Real-Time Sensing of Upper Extremity Movement Diversity Using Kurtosis Implemented on a Smartwatch

Abstract

Wearable activity sensors typically count movement quantity, such as the number of steps taken or the number of upper extremity (UE) counts achieved. However, for some applications, such as neurologic rehabilitation, it may be of interest to quantify the quality of the movement experience (QOME), defined, for example, as how diverse or how complex movement epochs are. We previously found that individuals with UE impairment after stroke exhibited differences in their distributions of forearm postures across the day and that these differences could be quantified with kurtosis—an established statistical measure of the peakedness of distributions. In this paper, we describe further progress toward the goal of providing real-time feedback to try to help people learn to modulate their movement diversity. We first asked the following: to what extent do different movement activities induce different values of kurtosis? We recruited seven unimpaired individuals and evaluated a set of 12 therapeutic activities for their forearm postural diversity using kurtosis. We found that the different activities produced a wide range of kurtosis values, with conventional rehabilitation therapy exercises creating the most spread-out distribution and cup stacking the most peaked. Thus, asking people to attempt different activities can vary movement diversity, as measured with kurtosis. Next, since kurtosis is a computationally expensive calculation, we derived a novel recursive algorithm that enables the real-time calculation of kurtosis. We show that the algorithm reduces computation time by a factor of 200 compared to an optimized kurtosis calculation available in SciPy, across window sizes. Finally, we embedded the kurtosis algorithm on a commercial smartwatch and validated its accuracy using a robotic simulator that “wore” the smartwatch, emulating movement activities with known kurtosis. This work verifies that different movement tasks produce different values of kurtosis and provides a validated algorithm for the real-time calculation of kurtosis on a smartwatch. These are needed steps toward testing QOME-focused, wearable rehabilitation.