Running Economy in the Vertical Kilometer

nd promising variables are being developed to analyze performance and fatigue in trail running, such as mechanical power, metabolic power, metabolic cost of transport and mechanical ef ciency. The aim of this study was to analyze the behavior of these variables during a real vertical kilometer eld test. Fifteen trained trail runners, eleven men (from 22 to 38 years old) and four women (from 19 to 35 years old) performed a vertical kilometer with a length of 4.64 km and 835 m positive slope. During the entire race, the runners were equipped with portable gas analyzers (Cosmed K5) to assess their cardiorespiratory and metabolic responses breath by breath. Signi cant differences were found between top-level runners versus low-level runners in the mean values of the variables of mechanical power, metabolic power and velocity. A repeated-measures ANOVA showed signi cant differences between the sections, the incline and the interactions between all the analyzed variables, in addition to differences depending on the level of the runner. The variable of mechanical power can be statistically signi cantly predicted from metabolic power and vertical net metabolic COT. An algebraic expression was obtained to calculate the value of metabolic power. Integrating the variables of mechanical power, vertical velocity and metabolic power into phone apps and smartwatches is a new opportunity to improve

depending on the level of the runner. The variable of mechanical power can be statistically signi cantly predicted from metabolic power and vertical net metabolic COT. An algebraic expression was obtained to calculate the value of metabolic power. Integrating the variables of mechanical power, vertical velocity and metabolic power into phone apps and smartwatches is a new opportunity to improve performance monitoring in trail running. Keywords:performance monitoring; energy expenditure; human movement; trail running 1. Introduction Over the past decade, there has been a signi cant increase in interest in sport eld applications, driven by both users and technological companies. This interest has been propelled by advancements in the development of wearable sensors based on micro- electromechanical systems (MEMSs) [1]. These sensors nd application during training sessions and sports competitions, serving the purpose of monitoring the internal training load [2], scheduling workouts and tracking the athlete's tness level progression. To achieve this objective, it is essential to develop automated assessment methods that analyze highly accurate variables capable of re ecting the physiological, metabolic, biomechanical and neuromuscular state of the athlete. Additionally, these methods should be easily implemented in low-cost sensors, such as inertial measurement units, linear transducers, potentiometers and global navigation satellite systems, among others [3]. Trail running races have increasingly gained the interest of amateur and professional runners around the world due to their great accessibility and low economic cost. Speci cally, the vertical kilometer is a trend in trail running. In this modality, the athletes must complete a course of an approximately 1000 m vertical climb in a maximum of 5000 m total race length, although these parameters could change between different races, according to the rules of the International Skyrunning Federation [4]. Research on key performance parameters, both in road and trail running, has been a growing target of analysis by numerous health and sport science researchers. The aim of these studies is to understand in more depth those factors correlated with running Sensors2023,23, 9349.

in road and trail running, has been a growing target of analysis by numerous health and sport science researchers. The aim of these studies is to understand in more depth those factors correlated with running Sensors2023,23, 9349.

Sensors2023,23, 9349 2 of 19 performance to later be able to apply this knowledge in the creation of personalized trackers that can be implemented in phone apps and smartwatches. With technological advances, many scientists have developed new promising concepts whose assessment seems to be sensitive to physiological and biomechanical modi cations during running and which may be suitable real feedback measures of performance and training monitoring in trail running and vertical kilometers. These concepts are the running economy, the net metabolic power, the mechanical vertical center of mass power, the net mechanical ef ciency, the net metabolic cost of transport and the vertical net metabolic cost of transport. Running economy is de ned as the oxygen uptake (VO2) required to run a given distance or run at a given submaximal velocity [5]. This parameter can also be de ned and calculated in energy terms as the amount of energy liberated per liter of oxygen, denomi- nated in this case as net metabolic rate or power (Cmetab) (kcal min 1 kg 1 or W kg 1 ). It is calculated by measuring the steady-state consumption of oxygen (VO2) and the respira- tory exchange ratio [6] and is considered a physiological determinant of endurance running. This variable is multifactorial, depending on metabolic, cardiorespiratory, biomechanical and neuromuscular factors [7], such as heart rate, minute ventilation, substrate utilization, muscle ber type and core temperature, among many other variables, and is a new concept that re ects the physiological and neuromuscular state of the athlete [8]. It is currently considered more sensitive than VO2itself when used to observe performance differences between runners [7,9]. The mechanical vertical power of the center of mass (Cmec) is de ned as the external mechanical work performed to lift the body mass at each running stride, calculated by multiplying the vertical running velocity by the weight of the subject. Recent studies related to running power have found a linear relationship between running power and aerobic power (VO2consumption) [10,11]. In addition, lower limb power is related to running spatiotemporal improvements (increased contact time), reduction in the energy cost of running [12]

body mass at each running stride, calculated by multiplying the vertical running velocity by the weight of the subject. Recent studies related to running power have found a linear relationship between running power and aerobic power (VO2consumption) [10,11]. In addition, lower limb power is related to running spatiotemporal improvements (increased contact time), reduction in the energy cost of running [12] and reduction in the increase in energy cost of running due to fatigue in trail running [13]. Speci cally, in vertical kilometers, runners must overcome extreme uphill running slopes, lifting the center of body mass in each step more than in level running by increasing the net mechanical work. This mechanism entails an increase in energy expenditure and a poorer mechanical advantage for producing force against the ground by the hip extensors [14]. Finally, from the previous concepts, the parameters of net mechanical ef ciency, net metabolic cost of transport and vertical net metabolic cost of transport have emerged. The rst authors to evaluate these parameters were Margaria et al., (1963) [15] andMinetti et al., (2002) [16]. They calculated the net metabolic cost of transport (both walking and running) (cost of walking (Cw) and cost of running (Cr)) by dividing the metabolic power or rate by running or walking velocity (vertical velocity for the vertical net metabolic cost of transport (VCw and VCr)). This parameter is a key factor in road running [4] and describes the amount of energy needed to transport a kilogram of body mass per unit of distance covered (kcal kg 1 km 1 or J kg 1 m 1 ). In their studies, Margaria et al., (1963) [15] and Minetti et al., (2002) [16] observed that the metabolic cost of running (Cr) was dependent on gradient and independent of speed, except for the steepest positive slopes (above 15% or 8.5 ). Based on these data, subsequent studies have found a great increase in Cr between slopes among runners, whose cause is still unknown, since uphill Cr correlates with neither level Cr nor with biomechanical parameters, such as stride frequency, stride length and body mass index [17].

and independent of speed, except for the steepest positive slopes (above 15% or 8.5 ). Based on these data, subsequent studies have found a great increase in Cr between slopes among runners, whose cause is still unknown, since uphill Cr correlates with neither level Cr nor with biomechanical parameters, such as stride frequency, stride length and body mass index [17]. Likewise, there is no correlation between either the initial Cr values or the changes in Cr values before and after the trail running race with performance time, in contrast to the observed correlation in road running [18]. The increase in Cr with a positive incline is due to an increase in power output and greater muscular activity at all joints, especially in the hip [19]. Unlike level running, where the center of mass behavior oscillates cyclically and both potential and kinetic energy uctuation are in-phase during the stride [20], in uphill running above 15% (8.5 ), positive work predominately

Sensors2023,23, 9349 3 of 19 lifts the center of mass and decreases the use of elastic energy (the stretch–shortening cycle mechanism disappears) and bouncing mechanisms [21,22]. Consequently, the metabolic demand increases, coinciding with an increase in blood lactate values and cardiorespiratory values [17,19,23]. In connection with the concepts of mechanical and metabolic power, Margaria et al., (1963) [15] and Minetti et al., (2002) [16] also introduced the concept of net mechanical ef ciency (Eff) by explaining the ratio of these two variables. In their analysis, they observed that trained athletes were only 5–7% more ef cient than non-athletes [15]. They predicted that mechanical ef ciency was approximately 22–24% with positive slopes above 15% (8.5 ) and 25% above 20% (11.3 ), corresponding to concentric muscle contraction [15,16]. Peyr²-Tartaruga et al., (2018) [24] proposed that overall ef ciency in locomotion (walking and running) is determined by muscular ef ciency, de ned as the fraction of metabolic energy transformed into muscular mechanical work, and transmission ef ciency, de ned as the fraction of muscular mechanical work utilized as total work. However, for practical purposes, the concept net mechanical ef ciency (Eff) is considered the fraction of metabolic power transformed into mechanical power or total work. These authors also contended that if the ef ciency value was close to 25% (indicating pure concentric muscle ef ciency), it would suggest good ef ciency transmission. If the value exceeded 25%, it would indicate that passive elastic elements in series within muscles (fascial tissues) and tendons provided either the same or signi cant negative work. Based on the studies analyzed to date, most research has been conducted on a treadmill in trail running, and any study of the vertical kilometer was executed through a eld test. For these reasons, the present study aims to determine the correlation with performance in the previously mentioned concepts (Cmec, Cmetab, Cw, Cr, Vcw, VCr and Eff), as well as to observe the effect of fatigue on these concepts during the progress of a vertical kilometer eld test. 2. Materials and Methods 2.1. Participants Fifteen trained trail runners participated in the

For these reasons, the present study aims to determine the correlation with performance in the previously mentioned concepts (Cmec, Cmetab, Cw, Cr, Vcw, VCr and Eff), as well as to observe the effect of fatigue on these concepts during the progress of a vertical kilometer eld test. 2. Materials and Methods 2.1. Participants Fifteen trained trail runners participated in the study (eleven males, four females). Demographic, anthropometric and training level data are presented in Table. All runners had been training regularly for more than 3 years, and none of them had a history of musculoskeletal injuries in the last year. Before the experiment, all subjects were informed about the objectives, bene ts and risks of the investigation, and they signed an informed consent form. The experimental protocol received approval from the University Ethics Committee (Ref 005-19/20), and all procedures adhered to the principle of the Declaration of Helsinki. Table 1.Demographic, anthropometric and training level data. Men Women Age (years) 22–38 * 19–35 * 28.4 5.11 27.7 6.70 Height (cm) 174 4.54 163 2.36 Body mass (kg) 69.8 5.56 54 4.08 BMI (kg/m 2 ) 22.8 1.63 20.2 1.01 Running training duration per session (min) 52 7.58 60 21.6 Running training frequency per week (days/week) 4.40 1.14 4.75 1.26 Pre-test heart rate (bpm) 73.8 10.7 79.5 3.31 HR change (%) 16.1 4.99 61.2 56.6 VO2peak (mL/kg/min) 65.8 7.00 57.9 6.61 Values: Mean SD. BMI: body mass index. HR change: percentage change in heart rate during the vertical kilometer test. VO2peak achieved in the vertical kilometer test. *: age range of participants.

Sensors2023,23, 9349 4 of 19 2.2. Procedure Each participant completed a vertical kilometer (VK) route spanning 4.64 km with a positive slope of 835 m. The vertical kilometer entails a continuous uphill test, comprising natural segments with varying positive inclinations ranging from 0 to 20 on this speci c route. To facilitate analysis, the route was divided into three equal parts, each measuring 1.58 km, as illustrated in Figure. Within each of these segments, ve sections with a constant slope were chosen (0 , 5 , 10 , 15 , and 20 positive slope). Each section had to last a minimum of 30 s to extract stable physiological data. Furthermore, to ensure data stability, only the central 20 s of each section were analyzed, excluding the initial and nal portions of the positive slope.Sensors 2023, 23, x FOR PEER REVIEW 4 of 19 Values: Mean ± SD. BMI: body mass index. HR change: percentage change in heart rate during the vertical kilometer test. VO 2 peak achieved in the vertical kilometer test. *: age range of participants. 2.2. Procedure Each participant completed a vertical kilometer (VK) route spanning 4.64 km with a positive slope of 835 m. The vertical kilometer entails a continuous uphill test, comprising natural segments with varying positive inclinations ranging from 0° to 20° on this specific route. To facilitate analysis, the route was divided into three equal parts, each measuring 1.58 km, as illustrated in Figure 1. Within each of these segments, five sections with a con- stant slope were chosen (0°, 5°, 10°, 15°, and 20° positive slope). Each section had to last a minimum of 30 s to extract stable physiological data. Furthermore, to ensure data stability, only the central 20 s of each section were analyzed, excluding the initial and final portions of the positive slope. Figure 1. Vertical kilometer track. Race course divided into 3 sections of 1.58 km. 2.3. Measurements 2.3.1. Metabolic Data Throughout the entire course, the runners were equipped with a portable gas ana- lyzer (Cosmed K5 (Rome, Italy)) to assess cardiorespiratory and metabolic responses on a breath-by-breath basis.

section were analyzed, excluding the initial and final portions of the positive slope. Figure 1. Vertical kilometer track. Race course divided into 3 sections of 1.58 km. 2.3. Measurements 2.3.1. Metabolic Data Throughout the entire course, the runners were equipped with a portable gas ana- lyzer (Cosmed K5 (Rome, Italy)) to assess cardiorespiratory and metabolic responses on a breath-by-breath basis. This measurement was facilitated by a turbine flowmeter attached to a properly fitted face mask. The gas analyzer was secured to the runner’s back using a harness, and the entire system weighted 900 g. To ensure time alignment, the analyzed parameters from the gas analyzer (including GPS data) were synchronized and stored in the data logger. Calibration of the Cosmed system was performed before each measure- ment, using a calibration syringe (3L) for the turbine. The oxygen (O 2) and carbon dioxide (CO 2) sensors of the gas analyzer were also calibrated to ambient air conditions (20.93% O 2 and 0.03% CO2), along with delay calibration. Each experimental day commenced with determining the metabolic rate during a 10-min standing trial. Subsequently, rates of ox- ygen consumption (VO 2) and carbon dioxide production (VCO2) were measured using the Cosmed K5 analyzer. For statistical analysis, the data for each slope and section were av- eraged over the selected 20-s intervals. 1600 m 1400 m 1200 m 1000 m 800 m Figure 1.Vertical kilometer track. Race course divided into 3 sections of 1.58 km. 2.3. Measurements 2.3.1. Metabolic Data Throughout the entire course, the runners were equipped with a portable gas analyzer (Cosmed K5 (Rome, Italy)) to assess cardiorespiratory and metabolic responses on a breath- by-breath basis. This measurement was facilitated by a turbine owmeter attached to a properly tted face mask. The gas analyzer was secured to the runner's back using a harness, and the entire system weighted 900 g. To ensure time alignment, the analyzed parameters from the gas analyzer (including GPS data) were synchronized and stored in the data logger. Calibration of the Cosmed system was performed before each measurement, using a calibration syringe (3L) for the turbine. The oxygen

gas analyzer was secured to the runner's back using a harness, and the entire system weighted 900 g. To ensure time alignment, the analyzed parameters from the gas analyzer (including GPS data) were synchronized and stored in the data logger. Calibration of the Cosmed system was performed before each measurement, using a calibration syringe (3L) for the turbine. The oxygen (O2) and carbon dioxide (CO2) sensors of the gas analyzer were also calibrated to ambient air conditions (20.93% O2and 0.03% CO2), along with delay calibration. Each experimental day commenced with determining the metabolic rate during a 10-min standing trial. Subsequently, rates of oxygen consumption (VO2) and carbon dioxide production (VCO2) were measured using the Cosmed K5 analyzer. For statistical analysis, the data for each slope and section were averaged over the selected 20-s intervals.

Sensors2023,23, 9349 5 of 19 2.3.2. Calculations The calculation of mechanical vertical center of mass (COM) power (Watts/kg) utilized GPS velocity and incline, as expressed in (Equation (1)): Mechanical vertical COM power = g v sin ( ) (1) where represents the incline in degrees, and v is the instantaneous velocity in m/s. Net metabolic power (Watts/kg) was calculated from running respiratory measure- ments using the Peronnet and Massicot equation [6], adjusted by subtracting the standing metabolic rate measured 10 min before the test. The calculation is outlined in(Equation (2)): Net Metabolic power = ((16.89 VO2+ 4.84 VCO2)/kg) standing metabolic rate (2) The net mechanical ef ciency was derived by dividing the mechanical vertical COM power by the net metabolic power, as illustrated in (Equation (3)) [25]: Net mechanical ef ciency = Mechanical vertical COM power/Net metabolic power (3) The net metabolic cost of transport (J/kg/m) was computed by dividing the net metabolic power by the running velocity, representing the mean net metabolic cost per unit distance traveled parallel to the running surface. (Equation (4)) summarizesthis calculation: Net Metabolic COT = Net metabolic power/v (4) The vertical net metabolic cost of transport (J/kg/m) was determined by dividing the net metabolic power by vertical velocity, factored by the mean net metabolic cost to ascend a vertical meter. (Equation (5)) outlines this computation: Vertical Net Metabolic COT = Net metabolic power/v sin ( ) (5) 2.4. Statistical Analysis The following statistical analysis of the data was conducted: Normality testing: the Shapiro–Wilk test was used to assess the normality ofthe variables. Gender and performance level comparison: A T-student parametric test was employed to compare gender and performance level differences. The sample was divided into quartiles based on the nal test time, and values from the rst quartile were compared to the remaining quartiles. Comparison of assessed variables: A two-factor repeated-measures ANOVA was utilized to compare means across multiple analyzed variables. The analysis compared three sections and ve positive slopes in each section. Before applying ANOVA, the Mauchly's sphericity test was performed. If sphericity was rejected, the univariated F-statistic was used, adjusted with the

This study analyzes performance variables during a vertical kilometer field test.