Multi-joint Mechanics Dr. Ted Milner (KIN 416)

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1 Multi-joint Mechanics Dr. Ted Milner (KIN 416) Muscle Function and Activation It is not a straightforward matter to predict the activation pattern of a set of muscles when these muscles act on multiple limb segments or about multiple axes of rotation. Whether a muscle acts as an agonist, antagonist or stabilizer will depend on factors such as joint angles, link lengths, moment arms and force directions. In many cases, one muscle will couple joint torques about two axes of rotation, such as the biceps brachii, which couples elbow flexion and supination. This coupling will often produce undesired torques that must be counterbalanced by other muscles. Similarly, shoulder muscles may contribute to force in both desired and undesired directions at the hand. Again, these undesired forces must be counterbalanced by the actions of muscles which produce forces in opposite directions. When the direction of force at the endpoint of the limb is being controlled, e.g., at the hand, the contribution of a muscle to the endpoint force will depend on the orientation of the joint which it spans. For example, when the arm is held at the side with the upper arm vertical and the forearm horizontal, the elbow flexor and extensor muscles will contribute only to vertical forces. If the upper arm is lifted and held in the horizontal plane while the forearm is held vertically, the elbow muscles will contribute only to forces directed forward or backward. In still another configuration, both the upper arm and forearm may be held in the horizontal plane, in which case the elbow muscles contribute only to forces in the horizontal plane. The direction of torque produced by several shoulder muscles was examined by electrical stimulation of these muscles while the upper arm was held in different postures. It was shown that the relative contribution to flexion/extension and abduction/adduction varied dramatically with the amount of internal/external rotation of the humerus. This is represented by the angle ALPHA in Fig An angle ALPHA of 0 represents pure abduction, 90 represents pure flexion, 180 represents pure adduction and 270 represents pure extension. In situations such as these, where torques are multi-axial or where muscles contribute to forces applied by a more distal limb segment, muscle activation patterns must often be characterized from empirical data. Subjects are asked to produce isometric forces or to make movements in different directions. The activity in different muscles is then recorded and examined for directional tuning. Directional tuning curves may be represented as polar plots where the amount of activation for a particular muscle is plotted as a function of the force or movement direction (Figs. 8.2, 8.3). The shape of directional tuning curves may be different for the tonic and phasic components of movement and may shift as force or velocity increase. In the case of the shoulder, the directional tuning is seen more clearly when the test movements sweep through a circle than when the arm is swept back and forth along a

2 straight line. The activity of different muscles overlaps less during movements along the perimeter of a circle than during movements along its diameter (Fig. 8.4). The pattern of activation depends on the direction of motion since muscles can act as agonists, synergists or antagonists in different situations. Consequently, different muscles will be activated at different latencies with respect to movement onset (Figs. 8.4, 8.5). Similarly, a given muscle will be activated at different latencies depending on the movement direction (Fig. 8.6). Many muscles or their tendons span more than one joint. Biarticular muscles are the most common, e.g., rectus femoris, hamstrings, gastrocnemius, biceps brachii and triceps longus. The tendons of some finger flexors and extensors cross up to four joints. The existence of muscles that span several joints can provide a number of advantages to the musculoskeletal system.!"in the case of the fingers and wrist, most of the muscle mass is removed from the hand, reducing the inertia and allowing rapid response.!"frequently, the motion at neighboring joints is such that biarticular muscles undergo smaller changes in length than monoarticular muscles. Consequently, the muscle fibers do not undergo large changes in length and can remain on a favorable region of their length-tension curve. They will also have smaller shortening velocities, allowing them to produce higher forces during contraction. For example, during locomotion, the knee and ankle often flex and extend together, minimizing the length change that occurs in the gastrocnemius muscle.!"biarticular muscles can serve to reduce the amount of work that muscles must absorb (negative work) when a joint must rotate in one direction, but generate torque in the opposite direction (Figs. 8.7, 8.8). This happens frequently when the direction of force at the endpoint of the limb must be controlled. Uniarticular muscles appear to be activated for movements in a preferred direction (which may be correlated to the direction of maximum shortening), regardless of direction of externally applied force Biarticular muscles appear to be used to control force direction regardless of whether they shorten or lengthen The motion of one segment affects the motions at all segments to which it is linked. Whenever a body segment is moved, muscles acting on other segments must be activated to prevent undesired movement. Muscle function should not be interpreted only in terms of its action at the joint or joints which it spans. A major function may be to produce motion at a remote joint by

3 means of reaction torques. A small motion at a proximal joint can be transformed into a much larger motion at a distal joint. The mechanical impedance of a limb segment plays an important role in postural stability. Numerous muscles are often activated in advance of a voluntary movement to stabilize the skeleton in preparation for the perturbing action of a limb movement (Fig. 8.9). Most movements require the coordination of muscles acting at several joints. Some muscles act as movers, some as stabilizers and others as brakes. Unlike single joint movements where only the muscles attached to a limb segment can accelerate or decelerate it, in multi-joint movements, distant muscles can perform the same actions. The dynamics of limb movement dictate that the angular acceleration at any joint is affected by the torques produced at all of the other limb joints. This means, for example, that acceleration of the shoulder is affected by torque at the elbow and vice versa. Thus, muscles that cross only the elbow joint can influence the angular acceleration of the shoulder. Contraction of a muscle crossing a joint that has only a single degree of freedom must accelerate that joint in the direction of the torque which it produces, i.e., in the direction of contraction. However, that muscle may produce even greater acceleration at joints that it does not cross.!"the soleus muscle is a uniarticular muscle acting at the ankle joint. It acts to extend (plantar flex) the ankle (Fig. 8.10). It also produces a reaction torque that acts to extend the knee. When the knee is near full extension the soleus muscle will produce twice as much knee acceleration as ankle acceleration. As the knee is flexed, the contribution of the soleus muscle to knee acceleration decreases so that when the knee is close to full flexion, the soleus muscle contributes mostly to ankle extension (Fig. 8.11). A biarticular muscle which crosses two joints with parallel axes of rotation can either accelerate both joints in the same direction as the direction of torque which it produces or it can accelerate one of the joints in the direction opposite to the direction of the torque which it produces at that joint.!"the gastrocnemius muscle is a biarticular muscle which produces an extensor torque at the ankle and a flexor torque the knee (Fig. 8.11). Its actions at the two joints is determined by the ratio of its moment arms at the knee and ankle and by the knee angle. It could (a) flex the knee and extend the ankle, (b) extend the knee and extend the ankle, or (c) flex the knee and flex the ankle (Fig. 8.12). These effects are the result of the combined direct action of the muscle at the joint and the indirect effect of the reaction torque at the knee produced by the acceleration of the shank at the ankle.

4 !"If the moment arm ratio of the gastrocnemius is approximately 0.5, as may be the case in humans, it will always operate near the boundary of two regions. Consequently, the effect on the knee would be small and over most of the range of motion, the gastrocnemius would act to extend the ankle. Although near full knee extension, it would have little effect at either the ankle or the knee. In this case, its function might be more related to transferring power between the knee and ankle than in accelerating either of the joints. Muscles of the shoulder must often serve two distinct functions during movement of the arm. They must produce torque to hold the arm up against gravity and to accelerate or decelerate the arm. As the arm moves, its center of mass will also move in relation to the shoulder. The farther the center of mass is from the shoulder, the greater the muscle activity required to support the arm against gravity. During ballistic movements of the arm, such as throwing, muscle activation is often initiated in a proximal to distal sequence. During acceleration, shoulder muscles are activated before elbow muscles. On the other hand, during deceleration of ballistic movements, the muscles tend to be activated in the reverse order, i.e., the elbow muscles used to stop the movement are activated before shoulder muscles. Movement of the hand or fingertip often follows a path that is almost straight. This requires the coordinated action of several joints moving in parallel at different angular velocities and sometimes in different directions. Angular acceleration or angular velocity at one joint may create an undesired torque at another joint due to reaction forces or motion dependent forces such as centrifugal and Coriolis forces. Joint stiffness will help to limit the perturbing effect of these torques. The stiffer the joint, the less the undesired movement. Although such motion dependent torques will increase with movement speed, muscle activation will also increase, resulting in increased joint stiffness, which may help to offset the effects of greater perturbing torques. Multi-joint Reflex Responses Although reflex responses to limb perturbations have been thought to be quite stereotyped, it is now known that the same perturbation can produce different responses, depending on when it occurs during an action or depending on the nature of the action. These differences are often more evident in actions which involve the coordination of multiple joints than in actions involving only a single joint. Such differences in reflex responses can be classified either as differences in reflex gain, i.e., for the same amount of background muscle activation there is a difference in the size of the reflex response, or as differences in sign, i.e., for the same perturbation there is a change in the response from excitation to inhibition or vice versa.

5 Differences in gain have been observed when comparing actions such as standing, walking or running on a treadmill and walking on a narrow beam. It appears that the gain of the short-latency response, as measured by the H-reflex, is highest during standing and becomes progressively smaller for walking and running. It is also lower when walking on a narrow beam than walking on a treadmill (Fig. 8.13). The H- reflex (or Hoffman reflex) is the reflex response elicited by direct stimulation of Ia primary afferent fibers in a nerve. It is similar to the stretch reflex, but is initiated by direct electrical stimulation of nerve fibers, rather than by the mechanical activation of muscle spindles. Differences in sign have been observed in actions such as ball catching. Normally, the biceps muscle is inhibited by a perturbation which causes it to shorten. However, about 100 ms before a ball is caught, the reflex response reverses such that the biceps muscle is excited by the same perturbation (Fig. 8.14). This reflex reversal produces coactivation of the triceps and biceps muscles. Such a response may not produce a net torque. However, it leads to an overall increase in muscle activity, which increases the joint stiffness. When subjects are instructed to resist a perturbation, short-latency reflex responses typically result in increased activation of a muscle that is stretched and reduced activation of a muscle that is shortened. However, the degree of excitation or inhibition can be modified if muscles at neighboring joints are active or if motion of neighboring joints occurs. This is because the sensory afferents from muscles acting at one joint influence the activity of muscles acting at neighboring joints via intersegmental reflex pathways. These reflex pathways may be quite asymmetric. For example, in the case of the wrist and elbow it appears that the monosynaptic response of Ia afferents is not reciprocal in nature. Whereas, in one direction the effects are purely inhibitory, in the other direction the effects are both excitatory and inhibitory.!"elbow extensor muscles inhibit wrist extensor and flexor muscles.!"elbow flexor muscles inhibit wrist flexor muscles, but have no effect on elbow extensor muscles.!"wrist flexor muscles excite elbow flexor muscles, but inhibit elbow extensor muscles.!"wrist extensor muscles excite elbow flexor muscles, but inhibit elbow extensor muscles. In addition to reflex responses produced by changes in muscle length or load, there are also responses which are called nonautogenic responses. These are reflex responses which occur in muscles that are not directly affected by the perturbation. Such responses have been observed in muscles acting at proximal joints when a

6 perturbation is applied to a distal joint on either the ipsilateral or the contralateral side of the body. These reflexes are likely postural reflexes that stiffen the more proximal joints to resist any postural disturbances that might be caused by the perturbation. Reflex activation in response to perturbations producing various motions of the elbow and shoulder have been analyzed in some detail. These experiments demonstrate both autogenic and nonautogenic effects. In addition, they show that short-latency and long-latency reflex responses may perform different functions since they sometimes produce different effects in the same muscle. In some cases, long-latency reflex responses appear to be organized in a manner that coordinates the activity of muscles at several joints to compensate for the expected effects of the perturbation when the limb is moving. This may mean that muscles, which do not change length, or muscles that even shorten during the perturbation will be activated by long-latency reflex pathways.!"for example, if the upper arm is pulled backwards by a perturbation during a voluntary movement involving forward flexion of the shoulder and extension of the elbow, the shoulder will extend and the elbow flex. This produces an excitatory response in both the anterior deltoid and biceps muscles even though the biceps muscle may actually shorten during the perturbation. The biarticular biceps produces elbow flexor torque which is needed to offset the elbow extensor torque that would otherwise occur as the result of the reaction torque at the elbow produced by reflex activation of the anterior deltoid when it flexes the shoulder (Fig. 8.15). Under isometric conditions, long-latency reflex responses appear to be organized in such a way as to activate the same muscles that the subject would activate if moving the limb voluntarily in the opposite direction to the displacement produced by the perturbation.!"for example, if the biceps muscle is activated by a perturbation which causes forearm pronation, the triceps muscle is also activated to offset the elbow flexor torque produced by the biceps, despite the fact that there might be no motion of the elbow during the perturbation (Fig. 8.16). When a disturbing force is entirely unexpected, resistance to the disturbance is usually small. However, when a disturbance is anticipated, the neuromuscular system can prepare for it in advance. Muscles acting as antagonists across a joint can be coactivated and the effective gains of stretch reflexes can be increased for the duration of the disturbance. The most effective way to respond to a disturbance is to compute the effects beforehand and prepare a motor response that will exactly cancel the perturbation. This can only be done if the timing of the perturbation can be precisely determined. In many circumstances one may expect a perturbation, but not know exactly when it will

7 occur. In this case, an appropriate motor response could be learned and triggered by a particular pattern of activity from sensory receptors when the perturbation occurred. Although slower than the action of a servo-controller, such a triggered response would likely be more effective than a simple stretch reflex because the pattern of muscle activation selected by learning would be the most appropriate one to counteract the perturbation. An example of such a triggered response occurs in catching a ball. When a subject can watch the ball while it falls, there is anticipatory coactivation of antagonist muscles of the elbow and wrist, and the fingers begin flexing around the ball as it nears the hand, but prior to impact. At the time of impact there is a reflex response of short duration during which both flexor and extensor muscles of the elbow and wrist are activated. As a result, the impact of the ball produces only a small disturbance and there is little movement of the joints (Fig. 8.17). When the subject cannot watch the ball, but is given an auditory cue which allows the timing of the ball's release to be anticipated, there is little anticipatory muscle activity and no movement of the fingers before impact and, although the reflex responses at impact are stronger and last longer, they are less effective in preventing movement of the joints than the responses with vision. If no auditory cue is given, reflex responses are smaller and differently organized than when ball release is anticipated. In this case, the responses are even less effective in preventing movement of the joint (Fig. 8.17).

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