Introduction 2004 1997 1999 2001 2003 2005 1999 2001 2005b 2005 1992 1984 2002 2005b 2005b 2005b 2006 1997 2001 2005b 2001 2005b 2005b 2006 2005b 2005b 2006 1992 1998 1998 2006 2005b 2006 2000 2004 The aim of the present study was to examine the afference-based error corrections in detail using a kinesthetic tracking task, with a specific focus on the role of the muscle activity in the motor-driven arm, to elucidate the interplay of closed-loop and open-loop control processes in rhythmic bimanual coordination. We compared the performance during in-phase and antiphase coordination to further our understanding of the potential contribution of closed-loop control processes to the differential stability of these patterns. In addition, we examined the stability-related effects of bilateral muscle activation during kinesthetic tracking on the resulting coordinative stability. To address the latter issue we compared two conditions in which subjects were either instructed to keep the motor-driven limb relaxed, or to activate their muscles as if moving along with the imposed motor-driven movement. For the latter condition, the phase relations at the level of neural control signals (based on electromyographic data) and at the behavioral level (kinematics) were compared. The neural control signals represent the reference signal that may be used for the prediction of sensory consequences of the ongoing movement, whereas the kinematic phase relation reflects the actual quality of the performance. In both conditions, we performed an extensive analysis of the correlations between various kinematic variables to uncover the underlying structure of the timing corrections based on the (perceived) errors in the relative phase. Materials and methods Subjects 1971 Apparatus Subjects sat in a height-adjustable chair with their elbows slightly flexed and their feet supported. Each forearm was placed in the apparatus in a neutral position (thumbs up and palms facing inward), and its position was restrained (by the support surface on the medial and ventral side, by two vertical foam-coated supports on the dorsal side, and by one horizontal foam-coated support on the lateral side) to prevent movements about the elbow. Both hands were fixated against the flat manipulanda using two Velcro straps, with all fingers extended. The apparatus only permitted flexion–extension movements of the wrist in the horizontal plane. The right manipulandum was mounted on a potentiometer (Sakae, type FCP40A-5k, linearity 0.1%) to register wrist joint angles during active movement, while the left was connected to a servo-controlled motor that moved the hand passively. The potentiometer’s output voltage was digitized by a 12-bit ADC (Labmaster DMA) and stored on a microcomputer at a sampling frequency of 1,000 Hz. The active movements were recorded with a precision of about 0.1°. The passive movements were generated using a DC brush motor (PARVEX, type RS440GR) that was controlled by a PC-mounted servo controller (ACS-Tech80, type SB214). The maximum torque of the motor was such that subjects were unable to alter the trajectory of the applied movements, and the maximum error in the trajectory of the passive movements was 0.26°. Subjects wore earmuffs with built-in stereo earphones (Bilsom 787, Flex II), which provided a moderate level of ‘white’ background noise to eliminate any auditory feedback from the motion of the motor. A white opaque screen was used to eliminate visual feedback of the hand movements. Surface electromyograms (EMG) were obtained from M. flexor carpi radialis (FCR), and M. extensor carpi radialis (ECR) of both arms. A bipolar arrangement of disposable electrodes (Medicotest, Ag/AgCl-electrodes, square 5 × 5 mm pick-up area) was attached with a center-to-center distance of 2 cm after cleansing and abrasion of the skin. The electrodes were positioned in the center of the muscle belly on the line from origin to insertion as determined by palpation. EMG signals were sampled at 1,000 Hz (TMS International, type Porti5-16/ASD; 22 bits ADC) after band-pass filtering (0.5–400 Hz), and stored on a microcomputer. Procedure Subjects were instructed to perform smooth oscillatory movements about the right wrist in such a way that (1) peak flexion and peak extension of both wrists were attained simultaneously (in-phase pattern), or (2) peak flexion of one hand coincided with peak extension of the other hand (antiphase pattern). To achieve this, the timing of the active right wrist movements had to be coordinated with the motor-driven movements of the left wrist. Only subjects that were able to perform both movement patterns in at least one of two selection trials at the start of the experiment were included (one candidate subject failed to meet this criterion). After the selection trials the EMG electrodes were applied, and subsequently all subjects performed maximum voluntary contractions (MVCs) by generating an isometric flexion or extension torque with each arm for approximately 3 s. For the purpose of normalization of the EMG, the maximum root mean square (RMS) value of two separate MVC measurements was used in the analysis. Additional instruction was given to subjects with respect to the muscle activity in the left (driven) arm. Subjects were required either to keep the muscles of the left (driven) arm as relaxed as possible (relaxed condition) or to activate the muscles of the left arm as if they were moving along with the motor-driven manipulandum (active condition). The resulting 2 (Pattern) × 2 (Activity) = 4 conditions were performed in separate blocks of trials, the order of which was counterbalanced across subjects. Each block of trials started with at least four practice trials to familiarize the subjects with the task (if necessary, maximally four additional practice trials were allowed). Once the subject was able to perform the task properly, based on visual assessment by the experimenters, six experimental trials were performed that were used for the analysis. 2005b 2001 frequency amplitude frequency amplitude Data reduction (kinematics) 1 \documentclass[12pt]{minimal}
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$$ \Phi _{i} = 2\pi {{\left( {t^{\rm F}_{{y,i}} - t^{\rm F}_{{x,i}} } \right)}} \mathord{\left/ {\vphantom {{{\left( {t^{\rm F}_{{y,i}} - t^{\rm F}_{{x,i}} } \right)}} {{\left( {t^{\rm F}_{{x,i + 1}} - t^{\rm F}_{{x,i}} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {t^{\rm F}_{{x,i + 1}} - t^{\rm F}_{{x,i}} } \right)}} $$\end{document} \documentclass[12pt]{minimal}
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$$ \Phi _{i} = 2\pi {{\left( {t^{\rm E}_{{y,i}} - t^{\rm E}_{{x,i}} } \right)}} \mathord{\left/ {\vphantom {{{\left( {t^{\rm E}_{{y,i}} - t^{\rm E}_{{x,i}} } \right)}} {{\left( {t^{\rm E}_{{x,i + 1}} - t^{\rm E}_{{x,i}} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {t^{\rm E}_{{x,i + 1}} - t^{\rm E}_{{x,i}} } \right)}} $$\end{document} t y,i t x,i i 1995 1972 Φ Φ Fig. 1 i t j,i k k j y x i t j,i k i t j,i l l i i k  2005b R FC ε i t y,i i R FC R HC R FC R HC R xy R yy R xy R yy R HC R FC R FC R HC R xy R yy R FC R HC R yy R xy R yy R xy R FC 4 Data reduction (EMG) 1999 θ t fθ θ θ t f 2005b 1980 C W \documentclass[12pt]{minimal}
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$$ C_{W} = \frac{{{\int\limits_{f - \Delta f}^{f + \Delta f} {C_{{xy}} {\left( {{f}\ifmmode{'}\else$'$\fi } \right)}P_{y} {\left( {{f}\ifmmode{'}\else$'$\fi } \right)}d{f}\ifmmode{'}\else$'$\fi } }}} {{{\int\limits_{f - \Delta f}^{f + \Delta f} {P_{y} {\left( {{f}\ifmmode{'}\else$'$\fi } \right)}d{f}\ifmmode{'}\else$'$\fi } }}} $$\end{document} f f f P y C xy 1975 θ θ θ θ θ 2004 θ θ 1976 5 5 5 Statistical analysis t P f η 2 1988 1989 Results Φ Relative phase Φ 2 F P f Φ F P f Fig. 2 a Φ  b Φ black bars gray bars  Error bars  Φ 2 F P f F P f Φ Φ Movement amplitude F P f Temporal correlations between kinematic variables R FC R HC 3 R FC F P f F P f F P f R FC Fig. 3 R FC a R HC b R FC black bars gray bars R HC black bars gray bars  Error bars  R HC F P f F P f R HC F P f F P f R HC 3 R HC 3 R HC R FC 1 R HC R FC R HC R FC R HC R FC Materials and methods R yy R xy R FC R yy R xy R HC R FC R yy R xy R yy R xy R xy 4 F P f F P f R yy R yy 4 4 R yy R xy R FC 4 R yy R xy R FC R yy R xy R FC Materials and methods 4 R FC R FC R yy R HC Fig. 4  a R yy  b R xy c  d C yy C xy R FC C FC R FC R yy R xy R FC 3  Error bars a  b c  d HC HC  arrows R yy C yy a  c R xy C xy b  d  EMG 5 5 5 5 5 5 5 5 Fig. 5 a  right  c  left b  right  d  left filled symbols open symbols triangles  solid lines circles  dashed lines  Weighted coherence 6 F P f F P f F P f Fig. 6 C W black gray  Error bars  Temporal relations in the active condition 2004 Phase shifts between EMG and kinematics 5 1 F P f F P f F P f F P f Table 1 Phase shifts between rectified EMG and joint angles in the active condition (mean ± between-subjects SD) as determined from the cross-spectrum of these variables at the movement frequency Hand Muscle In-phase Antiphase Left FCR −148.2° ± 22.1° −137.5° ± 22.5° ECR −151.7° ± 27.8° −143.7° ± 33.5° Right FCR −123.1° ± 14.2° −131.6° ± 17.7° ECR −103.5° ± 17.7° −99.5° ± 15.2° Relative phasing of EMG 2 F P f F P f F P f 2 Table 2 Mean constant errors in the relative phase for kinematics and EMG in the active condition (mean ± between-subjects SD) Level In-phase Antiphase Kinematics −22.7° ± 10.4° −24.8° ± 11.4° EMG  FCR 0.1° ± 26.2° −18.8° ± 28.5°  ECR 24.9° ± 19.0° 19.4° ± 24.7°  Mean 12.5° ± 18.0° 0.3° ± 24.0° For the EMG the obtained values are presented for homologous FCR and ECR separately. The mean of the constant errors for FCR and ECR was adopted as the constant error of the neural control signal. Negative (positive) values indicate that the right limb is leading (lagging) the left limb Relative phasing of neural control signals and behavior 1 2 7 2 Fig. 7 left panel right panel  Circles θ ξ θ ξ  gray horizontal lines  dotted lines  Discussion 2005b Φ Φ 2001 Error corrections R HC Φ R FC Φ Materials and methods R yy R HC R yy R FC R FC R yy R HC R HC R FC R HC R FC R FC R yy R xy R FC R yy R HC R HC 3 2 R HC R FC R HC 1989 1994 2000 Materials and methods R HC R FC The effects of muscle activity in the driven limb 5 2005b 2006 1999 Φ Φ 2005b 2 R HC R FC 3 2005b 2 2 2 7 2000 2004 Timing of the EMG activity in the motor-driven arm 2005b 5 5 Flexor–extensor differences during active rhythmic wrist movement R yy 4 2004 1996 1998 2004 2005a Conclusion 2005b 2003 1984 2002 2005 2005b