# Patellar Tendon Force Differs Depending on Jump-Landing Tasks and Estimation Methods
## 4 Discussion
The knee joint moment was calculated by inverse dynamics and the patellar tendon moment arm was estimated by a regression equation using the knee flexion angle, obtained by dissection of cadaver specimens [27]. The static optimization method consists of multiplying the quadriceps tendon force with a ratio of the PTF and the quadriceps tendon force as a function of the knee flexion angle [28; 33]. The ratio of the PTF and the quadriceps tendon force represents the part of the quadriceps force that is distributed over the patellar tendon [28]. The latter method should provide a more realistic approach as it considers muscle co-contractions. Therefore, we hypothesized that the estimation of PTF calculated with the inverse dynamic method would be lower because this method does not consider muscle co-contractions [19]. However, the results revealed that the inverse dynamic method estimated statistically significant higher PTF peaks compared to the static optimization method. We speculated that this unexpected difference may be due to an underestimation of the ratio used in the static optimization method that represents the part of the quadriceps force that is distributed over the patellar tendon. This ratio was determined by a previous study using a mathematical model based on knee autopsies [28]. However, this latter study has several limitations. Firstly, the knees were obtained from cadavers of men who were around 77 years old, whereas our participants were on average 29 years old. A systematic review highlighted that the aging process appeared to be associated with a decrease in the elastic modulus and stiffness of collagenous tissues [34]. Thus, these potential differences in mechanical properties of the patellar tendon may have an impact on the PTF estimated by the static optimization method. Secondly, their ratio was not validated by in vivo experimental measurements because the authors did not have the required technical facilities [28]. These authors compared this ratio with the available literature and showed that it was lower than in a previous study [35]. The results of our study suggested that the consideration of muscle co-contractions alone does not result in a higher PTF, possibly due to the underestimated ratio of the PTF and the quadriceps tendon force used in the static optimization method. Interestingly, although statistically significant differences were found between both estimation methods, the results of both jump-landing tasks based on PTF peaks and loading rates were not different. Thus, regardless of the estimation method chosen, the overall conclusions would be: FJL induced higher forces and loading rates on the patellar tendon compared to VJL. The advantage of the static optimization method is that this method considers muscle co-contractions and may provide more biologically plausible values compared to the inverse dynamic method. However, the main limitation of the static optimization method is that the PTF values estimated were lower compared with the PTF values estimated through the inverse dynamic method which were known to be underestimated compared to reality [8; 9]. Researchers must consider both advantages and limitations when choosing the estimation methods according to their purposes. There are limitations in the current study that must be considered when interpreting the results. Firstly, the complete sequence of the jumping movement was not studied because the purpose of the current study was to focus on the landing phase which was considered a greater risk for the development of patellar tendinopathy. Another study focusing on the complete jumping task and highly comparable to volleyball practice would be needed to better understand the risk of injury in real practice conditions. Secondly, the PTF was estimated from a musculoskeletal model and not measured directly, which is currently not possible in vivo in healthy participants. Without these in vivo measurements, it is difficult to determine the true accuracy of the PTF estimation methods.