A possible correlation between the basal ganglia motor function and the inverse kinematics calculation

The main hypothesis of this study, based on experimental data showing the relations between the BG activities and kinematic variables, is that BG are involved in computing inverse kinematics (IK) as a part of planning and decision-making. Indeed, it is assumed that based on the desired kinematic variables (such as velocity) of a limb in the workspace, angular kinematic variables in the joint configuration space are calculated. Therefore, in this paper, a system-level computational model of BG is proposed based on geometrical rules, which is able to compute IK. Next, the functionality of each part in the presented model is interpreted as a function of a nucleus or a pathway of BG. Moreover, to overcome existing redundancy in possible trajectories, an optimization problem minimizing energy consumption is defined and solved to select an optimal movement trajectory among an infinite number of possible ones. The validity of the model is checked by simulating it to control a three-segment manipulator with rotational joints in a plane. The performance of the model is studied for different types of movement including different reaching movements, a continuous circular movement and a sequence of tracking movements. Furthermore, to demonstrate the physiological similarity of the presented model to the BG structure, the neuronal activity of each part of the model considered as a BG nucleus is verified. Some changes in model parameters, inspired by the dopamine deficiency, also allow simulating some symptoms of Parkinson’s disease such as bradykinesia and akinesia.     

Deducing planning variables from experimental arm trajectories: Pitfalls and possibilities

This paper investigates whether endpoint Cartesian variables or joint variables better describe the planning of human arm movements. For each of the two sets of planning variables, a coordination strategy of linear interpolation is chosen to generate possible trajectories, which are to be compared against experimental trajectories for best match. Joint interpolation generates curved endpoint trajectories calledN-leaved roses. Endpoint Cartesian interpolation generates curved joint trajectories, which however can be qualitatively characterized by joint reversal points.Though these two sets of planning variables ordinarily lead to distinct predictions under linear interpolation, three situations are pointed out where the two strategies may be confused. One is a straight line through the shoulder, where the joint trajectories are also straight. Another is any trajectory approaching the outer boundary of reach, where the joint rate ratio always appears to be approaching a constant. A third is a generalization to staggered joint interpolation, where endpoint trajectories virtually identical to straight lines can sometimes be produced. In examining two different sets of experiments, it is proposed that staggered joint interpolation is the underlying planning strategy.     

Constraints for joint angle control of the human arm

The targeting movements of a human arm were examined when restricted to a horizontal plane. The three joints at shoulder, elbow, and wrist are allowed to move. Thus, the system is redundant and needs constraints. A model calculation using a simple form of constraint is found to describe the experimental results: a cost function is applied to each joint. The constraint consists in minimizing the sum of the costs of all three joints. The cost functions might be interpreted as to describing the energy cost necessary to move the joint and/or represent a mechanism which avoids singularities.     

Identification of passive elastic joint moments in the lower extremities.

Musculotendon actuators produce active and passive moments at the joints they span. Due to the existence of bi-articular muscles, the passive elastic joint moments are influenced by the angular positions of adjacent joints. To obtain quantitative information about this passive elastic coupling between lower limb joints, we examined the passive elastic joint properties of the hip, knee, and ankle joint of ten healthy subjects. Passive elastic joint moments were found to considerably depend on the adjacent joint angles. We present a simple mathematical model that describes these properties on the basis of a double-exponential expression. The model can be implemented in biomechanical models of the lower extremities, which are generally used for the simulation of multi-joint movements such as standing-up, walking, running, or jumping.     

A network model for the control of the movement of a redundant manipulator

In an earlier investigation (Cruse and Brüwer 1987) an algorithmic model was proposed which describes targeting movements of a human arm when restricted to a horizontal plane. As three joints at shoulder, elbow and wrist are allowed to move, the system is redundant. Two models are discussed here which replace this algorithmic model by a network model. Both networks solve the static problem, i.e. they provide the joint angles which the arm has to adopt in order to reach a given point in the workspace. In the first model the position of this point is given in the form ofx —y coordinates, the second model obtains this information by means of a retina-like input layer. The second model is expanded by a simple procedure to describe movements from a start to an end point. The results qualitatively correspond to those obtained from human subjects. The advantages of the network models in comparison to the algorithmic model are discussed.     

Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps

A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk-head-arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum-height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models' prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.     

The linear co-variance between joint muscle torques is not a generalized principle

In 1996, Gottlieb et al. [Gottlieb GL, Song Q, Hong D, Almeida GL, Corcos DM. Coordinating movement at two joints: A principle of linear covariance. J Neurophysiol 1996;75(4):1760–4] identified a linear co-variance between the joint muscle torques generated at two connected joints. The joint muscle torques changed directions and magnitudes in a synchronized and linear fashion and called it the principle of linear co-variance. Here we showed that this principle cannot hold for some class of movements. Neurologically normal subjects performed multijoint movements involving elbow and shoulder with reversal towards three targets in the sagittal plane without any constraints. The movement kinematics was calculated using the X and Y coordinates of the markers positioned over the joints. Inverse dynamics was used to calculate the joint muscle, interaction and net torques. We found that for the class of voluntary movements analyzed, the joint muscle torques of the elbow and the shoulder were not linearly correlated. The same was observed for the interaction torques. But, the net torques at both joints, i.e., the sum of the interaction and the joint muscle torques were linearly correlated. We showed that by decoupling the joint muscle torques, but keeping the net torques linearly correlated, the CNS was able to generate fast and accurate movements with straight fingertip paths. The movement paths were typical of the ones in which the joint muscle torques were linearly correlated.     

Motor program coding representation from a handwriting generator model: The production of line responses

In this paper, a model is employed that describes handwriting behaviors activated by curvilinear and angular velocity generators postulated to initiate and regulate pen tip velocity profiles. This model accounts for the observed differences between straight and curved line production and the effect of movement precues on these responses. Of particular interest is the observed interaction between precue information and line execution type for reaction time. It is shown that differences in reaction time can be explained by the model as a function of the number of parameters that need to be specified. Moreover, there is some evidence that the biomechanical system reacts in a privileged manner to command pulses for specific directions, and that the central nervous system attempts to compensate for these asymmetries. These data are some of the first to show that the benefits of precue extend beyond reaction time and that movement execution characteristics are influenced by motor preparation.     

The relationship between joint strength and standing vertical jump performance

The effect of joint strengthening on standing vertical jump height is investigated by computer simulation. The human model consists of five rigid segments representing the feet, shanks, thighs, HT (head and trunk), and arms. Segments are connected by frictionless revolute joints and model movement is driven by joint torque actuators. Each joint torque is the product of maximum isometric torque and three variable functions of instantaneous joint angle, angular velocity, and activation level, respectively. Jumping movements starting from a balanced initial posture and ending at takeoff are simulated. A matching simulation reproducing the actual jumping movement is generated by optimizing joint activation level. Simulations with the goal of maximizing jump height are repeated for varying maximum isometric torque of one joint by up to +/-20% while keeping other joint strength values unchanged. Similar to previous studies, reoptimization of activation after joint strengthening is necessary for increasing jump height. The knee and ankle are the most effective joints in changing jump height (by as much as 2.4%, or 3 cm). For the same amount of percentage increase/decrease in strength, the shoulder is the least effective joint (which changes height by as much as 0.6%), but its influence should not be overlooked.     

Motion analysis of leg joints associated with escape turns of the cockroach,Periplaneta americana

Considerable information is now available on the neural organization of the escape system of the American cockroach. To relate these data to the behavior, we need detailed information on the movements made at the principle leg joints that produce the turn. We used motion analysis of high speed video records to acquire such information. Records from both free ranging and tethered animals were analyzed. 1. We analyzed individual joint movements using a tethered preparation. Stimuli from 4 different angles around the animal were used. For all wind angles, the femur-tibia (FT) joint on the mesothoracic leg that is ipsilateral to the wind source extended while the contralateral mesothoracic FT joint flexed. This moved both of these legs laterally toward the wind source. In freely moving animals the FT movements provide forces that turn the animal away from the wind source. 2. The ipsilateral mesothoracic coxa-femur (CF) joint extended for all wind angles. The contralateral mesothoracic CF joint extended in response to most winds from the rear, but switched to flexion in response to wind from the side and front. As a result of these joint movements, rear wind resulted in rearward movements of the contralateral mesothoracic leg, while side and front wind resulted in more forward movements of that leg. 3. The CF and FT joints for both ipsilateral and contralateral metathoracic legs extended to wind from the rear and switched to flexion as the wind was placed at more anterior positions around the animal. In freely moving animals, extension of these joints would push the animal forward. Flexion would pull the animal backward. 4. Several of the joints showed correlations between rate of movement and initial joint angle. That is, joints that were already flexed at the onset of stimulation tended to move at a faster rate to a final position than joints that started at a more extended position. 5. Metathoracic FT and CF joints showed a high degree of positive correlation during the escape movements. Indeed, many curves showing movement of metathoracic FT and CF joints with time were virtually identical.     

The three-dimensional kinematics and flexibility characteristics of the human ankle and subtalar joints--Part I: Kinematics

The in-vitro, three dimensional kinematic characteristics of the human ankle and subtalar joint were investigated in this study. The main goals of this investigation were: 1) To determine the range of motion of the foot-shank complex and the associated range of motion of the ankle and subtalar joints; 2) To determine the kinematic coupling characteristics of the foot-shank complex, and 3) To identify the relationship between movements at the ankle and subtalar joints and the resulting motion produced between the foot and the shank. The tests were conducted on fifteen fresh amputated lower limbs and consisted of incrementally displacing the foot with respect to the shank while the motion of the articulating bones was measured through a three dimensional position data acquisition system. The kinematic analysis was based on the helical axis parameters describing the incremental displacements between any two of the three articulating bones and on a joint coordinate system used to describe the relative position between the bones. From the results of this investigation it was concluded that: 1) The range of motion of the foot-shank complex in any direction (dorsiflexion/plantarflexion, inversion/eversion and internal rotation/external rotation) is larger than that of either the ankle joint or the subtalar joint.; 2) Large kinematic coupling values are present at the foot-shank complex in inversion/eversion and in internal rotation/external rotation. However, only a slight amount of coupling was observed to occur in dorsiflexion/plantarflexion.; 3) Neither the ankle joint nor the subtalar joint are acting as ideal hinge joints with a fixed axis of rotation.; 4) Motion of the foot-shank complex in any direction is the result of rotations at both the ankle and the subtalar joints. However, the contribution of the ankle joint to dorsiflexion/plantarflexion of the foot-shank complex is larger than that of the subtalar joint and the contribution of the subtalar joint to inversion/eversion is larger than that of the ankle joint.; 5) The ankle and the subtalar joints have an approximately equal contribution to internal rotation/external rotation movements of the foot-shank complex.     

Leg kinematics and muscle activity during treadmill running in the cockroach, Blaberus discoidalis : I. Slow running

We have combined high-speed video motion analysis of leg movements with electromyogram (EMG) recordings from leg muscles in cockroaches running on a treadmill. The mesothoracic (T2) and metathoracic (T3) legs have different kinematics. While in each leg the coxa-femur (CF) joint moves in unison with the femur-tibia (FT) joint, the relative joint excursions differ between T2 and T3 legs. In T3 legs, the two joints move through approximately the same excursion. In T2 legs, the FT joint moves through a narrower range of angles than the CF joint. In spite of these differences in motion, no differences between the T2 and T3 legs were seen in timing or qualitative patterns of depressor coxa and extensor tibia activity. The average firing frequencies of slow depressor coxa (Ds) and slow extensor tibia (SETi) motor neurons are directly proportional to the average angular velocity of their joints during stance. The average Ds and SETi firing frequency appears to be modulated on a cycle-by-cycle basis to control running speed and orientation. In contrast, while the frequency variations within Ds and SETi bursts were consistent across cycles, the variations within each burst did not parallel variations in the velocity of the relevant joints. Accepted: 24 May 1997     

Movement curvature planning through force field internal models

Human motion studies have focused primarily on modeling straight point-to-point reaching movements. However, many goal-directed reaching movements, such as movements directed towards oneself, are not straight but rather follow highly curved trajectories. These movements are particularly interesting to study since they are essential in our everyday life, appear early in development and are routinely used to assess movement deficits following brain lesions. We argue that curved and straight-line reaching movements are generated by a unique neural controller and that the observed curvature of the movement is the result of an active control strategy that follows the geometry of one’s body, for instance to avoid trajectories that would hit the body or yield postures close to the joint limits. We present a mathematical model that accounts for such an active control strategy and show that the model reproduces with high accuracy the kinematic features of human data during unconstrained reaching movements directed toward the head. The model consists of a nonlinear dynamical system with a single stable attractor at the target. Embodiment-related task constraints are expressed as a force field that acts on the dynamical system. Finally, we discuss the biological plausibility and neural correlates of the model’s parameters and suggest that embodiment should be considered as a main cause for movement trajectory curvature.     

Similarities in the Neural Control of the Shoulder and Elbow Joints Belie Their Structural Differences

Movement of the hand in three dimensional space is primarily controlled by the orientation of the shoulder and elbow complexes. Due to discrepancies in proprioceptive acuity, overlap in motor cortex representation and grossly different anatomies between these joints, we hypothesized that there would be differences in the accuracy of aimed movements between the two joints. Fifteen healthy young adults were tested under four conditions – shoulder motion with the elbow constrained and unconstrained, and elbow motion with the shoulder constrained and unconstrained. End point target locations for each joint were set to coincide with joint excursions of 10, 20 or 30 degrees of either the shoulder or elbow joint. Targets were presented in a virtual reality environment. For the constrained condition, there were no significant differences in angular errors between the two joints, suggesting that the central nervous system represents linked segment models of the limb in planning and controlling movements. For the unconstrained condition, although angle errors were higher, hand position errors remained the same as those of the constrained trials. These results support the idea that the CNS utilizes abundant degrees of freedom to compensate for the potentially different contributions to end-point errors introduced by each joint.     

The three-dimensional kinematics and flexibility characteristics of the human ankle and subtalar joint--Part II: Flexibility characteristics

The objective of the present study was to investigate the in-vitro, coupled, three-dimensional load-displacement and flexibility characteristics of the human ankle joint complex consisting of the talocrural and the talocalcaneal joints and to determine the effects that sectioning of the anterior talofibular ligament has on these characteristics. Similar to other anatomical joints such as the knee and the intervertebral joint, the ankle joint complex was found to exhibit highly nonlinear load-displacement characteristics with the angular displacement approaching asymptotic values as the external load was increased. Therefore, a procedure of incremental linearization was used to derive the flexibility characteristics of this structure. According to this procedure, external loads were applied to the calcaneus in small increments and its resulting three dimensional displacements were recorded. The incremental flexibility coefficients were then derived by assuming linear load-displacement relationship for each increment. From the results obtained from fifteen human ankle specimens, it was evident that the ankle joint complex exhibit highly coupled flexibility and load-displacement characteristics. It was further concluded that the ankle joint complex is the most flexible in the neighborhood of the unloaded, neutral position and that all the flexibility coefficients of the structure decrease rapidly toward the extremes of the range of motion. Rupture of the anterior talofibular ligament was found to have a significant effect on the load-displacement and flexibility characteristics of the ankle joint complex. This effect was manifested as a change in the load-displacement characteristics and a large increase in the flexibility coefficients primarily in those corresponding to rotations in the transverse and the coronal plane. The results of the present study can provide the necessary data base for the development of quantitative diagnostic technique for identifying the site and the extent of injury to the collateral ligaments of the ankle.     

Dynamics of the in-run in ski jumping: a simulation study

A ski jumper tries to maintain an aerodynamic position in the in-run during changing environmental forces. The purpose of this study was to analyze the mechanical demands on a ski jumper taking the in-run in a static position. We simulated the in-run in ski jumping with a 4-segment forward dynamic model (foot, leg, thigh, and upper body). The curved path of the in-run was used as kinematic constraint, and drag, lift, and snow friction were incorporated. Drag and snow friction created a forward rotating moment that had to be counteracted by a plantar flexion moment and caused the line of action of the normal force to pass anteriorly to the center of mass continuously. The normal force increased from 0.88 G on the first straight to 1.65 G in the curve. The required knee joint moment increased more because of an altered center of pressure. During the transition from the straight to the curve there was a rapid forward shift of the center of pressure under the foot, reflecting a short but high angular acceleration. Because unrealistically high rates of change of moment are required, an athlete cannot do this without changing body configuration which reduces the required rate of moment changes.     

A kinematic model of the shoulder complex to evaluate the arm-reachable workspace

Upper-arm evaluation including shoulder motion in physiotherapy has no three-dimensional tool for an arm-functioning evaluation, which hampers an uniform, objective comparison. Human shoulder complex models suffer from lack of shoulder girdle kinematic data. A kinematic shoulder-complex model with six degrees of freedom is proposed as the composition of the inner joint representing the shoulder-girdle joints and outer joint representing the glenohumeral joint. The outer shoulder joint has three perpendicular rotations: adduction/abduction, retroflexion/flexion and internal/external rotation of the humerus. The inner shoulder joint has two rotations, depression/elevation and retraction/protraction, and one translation, which are all dependent on the elevation angle of the humerus. The human arm-reachable workspace that represents the area within reach of the wrist is calculated on the basis of the shoulder-complex model and the additional elbow-joint direct kinematics. It was demonstrated that cross-sections of the calculated workspace are in agreement with the measured arm-reachable workspace in all three anatomical planes. The arm-reachable workspace volume and graphics were calculated and a comparison of the arm's workspaces during a patient's shoulder treatment was made. The obtained numerical and graphical arm-reachable workspaces can be used for arm-functioning evaluations in rehabilitation and ergonomics.     

Moiré patterns: an accurate technique for determination of the locus of the centres of rotation

This study describes an accurate technique for the determination of the centre of rotation of small angles. The moiré fringe method localizes the centre of rotation by defining two primary fringes, each of which is found by the intersection of three lines. The primary fringes intersect at the centre of rotation at 90 degrees to each other, the angle least likely to produce an error in measurement. By utilizing joints with known centres of rotation, we have found that the method is extremely accurate and reproducible to within 2 mm of the real centre for angular changes as small as 3 degrees. This technique is useful in evaluating whether a joint is a simple hinge, i.e. rotating about a single axis of rotation or whether the joint moves about a changing axis of rotation referred to as a locus or centrode.     

The red-fin Decapterus group (Perciformes: Carangidae) with the description of a new species, Decapterus smithvanizi

The carangid genus Decapterus can be defined by having a single finlet behind both the second dorsal and anal fins, and lacking scutes on the anterior curved part of the lateral line. We revised taxonomically the species of Decapterus with red-colored caudal fins (the red-fin Decapterus group) and established that the group consisted of the following four species: Decapterus akaadsi Abe 1958, distributed in the eastern Indian Ocean and West Pacific from the Andaman Sea to Indonesia, north to central Japan; Decapterus kurroides Bleeker 1855, distributed in the Indo-West Pacific from the Red Sea and eastern coast of Africa to eastern Australia, north to the Philippines; Decapterus smithvanizi sp. nov., occurring in the Andaman Sea, the South China Sea, and Indonesia; and Decapterus tabl Berry 1968, distributed circumglobally in tropical and subtropical seas. The diagnostic characters of these species are as follows: D. akaadsi—curved part of lateral line with 43–53 cycloid scales, straight part of lateral line with 26–29 scutes, head length 26.7–30.1 % SL, and body depth 24.0–27.9 % SL; D. kurroides—curved part of lateral line with 45–51 cycloid scales, straight part of lateral line with 30–32 scutes, head length 30.3–33.0 % SL, and body depth 23.4–26.4 % SL; D. smithvanizi—lower gill rakers 25–31, curved part of lateral line with 54–62 cycloid scales, body depth 19.4–22.5 % SL, pectoral-fin tip usually beyond the level of second dorsal-fin origin; D. tabl—tip of upper jaw usually hooked and opercular membrane partly serrated in larger specimens, lower gill rakers 28–33, curved part of lateral line with 61–72 cycloid scales, body depth 16.6–23.0 % SL, pectoral-fin tip not reaching to the level of second dorsal-fin origin.