**1. Introduction**

The use of accelerometers to measure physical activity (PA) in research have expanded tremendously since the millennium shift. An essential component of PA is the intensity performed, as PA intensity is related to the health benefits achieved [1]. Therefore, it is crucial that accelerometers provide accurate measures of PA intensity, which commonly involves determining time spent in different intensity levels such as light (LPA), moderate (MPA) and vigorous (VPA) physical activity.

These PA intensity measures have been used in cross-sectional and longitudinal epidemiological studies to investigate, for example, the age-related decline in PA from childhood into adulthood and associated factors, in an attempt to identify risk groups for future cardiometabolic disease [2–4].

Researchers working with development of PA intensity measures from accelerometers have mainly used energy expenditure determined from measured oxygen consumption as criterion method. The most common criterion measure of absolute PA intensity is Metabolic Equivalent of Task (MET), calculated as the quotient of gross energy expenditure and resting energy expenditure. However, MET is not directly comparable between children and adults, as the contribution of resting energy expenditure to gross energy expenditure changes from childhood into adulthood [5]. The resting energy expenditure decreases from about 2.0 kcal·kg−1·h−<sup>1</sup> at the age of 5 years to 1.0 kcal·kg−1·h−<sup>1</sup> at the age of 18 years. When children 8–12 and adolescents 15–18 years old walk at a speed of 5.6 km·h−<sup>1</sup> they reach a MET-value of 4.3 and 4.5, respectively, while running at 8.0 km·h−<sup>1</sup> contributes to a MET-value of 6.7 and 8.1, respectively [6]. When adults walk and run at these speeds, they reach the MET-value of about 5.0 and 9.0, respectively [7]. Importantly, despite their lower MET-values, the younger individuals would actually exert higher degree of effort with higher oxygen consumption per kg body weight compared to the older individuals [8,9] as they are moving with higher step frequency [10,11].

It is common in calibration of accelerometers to use 3.0 and 6.0 METs as cut-points for MPA and VPA, respectively, in both children and adults [12], but even higher values have been implemented in children, i.e., 4.0 and 7.0 METs [2,3,13], with the argument that it adjusts for their higher resting energy expenditure. In fact, we put higher requirements on children than on adults to achieve MPA and VPA. Therefore, the current calibration procedure for absolute PA intensity using MET cannot be used to compare the PA in different age-groups. Theoretically, this may contribute to underestimation of the PA in children relative to adults and incorrect conclusions concerning the decline in PA from childhood into adulthood and identification of individuals being physically inactive.

Attempts have been made to identify alternative criterion measures of activity intensity from oxygen uptake [14]. One such measure is the mass-specific net oxygen consumption (VO2net, mL·kg−1·min−1), subtracting resting oxygen uptake (VO2rest) from gross oxygen uptake (VO2gross). However, this measure is not equivalent by age, as it decreases from childhood into adulthood [14]. In biomechanical research VO2net is instead calculated by subtracting standing oxygen uptake (VO2stand) from VO2gross [10,11]. This definition considers the energy requirement of dynamic movement only and therefore matches the dynamic acceleration captured by accelerometers. The definition of subtracting VO2rest from VO2gross would also include oxygen consumption for muscular support during movement which is not captured by the accelerometer. The literature has not clearly demonstrated whether VO2net (VO2gross − VO2stand) as a measure of activity intensity is equivalent by age [8–11,15]. It would make sense that children have higher VO2net than adults at the same absolute speed (Speedabs) [8,9], as the they are moving with a higher degree of effort due to the higher step frequency [10,11]. Instead, the VO2net is more similar at the kinematically equivalent speed (Speedeq) [8,9,15], which reflects the Speedabs two individuals of different body size are moving at with the same degree of effort, i.e., shorter individuals would move at a slower Speedabs than taller individuals. Therefore, further investigations of the VO2net as a measure of activity intensity equivalent by age is warranted, relating it to the Speedeq to determine whether it reflects a similar effort performed by individuals of different body size and age. If it does, it can be used to calibrate accelerometer PA intensity measures equivalent by age to be implemented into epidemiological research for age-related investigations of PA.

The ActiGraph counts has been the most common accelerometer-based measure of PA activity intensity in research, mostly from hip recordings [12]. However, the processing of raw acceleration to counts demonstrates a measurement error of increasing attenuation of the counts with increasing PA intensity, which is greater in children than in adults [16,17]. This error was explained by the use of a too narrow band-pass filter. When the filter was expanded to a more optimal level, children and adults produced similar accelerometer outcomes from hip recordings for the same absolute movement

speed. This indicates that an accelerometer placed at the hip would capture total mechanical work in both children and adults, which would be identical at the same Speedabs [11,17]. The measurement error with the ActiGraph counts may have contributed to the confusion of the METs in the calibration of accelerometers, where children demonstrated both lower METs and lower counts than adults at the same Speedabs. In fact, children should have demonstrated lower METs but similar counts at the same Speedabs. These different outcomes would have contributed to different calibration equations and cut-points for PA intensity. While the comparability of accelerometer measures of PA intensity by age has been investigated for the hip placement, less is known about the thigh placement [17–19]. The thigh placement offers additional possibilities for assessment of sedentary time (sitting, standing), biking (i.e., cadence) as well as non-wear time.

Therefore, the aim of the present study was to investigate the calibration of hip and thigh accelerometers in children and adults using VO2net (VO2gross − VO2stand) as criterion for absolute PA intensity and the effect on assessment of free-living PA. With the application of a novel calibration procedure, this study may contribute to improve the assessment of PA intensity in children and to establish a measure of PA intensity equivalent by age.
