Subjects

Eighteen male swimmers participated in this experiment. No significant differences were detected (p > 0.05) in the basic characteristics of the subjects between the IPC group and the SHAM group (Table 1).

Table 1 Inter-group statistical analysis table of basic characteristics of subjects (N = 18)100-m freestyle performance test results

In this study, participants underwent three 100-m freestyle tests: one before the intervention, one after 4 weeks of intervention, and one after 8 weeks of intervention. Repeated-measures ANOVA was utilized, with pairwise comparisons performed following Bonferroni multiple comparison correction. The data are presented as the means ± standard deviations, accompanied by the corresponding 95% confidence intervals (Table 2). The results of the main effect test for overall performance across the three 100-m freestyle tests indicated F = 3.49, p = 0.08, η2 = 0.179, with a 95% CI of -0.29–4.64. This suggests marginal significance between subjects and a large effect size, indicating potential real differences among the overall groups. Pairwise comparisons between groups, adjusted for Bonferroni correction, revealed that in the test conducted after 8 weeks of intervention, the total time for the 100-m freestyle in the IPC group (57.57 ± 2.30) was significantly lower than that in the SHAM group (59.90 ± 2.30), F = 4.598, p = 0.048, d = 1.01, 95% CI = 0.03 to 4.63. The performance in the IPC group was significantly better than that in the SHAM group, indicating a large effect size. However, the results from the test conducted after 4 weeks of intervention revealed no significant difference between the IPC and SHAM groups, F = 2.478, p = 0.135, d = 0.74, 95% CI = -0.75–5.08. The results of the within-subject effect test for time demonstrated that F = 18.673, p < 0.001, η2 = 0.539, with the third test significantly differing from the first two tests (p < 0.001), and no difference was observed between the first two tests, indicating a significant improvement in performance during the later stage (Fig. 3a).

Table 2 Statistical table of repeated measures ANOVA results for subjects’ 100 m freestyle performance (N = 18)Fig. 3

Scatter box plot of 100-m freestyle performance and anaerobic power test results. Pre denotes the preintervention test, Mid denotes the test conducted after 4 weeks of intervention, and Post refers to the test administered 1 week after the completion of the 8-week intervention. The box plot illustrates the interquartile range (IQR) from the 25th to the 75th percentile, with the horizontal line within the box indicating the median. The small square within the box represents the mean, whereas the whiskers depict the mean ± standard deviation. Individual data points are represented as scatter points, with blue indicating the SHAM group and red indicating the IPC group. Note that some scatter points may overlap because of identical data values. A significance level of *p < 0.05 indicates significant differences between the IPC and SHAM groups in pairwise comparisons, following Bonferroni correction for multiple comparisons

A comparison of performance over the first 15 m across the three tests revealed a significant within-subject effect, with F = 23.562, p < 0.001, η2 = 0.596. Pairwise comparisons revealed significant differences between the third test and the first two tests (p < 0.001), whereas no significant difference was detected between the first two tests. The interaction effect between group and time was F = 0.387, p = 0.682, η2 = 0, indicating that there was no significant interaction effect. The between-subject effect test for groups revealed F = 0.002, p = 0.967, η2 = 0, with no significant differences found in the intergroup comparisons for each test, suggesting no significant intergroup differences in 15-m performance across the three tests (Fig. 3b).

A comparison of the first 50-m segment times across the three tests revealed a significant main effect of time, with F = 16.728, p < 0.001, η2 = 0.511, indicating that the performance of all the subjects changed significantly over time (Fig. 3c). The analysis of the interaction effect between group and time yielded F = 3.371, p = 0.036, η2 = 0.188, suggesting a significant interaction effect; this finding indicates that the trends in the changes in the first 50-m segment times over time differed between the IPC group and the SHAM group. The overall between-group effect was not significant, with F = 1.972, p = 0.179, η2 = 0.11, and the 95% CI ranged from − 0.415 to 0.40. After 4 weeks of intervention, the intergroup comparison revealed that the IPC group (27.72 ± 1.06) performed significantly better than the SHAM group did (29.06 ± 1.51), with F = 4.789, p = 0.044, d = 1.03, and a 95% CI of 0.04–2.65. The effect size was large, indicating substantial practical differences. However, after 8 weeks of intervention, the performance gap between the IPC group (27.43 ± 1.42) and the SHAM group (27.58 ± 1.02) narrowed, resulting in no significant difference (p = 0.793).

A comparison of performance in the last 50-m segment across the three tests revealed that the within-subject effect test indicated a marginally significant main effect of time, F = 3.296, p = 0.079, η2 = 0.171. The interaction effect was also marginally significant, F = 3.518, p = 0.070, η2 = 0.180, suggesting a trend toward differences among the groups. However, owing to the borderline significance, caution is warranted when interpreting these results. The between-subject effect test yielded a marginally significant result, F = 3.865, p = 0.067, η2 = 0.195, and a 95% CI of − 0.114 to 3.014, with a large effect size, indicating that the differences between groups may hold practical significance. Furthermore, the postintervention results at 8 weeks demonstrated that the IPC group (30.15 ± 1.00) significantly outperformed the SHAM group (32.32 ± 1.97), F = 8.678, p = 0.009, d = 1.39, and 95% CI of 0.61–3.73, reflecting a large effect size and practical significance (Fig. 3d).

The within-subjects test results for turning performance across the three tests indicated F = 7.811, p = 0.002, η2 = 0.328, demonstrating a significant main effect of time, with subjects’ turning performance changing notably over time (Fig. 3e). The between-subjects effect test results showed F = 4.295, p = 0.055, η2 = 0.212, with a 95% CI of − 0.006 to 0.542, suggesting a marginally significant overall between-group effect with a large effect size, implying that the differences between groups may hold practical significance. The mean turning performance within the SHAM group exhibited no significant change during the first 4 weeks but showed a noticeable trend change in the final 4 weeks. In contrast, the IPC group demonstrated a significant trend change during the first 4 weeks, followed by a smaller change in the last 4 weeks. Furthermore, a significant difference in turning performance was observed between the IPC group and the SHAM group after 4 weeks of intervention (5.4 ± 0.29 vs. 5.79 ± 0.35), with F = 6.402, p = 0.022, d = 1.21, and a 95% CI ranging from 0.063–0.712, indicating a large effect size and a substantial actual difference. The turning performance of the IPC group was significantly better than that of the SHAM group following 4 weeks of intervention.

Anaerobic power test results

The results of the anaerobic power test, which included the PP, AP, FI%, and tPP data from the Wingate 30 s test, are presented as the means ± standard deviations, along with the corresponding 95% confidence intervals (Table 3). The main effect of time on PP was significant, F = 8.387, p = 0.007, η2 = 0.344. Additionally, the interaction effect between time and group was significant, F = 9.463, p = 0.004, η2 = 0.372, indicating a large effect size. The pattern of change in PP over time differed between the IPC and SHAM groups. The between-subject effect was not significant, F = 0.498, p = 0.491, η2 = 0.03, and the 95% CI ranged from -150.49–75.32, indicating that there was no significant overall difference between the IPC and SHAM groups. The results from pairwise comparisons revealed that after 8 weeks of intervention, the PP of the IPC group (817.27 ± 144.77) was significantly greater than that of the SHAM group (674.93 ± 54.75), F = 7.611, p = 0.014, d = 1.30, and 95% CI of − 251.71 to 32.96, demonstrating a large effect size. No significant differences were observed between the groups at baseline and at the 4-week follow-up (p = 0.946, p = 0.719) (Fig. 3f).

Table 3 Statistical table of repeated measures ANOVA results for subjects’ Wingate 30 s test (N = 18)

The time main effect of the AP index was significant, F = 41.794, p < 0.001, η2 = 0.723, indicating a substantial change in the AP index over time. Additionally, the interaction effect between time and group for the AP index was significant, F = 37.802, p < 0.001, η2 = 0.703, suggesting distinct patterns of change in the AP index over time between the IPC group and the SHAM group. The between-subject effect of AP was not significant, F = 0.568, p = 0.462, η2 = 0.034, with a 95% CI of − 120.10 to 57.11, indicating that there was no significant overall difference between the IPC and SHAM groups. The results from pairwise comparisons revealed that after 8 weeks of intervention, the AP of the IPC group (679.60 ± 85.12) was significantly greater than that of the SHAM group (541.64 ± 78.33), with F = 12.799, p = 0.003, d = 1.69, and a 95% CI of − 219.70 to 56.21, indicating a large effect size. No significant differences were observed between the groups at baseline and at 4 weeks (p = 0.638, p = 0.645) (Fig. 3g).

The main effect of time on the FI% index was not significant (F = 1.495, p = 0.241, η2 = 0.085). Similarly, the interaction between time and group did not reach significance (F = 0.403, p = 0.552, η2 = 0.025), nor did the between-subjects effect (F = 1.135, p = 0.302, η2 = 0.066). However, pairwise comparisons between the IPC group and the SHAM group revealed that, following 8 weeks of intervention, the FI% in the IPC group (51.28 ± 6.20) was significantly lower than that in the SHAM group (60.34 ± 10.60), with F = 4.911, p = 0.042, d = 1.04, and a 95% CI ranging from 0.393–17.74, indicating a large effect size. No significant differences were observed between the groups at baseline and at 4 weeks (p = 0.067, p = 0.999) (Fig. 3h).

The main effects of time (F = 0.344, p = 0.627, η2 = 0.021), the interaction between time and group (F = 0.991, p = 0.356, η2 = 0.058), and the between-subjects effect (F = 0.019, p = 0.893, η2 = 0.001) for the tPP index were not significant. However, the pairwise comparison results between the IPC group and the SHAM group indicated that, following 8 weeks of intervention, the tPP index in the IPC group (2942.67 ± 1782.08) was significantly lower than that in the SHAM group (4758.00 ± 1830.71), with F = 4.544, p = 0.049, d = 1.00, 95% CI 9.98–3620.69, reflecting a large effect size. No significant differences were observed between the groups at baseline and at 4 weeks (p = 0.228, p = 0.835) (Fig. 3i).

Results of the blood lactate level, heart rate, and RPE

Following the 100-m freestyle test, blood lactate levels, heart rate, and RPE were measured. The RPE variable exhibited a nonnormal distribution and was thus analyzed via nonparametric tests. Comparisons of blood lactate levels and heart rates between groups were performed via repeated-measures ANOVA. The data are expressed as the means ± standard deviations (Table 4). The statistical analysis of blood lactate (Fig. 4a) revealed a significant within-subject time effect (F = 51.41, p < 0.001, η2 = 0.763) as well as a significant time × group interaction (F = 4.879, p = 0.014, η2 = 0.234), both indicating a large effect size. Notably, blood lactate levels significantly differed across various testing times. Furthermore, the patterns of change in blood lactate over time varied between the IPC and SHAM groups. The main effect between the IPC and SHAM groups was marginally significant (F = 3.71, p = 0.072, η2 = 0.188, 95% CI − 1.47 to 0.07), indicating a large effect size. Pairwise comparisons revealed that during the 4-week intervention, the blood lactate level in the IPC group (12.96 ± 0.90) was significantly greater than that in the SHAM group (11.88 ± 3.09), with F = 5.51, p = 0.032, d = 0.47, and a 95% CI of − 2.05 to − 0.10, indicating a small-to-medium effect size. After 8 weeks of intervention, the blood lactate level in the IPC group (16.07 ± 1.22) was also significantly greater than that in the SHAM group (14.7 ± 0.97), with F = 6.882, p = 0.018, d = 1.24, and a 95% CI of − 2.47 to 0.26, reflecting a large effect size. No significant difference in blood lactate levels was found between the groups at baseline (p = 0.507). Additionally, there were no significant differences in the RPE (Fig. 4b) or heart rate (Fig. 4c) between the groups across the pre, mid-, and postintervention measurements. The morning heart rate (Fig. 4d) and RPE (Fig. 4e) of the subjects were measured every Monday morning, and the results revealed no significant differences.

Table 4 Statistical analysis table of subjects’ blood lactate, heart rate, and RPE (N = 18)Fig. 4

Blood lactate, RPE, and heart rate scatter box plots and 8-week heart rate and RPE change curve charts

Results of Z score standardization, density distribution, and correlation analysis of the variable indicators

The posttest results revealed significant differences in various variables between the groups, suggesting the application of Z score standardization for 100-m freestyle performance, the Wingate 30 s test, and related physiological and biochemical variables assessed following the 8-week intervention in both the IPC and SHAM groups (Fig. 5a). This figure demonstrates that the changes in each variable effectively differentiate between the IPC and SHAM groups. In the IPC group, the trends for turn performance, tPP, RPE, FI, the latter 50-m performance, and overall 100-m performance were lower than those in the SHAM group, whereas the trends for PP, blood lactate, and AP were greater. Additionally, a density plot (Fig. 5b) was generated from the Z score values of each indicator variable, clearly illustrating the differing trends between the IPC and SHAM groups. The IPC group exhibited a leftward distribution and a downward trend in the performance of the last 50-m segment, 100-m performance, and tPP data. Conversely, the PP, AP, and BLA of the IPC group displayed a rightward distribution, indicating an increasing trend. Furthermore, a group correlation analysis based on the Z score values of each indicator variable was conducted, resulting in a correlation heatmap (Fig. 5c). In the IPC group, a significant positive correlation (p < 0.05) was observed among the performance indicators of the 100-m freestyle. Conversely, the performance indicators of the 100-m freestyle were negatively correlated with anaerobic power indicators and physiological-biochemical indicators, which were more concentrated and pronounced than those of the SHAM group. Notably, in the IPC group, the blood lactate concentration was significantly negatively correlated (p < 0.05) with overall performance in the 100-m freestyle, performance in the last 50 m, and performance in the first 15 m.

Fig. 5

Z score plot, density plot, and correlation heatmap of test variable metrics. a Z score representation. The color gradient represents the magnitude of the Z score, with smaller Z scores depicted in blue and larger Z scores depicted in red. The size of the circles corresponds to the absolute value of the Z score, where larger absolute Z scores are represented by larger circles and smaller absolute Z scores are represented by smaller circles. Panel b shows the density distribution plot of the Z scores for the test metrics, where the blue area represents the SHAM group and the red area represents the IPC group. Panel c displays a heatmap of correlations among the test metrics, where larger circles indicate greater absolute values of correlation, and smaller circles indicate smaller absolute values of correlation. Redder colors signify stronger positive correlations, whereas bluer colors indicate stronger negative correlations. Statistical significance is denoted as ***p < 0.001, **p < 0.01, and *p < 0.05