Is Fitts’ Law Continuous in Discrete Aiming?

The lawful continuous linear relation between movement time and task difficulty (i.e., index of difficulty; ID) in a goal-directed rapid aiming task (Fitts' law) has been recently challenged in reciprocal performance. Specifically, a discontinuity was observed at critical ID and was attributed to a transition between two distinct dynamic regimes that occurs with increasing difficulty. In the present paper, we show that such a discontinuity is also present in discrete aiming when ID is manipulated via target width (experiment 1) but not via target distance (experiment 2). Fitts' law's discontinuity appears, therefore, to be a suitable indicator of the underlying functional adaptations of the neuro-muscular-skeletal system to task properties/requirements, independently of reciprocal or discrete nature of the task. These findings open new perspectives to the study of dynamic regimes involved in discrete aiming and sensori-motor mechanisms underlying the speed-accuracy trade-off.     

Myocontrol in aging

Myoelectric (EMG) signals are used in assistive technology for prostheses, computer and domestic control. An experimental study previously conducted with young participants was replicated with elderly persons in order to assess the effect of age on the ability to control myoelectric amplitude (or myocontrol). Participants performed pointing tasks as the myoelectric amplitude was captured by a surface electrode in two modalities (sustained: stabilize the amplitude after reaching the desired level; impulsion: return immediately to resting amplitude). There was a significant decrease of performance with Age. However, the patterns of performance of young and aged were noticeably similar. The Impulsion modality was difficult (high rates of failure) and the speed-accuracy trade-offs predicted by Fitts' law were absent (bow-shaped patterns as function of target amplitude instead of logarithmic increase). Conversely, the reach phase of the Sustained modality followed the predictions of Fitts' law. However, the slope of the regression line with Fitts' index of difficulty was quite steeper in aged than in young participants. These findings suggest that 1) all participants, young and aged, adapt their reaching strategies to the anticipated state (sustained amplitude or not) and/or to the difficulty of the task, 2) myocontrol in aged persons is more fragile, i.e., performance is markedly degraded as the difficulty of the task increases. However, when individual performance was examined, some aged individuals were found to perform as well as the young participants, congruently with the literature on good aging.     

Estimation of psychomotor delay from the Fitts’ law coefficients

An intrinsic property of human motor behavior is a trade-off between speed and accuracy. This is classically described by Fitts’ law, a model derived by assuming that the human body has a limited capacity to transmit information in organizing motor behavior. However, Fitts’ law can also be realized as an emergent property of movements generated by delayed feedback. In this article, we describe the relationship between the Fitts’ law coefficients and the physiological parameters of the underlying delayed feedback circuit: the relaxation rate or time constant, and the psychomotor delay of the feedback process. This relationship is then used to estimate the motor circuit delay of several tasks for which Fitts’ law data are available in the literature. We consistently estimate the delay to be between 0 and 112 ms. A further consequence of this model is that not all combinations of slope and Y-intercept in Fitts’ law are possible when movements are generated by delayed feedback. In fact, it is only possible for an observed speed–accuracy trade-off to be generated by delayed feedback if the Fitts’ law coefficients satisfy ?0.482 ≤ a/b ≤ 3.343 [bits] where b represents the slope in bits per second and a represents the Y-intercept in seconds. If we assume human movement is generated by delayed feedback, then the Fitts’ law coefficients should always be restricted to this range of values.     

Über den Informationsgehalt manueller Zielbewegungen

Summary It is investigated, wether or not informationcontent might be regarded as a suitable index of difficulty for manual aiming movements. Formulations proposed by Fitts, Crossman and Welford are used as a basis. The experiments include aiming movements to contact plates as well as transfer of pins to holes. Error percentage and movement time are recorded. It is shown, that the formulation (A =length of movement; W =aiming tolerance) including the information transmitted in the kinaesthetic and in the visual feedback loop separately, leads to a plausible result in the case of the contact-plate-experiment. After certain corrections regarding an “effective tolerance” the formulation is applicable to pin-hole-movements too. The maximal amount of information transmitted is 16 bit corresponding to an aiming tolerance of 1.4 mm. The rate of transmission of information varies between 11 and 35 bit/s according to the aiming tolerance. The results are to a certain extent in line with the results of comparable experiments.      

Fitts' law is not continuous in reciprocal aiming

It takes longer to accomplish difficult tasks than easy ones. In the context of motor behaviour, Fitts'' famous law states that the time needed to successfully execute an aiming movement increases linearly with task difficulty. While Fitts'' explicit formulation has met criticism, the relation between task difficulty and movement time is invariantly portrayed as continuous. Here, we demonstrate that Fitts'' law is discontinuous in reciprocal aiming owing to a transition in operative motor control mechanisms with increasing task difficulty. In particular, rhythmic movements are implemented in easy tasks and discrete movements in difficult ones. How movement time increases with task difficulty differs in both movement types. It appears, therefore, that the human nervous system abruptly engages a different control mechanism when task difficulty increases.     

Performance limitations from delay in human and mechanical motor control

We discuss natural limitations on motor performance caused by the time delay required for feedback signals to propagate within the human body or mechanical control systems. By considering a very simple delayed linear servomechanism model, we show there exists a best possible speed-accuracy trade-off similar to Fitts' law that cannot be exceeded when delay is present. This is strictly a delay effect and does not occur for the ideal case of instantaneous feedback. We then examine the performance of the vector integration to endpoint (VITE) circuit as a model of human movement and show that when this circuit is generalized to include delayed feedback the performance may not exceed that of the servomechanism with an equal delay. We suggest the existence of such a limitation may be a ubiquitous consequence of delay in motor control with the implication that the index of performance in Fitts' law cannot arbitrarily large.     

Reaction time and movement duration influence on end point accuracy in a fast reaching task

In labor and sport physiology a great deal of interest concerns the conceptual model of governance of both rapid and precise target-directed movements. Widely known in the theory of motor control, Fitts' paradigm determines the time of motion, calculated from the distance to the target and the diameter of the target. However this paradigm does not take into account the time of preparation for movement, which can have a significant impact on accuracy. In addition, the literature highlights little evidence of temporal and spatial asymmetry in the production of fast and accurate movements. The aim of our work was to investigate the influence of the duration of the preparatory phase (reaction time - T(R)) and duration of protractile motion of the arm (T(M)) on the speed and accuracy of movement. Also, the in-dividual asymmetry of the temporal characteristics and accuracy of performance of movements were studied. We measured three aspects of translational motion of the arm to the computerized target: reaction time (T(R), s), time of motion of the arm (T(M), s), and error in the achievement of the target (deltaL, mm). The group of participants consisted of 12 healthy, right-handed, untrained girls, each of whom completed 5 series of 10 discrete movements by each of the left and right arms. Mathematical analysis of the results revealed the existence of five models of performance. Each model was represented in the participant's performance with different probability. The combination of high speed and high precision when the arm moved towards the target was found only in model 5, which combines a long period of preparation for the movement (T(R)) and a short time of motion (T(M)). The probability of its occurrence in the untrained subjects was very low (2-3%). We suggest that it may be possible to develop special methods of training, geared towards the ability to increase the probability of appearance of this model. Asymmetry of motor action appeared clearly evident only in the parameter of accuracy (right arm committed the least errors), especially when the reaction time (T(R)) and movement time (T(M)) were close to average values of the sample. This result enables us to recommend this method for the determination of "handedness". The results allow us to conclude that in the process of development of new motor skills which include both precise and rapid movements we must take into account the initial values of reaction time. We also think that Fitts' existing formula should be modified by including the parameter of reaction time.     

3D Active Stabilization System with Sub-Micrometer Resolution

Stable positioning between a measurement probe and its target from sub- to few micrometer scales has become a prerequisite in precision metrology and in cellular level measurements from biological tissues. Here we present a 3D stabilization system based on an optoelectronic displacement sensor and custom piezo-actuators driven by a feedback control loop that constantly aims to zero the relative movement between the sensor and the target. We used simulations and prototyping to characterize the developed system. Our results show that 95 % attenuation of movement artifacts is achieved at 1 Hz with stabilization performance declining to ca. 70 % attenuation at 10 Hz. Stabilization bandwidth is limited by mechanical resonances within the displacement sensor that occur at relatively low frequencies, and are attributable to the sensor's high force sensitivity. We successfully used brain derived micromotion trajectories as a demonstration of complex movement stabilization. The micromotion was reduced to a level of ～1 μm with nearly 100 fold attenuation at the lower frequencies that are typically associated with physiological processes. These results, and possible improvements of the system, are discussed with a focus on possible ways to increase the sensor's force sensitivity without compromising overall system bandwidth.     

Characterising Upper Limb Movements in Huntington's Disease and the Impact of Restricted Visual Cues

Background

Voluntary motor deficits are a common feature in Huntington''s disease (HD), characterised by movement slowing and performance inaccuracies. This deficit may be exacerbated when visual cues are restricted.

Objective

To characterize the upper limb motor profile in HD with various levels of difficulty, with and without visual targets.

Methods

Nine premanifest HD (pre-HD), nine early symptomatic HD (symp-HD) and nine matched controls completed a motor task incorporating Fitts'' law, a model of human movement enabling the quantification of movement timing, via the manipulation of task difficulty (i.e., target size, and distance between targets). The task required participants to make reciprocal movements under cued and blind conditions. Dwell times (time stationary between movements), speed, accuracy and variability of movements were compared between groups.

Results

Symp-HD showed significantly prolonged and less consistent movement times, compared with controls and pre-HD. Furthermore, movement planning and online control were significantly impaired in symp-HD, compared with controls and pre-HD, evidenced by prolonged dwell times and deceleration times. Speed and accuracy were comparable across groups, suggesting that group differences observed in movement time, variability, dwell time and deceleration time were evident over and above simple performance measures. The presence of cues resulted in greater movement time variability in symp-HD, compared with pre-HD and controls, suggesting that the deficit in movement consistency manifested only in response to targeted movements.

Conclusions

Collectively, these findings provide evidence of a deficiency in both motor planning, particularly in relation to movement timing and online control, which became exacerbated as a function of task difficulty during symp-HD stages. These variables may provide a more sensitive measure of motor dysfunction than speed and/or accuracy alone in symp-HD.     

Predictive feedback control and Fitts–law

Fitts’ law is a well established empirical formula, known for encapsulating the “speed-accuracy trade-off”. For discrete, manual movements from a starting location to a target, Fitts’ law relates movement duration to the distance moved and target size. The widespread empirical success of the formula is suggestive of underlying principles of human movement control. There have been previous attempts to relate Fitts’ law to engineering-type control hypotheses and it has been shown that the law is exactly consistent with the closed-loop step-response of a time-delayed, first-order system. Assuming only the operation of closed-loop feedback, either continuous or intermittent, this paper asks whether such feedback should be predictive or not predictive to be consistent with Fitts law. Since Fitts’ law is equivalent to a time delay separated from a first-order system, known control theory implies that the controller must be predictive. A predictive controller moves the time-delay outside the feedback loop such that the closed-loop response can be separated into a time delay and rational function whereas a non- predictive controller retains a state delay within feedback loop which is not consistent with Fitts’ law. Using sufficient parameters, a high-order non-predictive controller could approximately reproduce Fitts’ law. However, such high-order, “non-parametric” controllers are essentially empirical in nature, without physical meaning, and therefore are conceptually inferior to the predictive controller. It is a new insight that using closed-loop feedback, prediction is required to physically explain Fitts’ law. The implication is that prediction is an inherent part of the “speed-accuracy trade-off”.     

Lateral sensitivity modulation explains the flanker effect in contrast discrimination

We used a dual-masking paradigm to study how contrast discrimination can be influenced by the presence of adjacent stimuli. The task of the observer was to detect a target superimposed on a pedestal in the presence of flankers. The flankers (i) reduce the target threshold at zero pedestal contrast, (ii) shift the target threshold versus pedestal contrast (TvC) function horizontally to the left on a log-log plot at high pedestal contrasts, and (iii) reduce the size of pedestal facilitation at low pedestal contrasts. The horizontal shift at high pedestal contrasts suggests that the flanker effect is a multiplicative factor that cannot be explained by previous models of contrast discrimination. We extend the divisive inhibition model of contrast discrimination by implementing the flanker effect as a lateral multiplicative sensitivity modulation. This extended model provides a good account of the data.     

Directional prediction by the saccadic system

One popular and fruitful approach to understanding what influences the decision of where to look next has been to present targets in a series of trials either to the right or left of a central fixation point and examine sequential effects on saccadic latency. However, there is a problem with this paradigm: Every saccade to a target is necessarily followed by an equal and opposite movement back to the center, yet the potentially confounding influence of this refixation saccade is rarely considered. Here, we introduce a novel random-walk paradigm that eliminates this difficulty. Each successive target appears to the left or right of the previous one, allowing us to study long sequences of saccades uncontaminated by refixations. This exposes a new stimulus-history effect, which is remarkably prolonged and relates primarily to movement direction: A saccade reduces the latency for subsequent movements made in the same direction and retards those in the opposite direction. Although in conventional refixation paradigms this effect cancels out, it is of particular significance in the real world--where our fixation point shifts constantly with the object of interest--and reflects a prediction of the way that real objects typically move.     

A novel task for the investigation of action acquisition

We present a behavioural task designed for the investigation of how novel instrumental actions are discovered and learnt. The task consists of free movement with a manipulandum, during which the full range of possible movements can be explored by the participant and recorded. A subset of these movements, the 'target', is set to trigger a reinforcing signal. The task is to discover what movements of the manipulandum evoke the reinforcement signal. Targets can be defined in spatial, temporal, or kinematic terms, can be a combination of these aspects, or can represent the concatenation of actions into a larger gesture. The task allows the study of how the specific elements of behaviour which cause the reinforcing signal are identified, refined and stored by the participant. The task provides a paradigm where the exploratory motive drives learning and as such we view it as in the tradition of Thorndike [1]. Most importantly it allows for repeated measures, since when a novel action is acquired the criterion for triggering reinforcement can be changed requiring a new action to be discovered. Here, we present data using both humans and rats as subjects, showing that our task is easily scalable in difficulty, adaptable across species, and produces a rich set of behavioural measures offering new and valuable insight into the action learning process.     

Reaction time in the perceptual processing of taste quality

A series of experiments examined possible strategies human subjectsmight use in tasks requiring rapid detection or recognitionof a taste quality. In a reaction time (RT) paradigm, subjectswere to decide whether each of a series of stimuli flowed overthe tongue contained a previously designated target taste. Severaltasks of varying difficulty were used. The simplest task requiredsubjects to decide whether the target taste or water was presented.The most difficult task required discrimination between twodifferent target tastes in a series of mixtures formed by orthogonallycombining the target taste with two different irrelevant tastes.The speed at which subjects could detect and/or recognize targettastes was related to the RT for the particular taste. However,it was also clear that other variables, including the specificstimuli in the mixtures and the cognitive demands placed onthe subjects, influenced performance. These results suggestthat differences in taste onset time, as indexed by RT, canserve as a cue which subjects use to aid identification of singletastes in a mixture. It is concluded that the ease with whichsubjects can identify single tastes in a mixture is relatedto, among other variables, the differences in taste onset timebetween the tastes.     

The minimum endpoint variance trajectory depends on the profile of the signal-dependent noise

It has been proposed that the central nervous system determines reaching movement trajectories so as to minimize the positional variance of the endpoint in the presence of signal-dependent noise. The hypothesis well reproduces the empirical movement trajectories for noise to the control signal whose variance is proportional to the second power of the amplitude of the control signal. However, empirical studies do not necessarily exhibit such a simple signal-noise relationship. The studies exhibit a wide distribution of estimates of the value of the exponent. This discrepancy raises the question of how the minimum endpoint variance trajectory depends on the value of the exponent. To address this question, we calculated minimum endpoint variance trajectories in simulations in which the value of the exponent was varied from 0 to 3. We found that the optimal trajectories differed according to the value of the exponent, and the profiles of optimal trajectories gradually diverged from the empirical ones as the value approached 0, though this change was not remarkable for larger values. Moreover, the optimal trajectories failed to replicate Fitts' law when the value was not equal to 2. These results suggest that the acceptability of the minimum endpoint variance theory depends on the value of the exponent in our motor system.     

Linking Perception,Cognition, and Action: Psychophysical Observations and Neural Network Modelling

It has been argued that perception, decision making, and movement planning are in reality tightly interwoven brain processes. However, how they are implemented in neural circuits is still a matter of debate. We tested human subjects in a temporal categorization task in which intervals had to be categorized as short or long. Subjects communicated their decision by moving a cursor into one of two possible targets, which appeared separated by different angles from trial to trial. Even though there was a 1 second-long delay between interval presentation and decision communication, categorization difficulty affected subjects’ performance, reaction (RT) and movement time (MT). In addition, reaction and movement times were also influenced by the distance between the targets. This implies that not only perceptual, but also movement-related considerations were incorporated into the decision process. Therefore, we searched for a model that could use categorization difficulty and target separation to describe subjects’ performance, RT, and MT. We developed a network consisting of two mutually inhibiting neural populations, each tuned to one of the possible categories and composed of an accumulation and a memory node. This network sequentially acquired interval information, maintained it in working memory and was then attracted to one of two possible states, corresponding to a categorical decision. It faithfully replicated subjects’ RT and MT as a function of categorization difficulty and target distance; it also replicated performance as a function of categorization difficulty. Furthermore, this model was used to make new predictions about the effect of untested durations, target distances and delay durations. To our knowledge, this is the first biologically plausible model that has been proposed to account for decision making and communication by integrating both sensory and motor planning information.     

The dynamics of goal-directed rhythmical aiming

Based on the kinematics of goal-directed aiming movements in a reciprocal Fitts' task, a minimal limit cycle model is proposed that is capable of producing the behavior observed at levels of task difficulty ranging from 3 to 7. From graphical and statistical analyses of the phase planes, Hooke's planes and velocity profiles, we concluded that the minimal terms to be included in the model were (i) a nonlinear damping in the form of a self-sustaining, velocity-driven Rayleigh oscillator and (ii) a nonlinear stiffness in the form of a softening spring Duffing term. The model reproduced the kinematic patterns experimentally observed in rhythmical precision aiming, accounting for 95% of the variance. The coefficients in the model changed in a systematic way when distance and precision constraints were varied, and the meaning of these changes is discussed in the framework of the dynamical patterns approach. Received: 20 April 1998 / Accepted in revised form: 24 November 1998     

Two-dimensional crystallization of streptavidin: in pursuit of the molecular origins of structure, morphology, and thermodynamics

The streptavidin two-dimensional (2D) crystallization model has served as a paradigm for molecular self-assembly at interfaces. We have developed quantitative Brewster angle microscopy for the in situ measurement of spatially resolved relative protein surface densities. This allows investigation of both the thermodynamics and morphologies of 2D crystal growth. For crystal structure analysis, we employ TEM on grown crystals transferred to solid substrates. Comparison of results between commercially available streptavidin, recombinant streptavidin, and site-directed streptavidin mutants has provided insight into the protein protein and protein-lipid interactions that underlie 2D crystallization.     

Pain-related and cognitive components of somatosensory evoked potentials following CO2 laser stimulation in man

We recorded cortical potentials evoked by painful CO₂ laser stimulation (pain SEP), employing an oddball paradigm in an effort to demonstrate event-related potentials (ERP) associated with pain. In 12 healthy subjects, frequent (standard) pain stimuli (probability 0.8) were delivered to one side of the dorsum of the left hand while rare (target) pain stimuli (probability 0.2) were delivered to the other side of the same hand. Subjects were instructed to perform either a mental count or button press in response to the target stimuli. Two early components (N2 and P2) of the pain SEP demonstrated a Cz maximal distribution, and showed no difference in latency, amplitude or scalp topography between the oddball conditions or between response tasks. In addition, another positive component (P3) following the P2 was recorded maximally at Pz only in response to the target stimuli with a peak latency of 593 msec for the count task and 560 msec for the button press task. Its scalp topography was the same as that for electric and auditory P3. The longer latency of pain P3 can be explained not only by its slower impulse conduction but also by the effects of task difficulty in the oddball paradigm employing the pain stimulus compared with electric and auditory stimulus paradigms. It is concluded that the P3 for the pain modality is mainly related to a cognitive process and corresponds to the P3 of electric and auditory evoked responses, whereas both N2 and P2 are mainly pain-related components.