# Revealing the Mutual Information between Body-Worn Sensors and Metabolic Cost in Running

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## Abstract

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^{−1}). We show that information about the metabolic demand of running is contained in kinetic data. Additionally, we prove that the combination of three sensors (foot, torso, and lower arm) carries significantly more information than a single foot-worn sensor. We advocate for the development of running power systems that incorporate the sensors in watches and chest straps to improve the validity of running power and, thereby, long-term training planning.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Subjects and Testing Procedure

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^{−1}, had at least one year of distance running experience, and were injury-free for at least three months. Participants wore their own footwear and participated in a combined incremental and ramp exercise test to determine their velocity at the aerobic threshold (AeT) [26] and their $\dot{\mathrm{V}}{\mathrm{O}}_{2\mathrm{max}}$ [27]. The test protocol, which took place in a single laboratory visit, included an incremental $\dot{\mathrm{V}}{\mathrm{O}}_{2\mathrm{max}}$ signal sill test followed by a 25-min treadmill run with varying predetermined spatiotemporal running parameters after a 30-min rest.

#### 2.2. Accelerometer Data

#### 2.3. Relation between Energy and Sensors

#### 2.4. Extracting Information

#### 2.4.1. Deep Learning Model

#### 2.4.2. Indirect Proof of Mutual Information Content

## 3. Results

## 4. Discussion

#### 4.1. Limitations

#### 4.2. Future Work and Extensions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Tjelta, L.I. Three Norwegian brothers all European 1500 m champions: What is the secret? Int. J. Sport. Sci. Coach.
**2019**, 14, 694–700. [Google Scholar] [CrossRef] - Soulard, J.; Vaillant, J.; Balaguier, R.; Baillet, A.; Gaudin, P.; Vuillerme, N. Foot-Worn Inertial Sensors Are Reliable to Assess Spatiotemporal Gait Parameters in Axial Spondyloarthritis under Single and Dual Task Walking in Axial Spondyloarthritis. Sensors
**2020**, 20, 6453. [Google Scholar] [CrossRef] - Huang, Y.; Jirattigalachote, W.; Cutkosky, M.R.; Zhu, X.; Shull, P.B. Novel Foot Progression Angle Algorithm Estimation via Foot-Worn, Magneto-Inertial Sensing. IEEE Trans. Biomed. Eng.
**2016**, 63, 2278–2285. [Google Scholar] [CrossRef] - Falbriard, M.; Meyer, F.; Mariani, B.; Millet, G.P.; Aminian, K. Accurate Estimation of Running Temporal Parameters Using Foot-Worn Inertial Sensors. Front. Physiol.
**2018**, 9, 610. [Google Scholar] [CrossRef] - García-Pinillos, F.; Roche-Seruendo, L.E.; Marcén-Cinca, N.; Marco-Contreras, L.A.; Latorre-Román, P.A. Absolute Reliability and Concurrent Validity of the Stryd System for the Assessment of Running Stride Kinematics at Different Velocities. J. Strength Cond. Res.
**2021**, 35, 78–84. [Google Scholar] [CrossRef] - Scataglini, S.; Cools, E.; Neyrinck, J.; Verwulgen, S. An Exploratory Analysis of User Needs and Design Issues of Wearable Technology for Monitoring Running Performances. Adv. Intell. Syst. Comput.
**2021**, 1206, 207–215. [Google Scholar] [CrossRef] - Ettema, G.; Lorås, H.W. Efficiency in cycling: A review. Eur. J. Appl. Physiol.
**2009**, 106, 1–14. [Google Scholar] [CrossRef] - Barnes, K.R.; Kilding, A.E. Running economy: Measurement, norms, and determining factors. Sport. Med.-Open
**2015**, 1, 1–15. [Google Scholar] [CrossRef] - Muniz-Pardos, B.; Sutehall, S.; Gellaerts, J.; Falbriard, M.; Mariani, B.; Bosch, A.; Asrat, M.; Schaible, J.; Pitsiladis, Y.P. Integration of Wearable Sensors into the Evaluation of Running Economy and Foot Mechanics in Elite Runners. Curr. Sport. Med. Rep.
**2018**, 17, 480–488. [Google Scholar] [CrossRef] - Seiler, S.; Tønnessen, E. Intervals, thresholds, and long slow distance: The role of intensity and duration in endurance training. Sportscience
**2009**, 13, 1–27. [Google Scholar] - Baumgartner, T.; Held, S.; Klatt, S.; Donath, L. Limitations of Foot-Worn Sensors for Assessing Running Power. Sensors
**2021**, 21, 4952. [Google Scholar] [CrossRef] - Janssen, M.; Walravens, R.; Thibaut, E.; Scheerder, J.; Brombacher, A.; Vos, S. Understanding different types of recreational runners and how they use running-related technology. Int. J. Environ. Res. Public Health
**2020**, 17, 2276. [Google Scholar] [CrossRef] - Wasserman, D.H. Four grams of glucose. Am. J. Physiol.-Endocrinol. Metab.
**2009**, 296, E11–E21. [Google Scholar] [CrossRef] - Kreitzman, S.N.; Coxon, A.Y.; Szaz, K.F. Glycogen storage: Illusions of easy weight loss, excessive weight regain, and distortions in estimates of body composition. Am. J. Clin. Nutr.
**1992**, 56, 292S–293S. [Google Scholar] [CrossRef] - Jeukendrup, A.E. Nutrition for endurance sports: Marathon, triathlon, and road cycling. In Food, Nutrition and Sports Performance III; Routledge: Oxfordshire, UK, 2013; pp. 99–108. [Google Scholar] [CrossRef]
- Joyner, M.J. Modeling: Optimal marathon performance on the basis of physiological factors. J. Appl. Physiol.
**1991**, 70, 683–687. [Google Scholar] [CrossRef] - Hagan, R.; Strathman, T.; Strathman, L.; Gettman, L. Oxygen uptake and energy expenditure during horizontal treadmill running. J. Appl. Physiol.
**1980**, 49, 571–575. [Google Scholar] [CrossRef] - Mayhew, J. Oxygen cost and energy expenditure of running in trained runners. Br. J. Sport. Med.
**1977**, 11, 116–121. [Google Scholar] [CrossRef] - Snyder, K. Running Power Definition and Utility. 2020. Available online: https://blog.stryd.com/2020/12/17/running-power-definition-utility-article/ (accessed on 19 May 2021).
- Willems, P.; Cavagna, G.; Heglund, N. External, internal and total work in human locomotion. J. Exp. Biol.
**1995**, 198, 379–393. [Google Scholar] [CrossRef] - How to Lead the Pack: Running Power Meters & Quality Data. 2017. Available online: https://blog.stryd.com/2017/12/07/how-to-lead-the-pack-running-power-meters-quality-data/ (accessed on 19 May 2021).
- Morgan, D.; Martin, P.; Craib, M.; Caruso, C.; Clifton, R.; Hopewell, R. Effect of step length optimization on the aerobic demand of running. J. Appl. Physiol.
**1994**, 77, 245–251. [Google Scholar] [CrossRef] - de Ruiter, C.J.; Verdijk, P.W.; Werker, W.; Zuidema, M.J.; de Haan, A. Stride frequency in relation to oxygen consumption in experienced and novice runners. Eur. J. Sport Sci.
**2014**, 14, 251–258. [Google Scholar] [CrossRef] - Goodfellow, I.; Bengio, Y.; Courville, A. Deep Learning; MIT Press: Cambridge, MA, USA, 2016; Available online: http://www.deeplearningbook.org (accessed on 31 January 2022).
- Tishby, N.; Pereira, F.C.; Bialek, W. The information bottleneck method. arXiv
**2000**. [Google Scholar] [CrossRef] - Lehmann, M.; Berg, A.; Kapp, R.; Wessinghage, T.; Keul, J. Correlations between Laboratory Testing and Distance Running Performance in Marathoners of Similar Performance Ability. Int. J. Sport. Med.
**1983**, 4, 226–230. [Google Scholar] [CrossRef] - Midgley, A.W.; McNaughton, L.R.; Polman, R.; Marchant, D. Criteria for Determination of Maximal Oxygen Uptake. Sport. Med.
**2007**, 37, 1019–1028. [Google Scholar] [CrossRef] - Moore, I.S. Is There an Economical Running Technique? A Review of Modifiable Biomechanical Factors Affecting Running Economy. Sport. Med.
**2016**, 46, 793–807. [Google Scholar] [CrossRef] - Barnes, K.R.; Kilding, A.E. A Randomized Crossover Study Investigating the Running Economy of Highly-Trained Male and Female Distance Runners in Marathon Racing Shoes versus Track Spikes. Sport. Med.
**2018**, 49, 331–342. [Google Scholar] [CrossRef] - Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] - Kreer, J. A question of terminology. IRE Trans. Inf. Theory
**1957**, 3, 208. [Google Scholar] [CrossRef] - Cover, T.M.; Thomas, J.A. Entropy, relative entropy and mutual information. Elem. Inf. Theory
**1991**, 2, 12–13. [Google Scholar] - Kingma, D.P.; Ba, J. Adam: A method for stochastic optimization. arXiv
**2014**. [Google Scholar] [CrossRef] - Sárándi, I.; Linder, T.; Arras, K.O.; Leibe, B. MeTRAbs: Metric-Scale Truncation-Robust Heatmaps for Absolute 3D Human Pose Estimation. IEEE Trans. Biom. Behav. Identity Sci.
**2021**, 3, 16–30. [Google Scholar] [CrossRef] - Chen, J.; Little, J.J. Sports camera calibration via synthetic data. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, Long Beach, CA, USA, 16–17 June 2019. [Google Scholar]
- Xie, K.; Wang, T.; Iqbal, U.; Guo, Y.; Fidler, S.; Shkurti, F. Physics-based Human Motion Estimation and Synthesis from Videos. In Proceedings of the IEEE/CVF International Conference on Computer Vision, Nashville, TN, USA, 19–25 June 2021. [Google Scholar]
- Li, S.; Xue, J.J.; Hong, P.; Song, C.; He, Z.H. Comparison of energy expenditure and substrate metabolism during overground and motorized treadmill running in Chinese middle-aged women. Sci. Rep.
**2020**, 10, 1815. [Google Scholar] [CrossRef][Green Version] - Bailey, J.; Mata, T.; Mercer, J.A. Is the relationship between stride length, frequency, and velocity influenced by running on a treadmill or overground? Int. J. Exerc. Sci.
**2017**, 10, 1067. [Google Scholar] - McGillem, C.; Cooper, G. Continuous and Discrete Signal and Systems Analysis; Holt, Rinehart and Winston: New York, NY, USA, 1974. [Google Scholar]
- Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A.N.; Kaiser, L.; Polosukhin, I. Attention is all you need. Adv. Neural Inf. Process. Syst.
**2017**, 30. [Google Scholar] [CrossRef]

**Figure 1.**Overview of all collected data for a single athlete: the magnitude of accelerometers at 12 positions on the body (blue); red: heart rate; brown: running power (Stryd); orange: $\dot{\mathrm{V}}{\mathrm{O}}_{2}$; dashed lines = time section used for tests; in the left half is the last 60 s of each stage in the graded exercise test; on the right are the last 60 s of each modified running condition; black boxes mark the $\dot{\mathrm{V}}{\mathrm{O}}_{2}$ average for each section. Best viewed in color.

**Figure 2.**Exemplar protocol for the second part of the experiment and varying spatiotemporal parameters for a single subject. (

**a**) Oxygen consumption $\dot{\mathrm{V}}{\mathrm{O}}_{2}$ and running power as measured using a single foot-worn commercial sensor during the running conditions. (

**b**) Spatiotemporal running parameters of the subject in reaction to instructions for the experimental conditions. Reprinted with permission from Baumgartner et al. [11]. Best viewed in color.

**Figure 3.**(

**a**,

**b**) Picture of sensor suit from front/back. Sensor Beacons are attached to the runner in pink sewn-on pockets (yellow circles) at 12 locations: 2 × feet, 2 × shin, 2 × thigh, 2 × upper arm, 2 × lower arm, hip, and neck. (

**c**) Picture of the used Bluetooth beacon (weight = 6 g, diameter = 3 cm, coin for scale).

**Figure 4.**Correlation between $\dot{\mathrm{V}}{\mathrm{O}}_{2}$ and the average magnitude of acceleration $\mathcal{A}$ during (

**a**) the initial stage-ramp test and during (

**b**) the running experiment with altered running economy. Each line signifies a single athlete. The shade of blue of the line signifies the body weight of the athlete (darker = heavier). Dots signify the different stages in (

**a**) or altered running conditions in (

**b**).

**Figure 5.**(

**a**) Scatter plot of predicted $\dot{\mathrm{V}}{\mathrm{O}}_{2}$ (normalized by body weight and pace) versus correct $\dot{\mathrm{V}}{\mathrm{O}}_{2}$ for a completely trained network. Top: training on noise, middle: training on foot acceleration ${\mathcal{A}}_{\mathrm{f}}$, bottom: training on acceleration from the foot, torso, and arm ${}^{\mathrm{t}}{\mathcal{A}}_{\mathrm{f}}^{\mathrm{a}}$. The training target $\mathcal{L}$ is proportional to the coefficient of determination in this scatter plot and is optimized throughout training by updating the parameters of the model. (

**b**) The progression of training loss $\mathcal{L}$ over time for our model in the three different conditions. The average loss $\mathcal{L}$ of the last 20 training steps (red/blue/orange boxes) is used to compare noise/foot/foot+torso+arm in (

**c**). The single stray light gray shows the validation loss, which does not converge. (

**c**) Averages of final training losses $\mathcal{L}$ over 40 repetitions. Orange: Foot + torso + arm, blue: foot, red: noise. Lines = fitted student-t distribution over the respective repetitions. **: statistically significant difference, p < 0.001.

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**MDPI and ACS Style**

Baumgartner, T.; Klatt, S.; Donath, L.
Revealing the Mutual Information between Body-Worn Sensors and Metabolic Cost in Running. *Sensors* **2023**, *23*, 1756.
https://doi.org/10.3390/s23041756

**AMA Style**

Baumgartner T, Klatt S, Donath L.
Revealing the Mutual Information between Body-Worn Sensors and Metabolic Cost in Running. *Sensors*. 2023; 23(4):1756.
https://doi.org/10.3390/s23041756

**Chicago/Turabian Style**

Baumgartner, Tobias, Stefanie Klatt, and Lars Donath.
2023. "Revealing the Mutual Information between Body-Worn Sensors and Metabolic Cost in Running" *Sensors* 23, no. 4: 1756.
https://doi.org/10.3390/s23041756