Experimental Brain Research

, Volume 237, Issue 2, pp 453–465 | Cite as

Quantitative analysis of multi-element synergy stabilizing performance: comparison of three methods with respect to their use in clinical studies

  • Sandra M. S. F. Freitas
  • Paulo B. de Freitas
  • Mechelle M. Lewis
  • Xuemei Huang
  • Mark L. LatashEmail author
Research Article


A number of analyses associated with the uncontrolled manifold (UCM) hypothesis have been used recently to investigate stability of actions across populations. We explored whether some of those methods have an advantage for clinical studies because they require fewer trials to achieve consistent findings. We compared the number of trials needed for the analysis of inter-trial variance, analysis of motor equivalence, and analysis in the space of referent coordinates. Young healthy adults performed four-finger accurate force production tasks under visual feedback with the right (dominant) and left hand over three days. Three methods [analytical (M1), experimental (M2), and cumulative mean (M3) methods] were used to define the minimal number of trials required to reach certain statistical criteria. Two of these methods, M1 and M2, showed qualitatively similar results. Fewer trials (M1: 5–13, M2: 4–10) were needed for analysis of motor equivalence compared to inter-trial variance analysis (M1: 14–24, M2: 10–14). The third method (M3) showed no major differences among the outcome variables. The index of synergy in the inter-trial variance analysis required a very small number of trials (M1, M2: 2–4). Variables related to referent coordinates required only a few trials (under 3), whereas the synergy index in this analysis required the largest number of trials (M1: 24–34, M2: 12–16). This is the first study to quantify the number of trials needed for UCM-based methods of assessing motor coordination broadly used in clinical studies. Clinical studies can take advantage of specific recommendations based on the current data regarding the number of trials needed for each analysis thus allowing minimizing the test session duration without compromising data reliability.


Hand Synergy Variance Motor equivalence Referent coordinate 



The study was supported in part by NIH Grants NS082151 and NS095873.

Supplementary material

221_2018_5436_MOESM1_ESM.docx (18 kb)
Supplementary material 1 (DOCX 17 KB)
221_2018_5436_MOESM2_ESM.docx (38 kb)
Supplementary material 2 (DOCX 37 KB)


  1. Ambike S, Mattos D, Zatsiorsky VM, Latash ML (2016) Synergies in the space of control variables within the equilibrium-point hypothesis. Neurosci 315:150–161Google Scholar
  2. Bernstein NA (1967) The co-ordination and regulation of movements. Pergamon Press, OxfordGoogle Scholar
  3. Cuadra C, Bartsch A, Tiemann P, Reschechtko S, Latash ML (2018) Multi-finger synergies and the muscular apparatus of the hand. Exp Brain Res 236(5):1383–1393Google Scholar
  4. de Freitas PB, Freitas SMSF, Lewis MM, Huang X, Latash ML (2018) Stability of steady hand force production explored across spaces and methods of analysis. Exp Brain Res. Google Scholar
  5. Falaki A, Huang X, Lewis MM, Latash ML (2017a) Dopaminergic modulation of multi-muscle synergies in postural tasks performed by patients with Parkinson’s disease. J Electromyogr Kinesiol 33:20–26Google Scholar
  6. Falaki A, Huang X, Lewis MM, Latash ML (2017b) Motor equivalence and structure of variance: multi-muscle postural synergies in Parkinson’s disease. Exp Brain Res 235:2243–2258Google Scholar
  7. Falaki A, Jo HJ, Lewis MM, O’Connell B, De Jesus S, McInerney J, Huang X, Latash ML (2018) Systemic effects of deep brain stimulation on synergic control in Parkinson’s disease. Clin Neurophysiol 129(6):1320–1332Google Scholar
  8. Feldman AG (1980) Superposition of motor programs. I. Rhythmic forearm movements in man. Neurosci 5:81–90Google Scholar
  9. Feldman AG (1986) Once more on the equilibrium-point hypothesis. J Mot Behav 18:17–54Google Scholar
  10. Feldman AG (2015) Referent control of action and perception: challenging conventional theories in behavioral science. Springer, New YorkGoogle Scholar
  11. Furmanek M, Solnik S, Piscitelli D, Rasouli O, Falaki A, Latash ML (2018) Synergies and motor equivalence in voluntary sway tasks: the effects of visual and mechanical constraints. J Mot Behav. Google Scholar
  12. Hamill J, McNiven SL (1990) Reliability of selected ground reaction force parameters during walking. Hum Mov Sci 9(2):117–131Google Scholar
  13. Harris CM, Wolpert DM (1998) Signal-dependent noise determines motor planning. Nature 394(6695):780–784Google Scholar
  14. Hogan N, Sternad D (2007) On rhythmic and discrete movements: reflections, definitions and implications for motor control. Exp Brain Res 181(1):13–30Google Scholar
  15. James CR, Herman JA, Dufek JS, Bates BT (2007) Number of trials necessary to achieve performance stability of selected ground reaction force variables during landing. J Sport Sci Med 6(1):126–134Google Scholar
  16. Jo HJ, Park J, Lewis MM, Huang X, Latash ML (2015) Prehension synergies and hand function in early-stage Parkinson’s disease. Exp Brain Res 233:425–440Google Scholar
  17. Jo HJ, Maenza C, Good DC, Huang X, Park J, Sainburg RL, Latash ML (2016) Effects of unilateral stroke on multi-finger synergies and their feed-forward adjustments. Neurosci 319:194–205Google Scholar
  18. Jo HJ, Mattos D, Lucassen EB, Huang X, Latash ML (2017) Changes in multidigit synergies and their feed-forward adjustments in multiple sclerosis. J Motor Beh 49:218–228Google Scholar
  19. Krishnamoorthy V, Latash ML, Scholz JP, Zatsiorsky VM (2003) Muscle synergies during shifts of the center of pressure by standing persons. Exp Brain Res 152:281–292Google Scholar
  20. Latash ML (2010) Motor synergies and the equilibrium-point hypothesis. Mot Control 14:294–322Google Scholar
  21. Latash ML (2012) The bliss (not the problem) of motor abundance (not redundancy). Exp Brain Res 217:1–5Google Scholar
  22. Latash ML (2016) Towards physics of neural processes and behavior. Neurosci Biobehav Rev 69:136–146Google Scholar
  23. Latash ML (2017) Biological movement and laws of physics. Mot Control 21:327–344Google Scholar
  24. Latash ML, Huang X (2015) Neural control of movement stability: Lessons from studies of neurological patients. Neurosci 301:39–48Google Scholar
  25. Latash ML, Scholz JP, Schöner G (2002) Motor control strategies revealed in the structure of motor variability. Exerc Sport Sci Rev 30:26–31Google Scholar
  26. Latash ML, Levin MF, Scholz JP, Schöner G (2010) Motor control theories and their applications. Medicina 46:382–392Google Scholar
  27. Leone FC, Nottingham RB, Nelson LS (1961) The folded normal distribution. Technometrics 3:543–550Google Scholar
  28. Lewis MM, Lee EY, Jo HJ, Du G, Park J, Flynn MR, Kong L, Latash ML, Huang X (2016) Synergy as a new and sensitive marker of basal ganglia dysfunction: a study of asymptomatic welders. Neurotoxicology 56:76–85Google Scholar
  29. Martin JR, Budgeon MK, Zatsiorsky VM, Latash ML (2011) Stabilization of the total force in multi-finger pressing tasks studied with the ‘inverse piano’ technique. Hum Mov Sci 30:446–458Google Scholar
  30. Mattos D, Latash ML, Park E, Kuhl J, Scholz JP (2011) Unpredictable elbow joint perturbation during reaching results in multijoint motor equivalence. J Neurophysiol 106:1424–1436Google Scholar
  31. Mattos D, Schöner G, Zatsiorsky VM, Latash ML (2015) Motor equivalence during accurate multi-finger force production. Exp Brain Res 233:487–502Google Scholar
  32. Müller H, Sternad D (2003) A randomization method for the calculation of covariation in multiple nonlinear relations: illustrated with the example of goal-directed movements. Biol Cybern 89:22–33Google Scholar
  33. Olafsdottir H, Yoshida N, Zatsiorsky VM, Latash ML (2005) Anticipatory covariation of finger forces during self-paced and reaction time force production. Neurosc Lett 381(1–2):92–96Google Scholar
  34. Park J, Zatsiorsky VM, Latash ML (2010) Optimality vs. variability: an example of multi-finger redundant tasks. Exp Brain Res 207:119–132Google Scholar
  35. Park J, Wu YH, Lewis MM, Huang X, Latash ML (2012) Changes in multifinger interaction and coordination in Parkinson’s disease. J Neurophysiol 108:915–924Google Scholar
  36. Park J, Lewis MM, Huang X, Latash ML (2013) Effects of olivo-ponto-cerebellar atrophy (OPCA) on finger interaction and coordination. Clin Neurophysiol 124:991–998Google Scholar
  37. Parsa B, O’Shea DJ, Zatsiorsky VM, Latash ML (2016) On the nature of unintentional action: a study of force/moment drifts during multi-finger tasks. J Neurophysiol 116:698–708Google Scholar
  38. Reschechtko S, Latash ML (2017) Stability of hand force production: I. Hand level control variables and multi-finger synergies. J Neurophysiol 118:3152–3164Google Scholar
  39. Reschechtko S, Latash ML (2018) Stability of hand force production: II. Ascending and descending synergies. J Neurophysiol 120:1045–1060Google Scholar
  40. Sainburg RL (2005) Handedness: differential specializations for control of trajectory and position. Exerc Sport Sci Rev 33:206–213Google Scholar
  41. Scholz JP, Schöner G (1999) The uncontrolled manifold concept: Identifying control variables for a functional task. Exp Brain Res 126:289–306Google Scholar
  42. Scholz JP, Kang N, Patterson D, Latash ML (2003) Uncontrolled manifold analysis of single trials during multi-finger force production by persons with and without Down syndrome. Exp Brain Res 153:45–58Google Scholar
  43. Wu Y-H, Pazin N, Zatsiorsky VM, Latash ML (2012) Practicing elements vs. practicing coordination: changes in the structure of variance. J Mot Behav 44:471–478Google Scholar
  44. Wu Y-H, Pazin N, Zatsiorsky VM, Latash ML (2013) Improving finger coordination in young and elderly persons. Exp Brain Res 226:273–283Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Sandra M. S. F. Freitas
    • 1
    • 2
    • 3
  • Paulo B. de Freitas
    • 2
    • 3
    • 4
  • Mechelle M. Lewis
    • 3
    • 5
  • Xuemei Huang
    • 3
    • 5
    • 6
    • 7
  • Mark L. Latash
    • 2
    Email author
  1. 1.Graduate Program in Physical TherapyCity University of São PauloSão PauloBrazil
  2. 2.Department of KinesiologyThe Pennsylvania State UniversityUniversity ParkUSA
  3. 3.Department of Neurology, Milton S. Hershey Medical CenterThe Pennsylvania State UniversityHersheyUSA
  4. 4.Interdisciplinary Graduate Program in Health SciencesCruzeiro do Sul UniversitySão PauloBrazil
  5. 5.Department of Pharmacology, Milton S. Hershey Medical CenterThe Pennsylvania State UniversityHersheyUSA
  6. 6.Department of Radiology, Milton S. Hershey Medical CenterThe Pennsylvania State UniversityHersheyUSA
  7. 7.Department of Neurosurgery, Milton S. Hershey Medical CenterThe Pennsylvania State UniversityHersheyUSA

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