Dynamic Balance During Walking in Transfemoral Prosthesis Users: Step-to-Step Changes in Whole-Body and Segment Angular Momenta

Transfemoral prosthesis users (TFPUs) typically have a high risk of balance loss and falling. Whole-body angular momentum (<inline-formula> <tex-math notation="LaTeX">${\overrightarrow {H}}_{{\text {WB}}}{)}$ </tex-math></inline-formula> is a common measure for assessing dynamic balance during human walking. However, little is known about how unilateral TFPUs maintain this dynamic balance through segment-to-segment cancellation strategies. Better understanding of the underlying mechanisms of dynamic balance control in TFPUs is required to improve gait safety. Thus, this study aimed to evaluate dynamic balance in unilateral TFPUs during walking at a self-selected constant speed. Fourteen unilateral TFPUs and fourteen matched controls performed level-ground walking at a comfortable speed on a straight, 10-m-long walkway. In the sagittal plane, the TFPUs had a greater and smaller range of <inline-formula> <tex-math notation="LaTeX">$\overrightarrow {H}_{{\text {WB}}}$ </tex-math></inline-formula> compared to controls during intact and prosthetic steps, respectively. Further, the TFPUs generated greater average positive and negative <inline-formula> <tex-math notation="LaTeX">$\overrightarrow {H}_{{\text {WB}}}$ </tex-math></inline-formula> than did the controls during intact and prosthetic steps, respectively, which may necessitate larger step-to-step postural changes in the forward and backward rotation about the body center of mass (COM). In the transverse plane, no significant difference was observed in the range of <inline-formula> <tex-math notation="LaTeX">$\overrightarrow {H}_{{\text {WB}}}$ </tex-math></inline-formula> between groups. However, the TFPUs displayed smaller negative average <inline-formula> <tex-math notation="LaTeX">$\overrightarrow {H}_{{\text {WB}}}$ </tex-math></inline-formula> in the transverse plane than did the controls. In the frontal plane, the TFPUs and controls demonstrated similar range of <inline-formula> <tex-math notation="LaTeX">$\overrightarrow {H}_{{\text {WB}}}$ </tex-math></inline-formula> and step-to-step whole-body dynamic balance owing to the employment of different segment-to-segment cancellation strategies. Our findings should be interpreted and generalized with caution for the demographic features in our participants.

− → H WB than did the controls during intact and prosthetic steps, respectively, which may necessitate larger step-tostep postural changes in the forward and backward rotation about the body center of mass (COM). In the transverse plane, no significant difference was observed in the range of − → H WB between groups. However, the TFPUs displayed smaller negative average − → H WB in the transverse plane than did the controls. In the frontal plane, the TFPUs and controls demonstrated similar range of − → H WB and step-to-step whole-body dynamic balance owing to the employment of different segment-to-segment cancellation strategies. Our findings should be interpreted and generalized with caution for the demographic features in our participants.

I. BACKGROUND
M ORE than half of lower-limb prosthesis users fall at least once each year, and this rate has not improved over the last 20+ years [1], [2], [3], [4]. Transfemoral prosthesis users (TFPUs) reportedly fall more frequently than transtibial prosthesis users [1], [2], [3]. Approximately 15% of TFPUs with non-microprocessor knees were reported to have injurious falls that required care and considerable medical expenses [5]. According to a recently established systematic fall-type classification algorithm, falls in lower-limb prosthesis users could be caused by prosthesis factors as well as by destabilization of the whole-body during gait [4]. Therefore, maintaining whole-body dynamic balance is a prerequisite in unilateral TFPUs to realize continuous walking without falling.
Dynamic balance is defined as the ability to maintain stability during weight shifting activities, while changing the base of support [6], [7], [8], [9], [10]. Whole-body angular momentum ( ⃗ H WB ) is a useful measure to assess dynamic balance that accounts for the angular movements of all body segments around the body center of mass (COM) during walking and is tightly regulated [11]. The temporal rate of change of ⃗ H WB equals the net external moment on the body COM, which is determined by the cross-product of the ground reaction forces (GRFs) and their external moment arms.
Recent work has revealed that unilateral TFPUs generate asymmetric GRFs between intact and prosthetic limbs in the vertical, anterior/posterior, and mediolateral directions during walking [12], [13], [14], [15], [16], [17]. Further, unilateral TFPUs have been reported to have asymmetric step lengths [12] and center of pressure trajectories [6], [18], [19], which could directly induce asymmetric external moment arms between the two limbs. Due to these unique behaviors, unilateral TFPUs may demonstrate bilaterally asymmetric step-to-step average ⃗ H WB than people without amputation, which may lead to a loss of posture and whole-body destabilization.
In general, the average ⃗ H WB across strides is highly regulated as it remains close to zero during straight-line walking [20] due to segment-to-segment cancellations of segment angular momenta [11], [21], [22]. Although ⃗ H WB is modulated through whole-body kinematics, unilateral TFPUs generally demonstrate asymmetric lower-limb joint kinematics [23], [24] and trunk posture [25], [26]. These characteristics imply that effective control of ⃗ H WB to maintain dynamic balance requires asymmetric but adequate regulation of the rotational movements of all body segments in unilateral TFPUs. Previous studies revealed that unilateral transtibial prosthesis users exhibit a larger range of ⃗ H WB in the sagittal and frontal planes than do individuals without amputations during level [27], stair [28], and sloped walking [29]. Individuals with a unilateral ankle-foot orthosis have also been reported to display a similar range of sagittal and frontal ⃗ H WB compared to those without impairments [30]. However, little is known about how unilateral TFPUs maintain this dynamic balance through segment-to-segment cancellation strategies.
Thus, the objective of this study was to evaluate dynamic balance in unilateral TFPUs during walking at a self-selected constant speed. We compared the range of ⃗ H WB between TFPUs and individuals without amputation. As observed in the previous studies of the unilateral limb impairment [27], [28], [29], [30], we hypothesized that unilateral TFPUs would have different ranges of ⃗ H WB in the sagittal and frontal planes, but not in the transverse plane, compared to the individuals without amputation. Even though TFPUs have similar range of ⃗ H WB as individuals without amputation, this metric does not account for the average magnitude (and rotation direction) of ⃗ H WB during steps due to the asymmetric kinematics and morphological structures. A greater magnitude of average ⃗ H WB would necessitate step-to-step postural changes about the body COM. Hence, we also evaluated the average ⃗ H WB to characterize the magnitude of ⃗ H WB during intact and prosthetic steps. The average of ⃗ H WB can account for the sum of the time integral of positive and negative angular momenta of all segments [20]. Therefore, we quantified the contributions of each segment to the total ⃗ H WB . This method enables the evaluation of contributions of magnitude and duration of ⃗ H WB throughout the whole time-series of each step. As the successful regulation of ⃗ H WB through careful intersegmental coordination is essential to recover from perturbations and prevent falls [31], our findings may inform clinically relevant interventions aimed at enhancing dynamic stability to improve gait safety in TFPUs.

A. Participants
Fourteen unilateral TFPUs (4 females and 10 males) participated in this study (Table I). The TFPU cohort had a mean (standard deviation, SD) age of 32.6 (10.2) years, mean (SD) body height of 1.65 (0.10) m, and mean (SD) body mass of 60.0 (10.6) kg. Inclusion criteria required that participants be at least moderately active, unilateral transfemoral prosthesis users, while exclusion criteria included the presence of neuromuscular disorders, lower-limb functional limitations, or health concerns that might affect standing or walking. These criteria were confirmed with the primary care physician, physical therapist, or prosthetist of each participant during screening. Moreover, we utilized the Advanced Industrial Science and Technology (AIST) gait database to prepare 14 age-, gender-and walking-speed-matched individuals without amputation as controls [32]. The control cohort had a mean (SD) age of 32.5 (9.5) years, mean (SD) body height of 1.69 (0.09) m, and mean (SD) body mass of 66.9 (12.5) kg (Supplementary Table I). The study was approved by the AIST Institutional Review Board, and written informed consent was obtained from all subjects and the guardian of one subject prior to the experiment.

B. Experimental Procedure and Data Collection
The participants were requested to perform level overground walking at a comfortable, self-selected speed on a straight, 10-m-long walkway (Fig. 1). In total, 55 retro-reflective markers were attached to body landmarks in accordance with the Helen-Hayes marker set [33]. The participants were allowed sufficient practice walking along the walkway with markers attached to help maintain their natural gait during data collection trials. After the practice session, five successful trials wherein each participant properly stepped on a force plate with the intact and prosthetic foot were recorded. The instantaneous GRFs were recorded using nine walkway-embedded force plates (BP400600-1000PT and BP400600-2000PT, AMTI) at 2000 Hz. Instantaneous 3D coordinate data were obtained using the retro-reflective markers and recorded using a 3D optical motion capture system (VICON MX system, VICON Motion System, Oxford, UK) with 15 cameras at 200 Hz ( Fig. 1). For the control participants, 3D positional data and GRFs were collected at 200 Hz and 1000 Hz, respectively [34].

C. Data Analysis
The data were recorded and synchronized using Vicon Nexus software and post-processed using Visual 3D version 6.03.6 (CMotion, Germantown, MD, USA). The data were filtered using a fourth-order Butterworth low-pass filter with zero lag and a cut-off frequency of 10 Hz for the marker trajectories and 100 Hz for the GRF data [24]. For the control participants, the marker trajectory and GRF data were filtered using a fourth-order Butterworth low-pass filter with cut-off frequencies of 10 Hz and 50 Hz, respectively [32]. Because the kinetic data of the controls in the AIST database were collected at a sample frequency of 1000 Hz, their cut-off frequency was set to 50 Hz based on a previous study [24]. The timing of foot initial contact was defined as a rise of the vertical GRF above 16 N [15].
For biomechanical modelling, the segment masses were defined based on Dempster's regression equation relative to the actual total body mass calculated using the force plates in static pose [34]. For the prosthetic limb, we modeled the geometry of thigh, shank, and foot segments as a cone using medial and lateral landmarks to determine the proximal and distal segment radii. We then estimated the masses of these segments based on the participant-specific prosthetic components and residual limb length reported in Table I. After utilizing these prosthetic segment masses, we re-calculated the total body mass including the prosthetic components and distributed the incremental difference between the re-calculated body mass and actual body mass to the residual segments of the whole body. We iterated this optimization until the difference between the two masses was within 1% of the actual body mass (Supplementary Tables 2 and 3). Further, we estimated the COM position and inertial properties of each body segment, including the prosthesis, based on geometric approximations [35].
The Instantaneous ⃗ H WB was calculated using a 15-segment biomechanical model (head, trunk, pelvis, upper arms, forearms, hands, thighs, shanks, and feet) in Visual 3D. Righthanded orthogonal coordinate systems were defined for the segments of the prosthetic and intact limbs using the 3D coordinates of the retro-reflective markers (Fig. 1). ⃗ H WB was calculated from the tracked body segment kinematics as follows: H WB and the angular momentum of each segment as percentages of the prosthetic and intact limb steps for TFPUs and the right and left limb steps for the controls. The intact (left) step was defined as the time from the initial contact of the prosthetic (right) limb to that of the intact (left) limb, and vice versa for the prosthetic (right) step. The average value across five successful trials was used as the representative value for each participant. For analysis, the prosthetic (PST) and intact (INT) limbs of TFPUs correspond to the right and left limbs of control participants, respectively. In addition, we determined the segment contributions across all steps in each plane for each five segment groups: H T P T F PU s/Contr ols (head, trunk, pelvis), Ar m P ST /Right (upper arm, forearm, hand), Ar m I N T /Le f t , Leg P ST /Right (thigh, shank, foot), and Leg I N T /Le f t . The positive and negative contributions to ⃗ H WB were determined using the positive and negative areas under the curve of segment angular momenta during intact and prosthetic steps, respectively [20], which accounts for contributions from momenta magnitude and its duration during a step.

D. Statistics
First, we compared the range (peak-to-peak) of ⃗ H WB between the TFPUs and controls. We performed this comparison during the intact (left) and prosthetic (right) steps in the sagittal plane and during the prosthetic (right) limb gait cycle in the transverse and frontal planes, referring to the previous study [27], [28]. Second, the average ⃗ H WB during the intact (left) and prosthetic (right) steps were compared between the TFPUs and controls. The Shapiro-Wilk test was used to assess if the data distributions were significantly different than normal and results suggested that these data did not violate the assumption of normality. Hence, independent t-tests were employed to assess the main effect of group (TFPUs versus controls) for each limb step separately.
Further, we compared the positive and negative contributions of the five previously defined segment groups to ⃗ H WB during the intact and prosthetic steps. As these data violated the assumption of normality according to the Shapiro-Wilk test, the Friedman test was used to assess the main effect of the segment for each group independently, and the Wilcoxon test was conducted for limb comparison between the TFPUs and controls. If the main effect of segments was significant via the Friedman test, the Wilcoxon signed-rank test with Bonferroni correction was used as a post-hoc test. All analyses were conducted for each anatomical plane separately. Statistical significance was set according to a critical value of α = 0.05 in all statistical tests (SPSS v26.0, IBM, Armonk, NY, USA).

A. Whole-Body Angular Momentum
The averaged ⃗ H WB trajectories over 14 participants in three planes for the TFPUs and controls are displayed in Fig. 2A.  Fig. 3 shows the average waveforms of the segment angular momenta in the sagittal plane for the TFPUs and controls. The positive and negative contributions (i.e., the areas under the curves referring to different directions of rotation with respect to the anatomical references in Fig. 1) during the intact/left and prosthetic/right steps are illustrated in Fig. 4A-4L, respectively. The post-hoc comparisons of segment groups are The participants walked at a comfortable, self-selected speed on force plates embedded 10-m-long walkway. In total, 55 retro-reflective markers were attached to body landmarks in accordance with the Helen-Hayes marker set. Instantaneous 3D coordinate data were obtained using the retro-reflective markers and recorded using a 3D optical motion capture system. The sagittal, transverse, and frontal plane angular momentums are defined about the z, y, and x axes, respectively.  ( p < 0.001), and Ar m Le f t ( p < 0.001). The Wilcoxon rank sum test demonstrated that Leg I N T in the TFPUs was significantly smaller than Leg Le f t (Z = -3.860, p < 0.001).

C. Transverse Plane Segment Contributions
The average waveforms of the segment angular momenta in the transverse plane for the TFPUs and controls are displayed in the Fig. 3 For the negative contributions (against the prosthetic leg swing) during the prosthetic step ( Fig. 4H; transverse and negative) in the TFPUs, both Ar m P ST and Ar m I N T had significantly greater contributions than Leg P ST ( p < 0.001 and p < 0.001) and Leg I N T ( p < 0.001 and p < 0.001). In the controls, both Ar m Right and Ar m Le f t had significantly greater contributions than Leg Right ( p < 0.001 and p < 0.001) and Leg Le f t ( p = 0.041 and p = 0.001). The Wilcoxon rank sum test between the TFPUs and controls revealed that H T P T F PU s was significantly greater than H T P Contr ols (Z = -4.503, p < 0.001).

D. Frontal Plane Segment Contributions
The average waveforms of the segment angular momenta in the transverse plane are shown in the Fig. 3. The post-hoc comparisons of segment groups are summarized in Supplementary Tables 4 and 5. The main effect of the segment was significant for the TFPUs and controls under all conditions (χ 2 (4) > 21.029, p < 0.001). For the positive contributions (counterclockwise viewed from the front) during the intact step ( Fig. 4I; frontal and positive) in the TFPUs, the contribution of Leg P ST in the TFPUs was significantly smaller than that of Leg Right in the controls (Z = -3.538, p < 0.001). On the other hand, the contribution of Ar m P ST was significantly greater than Ar m Right (Z = -3.446, p = 0.001). For the negative contributions (clockwise viewed from the front) during the intact step ( Fig. 4J; frontal and negative) in the TFPUs, the contribution of Leg P ST in the TFPUs was significantly smaller than that of Leg Right in the controls (Z = -4.227, p < 0.001). However, the contribution of Ar m P ST was significantly greater than Ar m Right (Z = -3.078, p = 0.002).
The positive contributions (counterclockwise viewed from the front) during the prosthetic step was shown in Fig. 4K (frontal and positive) in the TFPUs. The contribution of Leg P ST in the TFPUs was significantly smaller than that of Leg Right in the controls (Z = -4.181, p < 0.001), whereas the contribution of Ar m I N T was significantly greater than that of Ar m Le f t (Z = -2.114, p = 0.035). For the negative contributions (clockwise viewed from the front) during the prosthetic step ( Fig. 4L; frontal and negative) in the TFPUs, the Wilcoxon rank sum test revealed that the contributions of Ar m I N T in the TFPUs were significantly greater than those of Ar m Le f t in the controls (Z = -3.446, p = 0.001). In contrast, Leg P ST in the TFPUs had a significantly smaller contribution than Leg Right in the controls (Z = -3.860, p < 0.001).

IV. DISCUSSION
We aimed to investigate the dynamic balance of unilateral TFPUs during walking at a self-selected constant speed. Regarding the range of ⃗ H WB in the sagittal plane, the TFPUs had a greater and smaller range compared to the controls during the intact and prosthetic steps, respectively. In the transverse plane, there was no significant difference in the range of ⃗ H WB between TFPUs and controls. These results supported our hypothesis that unilateral TFPUs would have different ranges of ⃗ H WB in the sagittal plane, but not in the transverse plane, compared to the individuals without amputation.
We did not observe a difference between the TFPUs and controls in the frontal plane, whereas transtibial prosthesis users have exhibited greater frontal ⃗ H WB compared to controls [27], [36]. Similarly, it has been reported that other groups with known balance impairments tend to exhibit a greater range of frontal plane ⃗ H WB than able-bodied controls [37]. The higher walking speed (0.14 m/s faster than [36]), lower body masses (29.3 kg lighter than [27]), younger age (13.7 years younger than [27]) and high functional levels in the participants of this study may have contributed to these discrepancies between the previous findings and our findings.
As for the average of ⃗ H WB in the sagittal plane, the TFPUs generated greater average positive (rotating backward) and negative (rotating forward) ⃗ H WB values than the controls during the intact and prosthetic steps, respectively. In the transverse plane, the TFPUs generated average ⃗ H WB values similar to those of controls during intact steps but smaller average positive ⃗ H WB values than controls during the prosthetic steps. These finding partially supported our hypothesis that unilateral TFPUs would have different step-to-step average ⃗ H WB values than the non-impaired controls. In the frontal plane, the average ⃗ H WB value of the TFPUs was similar to that of controls during both steps, which did not support the hypothesis.
At the initial contact of the prosthetic and intact limbs, the prosthetic limb is anterior and posterior to the body COM, respectively. Thus, the reduced prosthetic braking GRF could increase the positive time rate of change of the sagittal ⃗ H WB during the intact step, while the reduced prosthetic propulsive GRF could reduce that during the prosthetic step [17]. Indeed, reduced braking GRF in the prosthetic limb has also been reported in the walking of unilateral transtibial prosthesis users as the most likely means of increasing the sagittal ⃗ H WB [27]. Similarly, in the transverse plane, the decreased prosthetic propulsive GRF could reduce the positive time rate of change of the transverse ⃗ H WB during the prosthetic step.

A. Sagittal Plane Angular Momentum
In the sagittal plane, the angular momentum between intact (left) and prosthetic (right) steps did not sum to zero. This means that TFPUs and controls possess a negative amount of ⃗ H WB throughout gait cycle while achieving steady-state walking. Hinrichs explained that this phenomenon occurs because the change in the inertial property of the body during stride is induced by the overall clockwise rotation of the legs (as shown in Fig. 4A-4D herein) [38]. This angular momentum INT and PST indicate the intact and prosthetic legs, respectively. The asterisks ( * , * * ) indicate significant differences between the TFPUs and controls (p < 0.05 and p < 0.01, respectively). The daggers ( †), pound signs (#), dollar signs ($), and pilcrows ( ¶) indicate significant differences between Head + Trunk + Pelvis, Arm (prosthetic/right side), Arm (intact/left side), and Leg (prosthetic right side) at p < 0.05, respectively. contributed by the legs prevents the rest of the body from rotating forward even though the whole-body possesses a negative amount of ⃗ H WB . In the sagittal plane, the TFPUs had an average positive ⃗ H WB value (rotating backward) during intact steps and negative ⃗ H WB value (rotating forward) during prosthetic steps. Meanwhile, the average ⃗ H WB values of the controls were effectively zero during both steps (-0.004±0.001 during the left step and -0.005±0.002 during the right step; Fig. 2C). These results indicate that unilateral TFPUs have larger stepto-step postural changes in forward and backward rotation about the body COM when compared to controls.
In accordance with previous studies, the leg segment contributions were dominant among all segment groups in the sagittal plane [11], [21], [22] (Fig. 4A-4D). For both steps, Leg P ST in the TFPUs had smaller contributions than the Leg Right in the controls (Fig. 4B and 4C), and these contributed to increased differences in ⃗ H WB between the TFPUs and controls (Fig. 2C). A partial explanation may be the lighter mass properties of the prosthetic leg segments compared to those of the intact control legs. As the mass of the shank segment was less than half of that in the non-impaired leg in our model on average (1.26±0.39 vs. 2.94±0.48 kg), the effect of the mass properties could be sufficient to generate such differences between Leg P ST and Leg Right . Together, Leg I N T in the TFPUs had smaller contributions than Leg Le f t in the controls for both steps (Fig. 4A and 4D), but this limb difference actually helped reduce the overall difference in ⃗ H WB between the two groups (Fig. 2C). As momentum is the product of mass and velocity, the segment angular momentum can be modulated by changing the velocity of each segment movement [38], [39]. Given that the intact legs of the TFPUs had similar masses to those of the non-impaired legs in the controls, the contribution of Leg I N T was decreased by a reduction in the velocity of the intact leg movement compared to the controls in the sagittal plane. In particular, during an intact step in the sagittal plane, TFPUs must also work to prevent prosthetic knee buckling, which requires additional postural control demands [40], [41]. Consequently, a cautious gait to enhance postural control may lead to less dynamic movement of the intact leg to control the whole-body postural balance and mitigate the risk of prosthetic knee buckling.

B. Transverse Plane Angular Momentum
The average values of ⃗ H WB in the transverse plane were negative (toward the intact leg swing) and similar between the TFPUs and controls during the intact steps. However, the TFPUs had smaller positive ⃗ H WB values (toward the prosthetic leg swing) than the controls during the prosthetic steps and close to zero (TFPUs: 0.001±0.002; controls: 0.004±0.001; Fig. 2C). A previous study demonstrated that the average transverse-plane ⃗ H WB magnitude (towards inside leg swing) in non-impaired controls during 90 • turns was smaller than that in straight-line walking [20]. This motor behavior enables individuals to redirect their walking progression during a more challenging 90 • turn with each step. In our study, TFPUs demonstrated behavior during straight-walking that is similar to that during turning in non-impaired controls. Accordingly, maintaining the direction of progression during straight-line walking may be more challenging in unilateral TFPUs than in the controls.
Similar to the sagittal plane, Leg P ST in the TFPUs had smaller contributions than Leg Right in the controls during the prosthetic steps (Fig. 4G). Additionally, an exaggerated negative H T P T F PU s contribution was observed, which could be due to the greater trunk but similar pelvic range of motion compared to that of the controls [42]. These characteristics contributed to an increased difference in the average ⃗ H WB between the two groups (Fig. 2C). Although the arms of the TFPUs showed no differences compared to those of the controls, natural arm swinging during human gait is known to counterbalance leg swing-generated momentum and reduce the transverse plane ⃗ H WB value to facilitate gait stability [43], [44], [45]. In addition, the coordination between trunk and pelvis rotation in the transverse plane is largely influenced by arm swing [46]. Hence, arm swinging in unilateral TFPUs appears critical for maintaining a dynamic balance of TFPUs in the transverse plane, and these contributions warrant further study to inform gait training interventions.

C. Frontal Plane Angular Momentum
In the frontal plane, the TFPUs demonstrated average ⃗ H WB values similar to those of the controls during both steps, where both groups had average ⃗ H WB values effectively equal to zero (TFPUs: 0.001±0.001; controls: 0.000±0.001 during intact steps and TFPUs: -0.001±0.001; controls: 0.000±0.001 during prosthetic steps; Fig. 2C). Thus, the TFPUs and controls could have similar step-to-step postural changes in the frontal plane. As human walking is unstable in the medio-lateral direction [46], [47], [48], [49], unsuccessful regulation of frontal-plane angular momentum would lead to greater postural control demand and higher risk of falling [36], [50]. TFPUs suffer from disrupted sensory input, and thus a reasonable adaptation to compensate for a lack of balance confidence is to shorten the prosthetic stance time [6] and generate unique compensatory medio-lateral GRF patterns [15]. Therefore, these compensations could reflect a proactive means of decreasing the risk of falling and achieve dynamic balance similar to that of the controls in the frontal plane.
Although the frontal whole-body dynamic balance in the TFPUs was similar to that in the controls, these results suggest different strategies in segment-to-segment cancellation between the two groups. Similar to the sagittal and transverse planes, the positive and negative Leg P ST contributions in the TFPUs were smaller than the Leg Right values of the controls under all conditions (Fig. 4I-4L). Although these discrepancies generated the observed differences in average sagittal and transverse plane ⃗ H WB between the two groups, the arms of the stance leg side contributed to decreasing those differences during both steps in the frontal plane ( Fig. 4I-4L). The arm contribution to regulation of frontal-plane ⃗ H WB is generally underappreciated because the arms have lesser contributions than other segments [11], [21], [22]. However, our results suggest that the exaggerated arm swinging on the stance leg side may help restore the medio-lateral ⃗ H WB balance in unilateral TFPUs.

D. Clinical Significance
Of note, an imbalance in the whole-body angular momentum of the TFPUs in the sagittal and transverse planes was induced partially due to the smaller mass of the prosthetic leg compared to the intact leg. These findings may suggest that strategically adding weight to the prosthetic leg in TFPUs could reduce the step-to-step change in the average ⃗ H WB value and improve the whole-body dynamic balance. A previous article reported that some TFPUs prefer weight addition because they felt more comfortable or experienced better balance [51]. Further, the preferred position and mass of the added weight amongst TFPUs was individual-specific [52]. However, adding weight may encourage changes in the swinging velocity of the prosthetic limb that could counter the potential benefits to momentum, while gait training to direct limb control could also be effective. Consequently, the relationships between weight addition, gait training, and dynamic balance should be explored further for appropriate selection and prescription of prosthetic components in unilateral TFPUs. Czerniecki et al. reported that the addition of up to 1.34 kg to the center of a prosthetic shank did not significantly increase the rate of oxygen consumption in TFPUs [53]. However, the trade-offs between metabolic costs and altering the prosthetic mass and mass distribution should be further studied and considered clinically.

E. Limitations
The results of our study are only applicable to relatively young and active TFPUs, given the sample demographics. The participants included in this study were on average 32.6 ± 9.8 years old (13.7 years younger than [27]) and were all able to run with running-specific prostheses; thus, they were categorized as functional level K4 with the ability or potential for prosthetic ambulation that exceeds basic ambulation skills [54]. Depending on the functional level, TFPUs are known to have different physical performances [55]. Moreover, we did not consider the fall history in this study, which is also associated with mobility in lower-limb prosthesis users [56]. Therefore, future studies should explore how functional level and fall history influence the average ⃗ H WB as well as the segment-to-segment momentum cancellation strategies of older and less functional TFPUs. In addition, walking speed was a major limitation of our study. A previous epidemiological study on the circumstances of falls in TFPUs showed that a significant number of falls occur not only during walking but also during transfers, turning, and missing a step, all of which are activities that require considerably lower walking speeds [4]. In able-bodied individuals, dynamic balance and ⃗ H WB control during perturbed slow walking have been shown to be considerably more demanding and to require "in-stance", rather than "stepping" balance strategies [57]. Similar findings have been reported for transtibial prosthesis users walking slowly and facing perturbations [58]. Thus, future studies should also focus on the effect of lower walking speed on ⃗ H WB control in TFPUs. Another potential limitation is the insufficient consideration of intra-subject variability in instantaneous ⃗ H WB . In our Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. experiment, participants walked naturally across a walkway