Improvement in modelling of physiological tremor by inclusion of grip force in quaternion weighted Fourier linear combiner

Physiological tremor is an involuntary oscillatory movement of body parts particularly exhibited in hands. The unintended vibrations due to tremor causes tip of the microsurgical tools to fluctuate unnecessarily causing unacceptable imprecisions in micro-surgeries. All the existing algorithms such as weighted Fourier Linear Combiner (wFLC), and its extensions, treat three x, y and z axes of tremor as three independent channels. However our correlation and coherence analysis showed that there is significant coupling between tremor channels. More importantly grip force by which a surgeon holds a surgical device also shows significant coupling with three tremor channels, which has never been investigated before. We first modelled the tremor in 3 dimensions (3-D) using quaternion algebra, and found 27% improvement which we have presented in our previous work. In this paper, we show modelling tremor in 4 dimensions by incorporating grip force and three tremor channels further exploits the cross-channel coupling information which is naturally inherent between force and xyz tremor channels. Using quaternion algebra we extract this coupling information to improve the tremor modelling performance. We show that estimation performance of tremor improves by 45% using 4-D model instead 3-D, yielding overall improvement of 65% from 1-D to 4-D.