# Comparison of Gait Smoothness Metrics in Healthy Elderly and Young People
## 1 Introduction
Although the HR metric has the potential to detect cognitive impairment onset and assess its severity, criticism has emerged regarding its reliability [2]. To quantify smoothness using these metrics, it is necessary to collect gait data. In the clinical field, stereophotogrammetric systems are considered the golden standard for recording gait kinematics of the CoM [8; 15]. Over the past decade, however, interest in adopting inertial measurement systems (IMUs) to assess gait kinematics has grown [22; 23], and results point to their suitability to assess gait characteristics. For example, a single unit placed on the lumbar zone has been used to investigate gait speed sensitivity [24] and evaluate spatiotemporal parameters and COM kinematics [2]. Several clinical research studies computed, through an IMU positioned on the lumbar zone, SPARC on both linear accelerations and angular velocities across the three directions (interoposterior, AP; mediolateral, ML; and vertical, V) [9; 10; 21] or on angular velocities [18; 20]. In addition, [PERSON]'s and [PERSON]'s research groups applied HR to linear accelerations in two different populations (elderly and children) to investigate the correlation of smoothness with cognitive impairment in the former case and to characterize gait development during childhood and early adolescence in the latter [2; 17]. Beyond clinical contexts, HR was employed on linear acceleration signals gathered via an IMU to investigate its ability to assess smoothness [3; 25]. These evaluations encompassed comparing different walking tasks realized by both a cohort of healthy young individuals and a group of healthy aged individuals. Moreover, [PERSON]'s research was conducted with a sample comprising over 70% women, potentially introducing bias into the study. However, [PERSON] et al. [17] suggested that HR should more properly be used only to quantify gait symmetry because of its lack of consistency in calculating smoothness, in partial agreement with what [PERSON] et al. [2] observed regarding its reliability. [PERSON] et al. employed the LDLJ and SPARC metrics, to assess both task- and age-related disparities in head and body CoM patterns recorded through an optical system. Their study involved walking and stair ascent and descent in both healthy elderly and young adults [16]. A major limitation of this study is in the process of deriving velocities, accelerations and jerk signals of the CoM by performing up to three subsequent derivatives from the position data acquired using a stereophotogrammetric capture system. This derivative-based procedure can potentially introduce noise, affecting the calculation of smoothness. In light of the limitations identified in the existing literature concerning the evaluation of smoothness and the exploration of aging effects, this paper aims to apply HR, LDLJ and SPARC metrics to acceleration and angular velocity signals collected during walking by means of an IMU placed on the lumbar region. A comparison is made between a healthy elderly population and a healthy young population. Therefore, the objective is to investigate the metrics' reliability and robustness, discerning potential differences among them, and establish whether any or all of these metrics can serve as reliable benchmarks in assessing variations in smoothness between younger and elderly individuals during walking.