Complex networks analysis reinforces centrality hematological role on aerobic–anaerobic performances of the Brazilian Paralympic endurance team after altitude training

This study investigated the 30-days altitude training (2500 m, LHTH-live and training high) on hematological responses and aerobic–anaerobic performances parameters of high-level Paralympic athletes. Aerobic capacity was assessed by 3000 m run, and anaerobic variables (velocity, force and mechanical power) by a maximal 30-s semi-tethered running test (AO30). These assessments were carried out at low altitude before (PRE) and after LHTH (5–6 and 15–16 days, POST1 and POST2, respectively). During LHTH, hematological analyzes were performed on days 1, 12, 20 and 30. After LHTH, aerobic performance decreased 1.7% in POST1, but showed an amazing increase in POST2 (15.4 s reduction in the 3000 m test, 2.8%). Regarding anaerobic parameters, athletes showed a reduction in velocity, force and power in POST1, but velocity and power returned to their initial conditions in POST2. In addition, all participants had higher hemoglobin (Hb) values at the end of LHTH (30 days), but at POST2 these results were close to those of PRE. The centrality metrics obtained by complex networks (pondered degree, pagerank and betweenness) in the PRE and POST2 scenarios highlighted hemoglobin, hematocrit (Hct) and minimum force, velocity and power, suggesting these variables on the way to increasing endurance performance. The Jaccard’s distance metrics showed dissimilarity between the PRE and POST2 graphs, and Hb and Hct as more prominent nodes for all centrality metrics. These results indicate that adaptive process from LHTH was highlighted by the complex networks, which can help understanding the better aerobic performance at low altitude after 16 days in Paralympic athletes.

Physical training. The altitude training was carried out in Colombia, at 2500 m. Throughout the period, the athletes and the technical team remained in the same residence, which facilitated controlling nutrition, hydration and post-workout recovery. During the entire training period, athletes were accompanied by a multidisciplinary team composed of physiotherapist, massage therapist, nutritionist and psychologist.
The training strategies presented in Fig. 2 included 7-day microcycles, with 12 training sessions: two sessions characterized by interval training (greater intensity), two strength training sessions in the gym, one training session with greater volume, two flexibility sessions and five sessions of lighter training (i.e., regenerative), amounting to 130-186 km (weekly). Regardless of disability or gender, the athletes do not present important limitations in the motor gesture to the running, and because they are athletes with a high-technical level, the training structure was similar for all participants. The training program respected the acclimatization period, with the training sessions taking place with progression of intensity and quantity during the altitude period. The training intensity was determined based on the evaluations of 3000 m, following the observations of Lourenço et al. 30 . According to this author, results coming from a maximum run of 3000 m can provide information to determine different intensity zones; that is, Zone 1, running velocity referring to the ventilatory threshold (vLT); Zone 2, between vVT and respiratory compensation point (vRCP), and Zone 3, above vRCP 30 . Four weeks before starting the training, as well as at the training period at 2500 m, the exercises were characterized by 3-week microcycles, with progressive increase in workload, followed by a less intense week. At altitude, endurance and interval training with distances equal to or greater than 400 m were performed in the same way as is performed at low altitudes, considering the total running volume. However, the intensities were reduced from 10 to 8% in the first week, 6% in the second week and 3% in the other days at 2500 m. On the other hand, speed stimuli with distances shorter than 400 m, as well as muscle strengthening training, did not change when compared to training performed at low altitudes. In the first week after returning, sessions were performed with reduced volume Figure 1. Hematological and physical performance evaluations performed before (PRE), the ascent to altitude, during the stay in Colombia (2500 m) and after returning to lower altitudes (POST). Procedures performed during the entire period of training and evaluations. Assessment schedules: PRE-days -2 and -1 (before the altitude period), POST1-days 5 and 6 (after the altitude period), POST2-days 15 and 16 (after the altitude period). For these moments, the sequential tests performed were anaerobic (AO30) and aerobic (3000 m), respectively.

Scientific Reports
| (2022) 12:1148 | https://doi.org/10.1038/s41598-022-04823-w www.nature.com/scientificreports/ and intensity, respecting the readaptation period. Then, in the second week after returning, the training was characterized by an increase in specific exercises, with a decrease in quantity and an increase in intensity (Fig. 2).

Running evaluations. 3000 m test for performance evaluation. All 3000 m tests were carried out in São
Paulo city, on a synthetic rubber track with official measures (400 m). The tests were always carried out in the morning, after a standard warm-up routine of 15 min of continuous running at 12-13 km h −1 , 5 min of dynamic stretching, 10 min of coordination exercises and three to four repetitions of 80 m with progressive rhythm running, followed by 5 min for the return of physiological responses to rest. The total time of the 3000 m tests was recorded with a Casio digital stopwatch, model Hs-80tw-1DF, used for comparisons between PRE, POST1 and POST2.
Anaerobic test: all-out of 30 s (AO30) in semi-tethered running. Of the ten participants who carried out the 3000 m tests and blood tests, eight were also submitted to a 30-s semi-tethered running (AO30). In this case, six men and two women were evaluated (34.3 ± 9.2 years, 63.5 ± 6.1 kg, 170.5 ± 4.2 cm). Among these, three athletes had visual impairment, one athlete, mild physical impairment in the upper limb, and four were guide athletes, that is, able-bodied individuals.
To assess the velocity, force and consequently the mechanical power of the running, the athletes were submitted to the 30-s test in semi-tethered running (AO30). The test was carried out with the athletes tethered to a sensorized equipment (variable-resistance car-VRC), to obtain records with high-frequency signals that were recorded in an on-board computer. The prototype (VRC) was developed in the Laboratory of Applied to Sport Physiology (LAFAE), Unicamp-Limeira-SP (Fig. 3) 31 . In this assessment protocol, athletes were instructed to run as fast as possible for 30 s, attached to the VRC by means of a traction belt and a steel cable, connected to a calibrated dynamometer, allowing the system to measure the application of drag force from records and signals www.nature.com/scientificreports/ (1000 Hz) using the LabView-SignalExpress software. A disk brake in both rear VRC wheels enabled the imposition of resistance, set at 9% of body mass 31 . The velocity was obtained from the Hall-effect sensor attached to the front fork (which fixed the wheel), and four magnets were inserted equidistantly into the wheel rim (16 in. in diameter), capturing and sending signals to the computer each time it the magnets crossed the sensor. The force and Hall-effect sensors signals were synchronized and analyzed using a dedicated algorithm in the MatLab environment. Thus, the power was obtained by the product of the force and velocity data of the VRC ergometer. All AO30 tests were performed on the official athletics track, at low altitude (760 m), 2 days before the start of altitude training (PRE), as well as 5 days and 15 days after returning to lower altitudes (POST1 and POST2, respectively). During the AO30, the participants were verbally encouraged to maintain the maximal velocity throughout the whole all-out test. The maximal, mean and minimum of power, force and velocity were used as measurements, as well as fatigue indexes (FI) for each one of these mechanical parameters. The force and power parameters were normalized by athlete body mass. The FI was obtained as the decay (%) from the highest to the lowest value.    32 , after being processed step-by-step in algorithms specifically built for the study in MatLab environment (MathWorks Inc.). The complex networks were built considering non-directed relations and with weight, graphs G = (V, E, w), for both scenarios, where V (vertices) represents nodes and E (edges), the interactions between two variables in this network. Weights were calculated by the correlation value 33 , according to Pereira et al. 23 , using critical r of 0.5 (moderate correlation). The centrality metrics adopted for the analysis were the pondered degree, pagerank and betweenness.
The comparisons between two complex networks, built considering the PRE and POST2 scenarios and hereinafter referred to as G PRE and G POST2 , were performed using the weighted Jaccard distance 34,35 , in two fashions toward having a graph-and node-based dissimilarity measurement. In both cases, this measure assumes higher values if two networks or pairs of nodes being compared are dissimilar and lower values if they are similar.
To compute the dissimilarity measure between two complex networks in a graph-based fashion, we computed the weighted Jaccard distance between two networks G PRE and G POST2 , as suggested by Tantardini et al. 35 . More precisely, let G PRE = (V PRE , E PRE ) and G POST2 = (V POST2 , E POST2 ) two networks aligned and with adjacency matrices adj(G PRE ) = A and adj(G POST2 ) = B, respectively. The weighted Jaccard distance is d GWJ = 1 − J GW (G PRE , G POST2 ), where J GW is the Jaccard index defined as: where V = V PRE = V POST2 . In turn, the node-based measurement for a node of interest v was achieved by computing the weighted Jaccard similarity as suggested by Fender et al. 34 : where w(x) refers to a centrality measurement of the node x. Thus, the node-based weighted Jaccard distance can be defined as d NWJ = 1 − J NW (v), which give us a measurement of how a node of interest v is dissimilar to their neighborhood. In this study, we used these metrics to measure how the POST2 phase affected some variables considered in our study.
Results 3000 m tests. The performance results in the 3000 m running test (Fig. 4), showed that nine of the ten participants presented their best result at POST2 (i.e., at 16 days after returning from altitude training). Another point observed was that, when compared to PRE, nine athletes decreased their performance on the 6th after returning (POST1).
Analysis by complex networks. Figure 7 presents graphs for the centrality metrics pondered degree (panel   The comparison between networks built from PRE and POST2 scenarios showed a dissimilarity of d GWJ = 0.852. Furthermore, Fig. 8 shows a comparison between graphs built from the PRE and POST2 scenarios using the node-based weighted Jaccard distance for the Hb and Hct variables. We also observed that both variables presented a higher dissimilarity among their neighbors for the POST2 scenario, in comparison to the PRE scenario.

Discussion
The main findings of our study show a positive effect of LHTH on the hematological responses of athletes during altitude training and increase in anaerobic parameters and performance when running after 15-16 days of readaptation to low altitude, suggesting that this strategy is significant for high-performance athletes, in the case of elite runners of the Brazilian Paralympic team. It is important to highlight the quality of the athletes submitted to LHTH for 30 days, as well as the refined training set of physical performance tests used in our study.
The benefits of living high-training high (LHTH) to improve performance at low altitude are controversial. This is due to factors that may directly influence the results: (1) insufficient hypoxic effect to stimulate the total volume of red blood cells/hemoglobin mass, due to insufficient altitude (< 2000 to 2200 m) and/or an insufficient period of exposure, < 3-4 weeks; (2) insufficient training stimuli to improve the function of the neuromuscular and cardiovascular system;( 3) overtraining, stress symptoms and infections 10 . However, when we consider the total time of the different moments of the 3000 m tests, we can state that the effects of altitude and the training performed generated similar adaptations for all the participants, confirming the hypothesis of positive influences of altitude training on aerobic capacity.
In the present study, the altitude of 2500 m was chosen to LHTH for two main reasons. The first is related to the fact that it has been added and suggested that altitudes between 2000 and 2500 m seem "ideal" for erythropoietic, physiological adaptations and endurance performance improvements 2,36 . Chapman et al. 22 , using the LHTL model, when they submitted university runners to four different altitudes (1780, 2085, 2454, and 2800 m) for 4 weeks, they found that only runners living at moderate altitudes (2085 and 2454) increased (2-3%) a 3000 m time trial immediately and 2 weeks after the return to sea level. The second refers to the attempt to guarantee hematological adaptations, but concomitantly, without a great reduction in the absolute intensity of the aerobic training, mainly because the investigated athletes compete in endurance events and the training phase was part of a Paralympic cycle. Studies have clearly shown that during training performed at altitude as the absolute training intensities at the anaerobic threshold and at VO 2peak are reduced [37][38][39] and this aspect was predicted in our schedule (Fig. 2).
Studies that analyze performance after returning from altitude are scarse 22 . Most evaluate performance before the onset of training and shortly after returning, thus losing important information within a 2-3-week window. In the training model presented in this research, the athletes performed tests of 3000 m before starting training at 2500 m (altitude) and repeated the tests with 6 and 16 days after altitude exposure. In the tests performed 6 days after returning, nine of the ten athletes showed a decrease in performance. However, 16 days after readaptation at low altitudes, nine of the ten athletes had their best result of the entire season, with a reduction of 15.4 s in the 3000 m race between the initial evaluation and POST2. Similar results were found by Levine and Stray-Gundersen 40 , who reported improvements of 13.4 s in a 5000 m race, 14 and 21 days after returning from altitude-in the case of athletes who performed the LHTL training model. The results in both the LHTH and LHTL models suggest that the effects of altitude training can be maintained for up to 3 weeks.
Levine and Stray-Gundersen 1 reported that due to lower oxygen availability, stress stimuli tend to occur at reduced intensities, leading to losses in velocity gain. In our study, the results from 30 s semi-tethered running showed that, 5 days after returning from a 30-day phase of training at altitude at 2500 m, six of the eight evaluated athletes had a decrease in velocity and mechanical power, which may be associated with a decrease in intensity www.nature.com/scientificreports/ during the interval training in hypoxia. On the other hand, after a 15-day rehabilitation phase, seven of the eight evaluated athletes achieved the best outcomes of their careers.
Regarding the force component obtained in AO30, we verified reduced values (p < 0.05) in POST1 and POST2. Of the eight athletes studied, only one did not show lower results in force after the intervals when returning from hypoxia training. A study conducted with humans 41 aiming to isolate the effect of reduced partial oxygen pressure, with progressive elevation to extreme altitudes (equivalent to the peak of Mount Everest), was conducted in order to verify the behavior of lower and upper limbs muscles at the end of 40 days in simulated hypoxia. The data revealed, by computed tomography, that muscle areas were smaller after chronic exposure to altitude, and that the cross sections of Type I and II fibers were also reduced 41 . Similar results were observed in animals under similar conditions, when the authors observed elevated protein expression of myostatin, with significant muscle atrophy 42 . Vargas-Pinilla 19 reports that training under hypoxia reduces muscle strength and power, corroborating thus our results. This suggests the need for adjustments in strength training during LHTH periods, since in POST2 all athletes had their best personal result in the 3000 m test. This led to questioning on whether better performance could be observed if muscle strength is not reduced after chronic hypoxia.
To evaluate hematological changes, the athletes in our study were submitted to blood tests before the training (PRE), during exposure to chronic hypoxia at an altitude of 2500 m (days 1, 12, 20 and 30) and 15 days after returning (POST2). In 2016, Garvican-Lewis et al. 6 questioned whether responses from a longer stay at lower altitudes could cause the same response in hemoglobin concentration, when compared with a shorter exposure time at higher altitudes. More recent studies, using the same statistical approach proposed in a meta-analysis by Gore et al. 43 , suggested a model to determine the hypoxic dose, called "kilometer-hour", which is the multiplication of km, indicating the altitude used for exposure and the total duration of exposure in hours (km h). The model suggests a 3.3% increase in hemoglobin mass per 1.0 km h. In this sense, our study used 2.5 km of altitude and 720 h, totaling 1.8 km h. Thus, an increase of 6.8% in hemoglobin levels is quite compatible with this prediction. This parameter has been considered an indicator of stress external to hypoxia 6 . In our study, athletes confirmed such adaptations at day 30. Considering our model, with 30 days of LHTH training, amounting to 720 h of exposure at 2500 m, our data showed a gain of 6.8% in hemoglobin levels (g dL −1 ). Although the immune system is impaired by exposure to hypoxia 44 , Pyne et al. 45 when investigating the immune responses after 21 days of training at 2102 m, found, in addition to other changes, significant reductions of 38% without the number of leukocytes from elite swimmers, followed by increases in the production of interleukin-1beta induced by mitogen (IL-1beta), IL-4 and interferon-gamma (IFN-gamma). When comparing the smallest changes observed in the members of the technical committee, who were exposed to the same altitude dose, but did not perform the training program, and therefore were used as a control group, these authors concluded that although some immunological parameters are changed with training at moderate altitude, as training-induced changes may be secondary to those induced solely by altitude.
In this study, lymphocytes and platelets increased by 53 and 22% respectively after the first day of altitude exposure (d1) and remained high, but stable, until the end of exposure (d30), with values returning to baseline levels (PRE), after 16 days (POST2) of return to low altitude. In contrast, monocytes reduced by 56% in d1, remained stable until d30 and increased again to values close to PRE, after POST2. Additionally, despite the significant changes in some immunological markers during the LHTH model, the values will remain within the reference ranges. Furthermore, unlike the findings by Pyne et al. 45 , in the present investigation, the leukocytes were not altered during the 4 weeks of LHTH. Brugniaux et al. 44 , when investigating the effects of LHTL performed at different altitudes [1200 (control group), 2500, 3000 and 3500 m], only found a significant increase in the amount of leukocytes when the altitude was 3500 m. Thus, our findings reinforce the results of previous studies that demonstrated that athletes, in general, can tolerate 4 weeks of LHTH, without major changes in the immune system.
Although the effects were satisfactory, we realized that by the time the athletes presented their best results in the 3000 m tests, that is, 16 days after altitude exposure, hemoglobin rates had already returned to their values in the PRE moment. With this, it is interesting to note that although greater hemoglobin rates are important to increase oxygen transport, such changes did not necessarily need to remain high for the athlete to achieve peak performance in tests with aerobic predominance, at least in the training model used. Gore et al. 14 emphasize that improvements in performance after altitude training may be associated with a set of factors, not only related to hematological changes, but also greater muscle efficiency, probably at the mitochondrial level, angiogenesis, glucose availability, as well as greater clearance and ability to tolerate lactic acid production at sea level.
The analysis of centrality in complex networks sought to understand, through graphs, the integration of the studied variables before (PRE) and 15 days after altitude training of athletes at lower altitudes (POST2). We chose these two scenarios, considering that we observed, by conventional statistics, a significant reduction of time in the 3000 m (T3K) in POST2. As these athletes were mainly focused on long-distance and medium-distance running, the search for strategies such as the one investigated in our study (hypoxia-altitude training) is intended to have this better performance. We sought to study, through complex networks, how the different variables are integrated in the two scenarios, in order to understand, in terms of centrality (pondered degree, pagerank, and betweenness), how such relationships are established before and after the success with LHTH strategy. The graphs referring to pondered degree showed interesting characteristics before and 15 days after altitude training. In the PRE scenario, the graph presented slightly higher density than in the POST2 scenario (0.446 vs 0.418). Furthermore, the graph-based weighted Jaccard distance (dGWJ) showed that both networks PRE and POST2 are highly dissimilar, which corroborate the results summarized in Fig. 7. Moreover, in the POST2 scenario, the node-based weighted Jaccard distances (dNWJ) revealed that both variables Hb and Hct presented higher dissimilarity values from their node's neighbors, compared with the PRE scenario. These results suggest to us that both variables have their discriminability properties increased in the POST2 scenario. In addition, there was a greater balance between the nodes in the positions of higher centralities (ranking) in the first scenario. After www.nature.com/scientificreports/ altitude training, graph analysis indicated higher ranking for parameters related to hematological characteristics, which was strongly evidenced for Hb and Hct, establishing that such nodes increased their connectivity with the others studied. We also emphasize other physiological parameters clearly related to oxygen transport, which had their privileged positions in the POST2 graph-MCHC and RBC, for example. These responses to altitude reveal that, even for athletes with reduced capacity to adapt to training, due to the high performance already achieved, the effects of hypoxia in the LHTH model are quite effective. In relation to the pondered degree, in both scenarios, the T3K did not show much change in position between the training strategy adopted (13th and 11th). However, the minimum values of power, force and velocity, which were not different from the conventional statistics between the two moments, were presented in the analysis by complex networks, with significant evidence in the POST2 scenario, thus presenting a greater number of connections with other parameters. These nodes started in extremely low-ranking positions in the PRE scenario, and rose to incredible prominence in the POST2 graph. Considering these variables (HCHC and RBC) as of great importance for aerobic activities, the new higherranking positions of these nodes in the studied centralities (pondered degree, pagerank and betweenness) could mean that a greater interaction with the other analyzed parameters seems to be essential for high endurance performance. This brings understanding closer to justify the shortest times obtained for the 3000 m run after 15 days of return from training at altitude.
Quite interestingly, in terms of importance, all these vertices had similar design to the pagerank metric, suggesting that these first-grade parameters have more influence when compared to other parameters. This is in line with the strategy of high-altitude training, since in this metric the optimal placement of a node does not necessarily involve the number of connections, but rather with the connections with other centralizing nodes. For pagerank, the position of the T3K was the same in both scenarios (14th), suggesting equal integration between the other parameters that remained unchanged with the intervention at higher altitudes. This may suggest that, regarding performance, the relationship between nodes gives energy support to the task that, in fact, leads to gains in sports performance. Finally, despite Hb and Hct already appeared as important nodes in the intermediation between pair of nodes in PRE scenario, betweenness centrality analysis highlighted these nodes in POST2 condition, reinforcing their significance in an integrated way, potentiated by altitude training (Fig. 8, panel C). Thus, even with a consensus on superior endurance performance after training at altitude, our study showed that, for some aerobic parameters, there was no statistical significance (PRE versus POST2) when applied to the conventional analysis. However, especially for Hb and Hct, the analysis of complex networks reinforces these nodes as having the greatest centrality, which, despite showing minimal changes, are sufficient to promote the best performance in an integrative way.

Conclusion
Our study confirms the positive effects of the LHTH model for high-performance long-distance Paralympic runners. Altitude can raise hematocrit and hemoglobin levels after 30 days of intervention, even for already highly trained athletes. After 5 days of readaptation, athletes showed a reduction in velocity, force and mechanical power in AO30, but after 16 days of readaptation at low altitudes, variables related to power and velocity returned to their initial conditions. Although losses did occur shortly after 5 days of readaptation, the performance in running 3000 m after 16 days of readaptation at low altitudes was high compared to the conditions that preceded altitude training, suggesting a clear beneficial effect of the LHTH model. Furthermore, the integrated model of complex networks confirms the prominence of hematological parameters, especially hematocrit and hemoglobin, as central nodes in this adaptive process. Thus, this study suggests that the LHTH model at an altitude of 2500 m for 30 days, followed by a period of 15-16 days of readaptation to low altitude, is effective in improving the physical performance of long-and medium-distance runners.

Study limitations.
Despite well conducted, our study shows some limitations. (1) In POST1 there is no hematological analysis, as it was performed on the last day of altitude and considering the resumption of training already focused on the next competitions, due to logistics, it was not possible to perform it after 5 days of returning from altitude; (2) despite the athletes were accompanied in the PRE, altitude and POST periods by nutritionists from the Brazilian Paralympic team, nutritional analysis was not conducted in the present study. In future opportunities, certainly we will follow this way; (3) the sample size was not to be higher because all Brazilian Paralympic athletes who perform tests in world competitions and Paralympics were studied. This choice of subjects was taken precisely for applications in complex networks, since due to the athletic conditions of these, we have a sample that is very focused on application in high performance; (4) in a way, the above limitation leads to the absence of a control group, as it is not possible to carry out a different treatment for the development of performance for athletes of this level. Thus, randomizing the study could hinder the sport development of this very specific sample of athletes. Future studies by our group will seek to minimize such limitations.