**3. Results**

#### *3.1. Step Detection*

All participants completed the three first speeds of the protocol, and one participant stopped after 4.5 km/h. A total of 38 out of 48 could complete the first running speed (7.5 km/h) and 25 completed the whole protocol. At walking speeds (1.5, 3, 4.5, and 6 km/h), the AP device was the most accurate. The corresponding MAPEs were 6.39, 0.95, 0.99, and 2.44, respectively (Table 2). For SX, the corresponding MAPEs were 9.73, 3.97, 2.91, and 6.28, respectively. The AG was the least accurate at the lower walking speeds but improved its accuracy from 4.5 km/h with MAPEs of 88.69, 31.50, 4.25, and 2.44, respectively. At the running speeds (7.5 and 9 km/h) the AG device performed better with MAPEs of 4.43 and 2.63, respectively. For the SX and the AP, the MAPEs were 2.26, 4.47, and 3.99, 5.18, respectively. The SX device estimate of the total number of steps differed by 3.48% and for the AP and the AG by 4.37% and 17.80%, respectively. Significant differences between direct measurement and accelerometer estimated steps were observed at 1.5 km/h and a first running speed (*p* < 0.000) for the AP. For the SX device, significant differences were observed at all speeds except 4.5 km/h and a first running speed (*p* < 0.05) between device estimates and direct observation, and for the AG at speeds of 1.5 and 3 km/h as well as in the first running speed (*p* < 0.000). The intraclass correlations were significant (*p* < 0.030) at all speeds for all devices except for the AG at 3 km/h (*p* = 0.646). For the AP device, the correlation coefficients were excellent (>0.90) and for the SX good or excellent (>0.75 and >0.90, respectively), except for the lowest speed where the correlation was moderate (0.61). For the AG, the correlation coefficients were excellent (>0.90) while running and brisk walking (6 km/h), good (>0.75) with the first running speed, and moderate or poor (>0.50, <0.50, respectively), at speeds of 1.5, 3 and 4.5. The R<sup>2</sup> values for the regressions between actual and estimated steps were 0.948 for the SX, 0.963 for the AP, and 0.821 for the AG (Supplementary Materials). For the Bland–Altman plots the means, standard deviations, and 95% confidence intervals were −14.7 ± 30.3, upper 44.7, lower −74.2, respectively, for the SX (Figure 1A), −4.0 ± 12.8, upper 21.1, lower −29.0, respectively, for the AP (Figure 2A) and −76.39 ± 104.9, upper 129.3 and lower −282.0, respectively, for the AG (Figure 3A).

**Table 2.** Step detection statistics. Mean absolute percentage error (MAPE), paired sample *t*-test statistics with mean ± SD, lower and upper limits for 95% confidence intervals and *p*-values, and intraclass correlation (ICC) statistics with 95% CI presented for every accelerometer at separate speeds and for total duration of exercise protocol. \* Shows statistical significance.


**Figure 1.** Bland-Altman plots for the Sartorio Xelometer. (**A**). Step detection compared to the direct (video) measurement. All six speeds have been plotted separately. (**B**). EE estimation compared with indirect (IC) calorimetry. Solid line marks the mean and dotted lines show the −1.96–1.96 SD limits.

**Figure 2.** Bland-Altman plots for the activPAL. (**A**). Step detection compared to the direct (video) measurement. All six speeds have been plotted separately. (**B**). EE estimation compared with indirect (IC) calorimetry. Solid line marks the mean and dotted lines show the −1.96–1.96 SD limits.

**Figure 3.** Bland-Altman plots for the ActiGraph GT3X. (**A**). Step detection compared to the direct (video) measurement. All six speeds have been plotted separately. (**B**). EE estimation compared with indirect (IC) calorimetry. Solid line marks the mean and dotted lines show the −1.96–1.96 SD limits.

### *3.2. Energy Expenditure Estimation*

All three devices were inaccurate in estimating energy expenditure (Table 3). The SX had the most accurate estimates of EE upon the complete exercise protocol with a MAPE of 18.43. The MAPEs for total EE were 49.62 for the AP and 36.16 for the AG with significant but poor intraclass correlations (*p* < 0.05, ICC < 0.50). For the SX, the speed-wise MAPEs from 1.5 km/h to the second running speed were 15.15, 17.60, 19.02, 21.41, 18.03, and 19.74. respectively. For the AP, the values were 12.36, 16.29, 27.82, 43.82, 56.10, 57.38 and for the ActiGraph 59.45, 40.67, 28.92, 29.88, 29.61 and 32.09, respectively. At all speeds for all three devices, there were significant differences between accelerometer estimates and indirect calorimetry (*p* ≤ 0.005), and no significant intraclass correlations were observed (*p* > 0.120). The R2 values for the regression between indirect calorimetry and device estimated EE (when considering all speeds together) were 0.81 for the SX, 0.75 for the AP, and 0.745 for the AG (Supplementary Materials). For the Bland–Altman plots the means, standard deviations, and 95% confidence intervals were for the SX (Figure 1B): −1.4 ± 2.0, upper 2.5, lower −5.3, respectively, for the AP (Figure 2B): −1.4 ± 1.5, upper 1.6, lower −4.5, respectively, and for the AG (Figure 3B): −2.6 ± 2.6, upper 2.5 and lower −7.8, respectively. **Table 3.** Energy expenditure (EE) estimation statistics. Mean absolute percentage error (MAPE), paired sample *t*-test statistics with mean ± SD, lower and upper limits for 95% confidence intervals and *p*-values and intraclass correlation (ICC) statistics with 95% CI presented for every accelerometer at separate speeds and for total duration of exercise protocol. \* Shows statistical significance.


### **4. Discussion**

We measured overweight and obese subjects without diseases or disabilities that could affect their gait. Forty-eight subjects performed an exercise protocol on a treadmill consisting of six different speeds, which were chosen to reflect the locomotion speeds of overweight, obese, and elderly people. The main objective was to study the accuracy of step detection and EE estimation with three known research accelerometers (SX, AP, and AG) in overweight and obese subjects. For step detection, similar accuracies for step detection were observed in this overweight/obese population as in normal weight subjects [18]. Energy expenditure estimates were inaccurately measured in all three devices.

All three devices accurately estimated step detection when gait speed exceeded 4 km/h. Only the AG was inaccurate during slow walking speeds of 1.5 and 3 km/h with MAPE-% of 88.7 and 31.5, respectively. The AP showed the highest correlations between video camera-recorded steps and device step counts (ICC > 90). Step detection accuracy in overweight and obese people was similar compared to normal weight subjects with the exception that the AP was more accurate in estimating step counts during running in overweight and obese subjects [18]. Similar discrepancies have been reported by Feito and colleagues (2012) [20] who showed the increasing accuracy with increasing speed in the AG. Lee and colleagues [24] found a significant underestimation of step counts by AG at the speed of 3.2 km/h. We did not use the low-frequency extension for the AG data, since it has been shown to give indefinite results when applied to free-living data [25,26].

All accelerometers were inaccurate for estimating EE. The SX provided the smallest overall error percentages in the range of 15.15–21.41, while the AP and the AG ranged between 12.36–57.4 and 28.9–59.45, respectively. The accuracy of the AP EE estimation was at its highest during slow walking speeds (1.5 and 3 km/h) and decreased with speed. For the AG, an opposing trend was observed, the EE estimation accuracy was higher at speeds exceeding 4 km/h. For the SX, the EE estimation error was 12% smaller in overweight/obese subjects compared to normal weight subjects (MAPE 18.4 < 30.3) [18]. The opposite was observed with the AP and ActiGraph, both showing lower EE estimation accuracy with overweight subjects. The SX EE estimation is based on MAD and had the most accurate method of the three and is in line with the results of Diniz-Sousa and colleagues [23].

Applying accelerometry to overweight/obese populations is challenging. The excess body fat increases the energy used in bodily movements and can cause the accelerometer to be placed at an angle that has been shown to decrease accuracy [16]. If the manufacturer of the accelerometer has used a normal weighted population for algorithm development, inaccuracy will increase when applied to overweight people. The comparison of the different studies with objectively measured physical activity measures is problematic since the different manufacturers use their own methods and algorithms. Accelerations as g-values are further processed into steps, counts, and MET units for further analysis. Depending on the method, habitual daily PA can be classified differently into commonly used PA intensity classes such as light, moderate and vigorous [9]. Considering these points together with the discrepancies concerning wear location, time, signal processing, and filtering [8], a standardized method of measurement is needed to create accurate, specified, and personalized PA recommendations.

Our study is the first to evaluate the accuracy of EE estimation of these accelerometers at realistic walking and running speeds in overweight and obese subjects. The use of a video camera to record true step numbers, the use of both sexes, and a wide range of ages and BMIs are the strengths of this study. Our limitations include the lack of self-selected locomotion speed and the exclusion of any wrist-worn accelerometers. The gait speeds chosen are sufficient in covering the spectrum of overweight human locomotion speeds. Our results will guide users studying physical activity in different populations in the interpretation of their results and their conclusions towards public health recommendations.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/jcm11123267/s1. Figure S1. Regression plots for Sartorio Xelometer. Figure S2. Regression plots for activPAL. Figure S3. Regression plots for ActiGraph GT3X.

**Author Contributions:** Conceptualization, K.-H.H., J.L., V.S., M.T. and D.G.; methodology, V.S., L.N. and R.J.; software, V.S.; formal analysis, V.S.; investigation, V.S., L.N. and R.J.; resources, K.-H.H. and M.T.; data curation, V.S.; writing—original draft preparation, V.S.; writing—review and editing, K.-H.H., J.L., V.S., R.J., L.N., M.T. and D.G.; visualization, V.S.; supervision, K.-H.H.; project administration, V.S.; funding acquisition, K.-H.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** The study was conducted in accordance with the Declaration of Helsinki and approved by the Northern Ostrobothnia Hospital district ethical committee in Oulu, Finland (EETTMK 26/3/21).

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Acknowledgments:** We thank all the participants and organizations of the University of Oulu and Oulu University of Applied Sciences for their help in recruitment.

**Conflicts of Interest:** J.L. and K.-H.H. are co-inventors of the Sartorio Xelometer and members of the board of Sartorio OY. J.L. and K.-H.H. did not participate in the study sessions or data acquisition and handling (V.S. and R.J.) or the statistical analysis of the results (V.S.). The remaining authors declare no competing interests.
