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Abstract Background The above-knee amputation of a lower limb is a severe impairment that affects significantly the ability to walk; considering this, a complex adaptation strategy at the neuromuscular level is needed in order to be able to move safely with a prosthetic knee. In literature, it has been demonstrated that muscle activity during walking can be described via the activation of a small set of muscle synergies. The analysis of the composition and the time activation profiles of such synergies have been found to be a valid tool for the description of the motor control schemes in pathological subjects. Methods In this study, we used muscle synergy analysis techniques to characterize the differences in the modular motor control schemes between a population of 14 people with trans-femoral amputation and 12 healthy subjects walking at two different (slow and normal self-selected) speeds. Muscle synergies were extracted from a 12 lower-limb muscles sEMG recording via non-negative matrix factorization. Equivalence of the synergy vectors was quantified by a cross-validation procedure, while differences in terms of time activation coefficients were evaluated through the analysis of the activity in the different gait sub-phases. Results Four synergies were able to reconstruct the muscle activity in all subjects. The spatial component of the synergy vectors did not change in all the analysed populations, while differences were present in the activity during the sound limb’s stance phase. Main features of people with trans-femoral amputation’s muscle synergy recruitment are a prolonged activation of the module composed of calf muscles and an additional activity of the hamstrings’ module before and after the prosthetic heel strike. Conclusions Synergy-based results highlight how, although the complexity and the spatial organization of motor control schemes are the same found in healthy subjects, substantial differences are present in the synergies’ recruitment of people with trans femoral amputation. In particular, the most critical task during the gait cycle is the weight transfer from the sound limb to the prosthetic one. Future studies will integrate these results with the dynamics of movement, aiming to a complete neuro-mechanical characterization of people with trans-femoral amputation’s walking strategies that can be used to improve the rehabilitation therapies.

The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organisation. Towards validating this hypothesis, it is however important to understand if muscle synergies can reduce the state-space dimensionality while suitably achieving task control. In this paper we present a scheme for investigating this reduction, utilising the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies instead constrains the dynamic behaviour of a system in trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then use this method to investigate the consequence of minimisation of this dimensionality for a given task. These methods are tested in simulation on a linear (tethered mass) and a nonlinear (compliant kinematic chain) system; dimensionality of various reaching trajectories is compared when using idealised temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles are obtained as the solution to reaching tasks in both of the test systems. We also investigate the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a synergy basis and trajectory-specific DR of motor behaviours results from usage of muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, developmental skill acquisition and robotics are then discussed.