Identificación de segmentos

The principal components selected for the ML force and their corresponding regions of variance are represented in Figure 3.39. Much of the medial/lateral force is included in the first PC; including the lateral peak around the time of the heel strike transient, and from terminal loading response towards terminal stance. The second PC didn’t represent more than 50% of the variance at any point of the gait cycle, however upon further inspection contained useful information. This is a drawback to the selection technique adopted by Jones (2004), which is discussed further in Section 4.2.8. The explained variance of the three components was 62.3%, 13.5%, 6.8%, respectively, resulting in 82.6% of the total variance being represented.

The reconstruction of the original data using the three PCs individually is shown in Figure 3.40. Much like many other PCs that have been defined, the first PC reconstructs a change in magnitude throughout the entirety of stance phase. The mediolateral GRF is related to the movement of the centre during the of mass during walking: the COM is decelerated within the coronal plane from heel strike to midstance and then accelerated

Figure 3.39 Mediolateral ground reaction force of NP (solid black, dotted standard deviation),

A

B

C

Figure 3.40 Reconstruction of the original mediolateral ground reaction force data using only

the retained principal components, PC 1-3, individually. For each PC, the subject with the highest and lowest PC scores are reconstructed, alongside the mean and STD PC scores.

towards the other limb in the second half of stance. Both require a medial GRF, and deceleration and propulsion phases contribute to the presence of two peaks. The movement of the COM in the coronal plane is related to gait velocity and coronal plane stability; if the COM moves lateral to the supporting limb this can increase the risk of falls (Hof et al., 2005).

Sagittal Moment

The principal components selected for the knee flexion moment and their corresponding regions of variance are represented in Figure 3.41. The first principal component represents most the waveform and includes the loading response, midstance, and terminal stance. Within these regions, it appears that, on average, OA subjects have a smaller magnitude of both flexion and extension moments. The second PC represents a small area before the first peak of the extension moment; where the COM has generally progressed over the supporting limb and the COP progresses towards the front of the foot. The explained variance of the two components was 54.5% and 16.8% respectively, resulting in a total representation of resulting in a total variance of 71%.

Figure 3.41 Knee flexion/extension moment of NP (solid black, dotted standard deviation), and

OA subjects (dashed), with regions of retained PC interpretation shaded. Moments have been normalised and expressed as a percentage of bodyweight*height.

A

B

Figure 3.42 Reconstruction of the original knee flexion/extension moment waveform using only

the retained principal components, PC 1-3, individually. For each PC, the subject with the highest and lowest PC scores are reconstructed, alongside the mean and STD PC scores.

Moments have been normalised and expressed as a percentage of bodyweight*height.

The reconstruction of the individual PCs is shown in Figure 3.42. The first PC reconstructs an intuitive relationship between an increased flexion moment during loading response and midstance, and an increased extension moment during terminal stance. There also appears to be a relationship between a decreased peak of the flexion moment, and an early transition towards an extension moment. The second PC reconstructs mainly the extension moment peak towards terminal stance without affecting the flexion moment peaks, indicating that some subjects may avoid the extension peak without affecting the rest of the sagittal knee moment.

Coronal moment

The principal components selected for the knee flexion moment, and their corresponding regions of variance, are represented in Figure 3.43A. The first PC represents most of the variance throughout the duration of stance phase, during which it appears that, on average, OA subjects have an increased adduction moment. The second PC appears to represent only a small amount of variance towards the very end of stance phase. The explained variance of the two components was 80.3% and 6.8% respectively, resulting in a total representation of variance of 81%.

The reconstruction of the waveform using the two selected PCs is shown in Figure 3.44, B & C. The first PC reconstructs the change in magnitude of the adduction moment throughout the entirety of the stance phase. While subtle, it also appears that an increased magnitude of the adduction moment may be related to a small abduction moment towards toe-off. The reconstruction using the second PC accounts for very small changes in the amount of a dip between the two adduction moment peaks, as well as what appears to be differences in timing of these peaks.

Figure 3.43 Knee adduction moment of NP (solid black, dotted standard deviation), and OA

Figure 3.45 Reconstruction of the original knee adduction moment waveform using only the

retained principal components, PC 1-3, individually. For each PC, the subject with the highest and lowest PC scores are reconstructed, alongside the mean and STD PC scores. Moments

have been normalised and expressed as a percentage of bodyweight*height.

Transverse Moment

The principal components selected for internal knee moment and their corresponding regions of variance are represented in Figure 3.46. The first principal component represents the region of loading response and the second half of stance; where typically a peak external and internal moment would occur respectively (Brandon and Deluzio, 2011). The second PC appears to represent a region of variance towards the end of

loading response and the beginning of midstance. The explained variance of the two components was 60.9% and 25.8% respectively, resulting in a total variance of 87%.

The reconstruction of the waveform using the two selected PCs is shown in Figure 3.47. The reconstruction of the first PC shows an unexpected relationship between the first and second peaks of the transverse knee moment: if the first peak is an internal moment, the second peak is more likely to be an external, and vice versa. Other studies on transverse knee moments find NP subjects generally have a biphasic transverse moment with an external first peak and an internal second peak, which reduce in magnitude with severe OA (Brandon and Deluzio, 2011). One potential cause which could have resulted in this unexpected finding was that the positive definition of the knee moment might have been defined differently for each leg. The MATLAB code was double-checked, and this wasn’t the case. Also, the transverse knee moments for the NP subjects, where the right knee was used, was compared to those of the left knee and no pattern of inverted sign convention was visible. The results for the transverse knee moments will therefore still be considered but will be treated with caution.

Figure 3.46 Knee internal moment of NP (solid black, dotted standard deviation), and OA

subjects (dashed), with regions of retained PC interpretation shaded. Moments have been normalised and expressed as a percentage of bodyweight*height.

The second PC also appears to show a relationship between an internal moment throughout the beginning of stance, and an external moment during terminal stance. The second PC, however, reconstructs a prolonged internal or external moment throughout midstance, and hence a later transition towards the second peak.

Figure 3.47 Knee internal moment of NP (solid black, dotted standard deviation), and OA

subjects (dashed), with regions of retained PC interpretation shaded. Moments have been normalised and expressed as a percentage of bodyweight*height.

Classification Results

The classifier was trained on the retained PCs of the 18 NP and 20 OA subjects for whom joint moments and mediolateral forces could be calculated. The results of the LOO classification accuracy are shown in Table 3.7. Also shown, for a fair comparison, are the classification results when trained with the same subjects but without the additional joint moments and mediolateral force data added.

Similarly to the previous two datasets, the KC/S and KC definition consistently achieved

more favourable results than that of KS. The definition using KC/Sachieved slightly greater

LOO classification accuracy than KCwhen using the expanded variables. Overall, the

KC/S definition also performed most accurately when using the original variables, despite

LOO accuracy being lower for θ and θA definitions.

The original definition of the midpoint of the control function used by (Jones, 2004), θO, didn’t perform as poorly as in the previous datasets. This is because the two groups were of similar size (18 vs 20) and the global average was therefore only slightly biased towards the OA group. As in the previous two datasets, the θS proved the best-performing theta definition, followed by θA.

Table 3.7 Classification results of the 20 OA and 18 NP subjects for which it was possible to

calculate mediolateral GRF and joint moments, using the PCs defined within this study, comparing definitions of control variables k and θ.

LOO classification accuracy (%)

K definition Theta definition Moments added Without moments

Kc θO 97.4 94.7 θA 100 94.7 θS 100 97.4 Ks θO 94.7 92.1 θA 94.7 89.5 θS 94.7 89.5 Kc/s θO 100 92.1 θA 100 92.1

Table 3.8 The ranking of classification input variables in for the 20 OA and 18 NP subjects for

which it was possible to calculate mediolateral GRF and joint moments, using the PCs defined within this study. The additional PCs defined within this section are highlighted in bold.

Rank Classification

accuracy (%) Variable

1 97.4 GRF Ant/posterior PC1

2 89.5 GRF Vertical PC1

3 81.6 Average Knee Girth

4 81.6 Knee Flexion Moment

PC1

5 81.6 Knee Flexion Angle PC2

6 81.6 GRF Mediolateral PC2 7 76.3 AP Knee Depth 8 73.7 Knee Int/external Moment PC1 9 71.1 GRF Mediolateral PC3 10 68.4 ML Knee Width 11 68.4 Knee Ad/Abduction Moment PC1

12 68.4 Knee Flexion Moment

PC2

13 63.2 Knee Int/external Mom

PC2

14 60.5 GRF Vertical PC2

15 57.9 Knee Ad/Abduction Angle PC1

16 57.9 Knee Int/external Angle PC2

17 55.3 GRF Mediolateral PC1

18 55.3 Knee Ad/Abduction Angle PC2

19 52.6 Knee Flexion Angle PC1

20 52.6 Knee Ad/Abduction

Moment PC2

21 52.6 GRF Ant/posterior PC2

22 50.0 Knee Flexion Angle PC3

23 50.0 GRF Ant/posterior PC3

24 47.4 Knee Int/external

Moment PC2

Figure 3.48 Simplex plots to illustrate the LOO classification of 20 OA (red cross), and 18 NP

(blue circle), subjects, A) Using the original input variables selected by (Jones, 2004), and the updated PC definitions of Section 3.6.2 B) Using the addition of mediolateral GRF and knee joint moments. In both instances, the Kc/s and the θS control parameter definitions have been