## 4 Discussions  
The present study identified eight modes in the range of 0-150 Hz. Six modes are identified in 80% of the tests. The fifth mode seems difficult to exploit given its low repeatability in the identification. This mode is most certainly due to a measurement artifact. Two of these eight modes (54.55 Hz and 126.86 Hz) are in agreement with the numerical modes, and the identification is supported by an analysis of modal deformations. The parameters used in the updated model clearly match both physical and anatomical realities. This proves that an FE model, once updated, is a possible approach to simulate the mechanical behavior of human lower limbs. It should be noted that these two modes are differentiated by the sensor located in the middle of the tibia. The tibia actually contains a vibration node for solicitations around 118 Hz. On the other hand, the thigh does not have a vibration node in the frequency range of interest. In order to validate the numerical model, this study proposes a methodology that allows describing the modal behavior of the leg with no direct measures. This methodology can come in addition to those used in the literature that focus on modal parameters of a particular bone. One can distinguish two main in vivo methods that are compared in the work of [PERSON] in the late 1980s [35]. The Impulse Response (IFR) method involves generating impact with a shock hammer where the leg is relaxed and left hanging. The Bone Resonance Frequency (BRA) method consists of generating a sinusoidal signal over a frequency range with a vibrating shaker. These methods involve the measurement of the forces and their responses on the bone: it is therefore impossible to carry out measurements under real conditions. An OMA offers an interesting alternative, being an application in real conditions where the input forces are not known. Recent developments in OMA make it possible to identify the modal parameters, with possible applications in various sports with stationary impacts or noise. In terms of instrumentation, the proposed setup (featuring four sensors) extracts two modes in the 0-150-Hz range. The sensor in the middle of the tibia is essential to differentiate modes. It might be wise to deploy a fifth sensor in the middle of the thigh to observe a possible modal deformation displaying a vibration node on the femur. However, properly attaching the sensor would be difficult in view of the presence of the rectus femoris. Experimental studies propose a mathematical modeling of the phenomenon and could be integrated directly into the FE model [36]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Frequencies** & **Mode 3** & **Mode 8** \\ \hline Mean experimental frequencies (Hz) & 52.54 & 118.94 \\ Confidence interval (Hz) & 51.17–53.91 & 117.13–120.75 \\ Initial model (Hz) & 54.55 & 126.85 \\ Updated model (Hz) & 51.17 & 120.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison between the confidence interval and the frequencies calculated by the numerical model. Concerning the identified frequencies, the frequency of 52.54 Hz is very similar to that found in previous studies [37; 38]. Both resonance frequencies were determined by using a vibratory excitation at different frequencies between 10 and 90 Hz. The resonance frequency of the ankle was found to lie in the 40-50-Hz range. The modal deformation of the second mode at 126.9 Hz matches the modal deformations of the tibia, which is identified experimentally in the work of [PERSON] [39] and numerically in that of [PERSON] [40]. The latter highlights the torsional modes obtained for higher values (521 Hz). The protocol of the present study unfortunately prevents the measurement of this deformation. Considering results in a qualitative way, the frequency values lie in wide ranges. The tibia study shows that the bending resonance frequencies are of the order of magnitude 270 Hz and 340 Hz [39]. The modal frequencies for the femur are quite controversial.