Abstract
study investigated the impact of post-activation performance enhancement (PAPE) on the parameters of the 3 min all-out test (3MT) in non-motorized tethered running, ap- plying the concept of complex networks for integrative analysis. Ten recreational runners underwent anthropometric assessments, a one-repetition maximum test (1RM), a running ramp test, and 3MT trials under both PAPE and CONTROL conditions across five sep- arate sessions. The conditioning activity consisted of two sets of six back squats at 60% 1RM. For each scenario, complex network graphs were constructed and analyzed using Degree, Eigenvector, PageRank, and Betweenness centrality metrics. In the PAPE condi- tion, anthropometric parameters and parameters related to aerobic efficiency exhibited greater centrality, ranking among the top five nodes. Paired Student’s t-tests (p≤0.05) revealed significant differences between conditions for end power (EP-W) (CONTROL: 407.83±119.30 vs. PAPE: 539.33±177.10 (effect size d =−0.84)) and end power relativized by body mass (rEP-W·kg −1 ) (CONTROL: 5.38±1.70 vs. PAPE: 6.91±2.00 (effect size d =−0.76)), as well as for the absolute and relative values of peak output power, mean output power, peak force, and mean force. These findings suggest that PAPE alters the configuration of complex networks, increasing network density, and may enhance neu- romuscular function and running economy. Moreover, PAPE appears to modulate both aerobic and anaerobic contributions to performance. These results highlight the importance of network-based approaches for advancing exercise science and providing individualized strategies for training and performance optimization.
force, and mean force. These findings suggest that PAPE alters the configuration of complex networks, increasing network density, and may enhance neu- romuscular function and running economy. Moreover, PAPE appears to modulate both aerobic and anaerobic contributions to performance. These results highlight the importance of network-based approaches for advancing exercise science and providing individualized strategies for training and performance optimization. Keywords:post-activation performance enhancement; 3 min all-out test; complex network 1. Introduction The three-minute all-out test (3MT) was developed from the original 1/time linear model of critical power (CP) [1], where end power (EP) defines the boundary between heavy and severe exercise domains, and the work above this point represents the work above end power (WEP) [2]. The 3MT provides a time-efficient, non-invasive assessment of aerobic and anaerobic performance, validated across different ergometers including non-motorized treadmill (NMT) running [3–6]. In this context, the 3MT offers relevant information for monitoring and prescribing high-intensity training [7,8]. Conducting the 3MT on a NMT may provide a more refined understanding of force application in the Complexities2026,2, 1 https://doi.org/10.3390/complexities2010001
Complexities2026,2, 1 2 of 16 generation of running power, owing to the high movement specificity of this ergometer and the direct derivation of its performance metrics from mechanical parameter kinetics [6]. Performance in high-intensity running depends on muscle power output, which in turn relies on the balance between fatigue and the stability of force–velocity production [9]. Acute improvements in output power may be achieved through warm-up strategies such as post-activation performance enhancement (PAPE). PAPE consists of a conditioning activity (CA) involving voluntary muscle contractions, which enhance subsequent performance by increasing contractile activity during voluntary actions [10]. This potentiation can shift the balance between fatigue and the rate of force development (RFD), benefiting power-dependent efforts [10,11]. PAPE-induced enhancements have been documented across various exercise modalities and conditioning activity paradigms [4,5,12–15]. Recent systematic evidence suggests that CA incorporating resisted exercise exerts a statistically significant effect on both jumping and running performance [16], with these improvements being particularly pronounced during the initial acceleration phases of sprinting following resisted-running CA [11]. Traditional statistical methods are largely based on linear and pairwise comparisons, which limit their ability to capture the multidimensional and nonlinear interactions that typically underlie physical performance. In contrast, complex computational network models provide an integrative analytical framework for interpreting biological processes in sports science [17–20]. Exercise performance depends on systemic homeostatic adjustments that emerge from the dynamic interplay among multiple physiological systems, and these interdependencies can be more comprehensively characterized through network-based approaches. For instance, the Weighted Degree metric represents the number of connections at each node, determining its relative importance and influence. The Eigenvector metric accounts for the relevance of a node’s neighbors, whereas Pagerank evaluates influence based on the significance of connected nodes, allowing a node to achieve a high Pagerank score even with relatively few but highly influential links [18]. The Betweenness metric identifies nodes that frequently occur along the shortest paths between others, emphasizing their role as key connectors within the network [20]. Previous research on PAPE has demonstrated improvements in force, power, and sprint performance following high-intensity conditioning activities [10,15]. However, the underlying mechanisms remain only partially
Pagerank score even with relatively few but highly influential links [18]. The Betweenness metric identifies nodes that frequently occur along the shortest paths between others, emphasizing their role as key connectors within the network [20]. Previous research on PAPE has demonstrated improvements in force, power, and sprint performance following high-intensity conditioning activities [10,15]. However, the underlying mechanisms remain only partially understood, particularly regarding the coor- dination between anthropometric and physiological determinants. Traditional analyses typically address isolated variables, thereby overlooking how their interdependencies con- tribute to overall performance modulation. We propose that the application of a complex network computational model may provide deeper insights into the systemic effects of PAPE during high-intensity efforts, such as the 3MT performed on NMT tethered run- ning. This approach consistently yields both physiological and mechanical parameters suitable for relational analyses. Previous studies by our group have successfully applied centrality metrics (Degree, Eigenvector, PageRank, and Betweenness) to phenomena re- lated to exercise physiology [17,18], sports performance [20], and inspiratory muscle pre- activation [20]. In this context, the present study aimed to investigate the effects of PAPE on 3MT parameters in NMT tethered running using complex network centrality metrics. We hypothesized that PAPE would improve both aerobic and anaerobic outcomes in the 3MT, and that network analysis would more accurately capture the modulations induced by the CA protocol. https://doi.org/10.3390/complexities2010001
Complexities2026,2, 1 3 of 16 2. Materials and Methods 2.1. Subjects The study evaluated ten active male runners (23±4 years; 79.6±17.3 kg (BM); 179±0.08 cm (height); 7.3±2.6% of body fat (%BF); 73.51±14.4 of lean mass (LM)) familiarized with running training sessions twice a week and regional competitions with over 5 km paths. Informed consent was obtained from all subjects. The research was conducted in accordance with the ethical recommendations of the Declaration of Helsinki and all experiments were approved by the Research Ethics Committee of the Faculty of Medical Sciences of the University of Campinas (protocol number [61934516.5.0000.5404] and date of approval [29 November 2016]). Participants were eligible for inclusion if they were able to safely perform the back squat exercise and if they self-reported no metabolic, cardiovascular, respiratory, or orthopedic disorders, as well as no use of medications or recreational drugs. Individuals were excluded if they had maintained a running training routine involving running at least two or three times per week during the previous six months. According to the study criteria, all ten participants could participate in this research. A minimum sample size of ten subjects was calculated for statistical power using G*Power software 3.1.9.2, considering anαerror of 0.05, a power (1-β) of 0.8 and effect size de (ES) of 1.2 [21]. The effect size was obtained in preliminary analyses (pilot study). 2.2. Experimental Design This study employed a randomized within-subject crossover design. Experimental conditions were carried out in five different day testing sessions (Figure, Panel A). In the first section, the participants received information about the experimental design and signed the consent form. In addition, they performed anthropometric measurements [22], and familiarization with the equipment and protocols. During the second visit, researchers measured the subjects’ ventilatory threshold 1 (VT1) (10.0±1.2 km h −1 ) and ventila- tory threshold 2 (VT2) (12.7±1.3 km h −1 ), their maximum oxygen uptake (VO2max) (49.62±7.04 mL·kg −1 · min −1 ), intensity corresponding to maximum oxygen uptake (iVO2max) (17.26±1.39 km h −1 ), and the percentage of ventilatory threshold 2 corre- sponding to iVO2max (%VT2-iVO2max) (73.76±3.13%) [23]. On their third visit,
1 (VT1) (10.0±1.2 km h −1 ) and ventila- tory threshold 2 (VT2) (12.7±1.3 km h −1 ), their maximum oxygen uptake (VO2max) (49.62±7.04 mL·kg −1 · min −1 ), intensity corresponding to maximum oxygen uptake (iVO2max) (17.26±1.39 km h −1 ), and the percentage of ventilatory threshold 2 corre- sponding to iVO2max (%VT2-iVO2max) (73.76±3.13%) [23]. On their third visit, the 1RM of the participant’s lower limbs with free barbell back squat (1RM = 116.6±28.7 kg) was determined to establish PAPE loads [24]. The study followed with two other evaluation sessions (conducted on random different days and counterbalanced across participants through simple random draw), during which participants performed the 3MT in tethered running on a non-motorized treadmill (NMT) [6] under prior CA intervention (PAPE) and control (CONTROL) conditions. The interval between test sessions ranged from 48 to 72 h. Data collection lasted 15 days, counting from a participant’s first to last visits. Every session involving participants’ data collection and trials took place in a temperature and humidity-controlled room (23 ◦ C and with an average humidity of 51%). The study continuously measured the participants’ oxygen uptake (VO2) and car- bon dioxide production (VCO2) during the ramp test and all two 3MT tests by using a gas analyzer (K4b 2 , Cosmed, Albano Laziale, Italy). By analyzing such data, the re- searchers determined the ventilatory parameters of VO2max, VT1, VT2, iVO2max, and %VT2-iVO2max in the ramp test [23]. In addition, the mean oxygen consumption during the final thirty seconds of 3MT (Epc), the peak oxygen consumption during 3MT (3MT VO2peak), and 3MT excess post-exercise oxygen consumption (EPOC) were calculated by adopting bi-exponential analyses recommended for the severe intensity of exercise [25]. https://doi.org/10.3390/complexities2010001
Complexities2026,2, 1 4 of 16 Figure 1. Panel(A). Experimental design timeline showing the five visits made by the partici- pants. 3MT = 3 min all-out tethered running test; CONTROL = no conditioning activity before 3MT; PAPE = post-activation potentiation enhancement by conditioning activity before 3MT;1RM = one maximal repetition test.Panel(B). Scenarios for constructing the complex networks and com- plex network nodes used in these two scenarios.Legend: BM = body mass, Height = height, % BF = % of body fat, LM = lean mass, 1RM = one maximal repetition, VT1 = ventilatory threshold 1, VT2 = ventilatory threshold 2, VO 2max = maximum oxygen uptake, iVO 2max = intensity cor- responding to maximum oxygen uptake, %VT2-iVO 2max = percentage of ventilatory threshold 2 corresponding to iVO 2max, EP = end power, rEP = end power relativized by body mass, WEP = work above end power, rWEP = work above end power relativized by body mass, HRpost = post-testheart rate, CK24h = 24 h post-test creatine kinase, [Lac peak] = post-test peak lactate concentration, 3MT VO 2peak = peak of oxygen consumption during 3MT, EPc = mean oxygen consumption dur- ing EP, EPOC = excess post exercise oxygen consumption, RPE = rating-of-perceived-exertion, Ppeak = peak output power, rPpeak = peak output power relativized by body mass, Pmean = mean output power, rPmean = mean output power relativized by body mass, Fpeak = peak force, rFpeak = peak force relativized by body mass, Fmean = mean force, rFmean = mean force relativized by body mass, Vpeak = peak velocity, and Vmean = mean ve- locity. 2.3. PAPE Protocol Subjects underwent a 5 min warm-up by walking on a motorized treadmill at6 km h −1 before PAPE and CONTROL conditions. For the PAPE condition, participants carried out the warm-up previously described and added to two series of six back squats at 60% 1RM (1RM = 70.0±17.2 kg) [26], with a 2 min rest interval between both tasks [27] and a5 min interval before starting 3MT on an NMT [28]. The choice of the CA protocol aimed to activate the main muscle groups involved
condition, participants carried out the warm-up previously described and added to two series of six back squats at 60% 1RM (1RM = 70.0±17.2 kg) [26], with a 2 min rest interval between both tasks [27] and a5 min interval before starting 3MT on an NMT [28]. The choice of the CA protocol aimed to activate the main muscle groups involved during running and maintaining a balance of moderate effort volume–intensity since 3MT requires maximum effort. 2.4. 3MT All-Out Protocol For the 3MT tests, the study used a standardized NMT where subjects ran with a belt attached to their waists by an inextensible steel cable with a load cell (CSL/ZL-500, MK https://doi.org/10.3390/complexities2010001
Complexities2026,2, 1 5 of 16 Controle e Instrumentação Ltda., São Paulo, Brazil), directly measuring their horizontal force [6]. The study captured their vertical force during a running test by using four load cells positioned under a platform (NMT). Signals captured mechanical measures (LabView Signal Express 2009 National Instruments ® , Austin, TX, USA) with 1000 Hz acquisition. All mechanical parameters of peak output power (Ppeak-W/rPpeak-W·kg −1 ), mean output power (Pmean-W/rPmean-W·kg −1 ), peak force (Fpeak-N/rFpeak-N·kg −1 ), and mean force (Fmean-N/rFmean-N·kg −1 ) were displayed in both absolute and relative body mass values. Peak velocity (Vpeak-m·s −1 ) and mean velocity (Vmean-m·s −1 ) were also recorded. The methodological details about the signals captured mechanical measures are visualized in Supplementary File S1.1. Subjects were told to start running as fast as possible on the NMT system as soon as they heard a signal. The study considered successful the sessions in which a subject could run along with the whole 3 min task—always assisted by a researcher, who constantly gave them verbal incentives without disclosing how much time was left to finish the task. After every test in each session, subjects filled out a form about their rating of perceived exertion (RPE) [29]. 2.5. Blood Lactate, HR, and CK Measurements Blood samples were collected from the participants’ ear lobes at rest ([Lac rest], mmol·L −1 ) and 5 min post-3MT ([Lac post], mmol·L −1 ), as well as at rest (CK rest, U·L −1 ) and 24 h after exercise (CK24h, U·L −1 ). Lactate and creatine kinase concentrations were determined by standard enzymatic spectrophotometric methods (BIOCLIN ® , Delft, The Netherlands, ref. K010) [30]. The biochemical analyses followed standardized and vali- dated procedures, with precision and reproducibility confirmed by internal quality-control tests and intra-assay variation within acceptable limits for enzymatic methods (Supple- mentary File S1.2). Heart rate (HR) was recorded continuously (beat-by-beat) using heart rate monitors (Polar, RS800CX) at rest (HR rest, bpm) and immediately after each test (HR post, bpm). 2.6. WEP and EP Computations The study collected and analyzed each subject’s kinetics output power according to time.
internal quality-control tests and intra-assay variation within acceptable limits for enzymatic methods (Supple- mentary File S1.2). Heart rate (HR) was recorded continuously (beat-by-beat) using heart rate monitors (Polar, RS800CX) at rest (HR rest, bpm) and immediately after each test (HR post, bpm). 2.6. WEP and EP Computations The study collected and analyzed each subject’s kinetics output power according to time. The standard feature curve of 3MT kinetics output power involves high values at first that decrease until stabilization is reached at the end of the test. In order to determine WEP and EP, the study followed 3MT original methodology [1], considering the average output power of the final 30 s of the test for subjects’ aerobic capacity measured in watts (EP—W) and the total area above the EP line for calculating their anaerobic capacity measure in kilojoules (WEP—kJ). The study considered the integral of the total area above the EP line (total area minus aerobic area). The study relativized data by the individuals’ body mass by dividing obtained values by their mass in kg to obtain (rEP-W·kg −1 ) and (rWEP-kJ·kg −1 ). 2.7. Statistical Analysis We used the software MatLab ® 7.0 (MathWorks™) to carry out the digital signal pro- cess and statistical data treatment—acquisition rate of the signals of mechanical parameters (1000 Hz)—and software Statistica 7.0 (Statsoft, Tulsa, OK, USA) for statistical analysis. According to the Kolmogorov–Smirnov and Levene tests, data presented normality and homogeneity, respectively. Thus, the study used methods already preconized in paramet- rical statistics. We used paired Student’s t-test (PAPE versus CONTROL conditions) for analyses involving only two variables for the same group. The effect sizes (ES) were inter- preted according to the scale proposed by Hopkins et al. (2009): <0.2 trivial, 0.2–0.6 small, 0.6–1.2 moderate, 1.2–2.0 large, 2.0–4.0 very large, and >4.0 extremely large [31]. Pearson’s linear regression test obtained the correlations between mechanical and physiological pa- https://doi.org/10.3390/complexities2010001
Complexities2026,2, 1 6 of 16 rameters using Statistica 7.0. Linearity was verified through scatterplots, and potential outliers were inspected visually. Only data meeting these assumptions were included in the analyses. The study described every measure in mean±standard deviation, and the significance level wasp≤0.05. 2.8. Complex Network Analysis For complex network analysis, the results referring to the anthropometric characteris- tics, conditioning, and mechanical parameters (such as those obtained in ramp, 1RM, and two conditions of the 3MT test in tethered running on a non-motorized treadmill) were allocated into two different scenarios (all nodes can be seen in Figure, Panel B), according to the experimental design (CONTROL and PAPE). For building the graphs (G = V, E, w), the nodes were obtained from the variables measured as unidirectional vertices (V) and edges (E) representing the interactions between these variables, and the weight function of the edges (w) was considered in the graphs. From the inserted nodes and the connections returned from the graphs and based on previous studies [17–20], the Weighted Degree, Betweenness, Pagerank, and Eigenvector centrality metrics were determined using Gephi software (version 0.10.1, Paris, France) implemented in the Java programming language (version 0.9.2), with images considering the Fruchterman–Reingold layout [32], after data processing by a specific algorithm for this purpose in the MATLAB environment. The networks presented 31 nodes and, like the threshold generally purposed in correlation networks construction [33], their edges were obtained by the statistically significant “r” values (p< 0.05) from all results evaluated by Pearson correlation in each scenario (PAPE and CONTROL). The comparisons between two complex network scenarios were per- formed using the weighted Jaccard distance in two fashions toward having a graph- and node-based dissimilarity measurement [34]. 3. Results Table two conditions for the values of EP absolute and rEP, and the mechanical parameters of Ppeak Pmean, Fpeak, and Fmean in absolute and relativized values. The other mechanical parameters and physiological data of WEP, blood lactate concentration, heart rate, oxygen consumption, and subjective perception of effort did not differ between PAPE and CON- TROL conditions. The increase in results for the PAPE condition versus the
of EP absolute and rEP, and the mechanical parameters of Ppeak Pmean, Fpeak, and Fmean in absolute and relativized values. The other mechanical parameters and physiological data of WEP, blood lactate concentration, heart rate, oxygen consumption, and subjective perception of effort did not differ between PAPE and CON- TROL conditions. The increase in results for the PAPE condition versus the CONTROL condition in 3MT parameters were 32.2% for EP and 28.4% for rEP, 15.7% for Ppeak and 15.1% for rPpeak, 23.9% for Pmean, and 22.2% for rPmean, 18.5% for Fpeak and 15.6% for rFpeak, and 24.8 for Fmean and 22.8% for rFmean. The d-Cohen test presented moderate effects when comparing both 3MT conditions (PAPE and CONTROL) for the following parameters: EP, rER, Ppeak, rPpeak, Pmean, rPmean, Fpeak, rFpeak, Fmean, and rFmean. In addition, the correlations between both proposed interventions (PAPE and CONTROL) for 3MT are shown in Table. The study also found significant correlations in 3MT application between WEP CONTROL and Ppeak CONTROL (r = 0.85,p= 0.02), and between rWEP CONTROL and rPpeak CONTROL (r = 0.67,p= 0.03), but not in PAPE conditions. WEP PAPE correlated negatively with VO2max (r =−0.78,p= 0.00) and positively with anthropometric parameters of BM (r = 0.72,p= 0.01) and LM (r = 0.68,p= 0.02). These correlations were not observed in the WEP CONTROL. https://doi.org/10.3390/complexities2010001
Description
The study explores how PAPE affects running performance metrics.