Assessing the limitations of the Banister model in monitoring training

The Fitness-Fatigue Model: What's in the Numbers?

PURPOSE

The purpose of this commentary is to outline some of the pitfalls when using the fitness-fatigue model to unravel the interaction between training load and performance. By doing so, we encourage sport scientists and coaches to interpret the parameters from the model with some extra caution.

CONCLUSIONS

Caution is needed when interpreting the fitness-fatigue model since the parameter values are influenced by the starting parameter values, the modeling technique, and the input of the model. Also, the use of general constants should be avoided since they do not account for interindividual differences and differences between training-load methods. Therefore, we advise sport scientists and coaches to use the model as a way to work more data-informed rather than working data-driven.

A Fitness-Fatigue Model of Performance in Peripheral Artery Disease: Predicted and Measured Effects of a Pain-Free Exercise Program

Banister impulse-response (IR) model estimates the performance in response to the training impulses (TRIMPs). In 100 patients with peripheral artery disease (PAD), we tested by an IR model the predictability of the effects of a 6-month structured home-based exercise program. The daily TRIMPs obtained from prescribed walking speed, relative intensity and time of exercise determined the fitness-fatigue components of performance. The estimated performance values, calculated from the baseline 6-min and pain-free walking distance (6MWD and PFWD, respectively) were compared with values measured at visits through regression models. Interval pain-free walking at controlled speed prescribed during circa-monthly hospital visits (5 ± 1) was safely performed at home with good adherence (92% of scheduled sessions, 144 ± 25 km walked in 50 ± 8 training hours). The mean TRIMP rose throughout the program from 276 to 601 a.u. The measured 6MWD and PFWD values increased (+33 m and +121 m, respectively) showing a good fit with those estimated by the IR model (6MWD: R² 0.81; PFWD: R² 0.68) and very good correspondence (correlation coefficients: 0.91 to 0.95), without sex differences. The decay of performance without training was estimated at 18 ± 3 weeks. In PAD, an IR model predicted the walking performance following a pain-free exercise program. IR models may contribute to design and verify personalized training programs.

Training load responses modelling and model generalisation in elite sports

This study aims to provide a transferable methodology in the context of sport performance modelling, with a special focus to the generalisation of models. Data were collected from seven elite Short track speed skaters over a three months training period. In order to account for training load accumulation over sessions, cumulative responses to training were modelled by impulse, serial and bi-exponential responses functions. The variable dose-response (DR) model was compared to elastic net (ENET), principal component regression (PCR) and random forest (RF) models, while using cross-validation within a time-series framework. ENET, PCR and RF models were fitted either individually (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{I}$$\end{document}MI) or on the whole group of athletes (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{G}$$\end{document}MG). Root mean square error criterion was used to assess performances of models. ENET and PCR models provided a significant greater generalisation ability than the DR model (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p = 0.018$$\end{document}p=0.018, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p < 0.001$$\end{document}p<0.001, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p = 0.004$$\end{document}p=0.004 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p < 0.001$$\end{document}p<0.001 for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ENET_{I}$$\end{document}ENETI, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ENET_{G}$$\end{document}ENETG, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PCR_{I}$$\end{document}PCRI and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PCR_{G}$$\end{document}PCRG, respectively). Only \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ENET_{G}$$\end{document}ENETG and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$RF_{G}$$\end{document}RFG were significantly more accurate in prediction than DR (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p < 0.001$$\end{document}p<0.001 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p < 0.012$$\end{document}p<0.012). In conclusion, ENET achieved greater generalisation and predictive accuracy performances. Thus, building and evaluating models within a generalisation enhancing procedure is a prerequisite for any predictive modelling.

International survey of training load monitoring practices in competitive swimming: How, what and why not?

OBJECTIVE

The purpose of this study is to identify the training load (TL) monitoring practices employed in real-world competitive swimming environments. The study explores data collection, analysis and barriers to TL monitoring.

DESIGN

Cross-sectional.

SETTING

Online survey platform.

PARTICIPANTS

Thirty-one responders working in competitive swimming programmes.

MAIN OUTCOME MEASURES

Methods of data collection, analysis, level of effectiveness and barriers associated with TL monitoring.

RESULTS

84% of responders acknowledged using TL monitoring, with 81% of responders using a combination of both internal and external TL, in line with current consensus statements. Swim volume (mileage) (96%) and session rate of perceived exertion (sRPE) (92%) were the most frequently used, with athlete lifestyle/wellness monitoring also featuring prominently. Thematic analysis highlighted that "stakeholder engagement", "resource constraints" or "functionality and usability of the systems" were shared barriers to TL monitoring amongst responders.

CONCLUSIONS

Findings show there is a research-practice gap. Future approaches to TL monitoring in competitive swimming should focus on selecting methods that allow the same TL monitoring system to be used across the whole programme, (pool-based training, dryland training and competition). Barriers associated with athlete adherence and coach/National Governing Body engagement should be addressed before a TL system implementation.

Is there Evidence for the Suggestion that Fatigue Accumulates Following Resistance Exercise?

It has been suggested that improper post-exercise recovery or improper sequence of training may result in an 'accumulation' of fatigue. Despite this suggestion, there is a lack of clarity regarding which physiological mechanisms may be proposed to contribute to fatigue accumulation. The present paper explores the time course of the changes in various fatigue-related measures in order to understand how they may accumulate or lessen over time following an exercise bout or in the context of an exercise program. Regarding peripheral fatigue, the depletion of energy substrates and accumulation of metabolic byproducts has been demonstrated to occur following an acute bout of resistance training; however, peripheral accumulation and depletion appear unlikely candidates to accumulate over time. A number of mechanisms may contribute to the development of central fatigue, postulating the need for prolonged periods of recovery; however, a time course is difficult to determine and is dependent on which measurement is examined. In addition, it has not been demonstrated that central fatigue measures accumulate over time. A potential candidate that may be interpreted as accumulated fatigue is muscle damage, which shares similar characteristics (i.e., prolonged strength loss). Due to the delayed appearance of muscle damage, it may be interpreted as accumulated fatigue. Overall, evidence for the presence of fatigue accumulation with resistance training is equivocal, making it difficult to draw the conclusion that fatigue accumulates. Considerable work remains as to whether fatigue can accumulate over time. Future studies are warranted to elucidate potential mechanisms underlying the concept of fatigue accumulation.

The Influence of Different Training Load Quantification Methods on the Fitness-Fatigue Model

PURPOSE

Numerous methods exist to quantify training load (TL). However, the relationship with performance is not fully understood. Therefore the purpose of this study was to investigate the influence of the existing TL quantification methods on performance modeling and the outcome parameters of the fitness-fatigue model.

METHODS

During a period of 8 weeks, 9 subjects performed 3 interval training sessions per week. Performance was monitored weekly by means of a 3-km time trial on a cycle ergometer. After this training period, subjects stopped training for 3 weeks but still performed a weekly time trial. For all training sessions, Banister training impulse (TRIMP), Lucia TRIMP, Edwards TRIMP, training stress score, and session rating of perceived exertion were calculated. The fitness-fatigue model was fitted for all subjects and for all TL methods.

RESULTS

The error in relating TL to performance was similar for all methods (Banister TRIMP: 618 [422], Lucia TRIMP: 625 [436], Edwards TRIMP: 643 [465], training stress score: 639 [448], session rating of perceived exertion: 558 [395], and kilojoules: 596 [505]). However, the TL methods evolved differently over time, which was reflected in the differences between the methods in the calculation of the day before performance on which training has the biggest positive influence (range of 19.6 d).

CONCLUSIONS

The authors concluded that TL methods cannot be used interchangeably because they evolve differently.

Monitoring the Heart Rate Variability Responses to Training Loads in Competitive Swimmers Using a Smartphone Application and the Banister Impulse-Response Model

PURPOSE

First, to examine whether heart rate variability (HRV) responses can be modeled effectively via the Banister impulse-response model when the session rating of perceived exertion (sRPE) alone, and in combination with subjective well-being measures, are utilized. Second, to describe seasonal HRV responses and their associations with changes in critical speed (CS) in competitive swimmers.

METHODS

A total of 10 highly trained swimmers collected daily 1-minute HRV recordings, sRPE training load, and subjective well-being scores via a novel smartphone application for 15 weeks. The impulse-response model was used to describe chronic root mean square of the successive differences (rMSSD) responses to training, with sRPE and subjective well-being measures used as systems inputs. Changes in CS were obtained from a 3-minute all-out test completed in weeks 1 and 14.

RESULTS

The level of agreement between predicted and actual HRV data was R2 = .66 (.25) when sRPE alone was used. Model fits improved in the range of 4% to 21% when different subjective well-being measures were combined with sRPE, representing trivial-to-moderate improvements. There were no significant differences in weekly group averages of log-transformed (Ln) rMSSD (P = .34) or HRV coefficient of variation of Ln rMSSD (P = .12); however, small-to-large changes (d = 0.21-1.46) were observed in these parameters throughout the season. Large correlations were observed between seasonal changes in HRV measures and CS (changes in averages of Ln rMSSD: r = .51, P = .13; changes in coefficient of variation of Ln rMSSD: r = -.68, P = .03).

CONCLUSION

The impulse-response model and data collected via a novel smartphone application can be used to model HRV responses to swimming training and nontraining-related stressors. Large relationships between seasonal changes in measured HRV parameters and CS provide further evidence for incorporating a HRV-guided training approach.

Autoregulation in Resistance Training: Addressing the Inconsistencies

Autoregulation is a process that is used to manipulate training based primarily on the measurement of an individual's performance or their perceived capability to perform. Despite being established as a training framework since the 1940s, there has been limited systematic research investigating its broad utility. Instead, researchers have focused on disparate practices that can be considered specific examples of the broader autoregulation training framework. A primary limitation of previous research includes inconsistent use of key terminology (e.g., adaptation, readiness, fatigue, and response) and associated ambiguity of how to implement different autoregulation strategies. Crucially, this ambiguity in terminology and failure to provide a holistic overview of autoregulation limits the synthesis of existing research findings and their dissemination to practitioners working in both performance and health contexts. Therefore, the purpose of the current review was threefold: first, we provide a broad overview of various autoregulation strategies and their development in both research and practice whilst highlighting the inconsistencies in definitions and terminology that currently exist. Second, we present an overarching conceptual framework that can be used to generate operational definitions and contextualise autoregulation within broader training theory. Finally, we show how previous definitions of autoregulation fit within the proposed framework and provide specific examples of how common practices may be viewed, highlighting their individual subtleties.

Acute:Chronic Workload Ratio: Conceptual Issues and Fundamental Pitfalls

The number of studies examining associations between training load and injury has increased exponentially. As a result, many new measures of exposure and training-load-based prognostic factors have been created. The acute:chronic workload ratio (ACWR) is the most popular. However, when recommending the manipulation of a prognostic factor in order to alter the likelihood of an event, one assumes a causal effect. This introduces a series of additional conceptual and methodological considerations that are problematic and should be considered. Because no studies have even tried to estimate causal effects properly, manipulating ACWR in practical settings in order to change injury rates remains a conjecture and an overinterpretation of the available data. Furthermore, there are known issues with the use of ratio data and unrecognized assumptions that negatively affect the ACWR metric for use as a causal prognostic factor. ACWR use in practical settings can lead to inappropriate recommendations, because its causal relation to injury has not been established, it is an inaccurate metric (failing to normalize the numerator by the denominator even when uncoupled), it has a lack of background rationale to support its causal role, it is an ambiguous metric, and it is not consistently and unidirectionally related to injury risk. Conclusion: There is no evidence supporting the use of ACWR in training-load-management systems or for training recommendations aimed at reducing injury risk. The statistical properties of the ratio make the ACWR an inaccurate metric and complicate its interpretation for practical applications. In addition, it adds noise and creates statistical artifacts.

Do Athlete Monitoring Tools Improve a Coach's Understanding of Performance Change?

PURPOSE

To assess a coach's subjective assessment of their athletes' performances and whether the use of athlete-monitoring tools could improve on the coach's prediction to identify performance changes.

METHODS

Eight highly trained swimmers (7 male and 1 female, age 21.6 [2.0] y) recorded perceived fatigue, total quality recovery, and heart-rate variability over a 9-month period. Prior to each race of the swimmers' main 2 events, the coach (n = 1) was presented with their previous race results and asked to predict their race time. All race results (n = 93) with aligning coach's predictions were recorded and classified as a dichotomous outcome (0 = no change; 1 = performance decrement or improvement [change +/- > or < smallest meaningful change]). A generalized estimating equation was used to assess the coach's accuracy and the contribution of monitoring variables to the model fit. The probability from generalized estimating equation models was assessed with receiver operating characteristic curves to identify the model's accuracy from the area under the curve analysis.

RESULTS

The coach's predictions had the highest diagnostic accuracy to identify both decrements (area under the curve: 0.93; 95% confidence interval, 0.88-0.99) and improvements (area under the curve: 0.89; 95% confidence interval, 0.83-0.96) in performance.

CONCLUSIONS

These findings highlight the high accuracy of a coach's subjective assessment of performance. Furthermore, the findings provide a future benchmark for athlete-monitoring systems to be able to improve on a coach's existing understanding of swimming performance.

Modelling Training Adaptation in Swimming Using Artificial Neural Network Geometric Optimisation

This study aims to model training adaptation using Artificial Neural Network (ANN) geometric optimisation. Over 26 weeks, 38 swimmers recorded their training and recovery data on a web platform. Based on these data, ANN geometric optimisation was used to model and graphically separate adaptation from maladaptation (to training). Geometric Activity Performance Index (GAPI), defined as the ratio of the adaptation to the maladaptation area, was introduced. The techniques of jittering and ensemble modelling were used to reduce overfitting of the model. Correlation (Spearman rank) and independence (Blomqvist β) tests were run between GAPI and performance measures to check the relevance of the collected parameters. Thirteen out of 38 swimmers met the prerequisites for the analysis and were included in the modelling. The GAPI based on external load (distance) and internal load (session-Rating of Perceived Exertion) showed the strongest correlation with performance measures. ANN geometric optimisation seems to be a promising technique to model training adaptation and GAPI could be an interesting numerical surrogate to track during a season.

Elite Swimmers' Training Patterns in the 25 Weeks Prior to Their Season's Best Performances: Insights Into Periodization From a 20-Years Cohort

Background

This study investigated the periodization of elite swimmers’ training over the 25 weeks preceding the major competition of the season.

Methods

We conducted a retrospective observational study of elite male (n = 60) and female (n = 67) swimmers (46 sprint, 81 middle-distance) over 20 competitive seasons (1992–2012). The following variables were monitored: training corresponding to blood lactate <2 mmol⋅L^-1, 2 to ≤4 mmol⋅L^-1, >4–6 mmol⋅L^-1, >6 mmol⋅L^-1, and maximal swimming speed; general conditioning and maximal strength training hours; total training load (TTL); and the mean normalized volumes for both in-water and dryland workouts. Latent class mixed modeling was used to identify various TTL pattern groups. The associations between pattern groups and sex, age, competition event, Olympic quadrennial year, training contents, and relative performance were quantified.

Results

For the entire cohort, ∼86–90% of the training was swum at an intensity of [La]_b ≤ 4 mmol⋅L^-1. This training volume was divided into 40–44% at <2 mmol⋅L^-1 and 44–46% at 2 to ≤4 mmol⋅L^-1, leaving 6–9.5% at >4–6 mmol⋅L^-1, and 3.5–4.5% at >6 mmol⋅L^-1. Three sprint TTL patterns were identified: a pattern with two long ∼14–15-week macrocycles, one with two ∼12–13 week macrocycles each composed of a balanced training load, and one with a single stable flat macrocycle. The long pattern elicited the fastest performances and was most prevalent in Olympic quadrennials (i.e., 4 seasons preceding the 2004, 2008, and 2012 Olympic Games). This pattern exhibited moderate week-to-week TTL variability (6 ± 3%), progressive training load increases between macrocycles, and more training at ≤4 mmol⋅L^-1 and >6 mmol⋅L^-1. This fastest sprint pattern showed a waveform in the second macrocycle consisting of two progressive load peaks 10–11 and 4–6 weeks before competition. The stable flat pattern was the slowest and showed low TTL variability (4 ± 3%), training load decreases between macrocycles (P < 0.01), and more training at 4–6 mmol⋅L^-1 (P < 0.01).

Conclusion

Progressive increases in training load, macrocycles lasting about 14–15 weeks, and substantial volume of training at intensities ≤4 mmol⋅L^-1 and >6 mmol⋅L^-1, were associated with peak performance in elite swimmers.

Optimizing Preseason Training Loads in Australian Football

PURPOSE

To investigate whether preseason training plans for Australian football can be computer generated using current training-load guidelines to optimize injury-risk reduction and performance improvement.

METHODS

A constrained optimization problem was defined for daily total and sprint distance, using the preseason schedule of an elite Australian football team as a template. Maximizing total training volume and maximizing Banister-model-projected performance were both considered optimization objectives. Cumulative workload and acute:chronic workload-ratio constraints were placed on training programs to reflect current guidelines on relative and absolute training loads for injury-risk reduction. Optimization software was then used to generate preseason training plans.

RESULTS

The optimization framework was able to generate training plans that satisfied relative and absolute workload constraints. Increasing the off-season chronic training loads enabled the optimization algorithm to prescribe higher amounts of "safe" training and attain higher projected performance levels. Simulations showed that using a Banister-model objective led to plans that included a taper in training load prior to competition to minimize fatigue and maximize projected performance. In contrast, when the objective was to maximize total training volume, more frequent training was prescribed to accumulate as much load as possible.

CONCLUSIONS

Feasible training plans that maximize projected performance and satisfy injury-risk constraints can be automatically generated by an optimization problem for Australian football. The optimization methods allow for individualized training-plan design and the ability to adapt to changing training objectives and different training-load metrics.

Modelling of optimal training load patterns during the 11 weeks preceding major competition in elite swimmers

Periodization of swim training in the final training phases prior to competition and its effect on performance have been poorly described. We modeled the relationships between the final 11 weeks of training and competition performance in 138 elite sprint, middle-distance, and long-distance swimmers over 20 competitive seasons. Total training load (TTL), strength training (ST), and low- to medium-intensity and high-intensity training variables were monitored. Training loads were scaled as a percentage of the maximal volume measured at each intensity level. Four training periods (meso-cycles) were defined: the taper (weeks 1 to 2 before competition), short-term (weeks 3 to 5), medium-term (weeks 6 to 8), and long-term (weeks 9 to 11). Mixed-effects models were used to analyze the association between training loads in each training meso-cycle and end-of-season major competition performance. For sprinters, a 10% increase between ∼20% and 70% of the TTL in medium- and long-term meso-cycles was associated with 0.07 s and 0.20 s faster performance in the 50 m and 100 m events, respectively (p < 0.01). For middle-distance swimmers, a higher TTL in short-, medium-, and long-term training yielded faster competition performance (e.g., a 10% increase in TTL was associated with improvements of 0.1–1.0 s in 200 m events and 0.3–1.6 s in 400 m freestyle, p < 0.01). For sprinters, a 60%–70% maximal ST load 6–8 weeks before competition induced the largest positive effects on performance (p < 0.01). An increase in TTL during the medium- and long-term preparation (6–11 weeks to competition) was associated with improved performance. Periodization plans should be adapted to the specialty of swimmers.

A nonlinear model for the characterization and optimization of athletic training and performance

Study aim: Mathematical models of the relationship between training and performance facilitate the design of training protocols to achieve performance goals. However, current linear models do not account for nonlinear physiological effects such as saturation and over-training. This severely limits their practical applicability, especially for optimizing training strategies. This study describes, analyzes, and applies a new nonlinear model to account for these physiological effects. Material and methods: This study considers the equilibria and step response of the nonlinear differential equation model to show its characteristics and trends, optimizes training protocols using genetic algorithms to maximize performance by applying the model under various realistic constraints, and presents a case study fitting the model to human performance data. Results: The nonlinear model captures the saturation and over-training effects; produces realistic training protocols with training progression, a high-intensity phase, and a taper; and closely fits the experimental performance data. Fitting the model parameters to subsets of the data identifies which parameters have the largest variability but reveals that the performance predictions are relatively consistent. Conclusions: These findings provide a new mathematical foundation for modeling and optimizing athletic training routines subject to an individual’s personal physiology, constraints, and performance goals.

From an indirect response pharmacodynamic model towards a secondary signal model of dose-response relationship between exercise training and physical performance

The aim of this study was to test the suitability of using indirect responses for modeling the effects of physical training on performance. We formulated four different models assuming that increase in performance results of the transformation of a signal secondary to the primary stimulus which is the training dose. The models were designed to be used with experimental data with daily training amounts ascribed to input and performance measured at several dates ascribed to output. The models were tested using data obtained from six subjects who trained on a cycle ergometer over a 15-week period. The data fit for each subject was good for all of the models. Goodness-of-fit and consistency of parameter estimates favored the model that took into account the inhibition of production of training effect. This model produced an inverted-U shape graphic when plotting daily training dose against performance because of the effect of one training session on the cumulated effects of previous sessions. In conclusion, using secondary signal-dependent response provided a framework helpful for modeling training effect which could enhance the quantitative methods used to analyze how best to dose physical activity for athletic performance or healthy living.

Knowledge is power: Issues of measuring training and performance in cycling

Mobile power meters provide a valid means of measuring cyclists' power output in the field. These field measurements can be performed with very good accuracy and reliability making the power meter a useful tool for monitoring and evaluating training and race demands. This review presents power meter data from a Grand Tour cyclist's training and racing and explores the inherent complications created by its stochastic nature. Simple summary methods cannot reflect a session's variable distribution of power output or indicate its likely metabolic stress. Binning power output data, into training zones for example, provides information on the detail but not the length of efforts within a session. An alternative approach is to track changes in cyclists' modelled training and racing performances. Both critical power and record power profiles have been used for monitoring training-induced changes in this manner. Due to the inadequacy of current methods, the review highlights the need for new methods to be established which quantify the effects of training loads and models their implications for performance.

A framework for prescription in exercise-oncology research

The field of exercise-oncology has increased dramatically over the past two decades, with close to 100 published studies investigating the efficacy of structured exercise training interventions in patients with cancer. Of interest, despite considerable differences in study population and primary study end point, the vast majority of studies have tested the efficacy of an exercise prescription that adhered to traditional guidelines consisting of either supervised or home-based endurance (aerobic) training or endurance training combined with resistance training, prescribed at a moderate intensity (50-75% of a predetermined physiological parameter, typically age-predicted heart rate maximum or reserve), for two to three sessions per week, for 10 to 60 min per exercise session, for 12 to 15 weeks. The use of generic exercise prescriptions may, however, be masking the full therapeutic potential of exercise treatment in the oncology setting. Against this background, this opinion paper provides an overview of the fundamental tenets of human exercise physiology known as the principles of training, with specific application of these principles in the design and conduct of clinical trials in exercise-oncology research. We contend that the application of these guidelines will ensure continued progress in the field while optimizing the safety and efficacy of exercise treatment following a cancer diagnosis.

A pilot study on quantification of training load: The use of HRV in training practice

Recent laboratory studies have suggested that heart rate variability (HRV) may be an appropriate criterion for training load (TL) quantification. The aim of this study was to validate a novel HRV index that may be used to assess TL in field conditions. Eleven well-trained long-distance male runners performed four exercises of different duration and intensity. TL was evaluated using Foster and Banister methods. In addition, HRV measurements were performed 5 minutes before exercise and 5 and 30 minutes after exercise. We calculated HRV index (TLHRV) based on the ratio between HRV decrease during exercise and HRV increase during recovery. HRV decrease during exercise was strongly correlated with exercise intensity (R = -0.70; p < 0.01) but not with exercise duration or training volume. TLHRV index was correlated with Foster (R = 0.61; p = 0.01) and Banister (R = 0.57; p = 0.01) methods. This study confirms that HRV changes during exercise and recovery phase are affected by both intensity and physiological impact of the exercise. Since the TLHRV formula takes into account the disturbance and the return to homeostatic balance induced by exercise, this new method provides an objective and rational TL index. However, some simplification of the protocol measurement could be envisaged for field use.

Training load quantification in elite swimmers using a modified version of the training impulse method

Prior reports have described the limitations of quantifying internal training loads using hear rate (HR)-based objective methods such as the training impulse (TRIMP) method, especially when high-intensity interval exercises are performed. A weakness of the TRIMP method is that it does not discriminate between exercise and rest periods, expressing both states into a single mean intensity value that could lead to an underestimate of training loads. This study was designed to compare Banister's original TRIMP method (1991) and a modified calculation procedure (TRIMPc) based on the cumulative sum of partial TRIMP, and to determine how each model relates to the session rating of perceived exertion (s-RPE), a HR-independent training load indicator. Over four weeks, 17 elite swimmers completed 328 pool training sessions. Mean HR for the full duration of a session and partial values for each 50 m of swimming distance and rest period were recorded to calculate the classic TRIMP and the proposed variant (TRIMPc). The s-RPE questionnaire was self-administered 30 minutes after each training session. Both TRIMPc and TRIMP measures strongly correlated with s-RPE scores (r = 0.724 and 0.702, respectively; P < 0.001). However, TRIMPc was ∼ 9% higher on average than TRIMP (117 ± 53 vs. 107 ± 47; P < 0.001), with proportionally greater inter-method difference with increasing workload intensity. Therefore, TRIMPc appears to be a more accurate and appropriate procedure for quantifying training load, particularly when monitoring interval training sessions, since it allows weighting both exercise and recovery intervals separately for the corresponding HR-derived intensity.

Identifying Optimal Overload and Taper in Elite Swimmers over Time

The aim of this exploratory study was to identify the most influential training designs during the final six weeks of training (F6T) before a major swimming event, taking into account athletes' evolution over several seasons. Fifteen female and 17 male elite swimmers were followed for one to nine F6T periods. The F6T was divided into two sub-periods of a three-week overload period (OP) and a three-week taper period (TP). The final time trial performance was recorded for each swimmer in his or her specialty at the end of both OP and TP. The change in performances (ΔP) between OP and TP was recorded. Training variables were derived from the weekly training volume at several intensity levels as a percentage of the individual maximal volume measured at each intensity level, and the individual total training load (TTL) was considered to be the mean of the loads at these seven intensity levels. Also, training patterns were identified from TTL in the three weeks of both OP and TP by cluster analysis. Mixed-model was used to analyse the longitudinal data. The training pattern during OP that was associated with the greatest improvement in performance was a training load peak followed by a linear slow decay (84 ± 17, 81 ± 22, and 80 ± 19 % of the maximal training load measured throughout the F6T period for each subject, Mean ± SD) (p < 0.05). During TP, a training load peak in the 1(st) week associated with a slow decay design (57 ± 26, 45 ± 24 and 38 ± 14%) led to higher ΔP (p < 0.05). From the 1(st) to 3(rd) season, the best results were characterized by maintenance of a medium training load from OP to TP. Progressively from the 4(th) season, high training loads during OP followed by a sharp decrease during TP were associated with higher ΔP. Key PointsDuring the overload training period, a medium training load peak in the first week followed by an exponential slow decay training load design was linked to highest performance improvement.During the taper period, a training load peak in the first week associated with a slow decay design led to higher performances.Over the course of the swimmers' athletic careers, better performances were obtained with an increase in training load during the overload period followed by a sharper decrease in the taper period.Training loads schedules during the final six weeks of training before a major swimming event and changes over time could be prescribed on the basis of the model results.

Rationale and resources for teaching the mathematical modeling of athletic training and performance

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.

What is Best Practice for Training Intensity and Duration Distribution in Endurance Athletes?

Successful endurance training involves the manipulation of training intensity, duration, and frequency, with the implicit goals of maximizing performance, minimizing risk of negative training outcomes, and timing peak fitness and performances to be achieved when they matter most. Numerous descriptive studies of the training characteristics of nationally or internationally competitive endurance athletes training 10 to 13 times per week seem to converge on a typical intensity distribution in which about 80% of training sessions are performed at low intensity (2 mM blood lactate), with about 20% dominated by periods of high-intensity work, such as interval training at approx. 90% VO2max. Endurance athletes appear to self-organize toward a high-volume training approach with careful application of high-intensity training incorporated throughout the training cycle. Training intensification studies performed on already well-trained athletes do not provide any convincing evidence that a greater emphasis on high-intensity interval training in this highly trained athlete population gives long-term performance gains. The predominance of low-intensity, long-duration training, in combination with fewer, highly intensive bouts may be complementary in terms of optimizing adaptive signaling and technical mastery at an acceptable level of stress.

Performance modeling in an Olympic 1500-m finalist: a practical approach

The purpose of this study was to test if a simplified impulse-response (IR) model would correlate with competition performances in an elite middle-distance runner over a period of 7 years that encompassed two Olympiads. Daily recorded pace and time obtained from training logs of this individual for the years 2000 to 2006 were used to calculate the impulse (training stress score, or TSS). The daily TSS was used to generate acute and chronic training loads (ATL and CTL, respectively), and a model response output, or p(t), was calculated based on the relationship p(t) = CTL - ATL. Competition performances (800 m-1 mile) were converted to Mercier scores (MS) and compared to p(t) and model parameters TSS, ATL, and CTL. MS was positively correlated with model output response p(t) (p < 0.01) and negatively with ATL (p < 0.01). Quadratic relationships were also observed between MS and both p(t) and CTL (p < 0.001), potentially indicating an optimal balance between fitness, fatigue, and performance. The results of this study demonstrate that the output of this simplified IR modeling approach correlates with performance in at least 1 elite athlete. Further studies are necessary to determine the generalizability of this method, but coaches may wish to use this approach to analyze previous training and performance relationships and iteratively modify training to optimize performance.

The analysis and utilization of cycling training data

Most mathematical models of athletic training require the quantification of training intensity and quantity or 'dose'. We aim to summarize both the methods available for such quantification, particularly in relation to cycle sport, and the mathematical techniques that may be used to model the relationship between training and performance. Endurance athletes have used training volume (kilometres per week and/or hours per week) as an index of training dose with some success. However, such methods usually fail to accommodate the potentially important influence of training intensity. The scientific literature has provided some support for alternative methods such as the session rating of perceived exertion, which provides a subjective quantification of the intensity of exercise; and the heart rate-derived training impulse (TRIMP) method, which quantifies the training stimulus as a composite of external loading and physiological response, multiplying the training load (stress) by the training intensity (strain). Other methods described in the scientific literature include 'ordinal categorization' and a heart rate-based excess post-exercise oxygen consumption method. In cycle sport, mobile cycle ergometers (e.g. SRM and PowerTap) are now widely available. These devices allow the continuous measurement of the cyclists' work rate (power output) when riding their own bicycles during training and competition. However, the inherent variability in power output when cycling poses several challenges in attempting to evaluate the exact nature of a session. Such variability means that average power output is incommensurate with the cyclist's physiological strain. A useful alternative may be the use of an exponentially weighted averaging process to represent the data as a 'normalized power'. Several research groups have applied systems theory to analyse the responses to physical training. Impulse-response models aim to relate training loads to performance, taking into account the dynamic and temporal characteristics of training and, therefore, the effects of load sequences over time. Despite the successes of this approach it has some significant limitations, e.g. an excessive number of performance tests to determine model parameters. Non-linear artificial neural networks may provide a more accurate description of the complex non-linear biological adaptation process. However, such models may also be constrained by the large number of datasets required to 'train' the model. A number of alternative mathematical approaches such as the Performance-Potential-Metamodel (PerPot), mixed linear modelling, cluster analysis and chaos theory display conceptual richness. However, much further research is required before such approaches can be considered as viable alternatives to traditional impulse-response models. Some of these methods may not provide useful information about the relationship between training and performance. However, they may help describe the complex physiological training response phenomenon.

Using mathematical modeling in training planning

This report aims to discuss the strengths and weaknesses of the application of systems modeling to analyze the effects of training on performance. The simplifications inherent to the modeling approach are outlined to question the relevance of the models to predict athletes' responses to training. These simplifications include the selection of the variables assigned to the system's input and output, the specification of model structure, the collection of data to estimate the model parameters, and the use of identified models and parameters to predict responses. Despite the gain in insight to understand the effects of an intensification or reduction of training, the existing models would not be accurate enough to make predictions for a particular athlete in order to monitor his or her training.