entailed modifying
knee flexion angle at the moment of initial foot contact. In the second
strategy, the angular displacement of knee joint was altered during landing,
while the third strategy included changing the angular displacement of the hip.

*2.1. Multi-Link Dynamic Model*

To construct a
dynamic model of the athlete, the limbs and body joints were represented as
rigid arms using the SimMechanics toolbox in MATLAB software (MATLAB R2010.
Natick, MA: The MathWorks Inc). Anthropometric data provided the necessary
information for model properties such as limb length, mass, and moment of
inertia. For females, a model with an average height of 1.67 m and a weight of
559 N was created, while for males, a model with an average height of 1.78 m
and a weight of 728 N was used. The data was based on anthropometric models
described by a previous study and modified for
Iranian athletes according to literature

The dynamic model consisted of three rigid links
representing the shank, thigh, and HAT (head, arms, and trunk), as well as
three hinged joints representing the ankle, knee, and thigh. The model was
considered two-dimensional in the sagittal plane (Caruntu and Moreno, 2019). The
inputs included the flexion angles of the hip, knee, and ankle joints at the
moment of initial foot contact with the ground, the amount of displacement in
these joints during the stop-jump landing, and landing time *et al.*, 2008; Yu, Lin, and Garrett, 2006)

*2.2. Finite Element Model (FEM)*

The precise
geometry and location were obtained from MR images in the sagittal section for
soft tissues and from CT images in the transverse section for the bones.
Initially, the image specifications, including size and spacing, were
determined. The images from each section were processed to generate a
three-dimensional geometric model of each knee structure. These geometric
models were further refined by smoothing, noise reduction, and creating a shell
model of the bones. Subsequently, knee joint structures were assembled using
CATIA (CATIA V5, Dassault Systèmes). The 3D knee model was finally used in the
ABAQUS finite element software (SIMULIA, ABAQUS, Dassault Systèmes) to analyze
stress distribution of the ACL under different landing strategies, using
corresponding torque input. In the finite element model depicted in Figure 1,
the bones were considered rigid bodies *et al.*, 2006; Beillas *et al.*,
2004; Moglo and Shirazi-Adl, 2003)*et al.*, 2004)

**Figure 1** The finite element model was developed
using ABAQUS software

In the
subsequent stage, the joint structures were meshed in preparation for analysis.
Details regarding mechanical properties, element types, and mesh types for each
knee joint structure are shown in Table 1 (Ruan *et al.*, 2008; Beillas *et al.*,
2004). To
complete the analysis, the torque exerted on knee derived from the dynamic
model, was applied as a load input. The solution was then obtained using the
explicit dynamic method, allowing for the calculation of stress distribution in
the ACL.

**Table 1** Mechanical
properties, element types, and mesh types for each knee joint structure

Knee joint structures |
Element type |
Density (g/cm |
Poisson's ratio |
Elastic modulus (MPa) |

Ligament |
2-node linear 3-D truss |
1 |
0.3 |
60 |

Meniscus |
Solid Homogeneous, 4-node
linear tetrahedron |
1.5 |
0.45 |
250 |

Bone |
Rigid, 4-node 3-D bilinear
rigid quadrilateral |
--- |
--- |
--- |

ACL |
Solid Homogeneous,4-node linear
tetrahedron |
1.2 |
0.45 |
60 |

Results and Discussion

The results of the dynamic model present knee joint torque obtained from simulating various stop-jump landing strategies. The kinematic data for both males and females were separately input into the multi-link dynamic model. Knee joint torque was then determined using the inverse dynamic method. As shown in Figure 2, the maximum normal torque of knee joint was found to be 0.43 for females and 0.30 for males. The results showed a strong correlation between torque values (r(13) = 0.949, p < 0.001), indicating similarity in overall knee joint torques during landing despite significant differences in peaks between males and females.

**Figure 2** Normalized knee joint torque in males
(solid line) and females (dashed line)

Analysis of different landing
strategies, depicted in Figure 3, showed that in the first strategy, increasing
the flexion angle of knee joint at the moment of initial foot contact led to a
decrease in the maximum torque for both males and females (Figure 3a).
Furthermore, these results showed a strong negative correlation between maximum
knee joint torques and angle of initial foot contact for both males (r(11) =
-0.997, p < 0.001) and females (r(12) = -0.999, p < 0.001).

In the second strategy, as the angular displacement of knee joint increased, the maximum torque initially decreased until a minimum value was reached. However, beyond this point, an increase was observed (Figure 3b). An optimal value was identified for the maximum angle of knee flexion. For females and males, this optimal value was determined to be 40.5 degrees and 51.4 degrees, respectively. The results showed an overall strong correlation between angular displacement of knee joint and the maximum torque for both males (r(17) = 0.733, p < 0.001) and females (r(21) = 0.901, p < 0.001). Similarly, in the third strategy, an analogous behavior was observed. As the displacement of the hip angles increased, the maximum torque of knee joint initially decreased until reaching a minimum value and then increased. This led to the identification of optimal angles for maximum thigh flexion. For females and males, these optimal angles were determined to be 101.3 degrees and 107.3 degrees, respectively. The results also showed a strong negative correlation between angular displacement of the hip joint and the maximum torque of knee joint for both males (r(11) = -0.967, p < 0.001) and females (r(16) = -0.958, p < 0.001).

**Figure 3** Maximum knee joint torque values in
different stop-jump landing strategies. In the first strategy (a) knee angle at
initial contact; in the second (b) the maximum knee flexion angle; and the
third strategy (c) the maximum hip flexion angle was changed. Solid lines (-)
represent males and dashed lines (- -) represent females

The FEM results illustrate the distribution of ACL stress derived from solving the finite element model under different landing strategies. Using knee joint torque distribution obtained from the dynamic model, a finite element model was used to simulate the joint movement under the input torque. The result of this model determined stress distribution in ACL for both males and females. The maximum stress was found to be 6.30 MPa for females and 4.51 MPa for males. The temporal variation of the maximum stress distribution in ACL is shown in Figure 4.

**Figure 4** Maximum stress distribution in ACL over
time for males (solid line) and females (dashed line)

Females experienced 1.40 times higher maximum stress than males, despite the overall time series of landing being similar between the two groups and showing a strong correlation (r(20) = 0.999, p < 0.001). The implementation of the finite element model illustrated in Figure 5 aimed to assess stress distribution in various landing strategies, showing that females had greater ACL stress than males. In the first strategy, stress distribution was analyzed for two different angles of knee flexion at the moment of initial foot contact. The maximum ACL stress at angles of 14° and 39° was 6.5 MPa and 6.1 MPa respectively (Figure 6a). In the second strategy, considering the maximum angles of knee flexion during landing to be 24° and 41°, the maximum stress in ACL was recorded as 2.5 MPa and 1.4 MPa respectively (Figure 6b). In the third strategy, as the amount of hip displacement increased, the maximum stress decreased. At maximum thigh flexion angles of 39° and 46°, the maximum stress in ACL was measured as 8.4 MPa and 7.4 MPa, respectively (Figure 6c). In all of these results, there were strong correlations between the time series of ACL stress for two selected values of initial knee angle, knee displacement, and hip displacement. The correlation coefficients were r(20) = 0.995, 0.771, and 1.000 with p < 0.001 for all three sets, respectively.

**Figure 5** Simulation of the finite element model
and the distribution of von Mises stress in ACL for (a) females and (b) males

Stop-jump landing is
frequently executed in basketball and volleyball and is linked to a high risk
of ACL injury. The results show that gender differences in the kinetics of the
lower limbs are consistent with previous empirical studies. Based on the
dynamic model, females had greater knee joint torque than males, with a ratio
of 1.43. According to mechanical theories, the possibility of injury is
proportional to the value of joint torque. This suggests the risk of knee
injury in females is higher than in males. Similarly, previous studies reported
that the rate of ACL injury in female players was more than twice the rate
among male players *et al.*, 2009; Renstrom *et al.*, 2008)

**Figure 6** The
maximum ACL stress distribution over time in different stop-jump landing
strategies. In the first strategy (a), knee angles at initial contact are 14
(solid line) and 39 (dashed line). In the second strategy (b), the maximum knee
flexion angles are 24 (solid line) and 41 (dashed line). In the third strategy
(c), the maximum hip angles are 39 (solid line) and 46 (dashed line)

According to previous
studies, one of the effective factors in ACL injury is the low angle of knee
flexion *et al.*,
2009; Renstrom *et al.*, 2008; Yu and Garrett, 2007; Pollard, Sigward,
and Powers,* *2007; Yu, Lin, and Garrett, 2006)*et al.* concluded that knee flexion
angle was lower in females than in males *et al.*, 2002)

Through empirical studies
on the standing long jump, Yu and Garret concluded that the large angles of
knee and hip flexion during initial contact with the ground did not necessarily
reduce the forces from impact. The impact could be rather attributed to the
active movement of the joints

The evaluation of the results
obtained from the finite element model also confirmed the validity for
estimating ACL stress during landing. Stress decreased with an increase in knee flexion
angle at the initial contact of the foot. Therefore, ACL injury is affected by
knee flexion angle at the initial contact of the foot, as also reported in
previous studies *et al.*, 2009; Renstrom
*et al.*, 2008; Yu and Garrett, 2007; Yu, Lin, and Garrett, 2006)

Conclusion

In conclusion, based on the results and previous
empirical studies, the models developed can be used as effective tools for
predicting the probability of injury in various landing strategies. From a
technical and academic perspective, educators and stakeholders should advocate
for specific strategies aimed at reducing ACL injury. Strategies
comprise enhancing knee and hip biomechanics during landing tasks.
Specifically, increasing knee flexion at the moment of initial foot contact,
improving knee flexion displacement, and enhancing hip flexion displacement can
help to reduce the risk of ACL injury. In general, these strategies facilitate
shock absorption during landing, which in turn decreases torque on knee joint
and subsequently lowers the risk of ACL injury in athletes.

Supplementary Material

Filename | Description |
---|---|

R1-ME-6883-20240124135335.jpg | New Figure 5 |

R1-ME-6883-20240124135353.jpg | New Figure 6 |

R1-ME-6883-20240124135415.docx | Modified Figure Caption |

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