Actions involving the hand require positioning multiple fingers each with multiple degrees of freedom. However, we regularly perform complex actions without the need to consciously consider the position of each and every joint. Understanding the neural basis of finger coordination has many uses in rehabilitation and prosthetics.

### Small Synergistic Movement in Pianists

The aim of this study was to study the differences in finger movement between experienced and novice pianists with the aim of understanding more about how the fingers move:

• Individually - the joints
• Together - simultaneous movement
• Independently - sequential movement

Movement of the hands during piano playing was recorded using a data glove with 14 sensors measuring finger flexion and abduction. To study how the movement of the fingers differed between the experienced and novice players the concept of movement synergies was used.

Muscle Synergies:

• Fundamental patterns of movement
• Serve as building blocks for more complicated movements
• Reduce the complexity (degrees of freedom) to be controlled

Results showed that a small number of components accounted for the majority of the variance in the data but that these components are common across the groups. Classification results showed accurate classification was obtained from components accounting for only small amount of variance primarily related to the abduction of the fingers [1].

Finger Accuracy (%) No. Components VAF
Thumb 93.68 15/253 1.38
Index 94.81 14/212 0.11
Middle 93.40 17/409 2.70
Ring 96.52 18/115 5.97
Little 98.29 17/175 0.96
Classification results showing the accuracy, number of components and variance accounted for, for each of the fingers.

### Muscle Synergy Extraction

The muscles which control the fingers are primarily located in the forearm and for each gesture we perform multiple muscles are required. As with the movement we can also use synergies to represent the common patterns of muscle activity which serve as the building blocks to produce detailed movements associated with the control of the fingers.

Muscle synergy extraction can be performed using nonnegative matrix factorization. That is for a data matrix $$Y\in\mathbb{R}^{X\times N}$$ find nonnegative matrices $$W\in\mathbb{R}^{X\times K}$$ and $$H\in\mathbb{R}^{K\times N}$$ via $$\min_{W,H} D(Y||WH)\quad\text{ subject to}\quad W\geq 0,\quad H\geq 0$$ where $$D(\cdot)$$ is a measure of goodness of fit

To deal with the complexity of the neuromuscular system and extend beyond the variance accounted for as a measure we proposed a method based on using fuzzy entropy as a similarity measure [2]. Examples of the differences between the synergies extracted using 16 channels of EMG recorded from the arm show compared to an alternating least squares NMF our method places greater significance on a smaller number of muscles.

Example synergies for a value of k=3 for 2 different subjects.

### Code

Fuzzy entropy NMF code can be found here: Entropy_NMF

### References

1. Recruitment of Small Synergistic Movement Makes a Good Pianist
In Proc. Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2015, pp. 242–245.
2. Fuzzy Entropy Based Nonnegative Matrix Factorization for Muscle Synergy Extraction
In Proc. IEEE International Conference on Acoustics, Speech and Signal Processing, 2016, pp. 739–743.