Modeling the residual effects and threshold saturation of training: a case study of Olympic swimmers

Abstract

The aim of this study was to model the residual effects of training on the swimming performance and to compare a model that includes threshold saturation (MM) with the Banister model (BM). Seven Olympic swimmers were studied over a period of 4 +/- 2 years. For 3 training loads (low-intensity w(LIT), high-intensity w(HIT), and strength training w(ST)), 3 residual training effects were determined: short-term (STE) during the taper phase (i.e., 3 weeks before the performance [weeks 0, 1, and 2]), intermediate-term (ITE) during the intensity phase (weeks 3, 4, and 5), and long-term (LTE) during the volume phase (weeks 6, 7, and 8). ITE and LTE were positive for w(HIT) and w(LIT), respectively (p < 0.05). Low-intensity training load during taper was related to performances by a parabolic relationship (p < 0.05). Different quality measures indicated that MM compares favorably with BM. Identifying individual training thresholds may help individualize the distribution of training loads.

FIGURE 1

Hill function pattern for three different γ values when δ = 1 and κ = 10 (A); and for three different δ values when κ = 10 and γ = 1 (B). The saturation threshold is rapidly reached for high γ and low δ values.

FIGURE 2

Parabolic relationship between short-term low-intensity training load ( $\mathit{STE}{w}_t^{\mathit{LIT}}$) and performances (p_t), for the whole group of subjects. Performance on the vertical axis is expressed as a percentage of the personal record of each subject. Training load on the horizontal axis is expressed as a percentage of the maximal training load performed by each subject during the course of the study.

FIGURE 3

Modeled (line) and actual performances (square) for subject #5, calculated with MM and BM. Performance on the vertical axis is expressed as a percent of the personal record. Time on the horizontal axis is expressed in weeks. ${\mathrm{r}}_{\mathit{Adj}}^2$ and 95% CI for modeled performances are also represented. The 95% CI included 17/51 actual competitions for BM, versus 31/51 for MM.

FIGURE 4

Time response of performance for subject #2 (A) and #3 (B) to three training impulses of 100, 65 and 35% of the maximal training load, for BM (dotted line) and MM (solid line). Time in horizontal axis is expressed in weeks. In BM, training impulses were proportional to the training loads, with a higher load being related to more positive or negative effects. In MM, the relationship between loads and impulses was non-linear and had an upper limit. In subject #2, the responses to the 100% versus 65% of the maximal training load were distinctly different, consistent with a high upper limit. Conversely in subject #3, training impulses at 100% and 65% of the maximal training load elicited similar response patterns, suggesting a low upper limit.