Kinematics, kinetics and biomechanics of human gait are widely investigated fields of research. The biomechanics of locomotion has been described characterizing muscle activations and synergistic control, i.e, spatial and temporal patterns of coordinated muscle groups and joints. Both kinematic synergies and muscle synergies have been extracted from locomotion data, showing that in healthy people 4-5 synergies underlie human locomotion; such synergies are in general robust across subjects and might be altered in pathological gait, depending on the severity of the impairment. In this work, for the first time, we apply the mixed matrix factorization algorithm to locomotion data of 15 healthy participants to extract hybrid kinematic-muscle synergies, and show that they allow to directly link task space variables (i.e., kinematics) to the neural structure of muscle synergies. We show that kinematic-muscle synergies can describe the biomechanics of motion at a better extent than muscle synergies or kinematic synergies alone. Morevoer, this study shows that at a functional level, modular control of the lower limb during locomotion is underlied by an increased number of functional synergies with respect to standard muscle synergies and account for different biomechanical roles that each synergy may have within the movement. Kinematic-muscular synergies may have impact in future work for a deeper understanding of modular control and neuro-motor recovery in the medical and rehabilitation fields, as they associate neural and task space variables in the same factorization, including the evaluation of post-stroke, Parkinson and cerebral palsy patients, and in other fields such as sports.

In the last two decades, muscle synergies analysis has been commonly used to assess the neurophysiological  mechanisms underlying human motor control. Despite several synergy models and algorithms have been  employed for processing the electromyographic (EMG) signal, and neural substrates indicate their non?homogeneous origin, EMG patterns are usually preprocessed without separating phasic (movement-related) and tonic (anti-gravity and related to co-contraction) components. Using a comprehensive mapping of upper?limb point-to-point movements, synergies were extracted from phasic and tonic EMG signal separately, estimating the tonic components with a linear ramp model. The goodness of reconstruction (R2 ) as a function  of the number of synergies was compared, and synergies extracted from each dataset at three threshold levels (0.80, 0.85, 0.90) were retained for further analysis. Then, shared, phasic-specific, and tonic-specific synergies  were extracted from the two datasets concatenated. We found only few shared synergies, indicating that phasic  and tonic synergies have in general different structures. Shared, phasic-specific and tonic-specific synergies  were clustered separately and compared for evaluating differences in synergy composition. Phasic-specific  clusters were more numerous than tonic-specific ones and with a higher sparseness, suggesting that they were  more differentiated among subjects. The structure of the clusters indicated that phasic synergies identify  specific patterns related to the movement (sparse composition) while tonic synergies show co-contraction of  multiple muscles for joint stabilization and holding postures. These results suggest that phasic and tonic  synergies should be extracted separately, especially when performing muscle synergy analysis in patients with  abnormal tonic activity and for tuning devices with gravity support

The study of synergistic control has recently been improved with the introduction of a mixed-matrix factorization (MMF) algorithm that allows to remove the constrain of non-negativity on a customizable number of input channels, extending the range of application of the standard non-negative matrix factorization (NMF) algorithm. MMF can be used to extract kinematic-muscular synergies, where muscle data are non-negative and kinematic data are unconstrained, leading to synergies with positive and negative loads. The feature of analyzing negative data makes MMF also suitable for investigating the mixture of positive and negative waveforms that can be observed in the phasic electromyographic (EMG) signals recorded in a variety of movements of the upper-limb, as a result of the subtraction of tonic (gravity-related) EMG components.  Muscle synergies that include negative coefficients are necessary to provide a compact representation of these data and account for negative EMG waveforms. In this paper, muscle synergies were extracted using MMF on 16-channel phasic EMG signals in forward and backward reaching movements performed by 5 healthy participants. This paper shows the potential of the method, preliminary interpretation of the results, and possible applications for motor evaluation in the rehabilitation field.