A mathematical model of hind-limb control in cats when walking backward

The “walking backward” mode was achieved within a single model of cat hind-limb locomotion with the balance maintenance only due to a change in the controlling actions (in addition to the “forward walking” mode). The skeletal part of the model contains the spine, pelvis, and two limbs consisting of the thigh, shin, and foot. The hip joint and spine mount in the thoracic region have three degrees of freedom; the knee and ankle joints have one degree of freedom. The pelvis is rigidly connected to the spine. Control is performed by model muscles (flexors and extensors of the thigh, shin, and foot). The muscle activation is performed by the effects that are typical for motoneurons that control the muscles. The feet in the support phase touch the treadmill, which moves at a constant speed. The model qualitatively reproduces multiple characteristics of feline movements during forward and backward walking (supporting its validity).     

A method to predict muscle control in the kinematically and mechanically indeterminate human masticatory system

A method is proposed to generate muscle activation patterns for goal-directed movements of the human masticatory system. This system is special because apart from a larger amount of muscles than degrees of freedom its joints do not restrict its movements a priori. Therefore, each muscle is able to influence all six degrees of freedom which makes the system kinematically and mechanically indeterminate. Furthermore, its working space is principally determined by the dynamical properties of its muscles and not by passive constraints.The presented method determines the contribution of each degree of freedom to a movement of a reference point on the mandible. It avails of straightforward mathematical techniques like Linear Programming. It does not require a separate trajectory planning step. It was applied in a six degrees of freedom dynamical mathematical model of the human masticatory system. This model which was based upon rigid-body dynamics incorporating skull morphology and muscle architecture including dynamical properties. Movements were exclusively defined by a goal position of the mandibular reference point.The method proved to be robust in generating muscle activation patterns for both feasible and infeasible movement tasks. Generally, they were accomplished faster than habitually observed. If the task was infeasible the movement stopped at the outer boundary of the working space at the side of the unreachable goal. The method, therefore, enables to explore the working space of the mandible and the factors that are relevant for its boundaries.     

A three channel radio-controlled brain-stimulator for unrestrained animals

We have developed a project for biological radio-controlled electrostimulation, consisting in a three channel telestimulator, which has been used in our laboratories on animals unrestrained and complete freedom of movements. The system has been tested and used in many experiments which excellent results.     

Contribution of changes in translational, rotational, and vibrational degrees of freedom to the energy of complex formation of aromatic ligands with DNA

A method for calculation and analysis of the contribution of changes in translational, rotational, and vibrational degrees of freedom to the energy of complex formation of aromatic compounds with DNA duplex has been developed. The results of calculations of the thermodynamic parameters (ΔG, ΔH, ΔS) indicate that changes in the translational and rotational degrees of freedom destabilize, and changes in the vibrational degree of freedom stabilize the complexes, the energy contribution from the movements under consideration being predominantly of entropic character. It is shown that the energy components of changes in translational, rotational, and vibrational degrees of freedom are in the main comparable with the experimentally determined thermodynamic parameters, which requires consideration of these components in the energy analysis of complex formation of aromatic molecules with DNA. It has been found that the total contribution of changes in translational, rotational, and vibrational degrees of freedom to the Gibbs energy of complexing of aromatic molecules with DNA can be assumed to be on the average the same for different ligands and equal to 8.2 kcal/mol.     

Determination of the number of degrees of freedom of the trapeziometacarpal joint–An in vitro study

ObjectiveMost of the studies about trapeziometacarpal joint assume that it exhibits only two independent degrees of freedom, but the experimental or theoretical support for considering a two-degrees of freedom model is not always clear.Materials and methodsTherefore, an in vitro kinematic study has been designed to demonstrate, from experimental data, that only two of the trapeziometacarpal degrees of freedom (i.e., flexion/extension and adduction/abduction) are non-null and independent. Several movements of maximal amplitude in flexion, abduction and circumduction have been realized and the relative position and orientation of the segment coordinate system embedded on the first metacarpal with respect to that embedded on the trapezium have been collected using electromagnetic sensors. The trapeziometacarpal rotations have been described using a joint coordinate system and the joint displacements have been evaluated on the axes of this coordinate system.ResultsThe root mean square (RMS) values of the joint displacement components have been found small enough to assume that the trapeziometacarpal joint has no translation degrees of freedom. A paraboloid coupling equation has been found between the internal/external rotation angle and the two other, flexion/extension and adduction/abduction, angles.ConclusionThus, this study demonstrates that the trapeziometacarpal joint has only two independent rotational degrees of freedom, and further, the described methodology could also be used to determine the coupling laws between degrees of freedom of various joints.     

Flexibility and Repeatability of Finger Movements During Typing: Analysis of Multiple Degrees of Freedom

The kinematics of the hand and fingers were studied during various keystrokes in typing. These movements were defined by 17 degrees of freedom of motion, and methods were developed to identify simplifying strategies inthe execution of the task. Most of the analysis was restrictedto the 11 degrees of freedom of the fingers, neglecting thumband wrist motion. Temporal characteristics of the motion weredefined by computing principal components, and it was found thatonly a few (two to four) principal components were needed tocharacterize motion of each of the degrees of freedom.Hierarchical relationships among patterns within and betweendifferent degrees of freedom were identified using clusteranalysis. There was a considerable amount of consistency eachtime a given keystroke was executed by a subject, and thisrepeatability may imply a reduction in the number of degrees offreedom independently controlled by the nervous system. However,there also appears to be considerable flexibility in thecoordination of the many joints of the hand when examined acrossdifferent keys and across different subjects.     

The use of matrices in analyzing the three-dimensional behavior of the vestibulo-ocular reflex

The vestibulo-ocular reflex rotates the eye about the axis of a head rotation at the same speed but in the opposite direction to make the visual axes in space independent of head motion. This reflex works in all three degrees of freedom: roll, pitch, and yaw. The rotations may be described by vectors and the reflex by a transformation in the form of a matrix. The reflex consists of three parts: sensory, central, and motor. The transduction of head rotation into three neural signals, which may also be described by a vector, is described by a canal matrix. The neural, motorcommand vector is transformed to an eye rotation by a muscle matrix. Since these two matrices are known, one can solve for the central matrix which gives the strength of the connections between all the vestibular neurons and all the eye-muscle motoneurons. The role of the metric tensor in these transformations is described. This method of analysis is used in three applications. A lesion may be simulated by altering the elements in any or all of the three component matrices. By matrix multiplication, the resulting abnormal behavior of the reflex can be described quantitatively in all degrees of freedom. The method is also used to directly compare the differences in brain-stem connections between humans and rabbits that accommodate the altered actions of the muscles of the two species. Finally the method allows a quantitative assessment of the changes that take place in the brainstem connections when plastic changes are induced by artificially dissociating head movements from apparent motion of the visual environment.     

Adaptive cerebellar spiking model embedded in the control loop: context switching and robustness against noise

This work evaluates the capability of a spiking cerebellar model embedded in different loop architectures (recurrent, forward, and forward&recurrent) to control a robotic arm (three degrees of freedom) using a biologically-inspired approach. The implemented spiking network relies on synaptic plasticity (long-term potentiation and long-term depression) to adapt and cope with perturbations in the manipulation scenario: changes in dynamics and kinematics of the simulated robot. Furthermore, the effect of several degrees of noise in the cerebellar input pathway (mossy fibers) was assessed depending on the employed control architecture. The implemented cerebellar model managed to adapt in the three control architectures to different dynamics and kinematics providing corrective actions for more accurate movements. According to the obtained results, coupling both control architectures (forward&recurrent) provides benefits of the two of them and leads to a higher robustness against noise.     

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.     

Octopuses use a human-like strategy to control precise point-to-point arm movements

One of the key problems in motor control is mastering or reducing the number of degrees of freedom (DOFs) through coordination. This problem is especially prominent with hyper-redundant limbs such as the extremely flexible arm of the octopus. Several strategies for simplifying these control problems have been suggested for human point-to-point arm movements. Despite the evolutionary gap and morphological differences, humans and octopuses evolved similar strategies when fetching food to the mouth. To achieve this precise point-to-point-task, octopus arms generate a quasi-articulated structure based on three dynamic joints. A rotational movement around these joints brings the object to the mouth . Here, we describe a peripheral neural mechanism-two waves of muscle activation propagate toward each other, and their collision point sets the medial-joint location. This is a remarkably simple mechanism for adjusting the length of the segments according to where the object is grasped. Furthermore, similar to certain human arm movements, kinematic invariants were observed at the joint level rather than at the end-effector level, suggesting intrinsic control coordination. The evolutionary convergence to similar geometrical and kinematic features suggests that a kinematically constrained articulated limb controlled at the level of joint space is the optimal solution for precise point-to-point movements.     

A method for estimating three-dimensional human arm movement with two electromagnetic sensors

Measurement of upper-limb movements is important in various domains. In this article, an upper-limb three-dimensional movement recording technique is proposed based on only two electromagnetic sensors. Two joints are considered with a total of seven degrees of freedom (DoF; three translations and four rotations). The chosen sequence of joint rotations is compliant with ISB recommendations: the shoulder is modelled with a ball and socket joint with three DoF and the elbow with a one DoF revolute joint. This article is focused on the procedure used to calibrate and sense the upper-limb movements from the raw data coming from the flock of birds sensors. The principle of the method is to define the centre of the wrist, elbow and shoulder joints in the frame of the adequate sensor. This operation is done by performing calibration gestures. Results are proposed and commented.     

A method for estimating three-dimensional human arm movement with two electromagnetic sensors

Measurement of upper-limb movements is important in various domains. In this article, an upper-limb three-dimensional movement recording technique is proposed based on only two electromagnetic sensors. Two joints are considered with a total of seven degrees of freedom (DoF; three translations and four rotations). The chosen sequence of joint rotations is compliant with ISB recommendations: the shoulder is modelled with a ball and socket joint with three DoF and the elbow with a one DoF revolute joint. This article is focused on the procedure used to calibrate and sense the upper-limb movements from the raw data coming from the flock of birds sensors. The principle of the method is to define the centre of the wrist, elbow and shoulder joints in the frame of the adequate sensor. This operation is done by performing calibration gestures. Results are proposed and commented.     

Variational Principles in the Mechanics of Conformational Motions of Macromolecules in a Viscous Medium

The mechanics of the conformational motions of macromolecules due to rotations around the valence bonds in a viscous medium have been considered. The variational principles for the energy-dissipation rate during conformational motions in a viscous medium and the rate of the potential energy decrease of a macromolecule during conformational relaxation have been analyzed. The seeming contradiction between this principle and the principle of the minimum energy-dissipation rate is resolved. It is shown that the energy-dissipation rate must be optimal and minimal in order to simultaneously satisfy the conservation laws and fulfill the deterministic nature of classical trajectories. The generalization and analysis of the influence of thermal fluctuations and external forces on the variational principles for the conformational relaxation of macromolecules is carried out. A visual graphical geometric depiction has been developed using hyperspheres in the space of the velocities of chain nodes to describe conformational movements along many degrees of freedom in a viscous medium. The equipartition of the energy-dissipation rates (and the rates of potential energy decrease) among the conformational degrees of freedom is discussed.     

Vibrissal kinematics in 3D: tight coupling of azimuth, elevation, and torsion across different whisking modes

Perception is usually an active process by which action selects and affects sensory information. During rodent active touch, whisker kinematics influences how objects activate sensory receptors. In order to fully characterize whisker motion, we reconstructed whisker position in 3D and decomposed whisker motion to all its degrees of freedom. We found that, across behavioral modes, in both head-fixed and freely moving rats, whisker motion is characterized by translational movements and three rotary components: azimuth, elevation, and torsion. Whisker torsion, which has not previously been described, was large (up to 100 degrees), and torsional angles were highly correlated with whisker azimuths. The coupling of azimuth and torsion was consistent across whisking epochs and rats and was similar along rows but systematically varied across rows such that rows A and E counterrotated. Torsional rotation of the whiskers enables contact information to be mapped onto the circumference of the whisker follicles in a predictable manner across protraction-retraction cycles.     

Hand function: peripheral and central constraints on performance.

The hand is one of the most fascinating and sophisticated biological motor systems. The complex biomechanical and neural architecture of the hand poses challenging questions for understanding the control strategies that underlie the coordination of finger movements and forces required for a wide variety of behavioral tasks, ranging from multidigit grasping to the individuated movements of single digits. Hence, a number of experimental approaches, from studies of finger movement kinematics to the recording of electromyographic and cortical activities, have been used to extend our knowledge of neural control of the hand. Experimental evidence indicates that the simultaneous motion and force of the fingers are characterized by coordination patterns that reduce the number of independent degrees of freedom to be controlled. Peripheral and central constraints in the neuromuscular apparatus have been identified that may in part underlie these coordination patterns, simplifying the control of multi-digit grasping while placing certain limitations on individuation of finger movements. We review this evidence, with a particular emphasis on how these constraints extend through the neuromuscular system from the behavioral aspects of finger movements and forces to the control of the hand from the motor cortex.     

Biologically inspired kinematic synergies enable linear balance control of a humanoid robot

Despite many efforts, balance control of humanoid robots in the presence of unforeseen external or internal forces has remained an unsolved problem. The difficulty of this problem is a consequence of the high dimensionality of the action space of a humanoid robot, due to its large number of degrees of freedom (joints), and of non-linearities in its kinematic chains. Biped biological organisms face similar difficulties, but have nevertheless solved this problem. Experimental data reveal that many biological organisms reduce the high dimensionality of their action space by generating movements through linear superposition of a rather small number of stereotypical combinations of simultaneous movements of many joints, to which we refer as kinematic synergies in this paper. We show that by constructing two suitable non-linear kinematic synergies for the lower part of the body of a humanoid robot, balance control can in fact be reduced to a linear control problem, at least in the case of relatively slow movements. We demonstrate for a variety of tasks that the humanoid robot HOAP-2 acquires through this approach the capability to balance dynamically against unforeseen disturbances that may arise from external forces or from manipulating unknown loads.     

The simulation of aerial movement--III. The determination of the angular momentum of the human body

A method is presented for determining the angular momentum of the human body about its mass centre for general three-dimensional movements. The body is modelled as an 11 segment link system with 17 rotational degrees of freedom and the angular momentum of the body is derived as a sum of 12 terms, each of which is a vector function of just one angular velocity. This partitioning of the angular momentum vector gives the contribution due to the relative segmental movement at each joint rather than the usual contribution of each segment. A method of normalizing the angular momentum is introduced to enable the comparison of rotational movements which have different flight times and are performed by athletes with differing inertia parameters. Angular momentum estimates were calculated during the flight phases of nine twisting somersaults performed on trampoline. Errors in film digitization made large contributions to the angular momentum error estimates. For individual angular momentum estimates the relative error is estimated to be about 10% whereas for mean angular momentum estimates the relative error is estimated to be about 1%.     

The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements.     

Concurrent validity and reliability of a mobile tracking technology to measure angular and linear movements of the neck

The neck can be moved in six degrees of freedom. Current 3D-optoelectronic motion-capture systems capable of measuring these movements are inappropriate for use in clinical practice because they are stationary, expensive and time-consuming. We therefore developed a less complex 3D-tracking technology based on Steam®VR to measure six degrees of freedom in a clinical setting. The aim of this study was to assess the validity and reliability of this system.The developed prototype consists of two infrared-emitting lighthouses and sensors, mounted on the participant’s helmet and trunk belt, to detect the orientation of the head and trunk. The system was evaluated by means of an infrared light-reflecting marker tracking system. Twenty healthy participants, equipped with these sensors and markers, performed thirteen neck movement tasks. Linear and angular movements were measured. These tasks were repeated after six to eight days to assess test-retest reliability. Concurrent validity was assessed by the root mean square error, and reliability with generalizability theory.With an average root mean square error between 1.2 and 2.0° in angular and 0.4–0.5 cm in linear movements, the prototype was shown to precisely track these movements. Reliability of the prototype and the reference system was comparable for all tasks. A high contribution of participant’s variability to the observed variance was generally detected, with the exception of joint repositioning error and upper cervical flexion.The reliability was task-specific and did not differ between the systems. The prototype system was shown to be valid, although the reliability of the repositioning and upper cervical flexion tests needs to be reconsidered.