Neck injuries and the related pain have a high prevalence and represent an important health problem. To properly diagnose and treat them, practitioners need an accurate system for measuring Cervical Range Of Motion (CROM). This article describes the development and validation of an inexpensive, small (4 cm × 4 cm × 8 cm), light (< 200 g) and easy to use solution for measuring CROM using wearable inertial sensors. The proposed solution has been designed with the clinical practice in mind, after consulting with practitioners. It is composed of: (a) two wearable wireless MEMS-based inertial devices, (b) a recording and report generation software application and (c) a measurement protocol for assessing CROM. The solution provides accurate (none of our results is outside the ROM ranges when compared with previously published results based on an optical tracking device) and reliable measurements (ICC = 0.93 for interrater reliability when compared with an optical tracking device and ICC > 0.90 for test-retest reliability), surpassing the popular CROM instrument’s capabilities and precision. It also fulfills the needs for clinical practice attending to effectiveness, efficiency (4 min from setup to final report) and user’s satisfaction (as reported by practitioners). The solution has been certified for mass-production and use in medical environments.

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

Background: Elbow and wrist chronic conditions are very common among musculoskeletal problems. These painful conditions affect muscle function, which ultimately leads to a decrease in the joint’s Range Of Motion (ROM). Due to their portability and ease of use, goniometers are still the most widespread tool for measuring ROM. Inertial sensors are emerging as a digital, low-cost and accurate alternative. However, whereas inertial sensors are commonly used in research studies, due to the lack of information about their validity and reliability, they are not widely used in the clinical practice. The goal of this study is to assess the validity and intra-inter-rater reliability of inertial sensors for measuring active ROM of the elbow and wrist. Materials and Methods: Measures were taken simultaneously with inertial sensors (Werium^™ system) and a universal goniometer. The process involved two physiotherapists (“rater A” and “rater B”) and an engineer responsible for the technical issues. Twenty-nine asymptomatic subjects were assessed individually in two sessions separated by 48 h. The procedure was repeated by rater A followed by rater B with random order. Three repetitions of each active movement (elbow flexion, pronation, and supination; and wrist flexion, extension, radial deviation and ulnar deviation) were executed starting from the neutral position until the ROM end-feel; that is, until ROM reached its maximum due to be stopped by the anatomy. The coefficient of determination (r²) and the Intraclass Correlation Coefficient (ICC) were calculated to assess the intra-rater and inter-rater reliability. The Standard Error of the Measurement and the Minimum Detectable Change and a Bland–Altman plots were also calculated. Results: Similar ROM values when measured with both instruments were obtained for the elbow (maximum difference of 3° for all the movements) and wrist (maximum difference of 1° for all the movements). These values were within the normal range when compared to literature studies. The concurrent validity analysis for all the movements yielded ICC values ≥0.78 for the elbow and ≥0.95 for the wrist. Concerning reliability, the ICC values denoted a high reliability of inertial sensors for all the different movements. In the case of the elbow, intra-rater and inter-rater reliability ICC values range from 0.83 to 0.96 and from 0.94 to 0.97, respectively. Intra-rater analysis of the wrist yielded ICC values between 0.81 and 0.93, while the ICC values for the inter-rater analysis range from 0.93 to 0.99. Conclusions: Inertial sensors are a valid and reliable tool for measuring elbow and wrist active ROM. Particularly noteworthy is their high inter-rater reliability, often questioned in measurement tools. The lowest reliability is observed in elbow prono-supination, probably due to skin artifacts. Based on these results and their advantages, inertial sensors can be considered a valid assessment tool for wrist and elbow ROM.