Pii: S0304-3940(99)00842-3

Fitts' law states that the movement time (MT) of an aiming movement is a linear function of the index of dif®culty (ID), where IDˆ log2(2A/W), A is the movement amplitude, and W is the target width. This law implies that MT should remain unchanged as long as A/W remains constant (i.e. the absence of a scaling effect). The goal of this study was to investigate whether, during upright posture, reciprocal-pointing movements with the center of pressure location follow Fitts' law. Six subjects performed the task with six IDs factorially combined with four As. The results showed that for each A, MT was a linear function of ID. However, the slopes of the linear-regression lines increased with decreases in A. These ®ndings indicate the presence of a scaling effect which violates Fitts' law. q 1999 Published by Elsevier Science Ireland Ltd. All rights reserved. Keywords: Humans; Center of pressure; Posture; Scaling; Speed-accuracy trade-off; Motor control; Balance The study of how speed and accuracy trade off in human movement has often focused on how movement time (MT) varies as a function of movement amplitude (A) and target width (W). The most well-known formulation of this relationship was introduced by Fitts [4], who proposed that MT ˆ a 1 b z log2(2A/W), where a and b are empirical constants, and where log2(2A/W) was termed the index of dif®culty (ID). 1/b is considered an index of performance, since the higher its value, the less MT is affected by increases in task dif®culty. As many other formulations of the speed-accuracy trade-off [2,8,12,16], this relationship predicts that as long as A/W is constant, MT should remain unchanged. Hence, functions of this type reject the presence of a scaling effect, i.e. changes in MT with changes in scales (As and Ws) for a given ID. Though there exists studies reporting violations of this relationship [1,5,9,11], it has been veri®ed in a wide variety of tasks and, for this reason, is currently known as Fitts' law (for a review see Ref. [14]). Most of the studies dealing with Fitts' law have considered upper limb movements (involving the arm, wrist, or ®nger). To our knowledge, there are only two reports of studies investigating aiming movements performed with the lower limbs [3,7], and none investigating whole body movements. The aim of the present experiment was to establish whether Fitts' law can also account for whole body movements in which the lower limb muscles are the prime movers. Maintaining balance during upright standing is a complex task. The postural control system achieves this by integrating various types of information (visual, vestibular, and somatosensory) and relying on the passive properties of the musculo-skeletal system. The main parameter registered in balance studies is the center of pressure (COP) location using a force plate. The COP is the point of application of the resultant of vertical forces acting on the surface of support and represents the collective outcome of the postural control system and the force of gravity [17]. Aiming movements with online visual feedback of COP location is a common tool in the rehabilitation of patients with impaired balance [6,15]. In this study, we wanted to determine how fast and accurate people can displace their COP between targets of varying A and W. This task is challenging since even when people are asked to maintain their COP at their preferred location, the range of COP displacements is approximately 1 cm (see results later). The presence of such variability in the postural control system may be a limiting factor of performance when A and W approach this value. Six healthy adult subjects (®ve males and one female) were asked to perform reciprocal-pointing movements Neuroscience Letters 277 (1999) 131±133 0304-3940/99/$ see front matter q 1999 Published by Elsevier Science Ireland Ltd. All rights reserved. PII: S0304-3940(99)00842-3 www.elsevier.com/locate/neulet * Corresponding author. Tel.:/fax: 11-814-863-4424. E-mail address: [email protected] (F. Danion) with the COP location. The mean subject age, height, and mass were 28.5 ^ 3.6 years, 176 ^ 6 cm, and 71.2 ^ 7.4 kg, respectively. None of the subjects had any known history of postural or skeletal disorders and they all provided informed consent prior to testing according to the Of®ce of Regulatory Compliance of The Pennsylvania State University. The task was based on the original study of Fitts [4]. The subjects stood on a force plate where COP location was sampled at 50 Hz. Online visual feedback of COP location was displayed on a monitor adjusted at the subject's head height. Two targets were displayed on the screen as windows delimitated by two lines perpendicular to the antero-posterior (a-p) axis, while the COP location was represented by a cursor. The subjects' task consisted of performing oscillatory body movements, in such a way that they generated fore and back displacements of the cursor (COP) between the two targets (for a review of studies using similar virtual environments, see Ref. [14]). The subjects were asked to be as fast and as accurate as possible. A trial containing more than 10% of errors (overor undershoots of the target) was rejected and repeated. The mean percentage of errors across the 24 trials was 4.6 ^ 0.6%. During testing, the subjects stood barefoot in an upright bipedal posture with their arms at their sides. Prior to the experiment a training session was performed. A qualitative analysis revealed that the subjects used both hip and ankle strategies [13] to complete the task. Each trial was de®ned by two parameters, the amplitude between the centers of the two targets (A) and the index of dif®culty (ID). Four As (3, 4.5, 6 and 9 cm) were factorially combined with six IDs (1.4, 1.7, 2.0, 2.3, 2.6 and 2.9). Each subject performed all conditions (24 trials) in a pseudorandom sequence. The duration of a trial was 40 s. The target positions were speci®ed in relation to the preferred location of the subject's COP. The preferred location was determined as the mean position of the COP during 60 s of quiet standing without visual feedback. Due to known asymmetries of the stability limits along the a-p axis [6], the targets were positioned 2/3 forward and 1/3 backward with respect to the preferred location (our subjects were able to reach 11.1 ^ 1.4 cm forward and 6.7 ^ 1.9 cm backward without falling). Data processing was performed as follows. The ®rst 10 s of each trial were considered as an adaptation period and were discarded from the analysis. During the remaining 30 s, we counted the number of complete movement cycles performed. Then, considering each cycle as the concatenation of two sub-movements, the mean MT was calculated throughout this time window. Within each amplitude condition, speed related to accuracy in accordance with Fitts' law: MT was an increasing linear function of ID (Fig. 1). (The datum for ID ˆ 2:9 and A ˆ 6 cm was considered an outlier and was not included in the linear regression analysis.) Correlation coef®cients were signi®cant at all As (all r-values .0.93, all P-values ,0.01). However, as A increased, the slopes (b) of the linear-regression lines decreased (r ˆ 20:98, P , 0:01). The corresponding indices of performance were 1=b ˆ 2:86, 3.12, 4.69, and 7.96 ID/s for A ˆ 3, 4.5, 6 and 9 cm, respectively. To further explore the effects of ID and A, a two-way repeated-measures ANOVA on MT was performed. Consistent with Fitts' law, there was a main effect of ID (F…5; 25† ˆ 26:23, P , 0:001). However, there was also a main effect of A (F…3; 15† ˆ 16:27, P , 0:001), which implies the presence of a scaling effect. Lastly, in accordance with the values we obtained for 1/b, there was a signi®cant ID £ A interaction (F…15; 75† ˆ 5:23, P , 0:001). This ®nal result indicates that the regression lines for the different As were not parallel. The goal of this study was to investigate whether Fitts' law can account for whole body movements. The present ®ndings demonstrated that for each A, MT was a linear function of ID. However, the slopes of the linear-regression lines increased with decreases in A. This implies that A/W was not the only determinant of performance and constitutes a violation of Fitts' law [4] as well as of many of its derivatives [2,8,12,16]. A possible explanation for this scaling effect is related to the amount of COP variability present during quiet standing. This variability was estimated by asking the subjects to minimize the deviations of their COP from a stationary target placed on the preferred COP location. The mean 95% con®dence interval of the COP location was 0.84 ^ 0.17 cm. This value was very close to the W (0.80 cm) under A ˆ 3 cm and ID ˆ 2:9, where MT was the longest. This ®nding is consistent with the view that the inherent variability of the postural control system was a limiting factor of performance under small scales (As and Ws) and high IDs. However, it remains to be determined whether this explanation can account for systematic changes in MT/ID slopes with changes in scale. Despite the presence of the scaling effect, it is worth F. Danion et al. / Neuroscience Letters 277 (1999) 131±133 132 Fig. 1. Mean movement time (MT) as a function of index of dif®culty (ID) for different movement amplitudes (As): 3, 4.5, 6 and 9 cm. Linear regression lines and their corresponding correlation coef®cients are presented for each A. comparing our ®ndings to those reported in the literature. In particular, under our largest A, the results showed that people can achieve indices of performance that approached the one's observed in manual tasks (1/b < 10 ID/s for Fitts [4]). However, under the smallest A, the results revealed that, at comparable ID, people are much slower at displacing their whole body than their upper [4,7,10] and lower [3,7] limbs. This was further corroborated in a pilot study where subjects reported dif®culties for IDs over 3. These limitations are most likely a re ̄ection of biomechanical constraints, such as inertial and musculo-skeletal properties. In conclusion, Fitts' Law does not hold for whole body movements, as assessed with COP displacements. Future work should focus on determining whether the scaling effect we observed is directly related to the amount of COP variability present during quiet standing. Frederic Danion was supported by the Fyssen foundation. Marcos Duarte is thankful to FAPESP/Brasil for his scholarship. The experimental part of this work was performed in the Biomechanics Laboratory at the Department of Kinesiology of The Pennsylvania State University. The authors are thankful to J. Toby Mordkoff for helpful comments and to Vladimir Zatsiorsky and Mark Latash for providing their equipment. [1] Chi, C.F. and Lin, C.L., Speed and accuracy of eye-gaze pointing. Percept. Mot. Skills, 85 (1997) 705±718. [2] Crossman, E.R.F.W., The Measurement of Perceptual Load, Ph.D. thesis, University of Birmingham, Birmingham, UK, 1956. [3] Drury, C.G., Application of Fitts' law to foot-pedal design. Hum. Fact., 17 (1975) 368±373. [4] Fitts, P.M., The information capacity of the human motor system in controlling the amplitude of movement. J. Exp. Psychol. (HPP), 47 (1954) 381±391. [5] Fowler, B., Duck, T., Mosher, M. and Mathieson, B., The coordination of bimanual aiming movements: evidence for progressive desynchronization. Q. J. Exp. Psychol., 43 (1991) 205±221. [6] Hamman, R.G., Mekjavic, I., Mallinson, A.I. and Longridge, N.S., Training effects during repeated therapy sessions of balance training using visual feedback. Arch. Phys. Med. Rehabil., 73 (1992) 738±744. [7] Hoffmann, E.R., A comparison of hand and foot movement times. Ergonomics, 34 (1991) 397±406. [8] Hoffmann, E.R., Fitts' law with transmission delay. Ergonomics, 35 (1992) 37±48. [9] Kelso, J.A., Southard, D.L. and Goodman, D., On the nature of human interlimb coordination. Science, 203 (1979) 1029± 1031. [10] Langolf, G.D., Chaf®n, D.B. and Foulke, J.A., An investigation of Fitts' law using a wide range of movement amplitudes. J. Mot. Behav., 8 (1976) 113±128. [11] Latash, M. and Gottlieb, G., Hypothesis on the equilibrium point and variability of amplitude, speed and time of singlejoint movement (in Russian). Bio®zika, 35 (1990) 870±874. [12] MacKenzie, I.S., Fitts' law as a research and design tool for in human-computer interaction. Hum. Comput. Interact., 7 (1992) 91±113. [13] Nashner, L.M. and McCollum, G., The organization of human postural movements: a formal basis and experimental synthesis. Behav. Br. Sci., 8 (1985) 135±172. [14] Plamondon, R. and Alimi, A., Speed-accuracy trade-off in target directed movements. Behav. Br. Sci., 20 (1997) 279± 349. [15] Shumway-Cook, A., Anson, D. and Haller, S., Postural sway biofeedback: its effect on reestablishing stance stability in hemiplegic patients. Arch. Phys. Med. Rehabil., 70 (1989) 755±762. [16] Welford, A.T., Fundamentals of Skills, Barnes & Noble, New York, 1968. [17] Winter, D.A., Biomechanics and Motor Control of Human Movement, Waterloo Biomechanics, Waterloo, 1990. F. Danion et al. / Neuroscience Letters 277 (1999) 131±133 133