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13 The Utilization of Myotatic Feedback in Motor Control
Tutorials in Motor Behavior G.E. Stelmach and J . Requin (eds.1
0 North-Holland Publishing Company, 1980
13 THE UTILIZATION OF MYOTATIC FEEDBACK I N MOTOR CONTROL C.A.
Terzuolo, J.R.
Dufresne and J . F . S o e c h t i n g
L a b o r a t o r y of Neurophysiology U n i v e r s i t y of Minnesota M i n n e a p o l i s , Minnesota
I n t h i s p a p e r , we s h a l l t a k e up a few t o p i c s which are r e l a t e d t o t h e f u n c t i o n a l u t i l i t y of m y o t a t i c f e e d b a c k , t h a t i s , feedback a c t i o n s o r i g i n a t i n g from muscle r e c e p t o r s and c a p a b l e of modifying t h e motor o u t p u t t o t h e a g o n i s t and a n t a g o n i s t muscles d u r i n g d i f f e r e n t motor t a s k s . The r e s u l t s of o u r work on t h i s s u b j e c t may b e summarized as f o l l o w s : 1) Such r e f l e x a c t i o n s behave e s s e n t i a l l y l i k e a n e g a t i v e v e l o c i t y feedback d u r i n g t h e i n t e n t i o n a l arrest of f a s t , ongoing movements ( S o e c h t i n g , l 9 7 3 ; T e r z u o l o and V i v i a n i , 1974; V i v i a n i and T e r z u o l o , 1973). 2 ) The m y o t a t i c feedback can b e p a r a m e t e r i z e d i n terms of a n e g a t i v e feedback of p o s i t i o n , v e l o c i t y and a c c e l e r a t i o n . Such a p a r a m e t e r i z a t i o n h a s l e d t o t h e i d e n t i f i c a t i o n of s e p a r a t e and i n d e p e n d e n t l y r e g u l a t e d feedback l o o p s , s u b s e r v e d by d i f f e r e n t c e n t r a l a n a t o m i c a l s t r u c t u r e s (Dufresne e t a l , 1978; 1979a). 3 ) The g a i n i n e a c h of t h e s e feedback l o o p s depends on t h e motor t a s k (Dufresne e t a l , 1978; 1979b). INTRODUCTION When t o r q u e p e r t u r b a t i o n s a r e a p p l i e d t o a l i m b , changes in limb p o s i t i o n w i l l r e s u l t from t h e sum of t h e e x t e r n a l l y a p p l i e d t o r q u e and t h e t o r q u e g e n e r a t e d by muscular c o n t r a c t i o n . The a c t i v i t y of t h e s t r e t c h r e c e p t o r s i n t h e muscles i n v o l v e d can b e e x p e c t e d t o r e f l e c t t h e s e changes i n a n g u l a r p o s i t i o n and i t s d e r i v a t i v e s : v e l o c i t y and a c c e l e r a t i o n . The dependence of I a a f f e r e n t a c t i v i t y on t h e s e p a r a m e t e r s i s w e l l e s t a b l i s h e d ( c f . Matthews, 1972). S i n c e muscle f o r c e and a n g u l a r p o s i t i o n are n o t i n d e p e n d e n t , t h e act i v i t y o f Golgi tendon o r g a n a f f e r e n t s w i l l a l s o depend on t h e same paramet e r s . The e x t e n t t o which a l p h a motoneuron o u t p u t i s d e t e r m i n e d by r e f l e x a c t i v i t y , t h a t i s t h e e x t e n t t o which i t depends on a f f e r e n t a c t i v i t y from s t r e t c h r e c e p t o r s , can t h u s b e a s s e s s e d by a model r e l a t i n g EMG a c t i v i t y ( t a k e n a s t h e o u t p u t ) t o a n g u l a r p o s i t i o n and i t s d e r i v a t i v e s ( t a k e n as the input). E x p e r i m e n t a l l y , pseudo-random, sequences of t o r q u e p u l s e s were a p p l i e d a t t h e elbow j o i n t of normal a d u l t human s u b j e c t s . The t a s k s performed by t h e s u b j e c t s were s p e c i f i e d n o t only by t h e i n s t r u c t i o n s g i v e n (e.g. t o resist o r n o t t o r e s i s t t h e a p p l i e d t o r q u e ) b u t a l s o by t h e e x t e r n a l l y imposed c o n d i t i o n s (such as a c o n s t a n t t o r q u e l o a d ) . Thus t h e t e r m " o p e r a t i n g p o i n t " w i l l b e used t o s p e c i f y e a c h e x p e r i m e n t a l c o n d i t i o n . EMG a c t i v i t y of b i c e p s and t r i c e p s , f o r e a r m a n g u l a r p o s i t i o n and a c c e l e r a t i o n and t h e appl i e d t o r q u e were recorded,. In o u r r e s u l t s , EMG a c t i v i t y i s e x p r e s s e d in
23 I
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terms of impulse density (when recorded with intramuscular electrodes) or in terms of the amplitude of full-wave rectified surface recordings. The model we have chosen i s a simple one, namely a linear model with three feedback terms (position, velocity and acceleration). The time delay for each of these terms is assumed to be independent. The rationale for this assumption is as follows: The possibility of multiple feedback pathways with different time delays is thereby included in the model as well as the possibility of a central processing of afferent activity analogous to a mathematical differentiation or integration. In other words, different pathways might use different parameters of the input. The model is arbitrary in the sense that additional terms, such as derivatives higher than acceleration and nonlinear terms are excluded. However, the restriction of the model to linear terms will be justified below. LINEAR MODELS OF REFLEX BEHAVIOR The extent to which such a model is able to reproduce the observed EMG activity for a typical experiment i s shown in Fig. 1. This figure also illustrates the relative contribution by each term of the model. The top trace shows the average EMG activity of the biceps obtained when the subject was asked to resist the applied perturbation in the presence of a steady torque acting to extend the forearm. The torque sequence itself is given at the bottom of the figure. The estimated contribution to the motor output by each term is depicted by the traces labeled position, velocity and acceleration. The total feedback, i.e. the sum of the three terms is given by the trace labeled model.
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Velocity feedback Acceleration feedback
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Fig. 1. Fit of a linear feedback model to reflex activity evoked by torque perturbations. The model is given by: EMG(t) Ae(t-Ta)+Be(t-Tb)+C8(t-Tc)
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The computed EMG f i t s the e x p e r i m e n t a l d a t a q u i t e w e l l . The l e a s t s q u a r e e r r o r ( t h e squared d i f f e r e n c e between model and EMG) ranged from 25% t o 50% o f t h e v a r i a n c e i n d i f f e r e n t e x p e r i m e n t s . N e i t h e r t h e goodness of t h e f i t n o r t h e c o e f f i c i e n t s of t h e feedback terms depended on t h e s t r u c t u r e o f t h e sequence used. Furthermore, a s p e c t r a l a n a l y s i s of t h e e r r o r showed i t t o b e u n i f o r m l y d i s t r i b u t e d i n t h e f r e q u e n c y domain. A n o n l i n e a r a n a l y s i s of t h e e x p e r i m e n t a l d a t a a l s o s u g g e s t s t h a t t h e e r r o r i s m o s t l y due t o random n o i s e . N o n l i n e a r models i n c l u d i n g terms w i t h t h e s q u a r e and cube of t h e v e l o c i t y and a c c e l e r a t i o n reduced t h e e r r o r o n l y s l i g h t l y . By c a l c u l a t i n g second-order k e r n e l s f o r t h e impulse r e s p o n s e of EMG a c t i v i t y t o p u l s e s of t o r q u e , w e were a b l e t o show t h a t t h e a v e r a g e mot o r o u t p u t t o p a i r s of p u l s e s c l o s e l y approximates t h e a c t i v i t y o b t a i n e d by assuming a l i n e a r summation of t h e r e s p o n s e t o s i n g l e p u l s e s of t o r q u e . T h i s i s i l l u s t r a t e d i n F i g . 2 , which shows t h e a v e r a g e b i c e p s a c t i v i t y and a n g u l a r v e l o c i t y and a c c e l e r a t i o n f o l l o w i n g two p u l s e s of t o r q u e s e p a r a t e d by 20 msec. The l i g h t t r a c e , l a b e l e d l i n e a r , i s t h e b i c e p s a c t i v i t y p r e d i c t e d from t h e a v e r a g e r e s p o n s e t o a s i n g l e p u l s e of t o r q u e . The h e a v i e r t r a c e shows t h e e x t e n t o f n o n l i n e a r i n t e r a c t i o n between p a i r s of p u l s e s .
F i g . 2 . Impulse r e s p o n s e t o p a i r s of t o r q u e p u l s e s . The i m p u l s e r e s p o n s e w a s c a l c u l a t e d by c r o s s c o r r e l a t i n g t h e pseudo-random t o r q u e sequence w i t h b i c e p s EMG a c t i v i t y . Trace l a b e l e d l i n e a r shows r e s p o n s e c a l c u l a t e d from the f i r s t o r d e r k e r n e l , t h a t l a b e l e d n o n l i n e a r u s i n g a l s o t h e second o r d e r k e r n e l .
In c o n t r a s t t o t h e small improvement i n e r r o r when n o n l i n e a r models were used, a c o n s i d e r a b l e improvement i n t h e f i t of t h e model was o b t a i n e d when t h e feedback d e l a y s were p e r m i t t e d t o b e d i f f e r e n t . The a v e r a g e v a l u e s f o r 5 msec and 45 2 6 msec ret h e v e l o c i t y and a c c e l e r a t i o n d e l a y s were 25 s p e c t i v e l y (Dufresne e t a l , 1979a). The two time d e l a y s d i f f e r s u b s t a n t i a l l y w h i l e t h e i r s t a n d a r d d e v i a t i o n s are q u i t e s m a l l . The v e l o c i t y d e l a y i s comp a t i b l e w i t h s e g m e n t a l r e f l e x mechanisms, b e i n g c l o s e t o t h e l a t e n c y of t h e tendon j e r k i n man ( c . f . Hammond, 1960). The d e l a y f o r t h e a c c e l e r a t i o n feedback is c o m p a t i b l e w i t h t h e involvement of a s u p r a s p i n a l l o o p . The
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d e l a y f o r t h e p o s i t i o n term i s much l o n g e r (86 r e l a t i v e l y insensitive t o its value.
5
26 msec) and t h e model i s
A s f o r t h e adequacy of t h e model, we have a l r e a d y mentioned t h a t a s p e c t r a l a n a l y s i s of t h e e r r o r and t h e r e s u l t s of n o n l i n e a r modelling s u g g e s t t h a t t h e e r r o r is t o a l a r g e e x t e n t random n o i s e . Regarding t h e s p e c i f i c terms included i n t h e model, t h e v e l o c i t y parameter is g e n e r a l l y conceded t o b e prominent i n t h e o u t p u t of I a muscle s p i n d l e a f f e r e n t s (cf Matthews, 1 9 7 2 ) . The time d e l a y f o r t h e v e l o c i t y feedback is c l o s e t o t h a t t o b e expected f o r t h e monosynaptic r e f l e x . The a c c e l e r a t i o n parameter a l s o c o n t r i b u t e s s u b s t a n t i a l l y t o t h e motor o u t p u t ; t h e p o s i t i o n term is g e n e r a l l y n e g l i g i b l e . F i n a l l y , t h e dependence of t h e motor o u t p u t on t h e p a r a m e t e r s of t h e movement is n o t i n e v i t a b l e under o u r e x p e r i m e n t a l c o n d i t i o n s . EMG a c t i v i t y i n p a t i e n t s w i t h P a r k i n s o n i a n r i g i d i t y i s n o t w e l l related t o t h e p a r a m e t e r s of t h e movement and t h e moddelling e r r o r i n c r e a s e s g r e a t l y , d e s p i t e a b r i s k r e f l e x response t o t h e p ert u rb at io n . VELOCITY AND ACCELERATION FEEDBACK The b a r s i n t h e l e f t p a r t of F i g . 3 d e n o t e t h e a v e r a g e v a l u e s of t h e coe f f i c i e n t s f o r t h e v e l o c i t y and a c c e l e r a t i o n feedback terms. They r e p r e s e n t t h e average v a l u e s of r e s u l t s f o r t h e b i c e p s muscle from 16 e x p e r i m e n t s and 7 s u b j e c t s . These v a l u e s w e r e o b t a i n e d when t h e s u b j e c t s were i n s t r u c t e d t o resist t h e a p p l i e d p e r t u r b a t i o n . The mean t o r q u e was z e r o i n t h e s e e x p e r i ments.
Fig. 3 . Gain of t h e v e l o c i t y and a c c e l e r a t i o n feedback a t d i f f e r e n t operating points.
The r i g h t hand p o r t i o n of F i g . 3 shows how t h e two feedback c o e f f i c i e n t s v a r y w i t h t h e o p e r a t i n g p o i n t . T h e i r v a l u e s a r e e x p r e s s e d as a p e r c e n t a g e of t h e c o e f f i c i e n t s ' v a l u e s o b t a i n e d when t h e s u b j e c t s were i n s t r u c t e d t o resist a p e r t u r b a t i o n having a z e r o mean t o r q u e . The v a l u e s f o r t h e v e l o c i t y and a c c e l e r a t i o n feedback c o e f f i c i e n t s sometimes changed i n tandem. For example, t h e y b o t h i n c r e a s e d when t h e b i c e p s w a s active and opposed a mean
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t o r q u e t e n d i n g t o e x t e n d t h e f o r e a r m and d e c r e a s e d when i t a c t e d e s s e n t i a l l y as t h e a n t a g o n i s t (mean t o r q u e t e n d i n g t o f l e x t h e f o r e a r m ) . A t o t h e r operat i n g p o i n t s , a d i f f e r e n t i a l change i n t h e v a l u e s of t h e c o e f f i c i e n t s was obs e r v e d . For example, when t h e s u b j e c t s were i n s t r u c t e d n o t t o resist t h e a p p l i e d p e r t u r b a t i o n , t h e v a l u e of t h e v e l o c i t y f e e d b a c k was o n l y s l i g h t l y reduced, w h i l e t h a t of t h e a c c e l e r a t i o n feedback d e c r e a s e d t o 24% of t h e v a l u e o b t a i n e d when t h e s u b j e c t s were i n s t r u c t e d t o resist t h e a p p l i e d p e r turbation. Such a d i f f e r e n t i a l change i n t h e amount of v e l o c i t y and a c c e l e r a t i o n feedback i m p l i e s an independent r e g u l a t i o n o f t h e i r g a i n and s u g g e s t s t h e e x i s t e n c e of s e p a r a t e feedback l o o p s u t i l i z i n g d i f f e r e n t feedback p a r a m e t e r s . The s i g n i f i c a n t d i f f e r e n c e i n t h e v a l u e of t h e t i m e d e l a y s f o r t h e v e l o c i t y and a c c e l e r a t i o n feedback s u p p o r t s t h i s h y p o t h e s i s . Note t h a t i t i s l i k e l y t h a t e a c h of t h e s e l o o p s may u t i l i z e more t h a n one parameter and c o n v e r s e l y t h a t t h e t i m e d e l a y s of b o t h v e l o c i t y and a c c e l e r a t i o n feedback may r e p r e s e n t w,eighted a v e r a g e s o f two o r more l o o p s . More s p e c i f i c a l l y , i f t h e v e l o c i t y feedback i s p r o v i d e d by t h e a c t i v i t y of muscle s p i n d l e a f f e r e n t s and segmental r e f l e x mechanisms, p o s i t i o n and a c c e l e r a t i o n feedback a t t h e same l a t e n c y s h o u l d a l s o b e p r e s e n t . The model o n l y s u g g e s t s t h a t a c c e l e r a t i o n feedback a t l o n g e r l a t e n c i e s i s dominant. Regarding t h e v e l o c i t y f e e d b a c k , a c o n t r i b u t i o n by o l i v o - c e r e b e l l a r s t r u c t u r e s must b e c o n s i d e r e d . The e x p e r i m e n t a l e v i d e n c e f o r such a c o n t r i b u t i o n h a s been p r o v i d e d by a series of s t u d i e s on t h e i n t e n t i o n a l a r r e s t of f a s t movements i n man and i n t h e s q u i r r e l monkey ( S o e c h t i n g e t a l , 1976; T e r z u o l o and V i v i a n i , 1974). These s t u d i e s i n d i c a t e d t h a t t h e v e l o c i t y and a c c e l e r a t i o n feedback i s o p e r a t i o n a l d u r i n g f a s t movements which were b a l l i s t i c a l l y i n i t i a t e d . Under t h e s e c o n d i t i o n s , t h e motor o u t p u t t o a g o n i s t and antagon i s t was shown t o b e c a u s a l l y r e l a t e d t o t h e p a r a m e t e r s of t h e movement b o t h i n man and monkey. Such a c o u p l i n g between motor o u t p u t and t h e v e l o c i t y of t h e movement r e q u i r e s a c o n t r i b u t i o n by c e r e b e l l a r r e l a t e d a c t i v i t i e s , s i n c e i t was a b s e n t i n c e r e b e l l a r p a t i e n t s and markedly reduced i n monkeys w i t h l e s i o n s of t h e c e r e b e l l u m o r i n f e r i o r o l i v e . A l s o , s i n g l e u n i t r e c o r d i n g s from i n t e r p o s i t u s and r u b r a l neurons of c a t s p e r f o r m i n g t h e same t y p e of movement showed t h a t t h e v e l o c i t y p a r a m e t e r i s r e p r e s e n t e d i n t h e a c t i v i t y of t h e s e neurons d u r i n g t h i s t a s k (Burton and Onoda, 1978). Regarding t h e f u n c t i o n a l u t i l i t y of v e l o c i t y f e e d b a c k , such a f e e d b a c k can e f f e c t i v e l y damp o u t e x t e r n a l l y imposed p e r t u r b a t i o n s and o s c i l l a t i o n s which o c c u r d u r i n g t h e arrest of f a s t movements. I t is much less u s e f u l f o r an a c c u r a t e c o n t r o l of p o s i t i o n . Using a s i m p l e second o r d e r model ( c o n s i s t i n g of an i n e r t i a l mass, v i s c o u s damping and a s p r i n g ) f o r t h e mechanical and r e f l e x p r o p e r t i e s of t h e human forearm, w e have o b t a i n e d a n estimate f o r t h e v i s c o u s t i m e c o n s t a n t on t h e o r d e r of 1 . 3 t o 2.0 s e c o n d s when s u b j e c t s were i n s t r u c t e d n o t t o resist an a p p l i e d p e r t u r b a t i o n . When t h e y were asked t o r e s i s t , t h e v i s c o u s t i m e c o n s t a n t , a c c o r d i n g t o t h e model, d e c r e a s e d t o 100 t o 200 msec. I n t h e former c a s e , t h e b i c e p s was v i r t u a l l y s i l e n t ; i n t h e l a t t e r case, i t s a c t i v i t y was modulated r o u g h l y i n phase w i t h v e l o c i t y .
We have h y p o t h e s i z e d t h a t t h e a c c e l e r a t i o n feedback may i n v o l v e a t r a n s c o r t i c a l l o o p (Dufresne e t a 1 , 1 9 7 9 a ) . The h y p o t h e s i s i s based on t h e f o l l o w i n g c o n s i d e r a t i o n s : 1) The t i m e d e l a y i s c o m p a t i b l e w i t h s u c h a p o s s i b i l i t y , 2 ) t h e a c t i v i t y of p r e c e n t r a l c o r t i c a l u n i t s f o l l o w i n g t o r q u e p u l s e s changes i n a manner a p p r o p r i a t e t o m e d i a t e p a r t of t h e r e f l e x r e s p o n s e t o s u c h p u l s e s ( E v a r t s and T a n j i , 1976) and 3) t h e a c c e l e r a t i o n p a r a m e t e r i s r e p r e s e n -
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ted in their activity (Conrad et al., 1975). Moreover, when the sensory and cerebellar inflow to the sensory-motor cortex is interrupted by thalamic lesions, the only component of the motor output affected is the one which is correlated with the angular acceleration during ballistically initiated movements (Ranish and Soechting,l976). The contribution by a transcortical loop to the reflex response to single torque pulses has been the subject of much work and speculation in recent years (cf. Lee and Tatton, 1975). However, Ghez and Shinoda (1978) have shown that the so called M2 response which was attributed to a 10% latency loop is also obtained in aecerebrate and spinalized cats. Thus, evidence for a feedback of acceleration likely to involve a transcortical loop rests solely on the results obtained by modelling and the considerations summarized above. Assuming this hypothesis to be correct, we may consider the functional utility of such a loop. Phillips (1969) first postulated its existence and attributed to it a focussing action upon muscle spindle feedback while Evarts and Tanji (1974) suggested its function to be a modulation of reflex gain. Finally, Oguztoreli and Stein (1976) called attention to instabilities which are potentially introduced by a loop with a long delay time. Such instabilities would be obviated if the feed back parameter were to be acceleration. Indeed, for frequency components of changes in length below 6 Hz, an acceleration feedback would still lead velocity feedback at the time of their convergence upon a-motoneurons provided that the difference in delay between the two were less than 40 msec. Thus only during the sharpest transients, such as those resulting from a tendon tap,would the velocity feedback be initially dominant. The appropriateness of an acceleration feedback involving a transcortical loop may be more readily appreciated from the point of view of load compensation and the regulation of muscle force. Note that force and acceleration are mutually related although not equivalent (because of the visco-elastic properties of muscle). m our model we chose acceleration as one of the parameters since it was directly measurable, but we cannot exclude the possibility that force or its derivatives may be a more appropriate parameter. The afferent source of the acceleration feedback can only be surmised. An
acceleration component is present in the linear response of primary endings of muscle spindles to stretch (Poppele and Bowman, 1970). However, if the muscle spindles provided the source for this feedback, their activity would need to be differentiated centrally. Otherwise, the latency of the acceleration and velocity feedback terms would be the same. The involvement of Golgi tendon organ afferents in the acceleration feedback would be another possibility
.
The amplitude of the contribution by the acceleration feedback to the motor output ranged from 30% to 120% of that of the velocity feedback in our experiments. This ratio depends on the moment of inertia of the forearm and the motor and the duration of the longest torque pulse in a given sequence, both of these factors influencing the ratio of peak angular acceleration to peak angular velocity. Note that torque pulses produce large accelerations and that the contribution of the acceleration feedback can be expected to be less important under more physiological conditions. Also, given the low-pass
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filter characteristics of the transformation between a-motoneuron activity and muscle tension (cf. Partridge, 1 9 6 5 ) , the relative contribution of the acceleration feedback to muscle force is probably even less, although recruitment and/or synchronization of motor units and the potentiation of twitch tension which occurs for pairs of action potentials at short intervals (Burke et al., 1976; Robles and Soechting, 1979) may compensate for the drop in gain due to that transformation. The next topic we wish to address is the possibility of a central regulation of the gain of the velocity and acceleration feedback. First, it should be noted that a parallel increase or decrease in the value of the two coefficients may simply reflect a parallel change in the level of a-motoneuron excitability. The increase in the amplitude of the reflex activity when the muscle is tonically active and called upon to resist a steady torque (Dufresne et al., 1978; Marsden et al., 1972), which is illustrated in Fig. 3 , can be explained solely on this basis. However, the differential decrease in the values of the two feedback coefficients observed when the subjects are instructed not to resist the applied perturbation (Fig. 3) suggests the possibility of a central regulation of feedback gain independent from the level of a-motoneuron activity. REFLEX BEHAVIOR DURING INTENTIONAL MOVEMENTS The variations in the amplitude of reflex activity observed during intentionally generated movements also point to this possibility. Subjects produced sinusoidal movements of the forearm by tracking a sinusoidally modulated signal displayed on an oscilloscope. Figure 4A shows the variation in the full-wave rectified biceps EMG activity and the forearm angular velocity during such a tracking movement. The frequency was 1.8 Hz. During some trials, single extension pulses of torque were applied at different phases of the movement. The amplitude of the reflex activity evoked by the pulses of torque was measured and is shown at the bottom of Fig. 4A along with a sinusoid at the tracking frequency which gave the best fit to the data. The
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modulation of t h e a m p l i t u d e of t h e r e f l e x a c t i v i t y d u r i n g t h e s e c y c l i c movements was s u b s t a n t i a l , t h e l a r g e s t r e s p o n s e b e i n g f i v e times a s l a r g e as t h e s m a l l e s t . Furthermore, changes i n r e f l e x a m p l i t u d e d i d n o t c o i n c i d e w i t h t h e i n t e n t i o n a l l y produced modulation of b i c e p s EMG a c t i v i t y . In f a c t , t h e modulation of r e f l e x a c t i v i t y showed a phase l e a d of 53'+37' o v e r t h e unpert u r b e d b i c e p s motor o u t p u t a t a t r a c k i n g f r e q u e n c y of 1.8 Hz. These changes i n r e f l e x a m p l i t u d e do n o t depend on t h e i n t e n t i o n a l l y genera t e d c y c l i c motion. This was e s t a b l i s h e d by changing t h e phase between t h e i n t e n t i o n a l l y g e n e r a t e d motor o u t p u t and t h e a n g u l a r v e l o c i t y of t h e f o r e arm by means of a s p r i n g l o a d . The r e s u l t s of t h e s e e x p e r i m e n t s a r e shown i n Fig. 4B. The p h a s e l e a d of b i c e p s a c t i v i t y o v e r v e l o c i t y h a s been reduced by a p p r o x i m a t e l y 80' compared t o t h a t o b t a i n e d i n t h e absence o f a s p r i n g l o a d (Fig. 4A). The r e f l e x a m p l i t u d e i s s t i l l modulated i n an a p p r o x i m a t e l y s i n u s o i d a l f a s h i o n and l e a d s t h e i n t e n t i o n a l l y g e n e r a t e d b i c e p s EMG a c t i v i t y by 67O?3Oo, which i s n o t s i g n i f i c a n t l y d i f f e r e n t from t h e p h a s e l e a d shown i n F i g . 4A. By a p p l y i n g pseudo-random sequences of t o r q u e p u l s e s d u r i n g such s i n u s o i d a l t r a c k i n g movements and r e l a t i n g t h e evoked r e f l e x a c t i v i t y i n b i c e p s t o t h e changes i n p o s i t i o n , v e l o c i t y and a c c e l e r a t i o n produced by t h e s e p e r t u r b a t i o n s , w e were a b l e t o c h a r a c t e r i z e t h e v a r i a t i o n s of t h e c o e f f i c i e n t s of t h e v e l o c i t y and a c c e l e r a t i o n terms of t h e feedback model d u r i n g s u c h movements (Dufresne e t a l . , 1979b). The r e s u l t s of t h i s modelling s t u d y showed t h a t t h e g a i n s o f t h e v e l o c i t y and a c c e l e r a t i o n feedback b o t h v a r y . That of t h e v e l o c i t y feedback l e a d s t h e i n t e n t i o n a l l y g e n e r a t e d b i c e p s a c t i v i t y by 57Ot5' w h i l e t h a t of t h e a c c e l e r a t i o n feedback i s o n l y 1l0+1Zo when a s i g n a l v a r y i n g s i n u s o i d a l l y a t 1.8 Hz i s t r a c k e d . Note t h a t t h e phase l e a d obt a i n e d f o r t h e v e l o c i t y feedback a g r e e s w e l l w i t h t h a t of t h e a m p l i t u d e of t h e r e f l e x a c t i v i t y evoked by s i n g l e p u l s e s of t o r q u e and t h a t t h e changes i n t h e g a i n of t h e v e l o c i t y and a c c e l e r a t i o n feedback a r e n o t i n p h a s e . The major c o n c l u s i o n from t h e s e s t u d i e s w a s t h a t t h e feedback g a i n s a r e mod u l a t e d d u r i n g c y c l i c i n t e n t i o n a l l y c o n t r o l l e d movements, b u t t h a t t h i s mod u l a t i o n does n o t depend on t h e i n t e n t i o n a l l y g e n e r a t e d movement ( F i g . 4 ) . I f muscle s p i n d l e a c t i v i t y were r e s p o n s i b l e f o r t h e observed r e f l e x a c t i v i t y t h i s c o n c l u s i o n would imply t h a t muscle s p i n d l e o u t p u t should b e uncoupled from t h e changes i n muscle l e n g t h g e n e r a t e d i n t e n t i o n a l l y d u r i n g t h e t r a c k i n g t a s k . The r e a s o n i n g i s as f o l l o w s : t h e a m p l i t u d e of t h e change i n angul a r v e l o c i t y produced by t h e t o r q u e p u l s e s d i d n o t exceed 40% of t h e maximum v e l o c i t y of t h e t r a c k i n g movement. The i n t e n t i o n a l l y g e n e r a t e d movement should t h e r e f o r e b e prominently r e p r e s e n t e d i n t h e o u t p u t of p a s s i v e muscle s p i n d l e r e c e p t o r s . However, t h e a m p l i t u d e of t h e r e f l e x r e s p o n s e sometimes exceeded t h e maximum of t h e i n t e n t i o n a l l y g e n e r a t e d motor o u t p u t and w e found t h e same modulation of r e f l e x amplitude when t h e r e w a s no movement p r i o r t o a n e x t e n s i o n t o r q u e p u l s e ( t h e s u b j e c t w a s modulating b i c e p s a c t i v i t y by c o n t r a c t i n g i s o m e t r i c a l l y a g a i n s t a s t i f f wire, Dufresne e t a l . , 1979b) a s d u r i n g a t r a c k i n g movement. Furthermore, muscle s p i n d l e s become more s e n s i t i v e t o i n c r e m e n t a l changes i n muscle l e n g t h a t l o n g e r l e n g t h s (Poppele, 1973). T h e r e f o r e , one might e x p e c t t o f i n d a change i n t h e phase between r e f l e x and i n t e n t i o n a l motor o u t p u t when t h e phase between i n t e n t i o n a l v e l o c i t y and motor o u t p u t i s changed ( F i g . 4 ) . A l l t h e s e c o n s i d e r a t i o n s p o i n t t o a f u s i m o t o r b i a s on muscle s p i n d l e s d u r i n g t h e t r a c k i n g movement.
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Muscle spindles of intercostal muscles show evidence of extensive fusimotor biasing during respiration (von Euler, 1966). More recently, it has been found that the activity of primary afferents from muscle spindles can be poorly correlated with changes in muscle length during locomotion (Loeb and Duysens, 1979; Prochazka et al., 1976). If this is also the case under our experimental conditions, as the data suggest, then one may conclude that muscle spindle afferents operate essentially as "error detectors" during movements. That is, their activity would reflect mostly deviations from an anticipated trajectory. This interpretation suggests that y-static activity, adequate to maintain the muscle spindle's discharge when the muscle is shortening, is task and load dependent and not necessarily rigidly linked to a-motoneuron activity. The timing of y-activation should take into account the phase difference between intentional motor commands and the resulting motion. Since this phase difference is influenced by the external loading (Fig. 4 ) , a task-dependent modification of the timing of y-activity relative to a-activity would be required. ACKNOWLEDGMENTS This work was supported by USPHS Grants NS-2567 and NS-15018. Computer facilities were made available by Air Force Office of Scientific Research, Grant AFOSR- 122 1. REFERENCES Burke, R.E., Rudomin, P. and Zajac, F.E., The effect of activation history on tension production by individual muscle units, Brain Res. 109 (1976) 515-530.
Burton, J.E. and Onoda, N., Dependence of the activity of interpositus and red nucleus neurons on sensory input data generated by movement, Brain Res. 152 (1978) 41-63. Conrad, B., Meyer-Lohman, J., Matsunami, K. and Brooks, V.B., Precentral unit activity following torque pulse injections into elbow movements, Brain Res. 94 (1975) 219-236. Dufresne, J.R., Soechting, J.F. and Terzuolo, C.A., The response to pseudo-random torque disturbances of human forearm position, Neuroscience 3 (1978) 1213-1226. Dufresne, J . R . , Soechting, J.F. and Terzuolo, C.A., Reflex motor output to torque pulses in man: identification of short and long latency loops with individual feedback parameters, Neuroscience (in press). Dufresne, J.R., Soechting, J.F. and Terzuolo, C.A., Modulation of the myotatic reflex gain in man during intentional movements, submitted. Euler, C. von, Proprioceptive control in respiration, in: Granit, R. (ed.), Muscular Afferents and Motor Control (Almqvist and Wiksell, Stockholm, 1966) 289-322. Evarts, E.V. and Tanji, J . , Gating of motor cortex reflexes by prior instruction, Brain Res. 7 1 (1974) 479-494. Evarts, E.V. and Tanji, J., Reflex and intended responses in motor cortex pyramidal tract neurons of monkey, J. Neurophysiol. 39 (1976) 10691080.
Ghez, C. and Shinoda, Y., Spinal mechanisms of the functional stretch reflex, Exp. Brain Res. 32 (1978) 55-68. Hammond, P.H., An experimental study of servo action in human muscular control, Proc. 3rd Intern. Conf. Med. Electr. (1960) 190-199. Lee, R.G. and Tatton, W.G., Motor responses to sudden limb displacements in primates with specific CNS lesions and in human patients with motor
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system disorders, Can. 3. Neurol. 2 (1975) 285-293. 13) Loeb, G.E. and Duysens, J., Activity patterns in individual hindlimb
primary and secondary muscle spindle afferents during normal movements in unrestrained cats, J. Neurophysiol. 42 (1979) 420-440. 14) Marsden, C . D . , Merton, P.A. and Morton, H.B., Servo action in human voluntary movement, Nature 238 (1972) 140-143. 15) Matthews, P.B.C., Mammalian Muscle Spindles and their Control (Williams and Wilkins, Baltimore, 1972). 16) Oguztoreli, M.N. and Stein, R.B., Effects of multiple reflex pathways on oscillations in neuro-muscular systems, J. Math. Biol. 3 (1976) 8795. 17) Partridge, L.D.,
18) 19) 20) 21)
Modification of neural output by muscles: a frequency response study, J. appl. Physiol. 20 (1965) 150-157. Phillips, C.G., Motor apparatus of the baboon's hand, Proc. Roy. SOC. London, Ser. B 173 (1969) 141-174. Poppele, R.E., Systems approach to the study of muscle spindles, in: Stein, R . B . , Pearson, K.G., Smith, R.S. and Redford, J.B. (eds.), Control of Posture and Locomotion (Plenum, New York, 1973) 127-146. Poppele, R.E. and Bowman, R.J., Quantitative description of linear behavior of mammalian muscle spindle, J. Neurophysiol. 33 (1970) 59-72. Prochazka, A , , Westerman, R.A. and Ziccone, S.P., Discharges of single hindlimb afferents in the freely moving cat, J. Neurophysiol. 39 (1976)
1090-1103. 22) Ranish, N.A. and Soechting, J . F . ,
Studies on the control of some simple motor tasks. Effects of thalamic and red nucleus lesions, Brain Res.
102 (1976) 339-345. 23) Robles, S.S. and Soechting, J . F . , 24) 25) 26) 27)
28)
Dynamic properties of cat tenuissimus muscle, Biol. cybern. (in press). Soechting, J . F . , Modeling of d simple motor task in man: motor output dependence on sensory input, Kybern. 14 (1973) 25-34. Soechting, J.F., Ranish, N.A., Palminteri, R. and Terzuolo, C.A., Changes in a motor pattern following cerebellar and olivary lesions in the squirrel monkey, Brain Res. 105 (1976) 21-44. Terzuolo, C.A., Dufresne, J.R. and Soechting, J.F., Adaptive properties of the myotatic feedback, Prog. in Brain Res. (in press). Terzuolo, C.A. and Viviani, P., Parameters of motion and EMG activities during some simple motor tasks in normal subjects and cerebellar patients, in: Cooper, I.S., Riklan, M. and Snider, R.S. (eds.), The Cerebellum, Epilepsy and Behavior (Plenum, New York, 1974) 173-215. Viviani, P. and Terzuolo, C.A., Modeling of a simple motor task in man: intentional arrest of an ongoing movement, Kybern. 14 (1973) 35-62.
0 North-Holland Publishing Company, 1980
13 THE UTILIZATION OF MYOTATIC FEEDBACK I N MOTOR CONTROL C.A.
Terzuolo, J.R.
Dufresne and J . F . S o e c h t i n g
L a b o r a t o r y of Neurophysiology U n i v e r s i t y of Minnesota M i n n e a p o l i s , Minnesota
I n t h i s p a p e r , we s h a l l t a k e up a few t o p i c s which are r e l a t e d t o t h e f u n c t i o n a l u t i l i t y of m y o t a t i c f e e d b a c k , t h a t i s , feedback a c t i o n s o r i g i n a t i n g from muscle r e c e p t o r s and c a p a b l e of modifying t h e motor o u t p u t t o t h e a g o n i s t and a n t a g o n i s t muscles d u r i n g d i f f e r e n t motor t a s k s . The r e s u l t s of o u r work on t h i s s u b j e c t may b e summarized as f o l l o w s : 1) Such r e f l e x a c t i o n s behave e s s e n t i a l l y l i k e a n e g a t i v e v e l o c i t y feedback d u r i n g t h e i n t e n t i o n a l arrest of f a s t , ongoing movements ( S o e c h t i n g , l 9 7 3 ; T e r z u o l o and V i v i a n i , 1974; V i v i a n i and T e r z u o l o , 1973). 2 ) The m y o t a t i c feedback can b e p a r a m e t e r i z e d i n terms of a n e g a t i v e feedback of p o s i t i o n , v e l o c i t y and a c c e l e r a t i o n . Such a p a r a m e t e r i z a t i o n h a s l e d t o t h e i d e n t i f i c a t i o n of s e p a r a t e and i n d e p e n d e n t l y r e g u l a t e d feedback l o o p s , s u b s e r v e d by d i f f e r e n t c e n t r a l a n a t o m i c a l s t r u c t u r e s (Dufresne e t a l , 1978; 1979a). 3 ) The g a i n i n e a c h of t h e s e feedback l o o p s depends on t h e motor t a s k (Dufresne e t a l , 1978; 1979b). INTRODUCTION When t o r q u e p e r t u r b a t i o n s a r e a p p l i e d t o a l i m b , changes in limb p o s i t i o n w i l l r e s u l t from t h e sum of t h e e x t e r n a l l y a p p l i e d t o r q u e and t h e t o r q u e g e n e r a t e d by muscular c o n t r a c t i o n . The a c t i v i t y of t h e s t r e t c h r e c e p t o r s i n t h e muscles i n v o l v e d can b e e x p e c t e d t o r e f l e c t t h e s e changes i n a n g u l a r p o s i t i o n and i t s d e r i v a t i v e s : v e l o c i t y and a c c e l e r a t i o n . The dependence of I a a f f e r e n t a c t i v i t y on t h e s e p a r a m e t e r s i s w e l l e s t a b l i s h e d ( c f . Matthews, 1972). S i n c e muscle f o r c e and a n g u l a r p o s i t i o n are n o t i n d e p e n d e n t , t h e act i v i t y o f Golgi tendon o r g a n a f f e r e n t s w i l l a l s o depend on t h e same paramet e r s . The e x t e n t t o which a l p h a motoneuron o u t p u t i s d e t e r m i n e d by r e f l e x a c t i v i t y , t h a t i s t h e e x t e n t t o which i t depends on a f f e r e n t a c t i v i t y from s t r e t c h r e c e p t o r s , can t h u s b e a s s e s s e d by a model r e l a t i n g EMG a c t i v i t y ( t a k e n a s t h e o u t p u t ) t o a n g u l a r p o s i t i o n and i t s d e r i v a t i v e s ( t a k e n as the input). E x p e r i m e n t a l l y , pseudo-random, sequences of t o r q u e p u l s e s were a p p l i e d a t t h e elbow j o i n t of normal a d u l t human s u b j e c t s . The t a s k s performed by t h e s u b j e c t s were s p e c i f i e d n o t only by t h e i n s t r u c t i o n s g i v e n (e.g. t o resist o r n o t t o r e s i s t t h e a p p l i e d t o r q u e ) b u t a l s o by t h e e x t e r n a l l y imposed c o n d i t i o n s (such as a c o n s t a n t t o r q u e l o a d ) . Thus t h e t e r m " o p e r a t i n g p o i n t " w i l l b e used t o s p e c i f y e a c h e x p e r i m e n t a l c o n d i t i o n . EMG a c t i v i t y of b i c e p s and t r i c e p s , f o r e a r m a n g u l a r p o s i t i o n and a c c e l e r a t i o n and t h e appl i e d t o r q u e were recorded,. In o u r r e s u l t s , EMG a c t i v i t y i s e x p r e s s e d in
23 I
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terms of impulse density (when recorded with intramuscular electrodes) or in terms of the amplitude of full-wave rectified surface recordings. The model we have chosen i s a simple one, namely a linear model with three feedback terms (position, velocity and acceleration). The time delay for each of these terms is assumed to be independent. The rationale for this assumption is as follows: The possibility of multiple feedback pathways with different time delays is thereby included in the model as well as the possibility of a central processing of afferent activity analogous to a mathematical differentiation or integration. In other words, different pathways might use different parameters of the input. The model is arbitrary in the sense that additional terms, such as derivatives higher than acceleration and nonlinear terms are excluded. However, the restriction of the model to linear terms will be justified below. LINEAR MODELS OF REFLEX BEHAVIOR The extent to which such a model is able to reproduce the observed EMG activity for a typical experiment i s shown in Fig. 1. This figure also illustrates the relative contribution by each term of the model. The top trace shows the average EMG activity of the biceps obtained when the subject was asked to resist the applied perturbation in the presence of a steady torque acting to extend the forearm. The torque sequence itself is given at the bottom of the figure. The estimated contribution to the motor output by each term is depicted by the traces labeled position, velocity and acceleration. The total feedback, i.e. the sum of the three terms is given by the trace labeled model.
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Fig. 1. Fit of a linear feedback model to reflex activity evoked by torque perturbations. The model is given by: EMG(t) Ae(t-Ta)+Be(t-Tb)+C8(t-Tc)
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The computed EMG f i t s the e x p e r i m e n t a l d a t a q u i t e w e l l . The l e a s t s q u a r e e r r o r ( t h e squared d i f f e r e n c e between model and EMG) ranged from 25% t o 50% o f t h e v a r i a n c e i n d i f f e r e n t e x p e r i m e n t s . N e i t h e r t h e goodness of t h e f i t n o r t h e c o e f f i c i e n t s of t h e feedback terms depended on t h e s t r u c t u r e o f t h e sequence used. Furthermore, a s p e c t r a l a n a l y s i s of t h e e r r o r showed i t t o b e u n i f o r m l y d i s t r i b u t e d i n t h e f r e q u e n c y domain. A n o n l i n e a r a n a l y s i s of t h e e x p e r i m e n t a l d a t a a l s o s u g g e s t s t h a t t h e e r r o r i s m o s t l y due t o random n o i s e . N o n l i n e a r models i n c l u d i n g terms w i t h t h e s q u a r e and cube of t h e v e l o c i t y and a c c e l e r a t i o n reduced t h e e r r o r o n l y s l i g h t l y . By c a l c u l a t i n g second-order k e r n e l s f o r t h e impulse r e s p o n s e of EMG a c t i v i t y t o p u l s e s of t o r q u e , w e were a b l e t o show t h a t t h e a v e r a g e mot o r o u t p u t t o p a i r s of p u l s e s c l o s e l y approximates t h e a c t i v i t y o b t a i n e d by assuming a l i n e a r summation of t h e r e s p o n s e t o s i n g l e p u l s e s of t o r q u e . T h i s i s i l l u s t r a t e d i n F i g . 2 , which shows t h e a v e r a g e b i c e p s a c t i v i t y and a n g u l a r v e l o c i t y and a c c e l e r a t i o n f o l l o w i n g two p u l s e s of t o r q u e s e p a r a t e d by 20 msec. The l i g h t t r a c e , l a b e l e d l i n e a r , i s t h e b i c e p s a c t i v i t y p r e d i c t e d from t h e a v e r a g e r e s p o n s e t o a s i n g l e p u l s e of t o r q u e . The h e a v i e r t r a c e shows t h e e x t e n t o f n o n l i n e a r i n t e r a c t i o n between p a i r s of p u l s e s .
F i g . 2 . Impulse r e s p o n s e t o p a i r s of t o r q u e p u l s e s . The i m p u l s e r e s p o n s e w a s c a l c u l a t e d by c r o s s c o r r e l a t i n g t h e pseudo-random t o r q u e sequence w i t h b i c e p s EMG a c t i v i t y . Trace l a b e l e d l i n e a r shows r e s p o n s e c a l c u l a t e d from the f i r s t o r d e r k e r n e l , t h a t l a b e l e d n o n l i n e a r u s i n g a l s o t h e second o r d e r k e r n e l .
In c o n t r a s t t o t h e small improvement i n e r r o r when n o n l i n e a r models were used, a c o n s i d e r a b l e improvement i n t h e f i t of t h e model was o b t a i n e d when t h e feedback d e l a y s were p e r m i t t e d t o b e d i f f e r e n t . The a v e r a g e v a l u e s f o r 5 msec and 45 2 6 msec ret h e v e l o c i t y and a c c e l e r a t i o n d e l a y s were 25 s p e c t i v e l y (Dufresne e t a l , 1979a). The two time d e l a y s d i f f e r s u b s t a n t i a l l y w h i l e t h e i r s t a n d a r d d e v i a t i o n s are q u i t e s m a l l . The v e l o c i t y d e l a y i s comp a t i b l e w i t h s e g m e n t a l r e f l e x mechanisms, b e i n g c l o s e t o t h e l a t e n c y of t h e tendon j e r k i n man ( c . f . Hammond, 1960). The d e l a y f o r t h e a c c e l e r a t i o n feedback is c o m p a t i b l e w i t h t h e involvement of a s u p r a s p i n a l l o o p . The
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d e l a y f o r t h e p o s i t i o n term i s much l o n g e r (86 r e l a t i v e l y insensitive t o its value.
5
26 msec) and t h e model i s
A s f o r t h e adequacy of t h e model, we have a l r e a d y mentioned t h a t a s p e c t r a l a n a l y s i s of t h e e r r o r and t h e r e s u l t s of n o n l i n e a r modelling s u g g e s t t h a t t h e e r r o r is t o a l a r g e e x t e n t random n o i s e . Regarding t h e s p e c i f i c terms included i n t h e model, t h e v e l o c i t y parameter is g e n e r a l l y conceded t o b e prominent i n t h e o u t p u t of I a muscle s p i n d l e a f f e r e n t s (cf Matthews, 1 9 7 2 ) . The time d e l a y f o r t h e v e l o c i t y feedback is c l o s e t o t h a t t o b e expected f o r t h e monosynaptic r e f l e x . The a c c e l e r a t i o n parameter a l s o c o n t r i b u t e s s u b s t a n t i a l l y t o t h e motor o u t p u t ; t h e p o s i t i o n term is g e n e r a l l y n e g l i g i b l e . F i n a l l y , t h e dependence of t h e motor o u t p u t on t h e p a r a m e t e r s of t h e movement is n o t i n e v i t a b l e under o u r e x p e r i m e n t a l c o n d i t i o n s . EMG a c t i v i t y i n p a t i e n t s w i t h P a r k i n s o n i a n r i g i d i t y i s n o t w e l l related t o t h e p a r a m e t e r s of t h e movement and t h e moddelling e r r o r i n c r e a s e s g r e a t l y , d e s p i t e a b r i s k r e f l e x response t o t h e p ert u rb at io n . VELOCITY AND ACCELERATION FEEDBACK The b a r s i n t h e l e f t p a r t of F i g . 3 d e n o t e t h e a v e r a g e v a l u e s of t h e coe f f i c i e n t s f o r t h e v e l o c i t y and a c c e l e r a t i o n feedback terms. They r e p r e s e n t t h e average v a l u e s of r e s u l t s f o r t h e b i c e p s muscle from 16 e x p e r i m e n t s and 7 s u b j e c t s . These v a l u e s w e r e o b t a i n e d when t h e s u b j e c t s were i n s t r u c t e d t o resist t h e a p p l i e d p e r t u r b a t i o n . The mean t o r q u e was z e r o i n t h e s e e x p e r i ments.
Fig. 3 . Gain of t h e v e l o c i t y and a c c e l e r a t i o n feedback a t d i f f e r e n t operating points.
The r i g h t hand p o r t i o n of F i g . 3 shows how t h e two feedback c o e f f i c i e n t s v a r y w i t h t h e o p e r a t i n g p o i n t . T h e i r v a l u e s a r e e x p r e s s e d as a p e r c e n t a g e of t h e c o e f f i c i e n t s ' v a l u e s o b t a i n e d when t h e s u b j e c t s were i n s t r u c t e d t o resist a p e r t u r b a t i o n having a z e r o mean t o r q u e . The v a l u e s f o r t h e v e l o c i t y and a c c e l e r a t i o n feedback c o e f f i c i e n t s sometimes changed i n tandem. For example, t h e y b o t h i n c r e a s e d when t h e b i c e p s w a s active and opposed a mean
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t o r q u e t e n d i n g t o e x t e n d t h e f o r e a r m and d e c r e a s e d when i t a c t e d e s s e n t i a l l y as t h e a n t a g o n i s t (mean t o r q u e t e n d i n g t o f l e x t h e f o r e a r m ) . A t o t h e r operat i n g p o i n t s , a d i f f e r e n t i a l change i n t h e v a l u e s of t h e c o e f f i c i e n t s was obs e r v e d . For example, when t h e s u b j e c t s were i n s t r u c t e d n o t t o resist t h e a p p l i e d p e r t u r b a t i o n , t h e v a l u e of t h e v e l o c i t y f e e d b a c k was o n l y s l i g h t l y reduced, w h i l e t h a t of t h e a c c e l e r a t i o n feedback d e c r e a s e d t o 24% of t h e v a l u e o b t a i n e d when t h e s u b j e c t s were i n s t r u c t e d t o resist t h e a p p l i e d p e r turbation. Such a d i f f e r e n t i a l change i n t h e amount of v e l o c i t y and a c c e l e r a t i o n feedback i m p l i e s an independent r e g u l a t i o n o f t h e i r g a i n and s u g g e s t s t h e e x i s t e n c e of s e p a r a t e feedback l o o p s u t i l i z i n g d i f f e r e n t feedback p a r a m e t e r s . The s i g n i f i c a n t d i f f e r e n c e i n t h e v a l u e of t h e t i m e d e l a y s f o r t h e v e l o c i t y and a c c e l e r a t i o n feedback s u p p o r t s t h i s h y p o t h e s i s . Note t h a t i t i s l i k e l y t h a t e a c h of t h e s e l o o p s may u t i l i z e more t h a n one parameter and c o n v e r s e l y t h a t t h e t i m e d e l a y s of b o t h v e l o c i t y and a c c e l e r a t i o n feedback may r e p r e s e n t w,eighted a v e r a g e s o f two o r more l o o p s . More s p e c i f i c a l l y , i f t h e v e l o c i t y feedback i s p r o v i d e d by t h e a c t i v i t y of muscle s p i n d l e a f f e r e n t s and segmental r e f l e x mechanisms, p o s i t i o n and a c c e l e r a t i o n feedback a t t h e same l a t e n c y s h o u l d a l s o b e p r e s e n t . The model o n l y s u g g e s t s t h a t a c c e l e r a t i o n feedback a t l o n g e r l a t e n c i e s i s dominant. Regarding t h e v e l o c i t y f e e d b a c k , a c o n t r i b u t i o n by o l i v o - c e r e b e l l a r s t r u c t u r e s must b e c o n s i d e r e d . The e x p e r i m e n t a l e v i d e n c e f o r such a c o n t r i b u t i o n h a s been p r o v i d e d by a series of s t u d i e s on t h e i n t e n t i o n a l a r r e s t of f a s t movements i n man and i n t h e s q u i r r e l monkey ( S o e c h t i n g e t a l , 1976; T e r z u o l o and V i v i a n i , 1974). These s t u d i e s i n d i c a t e d t h a t t h e v e l o c i t y and a c c e l e r a t i o n feedback i s o p e r a t i o n a l d u r i n g f a s t movements which were b a l l i s t i c a l l y i n i t i a t e d . Under t h e s e c o n d i t i o n s , t h e motor o u t p u t t o a g o n i s t and antagon i s t was shown t o b e c a u s a l l y r e l a t e d t o t h e p a r a m e t e r s of t h e movement b o t h i n man and monkey. Such a c o u p l i n g between motor o u t p u t and t h e v e l o c i t y of t h e movement r e q u i r e s a c o n t r i b u t i o n by c e r e b e l l a r r e l a t e d a c t i v i t i e s , s i n c e i t was a b s e n t i n c e r e b e l l a r p a t i e n t s and markedly reduced i n monkeys w i t h l e s i o n s of t h e c e r e b e l l u m o r i n f e r i o r o l i v e . A l s o , s i n g l e u n i t r e c o r d i n g s from i n t e r p o s i t u s and r u b r a l neurons of c a t s p e r f o r m i n g t h e same t y p e of movement showed t h a t t h e v e l o c i t y p a r a m e t e r i s r e p r e s e n t e d i n t h e a c t i v i t y of t h e s e neurons d u r i n g t h i s t a s k (Burton and Onoda, 1978). Regarding t h e f u n c t i o n a l u t i l i t y of v e l o c i t y f e e d b a c k , such a f e e d b a c k can e f f e c t i v e l y damp o u t e x t e r n a l l y imposed p e r t u r b a t i o n s and o s c i l l a t i o n s which o c c u r d u r i n g t h e arrest of f a s t movements. I t is much less u s e f u l f o r an a c c u r a t e c o n t r o l of p o s i t i o n . Using a s i m p l e second o r d e r model ( c o n s i s t i n g of an i n e r t i a l mass, v i s c o u s damping and a s p r i n g ) f o r t h e mechanical and r e f l e x p r o p e r t i e s of t h e human forearm, w e have o b t a i n e d a n estimate f o r t h e v i s c o u s t i m e c o n s t a n t on t h e o r d e r of 1 . 3 t o 2.0 s e c o n d s when s u b j e c t s were i n s t r u c t e d n o t t o resist an a p p l i e d p e r t u r b a t i o n . When t h e y were asked t o r e s i s t , t h e v i s c o u s t i m e c o n s t a n t , a c c o r d i n g t o t h e model, d e c r e a s e d t o 100 t o 200 msec. I n t h e former c a s e , t h e b i c e p s was v i r t u a l l y s i l e n t ; i n t h e l a t t e r case, i t s a c t i v i t y was modulated r o u g h l y i n phase w i t h v e l o c i t y .
We have h y p o t h e s i z e d t h a t t h e a c c e l e r a t i o n feedback may i n v o l v e a t r a n s c o r t i c a l l o o p (Dufresne e t a 1 , 1 9 7 9 a ) . The h y p o t h e s i s i s based on t h e f o l l o w i n g c o n s i d e r a t i o n s : 1) The t i m e d e l a y i s c o m p a t i b l e w i t h s u c h a p o s s i b i l i t y , 2 ) t h e a c t i v i t y of p r e c e n t r a l c o r t i c a l u n i t s f o l l o w i n g t o r q u e p u l s e s changes i n a manner a p p r o p r i a t e t o m e d i a t e p a r t of t h e r e f l e x r e s p o n s e t o s u c h p u l s e s ( E v a r t s and T a n j i , 1976) and 3) t h e a c c e l e r a t i o n p a r a m e t e r i s r e p r e s e n -
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ted in their activity (Conrad et al., 1975). Moreover, when the sensory and cerebellar inflow to the sensory-motor cortex is interrupted by thalamic lesions, the only component of the motor output affected is the one which is correlated with the angular acceleration during ballistically initiated movements (Ranish and Soechting,l976). The contribution by a transcortical loop to the reflex response to single torque pulses has been the subject of much work and speculation in recent years (cf. Lee and Tatton, 1975). However, Ghez and Shinoda (1978) have shown that the so called M2 response which was attributed to a 10% latency loop is also obtained in aecerebrate and spinalized cats. Thus, evidence for a feedback of acceleration likely to involve a transcortical loop rests solely on the results obtained by modelling and the considerations summarized above. Assuming this hypothesis to be correct, we may consider the functional utility of such a loop. Phillips (1969) first postulated its existence and attributed to it a focussing action upon muscle spindle feedback while Evarts and Tanji (1974) suggested its function to be a modulation of reflex gain. Finally, Oguztoreli and Stein (1976) called attention to instabilities which are potentially introduced by a loop with a long delay time. Such instabilities would be obviated if the feed back parameter were to be acceleration. Indeed, for frequency components of changes in length below 6 Hz, an acceleration feedback would still lead velocity feedback at the time of their convergence upon a-motoneurons provided that the difference in delay between the two were less than 40 msec. Thus only during the sharpest transients, such as those resulting from a tendon tap,would the velocity feedback be initially dominant. The appropriateness of an acceleration feedback involving a transcortical loop may be more readily appreciated from the point of view of load compensation and the regulation of muscle force. Note that force and acceleration are mutually related although not equivalent (because of the visco-elastic properties of muscle). m our model we chose acceleration as one of the parameters since it was directly measurable, but we cannot exclude the possibility that force or its derivatives may be a more appropriate parameter. The afferent source of the acceleration feedback can only be surmised. An
acceleration component is present in the linear response of primary endings of muscle spindles to stretch (Poppele and Bowman, 1970). However, if the muscle spindles provided the source for this feedback, their activity would need to be differentiated centrally. Otherwise, the latency of the acceleration and velocity feedback terms would be the same. The involvement of Golgi tendon organ afferents in the acceleration feedback would be another possibility
.
The amplitude of the contribution by the acceleration feedback to the motor output ranged from 30% to 120% of that of the velocity feedback in our experiments. This ratio depends on the moment of inertia of the forearm and the motor and the duration of the longest torque pulse in a given sequence, both of these factors influencing the ratio of peak angular acceleration to peak angular velocity. Note that torque pulses produce large accelerations and that the contribution of the acceleration feedback can be expected to be less important under more physiological conditions. Also, given the low-pass
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filter characteristics of the transformation between a-motoneuron activity and muscle tension (cf. Partridge, 1 9 6 5 ) , the relative contribution of the acceleration feedback to muscle force is probably even less, although recruitment and/or synchronization of motor units and the potentiation of twitch tension which occurs for pairs of action potentials at short intervals (Burke et al., 1976; Robles and Soechting, 1979) may compensate for the drop in gain due to that transformation. The next topic we wish to address is the possibility of a central regulation of the gain of the velocity and acceleration feedback. First, it should be noted that a parallel increase or decrease in the value of the two coefficients may simply reflect a parallel change in the level of a-motoneuron excitability. The increase in the amplitude of the reflex activity when the muscle is tonically active and called upon to resist a steady torque (Dufresne et al., 1978; Marsden et al., 1972), which is illustrated in Fig. 3 , can be explained solely on this basis. However, the differential decrease in the values of the two feedback coefficients observed when the subjects are instructed not to resist the applied perturbation (Fig. 3) suggests the possibility of a central regulation of feedback gain independent from the level of a-motoneuron activity. REFLEX BEHAVIOR DURING INTENTIONAL MOVEMENTS The variations in the amplitude of reflex activity observed during intentionally generated movements also point to this possibility. Subjects produced sinusoidal movements of the forearm by tracking a sinusoidally modulated signal displayed on an oscilloscope. Figure 4A shows the variation in the full-wave rectified biceps EMG activity and the forearm angular velocity during such a tracking movement. The frequency was 1.8 Hz. During some trials, single extension pulses of torque were applied at different phases of the movement. The amplitude of the reflex activity evoked by the pulses of torque was measured and is shown at the bottom of Fig. 4A along with a sinusoid at the tracking frequency which gave the best fit to the data. The
B
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Fig. 4. Variation in reflex amplitude during tracking movements.
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modulation of t h e a m p l i t u d e of t h e r e f l e x a c t i v i t y d u r i n g t h e s e c y c l i c movements was s u b s t a n t i a l , t h e l a r g e s t r e s p o n s e b e i n g f i v e times a s l a r g e as t h e s m a l l e s t . Furthermore, changes i n r e f l e x a m p l i t u d e d i d n o t c o i n c i d e w i t h t h e i n t e n t i o n a l l y produced modulation of b i c e p s EMG a c t i v i t y . In f a c t , t h e modulation of r e f l e x a c t i v i t y showed a phase l e a d of 53'+37' o v e r t h e unpert u r b e d b i c e p s motor o u t p u t a t a t r a c k i n g f r e q u e n c y of 1.8 Hz. These changes i n r e f l e x a m p l i t u d e do n o t depend on t h e i n t e n t i o n a l l y genera t e d c y c l i c motion. This was e s t a b l i s h e d by changing t h e phase between t h e i n t e n t i o n a l l y g e n e r a t e d motor o u t p u t and t h e a n g u l a r v e l o c i t y of t h e f o r e arm by means of a s p r i n g l o a d . The r e s u l t s of t h e s e e x p e r i m e n t s a r e shown i n Fig. 4B. The p h a s e l e a d of b i c e p s a c t i v i t y o v e r v e l o c i t y h a s been reduced by a p p r o x i m a t e l y 80' compared t o t h a t o b t a i n e d i n t h e absence o f a s p r i n g l o a d (Fig. 4A). The r e f l e x a m p l i t u d e i s s t i l l modulated i n an a p p r o x i m a t e l y s i n u s o i d a l f a s h i o n and l e a d s t h e i n t e n t i o n a l l y g e n e r a t e d b i c e p s EMG a c t i v i t y by 67O?3Oo, which i s n o t s i g n i f i c a n t l y d i f f e r e n t from t h e p h a s e l e a d shown i n F i g . 4A. By a p p l y i n g pseudo-random sequences of t o r q u e p u l s e s d u r i n g such s i n u s o i d a l t r a c k i n g movements and r e l a t i n g t h e evoked r e f l e x a c t i v i t y i n b i c e p s t o t h e changes i n p o s i t i o n , v e l o c i t y and a c c e l e r a t i o n produced by t h e s e p e r t u r b a t i o n s , w e were a b l e t o c h a r a c t e r i z e t h e v a r i a t i o n s of t h e c o e f f i c i e n t s of t h e v e l o c i t y and a c c e l e r a t i o n terms of t h e feedback model d u r i n g s u c h movements (Dufresne e t a l . , 1979b). The r e s u l t s of t h i s modelling s t u d y showed t h a t t h e g a i n s o f t h e v e l o c i t y and a c c e l e r a t i o n feedback b o t h v a r y . That of t h e v e l o c i t y feedback l e a d s t h e i n t e n t i o n a l l y g e n e r a t e d b i c e p s a c t i v i t y by 57Ot5' w h i l e t h a t of t h e a c c e l e r a t i o n feedback i s o n l y 1l0+1Zo when a s i g n a l v a r y i n g s i n u s o i d a l l y a t 1.8 Hz i s t r a c k e d . Note t h a t t h e phase l e a d obt a i n e d f o r t h e v e l o c i t y feedback a g r e e s w e l l w i t h t h a t of t h e a m p l i t u d e of t h e r e f l e x a c t i v i t y evoked by s i n g l e p u l s e s of t o r q u e and t h a t t h e changes i n t h e g a i n of t h e v e l o c i t y and a c c e l e r a t i o n feedback a r e n o t i n p h a s e . The major c o n c l u s i o n from t h e s e s t u d i e s w a s t h a t t h e feedback g a i n s a r e mod u l a t e d d u r i n g c y c l i c i n t e n t i o n a l l y c o n t r o l l e d movements, b u t t h a t t h i s mod u l a t i o n does n o t depend on t h e i n t e n t i o n a l l y g e n e r a t e d movement ( F i g . 4 ) . I f muscle s p i n d l e a c t i v i t y were r e s p o n s i b l e f o r t h e observed r e f l e x a c t i v i t y t h i s c o n c l u s i o n would imply t h a t muscle s p i n d l e o u t p u t should b e uncoupled from t h e changes i n muscle l e n g t h g e n e r a t e d i n t e n t i o n a l l y d u r i n g t h e t r a c k i n g t a s k . The r e a s o n i n g i s as f o l l o w s : t h e a m p l i t u d e of t h e change i n angul a r v e l o c i t y produced by t h e t o r q u e p u l s e s d i d n o t exceed 40% of t h e maximum v e l o c i t y of t h e t r a c k i n g movement. The i n t e n t i o n a l l y g e n e r a t e d movement should t h e r e f o r e b e prominently r e p r e s e n t e d i n t h e o u t p u t of p a s s i v e muscle s p i n d l e r e c e p t o r s . However, t h e a m p l i t u d e of t h e r e f l e x r e s p o n s e sometimes exceeded t h e maximum of t h e i n t e n t i o n a l l y g e n e r a t e d motor o u t p u t and w e found t h e same modulation of r e f l e x amplitude when t h e r e w a s no movement p r i o r t o a n e x t e n s i o n t o r q u e p u l s e ( t h e s u b j e c t w a s modulating b i c e p s a c t i v i t y by c o n t r a c t i n g i s o m e t r i c a l l y a g a i n s t a s t i f f wire, Dufresne e t a l . , 1979b) a s d u r i n g a t r a c k i n g movement. Furthermore, muscle s p i n d l e s become more s e n s i t i v e t o i n c r e m e n t a l changes i n muscle l e n g t h a t l o n g e r l e n g t h s (Poppele, 1973). T h e r e f o r e , one might e x p e c t t o f i n d a change i n t h e phase between r e f l e x and i n t e n t i o n a l motor o u t p u t when t h e phase between i n t e n t i o n a l v e l o c i t y and motor o u t p u t i s changed ( F i g . 4 ) . A l l t h e s e c o n s i d e r a t i o n s p o i n t t o a f u s i m o t o r b i a s on muscle s p i n d l e s d u r i n g t h e t r a c k i n g movement.
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Muscle spindles of intercostal muscles show evidence of extensive fusimotor biasing during respiration (von Euler, 1966). More recently, it has been found that the activity of primary afferents from muscle spindles can be poorly correlated with changes in muscle length during locomotion (Loeb and Duysens, 1979; Prochazka et al., 1976). If this is also the case under our experimental conditions, as the data suggest, then one may conclude that muscle spindle afferents operate essentially as "error detectors" during movements. That is, their activity would reflect mostly deviations from an anticipated trajectory. This interpretation suggests that y-static activity, adequate to maintain the muscle spindle's discharge when the muscle is shortening, is task and load dependent and not necessarily rigidly linked to a-motoneuron activity. The timing of y-activation should take into account the phase difference between intentional motor commands and the resulting motion. Since this phase difference is influenced by the external loading (Fig. 4 ) , a task-dependent modification of the timing of y-activity relative to a-activity would be required. ACKNOWLEDGMENTS This work was supported by USPHS Grants NS-2567 and NS-15018. Computer facilities were made available by Air Force Office of Scientific Research, Grant AFOSR- 122 1. REFERENCES Burke, R.E., Rudomin, P. and Zajac, F.E., The effect of activation history on tension production by individual muscle units, Brain Res. 109 (1976) 515-530.
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