**4. Discussion**

The novelty of this study is to propose a criterion method (VO2net, mL·kg−1·min−1) to calibrate accelerometer PA intensity measures equivalent by age based on data collected at the hip and at the thigh. It was applied to our improved processing of acceleration data [16–19] to generate new cut-points for LPA, MPA, VPA and VVPA in children, adolescents and adults. These outcomes were supported by the finding that the relationship between Speedeq and VO2net (VO2gross − VO2stand) was similar in children, adolescents and adults, indicating that VO2net is a measure of similar effort in the three age-groups, in contrast to the more commonly used MET in accelerometer calibration which was not a measure of PA intensity equivalent by age. When our new cut-points for PA intensity levels were applied to free-living acceleration data from the hip, the difference in PA between children, adolescents and adults increased compared to the application of the standard MET-based cut-points. The importance of the findings in this study is to allow the possibility to directly relate the PA intensity level between age-groups and thereby more accurately investigate the age-related changes in PA from childhood into adulthood and associated factors. A larger decline in PA from childhood into adults may be expected compared to what is anticipated from previous research.

Two individuals of different body size perform an activity with different movement patterns. A short individual takes shorter steps with smaller acceleration amplitude but at higher frequency, while the taller individual takes longer steps with larger acceleration amplitude but at lower frequency [10,11,17]. Biomechanical theory demonstrates that the total mass-specific mechanical work is the same in short and tall individuals moving at the same Speedabs, but that the shorter individual generates more internal work related to the higher frequency of moving the limbs while the taller individual generates more external work related to the movement of the center of mass [10,11]. Consequently, one would expect an accelerometer placed at the hip to generate higher values in the taller individual while the opposite would occur with the placement on the thigh. Interestingly, our results (Figure 1A) show that the hip placement generates similar accelerometer output for the same Speedabs in children, adolescents and adults, indicating that all the acceleration signals captured represent total mechanical work. Hence, an accelerometer placed at the hip can be used to compare

the total mechanical work performed between age-groups. Instead, the thigh placement generated higher accelerometer output in the children compared to the other groups (Figure 1B), indicating that this placement captures more internal work which is not comparable between age-groups. In contrast to the results herein, the original ActiGraph counts from hip recordings are lower in children than in adults for the same Speedabs [25,26], while the opposite occur with the Euclidian Norm Minus One (ENMO) accelerometer output [27]. Consequently, none of these methods provide measures of mechanical work equivalent by age. In the case of the ActiGraph counts, this age difference is caused by a well-defined processing error [16]. In the case of the ENMO accelerometer output, it may be a processing error less clearly defined. With the ENMO method, all negative accelerations are set to zero after subtracting 1 g from the vector magnitude [27]. This means that acceleration signals generated with larger amplitude but at lower frequency (as in adults) will be excluded to larger extent compared to acceleration signals with a lower amplitude but at a higher frequency (as in children). In contrast, the ActiGraph counts and the accelerometer method developed in our research group are aggregations of both positive and negative accelerations.

Even if an accelerometer placed at the hip would capture total mechanical work at the same Speedabs, the activity is performed with different effort and energy cost in children compared to adults (Figure 2A) [8,9], and therefore has different physiological loads/health effects on the body. Consequently, an accelerometer output needs to be calibrated against a criterion measure of equivalent effort/load by age. The MET was developed to provide a criterion measure of absolute PA intensity. Our study showed that the MET was not equivalent by age as different values were achieved in children, adolescents and adults for the same Speedabs and Speedeq (Figure 3). If we compare the results in Figures 5 and 6, we clearly see the consequence of applying the MET-based accelerometer calibration: Higher accelerometer cut-points are set for younger individuals to reach MPA, VPA and VVPA, when they are actually performing the activity at these PA intensity levels with a higher degree of effort according to the Speedeq (Figure 3B) and with a higher energy cost according to the VO2net (Figure 4) compared to the older individuals. This calibration error will contribute to the underestimation of the PA in children relative to adults.

Alternative criterion measures of PA intensity equivalent by age have been investigated, for example mass-specific VO2gross (mL·kg−1·min−1), VO2net (VO2gross <sup>−</sup> VO2rest, mL·kg−1·min−1) and VO2allom (mL·kg−0.75·min<sup>−</sup>1) [14]. None of the measures was optimal for the PA intensity range. The allometric scaling seems to work well for ambulatory activities and the MVPA intensity range [14] and has previously been proposed as an accurate criterion measures for accelerometer calibration [28]. We based our choice of VO2net (VO2gross <sup>−</sup> VO2stand, mL·kg−1·min<sup>−</sup>1) on that this measure captures the dynamic movement only and therefore matches the dynamic acceleration captured by an accelerometer. Although, previous research has shown a remaining difference by age when this measure was related to Speedeq. For example, at Speedeq = 0.3, the VO2net was about 230 and 200 mL·kg−1·km−<sup>1</sup> in children and adults, respectively [8]. We also observed some fluctuations in the difference between the age-groups across Speedeq range (Figure 2B), but the relevance of these small differences and those found in the study by McCann et al. [8] is unclear and requires further investigations. We still find our results to provide a strong indication of VO2net as a criterion measure of PA activity intensity equivalent by age and suitable for accelerometer calibrations.

A limitation with the VO2net measure is that there are no established PA intensity cut-points as for the MET measure (i.e., 3.0 and 6.0 METs). We based our calibration procedure on the adult MET-values and cut-points for LPA, MPA, VPA and VVPA (Figure 4), as the MET as a measure of absolute PA intensity was initially developed in adults [29], and translated them to the corresponding VO2net. The same VO2net cut-points were thereafter applied to all three age-groups to represent PA intensity levels equivalent by age and used for the accelerometer calibration (Figure 5). As children, adolescents and adults produce the same total mechanical work at the same Speedabs [10,11], which is captured by an accelerometer at the hip (Figure 1A), and as VO2net differs between these age-groups at the same Speedabs (Figure 2A) due to different efforts related to step frequency [10,11] but is similar at the same

Speedeq (Figure 2B), these age-groups will present different regression lines between VO2net and the accelerometer output and consequently also different accelerometer cut-points (children < adolescents < adults). The somewhat smaller difference in the VO2net-acceleration regression lines between the age-groups with the thigh placement (Figure 5) is explained by differences in the accelerometer output, which is supported by the biomechanical literature showing that smaller individuals produce more internal work [10,11] and consequently more thigh acceleration. Our calibration procedure requires knowledge about speed of movement. An alternative procedure embraced in calibration and validation studies, is to let the participants perform walking and running at a self-selected pace not involving the measurement of movement speed [13]. It is possible that the self-selected paces correspond to the same Speedeq in different age-groups. The accelerometer calibration research field has postulated that a variety of activity types (including intermittent) should be included in calibration protocols to provide calibration algorithms representative of people's daily activity pattern [30], not only walking and running. Still, that protocol would include activities where the steady-state is not easily attained in order to accurately assess the oxygen consumption of an activity [23], which is the case for protocols including only continuous walking and running as in the present study.

The contribution of our study can be exemplified based on two large epidemiological studies where the PA has been compared between children and adults. Cross-sectional analyses of accelerometer data from the National Health and Nutrition Examination Survey (NHANES) have shown that boys and girls 6–11 years old spend 95 and 75 min daily in MVPA, respectively, while men and women 40–49 years old attained 35 and 19 min, respectively [2]. Longitudinal analyses of accelerometer data in the European Youth Heart Study between ages 9 and 15 years old demonstrated a decline in MVPA from 100 to 52 min daily in Swedish boys and from 73 to 44 min daily in Swedish girls [4]. In another sample in this study, there was a decline between ages 15 and 21 years old from 68 to 58 min daily in Swedish males and from 46 to 40 min daily in Swedish females. These studies used MET-based accelerometer cut-points for MPA and VPA, applying similar (3.0 and 6.0 METs) or higher (4.0, 7.0 vs. 3.0, 6.0 METs) MET-values in children compared to adults. Consequently, higher demands were required from the children to reach MPA or VPA than in the adults. Further, the acceleration data was processed to the original ActiGraph counts with its limitations to assess PA intensity [16–19]. In addition, the aggregation of the acceleration data was performed into 60 s epochs, which would be insensitive to the movement pattern of children [1]. The application of our improved processing of accelerometer data [17,18] and calibration procedure presented herein together with the use of 3 s epochs would have demonstrated a larger decline in MVPA from childhood into adulthood. Consequently, there may have been an underestimation of the change in the risk of future cardiometabolic disease in those studies.

A further complication with the widely adopted 3.0 MET cut-point is that it may have been set too low to accurately represent MPA in the general population. The American College of Sports Medicine Position Stand classify 4.8–7.1 METs and 4.0–5.9 METs as MPA in young respective middle-aged adults [31]. Further, 3.0 METs was already reached at comfortable walking by all age-groups in the present study as well as in other studies of children and adults [6,7,13,14]. Consequently, people would be considered physically active too easily. This issue requires further discussion to be settled, but a higher cut-point for MPA might be considered in investigations of the general population.

The present study has several strengths and limitations. Raw acceleration data were processed with algorithms improving assessment of PA intensity [17,18]. Further, short 3 s epochs were applied to improve assessment of children's PA pattern [1] as well as intermittent PA. Calibration of activity intensity cut-points was performed on a treadmill with four minutes at each speed. Previous studies with other accelerometers have showed inconsistent results concerning the impact of setting (treadmill vs. ground) on accelerometer output [32,33]. Calibration performed with walking and running on a treadmill may not be applicable to other types of activities. As we have commented on earlier in the discussion section, using oxygen consumption as criterion measure of PA intensity requires steady-state of oxygen consumption data [23]. Still, the steady-state requirement may be a challenge as a large part of free-living PA does not fulfill it. The present calibration included less data points in

the VPA range (see Figure 5) compared to the MPA and VVPA ranges which may affect the precision of resultant regression lines and cut-points. The calibration sample age-range of 9–44 years did not fully represent the free-living sample age-range of 4–67 years, which may affect the results of the free-living stub-study.
