# # Additional Physical Activity Metrics

Physical activity metrics are algorithms to aggregate raw accelerations signals acquired by acceleration sensors to values that correlate with the intensity of physical activity of a person wearing the acceleration sensor. Theses metrics can be used to estimate energy Expenditure or to directly classify physical activity into activity levels. Most metrics take care of filtering out gravity acceleration and non-movement high frequency acceleration.

## # Movement Acceleration Intensity (MovementAcceleration)

MAI is a metric based on VanSomeren1996. The acceleration signal is bandpass filtered (Butterworth 0.25-11Hz, 4th order) to remove parts that are not caused by bodily movement. The three axes are fused by the Euclidean norm. The final signal output is the mean value of the output intervall. movisens uses a output intervall of 4 seconds for energy expenditure estimation.

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## # Euclidian Norm (PaMetricEn)

The three axes of the 3D acceleration signal are fused to the vector magnitude by computation of the Euclidean norm. The final signal output is the mean value of the output intervall.

## # Euclidian Norm Minus One (PaMetricEnmo)

Metric ENMO is described in van Hees et al. (2013). The three axes of the 3D acceleration signal are first fused to the vector magnitude by computation of the Euclidean norm. Afterwards the value of gravitational acceleration on earth 1*g* is subtracted. To inhibit negative subtraction results values smaller than zero are set to zero. The final signal output is the mean value of the output intervall.

Literature:

- Van Hees, Vincent T., et al. "Separating movement and gravity components in an acceleration signal and implications for the assessment of human daily physical activity." PloS one 8.4 (2013): e61691.
- Bakrania, Kishan, et al. "Intensity thresholds on raw acceleration data: Euclidean norm minus one (ENMO) and mean amplitude deviation (MAD) approaches." PloS one 11.10 (2016): e0164045.

## # High-pass Filtered Euclidean Norm (PaMetricHfen)

Metric HFEN is described in van Hees et al. (2013). The acceleration signal is high-pass filtered (Butterworth 0.2Hz, 4th order) to reduce the effect of gravity on the metric output. The three axes are subsequently fused by computing the Euclidean norm. The final signal output is the mean value of the output intervall.

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## # High-pass Filtered Euclidean Norm plus (PaMetricHfenPlus)

Metric HFEN_{+} is described in van Hees et al. (2013). It is based on metric HFEN, which is described in the previous section. The idea behind the signal flow of HFEN_{+} is, that the low-pass filtered signal contains the gravitation. The metric output should correlate to the acceleration caused by physical activity. The influence of gravity should be minimized as a consequence. The value of gravitational acceleration on earth 1*g* is subtracted from the low-pass filtered signal (Butterworth 0.2Hz, 4th order). The result of this subtraction is claimed to include artificial accelerations of low-frequency. So, the result is added to the high-pass filtered signal subsequently after setting negative values to zero. The final signal output is the mean value of the output intervall.

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## # Band-pass Filtered Euclidean Norm (PaMetricBfenMean)

Metric BFEN is described in van Hees et al. (2013). It is similar to metric HFEN, but in addition to high-pass filtering the acceleration signal is low-pass filtered as well, resulting in a bandpass filtered (Butterworth 0.2-15Hz, 4th order) signal. By reducing the content of high frequencies, the influence of noise should be reduced. Subsequently to the filtering process the three axes are fused to the vector magnitude and finally the mean value of the output intervall is calculated.

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## # EEAC (PaMetricEeacMean)

The metric EEAC is described in Härtel et al. (2011). It describes the Euclidean norm of the deviation of the average. First the mean value of a set segment length (suggested by author: 1 second) is calculated and subtracted of the acceleration signal. The Euclidean norm is calculated subsequently. The final signal output is the mean value of the output intervall.

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## # Mean Amplitude Deviation (PaMetricMeanAmplitudeDeviation)

The metric MAD is described in Vähä-Ypyä et al. (2015). In the literature it is also called Vector Magnitude Count (VMC) to avoid the confusion between the two MAD acronyms used in accelerometry literature, one for mean amplitude deviation and one for median amplitude deviation. The metric makes use of the mean signal value to reduce the effect of the constant gravitational acceleration.

Literature:

- Vähä-Ypyä, Henri, et al. "Validation of cut-points for evaluating the intensity of physical activity with accelerometry-based mean amplitude deviation (MAD)." PloS one 10.8 (2015): e0134813
- Vähä‐Ypyä, Henri, et al. "A universal, accurate intensity‐based classification of different physical activities using raw data of accelerometer." Clinical physiology and functional imaging 35.1 (2015): 64-70.
- Bakrania, Kishan, et al. "Intensity thresholds on raw acceleration data: Euclidean norm minus one (ENMO) and mean amplitude deviation (MAD) approaches." PloS one 11.10 (2016): e0164045.
- Karas, Marta, et al. "Accelerometry data in health research: challenges and opportunities." Statistics in Biosciences (2018): 1-28.

## # Zero Crossing (PaMetricZeroCrossing)

The metric ZC is described by Acebo et al. (1999) and Jean-Louis et al. (2001). ZC is based on just one axis of the acceleration signal because it was designed for a mono-axial accelerometer. The algorithm counts the number of threshold crossings of the band-pass filtered (Butterworth 2-3Hz, 4th order) acceleration signal in an epoch. The downward facing axis of the accelerometer is used.

Literature:

- Acebo, Christine, et al. "Estimating sleep patterns with activity monitoring in children and adolescents: how many nights are necessary for reliable measures?." Sleep 22.1 (1999): 95-103.
- Jean-Louis, Girardin, et al. "Sleep estimation from wrist movement quantified by different actigraphic modalities." Journal of neuroscience methods 105.2 (2001): 185-191.

## # Proportional Integrating Measure (PaMetricPim)

The metric PIM is introduced by Jean-Louis et al. (2001). Like ZC, which is described in the previous section, PIM is based on just one axis of the acceleration signal because it was designed for a mono-axial accelerometer. The metric output of PIM is based on integration of the surface under the band-pass filtered (Butterworth 2-3Hz, 4th order) acceleration graph. The amplitude of that graph is bound to an upper limit (0.384*g*). The input of the algorithm is the signal of the downward facing axis of the accelerometer.

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## # Actiwatch 4 Counts (PaActiWatch4Counts)

The metric Actiwatch 4 Counts is introduced by CamNtech Ltd. Actiwatch 4 Counts are based on just one axis of the acceleration signal because it was designed for a mono-axial accelerometer. The counts are calculated by truncating the acceleration signal to a maximum of 5*g*. The resulting signal is high-pass (Butterworth 3Hz, 1st order) and low-pass (Butterworth 11Hz, 2nd order) filtered, downsampled to 32 Hz and scaled to values from 0 - 128. Subsequently the maximum in 1 second intervalls is picked and rounded to the nearest integer value. A dead band up to including value 2 is introduced. The final signal output is the sum over the output intervall.