Mid Sweden University

Purpose

The aim of this study was to develop and validate a bioenergetic model describing the dynamic behavior of the alactic, lactic, and aerobic metabolic energy supply systems as well as different sources of the total metabolic energy demand.

Methods

The bioenergetic supply model consisted of terms for the alactic, lactic, and aerobic system metabolic rates while the demand model consisted of terms for the corresponding metabolic rates of principal cycling work, pulmonary ventilation, and accumulated metabolites. The bioenergetic model was formulated as a system of differential equations and model parameters were estimated by a non-linear grey-box approach, utilizing power output and aerobic metabolic rate (MRae) data from fourteen cyclists performing an experimental trial (P2) on a cycle ergometer. Validity was assessed by comparing model simulation and measurements on a similar follow-up experimental trial (P3).

Results

The root mean square error between modelled and measured MRae was 61.9 ± 7.9 W and 79.2 ± 30.5 W for P2 and P3, respectively. The corresponding mean absolute percentage error was 8.6 ± 1.5% and 10.6 ± 3.3% for P2 and P3, respectively.

Conclusion

The validation of the model showed excellent overall agreement between measured and modeled MRae during intermittent cycling by well-trained male cyclist. However, the standard deviation was 38.5% of the average root mean square error for P3, indicating not as good reliability.

INTRODUCTION:Dynamic friction is an important parameter in cross-country skate skiing. A reduction of the dynamic frictional coefficient (µ) with 47%can increase the time to exhaustion with 50% when roller-ski skating [1]. With normal ski preparation µ may vary up to 15% due to theski base texture [2]. To isolate the impact of µ on race time, numerical simulations with a power-balance model could be used aspreviously demonstrated [3],[4]. Field measurements have provided more detailed relationships for propulsive power and drag areawith the skating sub-techniques, allowing more reliable simulations [5]. Thus, the aim of this study was to examine the impact ofdifferent dynamic frictional coefficients on the required time to complete a cross-country skate skiing.METHODS:A power balance model for cross-country skate skiing was implemented and solved in Matlab for skiers with body masses of 70, 80and 90 kg respectively. Propulsive power was modelled as a function of speed, acceleration and body mass [5]. Additionally, fivevalues of µ and three wind conditions were examined, giving a total of 45 combinations. These were all simulated on two differentcourses. Total race times were taken from a 15.6 km race (5 laps of the 3 km biathlon race course in Östersund) imported fromGPS-data. Speeds at specific inclination angles were taken from a fictional course with sections of constant inclination angle (meanspeed downhill, steady state speed on the uphill and flat). In the 15.6 km race the ambient winds were aligned to give either 4 m/stailwind in the majority of downhill sections and headwind uphill (4SW), the opposite (4NE) or zero wind. In the fictional course windwas either 4 m/s tailwind, 4 m/s headwind or zero through the entire race.RESULTS:The mean total race time in the 15.6 km race was 2240.7±141.1 s, with shorter race times for the heavier skier (90 kg 19.2±1.3 s < 80kg 22.2±1.3 s < 70 kg) and for tailwind uphill (4NE 5.0±2.0 s < zero wind 5.9±2.0 < 4SW). Changing µ from 0.013 to 0.015 increasedthe total race time for the 70, 80 and 90 kg skiers with 33.6 s (1.53%), 34.0 s (1.57%) and 34.0 s (1.58%) respectively. Changing µfrom 0.025 to 0.027 gave 34.6s (1.44%), 34.2s (1.44%) and 35.1s (1.49%) increased race time for the 70, 80 and 90kg skiersrespectively. The changes in speed from the 70 to 80 to 90 kg skiers were all below 0.43% on the uphill and between 0.70 and 1.53%on the flat and downhill. Changing µ gave largest change in speed for moderate downhill (e.g. 2.15%, µ 0.015 to 0.013) followed byflat (1.29%) and moderate uphill (1.22%).CONCLUSION:An absolute change in µ of 0.002, e.g. a different preparation of the skis, have slightly larger impact on faster (µ~0.014) than slowersnow (µ~0.026) but in both cases could turn the tide in a close race. This change in race time is generated mostly in sections withmoderate or no inclination angle.

The aim of this study was to investigate the influence of slope and speed on lower-limb kinematics and energy cost of running. Six well-trained runners (VO2max 72 ± 6 mL·kg−1·min−1) were recruited for the study and performed (1) VO2max and energy cost tests and (2) an experimental running protocol at two speeds, 12 km·h−1 and a speed corresponding to 80% of VO2max (V80, 15.8 ± 1.3 km·h−1) on three different slopes (0°, −5°, and −10°), totaling six 5-min workload conditions. The workload conditions were randomly ordered and performed continuously. The tests lasted 30 min in total. All testing was performed on a large treadmill (3 × 5 m) that offered control over both speed and slope. Three-dimensional kinematic data of the right lower limb were captured during the experimental running protocol using eight infrared cameras with a sampling frequency of 150 Hz. Running kinematics were calculated using a lower body model and inverse kinematics approach. The generic model contained three, one, and two degrees of freedom at the hip, knee, and ankle joints, respectively. Oxygen uptake was measured throughout the experimental protocol. Maximum hip extension and flexion during the stance phase increased due to higher speed (p < 0.01 and p < 0.01, respectively). Knee extension at the touchdown and maximal knee flexion in the stance phase both increased on steeper downhill slopes (both p < 0.05). Ground contact time (GCT) decreased as the speed increased (p < 0.01) but was unaffected by slope (p = 0.73). Runners modified their hip movement pattern in the sagittal plane in response to changes in speed, whereas they altered their knee movement pattern during the touchdown and stance phases in response to changes in slope. While energy cost of running was unaffected by speed alone (p = 0.379), a shift in energy cost was observed for different speeds as the downhill gradient increased (p < 0.001). Energy cost was lower at V80 than 12 km·h−1 on a −5° slope but worse on a −10° slope. This indicates that higher speeds are more efficient on moderate downhill slopes (−5°), while lower speeds are more efficient on steeper downhill slopes (−10°).

Purpose: To develop a method for individual parameter estimation of four hydraulic-analogy bioenergetic models and to assess the validity and reliability of these models’ prediction of aerobic and anaerobic metabolic utilization during sprint roller-skiing. Methods: Eleven elite cross-country skiers performed two treadmill roller-skiing time trials on a course consisting of three flat sections interspersed by two uphill sections. Aerobic and anaerobic metabolic rate contributions, external power output, and gross efficiency were determined. Two versions each (fixed or free maximal aerobic metabolic rate) of a two-tank hydraulic-analogy bioenergetic model (2TM-fixed and 2TM-free) and a more complex three-tank model (3TM-fixed and 3TM-free) were programmed into MATLAB. The aerobic metabolic rate (MRae) and the accumulated anaerobic energy expenditure (Ean,acc) from the first time trial (STT1) together with a gray-box model in MATLAB, were used to estimate the bioenergetic model parameters. Validity was assessed by simulation of each bioenergetic model using the estimated parameters from STT1 and the total metabolic rate (MRtot) in the second time trial (STT2). Results: The validity and reliability of the parameter estimation method based on STT1 revealed valid and reliable overall results for all the four models vs. measurement data with the 2TM-free model being the most valid. Mean differences in model-vs.-measured MRae ranged between -0.005 and 0.016 kW with typical errors between 0.002 and 0.009 kW. Mean differences in Ean,acc at STT termination ranged between −4.3 and 0.5 kJ and typical errors were between 0.6 and 2.1 kJ. The root mean square error (RMSE) for 2TM-free on the instantaneous STT1 data was 0.05 kW for MRae and 0.61 kJ for Ean,acc, which was lower than the other three models (all P &lt; 0.05). Compared to the results in STT1, the validity and reliability of each individually adapted bioenergetic model was worse during STT2 with models underpredicting MRae and overpredicting Ean,acc vs. measurement data (all P &lt; 0.05). Moreover, the 2TM-free had the lowest RMSEs during STT2. Conclusion: The 2TM-free provided the highest validity and reliability in MRae and Ean,acc for both the parameter estimation in STT1 and the model validity and reliability evaluation in the succeeding STT2. 

Downhill running poses challenges were the gradient is of importance for energy cost and oxygen uptake. While demonstrated that downhill running at a slight gradient is most efficient, the energy cost increases with a steeper gradient (1). However, the additional effect of running speed has not been studied for downhill running. Therefore, the aim of the study was to analyse the combined effect of gradient and speed in downhill running on oxygen cost and running economy. METHODS:Runners (n=6) were recruited for the study and performed 1) VO2max and running economy (J·kg-1·m-1) tests and 2) an experimental running protocol at two speeds,12 km·h-1 and 80% of the speed at VO2max (V80) and three gradients (0, -5° and -10°). V80 was higher than 12 km·h-1 for all participants. All testing was performed on a large treadmill 3x5 m (Rodby, Sweden) that were controlled for speed and gradient. The experimental protocol was performed continuously with 5 min at each workload in a randomized order, 30 min in total. VO2 was measured throughout the experimental protocol using a mixing chamber (Moxus Metabolic Cart, USA). RESULTS:VO2 expressed as ml·kg-1·min-1 increased because of speed (F1,5=27.8, p=0.003) and decreased with gradient (F1,5=87.6, p<0.001). Between -5° and -10°, VO2 decreased less during V80 compared to 12 km·h-1 shown by an interaction (F2,10=7.9, p=0.009). However, speed did not influence running economy (F1,5=0.9, p=0.38) while gradient increased running economy (F1,5=90.1, p<0.001). A non-significant interaction effect suggests a shift in running economy between -5° and -10° depending on speed (F2,10=3.5, p=0.07). The running economy at V80 was higher compared to 12 km·h-1 at -5° but reversed at -10°. While a relation between running economy at V80 -10°, V80 -5° and 12 km·h-1 -10° (rs>0.88, p<0.019) was found, no relations between running economy on level terrain and steep downhill running (-10°) were recognised. CONCLUSION:While we found no effect on running economy from speed alone, we did see a shift in the running economy for different speeds at an increased downhill gradient. This indicates that a high speed (V80) is more efficient at moderate downhill gradients, while a lower speed (12 km·h-1) is more efficient in steeper downhill gradients. While previous research demonstrate that gradient is of great influence to running economy, the findings of this study suggest that speed also affects the running economy in downhill running.

The purpose of this study was to evaluate and compare various power output estimates and estimate anaerobic energy supply during treadmill roller-skiing. Roller-skiing sprint time-trial performance on a treadmill was compared to numerical simulations of three different power output estimates; non-inertial power estimate (NIP), inertial power estimate (IP), and optimization power estimate (OP). The OP was in best agreement with the measured speed of the skier. However, the IP was in better agreement with the measured finishing time of the real time trial, which may suggest that the IP better approximated the mean power than the other two estimates. Moreover, the NIP and IP are more simplistic than the OP and thereby more practical from a scientific standpoint. Based on this we recommend the use of the IP estimate.

It has been shown theoretically that performance can be enhanced by varying power in parallel with variable ambient conditions. However, no theoretical model has considered aerobic substrate utilization dynamics, limited carbohydrate stores, force-velocity relationships, and proper efficiency modelling. Furthermore, no study has investigated optimal pacing for courses with continuously variable ambient wind directions. Therefore, the aim of this study was to develop a model for the optimization of pacing strategies in road cycling with an updated bioenergetics model. The purpose of this model was to optimize pacing strategies for courses with continuously variable wind directions on both short (2 km) and long (100 km) courses. For this purpose, a numerical model consisting of three sub-models was programmed into the MATLAB software. This model consisted of one mechanical simulation model for cycling locomotion, one bioenergetics model based on the Margaria-Morton-Sundström model, and the method of moving asymptotes for optimization of the pacing strategy. Results showed that by optimizing the pacing strategies, time gains of 4.9 and 5.7% were attained for the 2 km courses with and without an ambient wind of 5 m·s-1 respectively. The corresponding time gains for the 100 km courses were 1.4 and 2.0% with and without ambient wind respectively. The theoretical model in this study further resulted in all-out strategies for the flat 2 km courses with and without ambient wind. Moreover, the 100 km course without wind was met with a positive pacing strategy and the 100 km course with ambient wind was met with a compromise of positive pacing and variable power distribution in parallel with the variable ambient wind conditions. In conclusion, the model presented in this study performed more detailed bioenergetic simulations than previous pacing strategy optimization studies and this resulted in more detailed pacing strategies for long courses.

It is desirable to test sportswear and sports equipment at exactly the same conditions experienced during use. Although outdoor tests are in many cases the most adequate, they are at the same time quite complex, demand special measurement technology and wearable equipment. Results of such tests are often hard to interpret due to large variations because of rapidly varying ambient conditions and individual specifics of human objects, among other factors, which are hard or impossible to control. One common alternative is provided through indoor tests made in a stable, controlled environment. Controlling such parameters as temperature, wind speed and direction, air humidity with indoor facilities intended to replicate ambient conditions, and designed to house large objects, is a complex undertaking. Furthermore, replicating seasonal conditions complicates matters even more. A significant amount of research and development related to the operation of sports and other related equipment at high speeds and windy conditions has been carried out in wind tunnels with different degrees of climatic realism. However, the majority of such facilities are designed and constructed for the automotive industry, the aerospace industry and for marine research. A new wind tunnel facility, opened in March 2015 at the Sports Tech Research Centre at Mid Sweden University, is currently among the very few facilities in the world designed under the direct control of sports technology specialists and dedicated primarily to research and development within sports, outdoor clothing and footwear as well as equipment development and testing. The main goal when constructing this dedicated facility has been to successfully replicate ambient conditions for training and equipment testing in environments with controlled wind speed, temperature (+4 to +35°C) and precipitation (from fine mist to heavy downfall). The wind tunnel facility houses the largest moving belt in Sweden (5 m long and 2.7 m wide) which can be adjusted for leveled, uphill and downhill motion. The moving belt is placed in a 10 m2 test section in which the wind speed can be adjusted to match belt speed or independently up to 55 km/h (without narrowing the test section). A fog and rain system, mounted in the test section, can generate rainy conditions varying from fine mist to heavy monsoon. It is also possible to open the facility in order to allow experiments to be performed in wide range of outdoor, ambient conditions. This paper presents the basic parameters of the new wind tunnel facility. As this facility is open for wider international cooperation, we also report the general directions of current research and the future work planned to be carried out at this facility.

This thesis is devoted to the optimization of pacing strategies in two locomotive endurance sports; cross-country skiing and road cycling. It has been established that constant pace and variable power distributions are optimal if purely mechanical aspects of locomotion are considered in these sports. However, there is a lack of research that theoretically investigates optimal pacing for real world athletes who are constrained in their ability to generate power output through the bioenergetics of the human body.

The aims of this thesis are to develop numerical pacing strategy optimization models and bioenergetic models for locomotive endurance sports and use these to assess objectives relevant in optimal pacing. These objectives include: Investigate the impact of hills, sharp course bends, ambient wind, and bioenergetic models on optimal pacing and assess the effect of optimal pacing strategies on performance.

This thesis presents mathematical models for optimization of pacing strategies. These models are divided into mechanical locomotion, bioenergetic, and optimization models that are connected and programmed numerically. The locomotion and bioenergetic models in this thesis consist of differential equations and the optimization model is described by an iterative gradient-based routine. The mechanical model describes the relation between the power output generated by an athlete and his/her locomotion along a course profile, giving the finishing time. The bioenergetic model strives to mimic the human ability to generate power output. Therefore, the bioenergetic model is set to constrain the power output that is used in the mechanical locomotion model. The optimization routine strives to minimize the finishing time in the mechanical locomotion model by varying the distribution of power output along the course, still satisfying the constraints in the bioenergetic model.

The studies contained within this thesis resulted in several important findings regarding the general application of pacing strategies in cross-country skiing and road cycling. It was shown that the constant pace strategy is not optimal if ambient conditions change over the course distance. However, variable power distributions were shown beneficial if they vary in parallel with course inclination and ambient winds to decrease variations in speed. Despite these power variations, speed variations were not eliminated for most variable ambient conditions. This relates to the athlete’s physiological restrictions and the effect of these are hard to predict without thorough modeling of bioenergetics and muscle fatigue. Furthermore, it vi

was shown that substantial differences in optimal power distributions were attained for various bioenergetic models.

It was also shown that optimal braking and power output distributions for cycling on courses that involve sharp bends consisted of three or four phases, depending on the length of the course and the position of the bends. The four phases distinguished for reasonably long courses were a steady-state power phase, a rolling phase, a braking phase, and an all-out acceleration phase. It was also shown that positive pacing strategies are optimal on relatively long courses in road cycling where the supply of carbohydrates are limited. Finally, results indicated that optimal pacing may overlook the effect of some ambient conditions in favor of other more influential, mechanical or physiological, aspects of locomotion.

In summary, the results showed that athletes benefit from adapting their power output with respect not only to changing course gradients and ambient winds, but also to their own physiological and biomechanical abilities, course length, and obstacles such as course bends. The results of this thesis also showed that the computed optimal pacing strategies were more beneficial for performance than a constant power distribution. In conclusion, this thesis demonstrates the feasibility of using numerical simulation and optimization to optimize pacing strategies in cross-country skiing and road cycling.

Avhandlingen handlar om optimering av farthållningsstrategier inom längdskidåkning och landsvägscykling. Det finns ett utbrett stöd för att konstant fart och varierande effektfördelningar är optimala om endast mekaniska aspekter beaktas i dessa sporter. Ändå saknas teoretiska studier som undersöker optimal farthållning för verkliga idrottsutövare som är begränsade i sin förmåga att generera effekt genom kroppens bioenergetiska system.

Målen med den här avhandlingen är att utveckla metoder för bioenergetik och optimering av farthållningsstrategier i uthållighetsidrott. Dessutom är målet att undersöka påverkan av backar, svängar, omgivande vind och bioenergetisk modellering på den optimala farthållningsstrategin samt att utreda potentialen till prestationsförbättring med optimala farthållningsstrategier.

Avhandling presenterar matematiska modeller för optimering av farthållningsstrategier. Dessa modeller delas in i en mekanisk modell för förflyttning, en bioenergetisk modell och en optimeringsmodell. De mekaniska och bioenergetiska modellerna som presenteras i avhandlingen består av differentialekvation och optimeringsmodellen utgörs av en gradient-baserad algoritm. Den mekaniska modellen beskriver förhållandet mellan utövarens effekt och den resulterande rörelsen längs banan som ger tiden mellan start och mål. Den bioenergetiska modellen beskriver människokroppens olika energisystem och dess begränsningar att generera effekt. Den bioenergetiska modellen interagerar med optimeringsmodellen genom att utgöra dess begränsningar för vad den mänskliga kroppen klarar av. Sammanfattningsvis försöker optimeringsmodellen minimera tiden mellan start och mål i den mekaniska modellen genom att variera effekten längs banan. Samtidigt ser optimeringsmetoden till att denna effektfördelning inte kränker den bioenergetiska modellen.

Studierna som ingår i avhandlingen resulterade i flera viktiga upptäckter om generella tillämpningar av farthållningsstrategier inom längdskidåkning och landsvägscykling. Det visade sig att konstant fart inte är optimalt om omgivande betingelser varierade längs banans sträckning. Däremot var varierande effektfördelning fördelaktig om den varierar parallellt med banlutning och omgivande vindpåverkan för att minska fartens variationer. Trots denna variation, visade resultaten att fartvariationerna inte eliminerades helt. Detta har att göra med utövarens fysiologiska begränsningar, vars påverkan är svår att förutspå utan genomgående modellering av bioenergetik relaterat till muskeltrötthet. Dessutom viii

visade resultaten att olika bioenergetiska metoder gav upphov till betydande skillnader i de optimala farthållningsstrategierna.

Resultaten i avhandlingen visade också att optimal effektfördelning vid kurvtagning i landsvägscykling innehåller tre eller fyra faser. The fyra faser som var utmärkande på relativt långa banor var en tröskelfas, en rullfas, en bromsfas och en maximal accelerationsfas. Resultaten visar också att positiv farthållning är optimal på relativt långa banor i landsvägscykling där tillgången på kolhydrater är begränsad. Samtidigt visade resultaten på optimala farthållningsstrategier ibland att inverkan av omgivande betingelser förbisågs till fördel för med inflytelserika betingelser som påverkar framdrivningen.

Sammantaget visar resultaten i denna avhandling att utövare gagnas av att anpassa effekten med hänsyn till varierande terräng, omgivande vind, atletens egen fysiologiska och biomekaniska förmåga, banans längd och hinder såsom kurvor. Resultaten visar också att de optimala farthållningsstrategier med varierande effektfördelning som beräknats i denna avhandling förbättrar prestationen jämfört med konstanta effektfördelningar. Sammanfattningsvis visar denna avhandling på möjligheterna att använda numerisk simulering och optimering för att optimera farthållningsstrategier i längdskidåkning och landsvägscykling.