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

ning power is a popular measure to gauge objective intensity. It has recently been shown, though, that foot-worn sensors alone cannot re ect variations in the exerted energy that stems from changes in the running economy. In order to support long-term improvement in running, these changes need to be taken into account. We propose leveraging the presence of two additional sensors worn by the most ambitious recreational runners for improved measurement: a watch and a heart rate chest strap. Using these accelerometers, which are already present and distributed over the athlete's body, carries more information about metabolic demand than a single foot-worn sensor. In this work, we demonstrate the mutual information between acceleration data and the metabolic demand of running by leveraging the information bottleneck of a constrained convolutional neural network. We perform lab measurements on 29 ambitious recreational runners (age = 28 7 years, weekly running distance = 50 25 km, VO2max= 60.3 7.4 mL min 1 kg 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 signi cantly

lab measurements on 29 ambitious recreational runners (age = 28 7 years, weekly running distance = 50 25 km, VO2max= 60.3 7.4 mL min 1 kg 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 signi cantly 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. Keywords: running power; running economy; accelerometers; bluetooth low energy beacons; convolutional neural networks; information bottleneck 1. Introduction Accurate measurement of metabolic demand during running is relevant for both athletic training and rehabilitation [1]. Gold-standard methods to measure metabolic demand (such as indirect calorimetry via respiratory gas exchange) are infeasible in the eld and unpractical for everyday use by recreational runners. Similar to the use of power meters in cycling, foot sensors have recently been used for measuring power when running [2–6]. In contrast to cycling though [7], the ef ciency with which an individual converts metabolic intake into the force exerted on the ground during running, known as the running economy (RE) [8], can vary widely between individuals [9]. As such, it is important for long-term training success to consider changes in the running economy [10]. It has recently been shown that foot-worn sensors are limited when it comes to adaptation to changing the running economies [11]. In this work, we explore the possibility of improving the measurement of metabolic demand during running by leveraging additional sensors commonly worn by recreational runners [12]. By collecting data from a combination of foot-, torso-, and arm-based sensors, we aim to gain a more comprehensive understanding of the kinetics of an athlete and the relationship between kinetics, kinematics, and metabolism. Our results show that Sensors2023,23, 1756.

arm-based sensors, we aim to gain a more comprehensive understanding of the kinetics of an athlete and the relationship between kinetics, kinematics, and metabolism. Our results show that Sensors2023,23, 1756.

Sensors2023,23, 1756 2 of 14 the combination of these three sensors provides additional information about an athlete's metabolism. In addition, this investigation motivates further studies into the link between kinetics, kinematics, and metabolism and the potential for using these insights to inform the development of optimal running form. Long-distance running performance can be assessed by energy expenditure. Humans have limited, immediately available energy storage [13–15], and, therefore, the rate of energy consumption at a certain pace is the limiting factor for running performance [16]. A good proxy for energy expenditure is oxygen uptake, which has been shown to correlate highly with energy expenditure [17,18]. In our experiments, we directly measure the consumed oxygen VO2via a spirometry system, measuring the rate of oxygen consumption in liters per minute (L min 1 ). The factor between mechanical and metabolic oxygen consumption, i.e., the relative difference between the external work performed and energy consumed, is de ned as the running economyRE[8,19]. The more energy that is lost without being used for forward propulsion, the lower theRE[20]. The running economy can also be described as the factor between external and internal work, and we distinguish between the external mechanical energy that is observed in kinetic forces and the internal metabolic energy that is consumed by the athlete [20,21]. Our work is based on a study by Baumgartner et al. [11]. In their study, the authors aimed to determine the validity of foot-worn sensors for measuring running power. They found that while these sensors can accurately measure power under steadyREconditions, they are no longer valid whenREis altered. In their study, they conducted an experiment to alter participants' running style in ways that are known to affectRE[22,23] and found that the changes in metabolic cost were not re ected in power measured by the foot-worn sensors. They concluded that running power measured by these sensors is only a useful measure in situations where the athlete's running style does not vary or change. Therefore, using these devices to organize long-term training may not have the intended effects, as changes inREcan lead to arbitrary changes in displayed power.

not re ected in power measured by the foot-worn sensors. They concluded that running power measured by these sensors is only a useful measure in situations where the athlete's running style does not vary or change. Therefore, using these devices to organize long-term training may not have the intended effects, as changes inREcan lead to arbitrary changes in displayed power. In this work, we showcase unpublished data that was recorded simultaneously with the previous work by Baumgartner et al. [11]. The sensors in this previous investigation were based on acceleration data collected at the foot. In this follow-up investigation, we show that the previous results could be improved by using two additional sensors that many recreational runners already wear for their routine running: a watch on the arm and a chest strap. Using sensors at three different locations could yield a more accurate method for measuring running power. By measuring acceleration at three different body positions, it is possible to capture more information about the movement of the body on top of the forces being applied to the ground. This additional information can be used to accurately calculate mechanical power, which more closely relates to metabolic power than the power measured by just a single foot-worn sensor. In our experiment, we train deep neural networks to demonstrate the connection between data from accelerometers and respiratory gases. During the training process, the network is presented with a set of input-output pairs and attempts to learn a function that maps the input to the output. The network makes predictions for a given input and compares these predictions to the true output. The difference between the predicted and true output is known as the error. The network consists of multiple layers for transforming its input into an output. These transformations consist of multiplications and additions of various combinations of inputs, as well as pooling operations (such as averaging or taking the maximum) and non-linearities (setting any value below zero to zero). Each layer has a certain set of parameters that de ne its transformation and, therefore, determine how some input is transformed into

its input into an output. These transformations consist of multiplications and additions of various combinations of inputs, as well as pooling operations (such as averaging or taking the maximum) and non-linearities (setting any value below zero to zero). Each layer has a certain set of parameters that de ne its transformation and, therefore, determine how some input is transformed into an output [24]. During training, the network adjusts its parameters in an attempt to minimize the error. The process of adjusting the parameters is known as backpropagation: At each layer, the error is used to calculate the gradient of the error with respect to the layer's parameters. The gradient is then used to update the parameters in a direction that reduces the error.

Sensors2023,23, 1756 3 of 14 In our proof below, we use arguments inspired by the information bottleneck method as proposed by Tishby et al. [25]. They propose a framework for understanding the trade- off between the amount of information that can be preserved in a signal and the amount of information that can be transmitted through a communication channel. In our scenario, we use a channel with known, limited capacity, which is purposefully underpowered. We achieve this by de ning a model with less trainable parameters than data points. Thereby, we know that the only way that our model can pass information through this channel is by encoding signals about the actually observed phenomenon. We use this bottleneck to demonstrate that there is, in fact, information about the metabolic energy expenditure contained in accelerometer data. Moreover, using sensors at three separate, distributed locations allows for capturing more of that contained information. It follows that novel products for running power should combine foot-worn sensors with sensors in watches and heart-rate chest straps. The objective of the present study is to investigate avenues for improving the mea- surement of metabolic demand in the eld. We aim to mitigate the shortcomings of current commercial products by incorporating additional sensors typically worn by recreational runners. While a single foot-worn sensor does not contain enough information about the metabolic demand under changing running economy, we hypothesize that three sensors on the foot, torso, and arm allow improving approximations. 2. Materials and Methods 2.1. Subjects and Testing Procedure A total of 32 moderately endurance-trained runners participated in a controlled crossover trial. Due to partial Bluetooth connection problems, three out of the 32 sub- jects had to be excluded from this investigation, and in the following, we use data from the remaining 29 subjects: 19 males and 10 females with a mean age of 28 7 years and a mean BMI of 21.6 1.6. These participants had run an average of 50 25 km per week in the preceding four weeks, had a mean running VO2maxof 60.3 7.4 mL min 1 kg 1 , had at least

use data from the remaining 29 subjects: 19 males and 10 females with a mean age of 28 7 years and a mean BMI of 21.6 1.6. These participants had run an average of 50 25 km per week in the preceding four weeks, had a mean running VO2maxof 60.3 7.4 mL min 1 kg 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 VO2max[27]. The test protocol, which took place in a single laboratory visit, included an incremental VO2maxsignal sill test followed by a 25-min treadmill run with varying predetermined spatiotemporal running parameters after a 30-min rest. During the incremental exercise test, subjects performed four 3 min stages at increasing speeds, of which we considered the last 60 s each, as indicated by the dashed lines in Figure. During the “altered running economy” portion of the experiments, athletes ran with (1) their own running form, (2) increased step frequency, (3) decreased step frequency, (4) shortened ground contact time, (5) immobilized arms, and (6) their own form again to gauge fatigue. Each condition was run for 3 min, with a 1 min washout phase at a normal running form in between. The last 60 s of each condition were used for our investigation. We removed data from condition (5) from this investigation since it is not a natural running form and randomized the order of the remaining altered conditions. Figure testing procedure for the altered running conditions that are part of the experiment. The participants were instructed to refrain from intense exercise for 48 h prior to the test. Throughout the above tests, participants wore a heart rate monitor chest strap (Garmin, Olathe, KS, USA). Spirometric data was collected using a breath-by-breath spirometric system (Zan 600, Zan Messgeräte, Oberthulba, Germany) and calibrated prior to each test, following the manufacturer's instructions. In addition, capillary blood samples from the earlobe were taken during the 30

48 h prior to the test. Throughout the above tests, participants wore a heart rate monitor chest strap (Garmin, Olathe, KS, USA). Spirometric data was collected using a breath-by-breath spirometric system (Zan 600, Zan Messgeräte, Oberthulba, Germany) and calibrated prior to each test, following the manufacturer's instructions. In addition, capillary blood samples from the earlobe were taken during the 30 s rest periods between stages in the ramp test for lactate analysis (EBIOplus; EKF Diagnostic Sales, Magdeburg, Germany). The lactate analysis informed the pace at which the test with the modulated running economy was performed. All data, their synchronization, and the order of experiments are illustrated in Figure.

Sensors2023,23, 1756 4 of 14 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: VO2; 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 modi ed running condition; black boxes mark the VO2 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 VO2and 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. 2.2. Accelerometer Data Subjects wore custom-made sensor suits during the study, which consisted of com- pression pants and long-sleeve shirts with pockets that held battery-powered microcon- troller boards (Bluetooth beacons). To ensure a secure t and minimize sensor wobbling,

Sensors2023,23, 1756 5 of 14 each subject received a garment in their size out of a choice of ve typical clothing sizes (cf. Figurea,b). The Bluetooth beacons used in this study were about the diameter (3 cm) and weight (6 g) of a 2 Euro coin (cf. Figurec). They were based on the nRF51822 System-on-Chip microcontroller (Nordic Semiconductors, Trondheim, Norwegen) with built-in Bluetooth Low Energy and contained an MPU-6050 accelerometer (Invensense, San Jose, CA, USA) and other minor peripherals, as well as input and output capabilities. These beacons were powered by rechargeable 3.7 V cell batteries (LIR2032H) and were ordered pre-assembled from AliExpress in 2021 (search terms: “NRF51822 Bluetooth beacon”). A huge advantage of Bluetooth low-energy (BLE) is the namesake low energy con- sumption, which allowed us to run the described con guration for roughly four hours off batteries and without cables. This advantage was bought with low throughput. We developed customized rmware that allowed us to compress and bundle multiple sensor readings and subsequently unpack them onto the receiving master device. Using this method, we achieved accelerometer readings of up to 60 Hz. We calibrated the sensors by laying them at on the table for 30 s. Then subjects stood still with their arms down and jumped from just their ankles (i.e., trying to jump without bending their knees), facing the front of the treadmill. This way, we got the relative orientation of the accelerometer module of the sensors to the world-coordinate system of the treadmill laboratory. (a)(b)(c) 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). Before starting the tests, the subjects performed multiple jumps in order to later synchronize the data with video recordings. The frame in which the athlete reaches the highest point of their jump corresponds to the lowest acceleration between two peak accelerations of the jump-off and landing frames.

Bluetooth beacon (weight = 6 g, diameter = 3 cm, coin for scale). Before starting the tests, the subjects performed multiple jumps in order to later synchronize the data with video recordings. The frame in which the athlete reaches the highest point of their jump corresponds to the lowest acceleration between two peak accelerations of the jump-off and landing frames. An additional beacon with an extra button was also built for the purpose of marking the exact time at which the spirometric recording began, ensuring that VO2and accelerometer data could be synchronized. We recorded data from a total of 12 locations throughout the body: 2 foot, 2 shin, 2 thigh, 2 upper arm, 2 lower arm, hip, and neck (cf. Figurea,b). We will later focus on the output of just three sensors for each subject in order to create a realistic scenario in which recreational runners wear foot sensors, heart rate monitors, and watches. 2.3. Relation between Energy and Sensors Through our experiment, we show that there is information about the metabolism contained in acceleration data. We show the mutual information between the consumed oxygen VO2and the measured accelerationA. In and of itself, this connection is fairly

This study investigates the mutual information between body-worn sensors and metabolic cost in running.