Corresponding author: Jihong Park Tel +82-31-201-2721 Fax +82-31-204-8117 E-mail INTRODUCTION
One-repetition maximum (RM) is the maximum weight successfully lifted only once, but not more [1,2]. One-RM serves as not only a general indicator of an individual's maximal strength level [3,4] but also a means to determine relative workload (e.g., % of 1-RM) for specific training adaptations [5,6]. Direct 1-RM measurements typically involve increasing workload until repetition failure [2,7]. However, this approach has some drawbacks, as resistance-untrained individuals may be prone to injury caused by unaccustomed muscle contractions and incorrect posture [1]. Direct measurement of 1-RM among resistance-trained individuals is time-consuming, negatively affects performance due to muscle fatigue and residual discomfort, and increases the risk of injury caused by the required maximal effort [4,8]. An alternative method to indirectly estimate 1-RM for both resistance-trained and -untrained individuals is necessary to overcome these disadvantages.
The squat is a functional movement for both daily and athletic activities utilising the large and strong muscles of the lower extremities [9]. Consequently, it is often used in studies for estimating 1-RM [1,5,10]. Various methods have been used to estimate a workload for 1-RM squat, including the repetitions-to-failure method [11,12], movement velocity [1,13], anthropometric and body composition [5,14], workloads of leg press [15], and the rate of perceived exertion [16,17]. However, these methods have limitations, as additional measurements, such as movement velocity [18], anthropometric variations [19], body composition [20], or rate of perceived exertion [17] are required and may introduce potential measurement errors [16,18,21]. While a study [14] provided a field-applicable equation expressed in terms of relative lean body mass, it is specifically intended for estimating 1-RM. Therefore, there is a need for a more practical and simpler way to immediate estimation of a workload for a specific RM (e.g., 8-RM). In particular, a simple linear equation to calculate workload based on the number of repetitions at a given workload would be useful. Body weight is not only used when standardising strength [22] but also correlated with the workload of squat exercises [23]. Thus, the workload in simple linear equations normalised by body weight would provide a practical and convenient method for estimating workloads.
Therefore, the purpose of this study was to establish simple linear equations to predict workloads (in kg per body weight) for a specific RM during half-back squats in trained and untrained males. Prediction equations were derived based on the relationship between workload and repetitions [24-26]. Trained and untrained individuals have different capacities to generate force [27] and recover from exercise-induced fatigue [28], a larger variation (e.g., coefficient of variation) in workloads between trained and untrained groups was expected; thus, data from the two groups were separately collected and analysed. Secondarily, the prediction accuracy of the established equations was examined. The mean absolute percentage error (MAPE) [29] is predominant in assessing regression model quality. The results of this study, in the form of simple linear equations, would not only provide an easy and fast method to predict an appropriate workload for specific RM but also reduce the burden of maximal effort and the risk of injury.
METHODS
1. Participants
Previous studies on predicting workload using regression equations [4,14,30] included groups with 11 [4] and 15 [14,30] participants. We recruited 18 individuals for each group to ensure an adequate sample size and account for potential dropouts.
The trained group included individuals who were able to perform a squat exercise with 150% of their body weight. The criterion of 150% was chosen because it is a common benchmark for distinguishing an untrained population in both the field and existing literature [5,31]. Addition criteria included individuals who had been participating in regular squat training sessions and attending at least six sessions per month for the past 12 months [10]. The untrained group consisted of individuals who had not participated in lower extremity resistance training for six consecutive months and had not regularly engaged in any physical activity, including lower extremity resistance training, within the last year. The exclusion criteria were individuals with lower extremity or lower back injuries over the past six months or a history of lower extremity or lower back surgery. Participants read the testing procedures and provided informed consent before data collection. The University's Institution-al Review Board approved the study (approval #: KHGIRB-22-128).
2. Testing procedures
Our final outcomes, the simple linear equations, were derived based on the inverse relationship between workload and repetitions [24-26]. Initially, linear equations for the trained and untrained groups were developed through a pilot study, then these initial equations were subsequently refined and updated using data collected from a larger number of participants (18 for each group).
3. Squat exercises
Participants (particularly those in the untrained group) received instructions on performing (movement, velocity, breathing, resting interval, etc.) half back squat on a Smith machine (Multipower, Technogym, Cesena, Italy) and were given ample practice after a 5-minute self-selected warm-up activity. Specifically, participants prepared for squat exercises from a standing position (upright with knees and hips extended: Fig. 1A) and then proceeded to squat down until their thighs were parallel to the ground [13] (Fig. 1B) before returning to the starting position (Fig. 1A). All participants performed squat exercises barefoot to minimise kinetical variations and account for the effects of footwear midsoles. Additionally, participants aligned their calcaneus or the lateral malleolus (or a position between them) with the vertical pole (e.g., sliding rail) of the Smith machine (to facilitate comfortable squat movements, Fig. 2). The distance between participants’ feet was identified by their shoulder width, with both feet positioned parallel or externally rotated up to 20°. An instructor visually confirmed the participants’ half squat depth during the practice period and marked it by tying an elastic band, which was considered a guide for maintaining the consistent squat depth. A metronome (set at 65 beats per minute), in which participants were instructed to squat down in two beats and up in two beats was used to guide the velocity of squat movements. Breathing instructions included inhaling and exhaling while squatting down and up, respectively [32]. Participants were advised to request assistance by saying “ help” if a spotter was needed and instructed to have walking rest between sets as desired. Two researchers provided verbal encouragement, such as “ one more” or “ keep going” throughout the exercises.
4. Pilot study
Three trained and three untrained individuals visited a weightlifting room, where they familiarised themselves with the testing procedures and gave informed consent. The pilot study aimed to obtain the initial simple linear equations by incrementally increasing workloads in each set to establish the inverse relationship between workloads and repetitions. Trained individuals were asked to perform their 18-, 15-, 12-, 10-, and 8-RM for sets 1 through 5. Untrained individuals began with a workload of 10 kg (in addition to the weight of the horizontal bar: 8.0 kg according to the manufacturer's information) for the first set. Workloads for subsequent sets were consistently increased (e.g., adding 5-10 kg, determined by participants) based on the participants’ perceived intensity and the level of correct posture (described above). The initial simple linear equations were obtained by conducting linear regression following the workload (normalised by body weight) and the repetitions for the trained (Equation 1A) and untrained (Equation 1B) groups, respectively.
Equation 1. Initial simple linear equations
5. Data collection
Eighteen trained males (age: 22.7±0.9, height: 175.4±2.6 cm, weight: 78.1±2.6 kg, body mass index: 25.4±1.6 kg/m2, lean body mass: 67.0±0.7 kg) and 18 untrained males (age: 21.4±0.7, height: 176.4±3.5 cm, weight: 74.5±3.5 kg, body mass index: 23.9±1.7 kg/m2, lean body mass: 61.1±1.0 kg) volunteered. Upon arrival at the weightlifting room, participants read the testing procedures and provided written informed consent. Participants performed five sets of squat exercises as described in the pilot study section after taking a bioelectrical impedance measurement (In-body 770, Seoul, Korea) and completing a health-related questionnaire.
The workload was identified using simple linear equations (Equation 1). Expected repetition was defined as the number of squats to be completed in each set: 18, 15, 12, 10, and 8 for sets 1 through 5, respectively. Participants were not informed of these expected repetitions but asked to perform as many squats with their maximal effort. Actual repetition was defined as the number of squats completed with correct posture (described above) without any assistance, and repetitions completed with assistance were excluded. The workload was applied to the nearest increment of 2.5 kg (by adding a 1.25-kg plate on each side of the bar), including the weight of the horizontal bar (8.0 kg). During the 5-minute rest interval, participants were instructed to walk around [33] and an additional 1-min walking rest was given if needed.
The workload was determined by substituting expected repetition into equation 1. The actual repetitions in each set identified the workload for the next set after the first set of squat exercises (Table 1). A workload of 10 kg was either removed or added to the workload of the next set [34], respectively, if actual repetitions fell outside the cutoff range. In particular, a workload of 112.2 kg was performed at the second set (102.2 kg+ 10 kg) if a trained individual weighing 80 kg completed 22 repetitions in the first set.
Table 1.
Procedures for adjustment of workload in each set
Workload per body weight was calculated from equation 1, which determined the workload (multiple by body weight) in each set. If the actual repetitions were greater or less than the cutoff ranges, a workload of 10 kg was added or removed, respectively.
6. Statistical analyses
All data, including participants’ demographic information, the workload, actual repetitions, and rest intervals completed in each set, were recorded with spreadsheet software (Excel 365; Microsoft Corporation, Seattle, USA) and statistically analysed with a statistical package (SAS 9.4, SAS Institute, Cary, USA). Independent t-tests were performed to test differences in demographic information between groups. Descriptive statistics, including means, 95% confidence intervals, coefficient of variations for workloads and actual repetitions, were calculated. The alpha level was set at 0.05 for all statistical tests.
Simple linear regressions with standard error of estimate (SEE) using the workload and the actual repetitions in the trained or untrained group were separately conducted to obtain the final equations. Correlations between the workloads and actual repetitions completed in each set were evaluated for the trained and untrained groups using the Pearson correlation coefficient.
MAPEs [35] for each participant were calculated to examine the prediction accuracy of the final equations in each group. Initially, the estimated workload was subtracted from the heaviest workload performed by the same participant, then divided by the heaviest workload, and fi-nally multiplied by 100 (Equation 2).
Equation 2. Mean absolute percentage error
Estimated workload: calculated by substituting the actual repetition for the heaviest workload, then multiplied by body weight
RESULTS
1. Descriptive results
Age (p =.24), height (p =.69), body weight (p =.20), body mass index (p =.22), and lean body mass (p =.59) did not differ between groups (Table 2). The average values of the workloads were 92.3 kg, 103.4 kg, 108.3 kg, 110.2 kg, and 111.3 kg and actual repetitions were 18.9, 12.4, 9.1, 7.4, and 6.8 for the trained group (Table 3), whereas 34.6 kg and, 46.1 kg, 53.1 kg, 57.2 kg, and 60.6 kg and 20.8, 16.7, 12.9, 10.3, and 8.9 repetitions for the untrained group for sets 1 through 5, respectively. The average rest periods for the trained and untrained groups were 5.8 minutes and 6.1 min, respectively (Table 3).
Table 2.
Participant demographics
Table 3.
the workloads, actual repetitions, and rest intervals
Two trends were observed that the coefficient of variations (CVs) increased as the sets were performed, regardless of the group, and was higher in the untrained group relative to the trained group, regardless of the set (Table 3).
2. Final simple linear equations
The final simple linear equations for the trained (Equation 3A) and untrained (Equation 3B) groups were established based on the workload and actual repetitions.
Equation 3. Final simple linear equations
DISCUSSION
The purpose of this study was to establish and test the prediction accuracy of simple linear equations to predict workloads corresponding to specific RMs during half back squat exercises for trained and untrained individuals. The calculated MAPEs are considered good for estimating the workload [35], especially for the trained group. The calculated systematic bias for each group indicates that prediction accuracy is within a tolerable level [36,37]. Combining the results of statistical analyses, our data indicate that the simple linear equations exhibit high accuracy and are valid for practical applications. Established equations in our study estimate a workload based on an individual's body weight, which would be an update of previously reported RM estimations on squat exercises [14] and useful when identifying an initial workload and setting the workload following the specific RMs for the training purpose. The equations demonstrated additional advantages of saving time and minimising the injury risk.
The CVs of the workload seemed to increase as the sets progressed, regardless of groups. Additionally, the CVs of the workload were higher in the untrained group compared to the trained group across all sets (Table 3). Especially in the last set, the CV of the workload in the untrained group (32.7%) was approximately twice as high as that in the trained group (14.7%), despite the similar 95% confidence intervals in each group (trained: 5.4 kg; untrained: 6.5 kg). This could be associated with a mean difference in the workloads between groups (trained group: 111 kg; untrained group: 61 kg). Additionally, the CV of the actual repetition is higher in the untrained group (35%) than in the trained group (26%) that variations in individual ability to recover from muscle fatigue could have affected the CVs of the workload as the sets progressed. The MAPE was lower in the trained group, relative to the untrained group, indicating that the linear equation prediction from the trained group was more accurate than the untrained group. These calculations are in line with the previous data, showing that the trained group demonstrated higher accuracy (<10%), while the untrained group fell within the “ reasonable prediction” range (20-50%) [35,36]. This variation could be attributed to between-subject differences in the capacity to complete the number of repetitions each set. For example, average values of the heavier workloads in each group (trained: 115 kg; untrained: 64 kg) and actual repetitions (trained: 1.7; untrained: 3.7) could explain the difference.
A previous study [14] reported the equations of squat exercises for the trained (y=2.825x-84.6) and untrained (y=1.6938x-37.6) groups (x=body weight; y=workload of 1-RM). By substituting the average body weight of our participants (trained: 78 kg; untrained: 75 kg) into the previous equations [14], we calculated the estimated 1-RM workloads as 136 kg for the trained and 89 kg for the untrained group. When using our simple linear equations, the corresponding values for the trained and untrained were 114 kg and 64 kg, respectively. The discrepancies between the results from the previous [14] and our equations may be attributed to the parameters used in the linear regressions. The previous study used the relationship between a 1-RM workload and lean body mass [14], whereas our study utilised the workload (standardised by body weight) and actual repetitions. Furthermore, our simple linear equations were derived from a higher number of repetitions (i.e., 18, 15, and 12 for the first three sets) compared to the previous study (i.e., 6-12 repetitions) [14]. While performing fewer than 10 repetitions is recommended when predicting 1-RM [38], the discrepancies in estimated workload, particularly 1-RM, from our equations could be associated with the higher number of repetitions.
Although statistically significant, calculated correlation values in our data are not robust. This result could be influenced by between-subject variations in several factors such as experience, motivation, fatigue perception, metabolic energy systems. Other study limitations related to the methodological issues should also be noted. Several factors regarding the squat exercise procedures and parameters should be considered when applying the equations. Participants performed half-back squats on a Smith machine, which could offer different movement mechanics to free weights [9] or other squat exercise types such as front or full squats [34,39]. The start position of the squat exercise was identified according to the participant's preference (aligning from the calcaneus to the lateral malleolus with the vertical pole). We assumed that comfortable body positions and squatting movements were more important than standardising the lower extremity alignment across participants to produce maximal effort. The rest intervals were given at least 5-min and additional time was provided. Five (trained: n=3; untrained: n=2) participants had additional rest duration (up to 10-min). There were 7 out of 144 rest cases (< 5%). Additionally, blood lactate concentration and rate of perceived exertion (not reported in this manuscript) recorded at the end of each set did not differ. Thus, we assume that the variation in the rest interval had a minimal effect on the performance across participants.
CONCLUSION
The trained and untrained individuals performed five sets of half-back squat exercises. Recorded workloads and actual repetitions in each set were utilised to identify final linear equations to predict a workload (based on body weight) of specific RMs (trained: y=-0.0105x+1.4637; untrained: y=-0.0136x+0.87). With correlations between the workloads and actual repetitions (trained: r=-0.33; untrained: r=-0.39), the workload for a specific RM, using body weight as an input, can be simply calculated and applied in the field of strength and conditioning to save time and minimise injury risks. Although useful, athletes and coaches should be aware of the potential ranges of accuracy in predicting workload, with a MAPE of 9.4% for the trained and 20.9% for the untrained groups, respectively.
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