*3.3. Lower Extremity Joint Angles*

Ensemble curves of the difference in lower extremity joint angles (hip, knee, ankle joints) in the sagittal plane between the systems are illustrated in Figure 5.

The hip (top panel) and knee (middle panel) joint angles were biased toward the extension in the ML than MB throughout the stride cycle except briefly for the early swing phase for the hip joint, and early stance phase for the knee joint. On the other hand, ML showed a dorsiflexion-biased ankle joint angle (bottom panel) throughout the stride cycle.

— **Figure 5.** Ensemble curve of lower extremity joint angle differences in the sagittal plane between marker-based (MB) and markerless (ML) motion capture systems across the average 10 stride cycles for 16 participants. Differences were estimated as ML joint angles of each joint—MB joint angles of each joint.

#### **4. Discussion**

This study compared MB and ML systems with estimated lower extremity joint moments and powers during treadmill running. Significant differences were detected in the peak magnitudes for joint moments and powers and relative timings to peak estimated by the two systems. Greater peak magnitudes for hip extension and flexion moments, knee flexion moments, and ankle plantarflexion moments, along with their joint powers, were observed in the ML system. Meanwhile, significantly smaller peak magnitudes for knee extension moments coinciding with knee production power were observed.

We focused on the sagittal plane's joint angles, moments, and powers tendency was partly consistent with Kanko et al.'s study MB system's estimation resulted in greater flexion in all three joints. One possible We focused on the sagittal plane's joint angles, moments, and powers, since running is primarily a sagittal plane movement [31]. We observed greater hip and knee flexion angles and smaller ankle dorsiflexion angles in the MB system than in the ML system. The tendency was partly consistent with Kanko et al.'s study [19] (Figure 2 for lower extremity joint center, Figure 4 for segment angle and Figure 5 for joint angle), showing that the MB system's estimation resulted in greater flexion in all three joints. One possible explanation may be the model of the virtual foot. Visual3D introduces three methods to build the

virtual foot, which may affect the ankle joint angles. When we chose the heel and toe targets to define the proximal and distal ends of the foot, there was no disclosure for Kanko et al.'s foot model. Different from Kanko et al.'s results, we observed larger magnitudes of systematic differences in the knee and ankle joint angles but smaller magnitudes in the hip joint. Compared to walking in Kanko et al., running in the current project is related to greater lower extremity joint motion [32]. With greater joint motion, soft tissue artifacts can also be larger, leading to an additional 3◦ error in the joint angles. Additionally, inconsistent marker placement can contribute to a 5◦ error in the joint angles [14,33].

Compared to the MB system, the ML system's estimation resulted in greater magnitudes of peak hip flexion moment in the stance–swing transition phase and extension moment in the late swing phase, knee flexion moment in the late swing phase, and ankle plantarflexion moments in the early stance phase, but smaller knee extension moments in the early stance phase. Previous studies presented similar patterns of lower extremity joint moments during running estimated by MB systems. Schache et al. (2011) and Fukuchi et al. (2017) reported lower extremity joint moments at the speed of 3.5 m/s during overground and treadmill running, respectively [34,35]. Their results showed similar peak magnitudes of hip flexion and extension moments of −1.09 and 0.91 Nm/kg (overground) and −1.15 and 1.37 Nm/kg (treadmill); knee flexion moments of −0.53 Nm/kg (overground); as well as the ankle plantarflexion moment with the values of 2.94 Nm/kg (overground) and 2.23 Nm/kg (treadmill). Besides, they reported similar knee extension moments with the values of 3.12 Nm/kg (overground) and 3.18 Nm/kg (treadmill). Consequently, joint powers also showed the same tendency. Despite the differences between overground and treadmill running, Schache et al.'s results revealed similar systematic differences to the present study. Compared to the MB system, the estimations from the ML system may result in greater hip moments and powers in the stance–swing transition and swing phase, knee moments and powers in the swing phase, as well as the ankle moments in the early stance phase, but less knee moments and power in the early stance phase.

The anthropometric model affects the results of the joint moments and powers. Once rigid body equations are set, the joint centers and moment of inertia about the center of mass eventually govern the relationships between kinetics and kinematics [20]. The systematic differences can be further explained by the variations of joint centers and segment mass centers.

It has been well-recognized that differences in hip joint center location can propagate to hip and knee kinematic and kinetic quantities, especially the hip moments concerning flexion/extension [36]. Besides, the propagation of flexion/extension moments is particularly sensitive to the anteroposterior hip joint center location. We observed that hip joint centers in the ML system were about 2 cm posterior to the MB system in the stance–swing transition and late swing phase. In addition, the sensitivity of hip moments to inertial property variations can be up to 40% [7]. Supported by our results, the thigh center of mass locations was about 2 cm superior in the ML than the MB system in the stance–swing transition phase. Similar to a previous study, greater changes occurred in the swing phase [7], and the ML system showed a biased posterior (about 2 cm) and anterior (about 1 cm) center of mass. For the knee joint, joint moments are sensitive to the differences in knee joint center locations [37]. Previous studies have reported that tibia surface movements affected the knee joint center by 1.1 cm and resulted in the most prominent joint moment in the stance phase [37]. Our results exhibited that knee joint centers differed around 1 cm in all directions and result in greater disparities in the leg center of mass in the early stance phase, which may explain the greater knee extension moment in the MB system. Moreover, our results exhibited a greater leg center of mass in the late swing phase, which may induce greater knee flexion moments. For the ankle joint, we observed less than 1 cm differences in all three directions. Previous studies indicated that average ankle joint position differences were less than 1 cm in the anteroposterior and mediolateral direction and around 2 cm in the vertical direction [19]. Plus, the foot center of mass locations varied greatly. The ML system was slightly biased in the lateral direction (<1 cm) with greater bias in the anterior

and superior directions (almost 3 cm). Such a difference may be induced by the marker placements of the first and fifth metatarsal heads. While the MB system reads the markers on the side of the first and fifth metatarsal heads, the markerless system might locate the foot center of mass based on the contour of the shoe. The different joint centers could affect moment arms, and the segment center of mass could affect the estimation of the moment of inertia. Together, they could lead to greater differences in the joint moments and powers.

The methodology differences between ML and MB systems that determine the estimation of poses (body segment positions and orientations) need further attention. To ensure the consistency of the computational algorithms, Visual3D has been used for segments and inverse dynamic solutions used for both systems. However, the MB system depends heavily on physical marker placements over external/internal anatomical landmarks (hardware), and the ML system relies on deep learning-based algorithms to estimate joint center locations (software). The deep learning pose estimation algorithms learn to identify joint centers from the training data. ML in the current study includes over 500,000 manually labeled digital images of the human body and employs biomechanically applicable training data that can identify 51 salient features of the human body [17–19]. The optimization methods examine the distance between the manually labeled training data and the estimated joint centers to reduce errors. This process is repeated with the entire training data until improvements between each iteration become negligible. The pose estimation algorithm is then tested on the new image and compared to the training dataset [38]. However, any omissions or biases implicit within training datasets could propagate to situations where the training was weak [19]. Note that the inverse dynamic method is very sensitive to joint center locations, because the estimation of the net joint moments includes the cross product of forces and their moment arms, where the length of moment arms is largely affected by joint center locations [37]. A previous marker-based study has reported that 2 cm superior and 2 cm lateral placement of the hip joint center can decrease the moment of arms of the hip joint by about 28% [38]. Supported by our results, systematic differences in joint center positions have been observed, which might affect moment arms and lead to disparities in joint moments and powers. However, it remains unclear if the differences are caused by marker-based joint center errors induced by soft tissue artifacts [11] or propagations from a weak training dataset.

While the ML system may still be considered in its infancy, evidence from previous studies demonstrated its potential for clinical applications. Since pose estimation algorithms are not dependent on markers attached to the skin, soft tissue artifact errors and human errors usually induced by the MB systems can be eliminated [39]. Studies also presented that the markerless system can extract new information from old datasets [40,41]. Therefore, the ML system can be beneficial in the streamlined monitoring of changes in disease progression [41], rehabilitation [42], athletic training, and competitive sports [43]. In addition, the Theia3D markerless system has shown strong results in the inter-session joint angles variability during walking with loose clothing conditions [18], which the MB systems cannot realize. More importantly, data collection can be completed in a much shorter time than the MB systems [18]. Such benefits could facilitate data collection in a more convenient area with less effect on people's gait [44], when time is limited, and they are wearing more comfortable clothing.

However, the differences observed here could have significant implications. For example, previous studies have shown that the values of hip extension and knee flexion moments in the initial stance and late swing phase were important factors in discussing hamstrings injuries during sprinting [45,46]. The greater hip extension and knee flexion moments observed in the late swing with the ML system could impact the hamstring injury-related discussions. Similar to hamstrings, the biarticular rectus femoris plays an important role in the energy transfer between the hip and knee joints. Greater rectus femoris stress is associated with greater hip flexion and knee extension moments. We have observed, with the ML in comparison with the MB system, greater hip flexion moments in the stance to swing transition phase, greater hip power absorption in the late stance phase, and greater hip joint power production in the early swing phase, which could lead to a greater rectus femoris contraction estimation during the stance–swing transition. A previous study showed that greater rectus femoris contraction could lead to greater patellar tendon tension, a risk factor for patellofemoral pain during running [47]. Thus, joint moment/power estimated by the ML system can lead to different assessments for the risk factors of hamstring injuries, patellofemoral pain, and maybe other relevant discussions compared to the MB system. With different risk factor analyses based on the MB or ML systems, clinicians, coaches, and athletes could arrive at different decisions in their practices.

The following limitations of the current work should be noted. First, our participant pool was limited to recreationally active young adults. Different population groups may have anatomical deformities, affecting the comparison between the systems. Second, we analyzed treadmill running, where the treadmill settings may constrain the speed. Additionally, the hardware and the marker placements are unique to each lab. Despite our updated Vicon high-resolution video cameras employed for markerless data, the Vicon Bonita series infrared cameras used here do not provide us with the highest resolution available on the market. Lower camera resolution may cause trajectory errors in the identifications of landmarks [48]. Therefore, future studies should attempt to replicate the results in different populations using different speeds and hardware settings.

#### **5. Conclusions**

This study is the first to compare the inverse dynamic outcomes of lower extremity kinetics estimated by the marker-based and markerless systems. We have observed differences in joint moments and powers between the two systems, which could be partially related to the estimations of joint centers and segment center of mass (pose estimations). Although the accuracy and precision of pose estimations between the two systems require further testing, the strengths of the markerless system are apparent. The significantly less data collection and processing time contribute greatly to a more versatile application. With the progression of pose estimation software, the markerless system can be further employed in clinical biomechanics and sports medicine.

**Author Contributions:** Conceptualization, L.L.; methodology, L.L. and K.D.; validation, J.P. and K.D.; formal analysis, H.T., K.D. and J.P.; investigation, H.T.; data curation, J.P.; writing—original draft preparation, H.T.; writing—review and editing, L.L., K.D. and B.M.; visualization, H.T.; supervision, L.L.; project administration, L.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** The study was conducted in accordance with the Declaration of Helsinki, and approved by the Georgia Southern University Ethics Committee (protocol code H22732, 07/08/2022).

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study. Written informed consent has been obtained from the patient(s) to publish this paper.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

