Participants

Seventy-two healthy participants (age = 25.7 ± 4.4 years; height = 169.2 ± 9.8 cm; body mass = 67.7 ± 11.2 kg; one repetitions maximum (1RM) in squat = 95.5 ± 28.7 kg; ratio 1RM/body mass = 1.4 ± 0.3) took part in the study (Table 1). Recruitment of participants began on March 1, 2021, and ended on June 31, 2021. Prior to participation, each subject provided written informed consent, which was approved by the ethics committee of the University (PID2019-109632RB-100), and which adhered to the Declaration of Helsinki. The Office of Responsible Research (OIR), as the University’s ethics committee, approves the research ethics statement under register 2019.417.E.OIR; 2020.34.E.OIR and reference DCD.RSS.02.19.

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Table 1. Participant characteristics: Gender, n, age, height, body mass, 1RM squat, 1RM/body mass.

https://doi.org/10.1371/journal.pone.0307949.t001

Participants were instructed to maintain their normal lifestyle, including nutritional and hydration states. Caffeine intake was not allowed in the 3 h before measurements. In addition, resistance training sessions were not allowed in the 72 h before the experimental sessions. All participants had at least one year of experience in resistance training in the squat exercise and they had no injuries during the six months prior to the study.

Procedure

Participants attended three testing sessions separated by at least 72 h. To avoid experimental data bias variability, participants were scheduled at the same time for each session. On day one the participants performed the 1RM squat test after being familiarized with the warm-up protocol. The squat depth was in the parallel squat position [18]. The 1RM test was performed following an established protocol, which required the load to be progressively increased until the mean propulsive velocity was below 0.5 m/s as several studies advocate the use of movement velocity for 1RM estimation [19]. The estimated 1RM was automatically calculated by the specialized software of the linear position transducer (T-Force System, Ergotech, Spain). In the second and third sessions the participants performed the experimental protocol, which consisted of a total of five sets of four consecutive repetitions (e.g., no rest between them) in the squat exercise. The back-squat exercise required the subjects to rest the bar on their trapezius and then squat to the parallel position, which was defined as when the greater trochanter of the femur was lowered to the same level as the knee. Adequate depth of the repetition was ensured by placing a small bar at the individual height at which each participant had to descend to touch it lightly with the buttocks and perform the ascent. Participants performed one set with each of the following loads: 10%, 30%, 50%, 70%, and 90% of 1RM at a preferred velocity. The order of loads was balanced between the participants. Rest intervals between sets were 4 min.

Data collection and analysis

To determine RM and monitor mean propulsive velocity during the set protocol, a linear encoder system was employed (T-Force Dynamic Measurement System, Ergotech, Murcia, Spain). The platform force data required for analysis were obtained using a Kistler (Switzerland, Mode 9287BA), which was calibrated with InstaCal software (Measurement Computing Corporation, Norton, USA) before starting the protocol. Acceleration signals were recorded utilizing one IMU made by STT-System (San Sebastián, España). The IMU was situated in the lumbar region at the level of the iliac crest between the L3 and L5 vertebra. Both the force platform and IMU were registered at 100 Hz through the iSenTM software (STT-System, San Sebastián, Spain). The SD and variability structure of the acceleration modulus time series were analyzed. The modulus (or vector) of the acceleration was obtained by calculating the square root of the sum of the values recorded on the Z, X and Y axes squared. The series were analyzed using DFA for the fractal scaling, FuzzyEn and SampEn, for analyzed the regularity or predictability. FuzzyEn was calculated using a protocol set out by Chen et al. [9], the parameters used were m = 2, r = 0.2 * SD, and n = 2. SampEn was calculated using a protocol set out by Yentes et al. [20], the parameters used were m = 2 and r = 0.2 * SD. DFA was calculated according to Peng et al. [8] and using windows of one-second duration. The windows’ duration was adjusted based on the sampling frequency. Therefore, we used 4 initial windows and 100 final windows. The use of IMUs for the study of variability through acceleration in such protocols has shown moderate to good reliability and a relatively low standard error of measurement [21].

Statistical analysis

The data obtained were analyzed using JASP 0.17.1.0 (Jeffreys’s Amazing Statistics Program). The normality of the variables was assessed using the Kolmogorov-Smirnov test. Repeated measures ANOVAs with one factor (5 x 1) were then performed on the different loadings, using analyses to see if there were differences in the different percentage loadings on the variables’ DFA, FuzzyEn, SampEn, and SD. A post-hoc analysis was performed to analyze pairwise comparisons and the Bonferroni correction was applied. The level of statistical significance was considered p < 0.05. Partial eta squared (η²p) was calculated as a measure of effect size and to provide a proportion of the total variance attributable to the factor. Effect size values ≥ 0.64 were considered strong, around 0.25 were considered moderate, and ≤ 0.04 were considered small [22].

Load intensity and amount of variability

Increasing load intensity is one variable that can condition motor patterns in squat execution [23]. In our study, the standard deviation showed a significant decrease in the variability of movement with increasing intensity from the 70% load when analyzing the IMU, while the force platform shows an increase in this variable at the first loads, stabilizing from 50%. Our results on the force platform for variability are consistent with those found in other studies where increasing force production increases SD [24–26]. Nevertheless, IMUs showed the opposite trend, with lower SD values of movement acceleration in the higher intensity loads. To understand the reason for these differences, we need to examine the data recorded by these instruments. The force platform records peak forces that are directly influenced by increasing mass with increasing load intensity, as adding weight to the barbell produces higher impulses and peak forces compared to lower loads performing the same movement [27]. Nevertheless, this variability measured by the standard deviation during movement is similar in higher loads, where variations in peak force become less pronounced [28]. On the other hand, IMUs record accelerations, i.e., changes in motion without the influence of mass, and changes in mass do not directly affect acceleration signal as force measured from platform. This indicates that IMUs better reflect adjustments in motion expressed in force variability. Therefore, decreases in SD in our study are similar to other studies looking at other variables, such as execution variability velocity, in which a decrease in velocity variability obtained through IMUs have been observed [29]. In any case, our results show that a linear measure such as SD is insufficient to discriminate load intensity and needs to be complemented by non-linear measures such as motion complexity analysis [6, 7].

Load intensity and complexity

One of the most important aspects we analyzed in our study is the influence of constraint, how load intensity is a constraint affecting movement complexity, not only on the amount of movement variability. The increase in load intensity modified the IMUs in different ways and the force plate signal. Thus, complexity from the IMU signal augmented higher loads (higher SampEn and FuzzyEn values, and lower DFA values). Different results were found for the force platform where FuzzyEn, SampEn, and DFA results were lower when load was increased.

The different trends found in the FuzzyEn and SampEn results for the IMU and force platform may be due to what was discussed in the previous section, where the platform records force production in the base of support. These force values are affected by the mass being moved during the squat movement, whereas the IMU only records the acceleration of the movement despite the mass displacement. In addition, the differences found between the loads for FuzzyEn and SampEn of the force platform are at low loads, as is the case for the force platform when measuring the SD. Due to the mathematical formulation of FuzzyEn and SampEn, which includes SD for the calculation of the formula, the range of the signal may affect the resulting FuzzyEn and SampEn values [9, 20]. As the SD was different in the force platform compared to the IMU due to the increase in peak forces caused by the influence of the increased mass, FuzzyEn and SampEn values could show different trends in force platform compared to the IMU. It is precisely these changes in trend and the significant difference that are found with increases in load intensity up to approximately 50% such as in the SD values. In contrast, Fuzzy and SampEn calculated from the IMU signal appear useful for discriminating between loads during squat movement. In opposition to other constraints such as injury [30] or acute fatigue [16], where a reduction in motor variability has been observed (lower entropy values), our results show an increase in motor variability (greater entropy values) according to load increase. Thus, a constraint such as load increases the degree of motor variability to allow an adaptive response to a more challenging situation [14].

These increase in complexity in IMU with increasing load are from the DFA results from the IMU and force platform. The DFA analysis from both devices showed a trend of decreasing DFA values with higher loads, especially up to 30% RM. These results are in accordance with the hypothesis that a more difficult task modifies action in the central nervous system, resulting in greater motor variability for better adaptation to the constraint [31]. Our results in motor variability are different from previous studies in force signal, where submaximal contractions and isometric actions have been preferentially studied [32]. In submaximal actions, the goal of the task can be accomplished with the activation of fewer motor units and the interaction of a reduced number of muscle fibers. Thus, when performing a given task that requires little effort from the system, the reduced number of muscle fibers and motor units needed to complete the task are related to fewer possible solutions of muscle activation, enough to complete the task. In the present study, dynamic and high intensity tasks were selected for the experiment, requiring higher motor unit recruitment, demanding higher intramuscular coordination [33] and, therefore, increasing the complexity of the force output.

From our results, when the difficulty of a task is increased, it becomes more demanding for a person, and movement complexity tends to increase because of adapting to this level of difficulty to successfully complete the task. To the best of our knowledge, no prior studies examined the effect that the load in dynamic strength tasks may have on the complexity of force variability. Previous studies have found increases in variability complexity increasing the difficulty of a strength movement including, for example, an external constraint, such as handling a rugby ball [14], or in dual task conditions in postural control tasks [34]. Other studies on non-fatigued muscles have shown that decreases in variability (lower coefficient of variation, CV) but increases in complexity (higher SampEn) in knee extensor strength are associated with increased performance in balance testing [35]. This increase in balance test performance may resemble the increase in squat performance in our study.

A limitation of our study is that there is a difference in the duration of the time series. This was due to the inherent variability of each individual and the differences in the loads. In addition, in the 90% 1RM series. Some participants were not always able to complete the prescribed four repetitions of this set due to the level of effort required. This may have affected the non-linear tools and the availability of data for inclusion in our analyses. This limitation may provide valuable information for future research and suggest areas for improvement in experimental design. It should also be noted that since there are hardly any studies on acceleration signals in force training, different methodological issues should be investigated in this respect, such as the effect of non-stationarity.