Chapter 9: The Nature and Structure of Feasible Sets (under construction)

Last updated Dec. 26 2015 by Francisco Valero-Cuevas


An engineering perspective is inherently incomplete when applied to science. However, as per the words of Galileo Galilei at the beginning of this book, science is also not complete without a mathematical foundation. Our large community applied this mathematics-based perspective for decades to understand motor control. This has resulted in a large, informative, useful, and fruitful body of work. I now comment briefly on how the neuromechanical framework of this book applies to some current tenets, theories, and debates in motor control. In particular, if we agree that the mechanical principles outlined in this book are relevant to the structure of vertebrate limbs, then the nature and structure of the feasible sets they allow are relevant to their neural control. In this chapter I present brief descriptions of how our community has approached understanding the nature and structure of the high-dimensional feasible activation sets.

Forum and commentary:

Coming soon!


All code to produce vectormaps with MatLab, and plot descriptive statistics with R

Valero-Cuevas FJ, Cohn BA, Yngvason HF, Lawrence EL.   
Exploring the high-dimensional structure of muscle redundancy via subject-specific and generic musculoskeletal models   
Journal of Biomechanics, ASB Special Issue, 48(11): p. 2887-96, 2015.  

Explore vectormap code on GitHub
Download up-to-date code as a Zip File
To walk through a well-commented usage of the library, open Matlab, set the working directory to the main vectormap folder, & run through the following file line by line:

edit test_task_vector_bounds

Additional references and suggested reading:

Coming soon!

References in book:

  1. J.J. Kutch, F.J. Valero-Cuevas, Muscle redundancy does not imply robustness to muscle dysfunction. J. Biomech. 44(7), 1264–1270 (2011)
  2. M.H. Sohn, J.L. McKay, L.H. Ting, Defining feasible bounds on muscle activation in a redundant biomechanical task: practical implications of redundancy. J. Biomech. 46(7), 1363–1368 (2013)
  3. R.H. Clewley, J.M. Guckenheimer, F.J. Valero-Cuevas, Estimating effective degrees of freedom in motor systems. IEEE Trans. Biomed. Eng. 55, 430–442 (2008)
  4. Wikipedia contributors. Principal components analysis. Wikipedia, The Free Encyclopedia. Accessed 29 May 2015
  5. A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis, vol. 46 (Wiley, New York, 2004)
  6. E.R. Kandel, J.H. Schwartz, T.M. Jessell, et al., Principles of Neural Science, vol. 4 (McGraw Hill, New York, 2000)
  7. J.V. Basmajian, C.J. De Luca, Muscles Alive. Muscles Alive: Their Functions Revealed by Electromyography, vol. 278 (Williams & Wilkins, Baltimore, 1985), p. 126
  8. G.E. Loeb, Electromyography for Experimentalists (University of Chicago Press, Chicago, 1986)
  9. M.C. Tresch, V.C.K. Cheung, A. d’Avella, Matrix factorization algorithms for the identification of muscle synergies: evaluation on simulated and experimental data sets. J. Neurophysiol. 95(4), 2199–2212 (2006)
  10. T.J. Burkholder, K.W. van Antwerp, Practical limits on muscle synergy identification by nonnegative matrix factorization in systems with mechanical constraints. Med. Biol. Eng. Comput. 51(1–2), 187–196 (2013)
  11. M.N. Moghadam, K. Aminian,M. Asghari,M.Parnianpour, How well do the muscular synergies extracted via non-negative matrix factorisation explain the variation of torque at shoulder joint? Comput. Methods Biomech. Biomed. Eng. 16(3), 291–301 (2013)
  12. M.K. Steele, M.C. Tresch, E.J. Perreault, Consequences of biomechanically constrained tasks in the design and interpretation of synergy analyses. J. Neurophysiol. 113(7), 2102–2113 (2015)
  13. E. Bizzi, V.C.K. Cheung, The neural origin of muscle synergies. Front. Comput. Neurosci. 7, 51 (2013). doi:10.3389/fncom.2013.00051
    1. L.H. Ting, J.L. McKay, Neuromechanics of muscle synergies for posture and movement. Current Opin. Neurobiol. 17(6), 622–628 (2007)
  14. M.C. Tresch, A. Jarc, The case for and against muscle synergies. Current Opin. Neurobiol. 19(6), 601–607 (2009)
  15. L.H. Ting, J.M. Macpherson, A limited set of muscle synergies for force control during a postural task. J. Neurophysiol. 93(1), 609–613 (2005)
  16. A. d’Avella, E.Bizzi, Shared and specific muscle synergies in natural motor behaviors. Proc. Natl. Acad. Sci. USA 102(8), 3076–3081 (2005)
  17. J.J. Kutch, A.D. Kuo, A.M. Bloch, W.Z. Rymer, Endpoint force fluctuations reveal flexible rather than synergistic patterns of muscle cooperation. J. Neurophysiol. 100(5), 2455–2471 (2008)
  18. J.J. Kutch, F.J. Valero-Cuevas, Challenges and new approaches to proving the existence of muscle synergies of neural origin. PLoS Comput. Biol. 8(5), e1002434 (2012)
  19. M.L. Latash, J.P. Scholz, G.Schoner, Toward a new theory of motor synergies. MotorControl 11(3), 276 (2007)
  20. M.L.Latash, Synergy (Oxford University Press, USA, 2008)
  21. A. d’Avella, M. Giese, T. Schack, Y.P. Ivanenko, T. Flash, Modularity in motor control: from muscle synergies to cognitive action representation, in Frontiers in Computational Neuroscience Research Topics (Frontiers Media SA, 2012)
  22. C. Alessandro, I. Delis, F. Nori, S. Panzeri, B. Berret, Muscle synergies in neuroscience and robotics: from input-space to task-space perspectives. Front. Comput. Neurosci. 7, 43 (2013). doi:10.3389/fncom.2013.00043
  23. E. Bizzi, F.A. Mussa-Ivaldi, S. Giszter, Computations underlying the execution of movement: a biological perspective. Science 253(5017), 287–291 (1991)
  24. S.F. Giszter, F.A. Mussa-Ivaldi, E. Bizzi,C onvergent force fields organized in the frog’s spinal cord. J. Neurosci. 13(2), 467–491 (1993)
  25. S. Giszter, V. Patil, C. Hart, Primitives, premotor drives, and pattern generation: a combined computational and neuroethological perspective. Prog. Brain Res. 165, 323–346 (2007)
  26. S.F. Giszter, Motor primitives–new data and future questions. Current Opin. Neurobiol. 33, 156–165 (2015)
  27. M. Berniker, A. Jarc, E. Bizzi, M.C. Tresch, Simplified and effective motor control based on muscle synergies to exploit musculoskeletal dynamics. Proc. Natl. Acad. Sci. 106(18), 7601– 7606 (2009)
  28. M.H. Schieber, M. Santello, Hand function: peripheral and central constraints on performance. J. Appl. Physiol. 96(6), 2293–2300 (2004)
  29. H. van Duinen, S.C. Gandevia, Constraints for control of the human hand. J. Physiol. 589(23), 5583–5593 (2011)
  30. F. Mechsner, D. Kerzel, G. Knoblich, W. Prinz, Perceptual basis of bimanual coordination. Nature 414(6859), 69–73 (2001)
  31. J. Ren, S. Huang, J. Zhang, Q. Zhu, A.D. Wilson, W. Snapp-Childs, et al., The 50s cliff: a decline in perceptuo-motor learning, not a deficit in visual motion perception. PLoS ONE 10(4), e0121708 (2015). doi:10.1371/journal.pone.0121708
  32. N. Kang, J.H. Cauraugh, Bimanual force variability in chronic stroke: With and without visual information. Neurosci. Lett. 587, 41–45 (2015)
  33. J.P. Scholz, G. Schöner, The uncontrolled manifold concept: identifying control variables for a functional task. Exp. Brain Res. 126, 289–306 (1999)
  34. G.E. Loeb, Overcomplete musculature or underspecified tasks? Motor Control 4(1), 81–83 (2000)
  35. M.Spivak,CalculusonManifolds,vol.1(WABenjamin,NewYork,1965)
  36. K. Rácz, F.J. Valero-Cuevas, Spatio-temporal analysis reveals active control of both task- relevant and task-irrelevant variables. Front. Comput. Neurosci. 7, 155 (2013). doi:10.3389/ fncom.2013.00155
  37. J. Milton, T. Insperger, G. Stepan, Human balance control: dead zones, intermittency, and micro-chaos. Mathematical Approaches to Biological Systems (Springer, Berlin, 2015), pp. 1–28 156 9 The Nature and Structure of Feasible Sets
  38. L.A. Elias, R.N. Watanabe, A.F. Kohn, Spinal mechanisms may provide a combination of intermittent and continuous control of human posture: Predictions from a biologically based neuromusculoskeletal model. PLoS Comput. Biol. 10(11), e1003944 (2014)
  39. J.G. Milton, Intermittent motor control: the “drift-and-act” hypothesis. Progress in Motor Control (Springer, Berlin, 2013), pp. 169–193
  40. A. de Rugy, G.E. Loeb, T.J. Carroll, Are muscle synergies useful for neural control? Front. Comput. Neurosci. 7, 19 (2013). doi:10.3389/fncom.2013.00019
  41. S. Grillner, Control of locomotion in bipeds, tetrapods, and fish. Comprehensive Physiology (John Wiley & Sons, 2011),
  42. K. Rácz, D. Brown, F.J. Valero-Cuevas, An involuntary stereotypical grasp tendency pervades voluntary dynamic multifinger manipulation. J. Neurophysiol. 108(11), 2896–2911 (2012)
  43. L.H. Ting, S.A. Chvatal, S.A. Safavynia, J.L. McKay, Review and perspective: neuromechanical considerations for predicting muscle activation patterns for movement. Int. J. Numer. Methods Biomed. Eng. 28(10), 1003–1014 (2012)
  44. F.J. Valero-Cuevas, M. Venkadesan, E. Todorov, Structured variability of muscle activations supports the minimal intervention principle of motor control. J. Neurophysiol. 102, 59–68 (2009)
  45. W.J. Kargo, S.F. Giszter, Rapid correction of aimed movements by summation of force-field primitives. J. Neurosci. 20(1), 409–426 (2000)
  46. W.J. Kargo, S.F. Giszter, Individual premotor drive pulses, not time-varying synergies, are the units of adjustment for limb trajectories constructed in spinal cord. J. Neurosci. 28(10), 2409–2425 (2008)
  47. T. Drew, J. Kalaska, N. Krouchev, Muscle synergies during locomotion in the cat: a model for motor cortex control. J. Physiol. 586(5), 1239–1245 (2008)
  48. F.J. Valero-Cuevas, A mathematical approach to the mechanical capabilities of limbs and fingers. Adv. Exp. Med. Biol. 629, 619–633 (2009)
  49. R. Balasubramanian, Y. Matsuoka ,Biological stiffness control strategies for the anatomically correct testbed (act) hand, in IEEE International Conference on Robotics and Automation. ICRA 2008 (IEEE, 2008), pp. 737–742
  50. G. Raphael, G.A. Tsianos, G.E. Loeb, Spinal-like regulator facilitates control of a two-degree of-freedom wrist. J. Neurosci. 30(28), 9431–9444 (2010)
  51. D.E. Koditschek, Task encoding: toward a scientific paradigm for robot planning and control. Robot. Auton. Syst. 9(1), 5–39 (1992)
  52. H. Lipson, J.B. Pollack, Automatic design and manufacture of robotic lifeforms. Nature 406(6799), 974–978 (2000)
  53. R. Pfeifer, J. Bongard, How the Body Shapes the Way We Think: A New View of Intelligence (MIT Press, Cambridge, 2006)
  54. R.A. Brooks, Artificial life and real robots, in Toward a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life (1992), p. 3
  55. F.J. Valero-Cuevas, J.W. Yi, D. Brown, R.V. McNamara, C. Paul, H. Lipson, The tendon network of the fingers performs anatomical computation at a macroscopic scale. IEEE Trans. Biomed. Eng. 54, 1161–1166 (2007)
  56. L.H. Ting, S.A. Kautz, D.A. Brown, F.E. Zajac, Phase reversal of biomechanical functions and muscle activity in backward pedaling. J. Neurophysiol. 81(2), 544–551 (1999)
  57. J.B. Dingwell, J. John, J.P. Cusumano, Do humans optimally exploit redundancy to control step variability in walking? PLoS Comput. Biol 6(7), e1000856 (2010)
  58. K.G. Keenan, V.J. Santos, M. Venkadesan, F.J. Valero-Cuevas, Maximal voluntary fingertip force production is not limited by movement speed in combined motion and force tasks. J. Neurosci. 29, 8784–8789 (2009)
  59. M. Venkadesan, F.J. Valero-Cuevas, Neural control of motion-to-force transitions with the fingertip. J. Neurosci. 28, 1366–1373 (2008)
    1. J. Bongard, V. Zykov, H. Lipson, Resilient machines through continuous self-modeling. Science 314, 1118–1121 (2006)
  60. J. Rieffel, F.J. Valero-Cuevas, H. Lipson, Morphological communication: exploiting coupled dynamics in a complex mechanical structure to achieve locomotion. J. Royal Soc. Interface (2009) (In Press)
  61. E. Theodorou, E. Todorov, F.J. Valero-Cuevas, Neuromuscular stochastic optimal control of a tendon driven index finger model, in American Control Conference (ACC) (IEEE, 2011), pp. 348–355
  62. E. Theodorou, J. Buchli, S. Schaal, A generalized path integral control approach to reinforcement learning. J. Mach. Learn. Res. 11, 3137–3181 (2010)
  63. M. Kalakrishnan, J. Buchli, P. Pastor, M. Mistry, S. Schaal, Learning, planning, and control for quadruped locomotion over challenging terrain. Int. J. Robot. Res. 30(2), 236–258 (2011)
  64. K.P. Körding, D.M. Wolpert, Bayesian integration in sensorimotor learning. Nature 427(6971), 244–247 (2004)
  65. T.D. Sanger, Distributed control of uncertain systems using superpositions of linear operators.Neural Comput. 23(8), 1911–1934 (2011)
  66. G.E.Loeb, Optimal isn’t good enough. Biol. Cybern. 106(11–12), 757–765 (2012)
  67. A. De Rugy, G.E. Loeb, T.J. Carroll, Muscle coordination is habitual rather than optimal. J. Neurosci. 32(21), 7384–7391 (2012)
  68. F.J. Valero-Cuevas, B.A. Cohn, H.F. Yngvason, E.L. Lawrence, Exploring the high-dimensional structure of muscle redundancy via subject-specific and generic musculoskeletal models. J. Biomech. 48(11), 2887–2896 (2015)
  69. J.L. McKay, T.J. Burkholder, L.H. Ting, Biomechanical capabilities influence postural control strategies in the cat hindlimb. J. Biomech. 40(10), 2254–2260 (2007)
  70. F.C. Anderson, M.G.Pandy, Dynamic optimization of human walking. J.Biomech.Eng.123(5), 381–390 (2001)
  71. F.J. Valero-Cuevas, N. Smaby, M. Venkadesan, M. Peterson, T.Wright, The strength-dexterity test as a measure of dynamic pinch performance. J. Biomech. 36, 265–270 (2003)
  72. J.M. Inouye, J.J. Kutch, F.J. Valero-Cuevas, A novel synthesis of computational approaches enables optimization of grasp quality of tendon-driven hands. IEEE Trans. Robot. 28(4), 958– 966 (2012)
  73. A.T. Miller, P.K. Allen,Graspit! a versatile simulator for robotic grasping. IEEE Robot .Autom. Mag. 11(4), 110–122 (2004)
  74. E. Todorov, Cosine tuning minimizes motor errors. Neural Comput. 14(6), 1233–1260 (2002)
  75. F.E. Zajac, Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17(4), 359–411 (1989)
  76. F.J. Valero-Cuevas, B.A. Cohn, M. Szedlák, K. Fukuda, B. Gärtner, Structure of the set of feasible neural commands for complex motor tasks, in 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Milan, Italy, August 2015. (IEEE Engineering in Medicine and Biology Society, 2015)
  77. R.L. Smith, Efficient monte carlo procedures for generating points uniformly distributed over bounded regions. Op. Res. 32(6), 1296–1308 (1984)
  78. V.J. Santos, F.J. Valero-Cuevas, A Bayesian approach to biomechanical modelling to optimize over large parameter spaces while considering anatomical variability, in Conference Proceedings of IEEE Engineering in Medicine & Biology Society, vol. 6 (2004), pp. 4626–4629
  79. V.J. Santos, C.D. Bustamante, F.J. Valero-Cuevas, Improving the fitness of high-dimensional biomechanical models via data-driven stochastic exploration. IEEE Trans. Biomed. Eng. 56, 552–564 (2009)
  80. F.J. Valero-Cuevas, H. Hoffmann, M.U. Kurse, J.J. Kutch, E.A. Theodorou, Computational models for neuromuscular function. IEEE Rev. Biomed. Eng. 2, 110–135 (2009)
  81. M. Dyer, A. Frieze, R. Kannan, A random polynomial-time algorithm for approximating the volume of convex bodies. J. ACM (JACM) 38(1), 1–17 (1991)
  82. L. Lovász, Hit-and-run mixes fast. Math. Program. 86(3), 443–461 (1999)
  83. I.Z. Emiris, V. Fisikopoulos, Efficient random-walk methods for approximating polytope volume. (2013), arXiv preprint arXiv:1312.2873
  84. R.O. Coats, A.D. Wilson, W. Snapp-Childs, A.J. Fath, G.P. Bingham, The 50s cliff:perceptuo-motor learning rates across the lifespan. PloS ONE 9(1), e85758 (2014)


Coming soon!

© Francisco Valero-Cuevas 2015