Fig 1.
The Banister impulse-response model.
Performance is a function of fitness and fatigue, which both increase in response to training, but by different magnitudes and following different timeframes. Adapted from Morton et al. (1990) [21].
Fig 2.
Linking the three energy systems with the three parameters of the power duration relationship.
A) The power output attainable for a given duration can be predicted from a 3-parameter critical power (CP) model, in which maximal power output is limited by Pmax, highest aerobically sustainable power output is limited by CP, and the finite work capacity above CP, curvature constant (W′), is primary limited by buffering capacity and muscle energy stores available for substrate-level phosphorylation. B) A schematic representation depicting the contribution of each energy system to power production in all-out exercise of 2.5 minutes. The relative contribution of each system is related to the parameters Pmax (the PCr system), W′ (the glycolytic system), and CP (the oxidative system). Constructed based on data from Baker et al., (2010), Morton (2006), and Vanhatalo et al., (2007) [14,52,53]. C) The contribution of the parameters of the 3-parameter CP model to a given power output plotted against power. D) The contribution of the parameters of the 3-parameter CP model to a given power output plotted against the maximal sustainable constant-load duration (D).
Fig 3.
Maximum power available (MPA) influences the strain experienced at a given power output.
MPA is a function of the amount of W′ expended. To generate 600 W when fresh (MPA = Pmax = 1200 W), is less strenuous (grey dot) as compared to a situation where MPA is reduced to 1000, 800, or 600 W (blue, yellow, and red dot, respectively). When MPA = CP = 300 W, W′ is fully depleted and generating 600 W is not possible.
Fig 4.
Limitations of using training stress score (TSS) to estimate the load of a session.
A) A 20-min continuous effort at 350 W and associated training load metrics. B) A 20x1-min interval session at 350 W with 1-min passive rest. The example athlete’s parameters are listed in panel A. In both A and B, work completed is the same. TSS for scenario B is higher than for A despite greater expected metabolic perturbations in A. Strain score (SS) is higher for scenario A than for B, better reflecting the expected physiological strain of these efforts. At task failure, MPA (maximum power available) equals task power output. FTP = functional threshold power; CP = critical power; W′ = work prime; Pmax = maximal power output; NP = normalized power; IF = intensity factor. FTP and CP are assumed to be equal.
Fig 5.
A comparison of total work, training stress score (TSS), and strain score (SS) in four different cycling sessions of 10 minutes.
Despite the different types of training sessions, the TSS values resulting for A, B, and D are similar. SSCP, SSW′, and SSPmax represent the strain on the aerobic, glycolytic, and PCr energy systems, respectively, which reflects the training load of critical power (CP), work prime (W′), and maximal power (Pmax), respectively. The breakdown of SS into three dimensions allows for a more detailed analysis of the type of training performed. MPA = maximum power available, CP = critical power; W′ = work prime; Pmax = maximal power output.
Fig 6.
Example of predicted progression of fitness (g), fatigue (h), and performance (p).
The simulation assumes 100 days of daily training at a constant (A) or variable (B) average training load of w(t) = 50 followed by 100 days of detraining at w(t) = 0, modelled using equations 14, 15, and16. Values for the weighting factors k1 and k2 are 1 and 1.5, respectively, and the time constants τ1 and τ2 are 20 days and 7 days, respectively. Units for g, h, and p on the y-axis are arbitrary. Despite an overall identical accumulated training load of 5000 units over the training period, the performance peak in the variable program (B) is greater than that of the constant program (A).
Table 1.
Example of the strain score calculation for different levels of MPA.
Fig 7.
A hypothetical example of how a three-dimensional impulse model predicts changes in performance.
Performance of the oxidative system (A), the glycolytic system (B), and the PCr system (C) changes based on changes in fitness and fatigue for each system. The performance outcome (a.u.) at a given timepoint can be translated into critical power (CP), work prime (W′), and maximal power output (Pmax) using a conversion factor to get units of W, kJ, and W, respectively. Parameter values for the model (weighting factors k1 and k2 and the time constants τ1 and τ2) can be experimentally determined for each system. In this simulation, w(t) is repeated daily and is 80, 18, and 2, for CP, W’, and Pmax, respectively.
Fig 8.
An example of an athlete’s training data collected over~2.5 years visualized in a performance management chart (PMC).
A) One-dimensional PMC with overall fitness, fatigue, and form (performance readiness). Panels B, C, and D illustrate the three-dimensional model and the independent evolution of critical power, W′, and Pmax, respectively, over the same period.
Table 2.
Reported time constants for fitness (τ1) and fatigue (τ2) in endurance sports.