The complexity of human walking: a knee osteoarthritis study

Abstract

This study proposes a framework for deconstructing complex walking patterns to create a simple principal component space before checking whether the projection to this space is suitable for identifying changes from the normality. We focus on knee osteoarthritis, the most common knee joint disease and the second leading cause of disability. Knee osteoarthritis affects over 250 million people worldwide. The motivation for projecting the highly dimensional movements to a lower dimensional and simpler space is our belief that motor behaviour can be understood by identifying a simplicity via projection to a low principal component space, which may reflect upon the underlying mechanism. To study this, we recruited 180 subjects, 47 of which reported that they had knee osteoarthritis. They were asked to walk several times along a walkway equipped with two force plates that capture their ground reaction forces along 3 axes, namely vertical, anterior-posterior, and medio-lateral, at 1000 Hz. Data when the subject does not clearly strike the force plate were excluded, leaving 1-3 gait cycles per subject. To examine the complexity of human walking, we applied dimensionality reduction via Probabilistic Principal Component Analysis. The first principal component explains 34% of the variance in the data, whereas over 80% of the variance is explained by 8 principal components or more. This proves the complexity of the underlying structure of the ground reaction forces. To examine if our musculoskeletal system generates movements that are distinguishable between normal and pathological subjects in a low dimensional principal component space, we applied a Bayes classifier. For the tested cross-validated, subject-independent experimental protocol, the classification accuracy equals 82.62%. Also, a novel complexity measure is proposed, which can be used as an objective index to facilitate clinical decision making. This measure proves that knee osteoarthritis subjects exhibit more variability in the two-dimensional principal component space.

Figure 1. Data capturing.

Figure 1a is the real, lab-based environment, Figure 1c is the computer reconstruction, whereas Figure 1b an overlay of the two.

Figure 2. The blue curve corresponds to the mean GRF curve, whereas the blue shaded region indicates the precision of plus minus one standard deviation.

Accordingly, the foot which has knee OA is depicted in red.

Figure 3. GRFs for an random indicative subject.

Figure 4. The goodness of fit of a Gaussian distribution to the actual empirical distribution of the GRFs patterns for (a) normal subjects and (b) knee OA subjects.

Probability distributions over GRF patterns. Solid red lines is Gaussian distributions with mean and standard deviation matched to the empirical GRFs histograms. The data and the matching Gaussian distributions appear as bell-shaped.

Figure 5. The proposed complexity measure for the first 36 PCs.

In the lower PC dimensional space knee OA subjects have a tendency to present lower values.

Figure 6. How much variability is explained as a function of the number of the components.

The x-axis corresponds to the number of PCs, whereas the y-axis the percentage of the variance of the GRF patterns explained by the respective number of PCs. It is evident that human walking is a complex process, since the slope starts at a low point (1 PC explains just above 30% of the variability of the combined data) and the slope progresses slowly.

Figure 7. Projection of the GRF patterns in 2-D PC space (i.e. the first two PCs).

The two classes are not separable.

Figure 8. PC visualisations as discriminants of the two classes: normal subjects vs. knee OA subjects.