Abstract
Although the cerebellum has been shown to be critical for the acquisition and retention of adaptive modifications in certain reflex behaviors, this structure’s role in the learning of motor skills required to execute complex voluntary goal-directed movements still is unclear. This study explores this issue by analyzing the effects of inactivating the interposed and dentate cerebellar nuclei on the adaptation required to compensate for an external elastic load applied during a reaching movement. We show that cats with these nuclei inactivated can adapt to predictable perturbations of the forelimb during a goal-directed reach by including a compensatory component in the motor plan prior to movement initiation. In contrast, when comparable compensatory modifications must be triggered on-line because the perturbations are applied in randomized trials (i.e., unpredictably), such adaptive responses cannot be executed or reacquired after the interposed and dentate nuclei are inactivated. These findings provide the first demonstration of the condition-dependent nature of the cerebellum’s contribution to the learning of a specific volitional task.
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References
Albus JS (1971) A theory of cerebellar function. Math Biosci 10:25–61
Baizer JS Glickstein M (1974) Proceedings: role of cerebellum in prism adaptation. J Physiol 236:34P–35P
Baizer JS, Kralj-Hans I, Glickstein M (1999) Cerebellar lesions and prism adaptation in macaque monkeys. J Neurophysiol 81:1960–1965
Barto AG, Fagg AH, Sitkoff N, Houk JC (1999) A cerebellar model of timing and prediction in the control of reaching. Neural Comput 11:565–594
Bernstein NA (1967) The coordination and regulation of movements. Pergamon Press, New York
Bhushan N, Shadmehr R (1999) Computational nature of human adaptive control during learning of reaching movements in force fields. Biol Cybern 81:39–60
Bloedel JR, Bracha V (1995) On the cerebellum, cutaneomuscular reflexes, movement control and the elusive engrams of memory. Behav Brain Res 68:1–44
Bracha V, Webster ML, Winters NK, Irwin KB, Bloedel JR (1994) Effects of muscimol inactivation of the cerebellar interposed-dentate nuclear complex on the performance of the nictitating membrane response in the rabbit. Exp Brain Res 100:453–468
Bracha V, Irwin KB, Webster ML, Wunderlich DA, Stachowiak MK, Bloedel JR (1998) Microinjections of anisomycin into the intermediate cerebellum during learning affect the acquisition of classically conditioned responses in the rabbit. Brain Res 788:169–178
Evarts EV, Tanji J (1976a) Reflex and intended responses in motor cortex pyramidal tract neurons of monkey. J Neurophysiol 39:1069–1080
Evarts EV, Tanji J (1976b) Anticipatory activity of motor cortex neurons in relation to direction of an intended movement. J Neurophysiol 39:1062–1079
Ghez C, Gordon J, Ghilardi MF (1995) Impairments of reaching movements in patients without proprioception. II. Effects of visual information on accuracy. J Neurophysiol 73:361–372
Gilman S, Carr D, Hollenberg J (1976) Kinematic effects of deafferentation and cerebellar ablation. Brain 99:311–330
Gilman S, Bloedel JR, Lechtenberg R (1981) Disorders of the cerebellum. Davis Co., Philadelphia,
Hore J, Vilis T (1984) Loss of set in muscle responses to limb perturbations during cerebellar dysfunction. J Neurophysiol 51:1137–1148
Hoy MG, Zernicke RF (1985) Modulation of limb dynamics in the swing phase of locomotion. J Biomech 18:49–60
Ito M (1984) The cerebellum and neural control. Raven Press, New York
Ito M (1993) Synaptic plasticity in the cerebellar cortex and its role in motor learning. Can J Neurol Sci 20 [Suppl 3]:S70–S74
Kolb FP, Irwin KB, Bloedel JR, Bracha V (1997) Conditioned and unconditioned forelimb reflex systems in the cat: involvement of the intermediate cerebellum. Exp Brain Res 114:255–270
Krupa DJ, Thompson RF (1997) Reversible inactivation of the cerebellar interpositus nucleus completely prevents acquisition of the classically conditioned eye-blink response. Learn Mem 3:545–556
Marr D (1969) A theory of cerebellar cortex. J Physiol (Lond) 202:437–470
Martin JH (1991) Autoradiographic estimation of the extent of reversible inactivation produced by microinjection of lidocaine and muscimol in the rat. Neurosci Lett 127:160–164
McCormick DA, Thompson RF (1984) Cerebellum: essential involvement in the classically conditioned eyelid response. Science 223:296–299
Miall RC, Wolpert DM (1996) Forward models for physiological motor control. Neural Netw 9:1265–1279
Milak M, Shimansky Yu, Bracha V, Bloedel JR (1997) Effects of inactivating individual cerebellar nuclei on the performance and retention of a complex, operantly conditioned forelimb movement. J Neurophysiol 78:939–958
Rothwell JC, Traub MM, Day BL, Obeso JA, Thomas PK, Marsden CD (1982) Manual motor performance in a deafferented man. Brain 105:515–542
Salisachs P (1981) Unusual presentation of Charcot-Marie-Tooth disease—incoordination with absent or minimal wasting. J Neurol Sci 50:175–180
Sanes JN, Evarts EV (1984) Motor psychophysics. Hum Neurobiol 2:217–225
Schweighofer N, Spoelstra J, Arbib MA, Kawato M (1998) Role of the cerebellum in reaching movements in humans. II. A neural model of the intermediate cerebellum. Eur.J.Neurosci. 10:95–105
Shimansky YP (2000) Spinal motor control system incorporates an internal model of limb dynamics. Biol Cybern 83:379–389
Shimansky Y, Saling M, Wunderlich D, Bracha V, Stelmach G, Bloedel JR (1997) Impaired capacity of cerebellar patients to perceive and learn two-dimensional shapes based on kinesthetic cues. Learn Mem 4:36–48
Shimansky Y, Bauer R, Bracha V, Bloedel JR (1999a) Modulation of simultaneously recorded cerebellar cortical and nuclear cells during adaptation to expected and unexpected perturbations of reaching movements in cats. Soc Neurosci Abst 25:1560
Shimansky YP, Timmann D, Kolb FP, Diener HC, Bloedel JR (1999b) A role for the cerebellum in perceiving patterns in different sense modalities. In: Killeen PR, Uttal WR (eds) Fechner Day 99: the end of 20th century psychophysics. Proceedings of the 15th Annual Meeting of the International Society for Psychophysics, Tempe, AZ, USA. The International Society for Psychophysics, pp 62–67
Stein JF, Glickstein M (1992) Role of the cerebellum in visual guidance of movement. Physiol Rev 72:967–1017
Strick PL (1979) Control of peripheral input to the dentate nucleus by motor preparation. In: Massion J, Sasaki K (eds) Cerebro-cerebellar interactions. Elsevier/North Holland, Amsterdam, pp 185–201
Thach WT (1978) Correlation of neural discharge with pattern and force of muscular activity, joint position, and direction of intended next movement in motor cortex and cerebellum. J Neurophysiol 41:654–676
Thach WT, Goodkin HP, Keating JG (1992) The cerebellum and the adaptive coordination of movement. Annu Rev Neurosci 15:403–442
Thompson RF, Krupa DJ (1994) Organization of memory traces in the mammalian brain. Annu Rev Neurosci 17:519–549
Thoroughman KA, Shadmehr R (1999) Electromyographic correlates of learning an internal model of reaching movements. J Neurosci 19:8573–8588
Wada Y, Kawato M (1993) A neural network model for arm trajectory formation using forward and inverse dynamics models. Neural Netw 6:919–932
Wang JJ, Shimansky Y, Bracha V, Bloedel JR (1998) Effects of cerebellar nuclear inactivation on the learning of a complex forelimb movement in cats. J Neurophysiol 79:2447–2459
Weiner MJ, Hallett M, Funkenstein HH (1983) Adaptation to lateral displacement of vision in patients with lesions of the central nervous system. Neurology 33:766–772
Winter D (1979) Biomechanics of human movement. John Wiley, New York
Wolpert DM, Ghahramani Z, Jordan MI (1995) An internal model for sensorimotor integration. Science 269:1880–1882
Acknowledgements
The study was supported by US National Institutes of Health (NIH) Grants NS30013 and NS21958.
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Appendix: procedure for the analysis of forelimb dynamics
Appendix: procedure for the analysis of forelimb dynamics
General ideas
At the time of our developing software for the analysis of the experimental data, to the best of our knowledge, no 3-D model of the dynamics of a three-segmented forelimb that could be used for our purposes had been described in the literature. The procedure we utilized for the derivation of the equation system describing forelimb movement dynamics in 3-D space is presented below. This procedure is based on Lagrange’s principle, according to which the equations of dynamics of a certain mechanical system are presented as \({{\partial L} \over {\partial q_{k} }} - {{d} \over {dt}} {{\partial L} \over {\partial \dot{q}_{k} }} = 0\), where L is the Lagrangian function \(L = L{\left( {q_{1} ,...,q_{n} ,\dot{q}_{1} ,...,\dot{q}_{n} } \right)}\) describing the mechanical energy of the system and q 1,...,q n are the system’s generalized coordinates. An external constraint g(q 1,q 2,...q n )=0 can be accounted for by the method of undetermined multipliers. According to this method, the Lagrangian function should include an additional term λ(t)·g(q 1,q 2,...q n ), where λ is the undetermined multiplier corresponding to the constraint. To calculate the corresponding variational component, the constraint equation should be presented in the differential form \({\sum\limits_j {h_{j} } }\dot{q}_{j} = 0\), or \({\sum\limits_j {h_{j} } }\delta q_{j} = 0\), where h j =dg/dq j . In case of the presence of external forces and torques, the Langrangian function L should include work done by generalized forces. Finally, Euler’s equation with regard to the generalized coordinate q k is
where T and V are kinetic and potential energy, respectively, Q k is the generalized force corresponding to the coordinate q k , and λ i is the undetermined multiplier corresponding to the i-th constraint.
The crucial advantage of Lagrange’s approach over the method of Newton-Euler laws of motion is that the user only has to write a formula for the Lagrangian function describing mechanical energy of the limb. The actual derivation of the differential equation system can be done automatically by a symbolic manipulation software package, such as Mathematica, Maple, or Macsyma. The latter package was used in this study not only to derive the equation system, but also to generate a C-language code for the computation of the elements of the equation system matrix with relation to generalized forces. This code then was included without any modification into a C++ program written for the data analysis. The Lagrangian function used to describe the mechanical energy of a cat forelimb is described below.
Forelimb as a mechanical system
The motion of the upper arm segment is described as a pure rotation with respect to a non-inertial coordinate system whose center is at the shoulder joint (mechanically a ball-joint). The non-inertial coordinate frame is moving parallel to the coordinate system fixed with relation to the external observer. The lower arm segment is viewed as a combination of two coaxial parts (connected at the segment’s center of mass). Wrist rotation is presented as the rotation of these parts against each other around their common longitudinal axis. Any changes in the inertia momentum of the whole lower arm segment caused by such rotation are considered insignificant and are neglected. The wrist joint is modeled as a hinge-joint representing wrist flexion. Radial deviation is neglected because of its relatively narrow range.
Constant parameters and variables
The first subscript in the name of a constant or variable related to a certain segment of the forelimb denotes the segment: a, b, c, and d corresponding to upper arm, elbow part of lower arm, wrist part of lower arm, and paw, respectively. The first subscript in the name of a constant or variable related to a certain joint denotes the joint: s, e, r, and w corresponding to shoulder, elbow, the virtual joint introduced for expressing wrist rotation (see explanations above), and wrist, respectively. The second subscript denotes the number of space coordinate (either in the observer’s coordinate system or in the system attached to the limb segment, depending on the variable).
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l i and l i0 are the length of the segment i (i=a, b, c, or d) and the distance from the segment’s proximal end to its center of gravity
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m i is the mass of the segment i
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g=9.81 m/s2, the gravitational acceleration constant
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I ij is inertia momentum of the segment i related to the j-th axis of the coordinate system attached to the segment (the third axis is the segment’s longitudinal axis; note that for the upper limb segment the center of rotation is the shoulder joint and for other two segments the center of rotation is the segment’s center of mass)
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ϖ ij is the angular velocity component of the segment i corresponding to the j-th axis of the coordinate system attached to the segment
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e ij is a unitary vector representing the j-th axis of the coordinate system attached to the segment i in the observer’s coordinate system
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x ij is the j-th coordinate of the i segment’s center of mass in the observer’s coordinate system
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v ij is the j-th coordinate of the velocity of the i segment’s center of mass in the observer’s coordinate system
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γ ij is the angle between the longitudinal axis of the segment i with the j-th axis of the observer’s coordinate system
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ϕ i , ψ i , and θ i are Eulerian angles describing the orientation of the coordinate system attached to the segment i with relation to the observer’s coordinate system
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α i is the angle at the joint i (i=e, w)
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F ij is the component j (j=α, ϕ, ψ, or θ) of an external force (i.e., torque generated by active muscle contraction, tissue passive resistance, or any external force acting on the limb) corresponding to the joint i
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Q ij is the Lagrangian multiplier (here playing the role of a generalized force) corresponding to the j-th constraint (j=1, 2, 3, 4, or 5) at the limb joint i (i=e or w)
Lagrangian function of forelimb dynamics
Lagrangian function for the entire forelimb can be presented as the sum L=L K+L G+L F+L C, where indices K, G, F, and C denote components corresponding to kinetic energy (done by inertial forces), gravitation, work done by external forces (i.e., active muscle forces, external perturbation forces, and forces resulting from passive resistance of tissue), and joint constraints (resulting in interaction forces). Formulas describing these components are presented in detail below.
Kinetic energy
The expression describing kinetic energy has two components: rotational L Krot and translational L Ktr . The formula for the rotational component is the same for each segment of the forelimb: \(L_{{Krot}} = {{1} \over {2}}{\sum\limits_{j = 1}^3 {I_{{ij}} \omega ^{2}_{{ij}} } }\). Note that for the upper-arm segment the center of rotation is the shoulder joint and for other two segments the center of rotation is the segment’s center of mass). The translational component for the upper-arm segment is \(L_{{Ktr}} = m_{1} l_{{10}} {\sum\limits_{j = 1}^3 {a_{{sj}} \cos {\left( {\gamma _{{1j}} } \right)}} }\), where a sj is shoulder joint acceleration in the direction of the j-th coordinate of the observer’s coordinate system. The translational component formula for the lower limb and paw segments is \( L_{{Ktr}} = {{1} \over {2}}m_{{ij}} {\sum\limits_{j = 1}^3 {v^{2}_{{ij}} } } \).
Potential energy (due to gravitational field)
For the upper-arm segment, this component is described by L G=−m 1 gl 10cos(γ3). For the other two segments, it is L G=−m 1 gz, where g=9.81 m/s2, the gravitational acceleration constant, and z is the vertical coordinate of the segment’s center of mass.
Non-inertiality of shoulder joint
The shoulder joint is moved with the body, so the system of coordinates fixed with respect to the shoulder is not inertial. This is taken into account by adding gravity-type of work: m 1 l 10(a s ·e a ), where a s is the vector of shoulder joint acceleration.
Work of external forces
Shoulder joint: L sF=F sϕϕa+F sψψa+F sθθa. Elbow joint: L eF=F eααe. Wrist joint: L wF=F wϕ(ϕb-ϕc)+F wααw.
Work of interaction forces (due to joint constraints)
Elbow joint:
Wrist joint:
The data analysis described in Introduction focuses on the following six torque components (generalized forces): shoulder rotation (F sϕ), shoulder yaw (F sψ), shoulder elevation (F sθ), elbow flexion (F eα), wrist rotation (F wϕ), and wrist flexion (F wα). It is important to note once more that any external perturbation force contributes to these torque components.
The mass m i and inertia momentum I i1 of the forelimb segments were calculated on the basis of the body mass and segment length according to the method described in (Hoy and Zernicke 1985). The inertia momentum I i2 was set equal to I i1. The third momentum related to the longitudinal axis of the segment was calculated as I i3=m i r i 2/2, assuming that the segment approximates to a cylinder with the radius r i =√[m i /(πρ i l i )], where ρ i is the average density of the i-th segment’s tissue. Density estimates for human forelimb segments (Winter 1979) were used.
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Shimansky, Y., Wang, JJ., Bauer, R.A. et al. On-line compensation for perturbations of a reaching movement is cerebellar dependent: support for the task dependency hypothesis. Exp Brain Res 155, 156–172 (2004). https://doi.org/10.1007/s00221-003-1713-0
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DOI: https://doi.org/10.1007/s00221-003-1713-0