Journal of Motor Behavior, Vol. 43, No. 6, 2011 Copyright C  Taylor & Francis Group, LLC RESEARCH ARTICLE Directional Variability of the Isometric Force Vector Produced by the Human Hand in Multijoint Planar Tasks Jason Friedman 1,2 , Mark L. Latash 2 , Vladimir M. Zatsiorsky 2 1 ARC Centre of Excellence in Cognition and its Disorders, Macquarie University, Sydney, Australia. 2 Department of Kinesiology, The Pennsylvania State University, University Park. ABSTRACT. Numerous studies have examined control of force magnitude, but relatively little research has considered force direc- tion control. The subjects applied isometric forces to a handle and the authors compared within-trial variability when force is produced in different directions. The standard deviation of the force parallel to the prescribed direction of force production increased linearly with the targeted force level, as did the standard deviation of the force perpendicular to the instructed direction. In contrast, the standard deviation of the angle of force production decreased with increased force level. In the 4 (of 8) instructed force directions where the end- point force was generated due to a joint torque in only 1 joint (either the shoulder or elbow) the principal component axes in force space were well aligned with the prescribed direction of force produc- tion. In the other directions, the variance was approximately equal along the 2 force axes. The variance explained by the first princi- pal component was significantly larger in torque space compared to the force space, and mostly corresponded to positive correlation between the joint torques. Such coordinated changes suggest that the torque variability was mainly due to the variability of the com- mon drive to the muscles serving 2 joints, although this statement needs to be supported by direct studies of muscle activation in the future. Keywords: direction, isometric force, torque, variability T he control of force magnitude has been studied in depth (reviewed in Carlton & Newell, 1993). In a study of rapid, uncorrected isometric unidimensional force production to a target (sometimes termed impulse force), it was observed that the standard deviation of the force magnitude at the tar- get, across trials, increased approximately linearly with the magnitude of the target force (Schmidt, Zelaznik, Hawkins, Frank, & Quinn, 1979). This finding has been replicated in studies using constant visual feedback gain (Hamilton, Jones, & Wolpert, 2004; Slifkin & Newell, 1999)—for ex- ample, 1 cm on the screen equals the same force for all levels of target force production—and scaled feedback (Shapkova, Shapkova, Goodman, Zatsiorsky, & Latash, 2008; Tracy, Mehoudar, & Ortega, 2006), where 1 cm equals a fixed pro- portion of the target force. The variability has been observed to level off at about 65% of maximal force and then de- crease at higher levels (Sherwood & Schmidt, 1980). Later studies suggested that the force magnitude variability is also dependent on the time to produce the peak force, rather than force magnitude only (Hong, Lee, & Newell, 2007; Newell & Carlton, 1988; Slifkin & Newell, 2000). In contrast, there are fewer studies on the variability of force direction. These studies can be classified into two groups that deal with exploring the force production in (a) single 2- or 3-D joints (e.g., Kutch, Kuo, Bloch, & Rymer, 2008) or (b) in planar kinematic chains. Due to evident rea- sons, these tasks are biomechanically quite different. Kutch et al. (2008), studying the endpoint force during isometric force production of the index finger metacarpopha- langeal joint in different directions found that fluctuations in the covariance of force projections on the coordinate axes were dependent on whether the direction of force produc- tion was close to the direction of muscle action of one of the muscles involved. From this finding, they inferred that muscles are recruited flexibly and not according to fixed groupings. Studies on the effect of the force direction on the force variability in multilink tasks have been mainly limited to fingertip force production in the flexion–extension plane. It was observed that the target direction significantly affected the variable error of the force direction, but not the constant error (Gao, Latash, & Zatsiorsky, 2005). Force direction vari- ability was shown to be larger in one-finger tasks as compared with four-finger tasks and larger for force production down- ward and toward the body as compared with other directions (Kapur, Friedman, Zatsiorsky, & Latash, 2010). Valero- Cuevas, Venkadesan, and Todorov (2009) examined muscle coordination using electromyograms during fingertip isomet- ric force production and found that the variance is consis- tently lower in task-revelant parameters than at the muscle level. There is not a clear consensus about the source of vari- ation observed in force production, although it is generally assumed to reflect neuromotor noise (reviewed in Newell, Deutsch, Sosnoff, & Mayer-Kress, 2006). It has been as- sumed that the amount of noise increases with the neural signal, the phenomenon known as signal-dependent noise (Harris & Wolpert, 1998). Jones, Hamilton, and Wolpert (2002) concluded that the signal-dependent noise is mostly related to neural sources. In an experiment involving ex- tension of the distal phalange of the thumb, they found that when the same muscles were electrically stimulated, the vari- ation (noise) did not increase with the force level. Peripheral sources may also contribute to the variability of the motor output, and attempts have been made to distinguish between these two sources (Wing & Kristofferson, 1973). Correspondence address: Jason Friedman, ARC Centre of Ex- cellence in Cognition and its Disorders, C5C Level 4, Macquarie University, Sydney, NSW 2109, Australia. e-mail: jason.friedman@ mq.edu.au 451 Downloaded by [Macquarie University] at 03:19 04 December 2011