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Force-Velocity Profile: Imbalance Determination and Effect on Lower Limb Ballistic Performance

DOI 10.1055/s-0033-1354382 Int J Sports Med For personal use only. No commercial use, no depositing in repositories.

Publisher and Copyright © 2013 by Georg Thieme Verlag KG Rüdigerstraße 14 70469 Stuttgart ISSN 0172-4622 Reprint with the permission by the publisher only

Training & Testing

Force-Velocity Profile: Imbalance Determination and Effect on Lower Limb Ballistic Performance

Authors

P. Samozino1, P. Edouard2, 3, S. Sangnier4, 5, M. Brughelli6, P. Gimenez3, J.-B. Morin3

Affiliations

Affiliation addresses are listed at the end of the article

Key words ▶ jump ● ▶ muscle mechanical ● properties ▶ maximal power output ● ▶ optimal force-velocity profile ● ▶ explosive push-off ● ▶ strength training ●

Abstract

▼

This study sought to lend experimental support to the theoretical influence of force-velocity (F-v) mechanical profile on jumping performance independently from the effect of maximal power output (Pmax). 48 high-level athletes (soccer players, sprinters, rugby players) performed maximal squat jumps with additional loads from 0 to 100 % of body mass. During each jump, mean force, velocity and power output were obtained using a simple computation method based on flight time, and then used to determine individual linear F-v relationships and Pmax values. Actual and optimal F-v profiles were computed for each subject to quantify mechanical F-v imbalance. A multiple regression analysis showed, with a high-adjust-

Introduction

▼ accepted after revision August 02, 2013 Bibliography DOI http://dx.doi.org/ 10.1055/s-0033-1354382 Published online: 2013 Int J Sports Med © Georg Thieme Verlag KG Stuttgart · New York ISSN 0172-4622 Correspondence Dr. Pierre Samozino Laboratory of Exercise Physiology (EA4338) Université de Savoie UFR CISM – Technolac Le Bourget du Lac 73376 France Tel.: + 33/4/79 75 81 77 Fax: + 33/4/79 75 81 48 [email protected]

Ballistic performances are a key factor in numerous sport activities and can be defined as the ability to accelerate a mass as much as possible in the shortest time possible, be it one’s own body mass (e. g. sprints or jumps) or an external mass (e. g. throws). Success in such performances has been closely related to the maximal power output (Pmax) limbs can develop [11, 32, 33]. Instantaneous power output is the product of the external force developed by velocity. A recently validated theoretical integrative approach of jumping showed that ballistic performance is also influenced by the force-velocity (F-v) mechanical profile (henceforth referred to as “F-v profile”) of the lower limb neuromuscular system (henceforth referred to as “lower limbs”), independently from Pmax [30]. This F-v profile, normalized to body mass, represents the ratio between the external force developed and velocity maximal capabilities, and can be determined by the slope of the F-v relationship [30]. The relationship between performance and F-v profile is

ment quality (r² = 0.931, P < 0.001, SEE = 0.015 m), significant contributions of Pmax, F-v imbalance and lower limb extension range (hPO) to explain interindividual differences in jumping performance (P < 0.001) with positive regression coefficients for Pmax and hPO and a negative one for F-v imbalance. This experimentally supports that ballistic performance depends, in addition to Pmax, on the F–v profile of lower limbs. This adds support to the actual existence of an individual optimal F-v profile that maximizes jumping performance, a F-v imbalance being associated to a lower performance. These results have potential strong applications in the field of strength and conditioning.

curvilinear (inverse U shape) with an apex corresponding to an optimal F-v profile maximizing performance. For each individual, an optimal F-v profile can then be accurately determined and represents the best balance between its force and velocity capabilities. For a given Pmax, an unfavorable balance between force and velocity qualities can lead to a ~30 % lower performance [30]. Thus, considering both Pmax and the individual F-v profile compared to the optimal one might be of great interest for exploring ballistic performances and optimizing athletic training. The aforementioned theoretical approach took account of both movement dynamics of the body center of mass during jumping and external mechanical limits of the entire lower limb neuromuscular system [29, 30]. The latter was considered as a complete force generator system characterized by Pmax, F-v profile and range of motion values. This approach was based on equations recently validated in comparison to experimental measurements [30]. However, no experimental data has thus far supported the theoretical influence of F-v profile on ballistic

Samozino P et al. Force-Velocity Profile: Imbalance Determination … Int J Sports Med

Training & Testing

performance and the existence of an individual optimal F-v profile value, mainly due to (i) the curvilinear relationship between F-v profile and performance preventing direct correlation analysis and (ii) the difficulty in experimentally isolating the effect of the F-v profile independently from the large effect of Pmax. Indeed, these 2 variables, though theoretically independent, often change together similarly in studies testing athletes with different training backgrounds [32, 33] or different training protocols [6, 7, 10, 15, 22]. The aim of this study was to bring experimental support to the theoretical influence of F-v profile on jumping performance independently from the effect of Pmax. In addition to the previously demonstrated positive relation with Pmax, it was hypothesized that jumping performance would be negatively related to the magnitude of the F-v imbalance.

Method

▼

Population 48 international and national-level athletes (31 soccer players, 11 sprinters and 6 rugby players) participated in the study (age (mean ± SD) 20.9 ± 4.4 years; body mass 75.8 ± 12.0 kg; height 1.79 ± 0.06 m). All subjects were free of musculoskeletal pain or injury during the period of the study and gave their written informed consent to participate in this study after being informed about the procedures, which complied with the Declaration of Helsinki. This study met the ethical standards of the International Journal of Sports Medicine [16].

1

⎛ h ⎞ Fabs = mg ⎜ + 1⎟ ⎝ hPO ⎠ v=

2

gh 2

with m being the total mass (sum of body mass + additional load, in kg), g the gravitational acceleration (9.81 m.s − 2), hPO the vertical distance covered by the CM during push-off corresponding to the extension range of lower limbs (in m) and h the jump height (in m). Here, hPO was determined as the difference between the extended lower limb length with maximal foot plantar flexion (great trochanter-toe distance) and the vertical distance between the great trochanter and ground in the starting position. h was obtained from flight time applying fundamental laws of dynamics [3], flight time being measured using an infrared timing system (Optojump, Microgate, Bolzano, Italy). For the following analyses, force values were normalized to the subject’s body mass (i. e., the moving mass during unloaded jumping movements), since jumping performance has been directly related to normalized force ( F in N.kg − 1, [29]). From F and v values, individual linear F-v relationships were determined by least-squares linear regressions [5, 27, 33] to obtain for each subject (i) the F-v profile normalized to body mass (SFv, slope of the F-v curve, in N.s.kg − 1.m − 1) and (ii) Pmax (in W.kg − 1) computed here by: Pmax =

3

F0 .v0 4

Procedure and data analysis Each subject performed one session of maximal squat jump tests to determine their Pmax, F-v profile and F-v imbalance. For each subject, the vertical distance between the ground and the right leg great trochanter was measured in a 90 °-knee angle crouch position [28]. After a 10-min warm-up, each subject performed maximal squat jumps in 5 randomized loading conditions: additional loads of 0, 25, 50, 75 and 100 % of their body mass. Subjects stood still holding a barbell across their shoulders for additional-loads conditions or with arms crossed on the torso for the unloaded condition. They then initiated the squat jump with a downward movement to reach their individual 90 °-knee angle starting crouch position (measured beforehand as the vertical distance between the ground and the right leg great trochanter, and checked by the experimenter using a vertical rule before trials [28]). After maintaining this position for at least 1 s, they were asked to apply force as rapidly as possible and to jump for maximum height. Countermovement was verbally restricted and carefully checked. Subjects were instructed to keep constant downward pressure on the barbell throughout the jump with the chest upright, and asked to touch down the ground in the same leg position as they took off, i. e., extended leg in foot plantar flexion. If these requirements were not met, the trial was repeated. Subjects had to perform 2 correct trials by condition, only the best one being used in the analysis. Before this session, subjects were allowed enough supervised practice to correctly perform squat jumps without countermovement. During each trial, the mean vertical force developed by the lower limbs during push-off ( Fabs , absolute force in N) and the corresponding mean center of mass (CM) vertical velocity ( v , in m.s − 1) were determined using the equations and the methodology proposed and validated by Samozino et al. [28]:


with F0 and v0 being the theoretical maximal force the lower limbs can produce at null velocity (extrapolated intercept with force-axis, in N.kg − 1) and the theoretical maximal velocity at which lower limbs can extend under zero load (extrapolated intercept with velocity-axis, in m.s − 1), respectively [30, 32]. Note that Pmax must also be expressed here relative to the body mass in unloaded condition (in W.kg − 1, [30]), and not relative to body mass exponent 2/3 as suggested by scaling models and experimental data when the aim is to scale muscle power to the body size [23]. From Pmax and hPO values, the theoretical optimal SFv (SFvopt normalized to body mass, in N.s.kg − 1.m − 1) maximizing jumping performance were computed for each subject using equations proposed by Samozino et al. (appendix section in [30]). The F-v imbalance (FvIMB, in %) were then individually computed as: FvIMB = 100. 1 −

S Fv S Fv opt

4

The hypothetic maximal jump each subject could reach if he presented an optimal F-v profile (hmax, in m) was computed from his actual Pmax and hPO values, and using the following equation derived from previously validated equations [29, 30]:

hmax =

hPO 2 ⎛ S Fv opt 2 S opt ⎞ 2 + (2 − Pmax S Fv opt − g) + Fv ⎜ ⎟ hPO 2g ⎝ 4 2 ⎠

2

5

The theoretical loss of performance due to the F-v imbalance was computed for each subject as the percent difference between actual unloaded jump height and hmax (in percentage of hmax).

Training & Testing

ple regression analysis was performed with maximal unloaded jump height as the dependent variable, and FvIMB, Pmax (normalized to body mass) and hPO as independent variables. This multiple regression model was based on the previously proposed theoretical approach [30]. The effect of F-v profile was tested in regression analysis through FvIMB since the relationship between F-v profile and performance is curvilinear, while that between performance and FvIMB should be simply decreasing. The criterion for statistical significance was set at α = 0.05.

30 28

Force (N.kg–1)

26 y= –15.0 x +38.2

24 22 20 18 16

y= –8.99 x +29.6 r2 = 0.98 FvIMB = 40.0 %

Results

▼

14 12 0.2

0.6

1.4 1.0 Velocity (m.s–1)

Optimal F-v profile

1.8

2.2

Actual F-v profile

Fig. 1 Typical linear normalized force-velocity relationship (solid line) and the associated mechanical F-v profile (dotted line). Each circle represents a squat jump at a given additional load. The individual optimal F-v profile maximizing this subject’s jumping performance with no change in Pmax is represented by the dashed-line.

Table 1 Correlation matrix for all variables (n = 47, one outlier was removed).

unloaded h

Pmax

SFv

FvIMB

hPO

0.782 P < 0.001

− 0.247 P = 0.094 − 0.206 P = 0.164

0.066 P = 0.659 0.218 P = 0.141 0.0423 P = 0.778

0.303 P = 0.042 − 0.254 P = 0.085 0.0971 P = 0.516 0.170 P = 0.252

Pmax SFv FvIMB

h: jump height; Pmax: maximal power output; SFv: Force-velocity mechanical profile; FvIMB: Force-velocity imbalance; hPO: lower limb extension range

Table 2 Multiple regression analysis for the prediction of jump height (n = 47, one outlier was removed). Multiple regression model

r² 0.931

Independent variables Pmax FvIMB hPO Constant

Coefficient 0.0122 − 0.0810 0.617 − 0.174

SEE (m) 0.015 t 23.0 − 5.92 13.9 − 7.13

Individual F-v relationships were well fitted by linear regressions ▶ Fig. 1 presents an F-v curve for a typ(r² = 0.87–1.00; P ≤ 0.05). ● ical subject, compared to the theoretical F-v curve characterizing his optimal F-v profile that would maximize his jumping performance without changing Pmax. Mean values ( ± SD) of maximal unloaded jump height, hPO, Pmax, SFv, SFvopt and FvIMB were 0.38 ± 0.06 m, 0.36 ± 0.05 m, 29.7 ± 6.13 W.kg − 1, − 11.6 ± 7.36 N.s.kg − 1.m − 1, − 15.0 ± 1.30 N.s.kg − 1.m − 1 and 42.6 ± 34.4 %, respectively. When considering simple correlation analyses, jumping performance was significantly correlated to Pmax and ▶ Table 1). No simple correlation hPO, but not to SFv and FvIMB (● was found between the 3 independent variables (Pmax, FvIMB and hPO). The multiple regression analysis indicated that, when considered together, the 3 predictor variables accounted for a significant amount of jumping performance variability ▶ Table 2). Furthermore, the regression model (P < 0.001, ● showed a high quality of adjustment (r² = 0.931, P < 0.001) and ▶ Table 2, ● ▶ Fig. 2). It should be minimal error (SEE = 0.015 m) (● noted that, when only Pmax and hPO were considered as independent variables, the regression model also showed a good quality of adjustment (r² = 0.875, SEE = 0.020, P < 0.001), but lower than that when FvIMB was considered. The loss of perform▶ Fig. 3 ance due to individual F-v imbalance was 6.49 ± 6.25 %. ● presents the actual jump height reached by each subject (h expressed relatively to hmax) according to their F-v profile (SFv expressed relative to their personal SFvopt), as well as the corresponding theoretical changes predicted by the model (equation 5 with hPO and Pmax values arbitrarily set to the average values for the entire group).

P < 0.001 P < 0.001 < 0.001 < 0.001 < 0.001

SEE: Standard Error of Estimate; Pmax: maximal power output; FvIMB: Force-velocity imbalance; hPO: lower limb extension range

Statistical analyses All data are presented as mean ± SD. Normality and homogeneity of variance were checked before analyses. One highly strengthtrained subject had jump height, Pmax and FvIMB values more than 3 SD beyond average values for the group, and was therefore considered as outlier for statistical analyses. The degree of linear relationship between variables was examined using Pearson’s product moment correlation. To test the independent implication of Pmax and FvIMB on jumping performance, a multi-

Discussion

▼

The main finding of this study is the significant contribution of mechanical F-v imbalance to explain jumping performance variability. This constitutes experimental support for (i) the influence of the normalized F-v profile (characterized by the slope of the F-v relationship, SFv) on jumping performance independently from the large effect of Pmax, and (ii) the existence of an optimal F-v profile maximizing performance for each individual. These results lend experimental support to the previously proposed theoretical approach [30]. Simple correlations showed that jumping performance was highly associated with lower limb maximal power output, as previously observed with similar magnitude (e. g. [13, 32, 33], r ranging from 0.65 to 0.84), but not directly to SFv or FvIMB. This confirmed that jumping performance mainly depends on Pmax [30]. The absence of experimental correlation between performance and SFv was expected knowing the theoretical curvilinear Samozino P et al. Force-Velocity Profile: Imbalance Determination … Int J Sports Med

Training & Testing

Jump height predicted by model (m)

0.60

y=x

0.55

r=0.965

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.20

0.25

0.30 0.35 0.40 0.45 0.50 Jump height measured (m)

0.55

0.60

Fig. 2 Correlation between model-predicted and measured jump heights. Each point represents a subject: white points for soccer players, grey points for sprinters and black points for rugby players. The outlier (the point with a cross) was not considered in the correlation analysis. The solid line represents the identity line.

120

Jump height (% hmax)

100 80 60 40 20 0 0

50

100

Velocity profile

250 150 200 SFV (% SFVopt)

300

350

400

Force profile

Fig. 3 Actual jump height reached in unloaded condition (h expressed relatively to hmax) according to F-v profile (SFv expressed relatively to their personal SFvopt). Each point represents a subject: white points for soccer players, grey points for sprinters and black points for rugby players (a cross shows the outlier). The solid line represents theoretical changes predicted by the model (equation 5 with hPO and Pmax values arbitrarily set to the average values for the entire group).

relationship between these 2 variables [30]. Since Pmax and FvIMB are independent in theory, which was not contradicted here experimentally (absence of correlation between these 2 variables), the effect of FvIMB on jumping performance can be biased by the very large effect of Pmax. However, the multiple regression analysis, testing the effect of each independent variable independently from each other, showed that interindividual variability in jumping performance is partly explained by FvIMB. For a given Pmax, the higher FvIMB, the lower the jumping performance, which validates our hypothesis. Subjects presented here FvIMB ranging from 2.07 % (quasi perfect balance between force and velocity qualities) to 94.3 % (very high F-v imbalance), and even 248 % for the outlier. These F-v imbalances concerned both F-v profiles excessively oriented towards velocity capabilities (until FvIMB of 64.4 %) and F-v profiles excessively oriented towards Samozino P et al. Force-Velocity Profile: Imbalance Determination … Int J Sports Med

▶ Fig. 3). A subject presentforce qualities (until FvIMB of 248 %, ● ing a F-v imbalance (as computed here from SFvopt maximizing vertical jumps) means that he does not develop his Pmax against his body mass during a vertical jump [30]. This could be related to the Maximum Dynamic Output hypothesis proposed by Jaric and Markovic [19], which stated that the neuromuscular system is optimized, and in turn develops Pmax, in ballistic movements realized against its own body weight and inertia since it is likely designed to work optimally against loads most usually supported and mobilized [19, 24, 25]. However, when body mass is mobilized horizontally (horizontal jumps or displacements), the mechanical constraint to the movement is lower than the load represented by body weight during a vertical jump. Consequently, individuals used to running horizontally (as most of the ▶ Fig. 3) present subjects, notably soccer players or sprinters, ● can present optimal load-maximizing power during vertical jumping lower than their own body mass and thus present an F-v imbalance towards velocity qualities for vertical jumps. In contrast, rugby players used to and trained to perform displacements against resistive forces and to mobilize high training loads presented F-v imbalances towards force qualities, which is the ▶ Fig. 3). During the case here for 4 out of 6 rugby players (● present protocol, the latter developed their Pmax during vertical jumps against loads higher than their body mass (i. e., for additional loads from 25 to 100 % of their body mass). This would explain the large range of F-v imbalance observed here and support the recently proposed and debated influence of training history on the optimal load-maximizing power during vertical jumps [19, 21, 24–26]. Further studies are required to explore the exact origins of these large individual differences in F-v imbalance. The negative effect of the F-v imbalance on performance was quantified for each subject through the difference between their actual jump height reached during unloaded condition and the maximal height they would have reached if they had presented the same Pmax with an optimal F-v profile. The individual loss of performance due to the F-v imbalance ranged from 0 for sub▶ Fig. 3), jects presenting optimal profile to ~30 % for the outlier (● which is in line with the theoretical simulations performed by Samozino et al. [30]. Furthermore, since FvIMB is computed as the difference between a subject’s theoretically optimal and actual F-v profiles, the significant implication of F-v imbalance in jumping performance provides experimental support for the actual existence of an optimal F-v profile, specific to each individual, that maximizes jumping performance for a same given Pmax. This finding is of interest for better understanding the relationships between lower limb neuromuscular system mechanical properties and functional performance, notably for optimizing sport performance and training considering individual F-v profile in addition to Pmax. The F-v profile has been shown to be sensitive to specific training and to the additional loads used by athletes during strength training and conditioning: moving light loads (e. g., < 30 % of 1 repetition maximum) during maximal effort to orient F-v profile towards velocity qualities and moving heavy loads ( > 75–80 % of 1 repetition maximum) to improve strength capabilities [7, 20]. Consequently, training loads can be selected according to athlete’s individual F-v imbalance, which would lead to improved performance through both an increase in Pmax and an optimization of F-v profile. Simple correlations and multiple regressions showed that jumping performance was positively related to hPO. Thus, for a given Pmax and F-v profile, individuals with higher hPO (i. e., higher

Training & Testing

lower limb range of motion) presented higher performances since they can develop a higher mechanical work during the push-off phase. Even if this finding is not of great interest for training purposes (since hPO represents the personal optimal lower limb range of motion), it aids in understanding interindividual and interspecies differences in jumping performance, as previously discussed for humans with the influence of the starting position [1, 12, 31], and for animals through the effect of hind limb length or joint range of motion [1, 14, 18]. It is worth noting that multiple regression analysis determined that 93.1 % of the variation in jumping performance could be explained by variation in lower limb maximal power capabilities, F-v imbalance and lower limb extension range. In addition to the very low SEE (1.5 cm), this represents a very high prediction quality of human performance, from only 3 lower limb mechanical properties. However, based on the theoretical approach on which the regression analysis was based [30], these three variables should explain the entire interindividual variability in performance, which was not the case here (r² = 0.931). This difference can be due to measurement inaccuracies or to the imperfect reliability of the human performance, as reported by Hopkins [17], where a standard error of measurement of ~7 % for explosive movements was found. The validation of the equations used in the theoretical approach reported errors between theoretical and experimental values of about 6 % [30]. Moreover, a multiple regression analysis supposed linear relationships between dependent and independent variables, which is not exactly the case here (equation 6 in [30]), and which can contribute to increasing the model error of estimate. Finally, Pmax was computed using equation 3 from extrapolation of F-v curves on force and velocity-axis instead of using the apex of the powervelocity relationship [27, 33], the latter requiring more than 5 jumping conditions to properly model power-velocity polynomial regressions. Nevertheless, no difference in Pmax between these two methods has been reported with a bias lower than 2 % [30]. It should be noted that Pmax, jump height and hPO values obtained here are in line with previous studies [5, 27, 28, 30]. This study was based on a biomechanical approach aimed at describing the mechanical outputs that result from the action of the entire lower limb neuromuscular system, and not modeling the complex musculoskeletal structures at the origin of these outputs. The main limit of this approach could be the macroscopic level from which the multi-segmental neuromuscular system is considered, inducing (i) the description of its mechanical external capabilities by the empirically-determined F-v relationships, and (ii) the application of principles of dynamics to a whole body viewed as a system (these points have been discussed in detail in [29, 30]). The bias induced by the simplifications and approximations associated with this approach were shown to be low ( < 6 %) and trivial, which supported its validity ▶ Fig. 3, by [30]. This validity is also strengthened, as shown in ● the high agreement between measured performances and theoretical changes predicted by the model. The F-v linear model used to characterize the dynamic external capabilities of the lower limb neuromuscular system has been previously well supported and discussed during multi-joint lower limb extensions [4, 5, 27, 30, 33]. These overall dynamic external capabilities are the final result of the different mechanisms involved in limbs extension, and characterize the mechanical limits of the entire neuromuscular function in vivo. They are a complex integration of numerous individual muscle mechanical properties (e. g. intrinsic F-v and length-tension relationship, rate of force devel-

opment), some morphological factors (e. g. cross sectional area, fascicle length, pennation angle, tendon properties, anatomical joint configuration), neural mechanisms (e. g. motor unit recruitment, firing frequency, motor unit synchronization, inter-muscular coordination) and segmental dynamics [4, 7–9]. Our approach is also based on mechanical outputs averaged over the entire lower limb extension movement which appeared to be more representative of the muscular effort analyzed than instantaneous values [2]. Finally, it is worth noting that this study focused only on squat jump performance that does not involve all mechanical and neuromuscular mechanisms participating in the more natural counter-movement jumps. Even if one could expect to observe similar findings, further studies are currently undertaken to explore the effect of F-v imbalance on such kind of jumping performance. To conclude, this study lends experimental evidence that ballistic performance depends, in addition to Pmax, on the normalized F-v profile of lower limbs (slope of the F-v relationship) characterizing the ratio between their maximal normalized force and maximal velocity capabilities. Even if Pmax remains the main determinant, an F-v imbalance is associated with a lower performance. This result constitutes experimental support to the previous theoretical approach expressing ballistic performance as a function of lower limbs mechanical properties [29, 30], and presents numerous direct practical applications, notably in strength training and conditioning. Finally, this study proposes an applied approach to accurately determine (in field or laboratory conditions) both the individual maximum power output and the F-v imbalance, which could be developed in a more general method for testing the adaptation of mechanical properties of the lower limb neuromuscular system in a variety of maximum performance tasks.

Acknowledgements

▼

The authors thank James de Lacey (PhD student, Auckland University of Technology, New Zealand) for assisting with the data collection of the rugby players and all the subjects tested for their imbalance and their powerful implication in the protocol. Affiliations Laboratory of Exercise Physiology (EA4338), University of Savoie, Le Bourget du Lac, France 2 Department of Clinical and Exercise Physiology, Sports Medicine Unity, University-Hospital of Saint-Etienne, France 3 Laboratory of Exercise Physiology (EA4338), University of Lyon, Saint Etienne, France 4 Centre d’Etude des Transformations des Activités Physiques et Sportives (EA 3832), University of Rouen, France 5 Association Sportive de Saint-Etienne, France 6 Sports Performance Research Institute New Zealand, AUT University, Auckland, New Zealand 1

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Training & Testing

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