Jun-ichi Yamanishi, Mitsuo Kawato, Ryoji Suzuki Emilie Dolan Two Coupled Oscillators as a Model for the Coordinated Finger Tapping by Both Hands Jun-ichi Yamanishi, Mitsuo Kawato, Ryoji Suzuki Emilie Dolan

Background Oscillations Phase Difference Milliseconds – seconds – days Difference between two waves with the same frequency

Rhythmic movement is probably controlled by oscillatory neural networks Invertebrates Verberates Previous Paper (1979) Finger tapping in L/R hand controlled by separate oscillatory neural networks Assumption that coordinated finger tapping by both hands is controlled by two interacting neural networks

Method 2 Groups (all R handed) Learning 4 unskilled subjects, normal motor function 5 skilled subjects, studying piano Learning Tap the key in synchrony with L/R pacing signals Learn a tapping interval Delays between L and R signal chosen out of 10 steps Phase differences of 0.0, 0.1, 0.2… Called “standard phase differences”

Methods Cont’d Test Phase differences measured Pacing signals presented 10 times Subjects continue without signals until end (20 taps) Phase differences measured Accuracy found using SD of measured and standard delay

Results Systematic errors in SD during self-paced finger tapping

Phase difference 0  Synchronous rhythm Phase difference 0.5  Alternate rhythm Tendency to approach these rhythms Ex: phase difference of .1 has a systematic error of -30ms, phase difference comes to 70ms, shows a tendency to resemble synchronous rhythm.

Results Steady states: 0.0 and 0.5 Systematic error pattern Negative slope Includes 0.2 and 0.75 for skilled participants Systematic error pattern 4-5 subjects gather around avg at 0.0 and 0.5 Data splits in two for other points, bimodal distribution Why bimodal? Drawn towards 0.5, negative error Drawn towards 1.0, positive error

Results Systematic errors in SD during self-paced finger tapping

One Hand vs. Two

Model for Two Coupled Oscillators Suppose there is a neural circuit producing periodic outputs Not clarified physiologically 1979 Paper Find that network controlling R hand finger tapping has the same characteristics as the L

Relation between networks Is there a relation between the neural networks controlling both hands versus one hand? Assume timed oscillations in coordinated tapping Find points of equilibrium via equations In stable equilibrium, curve is closer to the horizontal

Distribution of stable and unstable equilibrium points

Symmetry between R and L phase transition curves Skilled are more symmetrical Most equilibrium points at 0.0 and 0.5 Finger tapping tends to be synchronous or alternate Not indicative of stability of equilibrium points

Degree of Stability Degree of stability (C) Negative is more stable Phase difference of high stability can be performed more accurately

Discussion Prediction of two coupled oscillators is in good agreement with data Interaction between two oscillators of unskilled subjects is stronger Weakened by learning There must be a higher motor center controlling the coupled system of two neural oscillators

Conclusion Greatest performance in synchronous and alternate rhythm Stable rhythm patterns Data support Neural mechanism controlling coordinated finger tapping may very well be composed of the coupled system of two neural oscillators, controlling the left and right hands respectively.

Equilibrium Equ’s ∆ø(ø) curve phase advance (∆ø>0) and delay (∆ø<0) plotted ø’(ø) is defined as follows from p-response curve: ø’(ø)= ø+∆ø(ø). Ø­2= 1-f(ø1)- ø1 = 1-( ø1+f(ø1))=F(ø1) (1) Ø’1= 1-g(ø2)- ø2 = 1-( ø2+g(ø2)) = G(ø2) (2) Ø­2= 1 - ( ø1+f(ø1))=F(ø1) (3) Ø’1= 1-( ø2+g(ø2)) = G(ø2) (4) |G’(ø2e)•F’(ø1e)| < 1 (5)

Degree of stability Equs ø1= ø1e + (G’•F’) δ Ci = 10 (G’(ø2e) •F’(ø1e)| - 1)