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Many recent commercial devices aim at providing a practical way to measure energy expenditure. However, those devices are limited in accuracy.
This study aimed to build a model of energy consumption during walking applicable to a range of sloped surfaces, used in conjunction with a simple, wearable device.
We constructed a model of energy consumption during gradient walking by using arguments based in mechanics. We built a foot monitoring system that used pressure sensors on the foot insoles. We did experiments in which participants walked on a treadmill wearing the foot monitoring system, and indirect calorimetry was used for validation. We found the parameters of the model by fitting to the data.
When walking at 1.5 m/s, we found that the model predicted a calorie consumption rate of 5.54 kcal/min for a woman with average height and weight and 6.89 kcal/min for an average man. With the obtained parameters, the model predicted the data with a rootmeansquare deviation of 0.96 kcal/min and median percent error of 12.4%.
Our model was found to be an accurate predictor of energy consumption when walking on a range of slopes. The model uses few variables; thus, it can be used in conjunction with a convenient wearable device.
Physical inactivity, despite its wellknown health risks [
Many of these devices use an accelerometerbased method to predict energy expenditure [
The energetics of human locomotion has been closely studied for decades. Early studies focused on energy expenditure during walking [
Previous studies were primarily of academic interest, although inexpensive commercial devices have recently been made available for personal or clinical use. Such devices offer noninvasive ways to measure daily caloric consumption, and they have been assessed by numerous validation studies in the literature [
This study proposes a model of walking energetics applicable to a range of slopes. The model is based on a simple equation and uses data from a wearable device. The method uses a foot monitoring system that can sense footsteps, which allows for direct measurement of step frequency. We found that a highaccuracy model can be developed for a range of upward and downward slopes. The fact that it is based on a direct measurement of footsteps allows the device to be versatile and applicable to diverse walking situations. The ability to track expenditure while walking on sloped surfaces is helpful for sloped outdoor ground and also indoor use of stairs or sloped treadmills.
For model development and validation, an experiment was devised in which 73 healthy participants (34 female, 39 male) walked on a treadmill. The participants had a mean age of 43.6 (SD 15.0) years, mean height of 168.3 (SD 10.5) cm, and mean weight of 68.1 (SD 12.1) kg. Participants were selected from healthy volunteers (age 20 to 60 years) who registered in the department of Sport Science, Pusan National University, Busan, Korea. We excluded participants who had cardiovascular, musculoskeletal, or neurological disorders to avoid any confounding factors or biases. The participants were asked to walk on a treadmill at various values of the incline angle,
Calorie consumption was measured with a COSMED K4b2 portable gas analyzer system. This indirect calorimetry, based on the gas analyzer system, measures oxygen consumption, from which energy expenditure is computed. This method has been validated as an accurate measure through numerous comparative studies [
Each participant also wore a foot monitoring system, consisting of shoe insoles equipped with eight pressure sensors. The insole used was a prototype developed by 3L Labs (Seoul, Korea), and provided to us for research purposes. A depiction of the foot monitoring system and the experimental setup is given in
A value of 0, 1, or 2 indicated the pressure on each of the pressure sensors and was recorded with a frequency of 10 Hz, which resulted in an array of 16 integers for each time step of 0.1 s. A snippet from example data is shown in
Illustration of the foot monitoring system (left) and a picture of a participant walking on an uphill treadmill wearing the K4b2 portable gas analyzer (right).
A sample of 4 seconds of raw data from the pressure sensors. The vertical position of each number of the array indicates the time, ordered from top to bottom at an increment of 0.1 seconds. Each column denotes a sensor, with left foot and right foot separated. The colored portions indicate when our algorithm decided the foot was off the ground.
Graph of total pressure from the left foot sole over an interval of 10 seconds obtained from the foot monitoring system from the same data as presented in Figure 2. The two dashed lines indicate the upper and lower thresholds used to calculate the step frequency.
After assigning a status to each time step, we counted the number of transitions from the onground to offground status and divided it by the time interval to obtain the frequency. As with the gas analyzer data, we omitted data for the first 50 s and the final 10 s. Only one shoe insole is required to calculate the step frequency; however, we used the average of both sides in this study.
Our model was constructed from considering the energy changes involved in walking. Suppose a participant with body mass
We first consider walking on a horizontal surface (ie,
Since we usually have no way to easily measure leg mass or leg velocity, we defined two ratios: (1) the ratio
This allowed us to rewrite equation 3 as
When walking on a horizontal surface perpendicular to the direction of gravity, there is no net change in potential energy. It changes when the subject is walking up or down a slope. We first considered upward inclines. When one walks up a slope of angle
List of equations of the model of energy expenditure during walking.
One might consider simply using the same formula for downhill inclines, in which case the term
Threedimensional scatterplot of data (dots) and model prediction (lines) of P versus P_{U} and P_{K} for women.
Threedimensional scatterplot of data (dots) and model prediction (lines) of P versus PU and PK for men.
The preceding model described leaves parameters
The full set of coefficients, obtained through linear regression, is given in
Coefficients for the full model reported with the rootmeansquare deviation (RMSD) on comparison with data. The values were obtained by two linear regressions.
Coefficient  Units  Women  Men 

—  0.662  0.517 

—  1.591  1.694 

—  0.575  1.086 

kcal/s  0.042  0.058 
RMSD  kcal/s (kcal/min)  0.016 (0.96)  0.016 (0.96) 
The fit resulted in a rootmeansquare deviation (RMSD) of 0.96 kcal/min for both women and men. A boxplot of the percentage errors of all trials is given in
Here
The predictions made by Fitbit Surge had an RMSD of 2.58 kcal/min (2.7 times that of the model) and a median percent error of 37.3% (3 times that of the model). However, this high error was mostly due to inaccuracies in sloped walking. When restricted to flat surfaces, the Fitbit Surge’s accuracy increased dramatically, whereas the model’s accuracy increased moderately. The Fitbit Surge’s RMSD on flat surfaces was 1.82 kcal/min (2.3 times that of the model, 0.79 kcal/min), and the median percent error was 18.4% (1.6 times that of the model, 11.2%). Distributions of percent errors are portrayed with boxplots in
Before discussing the implications of these results, we note that the variables
Equation 7 implies that
Boxplots of the percent errors of predictions made by the model and Fitbit Surge. Errors have been estimated via equation 9 in Figure 4.
Step frequency,
We developed a model based on rates of change in kinetic and potential energies. In general, it predicts linear dependence of the energy consumption on these rates; in particular, it predicts quadratic dependence of the energy consumption on the potential energy change in the case of downhill walking. The method, used in conjunction with a foot monitoring system, predicts energy expenditure with an RMSD of 0.98 kcal/min and a median percent error of 12.4%, lower than those of wristworn commercial devices in predicting energy expenditure for walking. With one simple piecewise function, the model adequately predicts energy expenditure for walking in a wide range of the gradient.
Notice the differences in parameter values between women and men. The appreciable difference in the value of
Although the model accounts for varying body mass and step frequency (cadence), this does not account for additional individual variations in parameter values due to walking gait and body dimensions. There may be ways to account for such variations without complicating the model. In addition, because the treadmill incline lies between 14° uphill and 14° downhill, we are not able to validate the model for more extreme slopes [
Prior studies have noted the strong correlations between
Other existing studies have studied energy expenditure during uphill and downhill walking [
Our method fits separately for women and men. Prior validation studies have found differences in the accuracy of devices between the two genders. A comparative validation study found that gender was one of the strongest predictors for accuracy, with a rate significantly higher for men than for women [
We have developed a model that predicts energy expenditure during walking on a gradient surface between 14° uphill and 14° downhill, with an RMSD of 0.98 kcal/min. The model has been used in conjunction with a wearable device, the foot monitoring system, which directly measures footsteps. Thus, it offers an accessible method of measuring energy expenditure in realistic walking settings, where gradient walking is common. Future work may test equation 1 (
rootmeansquare deviation
MY Choi acknowledges support from National Research Foundation of Korea through the Basic Science Research Program (grant No. 2016R1D1A1A09917318 and 2019 R1F1A1046285). MJ Shin and JJ Park acknowledge support from the Wearable Device R&D Project, Pusan National University Hospital, and KT (grant CMITKT05).
None declared.