*4.2. Results and Discussion*

For reasons of clarity, Figure 5 shows the mean of all 54 gait cycles of the measurement data. The first two subplots summarize the external loads measured by the adapter, while the other subplots show data captured by the sensor array. Due to the different measurement sites, all sensors captured the relative motion in pd-direction, while anteroposterior (ap) and mediolateral (ml) movement was only detected by sensor units affixed in the Sagittal and Coronal plane, respectively. The bottom subplot shows the SQUAL-values of each sensor unit.

The movement results show almost no motion during stance phase. This changes with the decrease of *F*pd at around 55% of the gait cycle: With less weight bearing on the prosthesis, the relative motion between residual limb and prosthetic socket increased. Most of the relative motion was detected during swing phase. Movements in ml-direction were of smaller magnitude compared to motion in the Sagittal plane.

Except for three sensor units in the first 5–10% of the gait cycle, SQUAL-values were relatively constant during stance phase. More changes could be observed during swing phase: Three sensor units (lat dist, ant prox, and ant dist) showed a SQUAL-value of 0 for the majority of swing phase. The SQUAL-values of two sensor units (post dist and lat mid) showed a brief break-in during the first and second half of swing phase, respectively.

**Figure 5.** Mean of measurement data of 54 gait cycles; from top to bottom: forces, torques, movement in proximodistal, anteroposterior, mediolateral direction, and SQUAL-values sensor units. The colors used for the sensor units correspond to Figure 4.

As stated in Section 2, the SQUAL-value is equal to 1/4 of the features the sensor uses to calculate its movement over the reference surface. Consequently, a SQUAL-value of zero means that the sensor cannot detect any features for movement calculation. This most likely stems from an out of bounds distance between sensor and reference surface (liner), which corresponds to movement of the residual limb normal to the sensor lens. During these time instants, the sensor does not continue to measure movement in its main axes. Thus, the shown movement data of the affected sensor units were underestimated for lower SQUAL-values (break-in during swing phase) and inconsequential at time instants with SQUAL-values of zero.

The small movement during stance phase might indicate the tight socket fit. With load bearing in the longitudinal direction, the residual limb is pressed radially against the socket wall. The resulting normal force between residual limb surface and socket wall leads to a high friction force, which prevents most of the relative movement during stance phase. This relatively constant position of the limb within the socket during stance phase has been observed previously [9]. Nevertheless, observed relative movements during stance phase show a uniform behavior in pd-direction while movement observations in ap- and ml-direction depend on the measuring site. Overall, the recorded movement of the residual limb inside the socket during stance phase might be described as sinking deeper into the socket, extending in the Sagittal plane and rotating internally in the Transverse plane.

The detected relative motion at the different socket locations during swing phase is mostly non-uniform: While negative motion in pd-direction is noted at measuring site post prox, the movement detected at ant prox is in the opposite direction. This might indicate a rotation of the socket relative to the residual limb in the Sagittal plane, which would correspond to the shank extending inside the socket. Compared to these two measuring sites, there is little movement detected in pd-direction at the other sites. In ap-direction, most relative motion is detected at lat prox in the first half of swing phase. Corresponding to the residual limb moving in posterior direction, this

matches the shank extending inside the socket. The data are in accordance with [4], which reports residual limb extension inside the socket in the first half of swing phase. In addition to having a smaller magnitude compared to the other directions, the observed movement in ml-direction at the two posterior measurement sites is qualitatively the same, with a maximum at about 90% of the gait cycle. Jointly with the movement indication in the opposite direction at ant prox (60–70% of GC), this might correspond to the shank performing an external rotation in the Transverse plane within the socket during swing phase.

Figure 6 summarizes peak-to-peak (P2P) values measured during the loading (0–55% GC) and unloading (55–100% GC) phase of each gait cycle at the different sites as box plots. The first four rows show the movement of the residual limb inside the socket in the Coronal plane, while the last three rows depict movement in the Sagittal plane. Contrary to data shown in Figure 5, only measurement data of each time instant captured at a corresponding SQUAL-value between 50 and 150 were included in the analysis. The third column shows the subsequent number of included gait cycles at each instant of time. Additionally, mean ± standard deviation of SQUAL-values of included data are shown in the rightmost column. Vertical lines indicate to which box plot (load vs. unload) the data belong.

The magnitude of relative motion between residual limb and prosthetic socket is quite small; no peak-to-peak values above 3.1 mm are recorded. Except for relative motion at lat dist, more relative motion is recorded during the unloading phase (last 45% of GC) compared to the loading phase (first 55% of GC). A tendency of peak-to-peak values being of greater magnitude during unloading phase compared to loading phase as well as for proximal measurement sites compared to those located more distally was observed.

Taking into account the distal fixation of the liner within the socket (pin lock system) and assuming a constant strain = <sup>Δ</sup>*<sup>l</sup> <sup>l</sup>*<sup>0</sup> along the pd axis of the liner led to higher peak-to-peak relative motion at proximal compared to distal measuring sites (*l*0,prox > *l*0,dist).

At the two anterior measurement sites as well as at lat dist, the collected movement data are of improvable quality during swing phase; the number of included gait cycles at the three sites was reduced from over 50 at 60% GC to less than 15 at 65% of GC. Time instants of the gait cycle without mean SQUAL-values indicate where the affected sensor units did not detect the necessary features for movement data calculation. At post dist and lat mid, a dip was observed in the number of included gait cycles at 65% and 95% of GC, respectively.

Peak-to-Peak movement data recorded during swing phase by the sensor units on the anterior side of the socket and at lat dist need to be interpreted with caution. The shown values only consider data of parts of the loading and unloading phase (compare SQUAL in rightmost column), which might not include maximal movements. Excluded data at 95% of GC would most likely not affect P2P calculation.

As stated previously, variations in SQUAL-value might stem from too much movement normal to the measurement plane of the corresponding sensor unit. Quantification of the dependency of SQUAL-values on measurement distance between sensor unit and reference surface as well as influence on displacement data might lead to the extension of usable sensor data information.

Compared to most studies quantifying residual limb socket peak-to-peak displacements of transtibial amputees using a socket with pin-lock suspension during walking [3,4,9,12], the detected movement within the pilot study was relatively small. A study investigating the variation of sock thickness on peak-to-peak relative motion shows a distinct decrease as sock thickness increased and vice versa [12]. These findings support the hypothesis of a tight socket fit being responsible for the small magnitudes of detected movement (particularly during stance). Another study presents P2P displacements normal to the socket wall ranging between 0.7 and 9.4 mm and varying for participants as well as measuring sites [10]. The data (see [10] ([Figure 7])) show a tendency of movements of greater magnitude at distal measuring sites compared to measuring sites placed most proximally. Additionally, a comparison of P2P displacements at the proximal measuring sites show consistently greater magnitudes on the anterior side. This supports the hypothesis of residual limb movement

normal to the socket wall being responsible for SQUAL-values of 0 at the measuring sites ant prox and ant dist (as well as lat dist).

**Figure 6.** Analysis of peak-to-peak values at the different measuring sites. The data of sites are arranged according to location on anatomical planes: Coronal plane (first four rows) and Sagittal plane (following three rows). The first two columns summarize peak-to-peak values of relative motion in 54 gait cycles in the two anatomical directions corresponding sensor location (pd and ml for Coronal plane, and pd and ap for Sagittal plane). The two columns on the right indicate the data basis underlying peak-to-peak calculations.
