The speed-curvature power law of movements: a reappraisal
Myrka Zago ; Adam Matic ; Tamar Flash ; et al. ; - ASI Sponsor
Oct - 2017
DOI: 10.1007%2Fs00221-017-5108-z

journal : Experimental Brain Research
type: Article Journal

Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685–690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.

keywords : Motor control, Drawing, Two-thirds power law, Statistical analysis

Notes : Acknowledgements [...] The work was supported by the Italian Space Agency (grant n. I/006/06/0 to F.L. and grant n. 2014-008-R.0 to M.Z.) [...]