Analyzing finger-movement trajectories with stochastic differential equations incorporating persistence

Fingertip positions can be tracked using a variety of motion capture methods, raising the question of how to describe, compare, measure effects on, and simulate finger-movement trajectories. This paper provides a solution using stochastic differential equations (SDEs). In this approach, finger positions are conceptualized as Brownian particles. Effects on finger positions, from the stimulus and experimental manipulations, are formalized using a potential function and associated force field. Unlike previous SDE approaches to model animal movements, the current treatment relates fingertip positions and potential functions using SDEs that account for movement persistence. Using the SDE approach, observed fingertip positions can be used to “solve” the potential function through conventional regression methods. The resulting potential functions can be used to summarize finger-movement trajectories, and to compare and simulate trajectories.