Introduction

The explosive vertical jump (EVJ) serves as a prevalent exercise modality utilized for the assessment and refinement of explosive power and vertical jumping proficiency in human physiology1. This method necessitates the rapid generation of sufficient force to effectuate a vertical ascent towards peak elevation. Throughout the EVJ maneuver, athletes commonly initiate from a static stance, harnessing elastic potential through flexion of the knees and hips. Subsequently, they execute swift extension of these articulations to engender explosive force, thereby launching the body aloft. The primary objective for athletes lies in attaining maximal vertical jump height, thereby gauging their explosive power and lower extremity musculature robustness2. The countermovement jump (CMJ) is commonly used to assess lower limb strength, explosive power, and muscle pre-activation capacity3. Both the explosive vertical jump (EVJ) and CMJ can be analyzed and compared by measuring ground reaction force (GRF). GRF data can reveal an athlete’s force output and dynamic characteristics, allowing for the evaluation of differences between various jumping techniques and the application and transfer of force during jumps4. By comparing the GRF curves of EVJ and CMJ, one can gain a deeper understanding of the differences in force output between these jumping actions5. This understanding can help optimize training programs and enhance jumping performance. The EVJ finds widespread application in various fields, particularly in competitive sports and strength training, including basketball, volleyball, track and field, among others6,7. Through EVJ training, athletes can enhance explosive power, vertical jumping ability, and the strength and coordination of lower limb muscles1. In practical application, many athletes and coaches often incorporate a certain interval before performing vertical jump training, hoping to achieve better training results through post-activation potentiation (PAP)8. PAP is a phenomenon that enhances muscle strength and performance by preceding high-intensity muscle contraction activities9. Following high-intensity muscle contraction activities (exceeding 85% of 1RM), the central nervous system triggers a series of adaptive physiological responses, including neuron activation, enhanced contractile capability of muscle fibers, and increased excitability of the central nervous system. These physiological responses lead to a short-term increase in strength for a period of time10,11,12. PAP is widely used, especially in strength training and competitive sports, commonly adopted by athletes and coaches to improve muscle strength and performance, increasing the high-intensity movement capabilities of explosive actions such as vertical jumps, squats, and lifts13,14.

After completing a set of high-intensity muscle contraction activities such as squats, bench presses, or jumps to activate the neuromuscular system, it is crucial to incorporate an appropriate intermittent time. This intermittent time is key as it allows the PAP effect to exert its optimal influence15. Following this intermittent period, participation in activities or competitive events necessitating heightened strength is advisable. At this juncture, owing to the phenomenon of PAP, enhancements in muscle strength and performance are anticipated16. Contemporary research findings underscore the multifaceted nature of PAP efficacy, with factors such as individualized training levels, activity intensity and duration, rest intervals, among others, exerting discernible influences13,17. Furthermore, recent investigations posit that the PAP phenomenon may correlate with enhancements in neuromuscular connectivity and biochemical alterations within muscle tissue18. Nevertheless, uncertainties persist concerning the efficacy of this training modality, optimal intermittent intervals, and specific training methodologies19.

In response to this, scholars both domestically and internationally have conducted various experiments and studies to explore the impact of different intermittent times on PAP and EVJ performance. Despite multiple studies suggesting that PAP can effectively enhance muscle strength and performance, there exists a divergence of results, leading to inconclusive findings. As of now, a definitive conclusion has not been reached. Therefore, the purpose of this meta-systematic review was to comprehensively analyze and summarize the existing relevant literature, to provide a comprehensive, systematic, and objective evaluation and summary of the effects of rest intervals on the enhancement of activation and explosive vertical jump performance, in order to clarify the effects of different rest intervals on explosive vertical jump CMJ and GFR, thus providing a research basis and reference for the practical application of this training method.

Materials and methods

Inclusion and exclusion criteria for literature

Studies had to satisfy all the following conditions:

  1. (1)

    Experimental studies should consist of pre-post design studies that compare observations before and after intervention.

  2. (2)

    Study participants referred to athletes aged between 18 and 30 years, who were healthy, unlimited sports types.

  3. (3)

    Intervention measures: the studies should involve the post-intermittent time PAP interventions, where appropriate interventions were applied to the study participants. The PAP induction methods were not limited and may include exercises such as squats, deadlifts, functional isometric squats, parallel squats, submaximal half squats, barbell half squats, heavy-loaded squats, and jump squats.

  4. (4)

    Outcome measures: the study detailed the heights of CMJ and the peak GRF values under the enhanced activation effect following different rest intervals.

Studies with any of following conditions had to be excluded:

  1. (1)

    Incompatibility with participant and intervention criteria;

  2. (2)

    Studies that did not involve post-intermittent time PAP interventions or did not include EVJ-related indicators;

  3. (3)

    Duplicate publications;

  4. (4)

    Retrospective literature, reviews, case reports, and briefings, etc.

Literature retrieval strategy

Databases were selected according to following conditions: relevant literature can be searched using keywords in databases such as CNKI, Wanfang, VIP, CBM, PubMed, Web of Science, and Google Scholar. The search period should cover the time from the establishment of each database to June 2024, and there were no language restrictions for the search.

Search strategies were described as follows: (1) Identification of keywords and associated expansions: keywords and related expanded terms were determined based on the pivotal content of the research topic, considering relevant subject matter extensions for retrieval. The retrieval keywords principally encompassed “post-activation potentiation”, “activation enhancement effect”, “PAP”, “explosive vertical jump”, “explosive vertical high jump”, and “intermittent time”. Additionally, expansion terms such as “muscle strength” and “training methods”, were included to cover a broader range of related content. PubMed specific retrieval strategies on the retrieval platform were as follows: #1 post-activation potentiation; #2 activation enhancement effect; #3 PAP; #4 explosive vertical jump; #5 explosive vertical high jump; #6 explosive vertical high jump; #7 intermittent time. The final retrieval equation was formulated as follows: (((((post activation potentiation) OR (Activation enhancement effect) OR (postactivation potentiation) OR (PAP)) AND ((Explosive vertical jump) OR (explosive Vertical High Jump) OR (explosive vertical jump))) AND ((intermittent time) OR (intermittent rest) OR (interval rest)))). (2) Joint search using logical operators: subject and expansion terms were combined into appropriate search queries using logical operators “or” and “and” to connect different keywords, finely tuning search results. For example, (intermittent time or rest intervals) and (activation enhancement effect or PAP) and (EVJ or vertical jump). (3) Browsing the reference lists of reviews: while consulting relevant reviews, one can meticulously peruse their reference lists to systematically retrieve literature pertinent to the research topic. Each document was scrutinized against inclusion and exclusion criteria to ascertain its relevance, thereby identifying potentially overlooked studies. By searching for potentially overlooked studies, a more comprehensive and integrated understanding of the current status and progress of the subject could be achieved.

Literature screening and quality assessment

Literature was screened using following procedures: two researchers conducted literature searches across various online databases according to pre-established screening criteria and procedures using a double-blind approach, utilizing various methods such as multiple database searches, manual searches, and exploration of professional journals to collect literature relevant to the research topic. The identified literature was imported into a reference management software (EndNote X8). The screening process entailed an initial selection phase predicated upon titles and abstracts, succeeded by a more exhaustive full-text scrutiny. Initially, each literature item’s title and abstract underwent review, and preliminary screening ensued in accordance with predetermined inclusion and exclusion criteria. Subsequent to this preliminary phase, the full text of each selected item underwent thorough examination to further refine the selection based on the stipulated criteria. Annotations were meticulously recorded during the screening process to facilitate subsequent statistical analyses of the outcomes. Two reviewers were tasked with literature data extraction and quality assessment, utilizing the Cochrane evaluation criteria independently. Instances where discordant evaluations arose between the two reviewers concerning a particular literature piece necessitated intervention by a third reviewer to adjudicate and resolve any discrepancies in the final assessment.

Literature quality assessment followed a structured procedure. Upon identifying literature meeting the inclusion criteria, a rigorous quality appraisal ensued. This entailed an examination of the literature’s reliability and credibility. The Cochrane Risk of Bias Tool served as the instrument for this assessment. Tailored for systematic reviews and meta-analyses, this tool comprehensively evaluates the quality and bias risk across randomized controlled trials and observational study designs, thereby extending its suitability to pre-post design studies. When applying the Risk of Bias Tool to assess pre-post studies, several critical aspects were scrutinized, including selection bias, information source bias, intervention bias, reporting bias, supplementary data bias, among others. Each aspect received a rating of high, medium, or low, facilitating a nuanced evaluation of the pre-post studies’ quality and risk.

Literature data extraction

Two literature reviewers extracted the required literature data, encompassing basic information and outcome indicators. (1) Extraction items determination: the required data items were firstly identified, including study characteristics, sample groups, PAP induction method, and study results. These items were typically derived from the research questions and objectives. (2) Establishment of Extraction tables/forms: a table or extraction form was created to record the extracted data. The format of the table should be clear, understandable, and capable of recording relevant information. (3) Compilation of extraction guidelines: extraction guidelines were written to assist extractors in collecting data. The guidelines should include definitions and explanations for each extraction item, as well as methods for recording and categorizing the obtained data. (4) Data extraction from the selected literature was performed, recording the required data according to the designated extraction table or guidelines to ensure accuracy, completeness, and consistency of recorded data. (5) Data organization and summarization: all extracted data were organized, summarized, and analyzed. The data organization process involved sorting, clarifying, summarizing, and consolidating the extracted data for calculating parameters or variables needed for statistical analysis. (6) Data quality assessment: the quality of the extracted data was assessed, and an evaluation and analysis of risk factors for bias were conducted. (7) Data recording and archiving: the extracted data were recorded in a database or spreadsheet, and the original versions of the literature, raw data, and extraction forms were saved for archiving purposes.

Methods for statistical analysis

The trial data extracted from the encompassed literature were individually compiled and statistically analyzed using Excel. Subsequently, meta-analysis of the included literature data was performed using RevMan 5.3. Heterogeneity analysis: preliminary heterogeneity testing of the literature was conducted using the chi-square test, with a significance level set at α = 0.05 and P < 0.05 indicating significance. Subsequently, quantitative assessment of heterogeneity results was performed using I2 in the RevMan 5.320. If I2 < 50%, a fixed-effect model (FEM) was employed for meta-analysis; in contrast, if I2 > 50%, a random-effects model (REM) was employed. A funnel plot (FP) analysis was conducted to assess potential publication bias, and forest plots were generated using RevMan 5.3. Z-values and P-values extracted from the results were used for judging the meta-analysis outcomes, with all effect sizes represented using a 95% CI. P < 0.05 was considered statistically significant for inter-group differences.

Results

Retrieved results of required literature

After inputting various keywords into online databases for searching, a total of 9 relevant articles were retrieved from the PubMed online database, 191 articles from Web of Science, and 35 articles from Google Scholar. Additionally, a total of 14 relevant articles were retrieved from Chinese databases including CNKI, Wanfang, VIP, and CBM. Altogether, 249 articles were retrieved across all databases. Following preliminary exclusion criteria, which involved removing duplicates, reviews, individual case reports, and other literature that did not meet the requirements, 138 articles remained. Upon reading the titles and abstracts, 75 irrelevant articles to EVJ were further excluded, leaving 63 articles. Subsequently, based on the inclusion criteria, a further screening process eliminated 40 articles that did not meet the criteria, resulting in 23 articles. After a thorough reading of the included literature, 2 articles without obtainable raw data were excluded, ultimately leaving 21 articles for analysis. The literature retrieval and screening process are illustrated in Fig. 1.

Figure 1
figure 1

Methods for literature retrieval.

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Brief characteristics of assigned literature

After the inclusion and exclusion criteria were applied, a total of 21 articles21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41 were obtained for the study. The first author, publication year, sample size, age, gender, height, weight, and other basic information were then systematically compiled, as outlined in Table 1. In total, a cumulative total of 327 participants were enrolled across the selected literature.

Table 1 Brief characteristics of assigned literature.
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Types of exercise items, induction measures, and intermittent time statistics in the literature

The enrolled literature was categorized and statistically analyzed based on the type of sports, induction measures, and intermittent time, with the results presented in Table 2. It can be observed that the they encompassed various sports types, including volleyball, rugby, soccer, basketball, track and field, etc. The methods for inducing PAP included exercises such as squats, deadlifts, functional isometric squat contractions, parallel squats, submaximal half squats, barbell half squats, heavy-load squats, and jump squats. It was evident from the text that this study primarily focused on squat-based PAP induction methods. The induction measures ranged from 40 to 90%, and intermittent time varied between 10 s and 24 min.

Table 2 Types of exercise items, induction measures, and intermittent time statistics in the literature.
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Quality of assigned literature

The quality of the enrolled 21 articles was assessed using the Cochrane Reviewer’s Handbook, and a summary figure and bar chart for the risk of bias assessment were generated using RevMan5.3, as explicated in Fig. 2 and Fig. 3. It became evident that the random sequence generation (selection bias (SB)) for all enrolled literature was categorized as “unclear risk”, while allocation concealment (SB) was consistently rated as “low risk”. Additionally, two articles have an “unclear risk” for blinding of outcome assessment (detection bias (DB)) and selective reporting (reporting bias (RB)), and one article has a “high risk” for blinding of outcome assessment (DB), selective reporting (RB), and other bias.

Figure 2
figure 2

Risk of bias for these literature.

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Figure 3
figure 3

Risk of bias for these literature.

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Impacts of the intermittent time of 10 ~ 15 s on EVJ

Among the literature, five articles reported the impact of intermittent time of 10 ~ 15 s following induction exercises on height of CMJ. The meta-analysis findings indicated remarkable heterogeneity among them in height of CMJ (I2 = 98%, P < 0.00001). Therefore, a REM was applied for the pooled effect size (PES) analysis. The meta-analysis unveiled no remarkable effect of intermittent time of 10 ~ 15 s following induction exercises on height of CMJ, with a PES of [MD = − 0.05, 95% CI: − 0.16 ~ 0.06; Z = 0.96, P = 0.34]. The above results were demonstrated in Fig. 4.

Figure 4
figure 4

Impacts of the intermittent time of 10 ~ 15 s on EVJ.

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Sensitivity analysis was conducted using the one-by-one method. It was observed that after excluding the study by Jensen RL et al. in 2003, there was a non-significant reduction in heterogeneity (I2 = 93%), and the significance of the results remained unaffected (MD [95% CI]: 0.00 [− 0.06, 0.07], P = 0.96). Furthermore, exclusion of studies with intervention intensity less than 75% (Crewther BT et al. 2011) did not significantly alter the outcomes (MD [95% CI]: − 0.04 [− 0.17, 0.09], P = 0.055).

Further subgroup analysis revealed that only three studies reported the impact of inter-set rest intervals of 10 to 15 s following induction exercises on the height of CMJ in males. Meta-analysis results indicated that gender (MD [95% CI]: − 0.02 [− 0.10, 0.06], P = 0.63), age, and the PAP induction method did not significantly influence CMJ height during inter-set rest intervals of 10 to 15 s (Table 3).

Table 3 Subgroup analysis for rest intervals of 10 to 15 s.
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Impacts of the intermittent time of 1 ~ 3 min on EVJ

Two studies investigated the impact of intermittent time of 1 min following induction exercises on height of CMJ under EVJ. Meta-analysis results signified no visible heterogeneity in height of CMJ (I2 = 0%, P = 0.65). Therefore, a FEM was employed for the PES analysis. The meta-analysis demonstrated that intermittent time of 1 min following induction exercises had no great impact on height of CMJ, with a PES of [MD = 0.01, 95% CI: − 0.02 ~ 0.04; Z = 0.48, P = 0.63]. Seven articles explored the effects of intermittent time of 2 min following induction exercises on height of CMJ under EVJ. Heterogeneity was not obvious in height of CMJ (I2 = 0%, P = 0.54), allowing for the use of a FEM for the PES analysis. The results indicated that the intermittent time of 2 min following induction exercises exhibited no great impact on height of CMJ under EVJ, with a PES of [MD = –0.00, 95% CI: – 0.02 ~ 0.01; Z = 0.59, P = 0.55]. Three articles investigated the effects of intermittent time of 3 min following induction exercises on the height of CMJ under EVJ. The meta-analysis demonstrated no visible heterogeneity in height of CMJ (I2 = 0%, P = 0.51), allowing for the use of a FEM for the PES analysis, which indicated that the intermittent time of 3 min following induction exercises exhibited a slight effect on height of CMJ, with a PES of [MD = – 0.00, 95% CI: – 0.03 ~ 0.03; Z = 0.38, P = 0.80]. Therefore, it can be concluded that intermittent time of 1 ~ 3 min following induction exercises held a remarkable impact on height of CMJ under the EVJ, with a PES showing [MD = – 0.00, 95% CI: – 0.01 ~ 0.01; Z = 0.38, P = 0.70]. The above results were detailed in Fig. 5.

Figure 5
figure 5

Impacts of the intermittent time of 1 ~ 3 min on CMJ.

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Due to the limited number of reported studies on the effects of inter-set rest intervals of 1 min and 3 min on peak GRF during explosive vertical jumps, with only one study each, meta-analysis was not conducted. However, there were two studies reporting the effects of a 2-min inter-set rest interval on peak GRF during explosive vertical jumps, thus meta-analysis was performed. The results indicated significant heterogeneity between the two studies regarding peak GRF (I2 = 95%, P < 0.00001). Therefore, a random-effects model was employed for the pooled effect size analysis. It was found that a 2-min inter-set rest interval following induction exercises did not significantly affect peak GRF during explosive vertical jumps, with a pooled effect size of [MD = − 245.35, 95% CI: − 731.69 to − 240.99; Z = 0.99, P = 0.32] (Fig. 6).

Figure 6
figure 6

Impacts of the intermittent time of 2 min on GRF.

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Impacts of the intermittent time of 4 min on EVJ

Twelve among enrolled studies reported the impact of 4 min of intermittent time following induction exercises on height of CMJ. The meta-analysis results revealed remarkable heterogeneity in height of CMJ (I2 = 75%, P < 0.00001). Therefore, the REM was applicable, and the results demonstrated a great effect of intermittent time of 4 min following induction exercises on height of CMJ. Specifically, PAP induction within 4 min of intermittent time sharply increased the height of CMJ for EVJ, with a PES of [MD = – 0.03, 95% CI: – 0.04 ~ – 0.01; Z = 2.71, P = 0.007], as explicated in Fig. 7.

Figure 7
figure 7

Impacts of the intermittent time of 4 min on CMJ.

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Four of enrolled studies reported the impact of 4 min of intermittent time following induction exercises on peak GRF for EVJ. The meta-analysis results revealed no visible heterogeneity in peak GRF (I2 = 91%, P < 0.00001). Therefore, the PES analysis was implemented using REM, and the findings demonstrated that 4 min of intermittent time following induction exercises did not pose a vital impact on peak GRF for EVJ, with [MD = − 138.59, 95% CI: − 417.95 ~ 140.76; Z = 0.97, P = 0.33]. The above details could be explicated in Fig. 8.

Figure 8
figure 8

Impacts of the intermittent time of 4 min on peak GRF.

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Impacts of the intermittent time of 5 min ~ 8 min on EVJ

Among the included literature, seven studies reported on the effects of a 5-min inter-set rest interval following induction exercises on the height of CMJ. Meta-analysis revealed no significant heterogeneity among these studies regarding CMJ height (I2 = 4%, P = 0.40). Utilizing a random-effects model for pooled effect size analysis, it was found that a 5 min inter-set rest interval following induction exercises significantly impacted CMJ height during explosive vertical jumps. Specifically, PAP induced by a 5 min rest interval significantly increased CMJ height, with a pooled effect size of [MD = − 0.02, 95% CI: − 0.03 to − 0.01; Z = 2.76, P = 0.006]. Due to the limited availability of literature reporting on the effects of a 6-min inter-set rest interval following induction exercises on CMJ height, meta-analysis was not conducted for this specific interval. Among the included literature, seven studies reported on the effects of an 8-min inter-set rest interval following induction exercises on the height of CMJ. Meta-analysis revealed no significant heterogeneity among these studies regarding CMJ height (I2 = 92%, P < 0.00001). Utilizing a random-effects model for pooled effect size analysis, it was found that an 8-min inter-set rest interval following induction exercises significantly impacted CMJ height during explosive vertical jumps. Specifically, PAP induced by an 8 min rest interval significantly increased CMJ height, with a pooled effect size of [MD = − 0.04, 95% CI: − 0.07 to − 0.01; Z = 2.28, P = 0.02]. Therefore, inter-set rest intervals of 5 to 8 min following induction exercises significantly influence CMJ height during explosive vertical jumps. In other words, post-activation potentiation induced by inter-set rest intervals of 5 to 8 min significantly increases CMJ height, with a pooled effect size of [MD = − 0.03, 95% CI: − 0.04 to − 0.01; Z = 2.71, P = 0.007] (Fig. 9).

Figure 9
figure 9

Impacts of the intermittent time of 5 ~ 8 min on CMJ.

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Impacts of the intermittent time of 10 ~ 20 min on EVJ

Two studies reported the impact of 10 min of intermittent time following induction exercises on height of CMJ for EVJ, and No visible heterogeneity was observed in height of CMJ among them (I2 = 0%, P = 0.94), as demonstrated in Fig. 10. Therefore, a REM was utilized for the PES analysis. It was evident that 10 min of intermittent time following induction exercises exhibited a little impact on height of CMJ for EVJ, showing a PES outcome of [MD = 0.00, 95% CI: – 0.02 ~ 0.03; Z = 0.09, P = 0.93]. Additionally, six studies mentioned the impact of 12 min of intermittent time following induction exercises on height of CMJ. The meta-analysis results signified obvious heterogeneity in height of CMJ (I2 = 96%, P < 0.0001). The PES analysis using a REM demonstrated that 12 min of intermittent time following induction exercises had a slight impact on height of CMJ, with a PES of [MD = − 0.04, 95% CI: − 0.08 ~ 0.01; Z = 1.56, P = 0.12]. Moreover, three studies reported the impacts of 16 min of intermittent time following induction exercises on height of CMJ. No visible heterogeneity was visualized in height of CMJ (I2 = 34%, P = 0.22). Therefore, a REM was suitable for PES analysis, and the obtained results signified that the intermittent time of 16 min following induction exercises was not obviously associated with the height of CMJ under EVJ [MD = 0.01, 95% CI: − 0.01 ~ 0.02; Z = 1.12, P = 0.26]. Furthermore, two studies mentioned the impact of 20 min of intermittent time following induction exercises on height of CMJ. The meta-analysis revealed remarkable heterogeneity in height of CMJ (I2 = 57%, P = 0.13). Therefore, PES analysis could be completed using a REM, and the results demonstrated that 20 min of intermittent time following induction exercises was not closely linked to the height of CMJ, with a PES of [MD = 0.00, 95% CI: − 0.01 ~ 0.02; Z = 0.51, P = 0.61]. In summary, induction exercises with 10 ~ 20 min of intermittent time had no great impact on height of CMJ, showing [MD = – 0.01, 95% CI: – 0.03 ~ 0.00; Z = 1.48, P = 0.14].

Figure 10
figure 10

Impacts of the intermittent time of 10 ~ 20 min on EVJ.

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Publication bias

The publication bias was analyzed using a FP, as presented in Fig. 11. Most of the studies were located within the inverted triangle of the FP, and the distribution of the scatter points in the FP was symmetric. This symmetrical distribution suggested the absence of remarkable publication bias.

Figure 11
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FP for publication bias.

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Discussion

The phenomenon of PAP was initially discovered in a 1982 animal experiment by Maning et al.42. In this work, intense isometric contractions were induced in the leg muscles of rats, leading to a significant increase in peak tension. Subsequently, Vandervoort et al. (1983)43 utilized the physiological concept of “activation-enhancement” in skeletal muscles. Subjects were instructed to perform maximal voluntary contractions of the anterior tibial muscle, and the observed muscle exhibited the physiological phenomenon of “activation-enhancement”. However, over the next 14 years, PAP did not attract much attention from scholars, and there were relatively few related studies until Brown and Loeb44 formally introduced the “post-activation potentiation effect” in 1998. This officially brought PAP into the academic spotlight as a means of improving strength performance, sparking significant interest and research in related fields. Presently, a growing body of research underscored PAP as a potent means to augment strength, swiftly enhancing athletes’ performance across diverse sports domains such as running, jumping, weightlifting, among others45,46,47. The salience of PAP resides in its capacity to amplify both muscle contraction force and speed, thereby augmenting overall athletic prowess48. Within sports contexts, the pivotal significance of muscle contraction force and speed is paramount, as enhancements in these domains facilitate athletes’ adept execution of skillful maneuvers, thereby fortifying their competitive edge49 and culminating in superior performance outcomes.

There are several induction methods for PAP, mainly including the following aspects50,51. (1) Maximal voluntary contractions: actions that involve maximal muscle contraction force can be implemented, such as maximal muscle contractions or exercises in maximal strength training. This can activate the muscles and induce the PAP effect. (2) Movement replication method: it induces the PAP effect by performing actions with similar biomechanical characteristics to the target movement. For instance, if the goal is to improve vertical jumping ability, one can start with several sets of light-load squats followed immediately by vertical jumps. (3) Explosive movements: it engages in explosive and rapid actions to activate the nervous system and induce the PAP effect. For example, performing quick sprints, jumps, or throwing actions. (4) Same-side inhibition method: after training one limb, immediately performing another action with the same limb. For instance, after weight training with the right arm, immediately performing an explosive movement with the right arm. (5) High-intensity training combination: the weight training and explosive movements are combined. This involves activating the muscles through weight training and then capitalizing on the PAP effect through explosive movements. The primary induction method discussed in the text is the squat induction method within the movement replication approach, aiming to investigate the impact of different intermittent times on the height of CMJ in EVJ. Numerous studies have already demonstrated that PAP can enhance human jumping ability. Jumping ability is a fundamental motor quality required in many sports, and the biomechanical characteristics of jumping movements are similar to those of various sports52,53. Additionally, the simplicity of jumping actions makes it conducive to achieving the maximum transfer of biomechanical enhancement effects.

In this study, inter-set rest intervals ranging from 10 s to 3 min following induction exercises did not show significant effects on the height of CMJ. This could be attributed to the fact that the generation of PAP involves the activation of the nervous system, which may not be fully optimized within a short duration, thus affecting the extent of force output performance54. Within the 10 s to 3-min inter-set rest intervals following induction exercises, the PAP effect may not have fully manifested, or the activation effect of the nervous system might be transient, insufficient to produce significant impacts. Shorter rest intervals may not allow sufficient muscle tissue recovery, leading to the accumulation of muscle fatigue55. This accumulated fatigue could potentially inhibit muscular explosive performance, affecting both force output and vertical jump performance, thereby rendering the PAP effect unable to significantly enhance CMJ height. The PAP effect may have different time windows for different individuals, and shorter rest intervals may not cover the optimal response time for some individuals56. Therefore, within the 10-s to 3-min inter-set rest intervals, this window may not have been fully utilized, resulting in less apparent effects. Research suggested that the effects of PAP may vary across different training stages and time periods, necessitating more precise control over rest intervals to achieve optimal outcomes57. Overall, the lack of significant effects on CMJ height within the 10-s to 3 min inter-set rest intervals following induction exercises may be attributed to factors such as the transient nature of neural activation and the accumulation of muscle fatigue. This underscores the importance of judiciously selecting rest intervals to maximize the utilization of PAP effects and enhance training and athletic performance. Furthermore, it was found that there was significant heterogeneity among the five included studies regarding the effects of inter-set rest intervals of 10 to 15 s following induction exercises on CMJ height. Through sensitivity analysis and subgroup analysis, it was discovered that intervention intensity, gender, age, and the method of PAP induction were not the primary factors causing heterogeneity. Therefore, it was speculated that these heterogeneous factors may stem from details such as sample characteristics, experimental design, and measurement methods, as well as potentially differing correlations with different types of exercises. Due to limited descriptions of relevant details in the included literature, further exploration and analysis of this heterogeneity are not feasible at present, indicating the need for further research in this area.

The results indicated that PAP induction with 4 min of intermittent time significantly increased height of CMJ in EVJ. However, it was observed that a 4-min inter-set rest interval following induction exercises did not significantly impact peak GRF during explosive vertical jumps. This implies that athletes can achieve higher rebound heights within appropriate rest intervals following PAP training, which is beneficial for improving jumping ability. Numerous studies already confirmed the positive effects of PAP on athletic performance, particularly in vertical jumping, where PAP training can enhance peak rebound height, jump height, and explosiveness58,59. Similarly, this study found that a 4-min inter-set rest interval following PAP induction significantly increased CMJ height, reinforcing the practical utility of PAP training in enhancing vertical jumping ability. A 4-min inter-set rest interval following PAP induction can elevate the activation level of the nervous system, improve neuromuscular coordination, and enable muscles to more effectively exert force, resulting in higher CMJ heights. Additionally, PAP may lead to enhancements in muscle contractile strength and explosive performance, resulting in superior muscle performance during vertical jumping and consequently increasing CMJ height. Overall, a 4-min inter-set rest interval following PAP induction significantly influences CMJ height during explosive vertical jumps, likely due to the combined effects of neural activation and improvements in muscle strength performance. However, in the case of peak GRF, its generation involves multiple factors including various muscle groups, neurotransmitters, and joint movements, which may be relatively complex. The 4 min interval may not be sufficient to fully demonstrate the impact of PAP on GRF. Therefore, while PAP exerts a more pronounced effect on CMJ height within 4 min, its influence on GRF may require a longer duration to fully manifest.

Furthermore, it was observed that a 5 to 8-min inter-set rest interval following PAP induction significantly increases CMJ height during explosive vertical jumps, while a 10 to 20-min inter-set rest interval following induction exercises does not show significant effects on CMJ height. These two findings reflect the time dependency and persistence of the PAP effect60. The period of 5 to 8 min following PAP induction is conducive to enhancing the performance of explosive movements, whereas the longer 10 to 20 min inter-set rest interval no longer significantly impacts CMJ height. PAP can enhance neuromuscular coordination, enabling muscle units to synergize better during movement, resulting in stronger force output and subsequently higher CMJ height61. During the 5 to 8 min inter-set rest interval following PAP induction, neural activation persists, and muscle strengthening and explosive capabilities remain at a higher level, allowing for greater force output during explosive movements62, thus enhancing CMJ height. Longer rest intervals may lead to the accumulation of fatigue factors, inhibiting muscular explosive performance, thereby preventing the sustained influence of the PAP effect on CMJ height63. During longer inter-set rest intervals following PAP induction (10 to 20 min), neural activation may gradually diminish, and the explosive capabilities of muscles may begin to decline or return to baseline levels64. This gradual decline or return to baseline may result in a weakening or disappearance of the PAP effect, thereby not significantly affecting explosive jump height. This implies that within appropriate rest intervals following training, athletes can achieve higher rebound heights, which is beneficial for improving jumping ability. However, during longer recovery periods, athletes’ CMJ height does not significantly change. Numerous studies have investigated the impact of PAP on athletic performance and have found that appropriate rest intervals can increase jump height and explosiveness65. However, the research results regarding the optimal length of recovery time are not consistent. Some studies found that shorter rest intervals are most effective for eliciting the PAP effect66, while others found longer rest intervals to be more effective67. Possible reasons include that adequate recovery time allows muscle activation to reach optimal levels and permits the central nervous system to refocus. Brief rest intervals can enhance explosiveness by inducing neural adaptation and activating the body’s biomechanical systems. However, longer recovery times may gradually return muscle performance to baseline levels, thereby reducing the manifestation of the PAP effect. The practical implication of the PAP effect is akin to further enhancing skeletal muscle performance following high-intensity muscle training, which can persist for a period of time14. Multiple studies indicated that the PAP effect is closely associated with the activity of the neuromuscular system, and the intensity of stimulation plays a crucial role in influencing the PAP effect68,69. Low-intensity stimulation does not provide adequate stimulation, while high-intensity stimulation can enhance neural transmission efficiency, thereby further increasing the PAP effect70. Additionally, by engaging in high-intensity repeated training, a series of chemical reactions in myosin may further increase muscle contraction power. Conversely, induction training with fewer repetitions will result in smaller overall skeletal muscle contraction force, thus reducing the manifestation of the PAP effect.

As a meta-analysis, this study still has notable limitations. Firstly, the study includes a limited number of literature sources and relatively few data samples, potentially affecting the reliability and generalizability of the research findings. Furthermore, some articles have only one inter-set rest interval, making it impossible to conduct relevant meta-analyses, which could also impact the stability and reliability of the study results. Due to the singular data source, there may be issues such as sample selection bias and differences in study designs, increasing the risk of conclusion bias. Additionally, to ensure the accuracy of meta-analysis results, a sufficient quantity and diversity of studies are required, a criterion not met by the inclusion of only one article. Moreover, all studies focus solely on CMJ height and GRF during explosive vertical jumps, potentially limiting the applicability of the results. Although this meta-analysis applied the Cochrane Collaboration’s tool for assessing the quality of included studies, there may still be some risk of bias. Future research efforts should focus on expanding the scope of literature inclusion, increasing the number of research samples, and striving to cover different regions, periods, and types of studies to enhance the credibility and generalizability of meta-analysis results. In addition to focusing on data analysis related to CMJ height and GRF during explosive vertical jumps, future studies could attempt to analyze data from multiple perspectives, considering different variables and factors to explore more comprehensive research results and conclusions. This will further enhance the scientific rigor and persuasiveness of the research, providing more reliable evidence and guidance for research and practice in related fields.

Conclusion

This study employed meta-analysis to investigate the effects of PAP inter-set rest intervals on the height of explosive vertical jumps. The results reveal that inter-set rest intervals of 4 min and 5 to 8 min significantly increase the height of explosive vertical jumps, while intervals shorter than 4 min or longer than 8 min do not affect the height of explosive vertical jumps. The conclusions of this study provide support for the optimal rest intervals for PAP training, aiding in the planning and implementation of practical training programs. Additionally, they serve as a reference for future research, which is significant for enhancing athletes’ explosiveness and competitive performance.