Direction Modulation of Muscle Synergies After a Stroke
Direction Modulation of Muscle Synergies After a Stroke
The aim of the study is to investigate the capacity of post-stroke individual (study group)
 to modulate their EMG muscle activation pattern (MAP) compared to healthy individuals
 (control group), and to correlate these capacities with their motor impairments. Twenty
 post-stroke individuals and 12 healthy individuals will participate in this study. each
 participant will carry out hand-reaching movements in multiple directions, monitored by an
 EMG device. The modulation of the EMG signal will be compared between groups in terms of
 EMG-MAP and in terms of muscle-synergies. Additionally the MAPs and synergies of the study
 group will be correlated with their Fugl-Meyer (FM) assessment scores. Analysis of the muscle
 synergies underlying the EMG signal will be carried out by the Non-negative Matrix
 Factorization (NMF) algorithm.
Introduction: Upper extremity function after a stroke is impaired and characterized by
 abnormal, stereotypical and uncoordinated movement pattern. Decreased neural drive in the
 damaged corticospinal system causing a decreased agonists motor units firing, spasticity,
 impaired motor coordination. A more comprehensive understanding of the way our brain controls
 and regulates limb-movements, through the spinal cord, may enhance more advanced
 rehabilitation techniques.

 Current concept in motor control suggest that the brain-cortex modulates and synchronizes the
 activation of discrete number of functional units within the brainstem and spinal cord. These
 neural functional units i.e. muscle synergies, when linearly combined facilitate the
 production of diverse limb-movements. This control mechanism may in a large extent explain
 the way the CNS reduces the dimensionality of the vast number of degrees of freedom embedded
 in the CNS to a discrete number of muscle synergies. Therefore, execution of a movement may
 only requires to linearly combine these synergies and regulates its intensity of activation
 along the time domain.

 The existence of such a control mechanism attracted the attention of both clinicians and
 scientists to use its properties to enhance motor recovery after a stroke. Therefore, studies
 emerged to investigate how cortical damage impact the synchronization of synergies, and also
 whether it changes the internal structure of the synergies. Despite numerous studies in this
 domain, there is lack of consensus regarding how stroke impact this control mechanism, and
 extent of correlation between the level of impairment and the synergy structure. The study
 objectives are to compare the synergy structure and the MAP in hand-reaching movements in
 multiple directions between post-stroke individuals and healthy individual, and to correlate
 between these properties and the motor impairments in post-stroke individuals.

 Methods:

 Participants: Twelve healthy volunteers (control group) and 20 post-stroke individuals (study
 group) will participate in the study. Inclusion criteria for the study group will be
 individuals, above the age of 20, who sustained unilateral cerebral stroke, with hemiparesis.
 Exclusion criteria for the trial are sensory aphasia, unilateral neglect and presence of
 other neurological disease such as Parkinson's disease or Alzheimer's disease.

 Equipment: The Hand-reaching Spatial Device (HRSD) is an adjustable, simple tool allowing
 standardization of hand pointing movement for 9 different directions between different
 participants. It is composed of two vertical rods to which are attached three semi-circular
 shelves. Each shelf contains three movable pointing pins that can be adjusted left and
 rightward to accommodate the variable arm length of each participant. The lowest shelf was
 located 10 cm above the table, the middle was located 35 cm above the table and highest 55 cm
 above the table. For each participant the HRSD was located at the maximum hand reach distance
 in front of the tested shoulder. The side pins were located at a 45-degree angle to the
 shoulder joint to both sides. The arrangement of the targets on the HRSD was designed to
 cover the majority of hand-reaching movements.

 Surface EMGs were recorded (Trigno 8, Delsys, Boston, MA) from 8 muscles of the shoulder
 girdle and arm: trapezius (TRS); deltoid anterior (AD), medial (MD), and posterior fibers
 (PD); and pectoralis major (PECT); infraspinatus (IS); biceps (BI); triceps (TRI). Electrodes
 were placed in accordance with the guidelines of the Surface Electromyography for the
 Non-Invasive Assessment of Muscles-European Community Project (SENIAM) [34]. Maximum
 voluntary contractions (MVCs) were performed prior to data collection to verify correct
 electrode placement and for normalization. One-minute rest periods followed each MVC to limit
 the possibility of fatigue. EMG signals were band-pass filtered (20-450 Hz), and sampled at
 2000 Hz.

 Protocol: The MVC was measured by standard muscle testing [35]. Then the participant sat in
 front of a table with his forearm resting in a comfortable position. The HRSD was located as
 mentioned above. Participants were requested to point to each target 5 times according to
 voice prompting that was activated by the EMG software every 10 seconds, for 45 pointing
 movements. The order of pointing targets was constant for all the participants.

 Data analysis EMG preprocessing Data analysis was performed using Matlab (The MathWorks,
 Inc.). EMGs were demeaned, follow by RMS calculation using overlapping window of 50 samples
 (25 millisecond around each timepoint). Mean baseline EMGs for each trial were subtracted
 from the averaged data for the sequence of reaching movements. Hence, the EMG data for each
 trial, a vector whose dimension was 8 (the number of muscles recorded), corresponded to
 active force generation beyond any residual baseline muscle activity. The EMG data was
 normalized in accordance to the Maximal Isometric Contraction (MVC) for each muscle.

 The NMF algorithm originally used by Lee and Seung (1999 and 2001), was applied to identify
 muscle synergies and their activation weights. An EMG pattern recorded in hand-reaching
 movements was modeled as a linear combination of a set of N muscle synergies, each of which
 specified the relative level of activation across 8 muscles, and activated by a time-varying
 activation coefficient:

 V^(M×T)≈W^(M×N)∙H^(N×T) (4) Where V is the EMG data set matrix with M as the number of
 muscles (8 muscles), T as the number of time samples, W is the synergy matrix and H is the
 coefficient matrix. W is m×n is a matrix with n synergies, m is the number of muscles, and H
 is the n×t matrix of synergy activation coefficients. Thus, each column of W represents the
 weights of each muscle for a single synergy, and each row of H represents how much the
 corresponding synergy was activated or used to generate force. In this model, it is possible
 for each muscle to belong to more than one synergy and thus the EMG of any single muscle
 might be attributed to simultaneous or sequential activations of several muscle synergies.

 In order to determine the optimal number of synergies for the whole group, the EMG data of
 all the targets were concatenated for each participant. Then the EMG's of the whole sample
 were concatenated before applying the NMF. The optimal number of synergies (d) was defined as
 the number of synergies that captured the highest of the total variance of the data,
 suggesting that additional synergies only captured small residual amounts of variation
 attributable to noise. This procedure allowed us to estimate the optimal number of synergies
 for the whole sample to execute any reaching movement in space regardless of the direction of
 the movement.

 The NMF algorithm required the number of synergies extracted to be specified before the
 application of the algorithm. Therefore, for each data set, the VAF was calculated while
 changing the number of synergies from 1 to 7. The VAF was calculated using the equation:

 VAF(H)=100%×(1-(|(|V-WH|)|_2^2)/(|(|V|)|_2^2 )) (6) Where V is the original matrix, and W and
 H are the derived, factorized matrices.

 Generalization of movement directions

 The aim at this stage of analysis was to establish whether a set of discrete number of
 synergies exist that control any reaching movement in space. Therefore, it was investigated
 how movement in certain directions could account for movements in other directions. The EMG
 data for each movement direction was pooled separately across the 8 muscles and concatenated
 it for the whole sample. In that way the derived set of synergies would have to account for
 the variance between different subjects, but would also be specific for that direction alone.
 The NMF was applied separately for each movement direction according to the equation:

 V_i≈W_i∙H_i (7) where i is the target number, which corresponded to specific movement
 direction in space. In this stage of analysis V_i (the EMG matrix) was given as an input for
 each target, i∈[1,9], and matrices W_i,H_i were updated iteratively. The study procedure
 included reaching for 9 different target directions in space, allowing us to further
 investigate if there was a single set of synergies that could account for movements in other
 directions.

 This was done by using a cross-validation technique between the V_i matrices and the W_j
 matrices by applying a modified version of the NMF algorithm, followed by corresponding VAF
 calculation changing the number of synergies (d) from only 3 to 5, and not from 1 to 7 based
 on the results of the NMF for all the participants and for all targets, as detailed in the
 results section. In the modified version of the algorithm, both V_i and W_j (the synergies
 matrix) were given as an input. Only the H_(i,j) coefficients matrix of target i, was updated
 and outputted.

 The cross validation process of the modified NMF was carried out for each combination of a
 data matrix V_i (of target i) and a synergy matrix W_j (of target j), resulting in 9×9
 matrices H_ji. For every i,j∈[1,9], we factorize V_i such that W_j H_ji≈V_i.

 The reference set of muscle synergies was chosen by calculating the VAF for each of the 9×9
 factorizations:

 VAF(H_ij )=100%×(1-(|(|V_i-W_j H_ij |)|_2^2)/(|(|V_i |)|_2^2 )) (8) assuming that consistent
 high values of VAF(H_ij) for a specific V_i may indicate that the synergies obtained from
 movements in this direction may accurately explain movement in other directions.

 Thus, for each predefined number of synergies (d) a 9×9 matrix was received in which each
 cell represented the accountability of a given synergy (row) to a specified direction
 (column). Each row in the resulting matrix represented the overall "performance" of the
 appropriate set of synergies, and so the row with the highest average VAF was chosen for the
 next stage of analysis.

 Direction modulation of muscle synergies Once the set of synergies (W_j ) was chosen, setting
 the activation coefficients for every target (H_ij,when i∈[9,1]), it was determined which
 synergies are dominant for each of the directions. For each number of synergies, the mean
 activation coefficient of every synergy for every direction was calculated. Setting the
 number of synergies to 4, for example, resulted in 9 vectors (one for each movement
 direction) of 4 values, representing the 4 synergies. Then, the average amplitude of each of
 the synergies across the direction of movement, and between movements in different directions
 across synergies, were measured.
Inclusion Criteria:

 -  Cortical stroke (study group)

 -  hemiparesis

 Exclusion Criteria:

 -  sensory aphasia

 -  complete arm paralysis

 -  unilateral neglect

 -  other neurological disease (PD, Alzheimer)