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Calculating Power Output and Training Stress in Swimmers: The Development of the SwimScore TM Algorithm
Abstract
Acknowledgments: The author wishes to express his gratitude to all of the amateur, elite, and professional athletes who have made their training and racing data available to him. Without these data, the development of new technology would be a much more difficult (if not impossible) enterprise. Legal Notes: SwimScoreis a trademark,of PhysFarm Training Systems LLC. Any commercial use of the algorithm requires a license from PhysFarm Training Systems, LLC. Non-commercial / academic,use is permitted free of charge provided that such use is properly referenced. TSS was first developed by Dr. Andrew Coggan, and is a trademark claimed by PeaksWare LLC. This work is Copyright 2008 by Dr. Philip Friere Skiba and PhysFarm Training Systems, LLC.
A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of athletic training and performance, which we henceforth call "performance modeling," is one such tool. Two models, the critical power (CP) model and the Banister impulse-response (IR) model, offer complementary information. The CP model describes the relationship between work rates and the durations for which an individual can sustain them during constant-work-rate or intermittent exercise. The IR model describes the dynamics by which an individual's performance capacity changes over time as a function of training. Both models elegantly abstract the underlying physiology, and both can accurately fit performance data, such that educating exercise practitioners in the science of performance modeling offers both pedagogical and practical benefits. In addition, performance modeling offers an avenue for introducing mathematical modeling skills to exercise physiology researchers. A principal limitation to the adoption of performance modeling is a lack of education. The goal of this report is therefore to encourage educators of exercise physiology practitioners and researchers to incorporate the science of performance modeling in their curricula and to serve as a resource to support this effort. The resources include a comprehensive review of the concepts associated with the development and use of the models, software to enable hands-on computer exercises, and strategies for teaching the models to different audiences.
The present study examined the relationship between lactic acid concentration in capillary blood and swimming velocity during 11 typical endurance exercises (continuous swimming for 30 and 60 min, interval swimming with distances between 50 and 400 m, and with rest periods of 10 and 30 s) and during the “two-speed test” recently described by Mader. It was expected that a better understanding of these relationships could provide evidence how to adjust training intensities from results obtained during the two-speed test.
Fifty-nine male swimmers of the German national level participated in this study. After a 30-min maximal swimming test, a mean lactic acid concentration of 4.01 ± 0.75mmol/l was found. The corresponding mean velocity was similar to the speed (V4) calculated for the 4mmol/l level on the basis of the results obtained during the two-speed test (2 × 400). During 30 min continuous swimming at 95% to 105% of the velocity V4, there was a significant correlation (r = 0.82, P < 0.001) between the swimming speed and the lactic acid concentration. In the 30-min maximal test, the velocity V4 correlated significantly with both the lactic acid concentration (r = -0.58, P < 0.005) and the swimming speed (r = 0.97, P < 0.001). During the interval exercises with rest periods of 10 s, the swimming velocities corresponding to the same lactic acid level as during continuous swimming, increased for the 50, 100, 200, and 400 m by 11.23%, 4.21%, 2.95%, and 2.02% of V4, respectively. With rest periods of 30s, the swimming velocity for the 100, 200, and 400 m increased by 7.34%, 4.22%, and 3.01% of V4, respectively. In spite of a constant swimming velocity during the interval series with rest periods of 30 s, we found a significant decrease of the lactic acid between the first and the third repetition.
Performance in endurance events is typically evaluated by the power or velocity that can be maintained for durations of 30 min. to four hours. The two main by-products of intense and prolonged oxidative metabolism that can limit performance are the accumulation of hydrogen ion (i.e. lactic acidosis) and heat (i.e. hyperthermia). A model for endurance performance is presented that revolves around identification of the lactate threshold velocity which is presented as a function of numerous morphological components as well as gross mechanical efficiency. When cycling at 80 RPM, gross mechanical efficiency is positively related to Type I muscle fiber composition, which has great potential to improve endurance performance. Endurance performance can also be influenced by altering the availability of oxygen and blood glucose during exercise. The latter need forms the basis for ingesting carbohydrate at 30-60 grams per hour during exercise. In laboratory simulations of performance, athletes fatigue due to hyperthermia when esophageal is approximately 40 degrees C, in association with near maximal heart rate and perceived exertion. It is likely that the central nervous system is involved in the aetiology of fatigue from hyperthermia. Dehydration during exercise promotes hyperthermia by reducing skin blood flow, sweating rate and thus heat dissipation. The combination of dehydration and hyperthermia during exercise causes large reductions in cardiac output and blood flow to the exercising musculature, and thus has a large potential to impair endurance performance. Endurance performance is optimized when training is aimed specifically at developing individual components of the model presented and nutritional supplementation prevents hypoglycemia and attenuates dehydration and hyperthermia. Indeed, the challenge at the transition to a new millennium is to synergistically integrate these physiological factors in training and competition.
Fourteen competitive cyclists who possessed a similar maximum O2 consumption (VO2 max; range, 4.6-5.0 l/min) were compared regarding blood lactate responses, glycogen usage, and endurance during submaximal exercise. Seven subjects reached their blood lactate threshold (LT) during exercise of a relatively low intensity (group L) (i.e., 65.8 +/- 1.7% VO2 max), whereas exercise of a relatively high intensity was required to elicit LT in the other seven men (group H) (i.e., 81.5 +/- 1.8% VO2 max; P less than 0.001). Time to fatigue during exercise at 88% of VO2 max was more than twofold longer in group H compared with group L (60.8 +/- 3.1 vs. 29.1 +/- 5.0 min; P less than 0.001). Over 92% of the variance in performance was related to the % VO2 max at LT and muscle capillary density. The vastus lateralis muscle of group L was stressed more than that of group H during submaximal cycling (i.e., 79% VO2 max), as reflected by more than a twofold greater (P less than 0.001) rate of glycogen utilization and blood lactate concentration. The quality of the vastus lateralis in groups H and L was similar regarding mitochondrial enzyme activity, whereas group H possessed a greater percentage of type I muscle fibers (66.7 +/- 5.2 vs. 46.9 +/- 3.8; P less than 0.01). The differing metabolic responses to submaximal exercise observed between the two groups appeared to be specific to the leg extension phase of cycling, since the blood lactate responses of the two groups were comparable during uphill running. These data indicate that endurance can vary greatly among individuals with an equal VO2 max.(ABSTRACT TRUNCATED AT 250 WORDS)
The purpose of this study was to investigate the validity of the lactate minimum test ([Lac-]BMIN) in the determination of the velocity at the maximal lactate steady state (V-MLSS), and to identify those physiological factors most closely associated with 8-km running performance.
Thirteen trained male runners (VO2max range 53-67 mL.kg-1.min-1) took part in an 8-km simulated race on flat roads and completed a comprehensive battery of laboratory tests.
Performance velocity was most strongly correlated with the estimated running velocity at VO2max (r = 0.93) and with V-MLSS (r = 0.92) and velocity at lactate threshold (V-Tlac) (r= 0.93). The running velocity at the ventilatory threshold (V-Tvent) (r = 0.81) and the [Lac-]BMIN (r = 0.83) also produced good correlations with performance velocity. Performance running velocity (mean +/- SEM 16.0 +/- 0.3 km.h-1) was not significantly different from V-MLSS (15.7 +/- 0.3 km.h-1). The running velocity at [Lac-]BMIN (14.9 +/- 0.2 km.h-1) was not significantly different from the V-Tlac (15.1 +/- 0.3 km.h-1) or V-Tvent (14.9 +/- 0.2 km.h-1) was not significantly different from the V-Tlac (15.1 +/- 0.3 km.h-1) or V-Tvent (14.9 +/- 0.3 km.h-1) but was significantly lower than the V-MLSS (P < 0.05). The [Lac-]BMIN provided the lowest correlation with V-MLSS (r = 0.61) and the worst estimate of V-MLSS (SEE = 0.75 km.h-1) compared with the other measures of lactate accumulation. The V-Tlac was not significantly different from V-MLSS and provided the highest correlation (r = 0.94) and a close estimate (SEE = 0.33 km.h-1) of the V-MLSS.
It is concluded that of the measures studied relating to blood lactate accumulation during submaximal exercise, V-Tlac provides the best estimate of the V-MLSS and the V-Tlac had equal predictive power for 8-km race performance.
The aim of this study was to propose a nonlinear model of the effects of training on performance. The new formulation introduced a variable to account for training-related changes in the magnitude and duration of exercise-induced fatigue.
Goodness-of-fit of the proposed model was compared with that of earlier models presented in the literature. Models were applied to six previously untrained subjects volunteers over a 15-wk endurance-training program composed of an 8-wk period with three sessions per week and a 4-wk period with five sessions, and the remaining weeks without training. Training sessions were composed of performance trial and intermittent exercise with 5-min work interspersed with 3-min recovery repeated four or five times. Performance was measured three times each week using average power during a 5-min all-out exercise.
The training program resulted in 30 +/- 7% improvement in performance. The proposed model exhibited significantly improved fit with actual performance obtained in each subject. Standard error was 6.47 +/- 0.71 W for the proposed model and from 9.20 +/- 2.27 W to 10.31 +/- 1.56 W for earlier models. The model output using model parameters averaged over the six subjects was found to be similar to data published elsewhere obtained in athletes with more intense training.
The data obtained allowed us to demonstrate an inverted-U-shape relationship between daily amounts of training and performance. The fit between experimental data and model-derived predictions in similar situations showed the usefulness of the proposed model to predict responses to training with varied regimens.
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