Numerical Study on Stress Field of Knee Meniscus in Jumping Gait

: In this paper, the numerical study focuses on the stress field of the knee meniscus in the two gaits of the jumping motion, and the knee injury and its knee protection effect are studied based on the stress field distribution characteristics of the knee meniscus. The jumping gait simulation was carried out by using a more detailed healthy knee model including bone, articular cartilage, meniscus, ligaments and peripheral soft tissues constructed by combining CT and MRI tomography, and the peak stress and its distribution area were analyzed based on the stress field characteristics of the meniscus, and the knee meniscus and its injury and protection under different knee pads were discussed. The results showed that the anterior angle of the meniscus on the medial knee joint was an area prone to injury in the take-off and landing gait. Under the knee pads, the peak stress of the meniscus decreases, and its distribution area gradually shifts from the anterior angle to the middle, and the functional knee pads with the optimized force load significantly alleviate the stress concentration of the meniscus. Therefore, the numerical study of the stress field of the knee meniscus provides theoretical support and optimization guidance for the design of functional knee pads.


INTRODUCTION
The meniscus is an important bearing tissue in the knee joint, which has the functions of maintaining the stability of the knee joint and buffering the shock, but due to its tissue and morphological characteristics, it cannot repair and regenerate itself after injury, which will cause knee joint lesions. Therefore, the daily protection of the knee meniscus is particularly important, among which wearing knee pads is a common protective measure.
The knee joint is at risk of injury during daily activities and sports such as walking, squatting, and jumping. Wang et al. (2022) found that when going downhill the probability of knee joint injury was higher than when walking flat because of the knee extension torque increased significantly. Hartmann et al. (2013) found that the angle of knee flexion in weight-bearing squats is an important influencing factor of knee joint injury. Tsarbou et al. (2021) found that jumping and landing after human fatigue can also cause knee joint injuries. Sun et al. (2022) discussed the influence of running speed on knee joint injury when stopping abruptly or jumping under different running speeds. Changes in the external load environment of the knee joint always increase the risk of its injury.
Wearing knee pads can effectively protect the knee joint, prevent its damage or delay the occurrence of knee joint diseases. Khadavi et al. (2015) found through survey a liumingjie1@126.com; b jiangtaoruan@163.com; c 13406176978@163.com; d xiaoxia@tiangong.edu.cn that when the knee joint is supported, it reduces the patient's pain; Rishiraj et al. (2012) found that when athletes wear rigid knee pads for platform jumping movements, the ground reaction force on the knee joint was reduced; Liu et al. (2019) used three-dimensional motion capture technology to verify that wearing knee pads has obvious protective effect on knee joints under some strenuous exercises, such as stopping abruptly, jumping and other movements; Schwarze et al. (2019) compared the force changes of the knee joint before and after wearing the knee brace through the human fall experiment, and found that the average peak impact force of the knee joint after wearing the knee brace was reduced by 15%; Zhang et al. (2020) selected a number of subjects of different ages to evaluate the protective performance of different types of knee pads by capturing dynamics data of the knee joint under jogging. It can be seen that most of the current studies discuss the efficacy of knee pads through the improvement of the external force environment of the knee joint, and there are few studies on the relationship between the internal stress field distribution characteristics of the knee joint and the protective performance of the knee pad.
Based on CT and MRI tomography scan data, a more realistic knee joint geometric model including bone, articular cartilage, anterior and posterior cruciate ligament, medial and lateral collateral ligament, patellar ligament, medial and lateral meniscus and peripheral soft tissues of the knee joint was constructed, and the two instantaneous gaits of taking-off and landing in healthy body jumping motion were numerically simulated by Abaqus finite element software, and the efficacy of knee pads with different force load distribution on the protection of knee meniscal injury was discussed based on the stress field distribution characteristics of the knee meniscus, which aims to provide mechanical theoretical support and technical guidance for the design of functional knee pads.

Geometry Model of the Knee Joint
A more detailed knee model including bone, articular cartilage, anterior and posterior cruciate ligament, medial collateral ligament, patellar ligament, lateral and medial meniscus and peripheral soft tissue was constructed using CT and MRI tomography data from the subject's (male, 24 years old, 172cm, 80kg) right knee joint, as shown in Figure 1.

Numerical Model of the Knee Joint
The knee 3D model is divided by tetrahedral elements, the number of elements in the model is 3222140, and the number of nodes is 709885. The specific material parameters of each tissue in the knee joint model are shown in Table 1. The bone, meniscus, articular cartilage, patellar ligament and peripheral soft tissues are defined as isotropic elastic materials, and the medial and lateral collateral ligaments and anterior and posterior cruciate ligaments are defined as hyperelastic materials (Zhang, et al., 2021;Shriram, et al., 2021), using the Neo-Hookean model, and their strain energy density function is shown in Equation (1).
where �� and � represent the Neo-Hooke material constants, which represent the volumetric material constant and the material incompressibility, respectively, ��� � � �� represents the Jacobian determinant of the elastic deformation gradient , ̅ � represents the first invariant of the Cauchy-Green deformation tensor �� � , and � � � � � � � represents the modified elastic deformation gradient. In the model, the anterior and posterior cruciate ligament, the medial and lateral collateral ligament, and the adjacent areas and bone tissues between the articular cartilage and bone, all peripheral soft tissues and the upper and lower ends of the ligaments are set as binding constraints, and no relative sliding occurs. The ligaments connected to the tibia at the anterior and posterior corners of the medial meniscus are simulated with a linear spring with a stiffness of 2000 N/mm, and the transverse ligaments connected between the anterior corners of the laeral and medial meniscus are also simulated with a linear spring with a stiffness of 200 N/mm (Mononen, et al., 2015;. Surface-to-surface contact between cartilage and cartilage and meniscus is set up with relative slip, soft tissue and knee joint are set with normal contact, and the surface is set with limited slip, and the contact property is defined as "hard" contact with a friction coefficient of 0.02.
The taking-off gait and the landing gait in jumping movement were simulated, and the vertical compressive loading, internal or external rotation moment and knee flexion angle on the sagittal plane in the gait were obtained by LifeMOD software. In the taking-off gait, the vertical compressive loading of the knee joint was 1378 N, the external rotation torque was 4.41 N•m, and the knee bending angle was 18.9°; In the landing gait, the vertical compressive loading of the knee joint is 1482 N, the internal rotation moment is 2.56 N•m, and the knee flexion angle is 7.9°. In the finite element simulation, the six degrees of freedom of the distal tibia and fibula are completely fixed, and the patella and femur are not constrained. A vertical compressive force is applied on the femur, an internal or external rotation moment is applied on the tibial platform, and a knee flexion angle is applied at the center of the line between the medial and medial condyle of the femur.
Apply a uniform load of 2.5 KPa (Yan, et al., 2018) over the outer surface of the knee joint, simulating the wearing of ordinary knee pads, as shown in Figure 2(a). In the area of the pressurized strap, as shown in Figure  2(b), add an additional 2.5 KPa load to simulate a sports knee pad.

Stress Field without Protection
Without protection, the medial meniscus stress field was mainly distributed in its anterior and middle corners, and the peak stress appeared in the anterior corner area; The stress field of the lateral meniscus is mainly distributed in its anterior angle; The stress value of the medial meniscus is greater than that of the lateral meniscus. During the taking-off gait, the peak stress of the medial and lateral meniscus was 20.35 MPa and 11.33 MPa, respectively; During landing gait, the peak stress of the medial and lateral meniscus was 14.14 MPa and 7.34 MPa, respectively, as shown in Figure 3.
(a) Taking-off gait (b) Landing gait Figure 3: Stress field of knee meniscal without protection (unit: MPa)

Stress Field under Ordinary Knee Pads
Protected under ordinary knee pads, the stress of the medial meniscus decreases and the stress of the lateral meniscus increases slightly, but the stress value of the medial meniscus is still large. There is no significant change in the stress distribution area, distributed in anterior and middle corner of the medial meniscus and in the anterior corner of the lateral meniscus. In the takingoff gait, the peak stress of the medial meniscus decreased to 19.87 MPa, and the peak stress of the lateral meniscus increased to 11.51 MPa. In landing gait, the peak stress of the medial meniscus decreases to 13.59 MPa and the lateral meniscus increases to 8.34 MPa, as shown in Figure  4.

Stress Field under Sports Knee Pads
Protected under the sports knee pads, the medial meniscus stress decreases and is still greater than the lateral meniscus stress. The stress of the lateral meniscus increases slightly in the taking-off gait and decreases slightly in the landing gait. In the taking-off gait, the peak stress of the medial meniscus decreases to 17.86 MPa and the lateral meniscus increases to 11.73 MPa; During the landing gait, the peak stress of the medial meniscus decreases to 12.78 MPa and the lateral meniscus decreases to 8.01 MPa, as shown in Figure 5.

Discussion of Knee Meniscus Injury and Protection
The taking-off gait and the landing gait are two typical gaits in the jumping movement, in which the vertical compressive load, internal or external rotation moment and knee flexion angle at the knee joint are large. Compare the peak stress of the knee meniscus under different protective conditions, as shown in Table 2. It can be seen that the medial meniscus is the main load bearing tissue structure of the knee joint, and the stress is greater than that of the lateral meniscus. With the increase of protective measures, the stress of the medial meniscus decreased significantly, the risk of its damage was reduced, and the stress of the lateral meniscus increased slightly. At the same time, with the of peak stress values gap between the inner and outer meniscus shrinks, the meniscus structure gradually shared the external load; The stress distribution area of the medial meniscus gradually shifts from the narrow and thin anterior corner to the wider middle and posterior part of meniscus, thereby reducing the risk of damage in the anterior corner area.

CONCLUSIONS
In taking-off and landing gait of the jumping movement, the anterior corner of the medial meniscus is an easily damaged area with peak stress. Under protection of the knee pads, the peak stress of the medial meniscus decreases and the peak stress distribution area also shrinks and shifts, which reduces the risk of meniscal injury. Moreover, under the condition of sports knee pads designed with optimized force load, the area with larger stress of the medial meniscus gradually shifted from the narrow and slender anterior corner to its wider middle and posterior part, indicating that the broad middle and posterior part of the medial meniscus began to bear load, and the stress concentration phenomenon was significantly improved. The peak stress of the lateral meniscus increased slightly, and the stress gap between the medial and lateral meniscus decreased, indicating that they gradually shared the load. This paper studies knee injury and its protective effect based on the stress field distribution characteristics of knee meniscus, which aims to provide mechanical theoretical support and technical guidance for the design and optimization of functional knee pads.