A novel approach to estimate the upper limb reaching movement in three-dimensional space

Abstract Background In spite of the complexity that the number of redundancy levels suggests, humans show amazingly regularities when generating movement. When moving the hand between pairs of targets, subjects tended to generate roughly straight hand trajectories with single-peaked, bell-shaped speed profiles. The original minimum-jerk model, in which limb displacement is represented by a fifth order polynomial, has been shown to predict qualitative features of experimental trajectories recorded in monkeys performing intermediate speed one-joint elbow movements to a target. However, it is difficult to compare a real (experimentally measured) movement to its equivalent minimum-jerk trajectory (MJT) because the exact start and end times and positions of real movements are usually not well defined: even discrete movements usually exhibit an extended period of low (but non-zero) velocity and acceleration before and after a movement, making estimation of the exact start and end times inaccurate. Aim The purpose of this study was to describe a method used for correctly fitting the minimum jerk trajectory to real movement data assuming that the minimum-jerk trajectory satisfies the same threshold condition as the real movement (the same position and the same percentage of maximum velocity), rather than the movements start and end at full rest. Thus, the original minimum-jerk model was revised. Materials and methods Starting from the original minimum-jerk model, in this work is proposed a method used for correctly fitting the minimum jerk trajectory to real movement data defined by a threshold condition. This method enables users to accurately compare a minimum-jerk trajectory to real movements. The latter were recorded using APDM inertial sensors. To estimate if the ideal model fits adequately the real reaching movements we consider three kinematic indexes. Results and Discussion: A total of 100 upper arm straight line reaching movements executed by healthy subjects were acquired. MJTs follow closely to the reaching movements when they have been computed considering the revised model. On the contrary, the MJTs do not follow the real profiles when considering the original formulation. This behaviour is confirmed when we consider the three kinematic indexes. These findings help us better understand important characteristics of movements in health. Future works will focus on the investigation of the performance of the upper arm straight line reaching movements in a larger healthy subjects sample and then in pathological conditions.