A dynamical model for mirror movements

Abstract

In an experiment involving the unimanual performance of rhythmic movements about the elbow joint, mirror movements (MM) (i.e., unintended, associated movements) were observed in the arm not instructed to move. The amplitude of these movements was small relative to that of the intended movements (in the order of 0.5 to 5%). Complex patterns of relative phasing were observed between the intended movements and the MM that were characterized by the presence of higher harmonics in the oscillating units. The patterns in question depended on the frequency of the intended movements, which was varied from 0.5 to 3 Hz. At low frequencies, cases of both in- and anti-phase coordination were observed amidst various other instances of phase locking. MM were smaller in the anti-phase than in the in-phase coordination. At higher frequencies, the occurrence of in-phase coordination was most common while instances of anti-phase coordination were absent. To account for these properties, a dynamical model for the coordination between large-amplitude intended movements and small-amplitude MM was derived in the form of a model of nonlinearly coupled nonlinear oscillators with unequal amplitudes. The derived model was shown to correspond well with many quantitative and qualitative features of the observed dynamics of MM, including frequency locking, stable in-phase and anti-phase coordination, coordination-dependency of mirror movement amplitudes, and the presence of higher harmonics. The implications of the obtained experimental and analytical results and numerical parameter optimizations for the study of MM were discussed.