Comparing multiple correspondence and principal component analyses with biomechanical signals. Example with turning the steering wheel.

The purpose of this article is to compare Principal Component Analysis (PCA) and a much less used method, i.e. MCA (Multiple Correspondence Analysis) with data being first changed into membership values to fuzzy space windows. For such a comparison, data from an experimental study about turning the steering wheel is used. In a didactic perspective, this article only considers one multidimensional signal with 5 components: 3 linked to the steering wheel angle and hand positions and 2 to hand effort variables. A discussion weighs out the pros and the cons of both methods with criteria such as the possibility to show complex relational phenomena, the analysis/computing time or the information loss inherent to the averaging stage (in the perspective to analyze several hundreds of large multidimensional signals).

Biomechanical comparison of isokinetic lifting and free lifting when applied to chronic low back pain rehabilitation.

The study compares free and isokinetic lifting using a multivariate statistical analysis. Each of the 13 male subjects performed three free lifts and three isokinetic lifts using a CYBEX LIFTASK. The measurement variables were obtained from a 3D video system, two force plates and two strain-gauge transducers. Coupling of fuzzy space-time windowing and multiple correspondence analysis was used to show the links between the variables and the differences between the experimental situations. Isokinetic lifting had almost no points in common with free-lifting, but there was a similar range of extension for the different joints. Most free-lifting strategies could not be used in isokinetic lifting, as constraints between the subject and his environment were different. The main drawback of the isokinetic lifting was due to the necessity for individuals to reach the machine speed, yielding high transient efforts. The maximum vertical effort at the L5/S1 joint was about 1600, 1500 and 1400N for low, medium and high speed, whereas it was lower than 1300N, irrespective of the load, during free lifting. In the context of chronic low back pain rehabilitation, movement strategies used in free lifting could not be relearnt using an isokinetic machine. A better understanding of the common points and differences between isokinetic movement and free movement could help rehabilitation physicians to plan rehabilitation programmes, taking advantage of each kind of movement.

Individual differences in tracking.

The present experiment compared differences in response strategy of participants performing a two-dimensional tracking task at three different levels of task difficulty. Twelve participants tracked an iconic aeroplane target as accurately as possible for nine repeated trials each of 5 min duration. The random input and individual response output were calculated in terms of direction and velocity. Specifically, for each 200-ms sample period, a calculated combination of eight trajectories and three velocities provided a 24 combinatorial description of both random input and participant response. Distributions across these combinations represent descriptive results and reflect individual characteristics. The distributions were compared using the technique of correspondence factor analysis. The outcome of this multidimensional method was that first, between-participants discrimination was best served by the up-vertical and low-velocity combination and, second, that the former pattern typified poor performers, while more skilled individuals used all directional options at the highest velocity level. Implications for individualized controls are examined.

Multiple correspondence analysis of biomechanical signals characterized through fuzzy histograms.

Data characterizing is considered the first and main stage of the statistical analysis. Rather than characterizing each biomechanical signal through one or few global indicators, such as the mean or the root mean square, this paper suggests first to cut the scale into several fuzzy windows and to summarize the data within each window through an occurrence indicator. These indicators become the analysis variables. They can be analyzed through the multiple correspondence analysis, which shows the most discriminant variables, connections between them, empirical situation classes and correspondences between these classes and the most discriminant variables. An example is considered for arguing our point of view; it concerns characterizing and analysis of forces situated at the hand, foot and back level in a load lifting task.

Multivariate graphical presentation for gait rehabilitation study.

This paper describes a procedure to determine the progress of the gait rehabilitation in relation to a reference obtained from a normal population. This procedure includes three stages: (1) data standardization, to give time and space aspects comparable from one individual to another; (2) monovariate and multivariate distance computation, to assess the difference between a disabled patient at a given time in the rehabilitation and the reference computed from individuals with a 'normal' gait; and (3) distance evolution. Since several variables are taken into account at the same time, the star view is proposed, each ray corresponding to the average distance between a given function of the patient undergoing rehabilitation and the corresponding reference function. Thus, as the rehabilitation process progresses, the distances are reduced and the star ray decreases. As a case study, the procedure is applied to the rehabilitation of a patient with an anterior cruciate deficient knee. Copyright 1998 Elsevier Science B.V.

Descriptive multidimensional statistical methods for analysing signals in a multifactorial biomedical database.

A methodology is presented to analyse multidimensional signals from several recording periods resulting from an experimental study on human or other living systems. The methodology is divided into two stages: intra-period analysis and inter-period analysis. The purpose of the first stage is to highlight general trends in multidimensional signal changes and the more informative components of the signals. The purpose of the second stage is to assess the influence of environmental or individual difference factors on a given signal component that appears to be discriminant in the first stage. To take into account the multivariable state of the system and the multi-observational aspect, a multidimensional descriptive statistical approach is used. The methods are correspondence analysis and hierarchical clustering. They are illustrated through an occupational medicine application from a study of sedentary posture.

Considering imperfections using 3D imaging system in angle obtaining, angle signal distance computing and multivariate distance graphing.

Fields such as medicine, biomechanics or ergonomics need to measure the positions and the rotational movements of body segments. The aim of this article is to underscore the problem of imperfection on angle measurement using a three-dimensional television system. First, the error on a single angle value is assessed through the classical Taylor's formula and through a simulating approach. Then the error is considered for an entire signal through either an experimental design or a simulating approach. To take into account such an error when comparing two angle multidimensional signals, a specific coding technique is suggested. Finally, two graphical patterns are proposed to show globally the distance between the signals with regard to the error.

Combined statistical study of joint angles and ground reaction forces using component and multiple correspondence analysis.

The purpose of this research is to propose a general methodology to draw gait patterns when including hip, knee and ankle angle excursions in the sagital plane and the three components of the ground reaction force. The multidimensional signal analysis procedure is divided into three main stages: 1) describing the six signals of each step through sliding averages computed for successive time windows, 2) analyzing separately the six step-by-window tables obtained for each signal through principal component analysis to reduce the excessive quantity of data, and 3) analyzing the most informative time windows of the six signals at the same time. To emphasize both linear and nonlinear relationships between the respective time windows, the signal range within a window is cut into fuzzy modalities such as, "low" "medium" and "large." The resulting table is investigated using multiple correspondence analysis. The outcomes are gait patterns combining both time and space aspects. The factor planes obtained from multiple correspondence analysis constitute initial data models so that new data obtained from pathological gait can be directly projected onto them. Such an operation can be used to show how the rehabilitation of a particular subject evolves in relation to normal gait patterns.

Biomechanical and epidemiological investigation of carpal tunnel syndrome at workplaces with high risk factors.

This paper deals with the problem of carpal tunnel syndrome (CTS) through investigations of both biomechanical and epidemiological data on seventeen high risk jobs. Biomechanical data were collected from continuous recording of prehension muscular efforts and wrist angular flexion-extension positions for each hand. In order to characterize both static and dynamic behaviours of signals, nine angle and four force indices were built for each hand. The epidemiological data evaluated the probability to contract the CTS (prevalence) on the dominant hand, the non-dominant hand, and both hands simultaneously. Biomechanical and epidemiological data were evaluated using multiple correspondence factor analysis which may consider heterogeneous variables to clarify non-linear relations in a very large data set. The CTS occurred twice more frequently on the two hands together (average 20%) than on the dominant hand alone. Such a result confirmed the outcome of other studies that non-occupational factors could be more important than occupational factors. The prevalence for both hands was highly correlated with the frequency of flexion and use of high forces. High or low flexions appeared to be a greater risk factor than high or low extensions.

Error and data coding in the multi-dimensional analysis of human movement signals.

This paper discusses two main problems of human motion data: their uncertainty and analysis. Considering the first point, a simulating method is proposed to assess the error. This approach is applied to a joint angle, computed from the positions of points obtained through a three-dimensional video-computer system. Considering the second point, a multi-variate methodology based on appropriate data coding and the correspondence factor analysis method is proposed. The outcomes of this allow the relations within the time windows of the variable set, the distances within the observation set and the correspondences between these two sets to be shown graphically. To illustrate this approach, two examples are considered: the analysis of the low back-pelvis angle in an ergonomical study about the sitting posture and the analysis of joint angles in the gait.

Patterns of relations between lower limb angle excursions during normal gait.

This paper deals with the analysis of data from a kinematic study of limb angle during normal gait. The first set of data deals with the variation of femur angle to the vertical, and of knee and ankle flexion-extension. The data are recorded on the System of Gestual Automatic 3D Analysis with a 50 Hz sampling rate. The second data set concerns morphological parameters. The data are obtained from 35 subjects. The time angle data are raw and are not to be related to a base position. The first stage of the angle analysis shows that a walking cycle can be characterized by 25 values. A factor analysis is then applied to these values for each angle in order to underscore the more informative instants. From this study, eight measurements are preserved. In the third stage, the same method is applied to both angles. It illustrates four ways to differentiate healthy subjects' walk. It also shows that the angles of femur and knee are strongly correlated and that there is a priori no clear relationship between the ankle and the two previous angles. The last stage is analysis of the morphological and angle parameters together. It brings to the fore the influence of sex and height for two groups of subjects.

[Multidimensional analysis of reactive forces of the foot during normal walking]. / Analyse multidimensionnelle des forces de réaction du pied au cours de la marche normale.

The authors present the analysis of the three components of ground reaction forces on both left and right feet on 50 subjects. Fourier analysis shows that a 25-Hz sampling is sufficient to fully characterize the normal gait. The approach used in order to study the data tables built for each component consisted in principal component factor analysis. This multivariate method, which looses the least possible information in relation to raw data, has indicated a high variability between subjects. Concerning the intrasubject variability, great asymmetry occurred between the forward and back forces. With respect to the relationship, the three components, the medial-lateral force was very independent of the two others. Particular classes of normal gait have been proposed.