**1. Introduction**

Obesity is one of the greatest threats to our health and wellbeing worldwide. In 2016, 1.9 billion (39%) adults were considered overweight, of which 650 million (13%) were obese [1]. Obesity is directly linked to disorders such as hypertension, type II diabetes, and cardiovascular disease, which can lead to further chronic disabilities [2]. In the USA alone, the costs of obesity for society are estimated to be USD 1.72 trillion yearly or 9.3% of their gross domestic product [3]. In Germany, the estimated direct and indirect costs are estimated at EUR 63.04 billion yearly or 1.87% of its gross domestic product [4]. These numbers are expected to climb since the prevalence of obesity is continuing to increase [5]. Proper diet and physical activity (PA) are the two most important strategies for weight loss and maintenance for the majority of patients. In addition, PA does not need additional financial resources and could be applied everywhere worldwide. The 2020 WHO Physical Activity Guidelines provide information on the health benefits of physical activity: Most

**Citation:** Stenbäck, V.; Leppäluoto, J.; Juustila, R.; Niiranen, L.; Gagnon, D.; Tulppo, M.; Herzig, K.-H. Step Detection Accuracy and Energy Expenditure Estimation at Different Speeds by Three Accelerometers in a Controlled Environment in Overweight/Obese Subjects. *J. Clin. Med.* **2022**, *11*, 3267. https://doi.org/ 10.3390/jcm11123267

Academic Editor: Władysław Jagiełło

Received: 4 May 2022 Accepted: 2 June 2022 Published: 7 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

adults should complete at least 150 min a week of moderate physical activity and musclestrengthening exercises two times a week, or 75 min of vigorous physical activity [6]. Unfortunately, a large proportion of adults do not attain the level of the recommended physical activity.

To accurately assess the effects of PA on populations and create personalized recommendations, more reliable and objective tools are needed. The current recommendations are still largely based on self-reported measures, which include, e.g., asking for information on time used for leisure, household, and transportation activities. Accelerometry is a commonly used objective method to measure PA, but multiple and significant considerations remain. Waist-worn accelerometers are more accurate than wrist-worn ones, data counting systems and the availability of raw data differ between devices, and differences in signal processing, step detection, and filtering exist as well [7–9]. The gait characteristics of the obese include, for example, slower speed and shorter stride length when compared to normal weight people [10]. For most overweight/obese and elderly people, the selfselected walking pace is 3 km/h or lower [11,12]; hence, these low speeds are important when using accelerometry with these subjects and evaluating health benefits. A maximal gait speed of 7 km/h was reported for elderly and elderly obese people in the Baltimore Longitudinal Study of Aging [13]. To capture the habitual PA via accelerometry in overweight, obese, and elderly populations, accurately measuring slow walking is of the utmost importance. The "Gold standard" technique for measuring energy expenditure (EE) is the double-labeled water method, which accurately measures the overall EE from a period longer than 3–4 days but is costly [14]. Direct calorimetry can also be used to measure EE but requires a thermally isolated chamber in which the subject is measured. Indirect calorimetry can be used to estimate EE from the use of O2 and the production of CO2 from the ventilation gasses. Furthermore, accelerometers can be used in EE estimation with or without heart rate measurement [15]. A recent review by Pisanu and colleagues states, that EE estimation with accelerometers in overweight and obese subjects is inaccurate [16]. In addition, an underestimation of EE during semi-structured activity protocol including, for example, household activities with the ActiGraph GT3X was observed to be 26% in overweight subjects [17]. Earlier, we showed in normal weight subjects that there are significant differences in the accelerometers' accuracy at different speeds, with decreasing accuracy at speeds of 3 km/h or less [18]. Few studies have investigated the accuracy of research-grade accelerometers in a controlled environment for step detection and EE estimation in overweight and obese people, and importantly, none have included gait speeds initiated at 1.5 km/h, a gait speed we have previously observed in people at risk of T2D [19]. Feito and colleagues (2012) studied the effect of BMI class to step detection accuracy with hip-mounted accelerometers at three different speeds (2.4, 4.0, and 5.6 km/h) and found an error-%s of 20–60% at the lowest speed with no difference between the BMI-classes [20]. Error percentages in EE estimation have been shown to be 40–31% in overweight and obese subjects using the Freedson 1996 cut-off points with speeds starting from 4 km/h [21].

Our aim was to investigate the accuracy of step detection and energy expenditure estimation at different speeds for three research-grade accelerometers in overweight and obese participants under controlled laboratory settings.

#### **2. Materials and Methods**

Forty-eight overweight and obese subjects participated in this study (24 males). Subjects were on average 37.4 ± 13.9 years old, and their mean body mass index (BMI, kg/m2) was 31.4 ± 3.8; they were 173.6 ± 10.3 cm tall, weighted 94.8 ± 15.5 kg, had a skeletal muscle percentage (SMM%) of 36.9 ± 6.2, fat percentage of 34.4 ± 10.1 and waist circumference of 99.2 ± 12.0 cm (Table 1). Exclusion criteria for the participants were BMI less than 25 or over 40, younger than 20 or older than 75 years, any disease or injury preventing normal movement, arthritis, high blood pressure, chronic cardiovascular diseases, or acute cardiovascular event during the last year, ventilatory diseases and pregnancy or lactation. None

of the subjects had undergone bariatric surgery for weight loss. This study was approved by the ethical committee in the Northern Ostrobothnia Hospital District (EETTMK 26/3/21). All the participants were healthy volunteers who gave their written informed consent in accordance with the Declaration of Helsinki. This study was conducted following national legislation, guidelines, and the Declaration of Helsinki.


**Table 1.** Characteristics of the study population. SMM = skeletal muscle mass.

All subjects participated in one measurement session conducted between 08:00 and 11:00 in the morning. Subjects were requested to fast at least 10 but not more than 16 h before their scheduled study session. They were also asked to avoid strenuous exercise on the day before and on the morning of the study session. Bioimpedance was used to determine the body composition (InBody 720, Biospace, Co, Ltd., Seoul, Korea). Energy expenditure was estimated via oxygen uptake and carbon dioxide production using indirect calorimetry (IC) (Vyntus CPX, Vyaire Medical GmbH, Hoechberg, Germany). Ergospirometer was calibrated every morning before the first subject and was considered valid for 4 h as instructed by the manufacturer. The contents of the gas were as follows: 5.0% CO2, 15.9 O2, and the remaining 79.1% N2. Resting metabolic rate (RMR) was estimated in a supine position using a Hans Rudolph 7450 V2 mask (Hans Rudolph, Shawnee, Kansas, USA) until the values plateaued for at least 10 min and the last 5 min of the measurement were used to calculate the RMR. Respiratory exchange ratio (RER) was required to stay between 0.90 and 0.70 during the 10-min period. Weir equation was used to calculate the metabolic rate (kcal/day) = 1.44 (3.94VO2 + 1.11VCO2). RMR defined the level of 1 metabolic equivalent (MET) for the subsequent EE estimation analysis.

After conducting the initial measurements, participants underwent an exercise routine on a treadmill (X-erfit 4000 Pro Run). The routine consisted of 6 speeds with a 4-min duration per speed with a total duration of 24 min. The speeds were 1.5, 3, 4.5, 6, 7.5, and 9 km/h. Acceleration to next speed took approximately 5 s at the beginning of each speed. A video camera was used to record participants' feet during the entire exercise. The videos were used to count the actual step numbers at every speed and were performed according to Sushames et al., 2016 [22]. Energy expenditure was recorded during physical activity with a Hans Rudolph 7450 V2 mask. Energy expenditure for each speed was calculated using the Weir equation from the last minute of each speed and multiplying that with 4. Transformation to metabolic equivalents (METs) was performed using RMR as the level 1 MET.

Three accelerometers were worn by subjects during the exercise protocol. A Sartorio Xelometer (SX) (Sartorio Oy, Oulu, Finland) and an ActiGraph GT3X (AG) (ActiGraph LLC, Pensacola, FL, USA) were attached with elastic belts on the right side of the hip and an activPAL (AP) (PAL Technologies Ltd., Glasgow, Scotland) worn on the right thigh, all following the manufacturers' recommendation. The data from the SX device was extracted using Sartorio software (v18) and detection algorithms provided by the manufacturer and were run on MATLAB R2019a for step counts, step intensities, and EE estimates (MET) [16]. For AP, PAL connect (v8.10.8.76) was used to set up the device and extract the data and PAL analysis (v8.11.2.54) to analyze the step counts and EE estimates (METhrs). The AP-derived MET-hours were transformed into METs. Finally, AG data was extracted with ActiLife (v6.13.4) and step counts were calculated using 1 s epochs and 100 Hz sampling rate. For EE (METs), Freedson Adult (1998) cut points were used (equation: MET rate = 1.439008 + (0.000795 × CPM) where CPM = counts per minute). In obese people, the mean amplitude deviation (MAD)—based method, such as the one in SX, provided the most accurate EE estimates (error-% 14.3) [23].

Mean absolute percentage errors (MAPEs) were calculated for every speed between the accelerometer-estimated step counts and actual steps (video) using the following equation:

$$M\% = \left(\frac{1}{n} \sum\_{t=1}^{n} \left| \frac{A\_t - F\_t}{A\_t} \right| \right) \times 100$$

Relevant disagreement was considered at MAPEs over 5%. EE data from the accelerometers and IC were analyzed as METs. To observe the similarity between methods, paired-samples *t*-tests, linear regression, and intraclass correlations (ICC) were calculated, and Bland–Altman plots generated. Paired samples *t*-tests were used to study the means of absolute values of observed and estimated measures (accelerometry vs. video, accelerometry vs. IC) and ICCs (Pearson) to study the reliability of the estimates. All statistical analyses were conducted, and figures generated using IBM SPSS Statistics v 26. *p*-values less than 0.05 were considered statistically significant. ICC over 0.90 was considered excellent, 0.75–0.90 good, 0.75–0.50 moderate, and less than 0.50 as poor. Results in the Tables are represented as mean ± standard deviation.
