Chapter 6: The Neural Control of Musculotendon Lengths and Excursions Is Overdetermined (under construction)

Last updated Dec. 26 2015 by Francisco Valero-Cuevas

Abstract:


This chapter introduces the mathematical foundations of the concept of obligatory kinematic correlations among joint angles and musculotendon lengths. As presented in Chap. 4, tendon excursions are overdetermined because the angles and angle changes of the few joints uniquely determine the lengths and excursions, respectively, of all musculotendons. This is the opposite of redundancy: there is a single and unique set of tendon excursions that can satisfy a given limb movement. This begs the question of how the nervous system controls the excursions of all musculotendons so that the limb can move smoothly. Essentially, if for some reason any of the musculotendons undergoing an eccentric contraction fails to lengthen to satisfy the geometric requirements of the joint rotations, at the very least the limb motion will be disrupted, and at worst the limb can lock up. Physiologically, the failure to accommodate the necessary length changes could be due to anatomical interconnections among muscles or tendons, neurally mediated resistance to lengthening due to short- or long-latency reflexes, or spinally- and cortically-mediated commands to the muscles. This chapter lays the foundation for understanding the interactions between muscle coordination and reflex mechanisms necessary for natural movement by providing a mathematical framework for the overdetermined nature of tendon excursions. This is done for the simplified case with no anatomical interconnections among muscles or tendons, but the conclusions and intuition provided reinforce the notion that the neural control of movement for tendon-driven limbs is in fact not as redundant as is currently thought. Recall that, as mentioned in Chap. 4, the term tendon suffices for most mathematical and mechanical analyses as it applies to both robots and vertebrates. When the analysis continues on to consider muscle mechanics and its neural control, I will prefer to use the term musculotendon.

Forum and commentary:


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Exercises:


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Additional references and suggested reading:


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References in book:


  1. R.M. Murray, Z. Li, S.S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC Press, 1994)
  2. T. Yoshikawa, Foundations of Robotics: Analysis and Control (MIT Press, Cambridge,1990)
  3. O. Bottema, B. Roth, Theoretical Kinematics (Dover Publications, 2012)
  4. S.A. Hummel, Frisbee flight simulation and throw biomechanics. Master’s thesis, University of California, (2003)
  5. 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)
  6. D.A. Winter, Biomechanics and Motor Control of Human Movement (Wiley,NewYork,2009)
  7. E. Todorov, Probabilistic inference of multijoint movements, skeletal parameters and marker attachments from diverse motion capture data. IEEE Trans. Biomed. Eng. 54(11), 1927–1939 (2007)
  8. J.Shotton,T.Sharp,A.Kipman,A.Fitzgibbon,M.Finocchio,A.Blake,M.Cook,R.Moore, Real-time human pose recognition in parts from single depth images. Commun. ACM 56(1), 116–124 (2013)
  9. 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)
  10. Y.T.Lee,H.R.Choi,W.K.Chung,Y.Youm,Stiffnesscontrolofacoupledtendon-drivenrobot hand. IEEE Control Syst. 14(5), 10–19 (1994)
  11. R.Alexander,G.M.O.Maloiy,R.F.Ker,A.S.Jayes,C.N.Warui,Theroleoftendonelasticity in the locomotion of the camel (camelus dromedarius). J. Zool. 198(3), 293–313 (1982)
  12. 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)
  13. I.D. Loram, C.N. Maganaris, M .Lakie, Active, non-spring-like muscle movements in human postural sway: how might paradoxical changes in muscle length be produced? J. Physiol. 564(1), 281–293 (2005)
  14. R.I. Griffiths,Shorteningofmusclefibresduringstretchoftheactivecatmedialgastrocnemius muscle: the role of tendon compliance. J. Physiol. 436(1), 219–236 (1991)
  15. T.A. McMahon, Muscles, Reflexes, and Locomotion (Princeton University Press, NewJersey, 1984)
  16. R.L. Lieber, Skeletal Muscle Structure, Function, and Plasticity (Lippincott Williams & Wilkins, Philadelphia, 2002)
  17. K.G. Keenan, V.J. Santos, M. Venkadesan, F.J. Valero-Cuevas, Maximal voluntary finger- tip force production is not limited by movement speed in combined motion and force tasks. J. Neurosci. 29, 8784–8789 (2009)
  18. A.A. Biewener, J.M. Wakeling, S.S. Lee, A.S. Arnold, Validation of hill-type muscle models in relation to neuromuscular recruitment and force–velocity properties: predicting patterns of in vivo muscle force. Integr. Comp. Biol. 54(6), 1072–1083, page icu070, (2014)
  19. R.H. Miller, A comparison of muscle energy models for simulating human walking in three dimensions. J. Biomech. 47(6), 1373–1381 (2014)
  20. G.A.Tsianos,C.Rustin,G.E.Loeb,Mammalianmusclemodelforpredictingforceandener- getics during physiological behaviors. IEEE Trans. Neural Syst. Rehabil. Eng. 20(2), 117–133 (2012)
  21. M.R.Rehorn,A.K.Schroer,S.S.Blemker,Thepassivepropertiesofmusclefibersarevelocity dependent. J. Biomech. 47(3), 687–693 (2014)
  22. E.J.Cheng,I.E.Brown,G.E.Loeb,Virtualmuscle:acomputationalapproachtounderstanding the effects of muscle properties on motor control. J. Neurosci. Methods 101(2), 117–130 (2000)
  23. K.C.Nishikawa,J.A.Monroy,T.E.Uyeno,S.H.Yeo,D.K.Pai,S.L.Lindstedt,Istitina‘winding filament’? A new twist on muscle contraction. Proc. R. Soc. Lond. B: Biol. Sci. 279(1730), 981–990 (2012)
  24. W.Herzog,M.Duvall,T.R.Leonard,Molecularmechanismsofmuscleforceregulation:arole for titin? Exerc. Sport. Sci. Rev. 40(1), 50–57 (2012)
  25. T.R. Leonard, W. Herzog, Regulation of muscle force in the absence of actin-myosin-based cross-bridge interaction. Am. J. Physiol.-Cell Physiol. 299(1), C14–C20 (2010)
  26. S.Dayanidhi,R.L.Lieber,Skeletalmusclesatellitecells:mediatorsofmusclegrowthduring development and implications for developmental disorders. Muscle Nerve 50(5), 723–732 (2014)
  27. 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)
  28. B.W. Tobalske, T.L. Hedrick, K.P. Dial, A.A. Biewener, Comparative power curves in bird flight. Nature 421(6921), 363–366 (2003)
  29. A.A. Biewener, Patterns of mechanical energy change in tetrapod gait: pendula, springs and work. J. Exp. Zool. Part A: Comp. Exp. Biol. 305(11), 899–911 (2006)
  30. J.M. Donelan, R. Kram, A.D. Kuo, Simultaneous positive and negative external mechanical work in human walking. J. Biomech. 35(1), 117–124 (2002)
  31. M.J.Srinivasan,A.Ruina,Computeroptimizationofaminimalbipedmodeldiscoverswalking and running. Nature 439(7072), 72–75 (2006)
  32. E. Pierrot-Deseilligny, D. Burke, The Circuitry of the Human Spinal Cord: Its Role in Motor Control and Movement Disorders (Cambridge University Press, Cambridge, 2005)
  33. T.D.Sanger,D.Chen,D.L.Fehlings,M.Hallett,A.E.Lang,J.W.Mink,H.S.Singer,K.Alter, H. Ben-Pazi, E.E. Butler et al., Definition and classification of hyperkinetic movements in childhood. Mov. Disord. 25(11), 1538–1549 (2010)
  34. C.S.Sherrington,Reflexinhibitionasafactorintheco-ordinationofmovementsandpostures. Exp. Physiol. 6(3), 251–310 (1913)35. C. Capaday, R.B. Stein, Amplitude modulation of the soleus H-reflex in the human duringwalking and standing. J. Neurosci. 6(5), 1308–1313 (1986)
  35. X.Hu,N.L.Suresh,W.Z.Rymer,Estimatingthetimecourseofpopulationexcitatorypostsy- naptic potentials in motoneurons of spastic stroke survivors. J. Neurophysiol. 113 (6), 1952– 1957, pp. jn-00946, (2014)
  36. C.M.Niu,S.K.Nandyala,T.D.Sanger,Emulatedmusclespindleandspikingafferentsvalidates vlsi neuromorphic hardware as a testbed for sensorimotor function and disease. Front. Comput. Neurosci. 8, (2014)
  37. C.M.Niu,J.Rocamora,W.J.Sohn,F.J.Valero-Cuevas,T.D.Sanger,Force–velocitypropertyof muscle is critical for stabilizing a tendon-driven robotic joint controlled by neuromorphic hard- ware, in Proceedings of the 6th International IEEE/EMBS Conference of Neural Engineering. (IEEE/EMBS, 2013)
  38. T. Buhrmann, E.A. Di Paolo, Spinal circuits can accommodate interaction torques during multijoint limb movements. Front. Comput. Neurosci. 8, (2014)
  39. Y.Masugi,T.Kitamura,K.Kamibayashi,T.Ogawa,T.Ogata,N.Kawashima,K.Nakazawa, Velocity-dependent suppression of the soleus H-reflex during robot-assisted passive stepping. Neurosci. Lett. 584, 337–341 (2015)
  40. B.A. Garner, M.G. Pandy, Estimation of musculotendon properties in the human upper limb. Ann. Biomed. Eng. 31(2), 207–220 (2003)
  41. R.V. Gonzalez, T.S. Buchanan, S.L. Delp, How muscle architecture and moment arms affect wrist flexion-extension moments. J. Biomech. 30(7), 705–712 (1997)
  42. E.Y. Chao, K.N. An, Graphical interpretation of the solution to the redundant problem in biomechanics. J. Biomech. Eng. 100, 159–167 (1978)
  43. B.I.Prilutsky,Musclecoordination:thediscussioncontinues.Mot.Control4(1),97–116(2000)
  44. H.Hultborn,Spinalreflexes,mechanismsandconcepts:fromEcclestoLundbergandbeyond. Prog. Neurobiol. 78(3), 215–232 (2006)
  45. E.P.Zehr,R.B.Stein,Whatfunctionsdoreflexesserveduringhumanlocomotion?Prog.Neu- robiol. 58(2), 185–205 (1999)
  46. G.E. Loeb, Overcomplete musculature or underspecified tasks? Mot. Control 4(1), 81–83 (2000)
  47. T.D.Sanger,D.Chen,M.R.Delgado,D.Gaebler-Spira,M.Hallett,J.W.Minketal.,Definition and classification of negative motor signs in childhood. Pediatrics 118(5), 2159–2167 (2006)
  48. F.E.Zajac,Howmusculotendonarchitectureandjointgeometryaffectthecapacityofmuscles to move and exert force on objects: a review with application to arm and forearm tendon transfer design. J. Am. Hand Surg. 17(5), 799–804 (1992)
  49. A. Andrew, Muscle and tendon contributions to force, work, and elastic energy savings: a comparative perspective. Exerc. Sport. Sci. Rev. 28(3), 99–107 (2000)
  50. N. Konow, T.J. Roberts, The series elastic shock absorber: tendon elasticity modulates energy dissipation by muscle during burst deceleration. Proc. R. Soc. Lond. B: Biol. Sci. 282(1804):2014–2800 (2015)
  51. C.Hanson-Carbonneau,M.Eng,A.S.Arnold,D.E.Lieberman,A.A.Biewener,Thecapacity of the human iliotibial band to store elastic energy during running. J. Biomech. (2015)
  52. R.M.Alexander,Tendonelasticityandmusclefunction.Comp.Biochem.Physiol.PartA:Mol. Integr. Physiol. 133(4), 1001–1011 (2002)
  53. C.N. Holt, T.J. Roberts, G.N. Askew, The energetic benefits of tendon springs in running: is the reduction of muscle work important? J. Exp. Biol. 217(24), 4365–4371 (2014)

Code:


FiveDOF_Model.mat: Download
Note: This .mat file should be downloaded for both python and matlab users as there is something in the python code to read in the .mat file.

FiveDOF_model_frisbee_throw.m: Download

FiveDOF_model_frisbee_throw.py: Download

© Francisco Valero-Cuevas 2015