A model of central commands (CCs) coming to the muscles during limb movements is proposed; it is based on experimental studies of the nonlinear dynamics of muscle contraction and of the parafrontal two-joint arm movements in humans. It is known that such CCs possess powerful hysteresis properties; levels of muscle activation rise within parts of the movement trajectories, where the muscles are actively shortened and overcome the action of an external force, but decrease during muscle stretching by the above force. Basing on an analogy with the classic thermodynamics, a “thermodynamic” model (T-model) is proposed, which allows one to predict the nonlinear functional interdependence of three basic parameters defining the muscle state, namely E (intensity of efferent activity), F (muscle force), and L (muscle length). The T-model includes the time-dependent integration of the equations defining the interrelations between infinitesimal changes of the above parameters, which are assumed to be the exact differentials. By inducing only one additional parameter, the hysteresis weight, the T-model can satisfactorily explain patterns of EMG records observed in real movements of the arm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. M. Hollerbach, “Computers, brains, and the control of movement,” Trends Neurosci., 5, 189–192 (1982).
M. Kawato, “Internal models for motor control and trajectory planning,” Curr. Opin. Neurobiol., 9, No. 6, 718–727 (1999).
D. M. Wolpert and Z. Ghahramani, “Computational principles of movement neuroscience,” Nat. Neurosci., 3, 1212–1217 (2000).
E. Bizzi, N. Hogan, F. A. Mussa-Ivaldi, and S. Giszter, “Does the nervous system use equilibrium-point control to guide single and multiple joint movements?” Behav. Brain Sci., 15, No. 4, 603–613 (1992).
A. G. Feldman, “Once more for the equilibrium point hypothesis (λ model) for motor control,” J. Mot. Behav., 18, No. 1, 17–54 (1986).
A. G. Feldman, “Space and time in the context of equilibrium-point theory,” Wiley Interdiscip. Rev. Cogn. Sci., 2, No. 3, 287–304 (2011).
G. C. Joyce, P. M. Rack, and D. R. Westbury, “Some mechanical properties of the cat soleus muscle at various stimulus rates,” J. Physiol., 197, No. 1, 23P–25P (1968).
P. M. Rack and D. R. Westbury, “The effects of length and stimulus rate on tension in the isometric cat soleus muscle,” J. Physiol., 204, No. 2, 443–460 (1969).
A. I. Kostyukov, “Muscle dynamics: dependence of muscle length on changes in external load,” Biol. Cybern., 56, Nos. 5/6, 375–387 (1987).
A. I. Kostyukov and O. E. Korchak, “Length changes of the cat soleus muscle under frequency-modulated distributed stimulation of efferents in isotony,” Neuroscience, 82, No. 3, 943–955 (1997).
A. I. Kostyukov, “Muscle hysteresis and movement control: a theoretical study,” Neuroscience, 83, No. 1, 303–320 (1998).
A. I. Kostyukov and V. L. Cherkassky, “Interaction of the movement-dependent, extrafusal and fusimotor aftereffects in the firing of the primary spindle endings,” Neuroscience, 76, No. 4, 1257–1266 (1997).
A. I. Kostyukov, S. V. Lytvynenko, N. V. Bulgakova, A. V. Gorkovenko, “Subthreshold activation of spinal motoneurones in the stretch reflex: experimental data and modeling,” Biol. Cybern., 100, No. 4, 307–318 (2009).
T. Tomiak, T. I. Abramovych, A. V. Gorkovenko, et al., “The movement- and load-dependent differences in the EMG patterns of the human arm muscles during twojoint movements (a preliminary study),” Front. Physiol., 7, No. 218 (2016); doi: https://doi.org/10.3389/fphys.2016.00218.
I. V. Vereshchaka, A. V. Gorkovenko, O.V. Lehedza, et al., “EMG patterns of the elbow- and shoulder-operating muscles in slow parafrontal upper limb movements under isotonic loading,” Neurophysiology, 50, No. 6, 466–474 (2018)
A. I. Kostyukov, O. V. Lehedza, A. V. Gorkovenko, et al., “Hysteresis and synergy of the central commands to muscles participating in parafrontal upper limb movements,” Front. Physiol. No. 10, 1441 (2019), doi:https://doi.org/10.3389/fphys.2019.01441
A. I. Kostyukov, “Theoretical analysis of the force and position synergies in two-joint movements,” Neurophysiology, 48, No. 4, 287–296 (2016).
T. Tomiak, A. V. Gorkovenko, A. N. Tal’nov, et al., “The averaged EMGs recorded from the arm muscles during bimanual “rowing” movements,” Front. Physiol., 6, No. 349 (2015); doi: https://doi.org/10.3389/fphys.2015.00349.
O.V. Lehedza, A.V. Gorkovenko, I.V. Vereshchaka, et. al., “Comparative analysis of electromyographic muscle activity of the human hand during cyclic turns of isometric effort vector of wrist in opposite directions,” Int. J. Physiol. Pathophysiol., 61, No. 2, 3–14 (2016).
O. V. Lehedza, “Manifestations of hysteresis in EMG activity of muscles of the human upper limb in generation of cyclic isometric efforts,” Neurophysiol.49, No. 3, 220–225 (2017).
G. B. Thomas, Jr. and R. L. Finney, Calculus and Analytic Geometry, 9th ed., Addison-Wesley (1996); ISBN 978-0201531749, 0201531747.
Y. A. Çengel and M. A. Boles, “Thermodynamics Property Relations,” in: Thermodynamics - An Engineering Approach, McGraw-Hill Series in Mechanical Engineering (3rd ed.). Boston, MA (1998); ISBN 0-07-011927-9.
A. I. Kostyukov, and T. Tomiak, “The force generation in a two-joint arm model: analysis of the joint torques in the working space,” Front. Neurorobot., 12, No. 77 (2018); doi: https://doi.org/10.3389/fnbot.2018.00077
I. V. Vereshchaka, W. Pilewska, M. Zasada, and A. I. Kostyukov, “Three-dimensional representation of equilibrium joint torques in two-joint movements of the upper limb,” Neurophysiology, 50, No. 6, 475–488. (2018).
A. V. Gorkovenko, “Theoretical analysis of the peculiarities of motor control at generation of two-joint isometric efforts by the human upper limb,” Neurophysiology, 50, No. 4, 309–321 (2018).
N. Dounskaia, “The internal model and the leading joint hypothesis: implications for control of multi-joint movements,” Exp. Brain Res.166, No. 1, 1–16 (2005).
N. Dounskaia, J. Goble, and W. Wang, “The role of intrinsic factors in control of arm movement direction: implications from directional preferences,” J. Neurophysiol.,105, No.3, 999–1010 (2011).
L. E. Karbach and J. Elfar, “Elbow Instability: Anatomy, Biomechanics, Diagnostic Maneuvers, and Testing,” J. Hand Surg., 42, No. 2, 118–126 (2017)
A. V. Gorkovenko, S. Sawczyn, N. V. Bulgakova, et. al., “Muscle agonist-antagonist interactions in an experimental joint model,” Exp. Brain Res.,222, 399–414 (2012).
T. E. Milner and C. Cloutier, “Damping of the wrist joint during voluntary movement,” Exp. Brain Res.,122, No.3, 309–317 (1998).
P. L. Gribble and D. J. Ostry, “Independent coactivation of shoulder and elbow muscles,” Exp. Brain Res.,123, No.3, 335–360 (1998).
A. M. Hill, A. M. J. Bull, A. L. Wallace, and G. R. Johnson, “Qualitative and quantitative descriptions of glenohumeral motion,” Gait Posture,27, No.2, 177–188 (2008).
C. D. Bryce and A. D. Armstrong, “Anatomy and biomechanics of the elbow,” Orthop. Clin. North Am.,39, No.2, 141–154 (2008).
B. M. Van Bolhuis, C. C. Gielen, and G. J. van Ingen Schenau, “Activation patterns of mono- and bi-articular arm muscles as a function of force and movement direction of the wrist in humans,” J. Physiol.,508, (Pt 1), 313–324 (1998).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kostyukov, A.I. A “Thermodynamic” Model of Central Commands Coming to the Muscles during Upper Limb Movements. Neurophysiology 51, 358–372 (2019). https://doi.org/10.1007/s11062-020-09830-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11062-020-09830-z