Analyses of Temporal Waveforms and Five Scalar Values, Normalised

The PCA outcome of both, temporal waveform data and scalar values, normalised to units showed that there is a difference between UTTA (solid and open red diamonds) and able-bodied (solid and open black circles) gait in PC2 (outcome number 1 and 3, Figure 5.8 a). In outcome number 1 the groups separated horizontally, i.e. they separated to the top and bottom of the graph and in outcome number 3, they separated vertically, i.e. to the right and left of the graph. Similar results were observed in the PCA analysis of temporal waveform data alone (Section 5.4.1), suggesting that scalar values did not add any additional information to the discrimination procedure. The Eigenspectrum of PC2 for the temporal waveforms (Figure 5.8 b) highlighted variables number 3, 17, 13 and 20, which corresponded to vertical GRF, sagittal knee joint angle, sagittal hip joint moment, and sagittal ankle joint angle. The Eigenspectrum of PC for the scalar values (Figure 5.8 c) highlighted variables number 3 and 5, which corresponded ankle net-work and ML MoS (For the outcome of PCA on temporal waveform data and scalar values, which were not normalised and with 7 scalar values see Appendix 2).

Figure 5.8 PCA outcome (a) and Eigenspectrum (b, c) comparing between individuals with UTTA and able-bodied individuals using temporal waveforms (b) and five scalar values (c), normalised to units.

Chapter 5: Results

123 The DFA outcome showed a classification between the gait of individuals with UTTA (solid and open red diamonds) and able-bodied individuals (solid and open black circles) and between the PROS and NONPROS limbs (Figure 5.8), similar to the classification of temporal waveform data alone (Section 5.4.1, Figure 5.5 c). The DF spectrum for this analysis corresponded with previous findings of individual analyses of temporal waveform data and scalar values, separately. The DF spectrum of temporal waveforms highlights variables number 17, 4 and 3, which correspond to sagittal knee joint angle, vertical GRF and medio-lateral GRF. The DF spectrum of the scalar values highlights variables 1, 3 and 5, which correspond to step length, ankle joint net-work and ML MoS. (For the outcome of DFA on temporal waveform data and scalar values, which were not normalised and with 7 scalar values see Appendix 2).

Figure 5.9 DFA classification outcome (a) and DF spectrum comparing between individuals with

Chapter 5: Discussion and Conclusion

124

5.5 Discussion and Conclusion

The aim of this study was to establish differences between UTTA and able-bodied gait using PCA and DFA providing a better understanding of LLA function. Differences in gait between the two groups were found and attributed to vertical GRF, sagittal hip joint moment and sagittal knee joint angle. The biomechanical variables measured in this study consisted of temporal-spatial, kinetic and kinematic variables, which were commonly reported in the literature during the investigation of forward progression and dynamic stability. These variables were chosen in particular because the continuous interchange between mobility and stability is required for walking without the risk of falling (Lakany, 2008) which is a common concern for individuals with LLA (Jayakaran et al., 2012). Different analysis methods were explored to establish a technique, which would allow important variables that differ between UTTA and able-bodied gait to be identified. The results demonstrated that for this particular application of multivariate statistical analyses methods, PCA on normalised temporal waveforms was the most suitable technique. However, there is not a single method that is applicable to all data and applications, instead, the best performing algorithm depends on the features of a data set (Harper, 2005).

In current methods, biomechanical variables were normalised to units, which was important as reflected by the Eigenspectra and DF spectra. This is because, using the covariance approach during PCA, the variables’ weightings depend on their magnitude. In biomechanics, a variable’s magnitude may be small or large depending on the joint or muscle groups driving it. Thus, investigating the difference between joints may incur bias if the difference between the two groups is based on the absolute magnitude. Hence, during the assessment of biomechanical variables using automatic gait recognition tools, normalisation of data should be incorporated. In this study, different multivariate statistical analyses of PCA and PCA followed by DFA, have been explored. Both methods identified differences between UTTA and able-bodied gait, however, since DFA is a supervised algorithm it seeks out differences. During the treatment of pathological gait, the aim is not to seek out differences but rather find naturally occurring differences that could be treated. Therefore, using PCA alone is sufficient since it highlights differences that occur in the gross structure of the data which can also be identified in the graphical profile of temporal waveforms as highlighted in the current results. Differences in the detailed structure may imply that an issue is present, however, these differences may not be easily identified in graphical profile and thus may be more difficult to treat.

Although differences may be identified in the graphical profile of the temporal waveform and traditional statistical approaches can be used to establish if a variable differs significantly between

Chapter 5: Discussion and Conclusion

125 a group/condition, it is still advantageous to use PCA for a number of reasons: (1) Interpretation of the graphical profile of temporal waveform and the selection of discrete parameters to perform the statistical analysis are subject to researcher bias, whilst PCA is an objective measure. (2) Since PCA can be used to analyse the entire temporal waveform, characteristics of biomechanical data such as time-dependance, are considered which would otherwise be ignored if discrete parameters were used to perform traditional statistical tests. (3) Although differences could be identified in the graphical profile, PCA can be used to quantify these differences (as will be demonstrated in Chapter 6) and different parts of the profile could be ranked in terms of variance using PC scores, as demonstrated by Soares et al. (2016). (4) PCA enables many variables to be compared simultaneously, and it does not only reveal if variables differ between groups/conditions as traditional statistical approaches do, but it also ranks the variables in terms of variance as shown in the Eigenspectrum of the current results. Thus in clinical applications it can provide an indication of which variables need to be targeted.

The results of the PCA outcome revealed that the differences between the gait of individuals with UTTA and able-bodied individuals were in PC2, indicating that PC1 does not necessarily always hold the information of interest. Thus, although PC1 holds the majority of the variance of the original data set, it cannot be expected that it contains the variables responsible for the discrimination between experimental groups which is a common, yet false assumption. This highlights the importance of the remaining PCs, as previously discussed by Phinyomark et al. (2016). Having said that, variables in the first few PCs have larger weighting factors and discriminating variables in lower ranked PCs have smaller weighting factors. Thus, similar to the DFA outcome, discriminating variables in lower ranked PCs may be more difficult to identify in 2D plots of temporal waveforms.

The Eigenspectrum of the PCA with the biomechanical variables of normalised temporal waveform data highlighted that in PC2 vertical GRF, sagittal knee joint angle and sagittal hip joint moment were the main variables to cause a difference between the gait of individuals with UTTA and able-bodied individuals. Soares et al. (2016) previously identified that the vertical GRF discriminated in PC1 between the control limb and the prosthetic limb, while PC2 discriminated between the control limbs and both the intact and prosthetic limbs. The magnitude of the vertical GRF was found to be much smaller on the prosthetic limb, which may have been a protective mechanism to reduce loading on the residual limb. However, it should be noted that the participants in the study by Soares et al. (2016) were individuals with UTFA, whilst in this study, individuals with UTTA were investigated. The discrimination may have occurred at

Chapter 5: Discussion and Conclusion

126 different PC since the level of amputation differed, i.e. fewer joints remain and thus larger compensation was required.

The results showed that temporal waveforms provided more information since they span the entire gait cycle compared to scalar values (Chau, 2001a). Previous studies suggest that continuous data provide a better discriminatory approach relative to discrete parameters (Deluzio et al., 1997). Schöllhorn et al. (2002) found that one in every three discrete parameters (scalar values) is likely to be misclassified. In this study, adding more scalar values to the analysis procedure did not improve the outcome. It should be noted, however, that although additional variables did not improve the classification outcome, one of the additional variables (speed) indicated discriminatory properties between the gait of individuals with UTTA and able-bodied individuals. Thus, the variables chosen during a discrimination procedure are of great importance. During the analysis of scalar values alone using PCA, the prosthetic limb differed from the intact limb of the individuals with UTTA and also the control limbs of the able-bodied individuals, but during the analysis of temporal waveforms alone both prosthetic and intact limbs differed from the control limbs. Using DFA did not only classify individuals with UTTA from the able-bodied individuals but also clustered prosthetic and intact limb separately. Previous studies investigating LLA gait using traditional statistics, reported similar findings, thus depending on the aims of a study, researchers may prefer to use DFA in addition to PCA since it provides a greater discrimination outcome.

The data in this study consisted of twenty temporal waveforms and seven scalar values of kinetic, kinematic and GRF variables, and demonstrates the ability of automatic gait recognition tools with large data sets. Previous research that compared between the gait of individuals with LLA and able-bodied individuals using automatic gait recognition tools limited the investigations to either kinematic, kinetic, GRF or EMG data (Miller et al., 2013), but recent studies demonstrated that the classification of only kinetic or kinematic variables alone might compromise the outcome (Schöllhorn et al., 2002). Assessing many variables simultaneously is not only time efficient but provides an instantaneous in-depth understanding, which can have great implications in clinical applications.

Biomechanical variables chosen for this analyses were often reported in the literature for the assessment of forward progression and dynamic stability, however, these variables were reported in the sagittal plane only. Previous studies that used automatic gait recognition report that variables from different planes have the potential to improve the classification results, thus providing a more comprehensive understanding of pathological gait (Schöllhorn et al., 2002). For example, studies report that the regulation of whole-body angular momentum is important to

Chapter 5: Discussion and Conclusion

127 prevent falls, particularly in the frontal plane (Miller et al., 2018). Furthermore, anterior-posterior CoM from the sagittal trajectory may provide more information regarding forward progression, however, in the current study, similar to previous research, only vertical CoM displacement and velocity were assessed, which were commonly reported for the assessment of dynamic stability. Thus, variables from different planes of motion are worthy of inclusion in future analyses. In this study, PCA was applied for data reduction and feature selection and DFA was applied for classification and were found to effectively compare between UTTA and able-bodied gait. Other studies have compared classification performance of different machine learning algorithms such as SMV, ANN and NB in order to assess powered prosthetic devices (Afzal et al., 2017; Chen et

al., 2013; Joshi & Hahn, 2016; Khan et al., 2018; Miller et al., 2013; Pew & Klute, 2017).

Findings indicated that some methods provide better discrimination and classification than others. Therefore, future research should explore the use of different machine learning algorithms to investigate if these provide more information and thus a better understanding of LLA function. In conclusion, investigating different techniques to compare UTTA and able-bodied gait in order to provide a better understanding of LLA function, has demonstrated that using PCA to assess normalised temporal waveforms of kinetic, kinematic and GRF data was an effective technique to evaluate LLA gait. It was established that both prosthetic and intact limbs differed from control limbs due to vertical GRF, sagittal knee joint angle and sagittal hip joint moment. This study demonstrates the ability of automatic gait recognition as a powerful diagnostic tool in a clinical setting.

Chapter 6: Identifying Subject-Specific Gait Characteristics of Individuals with Unilateral