Introduction
Assessment of neuromuscular function (2,4,7,9,10,12,14,18,20,23,25 3,5,8,13,14,15,27 1 17 10,17
Recently it has been suggested that accurate measures of power applied during resistance exercise can only be obtained if barbell and body center of mass parameters are combined (referred to as CM for clarity), multiplying the velocity of the barbell by the force applied to the CM (GRF) (3,5,11,19,28 5 17
Analysis of the CM using whole-body three-dimensional (3D) motion analysis and force platform analysis enables comparison of power applied during resistance exercise that is calculated by multiplying GRF by the velocity of the barbell, and the velocity of the CM (derived from 3D motion analysis and GRF data) independently. Further, it enables study of the effect that differences between the displacement and velocity of the barbell, the CM, and its composite body segments has on differences on power applied to the CM. Thus, it is critical that research using this type of analysis is undertaken so that methodological concerns about the misapplication of the combined method can be investigated and insight about the differences in measures of power applied to the CM obtained using the different methods gained (5,10,17
Therefore, the aim of this study was to compare measures of power obtained by multiplying GRF by the velocity of the barbell, GRF by velocity of the CM derived from 3D motion analysis, and GRF by velocity of the CM derived from GRF data. It was hypothesized that multiplying GRF by the velocity of the barbell would lead to a significant overestimation of the velocity of and the power applied to the CM.
Methods
Experimental Approach to the Problem
To compare measures of power obtained from different methods during lower-body resistance exercise, 10 resistance-trained men performed 3 sets of single maximal-effort back squats with 60% 1 repetition maximum (1RM) on 2 force platforms while 3 synchronized high-speed digital cameras recorded whole-body motion. Measures of power applied to the CM were obtained by multiplying GRF by the velocity of the barbell, GRF by the velocity of the CM derived from 3D motion analysis, and GRF by the velocity of the CM derived from GRF data; these were time normalized and compared using repeated measures analysis of variance (ANOVA). Further, the velocity of the barbell was compared with the velocity of the CM and the velocity of individual body segment centers of mass using 1-way ANOVA to gain insight about the factors underpinning differences.
Subjects
Ten physically active men with between 4 and 9 years of resistance exercise experience participated in this study. Their mean (±SD ) physical characteristics were as follows: mass, 82.3 (7.3) kg; stature, 1.77 (0.03) m; back squat 1RM, 140.5 (46) kg; and 1RM normalized to body mass: 1.69 (0.45) kg per kg of body mass. All volunteers had been free of lower-body pathology for at least 6 months before data collection. Ethical clearance was granted before data collection, and after a thorough explanation of the study aims and protocols, subjects provided written informed consent.
Procedures
Subjects attended 2 laboratory-based testing sessions. During the first session, maximal back squat strength (1RM) was established using a protocol similar to the one described and used by Wallace et al. (26 5,12,23
Instrumentation
Before data collection spherical, retroreflective markers illuminated by spotlights positioned behind each camera were affixed to the left and right barbell end and anatomical landmarks (see Figure 1 ).
Figure 1: The 18-point, 13-segment digital model illustrating the marker positions.
Three high-speed digital cameras (Basler A602fc-2; Basler, Ahrensburg, Germany) positioned around the front of and approximately 5 m from the subject recorded back squat performance after first recording a 17-point calibration frame (Peak Performance Technologies Inc., Englewood, CO, USA) (19 16
All performance footage was cropped to include 10 frames before the start and after the end of the propulsion phase (22 Figure 1 ). Markers affixed to the barbell ends were digitized automatically using Vicon Motus 9.2 software. However, the anatomical markers were not used to identify the remainder of the points of interest because back squat performance led to significant hip and shoulder marker dropout and shoulder marker skin artifact. Therefore, remaining points of interest were digitized manually.
After the digitization of all barbell and anatomical landmarks, data were reconstructed using Vicon Motus 9.2 software and raw data smoothed using a low-pass Butterworth filter with a cutoff frequency of 6 Hz that was selected using residual analysis described by Winter (29 7 22 9
Data of interest were displacement of the barbell and displacement of the CM derived from 3D motion analysis; velocity of the barbell and velocity of the CM derived from 3D motion analysis and velocity of the CM derived from GRF data; GRF and force applied to the CM derived by multiplying the acceleration of the CM obtained from 3D motion analysis by barbell and body mass; and power applied to the CM obtained by multiplying GRF by the velocity of the barbell, GRF by velocity of the CM derived from 3D motion analysis, and GRF by velocity of the CM derived from GRF data (see Figure 2 ). Only vertical displacement , velocity, acceleration, and force were considered.
Figure 2: Comparisons performed between the different methodologies.
Test-retest reliability of the 3D motion analysis and GRF data was found to match previously reported reliability data from our laboratory (16 displacement of the barbell: 3.2%; displacement of the CM derived from 3D motion analysis: 5.9%; velocity of the barbell: 3.4%; velocity of the CM derived from 3D motion analysis: 6.2%; velocity of the CM derived from GRF data: 3.1%; GRF: 0.9%; force applied to the CM obtained from 3D motion analysis: 3.3%; power applied to the CM obtained by multiplying GRF by the velocity of the barbell: 6.5%; power applied to the CM obtained by multiplying GRF by the velocity of the CM derived from 3D motion analysis: 6.3%; and power applied to the CM obtained by multiplying GRF by the velocity of the CM derived from GRF data: 3.2%.
Statistical Analyses
All results were presented as mean (±SD ) unless otherwise stated. Two-way repeated measures ANOVA was used to determine differences between measures of displacement , velocity, force, and power (dependent variables) obtained from the different methods (independent variables—Figure 2 ) across the time-normalized propulsion phase. Further, velocity of the different body segment centres of mass was compared with the velocity of the barbell using a 1-way ANOVA. An alpha of p ≤ 0.05 was used to indicate statistical significance, and post hoc analysis was performed where appropriate applying the Holm-Sidak correction. All statistical analyses were performed using SPSS (version 17.0 for Windows; SPSS Inc., Chicago, IL, USA). Effect sizes (d ) between the dependent variables obtained from the different methods were calculated using the methods described by Rhea (21
Results
Key results are presented in Figures 3–5 , which illustrate the significant differences found between the displacements and velocities of the barbell and CM derived from 3D motion analysis and their effect on power applied to the CM. There were no significant differences between the force applied to the CM derived from 3D motion analysis and GRF (p = 0.125), and velocity of the CM derived from 3D motion analysis and GRF data (p = 0.961), but multiplying GRF by the velocity of the barbell resulted in a significant overestimation of power applied to the CM when compared with measures of power obtained by multiplying GRF by the velocity of CM derived from either 3D motion analysis (18.7%; d = 1.06; p < 0.001) or GRF data (23%; p < 0.001; d = 1.21). Figure 6 illustrates the velocity of the barbell-and-body segment CM time normalized across the propulsion phase. The peak and mean propulsion phase velocities of the barbell were significantly greater than velocities of the foot (peak: 98.2%; d = 9.87, mean: 99.2%, d = 16.96), lower leg (peak: 91.9%; d = 8.18, mean: 94.3, d = 14.07), upper leg (peak: 56.9%; d = 4.74, mean: 56.7%, d = 7.15), and trunk (peak: 18.8%; d = 1.16, mean: 14.4%, d = 1.55) segment CM equivalents. However, differences between the velocity of the barbell and head, lower arm, and upper arm segment centres of mass did not exceed 5% (d = −0.25 to 0.30).
Figure 3: Comparison of time-normalized displacement of the barbell and center of mass (CM).
Figure 4: Comparison of time-normalized velocity of the barbell and center of mass (CM).
Figure 5: Comparison of time-normalized power applied to the barbell and center of mass CM; GRF = ground reaction force.
Figure 6: Comparison of time-normalized velocity of the barbell-and-body segment center of mass (CM); 3D = three-dimensional; GRF = ground reaction force.
Discussion
It is critical that the selection of methods used to obtain measures of power applied to the mass of interest during lower-body resistance exercise is based on an understanding of the theory that underpins the method and its limitations. Theoretically, investigators should obtain measures of power by multiplying the force applied to the mass of interest by its velocity (17 5,10,17
The results of this study supported the hypothesis that multiplication of GRF by the velocity of the barbell would lead to a significant overestimation of the velocity of and the power applied to the CM. This finding is of critical importance to strength and conditioning practitioners and investigators because it shows that the combined method is not valid. Calculations of power and the product of the force applied to a resistance and its resultant velocity must be based on force and velocity components that are recorded from the resistance of interest. Therefore, the velocity of the barbell should only be considered when the power applied to the barbell is of interest, and GRF should only be considered when the velocity of the CM, derived from 3D motion analysis or GRF, is available, and the power applied to the CM is of interest.
The lack of a significant difference between measures of force applied to the CM derived from 3D motion analysis and GRF and velocity of the CM derived from 3D motion analysis and GRF data indicated that the velocity of the CM can be accurately derived from GRF, countering suggestions made in recent research to the contrary (5
Significant differences found between the velocity of the barbell-and-body segment centres of mass provide insight regarding the factors that underpin what has been referred to as an underrepresentation of the velocity of the CM when derived from GRF (5
This suggests that strength and conditioning practitioners and investigators must be cognizant that a considerable portion of the CM is displaced at a rate that is significantly slower than the barbell during back squat performance and that this will affect the method that should be used to obtain measures of resistance exercise power.
To summarize, the velocity of the barbell significantly overestimates the velocity of the CM and, therefore, the power applied to the CM. This can and should be avoided by using methods that consider the force applied to and the velocity of specific masses of interest.
Practical Applications
The results of this study clearly demonstrated that strength and conditioning coaches and investigators should not obtain measures of power applied to the CM by using the increasingly popular method of combining the velocity of the barbell and the force applied to the CM. During back squat performance, the barbell undergoes significantly greater displacement at a significantly greater velocity compared with the CM. Therefore, strength and conditioning practitioners and investigators are urged to obtain measures of power by using the force applied to and the velocity of either the barbell or CM (10
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