Motor Control: Behavioral Emphasis (Part I)

An Overview
I have briefly presented the modern theories of motor control & learning many months ago. Although such concepts appeared after the '90s, the field has been in existence ever since the beginning of the last century. The current post is meant like a historical summary that stems from behavior perspectives. People began to ponder the basis and characteristics of movement productions as far back as 19th century. The field was heavily influenced by two separate but related fields: psychology (which was dominated by behaviorists) and the birth of neurophysiology (the study of the nervous system through electrophysiological recordings in animals).

Woodworth (1899) was one of the earliest pioneers in studying rapid arm movements and laid down the foundation of measurement such as movement speed, performance error, etc. Edward Thorndike (1914), in his Law of Effect, proposed how actions that are rewarded tend to be repeated. His ideas gave the foundation of instrumental conditioning in the field of psychology. Almost during the same period, Charles Sherrington talked about the concepts of reflexes, the final common pathway (alpha motor neurons), and sensory receptor of movements in which he coined the term proprioception. Moving to Eastern Europe, a Soviet scientist N. Bernstein made an influential contribution during 1930s where he called motor control as a degree-of-freedom problem (redundancy problem). This is because our limbs consist of various joints and each joint is connected to hundreds of muscle fibers that can be active separately. Correspondingly, different sets of motor activities capable of producing the same behavior are called motor equivalence. How does the brain know which muscle(s) to control among the various possible combination? A decade later, K. Lashley did studies on handwriting (1946) where he suggested the concept of a motor program inherent in each voluntary movement. This idea suggests the movements are based on an open-loop concept, undermining the role of sensory feedback. After WW-II ended, advancement in mathematics and information theory helped the formulation of a speed-accuracy trade-off by Paul Fitts (1954, 1964). Using a neat methodology, he discovered the link between movement speed and accuracy, now known as the Fitts' Law.

At the end of 1950's, the field of psychology shifted to themes in cognitive science that talked about attention and memory, a new euphoria for the scientific community. The concept of higher-order brain functions emerged and the flavor of motor behavior research shifted. Soon after, a strong interest focusing on "learning" appeared. In 1971, Jack Adams proposed a concept of closed-loop theory of motor learning in addition to other studies, e.g. short-term memory of movements. Mike Posner (1969) studied the role of attention, short-term memory, and movement control, expanding the concept of short-term memory storage and motor behavior. Fitts and Posner (1967) perhaps were known for their concept of three stages in motor skill acquisition. The role of attention on motor control and learning was also studied by S. Keele. His motor control thesis on the motor program was also quite influential (1968, 1986).

By the end of 1980s, integration of motor behavior and sports science gained momentum with goals of understanding motor skill learning, maintaining, and maximizing performance (e.g. F. Henry, John Whitting). At the same time, the field of neurophysiology also gained maturity in both animal studies and clinical works. This is the precursor of modern neuroscience. Rather than focusing on observable or products of behavior, scientists tried to elucidate the role of the brain or nervous system in performing movements. For example, Merton & Merton, Ian Boyd studied muscle spindles; Evarts and Georgopoulos respectively studied the neural discharge of a single neuron and ensemble of neurons in the motor cortex in awake behaving monkeys; Milner, Tulving, Tolman studied long-term memory; and Teuber for modern neuropsychology.

Interests in Bernstein's muscle coordination and redundancy problem reappeared in 1980's. On two separate occasions, Feldman and Bizzi came forward with his equilibrium point hypothesis to explain motor control. Another scientist, Latash proposed an improved theory of muscular coordination (or synergy). He said that the degree of freedom problem is solved in the brain by controlling a set of muscles doing the same job. The theory has been expanded: rather than the synergy of different neural circuits controlling movements, it refers to the synergy of the pattern of coordination such that the movement outcomes are stable and at the same time flexible. See Latash et al. (2007) for a nice summary.

Open-loop Processes and Motor Program
William James (1890) said that movement control is born out of a muscular contraction in response to either an external or internal event. This contraction produces a set of sensory feedback (now known as proprioception) from the muscles which in turn triggers another muscular contraction and so on. This sequence of events is also called the response-chaining hypothesis. In skilled movement, attention is needed for the initiation of the first action and subsequent series of actions can be 'automatically' running. The fundamental element of learning is by associating given feedback with the next action. This is the first proponent of an open-loop motor process. Our brain creates the very first muscular contraction in an effector or limb. There is no output monitoring, in the sense, no error correction. If something goes wrong or the environment changes, open-loop control can do no corrective actions. In contrast, a closed-loop process is used when we perform the online correction. In this particular case, afferent feedback provides information on the movement outcome. The discrepancy between the actual and planned (reference) movement is the basis for error correction.

Studies with deafferented animals and patients have shown that sensory feedback from the muscles is not critical for motor control. Although the trajectory isn't as smooth and accurate, movement production is still possible. James' theory is therefore not universally complete. Still, though, there are other experiments that may point to the existence of an open-loop executive controller. For example, the central pattern generator (the most popular experiment is the one involving decerebrated cats on a treadmill [FV Severin, et al. 1966]) and reflex responses. Furthermore, because sensory processing is slow, how can rapid movements be executed other than through an open-loop process?

Another example includes a study involving rapid elbow extension a 2-dof structure (Wadman, et al. 1979). Subjects were asked to perform an arm extension each trial. Such a simple but rapid action was shown to involve two agonist-antagonist muscles: biceps and triceps. To cause extension, the triceps muscle contracted as shown by the EMG burst, then the biceps muscle followed suit. At this point, the forearm slowed down. Subsequent on/off activity served to stabilize the arm position to a final stop. In a second condition, the structure was locked such that no movement was possible. Still, EMG activities appeared to be synch in time. Why is it so? It seems the control center (brain) was able to produce such stereotyped actions without the need to wait for the sensory feedback. This is a salient example of a motor program, that is, actions are pre-programmed in the brain. The motor program originated in the brain becomes the basis of the 'centralist' group, e.g. Lashley himself. This idea also suggests that the brain does not have to solve Bernstein's degree of freedom problem one by one, but rather the specific action born out of multiple joints or muscles.

Challenges to the concept of a motor program include storage space and producing novel movements never learned before. In terms of speech, e.g., if there are 100 types of sound produced, how many motor programs should a person have? For these reasons, Schmidt (1975) proposed a generalized motor program or GMP, that contains parameters that can be adjusted depending on the situation and purpose. Invariant features of certain movements are thought to be as a result of GMP. Each movement has its own invariant features or signatures. Parameters to be adjusted include: relative timing or duration, the sequence of events, force (impulse) generation, and thus muscles recruitment. Accordingly, the motor program tells the muscles when to turn on, how much force to produce, and when to turn off.

Equilibrium-point Hypothesis
According to this theory, the movement end-points are programmed by the brain and biomechanical properties of the muscle determine the trajectory. In other words, to produce a movement, the brain has to only specify where, not how/when. The model sees our musculoskeletal system as a mass-spring mechanism with stiffness, a force-length relationship. Inherently, muscle fibers are behaving like a spring where certain tension (unit: Newton) is associated with a certain muscle length or elbow angle (cm or degree). The length and tension become two invariant characteristics of the model. The best example comes from using biceps-triceps of the upper arm, an example of antagonistic muscles. Extension occurs because there is a "force" acting to stretch to the biceps. This force increases tension in the biceps but reduces tension in the triceps. Upon sudden "removal" of the force, the musculoskeletal structure goes back to an equilibrium point.

How does this theory explain movements? The model explains that the limb moves to a position defined by an equilibrium point between forces (or torques actually!) of opposing muscles. Let's use the same biceps-triceps example. Suppose at first, the elbow is at a 110º angle and the equilibrium point is defined as two length-tension curves, each for flexor and extensor muscle. The X-axis is the muscle length that defines an elbow angle, the Y-axis is the tension. Threshold length λ is defined as muscle length in "subthreshold state", in which the muscle begins to contract. When the flexor muscle is activated (biceps contract!), its length-tension curve shifts from line 1 to 2. This shift causes the equilibrium point to move towards flexion, i.e. from 110º to 80º. Moreover, the threshold length also shifts from λ₁ to λ₂. There are two versions of the model. The alpha model (Polit & Bizzi, 1978) says that this process involves no sensory feedback. The lambda model (Feldman, 1966, 1986) says that there is the involvement of muscle spindles to ensure accurate stiffness.

Close-loop Processes

Open loop (left) and close-loop (right) processes

Contrary to the open-loop motor control, the closed-loop model says that sensory feedback plays a crucial role in movement execution. According to this theory, an executive controller continuously monitors the difference between the actual movement produced by the effector or limb, and the intended movement goal (reference). If there is a discrepancy (error), the executive controller sends the command to the limb to correct for this error. This process is generally slower as it requires information processing, e.g. attention control. This is even so as the reference point may change from time to time. In addition, we now know that sensory afferents contain noise and require time (~200 msec) to travel to the cerebral cortex.

One source of sensory feedback comes from the somatosensory and vestibular systems. Although our limbs contain somatosensory feedback in the form of proprioception or kinaesthesia (spindles, joints, tendon organ), the visual system is arguably the most predominant source of perception. This has been shown in the classic literature (e.g. by Gibson, 1943; Adams, 1975; and Jordan, 1972 ). The notion "perception drives action" is the key to Gibson's theory. While the information carried by the proprioception is limited to own-body, the visual system tells us information about both own-body and external world or environment. Such a feedback source is called exteroceptor. For example: while performing an action, we understand that the body moves and at the same time the surrounding moves. Specifically, the apparent motion of objects in the visual scene caused by the relative motion between an observer and a scene is known as optical flow. We now know that the brain contains two visual streams: ventral visual stream (for object recognition or visual perception), and dorsal visual stream (for movement or motion, vision for action!).

The greatest strength of the closed-loop model is the ability to explain movements that are slow, e.g. tracking and tracing. Woodworth's throwing task shows how vision is useful especially when movement duration is > 200 msec. Further, visual feedback is useful during anticipatory activity if the stimulus is available long enough. Close-loop control is important for muscle stiffness by making use of information from the muscle spindle (Houk, 1976). Daily activities that require corrective actions are also considered, e.g. rotating a ball using the index finger. Unfortunately, many other movements that we make are much faster, e.g. aiming to grab a falling item, throwing or kicking a ball, etc. Such quick movements are termed ballistic and require rapid muscle contractions producing high movement velocity. In such a scenario, it is impossible to continuously process sensory feedback (Schmidt, 1972).

One evidence of the feedback influence to rapid movement comes from studies involving long-loop or transcortical reflex. Studies in primates and humans suggest the existence of a long-loop reflex following sudden perturbation of arm/hand position. The existence of two distinct EMG or electromyograph spikes, for example, indicates that there is another signal, M2 (~50-70 msec latency) to the motor neurons following the first, involuntary, short-latency monosynaptic reflex M1 (~30-50 msec latency). Once a source of controversy, this M2 signal is thought to be supraspinal, requires no conscious attention, and can be influenced by prior instructions. The next EMG burst following M2 is the voluntary movement itself and it is regulated by the cerebral cortex (> 150 msec latency).

Ballistic Movement: Reaching 
In principle, a motor task can be divided according to the start and endpoint into discrete, continuous, and serial tasks or skills. A discrete task is a motor task where there are a clear start and endpoint. A continuous task, on the other hand, is a motor task that is continuous and repeated (cyclical). A serial task is a special form of a discrete task in which movements are performed according to a certain sequence. In terms of speed, the motor task can be divided into slow and rapid or ballistic movements. We'll talk briefly about reaching movement here.

Woodworth first discussed this topic in detail a century ago. Ballistic reaching is prevalent in everyday lives, e.g. from movements performed during boxing, playing tennis, and daily voluntary movements such as reaching and grasping (prehension). Such movements are characterized by fast muscle contractions that yield very high speed/acceleration. Scientists thought this mechanism is too fast to be managed by a closed-loop controller in the brain.

While reaching primarily involves the muscular control that rotates shoulder and elbow joints, grasping involves more complex coordination among the five fingers. In most cases, both movements typically occur almost within one intended action in daily lives. The opening of the hand to grasp an object often happens well before the whole arm reaches the object. Does this mean reach-and-grasp is managed by the same motor GMP? According to Jeannerod (1984), reach-and-grasp consists of two behavior phases that utilize two independent neural channels working in parallel, both require a visual system to make visuomotor coordination possible. The two paths are:
1)  A fast initial, transport phase that brings the hand closer to the object,
     - Requires a channel that processes the object's extrinsic properties.
     - E.g. object location w.r.t the body, orientation, direction; viewer-centered coordinates.
2)  A slow, open-the-hand phase during which the hand makes contact with the object.
     - Requires another channel that uses the object's intrinsic properties.
     - These properties include e.g. object size, shape.

In later studies, Arbib et al. proposed that both channels are interdependent through temporal coordination which is necessary to ensure both phases are fulfilled correctly. Opponents to this theory (e.g. by Wing et al.) suggested another concept where spatial, instead of temporal, coordination is required. In another premise, Smeets and Brenner proposed that reach-and-grasp has no distinct temporal components and is nothing but pointing using thumb and finger.

Speed and accuracy 
"Haste makes waste". The fact that faster movements lead to lesser accuracy is known as the principle of a speed-accuracy trade-off. It was Woodworth who first did an experiment studying the relationship between voluntary aiming and its accuracy. He said that manual aiming consists of two phases. The first is an initial open-loop phase (initial adjustment) that propels the hand towards a target. The second phase is a current-control phase using visual feedback to land into the target. This and the following experiment make up a cornerstone of human motor control.

Half a century later, Fitts revisited the concept and showed a formulation of this trade-off. The formula says that average movement time (MT) is linearly related to the index of difficulty. This index is log [2A/W] where A is movement amplitude and W is target width to aim. Both A and W are tightly controlled during the experiment. His law suggests an inverse relationship between 'difficulty' of a movement and the completion time or speed. In the mathematical equation, a and b are Y-intercept and slope respectively. The slope represents a measure of 'controllability', the additional MT caused by an increase in the index of difficulty by a unit. Movements utilizing an upper limb exhibits a steeper slope than fingers. A higher slope is also shown in older adults. The log relationship is presumably due to information load (related to e.g. Hick's study). Subsequent studies have suggested that Fitts' Law can be found in many different situations: cyclical and discrete tasks, in children, adults, and used in neurological patients.

Experiment setup used by Fitts in his early days

Some models attempt to explain Fitts' Law. The most important one is probably the impulse variability model (Schmidt et al., 1979), a model of simple rapid aiming movements in which the variability of the impulse of forces leads directly to variations in the movement end-point of a limb. With this model, the initial phase (initial-impulse) of a ballistic movement is therefore crucial. Related to GMP, this impulse is like a code that tells arm muscles to produce forces within a certain time. The theory maintains that as the distance from a target increases, more force must be exerted, leading to greater variability in movement trajectory, decreasing the chances of hitting the target. To compensate for this, the movement time can be slowed down. A variant of this is by Meyer et al. called the optimized impulse variability model. According to this model, if an error occurs while performing an extremely rapid movement (e.g. the target overshoot or undershoot), a quick corrective movement follows after.

Although Fitts' Law was originally studied in terms of spatial accuracy, later studies discussed the characteristics of a temporal trade-off. This is relevant for example movement reaction time, preparatory time, etc, in baseball (see, e,g. Wing-Kristofferson timing model)


Reference: The writing and diagrams are based on a textbook, "Motor Control & Learning: a Behavioral Emphasis, 5ed" by RA Schmidt & T Lee.

Fundamental Concepts in Psychophysics

Classical Psychophysics
Psychophysics is all about quantifying and measuring perception and sensation. Perception and sensation refer to the way we interpret in incoming sensory information from the periphery, e.g. eyes for vision, ears for sound. They are what arises in the mind and thus a domain of cognitive psychology. The pioneer of psychophysics is G. Fechner, to whom this study originated. His interest was to find the relationship between a physical stimulus (an external entity that comes into contact with the body) and psychological perception (the mind) that arises from that stimulus.

The simplest method of psychophysics is the method of limits. Logically, there should be a minimum quantity, the weakest stimulus that can be detected. This quantity is called threshold or limen in Latin. In the method of limits, a trial begins with a set of stimuli in a specific order. The presentation can be in ascending or descending series. The experimenter then, little by little, increases the magnitude or intensity of the stimulus. Refer to the figure below, e.g. we can start with S1 presentation, up to S15. The participant answers “Yes” each time the stimulus is perceivable or “No” otherwise, each of which is recorded by the experimenter. Following this, the trial continues with the same presentation.

Another variant of this method is the staircase method where the stimulus is first provided with strong intensity and it is gradually reduced until the person makes mistake (descending order). The intensity is adjusted upward (ascending) until the person does not make mistake or detect it correctly. Soon after, again the stimulus intensity is reduced. Such a procedure is performed again and again. In general, staircase designs use a fixed-step size e.g. 1-up-n-down staircase. If the participant makes the correct response n times in a row, the stimulus intensity is reduced by one step size. One difficulty is determining the optimal step size.

A total opposite to the method of limits is the method of adjustment where the participant himself actively adjusts the stimulus magnitude until it is barely detectable.

Fig-1: Simple illustration of the method of limits. See how the psychometric function is produced in the right panel, with the threshold of detection defined as the intensity where the subject detects 50% of the time.

One main drawback of the method mentioned is that the participant is able to guess the intensity of the next stimulus in the queue. An improved and more popular version is the method of constant stimuli, in which the stimulus presentation in each trial is random so that the participant is unable to guess what the upcoming trial is, that is, the stimulus is constantly changing. For example trial-1 has S4, S2, S9, S6, S10, S11, and so on. In analyzing the data, we first produce a percentage of "Yes" responses over the whole trials for each different stimulus intensity and plot them in a graph. As seen in the figure, the graph is not an abrupt change but a gradual one, a profile known as the psychometric function. The reason for this is two things: the sensory system is noisy and that the criterion of the decision may change. Note that a criterion is in the mind of the participant whereas the threshold is the physical quantity of a stimulus. A single person can have changeable or a few criteria due to various factors. The detection threshold is defined as the stimulus magnitude in which it is perceivable 50% of the time.

To avoid a response that is biased by the criterion, another method called the method of two-alternative forced choices (2AFC) is used. There is one major difference. In the visual experiment, for example, a participant is presented with two light sources instead of one. The light can appear in either left or right source, with both intensity and location vary from one presentation to the other. The participant has to respond to either the left or right source. When unsure, he or she is forced to make a choice out of two possible scenarios, rather than simply saying “No”. In other words, the question is not whether you can detect a stimulus, but which one has the stimulus. Note that to provide fair tests, the # times the stimulus appears from the left and right source has to be the same. The experimenter also notes the correct answer, who will then compute % Correct responses. The threshold obtained from this method is relatively lower than the one from the previous methods. The resulting psychometric function is now running from 50% to 100%, because at its worst state when a person responds using the same choice each time, there is 50% chance correct. We can push the lower boundary to 0% by providing more choices to select but with the cost of a more confusing the test. In practice,two stimuli can be presented in a different time interval (temporal, e.g. being separated by 750 msec) or location (spatial, e.g. top-left and bottom-right).

Fig-2: Simple illustration of the two-alternative force choice between right and left source. See how the psychometric function is produced in the right panel.

So far the discussion is on the absolute threshold. There is also another term called differential threshold, i.e. the minimum difference in intensity or magnitude between a test and a reference stimulus such that they give a detectable perceptual difference. It is also called JND or 'just noticeable difference'. A pioneer in this differential sensitivity is Weber who has the name in Weber fraction k. In a later period, a different question arose: what is the relationship between stimulus magnitude and the resulting percept (a problem of scaling)? Fechner makes a bold assumption: the JNDs are perceived as being equal changes in perception. The magnitude of sensation is proportional to how many JNDs it is above the threshold. In other words, JND is a proxy to the sensation. Related to this, Weber-Fechner law states that the apparent increment in sensation declines with increasing level of stimulus. Example: an increase of 50 gram feels negligible for a 4 kg weight compared to a 0.5 kg weight.

Other topics in psychophysics will not be presented here: ratio scaling, Steven's power law, prothetic or metathetic continuum, multidimensional scaling, and static invariances.

Modern Psychophysics
The improvement in instrumentation and experimental design brings the birth of modern psychophysics that is dominated by the Signal Detection Theory, SDT, a concept borrowed from communication system during war. The threshold or limen in classical psychophysics is not without limitation. Moving away from measuring threshold without considering decision criterion, scientists moved on the performance during the task, both when the stimulus is present and when it is not. The main assumption is that our sensory system is inherently noisy. The noise can arise from an external source or internal source. It is a background activity and is typically thought to be a random process with a normal distribution. A sensory signal following a stimulus is superimposed on this background activity. Fig-3 shows two distributions of activity in the sensory system. The graph with stimulus presentation (S + N) is shifted to the right of the graph in the noise (N) condition; that is, it has a higher mean!

The main task is for the participant to judge whether, in a given trial, the activity belongs to S + N or to N only. In fact, SDT treats an observer as a binary classifier. If the participant feels that the signal can be detected, then S + N should be selected. The separation between two distributions is called sensitivity of a sensor or detector, given as d-prime (d'). It is essentially telling us how sensitive we are in detecting the real stimulus. Look at the figure below. We can compute, as in statistics, area under the distribution curve in each category, i.e. the probability (or proportion) to occur.

Fig-3: Conceptual diagram showing the distribution of activity in the sensory system following a noise-only (N) and a stimulus condition (S + N). Both graphs are assumed to follow a Gaussian distribution. According to SDT, a person has to judge whether in a given trial, the activity belongs to S + N or to N only. The difference between the two graphs is called d-prime (d') which represents sensitivity. The vertical line A, B, and C are analogous to the decision criterion β of the observer. (Taken from [*])

How to design and analyze a behavioral study using SDT? Simply, we first divide total trials, e.g. 100, into 50 trials with stimulus signal and 50 trials with noise only. The administration of the two sets is randomized (method of constant stimuli). Total "Yes" responses in trials with stimulus is called Hits, total "No" responses is Misses. On the other hand, total "Yes" responses in trials with noise only is called False Alarms, and "No" responses is Correct Rejection. Then we compute d' = Z_FA ‒ Z_Hit. The criterion can be quantified by taking the mean of to Z_FA and Z_Hit. Note that sign convention should be obeyed at all time when using the Z-table. A big d' means that the detector has a high ability of separating noise-only and signal. What does it mean to have d' = 0? It shows the person has no discrimination ability, the performance is at chance level. Theoretically, d' < 0 is a matter of interpretation although the nominal of Hits minus FalseAlarms can be negative. Meaning, subjects are preferentially responding to lures or distractors than to actual memory items.

Refer to Fig. 3. Note that the vertical lines are called the criterion that represents response bias. What if, for a given stimulus magnitude, the observer changes the criterion during the task? The line C will shift either to the right or left. Moving to the right (line A) means that the participant is adopting a conservative strategy as he is trying to prevent many false alarms. Conversely, shifting to the left symbolizes a more liberal strategy (line B). The phenomenon of shifting a criterion can also be depicted by another plot called receiver operating characteristic, ROC curve. For any given participant, there will only be one ROC curve that will apply in that experiment since the stimulus intensity is fixed, and the person has inherent sensitivity (d') to that stimulus. Moving along the ROC curve, we are able to estimate the conservative/liberal criterion employed. The ROC curve is also employed in other fields, e.g. medical diagnostic to test the performance of a binary classifier (disease or no-disease).

[*] Source: Levine's Fundamentals of Sensation and Perception; 3e edition.