Mixed matrix factorization: a novel algorithm for the extraction of kinematic-muscular synergies
TL;DR: In this paper, a mixed matrix factorization (MMF) algorithm based on a gradient descent update rule was proposed for extracting synergies from combined kinematic and muscular data.
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Abstract:Â Synergistic models have been employed to investigate motor coordination separately in the muscular and kinematic domains. However, the relationship between muscle synergies, constrained to be non-negative, and kinematic synergies, whose elements can be positive and negative, has received limited attention. Existing algorithms for extracting synergies from combined kinematic and muscular data either do not enforce non-negativity constraints or separate non-negative variables into positive and negative components. We propose a mixed matrix factorization (MMF) algorithm based on a gradient descent update rule which overcomes these limitations. It directly assesses the relationship between kinematic and muscle activity variables, by enforcing the non-negativity constrain on a subset of variables. We validated the algorithm on simulated kinematic-muscular data generated from known spatial synergies and temporal coefficients, by assessing the similarity between extracted and ground truth synergies and temporal coefficients when the data are corrupted by different noise levels. We also compared the performance of MMF to that of non-negative matrix factorization applied to separate positive and negative components (NMFpn). Finally, we factorized kinematic and EMG data collected during upper-limb movements to demonstrate the potential of the algorithm. MMF achieved almost perfect reconstruction on noiseless simulated data. It performed better than NMFpn in recovering the correct spatial synergies and temporal coefficients with noisy simulated data. It allowed to correctly select the original number of ground truth synergies. We showed meaningful applicability to real data. MMF can also be applied to any multivariate data that contains both non-negative and unconstrained variables.
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Figures
Table 1: Parameters for the simulation 
Figure 4: Dependence of the reconstruction R2, cancellation, spatial synergies similarity, temporal synergies similarity on algorithm parameters (đ and đ). The plots illustrate the R2 values achieved when varying đ and đ (top left panel) and the Cancellation Index (top right panel). Some regions, corresponding especially to high values of đ, can reduce cancellations but this effect is achieved with a reduction of spatial (bottom left) and temporal (bottom right) similarity of the extracted synergies. In the lower panel, a 3D surface reproduced the data of panel b together with the average level of cancellation of the ground truth data. We selected as values for the MMF-NMFpn simulations the following parameters: Îť=50 and Îź=0.1. 
Figure 5: Effect of noise on R2 curves and selection of number of synergies. The ground truth data is 
Figure 1: Simulation overview. Each simulation was divided into 3 parts. The first was the generation of a set of ground truth spatial synergies WGT and combination coefficients (or temporal components) CGT . In the second part of the simulation, we extracted the synergies with the MMF algorithm and with the NMFpn algorithm from the simulated data WGTâCGT corrupted by additive noise. Both algorithms included an initialization of the solutions (W0 and C0), iterative update based on gradient descent (MMF) or matrix multiplication (NMFpn), and a termination condition. Additionally, both algorithms were used to extract synergies with different noise levels to verify their robustness. Finally, the last step of the simulation was the comparison of the extracted synergies and coefficients with the ground truth ones. This assessment was based on comparing the reconstruction R2, the similarity between extracted and ground truth spatial synergies and combination coefficients, a cancellation index. 
Figure 6: Distribution of reconstruction R2, cancellation index, spatial synergy similarity and temporal synergy similarity for different noise levels. Boxplots for the distributions of R2 (top left), cancellation index (top right), spatial synergy similarity (bottom left), and temporal coefficients similarity (bottom right) achieved by the MMF (blue) and NMFpn (red) algorithms with different noise levels. Data for 4 kinematic DoF and 8 muscles are simulated as combinations of 5 ground truth kinematic-muscular synergies. 
Figure 2: Example of ground truth synergies and combination coefficients. Top panel: an example of 5 simulated ground truth kinematic-muscular synergies (đđđ); bottom panel: simulated time-varying synergy combination coefficients for 8 different targets in the 4D kinematic space (đđđ); middle panel: simulated data generated by the activation of the synergies modulated by the coefficients (X = WGT CGT). The dimensionality of the data is 12 (8 muscle activations, 4 joint accelerations).
Citations
The Number and Structure of Muscle Synergies Depend on the Number of Recorded Muscles: A Pilot Simulation Study with OpenSim
TL;DR: In this article , the authors compared the number and structure of muscle synergies when considering 12 muscles and 32 muscles of the upper limb, also including multiple muscle heads and deep muscles, and concluded that current studies may slightly underestimate the number of controlled synergies, even though the main structure of synergies is not modified when adding more muscles.
Number of trials and data structure affect the number and components of muscle synergies in upper-limb reaching movements
TL;DR: In this article , the authors investigated how data structure prior to synergy extraction, namely concatenation, averaging, and single trial, affected the number and components of muscle synergies and found that concatenated trials or reaching directions identified the highest number of synergies.
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Upper limb phasic muscle synergies with negative weightings: applications for rehabilitation
12 May 2023
TL;DR: In this article , muscle synergies were extracted using MMF on 16-channel phasic EMG signals in forward and backward reaching movements performed by 5 healthy participants, as a result of the subtraction of tonic (gravity related) EMG components.
2
Upper limb phasic muscle synergies with negative weightings: applications for rehabilitation
12 May 2023
TL;DR: 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, as a result of the subtraction of tonic (gravity related) EMG components.
2
Whole-Body Adaptive Functional Electrical Stimulation Kinesitherapy Can Promote the Restoring of Physiological Muscle Synergies for Neurological Patients
TL;DR: AFESK treatment induced favorable changes in muscle activation patterns in chronic neurologic patients, partially restoring muscular patterns similar to healthy people, as assessed in patients with impaired locomotor functions.
References
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â˘Book
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- 01 Jan 1967
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