Experiments were performed in normal and Parkinsonian subjects who were asked to maintain a constant finger position using time-delayed visual feedback. The finger position showed complex dynamics, with characteristic differences between normal and Parkinosonian subjects. Here we discuss some of the theoretical issues that must be resolved in order to understand the mechanisms that underlie the generation of these complex signals

Beuter, Anne

Glass, Leon

Labrie, Christiane

Milton, John

English

Scholarship@Claremont

Claremont CollegesScholarship @ ClaremontWM Keck Science Faculty Papers W.M. Keck Science Department11-1-1989Complex Motor Dynamics and Control in Multi-looped Negative Feedback SystemsAnne BeuterUniversity of Quebec at MontrealJohn MiltonClaremont McKenna College; Pitzer College; Scripps CollegeChristiane LabrieLeon GlassMcGill UniversityThis Conference Proceeding is brought to you for free and open access by the W.M. Keck Science Department at Scholarship @ Claremont. It has beenaccepted for inclusion in WM Keck Science Faculty Papers by an authorized administrator of Scholarship @ Claremont. For more information, pleasecontact scholarship@cuc.claremont.edu.Recommended CitationBeuter, A., J. Milton, C. Labrie, L. Glass. "Complex Motor Dynamics and Control in Multilooped Negative Feedback Systems."Conference Proceedings for the IEEE International Conference on Systems, Man and Cybernetics, vol. 3 (14-17 November 1989):899-902. DOI: 10.1109/ICSMC.1989.71426COMPLEX MOTOR DYNAMICS AND CONTROL I N  MULTI-LOOPED NEGATIVE FEEDBACK SYSTEMS 1 3 and Leon Glass Anne Beuter', John Milton', C h r i s t i a n e  Labrie  From 1)  Universit; du Q&bec 'a Montrgal, 2) The Univers i ty  of Chicago Hospi ta l s ,  and 3) McGill ITn!.versfty Abstract :  Experiments w e r e  performed i n  normid and Parkinsonian s u b j e c t s  who were asked t o  maintain a cons tan t  f i n g e r  p o s i t i o n  using a time-delayed v i s u a l  feedback. t i o n  showed complex dynamics, w i t h  c h a r a c t e r i s t i c  d i f f e r e n c e s  between normal and Parkinsonian s u b j e c t s .  Here we d i s c u s s  some of t h e  t h e o r e t i c a l  i s s u e s  t h a t  must be  resolved i n  order  t o  understand t h e  mechanisms t h a t  underly t h e  genera t ion  of t h e s e  complex s i g n a l s .  The f i n g e r  posi-  INTRODUCTION Goal d i r e c t e d  movements comprise most of human a c t i v i t y .  r e p e r t o i r e  t h a t  i n c r e a s e s  wi th  development and l e a r n i n g  and which is cont inuously modified by environmental and behaviora l  c o n s t r a i n t s .  I n  h e a l t h ,  vo luntary  movements and g e s t u r e s  are cons tan t ly  modified i n  order  t o  opt imize c e r t a i n  c r i t e r i a ,  e.g., energy, speed, gracefu l -  ness .  However, i n  d i s e a s e  motor dysfunct ion is o f t e n  charac te r ized  by t h e  presence of uncontrol-  l e d  o s c i l l a t i o n s  some of  which are very  complex, e.g., tremors, chorea, a t h e t o s i s .  The regu- l a t i o n  of movement involves  t h e  cooperat ion of m u l t i p l e  feedback loops opera t ing  a t  m u l t i p l e  l e v e l s  i n  t h e  per iphera l  and c e n t r a l  nervous system. Each feedback loop  has i ts  own charac- t e r i s t i c  t i m e  de lay  and gain.  Models of  m u l t i p l e  delayed feedback loops are capable  of generat ing complex dynamics (1) and t h u s  t h e s e  models o f f e r  a p o s s i b l e  explanat ion f o r  t h e  complex movements observed i n  h e a l t h  and d isease .  po in t ing  a f i n g e r ,  involve most of t h e  s t r u c t u r e s  of t h e  c e n t r a l  nervous system. I n  such a task ,  v i s u a l  input  is requi red  t o  a t t e n d  t o  t h e  t a r g e t  and t o  estimate t h e  discrepancy,  o r  e r r o r ,  between t h e  p o s i t i o n  of  t h e  f i n g e r  and t h e  p o s i t i o n  of t h e  t a r g e t .  This  e r r o r  g ives  rise t o  a s i g n a l  which is fed  back t o  t h e  mechanisms c o n t r o l l i n g  f i n g e r  movement and is used t o  a d j u s t  f i n g e r  p o s i t i o n  t h u s  minimizing t h e  e r r o r .  c y c l e  between perceived e r r o r  and movement product ion forms a c losed  feedback loop.  However, t h i s  feedback l i k e l y  involves  s e v e r a l  c o n t r o l  mechanisms (Figure 1 ) .  Afferent  s i g n a l s  a r i s i n g  from t h e  propr ioceptors  and t h e  r e t i n a  These movements form a v a s t  Even t h e  "simplest" movements, such as This  Figure 1: Neuroanatomical model of t h e  m u l t i p l e  loops  involved i n  c o n t r o l l i n g  a s imple movement of  t h e  index f i n g e r .  t r a v e l  by s e p a r a t e  pathways t o  t h e  c o r t e x  v i a  s e p a r a t e  n u c l e i  of t h e  thalamus and t h e  b a s a l  gangl ia .  The l i k e l y  f i r s t  sites of i n t e r a c t i o n  of t h i s  a f f e r e n t  information f o r  t h e  t a s k  of a l t e r i n g  f i n g e r  p o s i t i o n  are t h e  a s s o c i a t i o n  areas of t h e  cor tex ,  i .e.,  t h e  p a r i e t o - o c c i p i t a l  lobes.  Descending information t o  t h e  s p i n a l  cord and t h e  f i n g e r  v i a  t h e  c o r t i c o s p i n a l  and rubrospina l  tracts and ascending information from v i s i o n  ( i . e . ,  super ior  c o l l i c u l u s )  and limb movements ( i . e . ,  sp inocerebe l la r  t r a c t )  are modulated by t h e  cerebellum. guided movement t a s k s ,  i .e.,  t racking ,  i s  t h e  ease by which i t  is p o s s i b l e  t o  modify t h e  l a t e n c y  and/or ga in  of t h e  v i s u a l  feedback loop. Here we show t h a t  complex o s c i l l a t i o n s  i n  index f i n g e r  displacement can be produced by in t roduct ion  of a v i s u a l  de lay  i n t o  a s imple t racking  task .  ex ten t  t o  which t h e s e  observa t ions  can be  i n t e r p r e t e d  i n  t h e  contex t  of models of multi-looped feedback networks is discussed.  The r e s u l t s  are descr ibed more f u l l y  i n  1-3. An a l t e r n a t i v e  approach t o  t h e  s tudy of f i n g e r  movements i s  being developed by Kelso and co-workers (4). One of t h e  advantages of s tudying v i s u a l l y -  The 899 P -~ I I Authorized licensed use limited to: to the Claremont Colleges!. Downloaded on November 7, 2008 at 17:59 from IEEE Xplore.  Restrictions apply.METHODS J UI 3500.0b The experimental design i s  descr ibed i n  d e t a i l  elsewhere (1-3). B r i e f l y ,  s u b j e c t s  are requi red  t o  a d j u s t  t h e  p o s i t i o n  of t h e i r  index f i n g e r  t o  match t h e  p o s i t i o n  of a t a r g e t .  t h e  s u b j e c t s  are not  a b l e  t o  see t h e  p o s i t i o n  of t h e i r  index f i n g e r  i n  r e l a t i o n  t o  t h e  t a r g e t .  Ins tead  they look a t  a n  osc i l loscope  screen  on which two hor izonta l  l i n e s  are displayed.  One l i n e  is s t a t i o n a r y  and corresponds t o  t h e  t a r g e t .  The o t h e r  i s  c o n t r o l l e d  by t h e  index f i n g e r  a t  t h e  metacarpo-phalangeal j o i n t  as de tec ted  by a micro- displacement t ransducer  (LVDT). The s u b j e c t s  are asked t o  match t h e  two hor izonta l  l i n e s  as c l o s e l y  as poss ib le .  A v a r i a b l e  t i m e  delay is introduced by i n s e r t i n g  a n  analog de lay  l i n e  (bucket br igade type device)  between t h e  t ransducer  and t h e  osc i l loscope .  sc reen  t h e  s u b j e c t s  are only a b l e  t o  judge t h e  p o s i t i o n  of t h e i r  index f i n g e r  r e l a t i v e  t o  t h e  t a r g e t  a t  some t i m e  i n  t h e  p a s t .  I n  a d d i t i o n ,  t h e  feedback gain can be  increased by amplifying f i n g e r  movements so t h a t  r e l a t i v e l y  l a r g e r  displacements  a r e  seen on t h e  osc i l loscope  screen.  I n  t h e s e  experiments, a f i n g e r  displacement of 1 mm corresponds t o  a displacement of about 16 mm on t h e  o s c i l l o s c o p e  screen .  RESULTS However. Thus, by viewing t h e  o s c i l l o s c o p e  I The e f f e c t  of introducing a t i m e  de lay  i n  t h e  visuo-motor feedback loop is i l l u s t r a t e d  i n  F igures  2 and 3. When no t i m e  delay i s  i n s e r t e d  (Figure 2)  t h e  o s c i l l a t i o n s  recorded correspond t o  tremor. With a t i m e  de lay  of  1500 ms, i r r e g u l a r  f l u c t u a t i o n s  i n  f i n g e r  displacements  occur which are not  present  a t  zero delay (Figure 3).  The average inter-peak i n t e r v a l  of t h e  regular  o s c i l l a t i o n  i n c r e a s e s  cont inuously with t h e  t i m e  d e l a y  and i s  always between two and four  t i n e s  t h e  de lay .  in te rmicrent ly  during t h e  60 s record.  These slow o s c i l l a t i a n s  appear 1 3800. 3700. > J w ' I  I L U 5 3600. moo. 0 E! , 3700. > -1 0 3600.1 r' ' " 1 1 -' ' I  L U J 2 Figure 3: Finger o s c i l l a t i o n s  with a t i m e  de lay  of 1500 m s .  One i n t e r e s t i n g  phenomenon observed i n  a p a t i e n t  with Parkinson's d i s e a s e  (basa l  gangl ia  l e s i o n s )  is a n  abrupt  change i n  t h e  q u a l i t a t i v e  n a t u r e  of t h e  t i m e  series f o r  f i n g e r  displacement (Y'iwre '>. This phenomenon has  been repor ted  3800 0 ,0000  20000 40000 60000 80000 T I H E  IMILLSSECONOS) Figure  4: T r a n s i t i o n  i n  f i n g e r  o s c i l l a t i o n s  f o r  p a t i e n t  with Parksinson 's  d i s e a s e  a before  (5) and c o n s i s t s  of a n  abrupt  change i n  both t h e  amplitude and frequency of t h e  movement. DISCUSSION The v i s u a l l y  guided motor t a s k  descr ibed i n  t h i s  experiment is very simple. However, t h e  observed time s e r i e s  of f i n g e r  displacement generated by t h i s  t a s k  are e x t r a o r d i n a r i l y  compli- c a t e d .  H e r e  w e  b r i e f l y  d iscuss  some of t h e  t h e o r e t i c a l  i s s u e s  that must be resolved i n  order  t o  understand t h e  mechanisms t h a t  underly t h e  generat ion of t h e s e  complex s i g n a l s .  It i s  w e l l  known t h a t  nega t ive  feedback 900 Authorized licensed use limited to: to the Claremont Colleges!. Downloaded on November 7, 2008 at 17:59 from IEEE Xplore.  Restrictions apply.systems with s i n g l e  c o n t r o l  loops can be  d e s t a b i l i z e d  by increas ing  t h e  gain andfor  delay t o  produce r e g u l a r  o s c i l l a t i o n s  with per iods between two and four  t i m e s  t h e  delay (6) .  Although low frequency o s c i l l a t i o n s  with per iods of t h i s  magnitude are observed f o r  most s u b j e c t s ,  t h e s e  o s c i l l a t i o n s  do not  have a regular  waveform over t h e  e n t i r e  60 s record.  Indeed t h e  s t r i k i n g  f e a t u r e  of t h e  temporal record is not  t h e  s t a b i l i t y  of t h e  low frequency o s c i l l a t i o n s ,  but  r a t h e r  i t s  f l u c t u a t i n g  and aper iodic  na ture .  There are many mechanisms t h a t  may c o n t r i b u t e  t o  t h e  generat ion of time s i g n a l s  of t h i s  complexity. These include:  ( i )  t h e  i n t e r a c t i o n s  between t h e  m u l t i p l e  feedback loops;  ( i i )  t h e  i n t e r a c t i o n s  between feedforward and feedback loops;  and ( i i i )  t h e  p o s s i b i l i t y  t h a t  parameters i n  t h e  feedback system are not  cons tan t ,  but  may be regula ted  by t h e  state of t h e  system, o r  f l u c t u a t e  due t o  random i n p u t s  t o  t h e  c o n t r o l  sys tern. t h e  c o n t r o l  of movement (Figure l ) ,  it is poss ib le  t h a t  t h e  complex t i m e  series we  observe r e f l e c t  t h e  dynamics of multi-loop feedback systems. Previous workers (7 )  emphasized that m u l t i p l e  feedbacks would tend t o  s t a b i l i z e  feedback systems. This  i s  not  always t h e  case. I n  a recent  paper (1)  w e  found t h a t  m u l t i p l e  nega t ive  feedback could,  i n  some circumstances,  l ead  t o  d e t e r m i n i s t i c  c h a o t i c  dynamics i n  which t h e r e  w a s  a p e r i o d i c  dynamics wi th  s e n s i t i v e  dependence on t h e  i n i t i a l  condi t ions .  Thus, m u l t i p l e  nega t ive  feedbacks can lead  t o  a d e s t a b i l i z a t i o n  of t h e  dynamics and t o  complex temporal f l u c t u a t i o n s .  However, recent  s t u d i e s  (8)  have shown t h a t  a l though chaot ic  dynamics can be  found i n  m u l t i p l e  nega t ive  feedback systems, t h i s  i s  a comparatively rare phenomenon, a t  least i n  t h e  s p e c i a l i z e d  systems t h a t  were examined. Thus, it is  u n l i k e l y  t h a t  t h e  dynamics of  d e t e r m i n i s t i c  models of multi-loop negat ive  feedback systems can completely account f o r  t h e s e  observat ions.  One f a c t o r  t h a t  should be  considered i n  t h e o r e t i c a l  models of motor c o n t r o l  i s  t h e  r o l e  of feedforward c o n t r o l .  The organiza t ion  of goal- d i r e c t e d  movements genera l ly  can be  descr ibed f u n c t i o n a l l y  as a continuum. A t  one extreme, a movement t o  a t a r g e t  may be  cont inuously ad jus ted  using feedback mechanisms. A t  t h e  o t h e r  extreme, a movement may involve a series of preprogrammed commands unfolding i n  a feedforward mode with few o p p o r t u n i t i e s  of cur ren t  modi f ica t ion  by propr iocept ive  o r  o t h e r  feedback mechanisms. Mathematically, such preprogrammed commands can be incorporated i n t o  t h e o r e t i c a l  models by computing t h e  p o s i t i o n  a t  some f u t u r e  t i m e  and modifying muscular a c t i v i t y  based on t h e  devia t ion  of t h e  limb t i p  from i ts  des i red  l o c a t i o n .  Thus, both feedback and feedforward loops must be  considered i n  t h e o r e t i c a l  models of motor c o n t r o l  (9) .  de lay  and o t h e r  parameters descr ib ing  t h e  feedback loops,  i n  shaping t h e  observed dynamics must be considered.  One p o s s i b i l i t y  i s  that t h e s e  parameters are some func t ion  of t h e  c u r r e n t  s ta te  of t h e  system. For example, c o n t r o l  mechanisms Since m u l t i p l e  c o n t r o l  loops are involved i n  F i n a l l y  t h e  r o l e  of f l u c t u a t i o n s  i n  t h e  gain,  with state-dependent de lays  have been r e c e n t l y  considered i n  o ther  contex ts  ( L O ) .  Al te rna t ive ly  t h e r e  may be  s t o c h a s t i c  f l u c t u a t i o n s  i n  some of t h e s e  parameters s i n c e  they r e f l e c t  underlying neurophysiological  and molecular processes .  CONCLUDING REMARKS Further  experimental andfor  c l i n i c a l  s t u d i e s  are  needed t o  compliment t h e o r e t i c a l  approaches. with known l e s i o n s  i n  neura l  c e n t e r s  d i r e c t l y  involved i n  motor c o n t r o l  (Figure 1). Indeed by c a r e f u l  p a t i e n t  s e l e c t i o n  it is  p o s s i b l e  t o  i d e n t i f y  p a t i e n t  subgroups with w e l l  l o c a l i z e d  l e s i o n s .  i n  t h e  basa l  gangl ia  t h a t  occur  i n  p a t i e n t s  wi th  Parkinson 's  d i s e a s e  do not  g r e a t l y  a f f e c t  t h e i r  performance i n  t h i s  t racking  t a s k  i f  t h e i r  parkinsonian tremor i s  of r e l a t i v e l y  low amplitude (11). There is a need t o  extend t h e s e  s t u d i e s  i n  order  t o  examine p a t i e n t s  with c e r e b e l l a r  d i s e a s e  and o t h e r  neuro logica l  d i sorders .  Such a s t r a t e g y  i s  d i r e c t e d  a t  i d e n t i f y i n g  those  feedback loops which are c r i t i c a l  f o r  t h i s  motor task .  An i n t e g r a t i o n  of approaches from many d i s c i p l i n e s  inc luding  c o n t r o l  theory,  nonl inear  dynamics and neurology w i l l  be needed t o  under- s tand t h e  complex t i m e  series generated i n  t h e  neuromotor system regula t ing  f i n g e r  p o s i t i o n  under feedback c o n t r o l .  address  quest ions such as t h e  following: motor commands involve d i f f e r e n t  b r a i n  c i r c u i t s  f o r  feedback and feedforward modes? What are t h e  mechanisms respons ib le  f o r  dynamic switching between one mode and t h e  o t h e r ?  What are t h e  i n t e r a c t i o n s  between p e r i p h e r a l ,  s u b c o r t i c a l  and i n t r a c o r t i c a l  loops during goal-directed movement ? One approach i s  t o  s tudy p a t i e n t s  For example, we  have shown t h a t  l e s i o n s  W e  may then become a b l e  t o  Do Acknowledgements: This  work w a s  p a r t l y  supported by Natural  Sciences and Engineering Research Council (Canada) and Fonds pour l a  Formation de  Chercheurs et 1'Aide a l a  Recherche (Quebec) through t h e  Univers i ty  of Quebec and M c G i l l  Univers i ty .  1. 2. 3.  4 .  5. REFERENCES L. G l a s s ,  A. Beuter and D. Larocque, "Time de lays ,  o s c i l l a t i o n s  and chaos i n  phys io logica l  c o n t r o l  systems," MATH. BIOSCI. Vol. 90, pp. 111-125 : 1988. A.  Beuter, D. Larocque and L. Glass, "Complex o s c i l l a t i o n s  i n  a human motor system," J. MOTOR BEH. ( i n  p r e s s ) .  J . G .  Milton, A. Longtin, A. Beuter, M.C. Mackey and L. Glass, "Complex dynamics and b i f u r c a t i o n s  i n  neurology," J. THEORET. BIOL. Vol. 138, pp. 129-147 : 1989. G. Schoner and J.A.S. Kelso, "Synerget i t  theory of environmental ly-specif ied and learned p a t t e r n s  of movement coord ina t ion .  P a r t s  I and 11," BIOL. CYBERN. Vol. 58, V.S. Gurf inkel  and S.M. Osovets, "Mechanism of genera t ion  of o s c i l l a t i o n s  i n  t h e  tremor pp. 71-80; 81-89 : 1988. 901 T -- Authorized licensed use limited to: to the Claremont Colleges!. Downloaded on November 7, 2008 at 17:59 from IEEE Xplore.  Restrictions apply.form of  parkinsonism," BIOFIZIKA V d l .  18, pp. 731-738 : 1973. 6. il G l a s s  and M.C. Mackey. From c locks  t o  chaos: t h e  rhythms of l i f e .  Pr ince ton  Univers i tv  Press .  Pr inceton:  1988. 7 .  M.N. Oguztore l l i  and R.B. S te in ,  "The e f f e c t s  of m u l t i p l e  r e f l e x  pathways on t h e  o s c i l l a t i o n s  i n  neuro-muscular systems, I' J. MATH. BIOL. Vol. 3, pp. 87-101 : 1976. 8. L. Glass and C.P. Malta, "Chaos i n  mult i -  looped negat ive  feedback systems," ( i n  review).  9. H. Hemani and B.T. Stokes, "A q u a l i t a t i v e  d iscuss ion  of  mechanisms of feedback and feedforward i n  t h e  c o n t r o l  of locomotion," IEEE TRANS. BIOMED. ENG. Vol. BME-30, pp. 681-691 : 1983. 10. M.C. Mackey, "Commodity p r i c e  f l u c t u a t i o n s :  P r i c e  dependent de lays  and n o n - l i n e a r i t i e s  as explanatory f a c t o r s , "  J. ECON. THEORY ( i n  p r e s s ) .  11. A. Beuter, J . G .  Milton, C .  Labrie ,  L. Glass and S. Gauthier ,  "Effects  of delayed v i s u a l  feedba'ck on motor c o n t r o l  i n  Parkinson 's  d i sease ,"  ( i n  review). 902 - -77 Authorized licensed use limited to: to the Claremont Colleges!. Downloaded on November 7, 2008 at 17:59 from IEEE Xplore.  Restrictions apply.

Complex Motor Dynamics and Control in Multi-looped Negative Feedback Systems

Keck Graduate Institute

Claremont Colleges
Scholarship @ Claremont
WM Keck Science Faculty Papers W.M. Keck Science Department
11-1-1989
Complex Motor Dynamics and Control in Multi-
looped Negative Feedback Systems
Anne Beuter
University of Quebec at Montreal
John Milton
Claremont McKenna College; Pitzer College; Scripps College
Christiane Labrie
Leon Glass
McGill University
This Conference Proceeding is brought to you for free and open access by the W.M. Keck Science Department at Scholarship @ Claremont. It has been
accepted for inclusion in WM Keck Science Faculty Papers by an authorized administrator of Scholarship @ Claremont. For more information, please
contact scholarship@cuc.claremont.edu.
Recommended Citation
Beuter, A., J. Milton, C. Labrie, L. Glass. "Complex Motor Dynamics and Control in Multilooped Negative Feedback Systems."
Conference Proceedings for the IEEE International Conference on Systems, Man and Cybernetics, vol. 3 (14-17 November 1989):
899-902. DOI: 10.1109/ICSMC.1989.71426
COMPLEX MOTOR DYNAMICS AND CONTROL I N  MULTI-LOOPED NEGATIVE FEEDBACK SYSTEMS 
1 3 
and Leon Glass Anne Beuter', John Milton', C h r i s t i a n e  Labrie  
From 1)  Universit; du Q&bec 'a Montrgal, 2) The Univers i ty  of 
Chicago Hospi ta l s ,  and 3) McGill ITn!.versfty 
Abstract :  Experiments w e r e  performed i n  normid 
and Parkinsonian s u b j e c t s  who were asked t o  
maintain a cons tan t  f i n g e r  p o s i t i o n  using a 
time-delayed v i s u a l  feedback. 
t i o n  showed complex dynamics, w i t h  c h a r a c t e r i s t i c  
d i f f e r e n c e s  between normal and Parkinsonian 
s u b j e c t s .  Here we d i s c u s s  some of t h e  
t h e o r e t i c a l  i s s u e s  t h a t  must be  resolved i n  
order  t o  understand t h e  mechanisms t h a t  underly 
t h e  genera t ion  of t h e s e  complex s i g n a l s .  
The f i n g e r  posi-  
INTRODUCTION 
Goal d i r e c t e d  movements comprise most of 
human a c t i v i t y .  
r e p e r t o i r e  t h a t  i n c r e a s e s  wi th  development and 
l e a r n i n g  and which is cont inuously modified by 
environmental and behaviora l  c o n s t r a i n t s .  I n  
h e a l t h ,  vo luntary  movements and g e s t u r e s  are 
cons tan t ly  modified i n  order  t o  opt imize 
c e r t a i n  c r i t e r i a ,  e.g., energy, speed, gracefu l -  
ness .  However, i n  d i s e a s e  motor dysfunct ion is 
o f t e n  charac te r ized  by t h e  presence of uncontrol-  
l e d  o s c i l l a t i o n s  some of  which are very  complex, 
e.g., tremors, chorea, a t h e t o s i s .  The regu- 
l a t i o n  of movement involves  t h e  cooperat ion of 
m u l t i p l e  feedback loops opera t ing  a t  m u l t i p l e  
l e v e l s  i n  t h e  per iphera l  and c e n t r a l  nervous 
system. Each feedback loop  has i ts  own charac- 
t e r i s t i c  t i m e  de lay  and gain.  Models of  m u l t i p l e  
delayed feedback loops are capable  of generat ing 
complex dynamics (1) and t h u s  t h e s e  models o f f e r  
a p o s s i b l e  explanat ion f o r  t h e  complex movements 
observed i n  h e a l t h  and d isease .  
po in t ing  a f i n g e r ,  involve most of t h e  s t r u c t u r e s  
of t h e  c e n t r a l  nervous system. I n  such a task ,  
v i s u a l  input  is requi red  t o  a t t e n d  t o  t h e  t a r g e t  
and t o  estimate t h e  discrepancy,  o r  e r r o r ,  
between t h e  p o s i t i o n  of  t h e  f i n g e r  and t h e  
p o s i t i o n  of t h e  t a r g e t .  This  e r r o r  g ives  rise t o  
a s i g n a l  which is fed  back t o  t h e  mechanisms 
c o n t r o l l i n g  f i n g e r  movement and is used t o  a d j u s t  
f i n g e r  p o s i t i o n  t h u s  minimizing t h e  e r r o r .  
c y c l e  between perceived e r r o r  and movement 
product ion forms a c losed  feedback loop.  
However, t h i s  feedback l i k e l y  involves  s e v e r a l  
c o n t r o l  mechanisms (Figure 1 ) .  Afferent  s i g n a l s  
a r i s i n g  from t h e  propr ioceptors  and t h e  r e t i n a  
These movements form a v a s t  
Even t h e  "simplest" movements, such as 
This  
Figure 1: Neuroanatomical model of t h e  m u l t i p l e  
loops  involved i n  c o n t r o l l i n g  a s imple 
movement of  t h e  index f i n g e r .  
t r a v e l  by s e p a r a t e  pathways t o  t h e  c o r t e x  v i a  
s e p a r a t e  n u c l e i  of t h e  thalamus and t h e  b a s a l  
gangl ia .  The l i k e l y  f i r s t  sites of i n t e r a c t i o n  of 
t h i s  a f f e r e n t  information f o r  t h e  t a s k  of a l t e r i n g  
f i n g e r  p o s i t i o n  are t h e  a s s o c i a t i o n  areas of t h e  
cor tex ,  i .e.,  t h e  p a r i e t o - o c c i p i t a l  lobes.  
Descending information t o  t h e  s p i n a l  cord and t h e  
f i n g e r  v i a  t h e  c o r t i c o s p i n a l  and rubrospina l  tracts 
and ascending information from v i s i o n  ( i . e . ,  
super ior  c o l l i c u l u s )  and limb movements ( i . e . ,  
sp inocerebe l la r  t r a c t )  are modulated by t h e  
cerebellum. 
guided movement t a s k s ,  i .e.,  t racking ,  i s  t h e  ease 
by which i t  is p o s s i b l e  t o  modify t h e  l a t e n c y  and/or 
ga in  of t h e  v i s u a l  feedback loop. Here we show 
t h a t  complex o s c i l l a t i o n s  i n  index f i n g e r  
displacement can be produced by in t roduct ion  of a 
v i s u a l  de lay  i n t o  a s imple t racking  task .  
ex ten t  t o  which t h e s e  observa t ions  can be  
i n t e r p r e t e d  i n  t h e  contex t  of models of multi-looped 
feedback networks is discussed.  The r e s u l t s  are 
descr ibed more f u l l y  i n  1-3. An a l t e r n a t i v e  
approach t o  t h e  s tudy of f i n g e r  movements i s  being 
developed by Kelso and co-workers (4). 
One of t h e  advantages of s tudying v i s u a l l y -  
The 
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METHODS 
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The experimental design i s  descr ibed i n  
d e t a i l  elsewhere (1-3). B r i e f l y ,  s u b j e c t s  are 
requi red  t o  a d j u s t  t h e  p o s i t i o n  of t h e i r  index 
f i n g e r  t o  match t h e  p o s i t i o n  of a t a r g e t .  
t h e  s u b j e c t s  are not  a b l e  t o  see t h e  p o s i t i o n  of 
t h e i r  index f i n g e r  i n  r e l a t i o n  t o  t h e  t a r g e t .  
Ins tead  they look a t  a n  osc i l loscope  screen  on 
which two hor izonta l  l i n e s  are displayed.  One 
l i n e  is s t a t i o n a r y  and corresponds t o  t h e  t a r g e t .  
The o t h e r  i s  c o n t r o l l e d  by t h e  index f i n g e r  a t  t h e  
metacarpo-phalangeal j o i n t  as de tec ted  by a micro- 
displacement t ransducer  (LVDT). The s u b j e c t s  are 
asked t o  match t h e  two hor izonta l  l i n e s  as c l o s e l y  
as poss ib le .  A v a r i a b l e  t i m e  delay is introduced 
by i n s e r t i n g  a n  analog de lay  l i n e  (bucket br igade 
type device)  between t h e  t ransducer  and t h e  
osc i l loscope .  
sc reen  t h e  s u b j e c t s  are only a b l e  t o  judge t h e  
p o s i t i o n  of t h e i r  index f i n g e r  r e l a t i v e  t o  t h e  
t a r g e t  a t  some t i m e  i n  t h e  p a s t .  I n  a d d i t i o n ,  
t h e  feedback gain can be  increased by amplifying 
f i n g e r  movements so t h a t  r e l a t i v e l y  l a r g e r  
displacements  a r e  seen on t h e  osc i l loscope  screen.  
I n  t h e s e  experiments, a f i n g e r  displacement of 
1 mm corresponds t o  a displacement of about 16 mm 
on t h e  o s c i l l o s c o p e  screen .  
RESULTS 
However. 
Thus, by viewing t h e  o s c i l l o s c o p e  
I 
The e f f e c t  of introducing a t i m e  de lay  i n  
t h e  visuo-motor feedback loop is i l l u s t r a t e d  i n  
F igures  2 and 3. When no t i m e  delay i s  i n s e r t e d  
(Figure 2)  t h e  o s c i l l a t i o n s  recorded correspond 
t o  tremor. With a t i m e  de lay  of  1500 ms, 
i r r e g u l a r  f l u c t u a t i o n s  i n  f i n g e r  displacements  
occur which are not  present  a t  zero delay (Figure 
3).  The average inter-peak i n t e r v a l  of t h e  
regular  o s c i l l a t i o n  i n c r e a s e s  cont inuously with 
t h e  t i m e  d e l a y  and i s  always between two and four  
t i n e s  t h e  de lay .  
in te rmicrent ly  during t h e  60 s record.  
These slow o s c i l l a t i a n s  appear 
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Figure 3: Finger o s c i l l a t i o n s  with a t i m e  de lay  of 
1500 m s .  
One i n t e r e s t i n g  phenomenon observed i n  a 
p a t i e n t  with Parkinson's d i s e a s e  (basa l  gangl ia  
l e s i o n s )  is a n  abrupt  change i n  t h e  q u a l i t a t i v e  
n a t u r e  of t h e  t i m e  series f o r  f i n g e r  displacement 
(Y'iwre '>. This phenomenon has  been repor ted  
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T I H E  IMILLSSECONOS) 
Figure  4: T r a n s i t i o n  i n  f i n g e r  o s c i l l a t i o n s  f o r  
p a t i e n t  with Parksinson 's  d i s e a s e  
a 
before  (5) and c o n s i s t s  of a n  abrupt  change i n  both 
t h e  amplitude and frequency of t h e  movement. 
DISCUSSION 
The v i s u a l l y  guided motor t a s k  descr ibed i n  
t h i s  experiment is very simple. However, t h e  
observed time s e r i e s  of f i n g e r  displacement 
generated by t h i s  t a s k  are e x t r a o r d i n a r i l y  compli- 
c a t e d .  H e r e  w e  b r i e f l y  d iscuss  some of t h e  
t h e o r e t i c a l  i s s u e s  that must be resolved i n  order  
t o  understand t h e  mechanisms t h a t  underly t h e  
generat ion of t h e s e  complex s i g n a l s .  
It i s  w e l l  known t h a t  nega t ive  feedback 
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systems with s i n g l e  c o n t r o l  loops can be  
d e s t a b i l i z e d  by increas ing  t h e  gain andfor  delay 
t o  produce r e g u l a r  o s c i l l a t i o n s  with per iods 
between two and four  t i m e s  t h e  delay (6) .  Although 
low frequency o s c i l l a t i o n s  with per iods of t h i s  
magnitude are observed f o r  most s u b j e c t s ,  t h e s e  
o s c i l l a t i o n s  do not  have a regular  waveform over 
t h e  e n t i r e  60 s record.  Indeed t h e  s t r i k i n g  
f e a t u r e  of t h e  temporal record is not  t h e  
s t a b i l i t y  of t h e  low frequency o s c i l l a t i o n s ,  but  
r a t h e r  i t s  f l u c t u a t i n g  and aper iodic  na ture .  
There are many mechanisms t h a t  may c o n t r i b u t e  t o  
t h e  generat ion of time s i g n a l s  of t h i s  complexity. 
These include:  ( i )  t h e  i n t e r a c t i o n s  between t h e  
m u l t i p l e  feedback loops;  ( i i )  t h e  i n t e r a c t i o n s  
between feedforward and feedback loops;  and 
( i i i )  t h e  p o s s i b i l i t y  t h a t  parameters i n  t h e  
feedback system are not  cons tan t ,  but  may be 
regula ted  by t h e  state of t h e  system, o r  
f l u c t u a t e  due t o  random i n p u t s  t o  t h e  c o n t r o l  
sys tern. 
t h e  c o n t r o l  of movement (Figure l ) ,  it is 
poss ib le  t h a t  t h e  complex t i m e  series we  observe 
r e f l e c t  t h e  dynamics of multi-loop feedback 
systems. Previous workers (7 )  emphasized that 
m u l t i p l e  feedbacks would tend t o  s t a b i l i z e  
feedback systems. This  i s  not  always t h e  case. 
I n  a recent  paper (1)  w e  found t h a t  m u l t i p l e  
nega t ive  feedback could,  i n  some circumstances,  
l ead  t o  d e t e r m i n i s t i c  c h a o t i c  dynamics i n  which 
t h e r e  w a s  a p e r i o d i c  dynamics wi th  s e n s i t i v e  
dependence on t h e  i n i t i a l  condi t ions .  Thus, 
m u l t i p l e  nega t ive  feedbacks can lead  t o  a 
d e s t a b i l i z a t i o n  of t h e  dynamics and t o  complex 
temporal f l u c t u a t i o n s .  However, recent  s t u d i e s  
(8)  have shown t h a t  a l though chaot ic  dynamics can 
be  found i n  m u l t i p l e  nega t ive  feedback systems, 
t h i s  i s  a comparatively rare phenomenon, a t  least 
i n  t h e  s p e c i a l i z e d  systems t h a t  were examined. 
Thus, it is  u n l i k e l y  t h a t  t h e  dynamics of  
d e t e r m i n i s t i c  models of multi-loop negat ive  
feedback systems can completely account f o r  t h e s e  
observat ions.  
One f a c t o r  t h a t  should be  considered i n  
t h e o r e t i c a l  models of motor c o n t r o l  i s  t h e  r o l e  of 
feedforward c o n t r o l .  The organiza t ion  of goal- 
d i r e c t e d  movements genera l ly  can be  descr ibed 
f u n c t i o n a l l y  as a continuum. A t  one extreme, a 
movement t o  a t a r g e t  may be  cont inuously ad jus ted  
using feedback mechanisms. A t  t h e  o t h e r  extreme, 
a movement may involve a series of preprogrammed 
commands unfolding i n  a feedforward mode with few 
o p p o r t u n i t i e s  of cur ren t  modi f ica t ion  by 
propr iocept ive  o r  o t h e r  feedback mechanisms. 
Mathematically, such preprogrammed commands can be 
incorporated i n t o  t h e o r e t i c a l  models by computing 
t h e  p o s i t i o n  a t  some f u t u r e  t i m e  and modifying 
muscular a c t i v i t y  based on t h e  devia t ion  of t h e  
limb t i p  from i ts  des i red  l o c a t i o n .  Thus, both 
feedback and feedforward loops must be  considered 
i n  t h e o r e t i c a l  models of motor c o n t r o l  (9) .  
de lay  and o t h e r  parameters descr ib ing  t h e  
feedback loops,  i n  shaping t h e  observed dynamics 
must be considered.  One p o s s i b i l i t y  i s  that t h e s e  
parameters are some func t ion  of t h e  c u r r e n t  s ta te  
of t h e  system. For example, c o n t r o l  mechanisms 
Since m u l t i p l e  c o n t r o l  loops are involved i n  
F i n a l l y  t h e  r o l e  of f l u c t u a t i o n s  i n  t h e  gain,  
with state-dependent de lays  have been r e c e n t l y  
considered i n  o ther  contex ts  ( L O ) .  Al te rna t ive ly  
t h e r e  may be  s t o c h a s t i c  f l u c t u a t i o n s  i n  some of 
t h e s e  parameters s i n c e  they r e f l e c t  underlying 
neurophysiological  and molecular processes .  
CONCLUDING REMARKS 
Further  experimental andfor  c l i n i c a l  
s t u d i e s  are  needed t o  compliment t h e o r e t i c a l  
approaches. 
with known l e s i o n s  i n  neura l  c e n t e r s  d i r e c t l y  
involved i n  motor c o n t r o l  (Figure 1). Indeed by 
c a r e f u l  p a t i e n t  s e l e c t i o n  it is  p o s s i b l e  t o  
i d e n t i f y  p a t i e n t  subgroups with w e l l  l o c a l i z e d  
l e s i o n s .  
i n  t h e  basa l  gangl ia  t h a t  occur  i n  p a t i e n t s  wi th  
Parkinson 's  d i s e a s e  do not  g r e a t l y  a f f e c t  t h e i r  
performance i n  t h i s  t racking  t a s k  i f  t h e i r  
parkinsonian tremor i s  of r e l a t i v e l y  low 
amplitude (11). There is a need t o  extend t h e s e  
s t u d i e s  i n  order  t o  examine p a t i e n t s  with 
c e r e b e l l a r  d i s e a s e  and o t h e r  neuro logica l  
d i sorders .  Such a s t r a t e g y  i s  d i r e c t e d  a t  
i d e n t i f y i n g  those  feedback loops which are 
c r i t i c a l  f o r  t h i s  motor task .  
An i n t e g r a t i o n  of approaches from many 
d i s c i p l i n e s  inc luding  c o n t r o l  theory,  nonl inear  
dynamics and neurology w i l l  be needed t o  under- 
s tand t h e  complex t i m e  series generated i n  t h e  
neuromotor system regula t ing  f i n g e r  p o s i t i o n  under 
feedback c o n t r o l .  
address  quest ions such as t h e  following: 
motor commands involve d i f f e r e n t  b r a i n  c i r c u i t s  
f o r  feedback and feedforward modes? What are t h e  
mechanisms respons ib le  f o r  dynamic switching 
between one mode and t h e  o t h e r ?  What are t h e  
i n t e r a c t i o n s  between p e r i p h e r a l ,  s u b c o r t i c a l  and 
i n t r a c o r t i c a l  loops during goal-directed 
movement ? 
One approach i s  t o  s tudy p a t i e n t s  
For example, we  have shown t h a t  l e s i o n s  
W e  may then become a b l e  t o  
Do 
Acknowledgements: This  work w a s  p a r t l y  
supported by Natural  Sciences and Engineering 
Research Council (Canada) and Fonds pour l a  
Formation de  Chercheurs et 1'Aide a l a  Recherche 
(Quebec) through t h e  Univers i ty  of Quebec and 
M c G i l l  Univers i ty .  
1. 
2. 
3.  
4 .  
5. 
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Complex Motor Dynamics and Control in Multi-looped Negative Feedback Systems

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