A Quaternion Weighted Fourier Linear Combiner for Modeling Physiological Tremor

Goal: This paper offers a new approach to model physiological tremor aiming at attenuating undesired vibrations of the tip of microsurgical instruments. Method: Several tremor modeling algorithms, such as the weighted Fourier linear combiner (wFLC), have proved effective. They, however, treat the three-dimensional (3-D) tremor signal as three independent 1-D signals in the x-, y-, and z-axes. In addition, the force f by which a surgeon holds the instrument has never been taken into account in modeling. Hence, conventional algorithms are inherently blind to any potential multidimensional couplings. Results: We first show that there exists statistically significant subject-and task-dependent coherence between data in the x-, y-, z-, and f-axes. We hypothesize that a filter that models the tremor in 4-D (x, y, z, and f) yields a more accurate model of tremor. We, therefore, developed a quaternion version of the wFLC algorithm and termed it QwFLC. We tested the proposed QwFLC algorithm with real physiological tremor data that were recorded from five novice subjects and four experienced microsurgeons. Although compared to wFLC, QwFLC requires six times larger computational resources, we showed that QwFLC can improve the modeling by up to 67% and that the improvement is proportional to the total coherence between the tremor in xyz and the force signal. Conclusion: By taking into account interactions of the 3-D tremor and the force data, the tremor modeling performance enhances significantly.