# Loads on the Knee Joint Ligaments during Stair Climbing
## 4 Discussion  
The present study was designed to investigate the loads on internal knee joint structures during the relatively demanding task that is stair climbing. In particular, we were interested to know how the ligament tensions were related to the joint kinematics and muscle forces. This problem is of clinical interest because of its implication in rehabilitation and surgery planning, such as knee-joint arthroplasty and ligament reconstruction. A dynamic musculoskeletal model was adopted for this purpose, and was animated using data extracted from our repository [6]. This was just an exemplary analysis, referring to the specific anthropometry and pattern of movement of a single subject. Deeper investigation will be devoted to analysing the effects of subject size in relation to the step geometry (riser and tread) and the effects of gender and age. Developing a subject-specific model to be used in clinical practice could be an additional goal, with the aim of predicting the effects of ligament reconstruction or ligament removal in case of knee-joint arthroplasty. In our single case study, the pattern of muscle forces and tibiofemoral contact forces were obtained by taking into account ground-reaction forces, inertia forces and moments, the lever arms of muscles in relation to each joint rotational axis, and implementing an optimisation algorithm that minimises the maximum specific force. The phasic activities of the muscles acting on the knee joint predicted by the algorithm were in agreement with the data obtained in [36] through electromyography measurements on ten healthy young male subjects during stair climbing. As to the muscle forces, the contributions of different muscles to stair climbing is in good agreement with their function: the whole quadriceps was mostly active during the stance phase (see Figure 5a), with the VM and the VL exhibiting a high peak of contraction force (900 N) in the first half of the stance phase, thus confirming their main roles as knee extensors. The second peak of their activity corresponds to the peak of the gastrocnemius force (Figure 5c). This can be explained by considering the double-joint arrangement of the gastrocnemius (GAL and GAm). They are biparticular muscles acting as ankle plantar flexors and knee flexors. At late stance, they contribute to pushing off by producing a plantarflexion moment at the ankle joint. This entails a flexor effect at the knee, and thus the need for extensor muscles to counteract this effect. Differently from the rest of the quadriceps, the RF is active during the swing phase also, thus contributing to the hip-flexor moment required to raise the thigh and foot above the next step. Among the hamstring muscles (Figure 5b), the most intense force is produced by the SM at the beginning of stance phase. This is apparently in contradiction with the need for an extensor moment at that time. The problem of co-contraction of the quadriceps and hamstrings, when apparently only knee extension is required, has been deeply investigated in reference to the cycling task [37,38] where a similar condition  
Figure 8: Output of the model: tension of the different capsule components and deep MCL. occurs. The phenomenon is called '[PERSON] paradox' [39] and has been explained by considering the need to produce an extensor moment at the hip joint simultaneously with knee extension. In order to allow the SM to produce an extensor moment at the hip, the flexor moment produced at the knee must be counteracted by an additional activity of the extensor muscles. The effectiveness of this co-contraction of knee antagonist muscles depends on the ratio between the lever arms of the hamstring at the hip and knee [40]. Probably for this reason, the BFlh and the ST have different actions than the SM. Their main activity appears at mid and late stance, where knee flexion initiates. At late stance, the SM exhibits a peak of force as well.