The Dimensionality and Control of Human Walking

Abstract

The aim of the work presented in this thesis was to investigate the control mechanism of human walking. From motor control theory, a motor synergy has two main features, sharing and error compensation (Latash, 2008). Therefore, this thesis focused on these two aspects of the mechanism by investigating: the coupling and correlations between the joint angles, and the variability due to the compensation of “errors” during walking. Thus, a more complete picture of walking in terms of coordination and control would be drawn. In order to evaluate the correlations between joint angles and detect the dimensionality of human walking, a new approach was developed as presented in Chapter 3 that overcame an important limitation of current methods for assessing the dimensionality of data sets. In Chapter 4, this new method is applied to 40 whole body joint angles to detect the coordinative structure of walking. Chapters 5 and 6 focus on between-subject and within-subject kinematic variability of walking, respectively, and investigate the effects of gender and speed on variability. The findings on walking variability inspired us to further determine the relationships between joint angles and walking speed, the results of which are shown in Chapter 7. A summary of each individual study is presented in the following text. Chapter 3 Principal components analysis is a powerful and popular technique for the decomposition of muscle activity and kinematic patterns into independent modular v components or synergies. The analysis is based on a matrix of either correlations or covariances between all pairs of signals in the data set. A primary limitation of such matrices is that they do not account for dynamic relations between signals - characterised by phase differences or frequency-dependent variations in amplitude ratio - yet such relations are widespread in the sensorimotor system. Low correlations may thus be obtained and signals may appear ‘independent’ despite a dynamic linear relation between them. To address this limitation, the matrix of overall coherence values between signal pairs may be used. Overall coherence can be calculated using linear systems analysis and provides a measure of the strength of the relationship between signals taking both phase differences and frequency-dependent variation in amplitude ratio into account. Using the ankle, knee and hip sagittal-plane angles from six healthy subjects during over-ground walking at preferred speed, it is shown that with conventional correlation matrices the first principal component accounted for ~ 50% of total variance in the data set, while with overall coherence matrices the first component accounted for > 95% of total variance. The results demonstrate that the dimensionality of the coordinative structure can be overestimated using conventional correlation, whereas with overall coherence a more parsimonious structure is identified. Overall coherence can enhance the power of principal components analysis in capturing redundancy in human motor output. Chapter 4 The control of human movement is simplified by organising actions into linkages or couplings between body segments known as ‘synergies’. Many studies have vi supported the existence of ‘synergies’ during human walking and demonstrated that multi-segmental movements are highly coupled and correlated. Since correlations in the movements between body segments can be used to understand the control of walking by identifying synergies, the nature of the coordinative structure of walking was investigated. Principal components analysis uses information about the relationship between segments in movement and can identify independent synergies. A dynamic linear systems analysis was employed to compute the overall coherence between the movements of body segments. This is a measure of the strength of the relationship between movements where both amplitude and phase differences in the movements can be accounted for. In contrast, the Pearson moment product correlation coefficient only accounts for amplitude differences in the movements. Therefore, overall coherence was assumed to be a better estimate of the true relationship between segments. The present study investigated whole body movement in terms of 40 joint angles during normal walking. Principal components analysis showed that one synergy (component) could cumulatively account for over 86% of total variance when applying overall coherence, while seven components were required when using Pearson correlation coefficient. The findings suggested that the relationships between joint angles are more complex than the simple linear relations described by Pearson correlation coefficient. When the dynamic linear relation was considered, a higher correlation between joint angles and greater reduction of degree of freedom could be obtained. The coordinative structure of human walking could therefore be low dimensional and even simply explained by a single component. An additional degree of freedom could be required to perform an vii additional voluntary task during walking by superimposing the voluntary task control signal on the basic walking motor control program. Chapter 5 Walking is a complex task which requires coordinated movement of many body segments. As a practised motor skill, walking has a low level of variability. Information regarding the variability of walking can provide valuable insight into control mechanisms and locomotor deficits. Most previous studies have assessed the stride-to-stride walking variability within subjects; little information is available for between-subject variability, especially for whole body movement. This information could provide an indication of how similar the control mechanism is between subjects during walking. Forty joint angles from the whole body were recorded using a motion analysis system in 22 healthy subjects at four walking speeds. The between-subject variability of the waveform patterns of the joint angles was evaluated using the amplitude of the mean kinematic pattern (MP) and the standard deviation of the pattern (SDP) for each angle. Regression analyses of SDP onto MP showed that at each walking speed, SDP across subjects increased with MP at a similar rate for all angles except the hip and knee in the sagittal plane. This may indicate a different control mechanism for hip and knee sagittal-plane movements which had a lower ‘signal to noise’ ratio that all other angles. A strong linear relationship was observed between SDP and MP for all joint angles. The variability between male subjects was comparable to the variability between female subjects. A trend of decreasing slopes of the regression lines with walking speed was observed with fast walking showing least variability, possibly reflecting higher angular viii accelerations producing a greater ‘tightening’ of the joints compared to slow walking, so that the rate of increase of waveform variability with increased waveform magnitude is reduced. The existence of an intercept other than zero in the SDP - MP relations suggested that the coefficient of variation should be used carefully when quantifying kinematic walking variability, because it may contain sources of variability independent of the mean amplitude of the angles. Chapter 6 Although most previous studies of walking variability have examined within-subject variability, little information is available for the variability of the whole body. This study measured the within-subject variability of both upper and lower body joint angles to increase the understanding of the mechanism of whole body movement. Whereas the between-subject variability was investigated in chapter 5, the within-subject variability of the waveform patterns of the joint angles was evaluated here, again using the amplitude of the mean kinematic pattern (MP) and the standard deviation of the pattern (SDP) for each angle. The within-subject variability was clearly less than the between-subject variability reported in Chapter 5, showing as would be expected that the repeatability of joint motion was greater within than across individuals. The results again showed that hip and knee flexion-extension demonstrated a consistently lower variability compared to all other joint angles. Comparison of males and females showed that the repeatability of joint motion was lower in females, this difference being mostly centred around the angles of the foot. The within-subject variability showed a quadratic relationship with walking speed, with minimum variability at preferred speed. Analysis of the regressions between ix SDP and MP of the joint angles also showed significant differences between females and males, with females showing a higher slope of the SDP and MP relation. As was the case for between-subject variability, the slopes of the SDP vs MP regression lines again decreased with walking speed for within-subject variability. Chapter 7 The relationship between walking parameters and speed has been widely investigated but most studies have investigated only a few joint angles and little has been reported about the relationship between the kinematics of the upper body and walking speed. In this study the relationship between walking speed and the range of the joint angles was evaluated. Linear correlations with walking speed were observed in both upper and lower body joint angles. Different mechanisms may be applied by the upper and lower limbs in relation to changes in walking speed. While hip and knee flexion-extension were found to play the most important role in changing walking speed, changes of large magnitude associated with walking speed occurred at the shoulder, elbow and trunk, apparently the result of changes in balance requirements and to help stabilise the body motion.