Parallel Factor Analysis of gait waveform data: A multimode extension of Principal Component Analysis

Gait data are typically collected in multivariate form, so some multivariate analysis is often used to understand interrelationships between observed data. Principal Component Analysis (PCA), a data reduction technique for correlated multivariate data, has been widely applied by gait analysts to investigate patterns of association in gait waveform data (e.g., interrelationships between joint angle waveforms from different subjects and/or joints). Despite its widespread use in gait analysis, PCA is for two-mode data, whereas gait data are often collected in higher-mode form. In this paper, we present the benefits of analyzing gait data via Parallel Factor Analysis (Parafac), which is a component analysis model designed for three- or higher-mode data. Using three-mode joint angle waveform data (subjects×time×joints), we demonstrate Parafac's ability to (a) determine interpretable components revealing the primary interrelationships between lower-limb joints in healthy gait and (b) identify interpretable components revealing the fundamental differences between normal and perturbed subjects' gait patterns across multiple joints. Our results offer evidence of the complex interconnections that exist between lower-limb joints and limb segments in both normal and abnormal gaits, confirming the need for the simultaneous analysis of multi-joint gait waveform data (especially when studying perturbed gait patterns).     

The effect of perceived locomotor constraints on distance estimation

Two experiments were conducted to examine the ways in which the visual estimation of distance to a target is affected by constraints perceived to be placed on the subsequent locomotion to the target without vision. We hypothesized that an appraisal of impending effort would play a role in ascertaining the distance to be walked. In Experiment 1, the amount of resistance to walking was variable and unpredictable. One group of subjects performed against relatively low resistance, whereas another group performed against substantially greater resistance. In the low-resistance condition, no significant differences in CE, VE, time to target, or number of steps to target were found between any of the eight combinations of predictable or unpredictable resistances during walking. In the high-resistance condition, however, significant differences were found for CE and number of strides to target when resistance varied unpredictably during walking. Experiment 2 was similar in design but required subjects to walk with combinations of normal or short steps after they had viewed the target knowing only the gait type that would be used to begin locomotion. No differences in CE, VE, or time to target were found between four different combinations of gait type and predictability, under subjectively controlled conditions. When the step constraints were externally imposed, however, differences were found for CE. None of the results from either experiment, in which the number of strides needed to reach the target or the predictability of gait did not change from normal, supported the hypothesis that motor output requirements are necessary in forming a mental representation of the target position that can be used to walk to the target with eyes closed. Whichever locomotor technique was used to walk the estimated distance in these cases, the representation was able to be used independently. When walking mechanics were altered by externally imposed constraints, however, the success at reaching the estimated target position was reduced. These latter results are consistent with those obtained using up, down, and level walking and support the premise that mental representations used in blind walking are linked to the locomotor mechanics afforded by environmental conditions.     

The influence of aging on the spatial and temporal variables of gait during usual and fast speeds in older adults aged 60 to 102 years

BackgroundWith increases in life expectancy, it is important to understand the influence of aging on gait, given that this activity is related to the independence of older adults and may help in the development of health strategies that encourage successful aging in all phases of this process.Research questionTo compare gait parameters with usual and fast speeds for independent and autonomous older adults throughout the aging process (60 to 102 years old), and also to identify which of the gait variables are best for identifying differences across the different age groups.MethodsTwo hundred older adults aged between 60 and 102 years were evaluated. The sample was divided into 3 age groups: 60 to 79 years, 80 to 89 years and 90 years and over. The analyzed gait variables were: speed (meters/s), cadence (steps/min), stride time (seconds), step length (centimeters), double support (percentage of the gait cycle), swing (percentage of the gait cycle), step length variability (CoV%) and stride time variability (CoV%).ResultsGroup comparison regarding usual gait and fast gait revealed a significant difference in all gait variables. In addition, it can be seen that variables such as gait speed and step length showed greater effect sizes in intergroup comparison (usual gait: 0.48 and 0.47; fast gait: 0.36 and 0.40; respectively), possibly showing that these variables can better detect the changes observed with increasing age.ConclusionThere are differences in the gait performance of older adults from different age groups for usual and fast gait speeds, which is more evident regarding gait speed and step length variables. We recommend the use of usual gait for the identification of the effects of aging because, besides showing a higher effect size values it is more comfortable and requires less effort from older subjects.     

Swing phase mechanics of healthy young and elderly men.

This study examined the effect of ageing on the swing phase mechanics of young and elderly gait. Sagittal plane marker trajectories and force plate data were collected while 10 young (24.9+/-0.9 years) and eight elderly (68.9+/-0.4 years) subjects walked at their preferred walking speeds. Comparison between young and elderly gait was made for a range of spatial-temporal, kinematic and kinetic variables with emphasis given to identifying possible differences at toe-off, minimum metatarsal-phalangeal joint clearance and heel contact. In order to control for the confounding effect of gait velocity on the dependent variables, a multivariate analysis of covariance was used to identify differences between the young and elderly subjects due to age. In contrast to studies that have reported lower preferred walking speeds in the elderly compared to the young [J.O. Judge, R.B. Davis III, S. Ounpuu, Step length reductions in advanced age: the role of ankle and hip kinetics, Journal of Gerontology: Medical Sciences 51 (1996) M303-312; D.C. Kerrigan, M.K. Todd, U. Della Croce, L.A. Lipsitz, J.J. Collins, Biomechanical gait alterations independent of speed in the healthy elderly: evidence for specific limiting impairments, Archives of Physical and Medical Rehabilitation 79 (1998) 317-322], no differences in walking speed nor in the spatial-temporal variables that determine walking speed were detected. The elderly were however, found to have a greater hip extension moment at the time of minimum metatarsal-phalangeal joint clearance, and a significantly higher anterior-posterior velocity heel contact velocity that was linked to a significantly higher shank and foot angular velocity at heel contact. Since many gait variables are highly correlated with walking speed [C. Kirtley, M.W. Whittle, R.J. Jefferson, Influence of walking speed on gait parameters, Journal of Biomechanical Engineering 7 (1985) 282-288; D.A. Winter, Biomechanical motor patterns in normal walking, Journal of Motor Behaviour 15 (1983) 302-330], differences between young and elderly gait found in the present study may therefore be attributed to ageing, rather than a secondary effect of differences in gait velocity.     

The Effect of Perceived Locomotor Constraints on Distance Estimation

Two experiments were conducted to examine the ways in which the visual estimation of distance to a target is affected by constraints perceived to be placed on the subsequent locomotion to the target without vision. We hypothesized that an appraisal of impending effort would play a role in ascertaining the distance to be walked. In Experiment 1, the amount of resistance to walking was variable and unpredictable. One group of subjects performed against relatively low resistance, whereas another group performed against substantially greater resistance. In the low-resistance condition, no significant differences in CE, VE, time to target, or number of steps to target were found between any of the eight combinations of predictable or unpredictable resistances during walking. In the high-resistance condition, however, significant differences were found for CE and number of strides to target when resistance varied unpredictably during walking. Experiment 2 was similar in design but required subjects to walk with combinations of normal or short steps after they had viewed the target knowing only the gait type that would be used to begin locomotion. No differences in CE, VE, or time to target were found between four different combinations of gait type and predictability, under subjectively controlled conditions. When the step constraints were externally imposed, however, differences were found for CE. None of the results from either experiment, in which the number of strides needed to reach the target or the predictability of gait did not change from normal, supported the hypothesis that motor output requirements are necessary in forming a mental representation of the target position that can be used to walk to the target with eyes closed. Whichever locomotor technique was used to walk the estimated distance in these cases, the representation was able to be used independently. When walking mechanics were altered by externally imposed constraints, however, the success at reaching the estimated target position was reduced. These latter results are consistent with those obtained using up, down, and level walking and support the premise that mental representations used in blind walking are linked to the locomotor mechanics afforded by environmental conditions.     

Bow, range, and sequential effects in absolute identification: A response-time analysis

Accuracy and response-time (RT) measures were obtained in the absolute identification of line length. Different groups of subjects performed the task under different experimental conditions where range and relative spacing were the main independent variables. For comparison purposes, another group of subjects performed a digit-identification task. Results were analyzed for bow, range, and sequential effects using both accuracy and RT data. A preliminary analysis of RT distributions was also performed. Several phenomena previously documented using accuracy are reproduced, while new observations are reported for RT. The results show a dissociation between RT and accuracy in that the experimental manipulations sometimes affected accuracy but not necessarily RT.     

CPCA: A program for principal component analysis with external information on subjects and variables

A program is described for principal component analysis with external information on subjects and variables. This method is calledconstrained principal component analysis (CPCA), in which regression analysis and principal component analysis are combined into a unified framework that allows a full exploration of data structures both within and outside known information on subjects and variables. Many existing methods are special cases of CPCA, and the program can be used for multivariate multiple regression, redundancy analysis, double redundancy analysis, dual scaling with external criteria, vector preference models, and GMANOVA (growth curve models).     

Gait and risk of falls associated with frontal cognitive functions at different stages of Alzheimer's disease

ABSTRACT The decline in frontal cognitive functions contributes to alterations of gait and increases the risk of falls in patients with dementia, a category which included Alzheimer's disease (AD). The objective of the present study was to compare the gait parameters and the risk of falls among patients at different stages of AD, and to relate these variables with cognitive functions. This is a cross-sectional study with 23 patients with mild and moderate AD. The Clinical Dementia Rating was used to classify the dementia severity. The kinematic parameters of gait (cadence, stride length, and stride speed) were analyzed under two conditions: (a) single task (free gait) and (b) dual task (walking and counting down). The risk of falls was evaluated using the Timed Up-and-Go test. The frontal cognitive functions were evaluated using the Frontal Assessment Battery (FAB), the Clock Drawing Test (CDT) and the Symbol Search Subtest. The patients who were at the moderate stage suffered reduced performance in their stride length and stride speed in the single task and had made more counting errors in the dual task and still had a higher fall risk. Both the mild and the moderate patients exhibited significant decreases in stride length, stride speed and cadence in the dual task. Was detected a significant correlation between CDT, FAB, and stride speed in the dual task condition. We also found a significant correlation between subtest Similarities, FAB and cadence in the dual task condition. The dual task produced changes in the kinematic parameters of gait for the mild and moderate AD patients and the gait alterations are related to frontal cognitive functions, particularly executive functions.     

Gait and risk of falls associated with frontal cognitive functions at different stages of Alzheimer's disease

ABSTRACT

The decline in frontal cognitive functions contributes to alterations of gait and increases the risk of falls in patients with dementia, a category which included Alzheimer's disease (AD). The objective of the present study was to compare the gait parameters and the risk of falls among patients at different stages of AD, and to relate these variables with cognitive functions. This is a cross-sectional study with 23 patients with mild and moderate AD. The Clinical Dementia Rating was used to classify the dementia severity. The kinematic parameters of gait (cadence, stride length, and stride speed) were analyzed under two conditions: (a) single task (free gait) and (b) dual task (walking and counting down). The risk of falls was evaluated using the Timed Up-and-Go test. The frontal cognitive functions were evaluated using the Frontal Assessment Battery (FAB), the Clock Drawing Test (CDT) and the Symbol Search Subtest. The patients who were at the moderate stage suffered reduced performance in their stride length and stride speed in the single task and had made more counting errors in the dual task and still had a higher fall risk. Both the mild and the moderate patients exhibited significant decreases in stride length, stride speed and cadence in the dual task. Was detected a significant correlation between CDT, FAB, and stride speed in the dual task condition. We also found a significant correlation between subtest Similarities, FAB and cadence in the dual task condition. The dual task produced changes in the kinematic parameters of gait for the mild and moderate AD patients and the gait alterations are related to frontal cognitive functions, particularly executive functions.     

Effects of experimentally increased trunk stiffness on thorax and pelvis rotations during walking

Patients with non-specific low back pain, or a similar disorder, may stiffen their trunk, which probably alters their walking coordination. To study the direct effects of increasing trunk stiffness, we experimentally increased trunk stiffness during walking, and compared the results with what is known from the literature about gait coordination with, e.g., low back pain. Healthy subjects walked on a treadmill at 3 speeds (0.5, 1.0 and 1.5 m/s), in three conditions (normal, while contracting their abdominal muscles, or wearing an orthopedic brace that limits trunk motions). Kinematics of the legs, thorax and pelvis were recorded, and relative Fourier phases and amplitudes of segment motions were calculated. Increasing trunk stiffness led to a lower thorax–pelvis relative phase, with both a decrease in thorax–leg relative phase, and an increase in pelvis–leg relative phase, as well as reduced rotational amplitude of thorax relative to pelvis. While lower thorax–pelvis relative phase was also found in patients with low back pain, higher pelvis–leg relative phase has never been reported in patients with low back pain or related disorders. These results suggest that increasing trunk stiffness in healthy subjects causes short-term gait coordination changes which are different from those seen in patients with back pain.     

Clusterwise simultaneous component analysis for analyzing structural differences in multivariate multiblock data

Many studies yield multivariate multiblock data, that is, multiple data blocks that all involve the same set of variables (e.g., the scores of different groups of subjects on the same set of variables). The question then rises whether the same processes underlie the different data blocks. To explore the structure of such multivariate multiblock data, component analysis can be very useful. Specifically, 2 approaches are often applied: principal component analysis (PCA) on each data block separately and different variants of simultaneous component analysis (SCA) on all data blocks simultaneously. The PCA approach yields a different loading matrix for each data block and is thus not useful for discovering structural similarities. The SCA approach may fail to yield insight into structural differences, since the obtained loading matrix is identical for all data blocks. We introduce a new generic modeling strategy, called clusterwise SCA, that comprises the separate PCA approach and SCA as special cases. The key idea behind clusterwise SCA is that the data blocks form a few clusters, where data blocks that belong to the same cluster are modeled with SCA and thus have the same structure, and different clusters have different underlying structures. In this article, we use the SCA variant that imposes equal average cross-products constraints (ECP). An algorithm for fitting clusterwise SCA-ECP solutions is proposed and evaluated in a simulation study. Finally, the usefulness of clusterwise SCA is illustrated by empirical examples from eating disorder research and social psychology.     

Reliability of gait parameters in children under two years of age

The walking movement of children of school age and adults can be regarded as very consistent. However, few studies have reported reliability of gait parameters in very young children that may be used as normative data for the clinical assessment of gait. In the present study, nine normal children of ages 10 to 21 mo. were assessed cross-sectionally using three-dimensional video analysis and digitization to assess within-day reliability of gait kinematics. Between-subject differences in gait kinematics were also examined. In addition, one child was assessed at the onset of independent walking and at monthly intervals thereafter to assess changes in gait kinematics during the first 8 mo. of autonomous walking. The case study allowed the acquisition of pilot data for longitudinal studies of this age group. 10 kinematics variables regarded as indicators of efficient walking were measured, and reliability was assessed using one-way analysis of variance and coefficient of variation. The study showed that all children produced reliable within-day results; however, the gait of each child was unique. In the case study, the between-month differences in gait kinematics were significant. The findings may be of clinical interest for pediatricians and child neurologists given the lack of normative data for this age group.     

Effects of visual focus and gait speed on walking balance in the frontal plane

We investigated how head position and gait speed influenced frontal plane balance responses to external perturbations during gait. Thirteen healthy participants walked on a treadmill at three different gait speeds. Visual conditions included either focus downward on lower extremities and walking surface only or focus forward on a stationary scene with horizontal and vertical lines. The treadmill was positioned on a platform that was stationary (non-perturbed) or moving in a pattern that appeared random to the subjects (perturbed). In non-perturbed walking, medial–lateral upper body motion was very similar between visual conditions. However, in perturbed walking, there was significantly less body motion when focus was on the stationary visual scene, suggesting visual feedback of stationary vertical and horizontal cues are particularly important when balance is challenged. Sensitivity of body motion to perturbations was significantly decreased by increasing gait speed, suggesting that faster walking was less sensitive to frontal plane perturbations. Finally, our use of external perturbations supported the idea that certain differences in balance control mechanisms can only be detected in more challenging situations, which is an important consideration for approaches to investigating sensory contribution to balance during gait.     

Analysis of ordinal categorical data with misclassification

We develop a method for the analysis of multivariate ordinal categorical data with misclassification based on the latent normal variable approach. Misclassification arises if a subject has been classified into a category that does not truly reflect its actual state, and can occur with one or more variables. A basic framework is developed to enable the analysis of two types of data. The first corresponds to a single sample that is obtained from a fallible design that may lead to misclassified data. The other corresponds to data that is obtained by double sampling. Double sampling data consists of two parts: a sample that is obtained by classifying subjects using the fallible design only and a sample that is obtained by classifying subjects using both fallible and true designs, which is assumed to have no misclassification. A unified expectation–maximization approach is developed to find the maximum likelihood estimate of model parameters. Simulation studies and examples that are based on real data are used to demonstrate the applicability and practicability of the proposed methods.     

Three-dimensional joint kinematics of ACL-deficient and ACL-reconstructed knees during stair ascent and descent

Mechanical environmental changes in the knee are induced by altered joint kinematics under cyclic loading during activities of daily living after anterior cruciate ligament (ACL) injury. This is considered a risk factor in progressive cartilage degeneration and the early onset of osteoarthritis following ACL injury and even after reconstructive surgery. The purpose of this study was to examine 3D joint kinematics of ACL-deficient and ACL-reconstructed knees to health controls during stair ascent and descent. A 3D optical video motion capture system was used to record coordinate data from reflective markers positioned on subjects as they ascended and descended a custom-built staircase. Spatiotemporal gait and knee joint kinematic variables were calculated and further analyzed. The ACL-deficient knees exhibited a significant extension deficit compared to the ACL-intact controls. A more varus and internally rotated tibial position was also identified in the ACL-deficient knees during both stair ascent and descent. The ACL-reconstructed knees exhibited less abnormality in both spatiotemporal gait parameters and joint kinematics, but these variables were not fully restored to a normal level. The kinematic profiles of the ACL-reconstructed knees were more similar to those of the ACL-deficient knees when compared to the ACL-intact knees. This suggests that the ACL-reconstructed knees had been "under-corrected" rather than "over-corrected" by the reconstructive surgery procedure. Findings from this study may provide more insight with respect to improving ACL reconstruction surgical techniques, which may aid the early progression of cartilage degeneration in ACL-reconstructed knees.     

Feature extraction via KPCA for classification of gait patterns

Automated recognition of gait pattern change is important in medical diagnostics as well as in the early identification of at-risk gait in the elderly. We evaluated the use of Kernel-based Principal Component Analysis (KPCA) to extract more gait features (i.e., to obtain more significant amounts of information about human movement) and thus to improve the classification of gait patterns. 3D gait data of 24 young and 24 elderly participants were acquired using an OPTOTRAK 3020 motion analysis system during normal walking, and a total of 36 gait spatio-temporal and kinematic variables were extracted from the recorded data. KPCA was used first for nonlinear feature extraction to then evaluate its effect on a subsequent classification in combination with learning algorithms such as support vector machines (SVMs). Cross-validation test results indicated that the proposed technique could allow spreading the information about the gait's kinematic structure into more nonlinear principal components, thus providing additional discriminatory information for the improvement of gait classification performance. The feature extraction ability of KPCA was affected slightly with different kernel functions as polynomial and radial basis function. The combination of KPCA and SVM could identify young-elderly gait patterns with 91% accuracy, resulting in a markedly improved performance compared to the combination of PCA and SVM. These results suggest that nonlinear feature extraction by KPCA improves the classification of young-elderly gait patterns, and holds considerable potential for future applications in direct dimensionality reduction and interpretation of multiple gait signals.     

Oral Motor Abilities Are Task Dependent: A Factor Analytic Approach to Performance Rate

Measures of performance rates in speech-like or volitional nonspeech oral motor tasks are frequently used to draw inferences about articulation rate abnormalities in patients with neurologic movement disorders. The study objective was to investigate the structural relationship between rate measures of speech and of oral motor behaviors different from speech. A total of 130 patients with neurologic movement disorders and 130 healthy subjects participated in the study. Rate data was collected for oral reading (speech), rapid syllable repetition (speech-like), and rapid single articulator movements (nonspeech). The authors used factor analysis to determine whether the different rate variables reflect the same or distinct constructs. The behavioral data were most appropriately captured by a measurement model in which the different task types loaded onto separate latent variables. The data on oral motor performance rates show that speech tasks and oral motor tasks such as rapid syllable repetition or repetitive single articulator movements measure separate traits.     

Bayesian analysis of structural equation models with mixed exponential family and ordered categorical data

Structural equation models are very popular for studying relationships among observed and latent variables. However, the existing theory and computer packages are developed mainly under the assumption of normality, and hence cannot be satisfactorily applied to non‐normal and ordered categorical data that are common in behavioural, social and psychological research. In this paper, we develop a Bayesian approach to the analysis of structural equation models in which the manifest variables are ordered categorical and/or from an exponential family. In this framework, models with a mixture of binomial, ordered categorical and normal variables can be analysed. Bayesian estimates of the unknown parameters are obtained by a computational procedure that combines the Gibbs sampler and the Metropolis–Hastings algorithm. Some goodness‐of‐fit statistics are proposed to evaluate the fit of the posited model. The methodology is illustrated by results obtained from a simulation study and analysis of a real data set about non‐adherence of hypertension patients in a medical treatment scheme.     

Support vector machine for classification of walking conditions of persons after stroke with dropped foot

Walking with dropped foot represents a major gait disorder, which is observed in hemiparetic persons after stroke. This study explores the use of support vector machine (SVMs) to classify different walking conditions for hemiparetic subjects. Seven participants with dropped foot (category 4 of functional ambulatory category) walked in five different conditions: level ground, stair ascent, stair descent, upslope, and downslope. The kinematic data were measured by two portable sensor units, each comprising an accelerometer and gyroscope attached to the lower limb on the shank and foot segments. The overall classification accuracy of stair ascent, stair descent, and other walking conditions was 92.9% using input features from the sensor attached to the shank. It was further improved to 97.5% by adding two more inputs from the sensor attached to the foot. Stair ascent was also classified by the inputs from the foot sensor unit with 96% accuracy. The performance of an SVM was shown to be superior to that of other machine learning methods using artificial neural networks (ANN) and radial basis function neural networks (RBF). The results suggested that the SVM classification method could be applied as a tool for pathological gait analysis, pattern recognition, control signals in functional electrical stimulation (FES) and rehabilitation robot, as well as activity monitoring during rehabilitation of daily activities.     

Biomechanics of normal and pathological gait: implications for understanding human locomotor control

The biomechanical (kinetic) analysis of human gait reveals the integrated and detailed motor patterns that are essential in pinpointing the abnormal patterns in pathological gait. In a similar manner, these motor patterns (moments, powers, and EMGs) can be used to identify synergies and to validate theories of CNS control. Based on kinetic and EMG patterns for a wide range of normal subjects and cadences, evidence is presented that both supports and negates the central pattern generator theory of locomotion. Adaptive motor patterns that are evident in peripheral gait pathologies reinforce a strong peripheral rather than a central control. Finally, a three-component subtask theory of human gait is presented and is supported by reference to the motor patterns seen in a normal gait. The identified subtasks are (a) support (against collapse during stance); (b) dynamic balance of the upper body, also during stance; and (c) feedforward control of the foot trajectory to achieve safe ground clearance and a gentle heel contact.