Exploring speed–accuracy tradeoff in reaching movements: a neurocomputational model

Abstract

The tradeoff between speed and accuracy of human movements has been exploited from many different perspectives, such as experimental psychology, workspace design, human–machine interface. This tradeoff is formalized by Fitts’ law, which states a linear relationship between the duration and the difficulty of the movement. The bigger is the required accuracy in reaching a target or farther is the target, the slower has to be the movement. A variety of computational models of neuromusculoskeletal systems have been proposed to pinpoint the neurobiological mechanisms that are involved in human movement. We introduce a neurocomputational model of spinal cord to unveil how the tradeoff between speed and accuracy elicits from the interaction between neural and musculoskeletal systems. Model simulations showed that the speed–accuracy tradeoff is not an intrinsic property of the neuromuscular system, but it is a behavioral trait that emerges from the strategy adopted by the central nervous system for executing faster movements. In particular, results suggest that the velocity of a previous learned movement is regulated by the monosynaptic connection between cortical cells and alpha motoneurons.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

References

  1. 1.

    Alexander RM (1997) A minimum energy cost hypothesis for human arm trajectories. Biol Cybern 76(2):97–105. https://doi.org/10.1007/s004220050324

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Alstermark B, Isa T (2012) Circuits for skilled reaching and grasping. Annu Rev Neurosci 35:559–78. https://doi.org/10.1146/annurev-neuro-062111-150527

    Article  Google Scholar 

  3. 3.

    Antonietti A, Casellato C, Garrido JA, Luque NR, Naveros F, Ros E, D’ Angelo E, Pedrocchi A (2016) Spiking neural network with distributed plasticity reproduces cerebellar learning in eye blink conditioning paradigms. IEEE Trans Biomed Eng 63(1):210–9. https://doi.org/10.1109/TBME.2015.2485301

    Article  Google Scholar 

  4. 4.

    Ashe J (2005) What is coded in the primary motor cortex? In: Riehle A, Vaadia E (eds) Motor cortex in voluntary movements a distributed system for distributed functions. CRC Press, Boca Raton

    Google Scholar 

  5. 5.

    Azim E, Fink AJP, Jessell TM (2014) Internal and external feedback circuits for skilled forelimb movement. Cold Spring Harb Symp Quant Biol 79:81–92. https://doi.org/10.1101/sqb.2014.79.024786

    Article  Google Scholar 

  6. 6.

    Berthier NE, Keen R (2006) Development of reaching in infancy. Exp Brain Res 169(4):507. https://doi.org/10.1007/s00221-005-0169-9

    Article  Google Scholar 

  7. 7.

    Bieńkiewicz MMN, Craig CM (2015) Parkinson’s is time on your side? evidence for difficulties with sensorimotor synchronization. Front Neurol 6:249. https://doi.org/10.3389/fneur.2015.00249

    Article  Google Scholar 

  8. 8.

    Bizzi E, Ajemian R (2015) A hard scientific quest: understanding voluntary movements. Daedalus 144(1):83–95. https://doi.org/10.1162/DAED_a_00324

    Article  Google Scholar 

  9. 9.

    Bogacz R, Wagenmakers EJ, Forstmann BU, Nieuwenhuis S (2010) The neural basis of the speed-accuracy tradeoff. Trends Neurosci 33(1):10–6. https://doi.org/10.1016/j.tins.2009.09.002

    Article  Google Scholar 

  10. 10.

    Branch MA, Coleman TF, Li Y (1999) A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems. SIAM J Sci Comput 21:1–23. https://doi.org/10.1137/S1064827595289108

    MathSciNet  Article  MATH  Google Scholar 

  11. 11.

    Brodal P (2010) The central nervous system. Oxford University Press, Oxford

    Google Scholar 

  12. 12.

    Buhrmann T, Di Paolo EA (2014) Spinal circuits can accommodate interaction torques during multijoint limb movements. Front Comput Neurosci 8:144. https://doi.org/10.3389/fncom.2014.00144

    Article  Google Scholar 

  13. 13.

    Bullock D, Contreras-Vidal JL (1991) How spinal neural networks reduce discrepancies between motor intention and motor realization. Boston University, Center for Adaptive Systems and Department of Cognitive

  14. 14.

    Bullock D, Contreras-Vidal JL, Grossberg S (1993) Equilibria and dynamics of a neural network model for opponent muscle control. In: Bekey GA, Goldberg KY (eds) Neural networks in robotics, vol 202. Springer, Boston, MA, pp 439–457. https://doi.org/10.1007/978-1-4615-3180-7_25

    Chapter  Google Scholar 

  15. 15.

    Burke RE (2008) Spinal cord. Scholarpedia 3(4):1925. https://doi.org/10.4249/scholarpedia.1925

    Article  Google Scholar 

  16. 16.

    Card SK, English WK, Burr BJ (1978) Evaluation of mouse, rate-controlled isometric joystick, step keys, and text keys for text selection on a crt. Ergonomics 21(8):601–613. https://doi.org/10.1080/00140137808931762

    Article  Google Scholar 

  17. 17.

    Carmona-Duarte C, Ferrer MA, Parziale A, Marcelli A (2017) Temporal evolution in synthetic handwriting. Pattern Recognit 68:233–244. https://doi.org/10.1016/j.patcog.2017.03.019

    Article  Google Scholar 

  18. 18.

    Cheng EJ, Brown IE, Loeb GE (2000) Virtual muscle: a computational approach to understanding the effects of muscle properties on motor control. J Neurosci Methods 101(2):117–130. https://doi.org/10.1016/S0165-0270(00)00258-2

    Article  Google Scholar 

  19. 19.

    Corcos DM, Gottlieb GL, Agarwal GC (1988) Accuracy constraints upon rapid elbow movements. J Mot Behav 20(3):255–272. https://doi.org/10.1080/00222895.1988.10735445

    Article  Google Scholar 

  20. 20.

    Corcos DM, Gottlieb GL, Agarwal GC (1989) Organizing principles for single-joint movements. II. A speed-sensitive strategy. J Neurophysiol 62(2):358–368. https://doi.org/10.1152/jn.1989.62.2.358

    Article  Google Scholar 

  21. 21.

    Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evolut Comput 15(1):4–31. https://doi.org/10.1109/TEVC.2010.2059031

    Article  Google Scholar 

  22. 22.

    Davoodi R, Urata C, Hauschild M, Khachani M, Loeb GE (2007) Model-based development of neural prostheses for movement. IEEE Trans Biomed Eng 54(11):1909–1918. https://doi.org/10.1109/TBME.2007.902252

    Article  Google Scholar 

  23. 23.

    De Stefano C, Marcelli A, Parziale A, Senatore R (2010) Reading cursive handwriting. In: 2010 12th International conference on frontiers in handwriting recognition. IEEE, pp 95–100. https://doi.org/10.1109/ICFHR.2010.21

  24. 24.

    Diaz M, Ferrer MAA, Quintana Hernandez JJ (2019) Anthropomorphic features for on-line signatures. IEEE Trans Pattern Anal Mach Intell. https://doi.org/10.1109/TPAMI.2018.2869163

    Article  Google Scholar 

  25. 25.

    Djioua M, Plamondon R, Della Cioppa A, Marcelli A (2007) Deterministic and evolutionary extraction of delta-lognormal parameters: performance comparison. Int J Pattern Recognit Artif Intell 21(01):21–41. https://doi.org/10.1142/S0218001407005284

    Article  Google Scholar 

  26. 26.

    Eliasmith C, Anderson CH (2003) Neural engineering: computation, representation, and dynamics in neurobiological systems. MIT Press, Cambridge

    Google Scholar 

  27. 27.

    Farina D, Aszmann O (2014) Bionic limbs: clinical reality and academic promises. Sci Transl Med 6(257):257ps12. https://doi.org/10.1126/scitranslmed.3010453

    Article  Google Scholar 

  28. 28.

    Felton EA, Radwin RG, Wilson JA, Williams JC (2009) Evaluation of a modified fitts law brain-computer interface target acquisition task in able and motor disabled individuals. J Neural Eng 6(5):056002. https://doi.org/10.1088/1741-2560/6/5/056002

    Article  Google Scholar 

  29. 29.

    Fernandez L, Huys R, Issartel J, Azulay JP, Eusebio A (2018) Movement speed-accuracy trade-off in parkinson’s disease. Front Neurol 9:897. https://doi.org/10.3389/fneur.2018.00897

    Article  Google Scholar 

  30. 30.

    Fitts PM (1954) The information capacity of the human motor system in controlling the amplitude of movement. J Exp Psychol 47(6):381–391. https://doi.org/10.1037/h0055392

    Article  Google Scholar 

  31. 31.

    Gillan DJ, Holden K, Adam S, Rudisill M, Magee L (1992) How should fitts’ law be applied to human-computer interaction? Interact Comput 4(3):291–313. https://doi.org/10.1016/0953-5438(92)90019-c

    Article  Google Scholar 

  32. 32.

    Golub MD, Yu BM, Schwartz AB, Chase SM (2014) Motor cortical control of movement speed with implications for brain-machine interface control. J Neurophysiol 112(2):411–29. https://doi.org/10.1152/jn.00391.2013

    Article  Google Scholar 

  33. 33.

    Guglielmelli E, Asuni G, Leoni F, Starita A, Dario P (2006) Neurocontroller for Robot arms based on biologically inspired visuomotor coordination neural models. Wiley, New York. https://doi.org/10.1002/9780470068298.ch26

    Book  Google Scholar 

  34. 34.

    Hallett M, Shahani BT, Young RR (1975) Emg analysis of stereotyped voluntary movements in man. J Neurol Neurosurg Psychiatry 38(12):1154–1162. https://doi.org/10.1136/jnnp.38.12.1154

    Article  Google Scholar 

  35. 35.

    Hao M, He X, Xiao Q, Alstermark B, Lan N (2013) Corticomuscular transmission of tremor signals by propriospinal neurons in parkinson’s disease. PLoS ONE 8(11):1–13. https://doi.org/10.1371/journal.pone.0079829.

    Article  Google Scholar 

  36. 36.

    Heitz RP (2014) The speed-accuracy tradeoff: history, physiology, methodology, and behavior. Front Neurosci 8:150. https://doi.org/10.3389/fnins.2014.00150

    Article  Google Scholar 

  37. 37.

    Hochberg LR, Bacher D, Jarosiewicz B, Masse NY, Simeral JD, Vogel J, Haddadin S, Liu J, Cash SS, van der Smagt P, Donoghue JP (2012) Reach and grasp by people with tetraplegia using a neurally controlled robotic arm. Nature 485(7398):372–375. https://doi.org/10.1038/nature11076

    Article  Google Scholar 

  38. 38.

    Hodges J, Lehmann EL et al (1962) Rank methods for combination of independent experiments in analysis of variance. Ann Math Stat 33(2):482–497. https://doi.org/10.1214/aoms/1177704575

    MathSciNet  Article  MATH  Google Scholar 

  39. 39.

    Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6(2):65–70. https://www.jstor.org/stable/4615733

    MathSciNet  MATH  Google Scholar 

  40. 40.

    Holzbaur KRS, Murray WM, Delp SL (2005) A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control. Ann Biomed Eng 33(6):829–840. https://doi.org/10.1007/s10439-005-3320-7

    Article  Google Scholar 

  41. 41.

    Homayouni T, Underwood KN, Beyer KC, Martin ER, Allan CH, Balasubramanian R (2015) Modeling implantable passive mechanisms for modifying the transmission of forces and movements between muscle and tendons. IEEE Trans Biomed Eng 62(9):2208–2214. https://doi.org/10.1109/TBME.2015.2419223

    Article  Google Scholar 

  42. 42.

    Houk JC, Rymer WZ (2011) Neural control of muscle length and tension. Compr Physiol 2:257–323. https://doi.org/10.1002/cphy.cp010208

    Article  Google Scholar 

  43. 43.

    Huang HJ, Kram R, Ahmed AA (2012) Reduction of metabolic cost during motor learning of arm reaching dynamics. J Neurosci 32(6):2182–2190. https://doi.org/10.1523/JNEUROSCI.4003-11.2012

    Article  Google Scholar 

  44. 44.

    Ifft PJ, Lebedev MA, Nicolelis MAL (2011) Cortical correlates of fitts’ law. Front Integr Neurosci 5:85. https://doi.org/10.3389/fnint.2011.00085

    Article  Google Scholar 

  45. 45.

    Jankowska E (1992) Interneuronal relay in spinal pathways from proprioceptors. Prog Neurobiol 38(4):335–378. https://doi.org/10.1016/0301-0082(92)90024-9

    Article  Google Scholar 

  46. 46.

    Jiang N, Dosen S, Muller KR, Farina D (2012) Myoelectric control of artificial limbs–is there a need to change focus? IEEE Signal Process Mag 29(5):150–152. https://doi.org/10.1109/MSP.2012.2203480

    Article  Google Scholar 

  47. 47.

    Jin L, Li S, Yu J, He J (2018) Robot manipulator control using neural networks: a survey. Neurocomputing 285:23–34. https://doi.org/10.1016/j.neucom.2018.01.002

    Article  Google Scholar 

  48. 48.

    Jude A, Guinness D, Poor GM (2016) Reporting and visualizing fitts’s law: dataset, tools and methodologies. In: Proceedings of the 2016 CHI conference extended abstracts on human factors in computing systems, CHI EA ’16, pp 2519–2525. ACM, New York, NY, USA. https://doi.org/10.1145/2851581.2892364

  49. 49.

    Kasprisin J, Grabiner M (2000) Joint angle-dependence of elbow flexor activation levels during isometric and isokinetic maximum voluntary contractions. Clin Biomech 15(10):743–749. https://doi.org/10.1016/s0268-0033(00)00036-x

    Article  Google Scholar 

  50. 50.

    Kennedy P, Cresswell A (2001) The effect of muscle length on motor-unit recruitment during isometric plantar flexion in humans. Exp Brain Res 137(1):58–64. https://doi.org/10.1007/s002210000623

    Article  Google Scholar 

  51. 51.

    Leisman G (1989) Limb segment information transmission capacity. J Manipulative Physiol Ther 12(1):3–9

    Google Scholar 

  52. 52.

    Lemon RN, Kirkwood PA, Maier MA, Nakajima K, Nathan P (2004) Direct and indirect pathways for corticospinal control of upper limb motoneurons in the primate. In: Mori S, Stuart DG, Wiesendanger M (eds) Brain mechanisms for the integration of posture and movement, vol 143. Progress in brain research. Elsevier, Amsterdam, pp 263–279. https://doi.org/10.1016/S0079-6123(03)43026-4

    Chapter  Google Scholar 

  53. 53.

    Li S, He J, Li Y, Rafique MU (2017) Distributed recurrent neural networks for cooperative control of manipulators: a game-theoretic perspective. IEEE Trans Neural Netw Learn Syst 28(2):415–426. https://doi.org/10.1109/TNNLS.2016.2516565

    MathSciNet  Article  Google Scholar 

  54. 54.

    Li S, He X, Lan N (2014) Modular control of movement and posture by the corticospinal alpha-gamma motor systems. In: 2014 36th annual international conference of the IEEE engineering in medicine and biology society, pp 4079–4082. https://doi.org/10.1109/EMBC.2014.6944520

  55. 55.

    Li S, Zhang Y, Jin L (2017) Kinematic control of redundant manipulators using neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2243–2254. https://doi.org/10.1109/TNNLS.2016.2574363

    MathSciNet  Article  Google Scholar 

  56. 56.

    Li S, Zhuang C, Hao M, He X, Marquez JC, Niu CM, Lan N (2015) Coordinated alpha and gamma control of muscles and spindles in movement and posture. Front Comput Neurosci 9:122. https://doi.org/10.3389/fncom.2015.00122

    Article  Google Scholar 

  57. 57.

    Loeb GE (1983) Finding common groud between robotics and physiology. Trends Neurosci 6:203–204. https://doi.org/10.1016/0166-2236(83)90093-0

    Article  Google Scholar 

  58. 58.

    Loeb GE (2012) Optimal isn’t good enough. Biol Cybern 106(11):757–765. https://doi.org/10.1007/s00422-012-0514-6

    Article  Google Scholar 

  59. 59.

    Marcelli A, Parziale A, Santoro A (2012) Modeling handwriting style: a preliminary investigation. In: 2012 International conference on frontiers in handwriting recognition. IEEE, pp 411–416. https://doi.org/10.1109/ICFHR.2012.234

  60. 60.

    Marcelli A, Parziale A, Santoro A (2013) Modelling visual appearance of handwriting. In: International conference on image analysis and processing. Lecture notes in computer science, vol 8157, pp 673–682. https://doi.org/10.1007/978-3-642-41184-7_68

  61. 61.

    Marcelli A, Parziale A, Senatore R (2013) Some observations on handwriting from a motor learning perspective. In: AFHA, vol. 1022, pp 6–10. http://ceur-ws.org/Vol-1022/

  62. 62.

    Maruff P, Wilson P, Trebilcock M, Currie J (1999) Abnormalities of imagined motor sequences in children with developmental coordination disorder. Neuropsychologia 37(11):1317–1324. https://doi.org/10.1016/S0028-3932(99)00016-0

    Article  Google Scholar 

  63. 63.

    Mazzoni P, Hristova A, Krakauer JW (2007) Why don’t we move faster? Parkinson’s disease, movement vigor, and implicit motivation. J Neurosci 27(27):7105–16. https://doi.org/10.1523/JNEUROSCI.0264-07.2007

    Article  Google Scholar 

  64. 64.

    Meunier S, Pierrot-Deseilligny E (1998) Cortical control of presynaptic inhibition of ia afferents in humans. Exp Brain Res 119(4):415–426. https://doi.org/10.1007/s002210050357

    Article  Google Scholar 

  65. 65.

    Michmizos KP, Krebs HI (2014) Pointing with the ankle: the speed-accuracy trade-off. Exp Brain Res 232(2):647–57. https://doi.org/10.1007/s00221-013-3773-0

    Article  Google Scholar 

  66. 66.

    Mileusnic MP, Brown IE, Lan N, Loeb GE (2006) Mathematical models of proprioceptors. I. Control and transduction in the muscle spindle. J Neurophysiol 96(4):1772–88. https://doi.org/10.1152/jn.00868.2005

    Article  Google Scholar 

  67. 67.

    Mileusnic MP, Loeb GE (2006) Mathematical models of proprioceptors. II. Structure and function of the golgi tendon organ. J Neurophysiol 96(4):1789–802. https://doi.org/10.1152/jn.00869.2005

    Article  Google Scholar 

  68. 68.

    Miranda RA, Casebeer WD, Hein AM, Judy JW, Krotkov EP, Laabs TL, Manzo JE, Pankratz KG, Pratt GA, Sanchez JC, Weber DJ, Wheeler TL, Ling GS (2015) Darpa-funded efforts in the development of novel brain-computer interface technologies. J Neurosci Methods 244:52–67. https://doi.org/10.1016/j.jneumeth.2014.07.019

    Article  Google Scholar 

  69. 69.

    Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42(2):223–227. https://doi.org/10.1007/BF00236911

    Article  Google Scholar 

  70. 70.

    Morrison S, Anson JG (1999) Natural goal-directed movements and the triphasic emg. Motor Control 3(4):346–371. https://doi.org/10.1123/mcj.3.4.346

    Article  Google Scholar 

  71. 71.

    Mussa-Ivaldi FA, Miller LE (2003) Brain-machine interfaces: computational demands and clinical needs meet basic neuroscience. Trends Neurosci 26(6):329–334. https://doi.org/10.1016/S0166-2236(03)00121-8

    Article  Google Scholar 

  72. 72.

    Nicolelis MAL, Lebedev MA (2009) Principles of neural ensemble physiology underlying the operation of brain-machine interfaces. Nat Rev Neurosci 10:530. https://doi.org/10.1038/nrn2653

    Article  Google Scholar 

  73. 73.

    O’Reilly RC, Munakata Y, Frank M, Hazy T et al (2012) Computational cognitive neuroscience. Pedia Press, Mainz

    Google Scholar 

  74. 74.

    Osborne LC, Lisberger SG, Bialek W (2005) A sensory source for motor variation. Nature 437(7057):412–6. https://doi.org/10.1038/nature03961

    Article  Google Scholar 

  75. 75.

    Papaiordanidou M, Mustacchi V, Stevenot JD, Vanoncini M, Martin A (2016) Spinal and supraspinal mechanisms affecting torque development at different joint angles. Muscle Nerve 53(4):626–632. https://doi.org/10.1002/mus.24895

    Article  Google Scholar 

  76. 76.

    Parziale A, Della Cioppa A, Senatore R, Marcelli A (2019) A decision tree for automatic diagnosis of parkinson’s disease from offline drawing samples: experiments and findings. In: International conference on image analysis and processing. Lecture notes in computer science, vol 11751, pp 196–206. Springer. https://doi.org/10.1007/978-3-030-30642-7_18

  77. 77.

    Parziale A, Diaz M, Ferrer MA, Marcelli A (2019) Sm-dtw: Stability modulated dynamic time warping for signature verification. Pattern Recognit Lett 121:113–122. https://doi.org/10.1016/j.patrec.2018.07.029.

    Article  Google Scholar 

  78. 78.

    Parziale A, Festa J, Marcelli A (2015) A neurocomputational model of spinal circuitry for controlling the execution of arm voluntary movements. In: Rémi C, Prévost L, Anquetil E (eds) 17th Biennial conference of the international graphonomics society, drawing, handwriting processing analysis: new advances and challenges. International Graphonomics Society (IGS) and Université des Antilles (UA), Pointe-à-Pitre, Guadeloupe. https://hal.univ-antilles.fr/hal-01165882. Accessed 7 Dec 2019

  79. 79.

    Parziale A, Santoro A, Marcelli A, Rizzo AP, Molinari C, Cappuzzo AG, Fontana F (2014) An interactive tool for forensic handwriting examination. In: 2014 14th International conference on frontiers in handwriting recognition. IEEE, pp 440–445. https://doi.org/10.1109/ICFHR.2014.80

  80. 80.

    Pierrot-Deseilligny E, Burke DJ (2012) The circuitry of the human spinal cord: neuroplasticity and corticospinal mechanisms. Cambridge University Press, Cambridge

    Book  Google Scholar 

  81. 81.

    Pivetta C, Esposito MS, Sigrist M, Arber S (2014) Motor-circuit communication matrix from spinal cord to brainstem neurons revealed by developmental origin. Cell 156(3):537–48. https://doi.org/10.1016/j.cell.2013.12.014

    Article  Google Scholar 

  82. 82.

    Plamondon R (1995) A kinematic theory of rapid human movements. Part I. Movement representation and generation. Biol Cybern 72(4):295–307. https://doi.org/10.1007/bf00202785

    Article  MATH  Google Scholar 

  83. 83.

    Plamondon R (1995) A kinematic theory of rapid human movements. Part II. Movement time and control. Biol Cybern 72(4):309–320. https://doi.org/10.1007/bf00202786

    Article  MATH  Google Scholar 

  84. 84.

    Plamondon R, Alimi AM (1997) Speed/accuracy trade-offs in target-directed movements. Behav Brain Sci 20(2):279–303 (discussion 303–49). https://doi.org/10.1017/s0140525x97001441

    Article  Google Scholar 

  85. 85.

    Poletti C, Sleimen-Malkoun R, Decker LM, Retornaz F, Lemaire P, Temprado JJ (2017) Strategic variations in fitts’ task: comparison of healthy older adults and cognitively impaired patients. Front Aging Neurosci 8:334. https://doi.org/10.3389/fnagi.2016.00334

    Article  Google Scholar 

  86. 86.

    Prochazka A, Ellaway P (2012) Sensory systems in the control of movement. Compr Physiol 2(4):2615–27. https://doi.org/10.1002/cphy.c100086

    Article  Google Scholar 

  87. 87.

    Qiao H (2016) Innovating at the intersection of neuroscience and robotics. In: Brain-inspired intelligent robotics: the intersection of robotics and neuroscience, p 3. Science/AAAS

  88. 88.

    Qu HE, Niu CM, Li S, Hao MZ, Hu ZX, Xie Q, Lan N (2017) Neural computational modeling reveals a major role of corticospinal gating of central oscillations in the generation of essential tremor. Neural Regen Res 12(12):2035–2044. https://doi.org/10.4103/1673-5374.221161

    Article  Google Scholar 

  89. 89.

    Raphael G, Tsianos GA, Loeb GE (2010) Spinal-like regulator facilitates control of a two-degree-of-freedom wrist. J Neurosci 30(28):9431–44. https://doi.org/10.1523/JNEUROSCI.5537-09.2010

    Article  Google Scholar 

  90. 90.

    Rathelot JA, Strick PL (2009) Subdivisions of primary motor cortex based on cortico-motoneuronal cells. Proc Natl Acad Sci 106(3):918–923. https://doi.org/10.1073/pnas.0808362106

    Article  Google Scholar 

  91. 91.

    Reina GA, Moran DW, Schwartz AB (2001) On the relationship between joint angular velocity and motor cortical discharge during reaching. J Neurophysiol 85(6):2576–89. https://doi.org/10.1152/jn.2001.85.6.2576

    Article  Google Scholar 

  92. 92.

    Rodríguez-Fdez I, Canosa A, Mucientes M, Bugarín A (2015) Stac: a web platform for the comparison of algorithms using statistical tests. In: 2015 IEEE international conference on Fuzzy systems (FUZZ-IEEE). IEEE, pp 1–8. https://doi.org/10.1109/FUZZ-IEEE.2015.7337889

  93. 93.

    Sartori M, Lloyd DG, Farina D (2016) Neural data-driven musculoskeletal modeling for personalized neurorehabilitation technologies. IEEE Trans Biomed Eng 63(6):1341. https://doi.org/10.1109/TBME.2016.2538296

    Article  Google Scholar 

  94. 94.

    Schmidt RA (1975) A schema theory of discrete motor skill learning. Psychol Rev 82(4):225–260. https://doi.org/10.1037/h0076770

    Article  Google Scholar 

  95. 95.

    Senatore R, Marcelli A (2012) A neural scheme for procedural motor learning of handwriting. In: 2012 International conference on frontiers in handwriting recognition. IEEE, pp 659–664. https://doi.org/10.1109/ICFHR.2012.160

  96. 96.

    Senatore R, Marcelli A (2019) A paradigm for emulating the early learning stage of handwriting: performance comparison between healthy controls and parkinson’s disease patients in drawing loop shapes. Hum Mov Sci 65:89–101. https://doi.org/10.1016/j.humov.2018.04.007

    Article  Google Scholar 

  97. 97.

    Sergio LE, Hamel-Pâquet C, Kalaska JF (2005) Motor cortex neural correlates of output kinematics and kinetics during isometric-force and arm-reaching tasks. J Neurophysiol 94(4):2353–78. https://doi.org/10.1152/jn.00989.2004

    Article  Google Scholar 

  98. 98.

    Song D, Lan N, Loeb GE, Gordon J (2008) Model-based sensorimotor integration for multi-joint control: development of a virtual arm model. Ann Biomed Eng 36(6):1033–48. https://doi.org/10.1007/s10439-008-9461-8

    Article  Google Scholar 

  99. 99.

    Song D, Raphael G, Lan N, Loeb GE (2008) Computationally efficient models of neuromuscular recruitment and mechanics. J Neural Eng 5(2):175–84. https://doi.org/10.1088/1741-2560/5/2/008

    Article  Google Scholar 

  100. 100.

    International Organization for Standardization (2002) Ergonomic requirements for office work with visual display terminals (vdts)—part 9: requirements for non-keyboard input devices (ISO 9241-9). https://www.iso.org/standard/30030.html. Accessed 7 Dec 2019

  101. 101.

    Stefanovic F, Galiana HL (2014) A simplified spinal-like controller facilitates muscle synergies and robust reaching motions. IEEE Trans Neural Syst Rehabil Eng 22(1):77–87. https://doi.org/10.1109/TNSRE.2013.2274284

    Article  Google Scholar 

  102. 102.

    Stefanovic F, Galiana HL (2015) Efferent feedback in a spinal-like controller: reaching with perturbations. IEEE Trans Neural Syst Rehabilit Eng 24(1):140–150. https://doi.org/10.1109/TNSRE.2015.2439515

    Article  Google Scholar 

  103. 103.

    Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359. https://doi.org/10.1023/A:1008202821328

    MathSciNet  Article  MATH  Google Scholar 

  104. 104.

    Svensson CM, Coombes S, Peirce JW (2012) Using evolutionary algorithms for fitting high-dimensional models to neuronal data. Neuroinformatics 10(2):199–218. https://doi.org/10.1007/s12021-012-9140-7

    Article  Google Scholar 

  105. 105.

    Teka WW, Hamade KC, Barnett WH, Kim T, Markin SN, Rybak IA, Molkov YI (2017) From the motor cortex to the movement and back again. PLoS ONE 12(6):e0179288. https://doi.org/10.1371/journal.pone.0179288

    Article  Google Scholar 

  106. 106.

    Tsianos GA, Goodner J, Loeb GE (2014) Useful properties of spinal circuits for learning and performing planar reaches. J Neural Eng 11(5):056006. https://doi.org/10.1088/1741-2560/11/5/056006

    Article  Google Scholar 

  107. 107.

    Tsianos GA, Raphael G, Loeb GE (2011) Modeling the potentiality of spinal-like circuitry for stabilization of a planar arm system. In: Schouenborg J, Garwicz M, Danielsen N (eds) Brain Machine interfaces: implications for science, clinical practice and society. Progress in brain research, vol 194. Elsevier, pp 203–213. https://doi.org/10.1016/B978-0-444-53815-4.00006-6

  108. 108.

    Tsianos GA, Rustin C, Loeb GE (2012) Mammalian muscle model for predicting force and energetics during physiological behaviors. IEEE Trans Neural Syst Rehabil Eng 20(2):117–33. https://doi.org/10.1109/TNSRE.2011.2162851

    Article  Google Scholar 

  109. 109.

    Uchida TK, Seth A, Pouya S, Dembia CL, Hicks JL, Delp SL (2016) Simulating ideal assistive devices to reduce the metabolic cost of running. PloS ONE 11(9):e0163417. https://doi.org/10.1371/journal.pone.0163417

    Article  Google Scholar 

  110. 110.

    Valero-Cuevas FJ, Santello M (2017) On neuromechanical approaches for the study of biological and robotic grasp and manipulation. J Neuro Eng Rehabil 14(1):101. https://doi.org/10.1186/s12984-017-0305-3.

    Article  Google Scholar 

  111. 111.

    Van Geit W, De Schutter E, Achard P (2008) Automated neuron model optimization techniques: a review. Biol Cybern 99(4–5):241–51. https://doi.org/10.1007/s00422-008-0257-6

    MathSciNet  Article  MATH  Google Scholar 

  112. 112.

    Weiss P, Stelmach G, Adler C, Waterman C (1996) Parkinsonian arm movements as altered by task difficulty. Parkinsonism Relat Disord 2(4):215–223. https://doi.org/10.1016/S1353-8020(96)00026-0

    Article  Google Scholar 

  113. 113.

    Wierzbicka MM, Wiegner AW, Shahani BT (1986) Role of agonist and antagonist muscles in fast arm movements in man. Exp Brain Res 63(2):331–340. https://doi.org/10.1007/bf00236850

    Article  Google Scholar 

  114. 114.

    Wilson PH, Maruff P, Ives S, Currie J (2001) Abnormalities of motor and praxis imagery in children with dcd. Hum Mov Sci 20(1):135–159. https://doi.org/10.1016/S0167-9457(01)00032-X

    Article  Google Scholar 

  115. 115.

    Yang GZ, Bellingham J, Dupont PE, Fischer P, Floridi L, Full R, Jacobstein N, Kumar V, McNutt M, Merrifield R, Nelson BJ, Scassellati B, Taddeo M, Taylor R, Veloso M, Wang ZL, Wood R (2018) The grand challenges of science robotics. Sci Robot. https://doi.org/10.1126/scirobotics.aar7650

    Article  Google Scholar 

  116. 116.

    Yang J, Lee J, Lee B, Kim S, Shin D, Lee Y, Lee J, Han D, Choi S (2014) The effects of elbow joint angle changes on elbow flexor and extensor muscle strength and activation. J Phys Ther Sci 26(7):1079–1082. https://doi.org/10.1589/jpts.26.1079

    Article  Google Scholar 

  117. 117.

    Zielinski K, Laur R (2008) Stopping criteria for differential evolution in constrained single-objective optimization. Springer, Berlin, pp 111–138. https://doi.org/10.1007/978-3-540-68830-3_4

    Book  Google Scholar 

Download references

Acknowledgements

This study was partially funded by the “Bando PRIN2015-Progetto HAND” under Grant H96J16000820001 from the Italian Ministero dell’Istruzione, dell’ Università e della Ricerca.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Antonio Parziale.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Parziale, A., Senatore, R. & Marcelli, A. Exploring speed–accuracy tradeoff in reaching movements: a neurocomputational model. Neural Comput & Applic 32, 13377–13403 (2020). https://doi.org/10.1007/s00521-019-04690-z

Download citation

Keywords

  • Human movement
  • Speed–accuracy tradeoff
  • Fitts’ law
  • Neurocomputational model