Alexander A. Frolov

Feedback equilibrium control during human standing

Equilibrium maintenance during standing in humans was investigated with a 3-joint (ankle, knee and hip) sagittal model of body movement. The experimental paradigm consisted of sudden perturbations of humans in quiet stance by backward displacements of the support platform. Data analysis was performed using eigenvectors of motion equation. The results supported three conclusions. First, independent feedback control of movements along eigenvectors (eigenmovements) can adequately describe human postural responses to stance perturbations. This conclusion is consistent with previous observations (Alexandrov et al., 2001b) that these same eigenmovements are also independently controlled in a feed-forward manner during voluntary upper-trunk bending. Second, independent feedback control of each eigenmovement is sufficient to provide its stability. Third, the feedback loop in each eigenmovement can be modeled as a linear visco-elastic spring with delay. Visco-elastic parameters and time-delay values result from the combined contribution of passive visco-elastic mechanisms and sensory systems of different modalities

Axial synergies during human upper trunk bending

Abstract Upper trunk bending movements were accompanied by opposite movements of the lower body segments. These axial kinematic synergies maintained equilibrium during the movement performance by stabilizing the center of gravity (CG), which shifted on average across all the subjects by 1±4 cm in the anteroposterior direction and thus always remained within the support area. The aim of the present investigation was to provide an insight into the central control responsible for the performance of these synergies. The kinematic analysis was performed by the method of principal components (PC) analysis applied to the covariation between ankle, knee and hip joint angles and compared with CG shifts during upper trunk bending. Subjects were asked to perform backward or forward upper trunk bending in response to a tone. They were instructed to move as fast as possible or slowly (2 s), with high or low movement amplitudes. PC analysis showed a strong correlation between hip, knee and ankle joint changes. The first principal component (PC1) representing a multijoint movement with fixed ratios between joint angular changes, accounted, on average, for 99.7%±0.2% of the total angular variance in the forward trunk movements and for 98.4%±1.4% in the backward movements. The instructed voluntary regulation of the amplitude and velocity of the movement was achieved by adapting the bell-shaped profile of the velocity time course without changes in interjoint angular relations. Fixed ratios between changes in joint angles, represented by PC1, ensured localization of the CG within the support area during trunk bending. The ratios given by PC1 showed highly significant dependence on subjects, suggesting the adaptability of the central control to each subject’s biomechanical peculiarities. Subject’s intertrial variability of PC1 ratios was small, suggesting a stereotyped automatic interjoint coordination. When changing velocity and amplitude of the movement, the ratios remained the same in about half the subjects while in others slight variations were observed. A weak second principal component (PC2) was shown only for fast movements. In forward movements PC2 reflected the early knee flexion that seems related to the disturbances caused by the passive interaction between body segments, rather than to the effect of a central command. In fast backward movements, PC2 reflected the delay in hip extension relative to the movement onset in the ankle and knee that mirrors intersubject differences in the initiation process of the axial synergy. The results suggest that PC1 reflects the centrally controlled multijoint movement, defining the time course and amplitude of the movement and fixing the ratios between changes in joint angles. They support the hypothesis that the axial kinematic synergies result from a central automatic control that stabilizes the CG shift in the anteroposterior direction while performing the upper trunk bending.

Kinematics of human arm reconstructed from spatial tracking system recordings.

The kinematics of the human arm in terms of angles of rotations in the joints is reconstructed from the spatial tracking system (Fastrack() Polhemus) recordings. The human arm is modeled by three rigid bodies (the upper arm, the forearm and the hand) with seven degrees of freedom (three in the shoulder, two in the elbow and two in the wrist). Joint geometry parameters (orientations of the axes relative to the arm segments, the angles and the distances between the axes) have been calculated on the basis of passive rotations in the joints. The calculated parameters have been used to solve the direct kinematics problem for the reaching movements in different directions. The difference between calculated and recorded positions and accelerations of the hand has been used to assess the accuracy of the proposed method of kinematics reconstruction. The error analysis showed that spatial tracking system recordings and human arm kinematics reconstruction could reliably be used to accurately analyze multijoint movement in humans.

Why and how are posture and movement coordinated

In most motor acts, posture and movement must be coordinated in order to achieve the goal of the task. The focus of this chapter is on why and how this coordination takes place. First, the nature of posture is discussed. Two of its general functions are recognized; an antigravity role, and a role in interfacing the body with its environment such that perception and action can ensue. Next addressed is how posture is controlled centrally. Two models are presented and evaluated; a genetic and a hierarchical one. The latter has two levels; internal representation and execution. Finally, we consider how central control processes might achieve an effective coordination between posture and movement. Is a single central control process responsible for both movement and its associated posture? Alternatively, is there a dual coordinated control system: one for movement, and the other for posture? We provide evidence for the latter, in the form of a biomechanical analysis that features the use of eigenmovement approach.

Biomechanical analysis of movement strategies in human forward trunk bending. I. Modeling

Abstract. Two behavioral goals are achieved simultaneously during forward trunk bending in humans: the bending movement per se and equilibrium maintenance. The objective of the present study was to understand how the two goals are achieved by using a biomechanical model of this task. Since keeping the center of pressure inside the support area is a crucial condition for equilibrium maintenance during the movement, we decided to model an extreme case, called “optimal bending”, in which the movement is performed without any center of pressure displacement at all, as if standing on an extremely narrow support. The “optimal bending” is used as a reference in the analysis of experimental data in a companion paper. The study is based on a three-joint (ankle, knee, and hip) model of the human body and is performed in terms of “eigenmovements”, i.e., the movements along eigenvectors of the motion equation. They are termed “ankle”, “hip”, and “knee” eigenmovements according to the dominant joint that provides the largest contribution to the corresponding eigenmovement. The advantage of the eigenmovement approach is the presentation of the coupled system of dynamic equations in the form of three independent motion equations. Each of these equations is equivalent to the motion equation for an inverted pendulum. Optimal bending is constructed as a superposition of two (hip and ankle) eigenmovements. The hip eigenmovement contributes the most to the movement kinematics, whereas the contributions of both eigenmovements into the movement dynamics are comparable. The ankle eigenmovement moves the center of gravity forward and compensates for the backward center of gravity shift that is provoked by trunk bending as a result of dynamic interactions between body segments. An important characteristic of the optimal bending is the timing of the onset of each eigenmovement: the ankle eigenmovement onset precedes that of the hip eigenmovement. Without an earlier onset of the ankle eigenmovement, forward bending on the extremely narrow support results in falling backward. This modeling approach suggests that during trunk bending, two motion units – the hip and ankle eigenmovements – are responsible for the movement and for equilibrium maintenance, respectively.

Brain-Computer Interface Based on Generation of Visual Images

This paper examines the task of recognizing EEG patterns that correspond to performing three mental tasks: relaxation and imagining of two types of pictures: faces and houses. The experiments were performed using two EEG headsets: BrainProducts ActiCap and Emotiv EPOC. The Emotiv headset becomes widely used in consumer BCI application allowing for conducting large-scale EEG experiments in the future. Since classification accuracy significantly exceeded the level of random classification during the first three days of the experiment with EPOC headset, a control experiment was performed on the fourth day using ActiCap. The control experiment has shown that utilization of high-quality research equipment can enhance classification accuracy (up to 68% in some subjects) and that the accuracy is independent of the presence of EEG artifacts related to blinking and eye movement. This study also shows that computationally-inexpensive Bayesian classifier based on covariance matrix analysis yields similar classification accuracy in this problem as a more sophisticated Multi-class Common Spatial Patterns (MCSP) classifier.

Boolean Factor Analysis by Attractor Neural Network

A common problem encountered in disciplines such as statistics, data analysis, signal processing, textual data representation, and neural network research, is finding a suitable representation of the data in the lower dimension space. One of the principles used for this reason is a factor analysis. In this paper, we show that Hebbian learning and a Hopfield-like neural network could be used for a natural procedure for Boolean factor analysis. To ensure efficient Boolean factor analysis, we propose our original modification not only of Hopfield network architecture but also its dynamics as well. In this paper, we describe neural network implementation of the Boolean factor analysis method. We show the advantages of our Hopfield-like network modification step by step on artificially generated data. At the end, we show the efficiency of the method on artificial data containing a known list of factors. Our approach has the advantage of being able to analyze very large data sets while preserving the nature of the data

Biomechanical analysis of movement strategies in human forward trunk bending. II. Experimental study.

Abstract. The large mass of the human upper trunk, its elevated position during erect stance, and the small area limited by the size of the feet, stress the importance of equilibrium control during trunk movements. The objective of the present study was to perform a biomechanical analysis of fast forward trunk movements in order to understand the coordination between movement and posture. The analysis is based on a comparison between experimentally observed bending and hypothetical “optimal bending” performed on an infinitely narrow support, as presented in a companion paper. The experimental data were obtained from 16 subjects who performed fast forward bending while standing on a wide platform or on a narrow beam. The analysis is performed by decomposition of the movement into three dynamically independent components, each representing a movement along one of the three eigenvectors of the motion equation. The eigenmovements are termed “hip”, “ankle”, and “knee” eigenmovements, according to the dominant joint. The experimentally observed movement is characterized mainly by the hip and ankle eigenmovements, whereas the knee eigenmovement is negligible. Similarly to the “optimal bending” the ankle eigenmovement starts earlier and lasts longer than the hip eigenmovement. An early forward acceleration of the center of gravity in the ankle eigenmovement is caused by anticipatory changes in the ankle joint torque. This clarifies the role of the early tibialis anterior burst and/or soleus inhibition usually observed in electromyographic recordings during forward bending. The results suggest that the hip and the ankle eigenmovements can be treated as independently controlled motion units aimed at functionally different behavioral goals: the bending per se and postural adjustment. It is proposed that the central nervous system has to control these motion units sequentially in order to perform the movement and maintain equilibrium. It is also suggested that the hip and ankle eigenmovements can be regarded as a biomechanical background for the hip and ankle strategies introduced by Horak and Nashner (1986) on the basis of electromyographic recordings and kinematic patterns in response to postural perturbations.

Assessment of the accuracy of a human arm model with seven degrees of freedom.

We are proposing a human arm model that consists of three rigid segments with seven degrees of freedom. The shoulder joint was modeled as a ball-and-socket joint and the elbow and wrist joints were modelled as skew-oblique joints. Optimal parameters for this model were calculated on the base of in vivo recordings with a spatial tracking system. The criterion of optimality was defined as the minimum of the mean-square deviation between the experimentally obtained sensor positions and orientations and their positions and orientations calculated by solving the direct kinematics problem. The minimal value of the direct kinematics error was found to be 0.5-0.6cm for sensor positions and 5-7 degrees for sensor orientations. We are proposing that these values serve as the assessment for the accuracy of the arm model.

Forearm postural control during unloading: anticipatory changes in elbow stiffness

Abstract In this study, the equilibrium-point hypothesis of muscle-torque generation is used to evaluate the changes in central control parameters in the process of postural-maintenance learning. Muscle torque is described by a linear spring equation with modifiable stiffness, viscosity, and equilibrium angle. The stiffness is considered to be the estimation of the central command for antagonist-muscle coactivation and the equilibrium angle to be the estimation of the reciprocal command for a shift of invariant characteristics of the joint. In the experiments, a load applied to the forearm was released. The subjects were instructed to maintain their forearm in the initial horizontal position. Five sessions of approximately twenty trials each were carried out by eight subjects. During two ”control” series, the load release was triggered by the experimenter. During three ”learning” series, the load supported by one forearm was released by the subject’s other hand. The elbow-joint angle, the angular acceleration, and the external load on the postural forearm were recorded. These recordings as well as anthropometric forearm characteristics were used to calculate the elbow-joint torque (which we called ”experimental”). Linear regression analysis was performed to evaluate the equilibrium angle, joint stiffness, and viscosity at each trial. The ”theoretical” torque was calculated using a linear spring equation with the found parameters. The good agreement observed between experimental and theoretical joint-torque time courses, apart from the very early period following unloading, argues in favor of the idea that the movement was mainly performed under a constant central command presetting the joint stiffness and the equilibrium angle. An overall increase in the stiffness occurred simultaneously with a decrease in the equilibrium angle during the ”learning” series in all the subjects. This suggests that subjects learn to compensate for the disturbing effects of unloading by increasing the joint stiffness. The mechanism possibly responsible for the presetting of the central control parameters is discussed.