Activation of Lower-Extremity Musculature during Squat Variations; Comparing Front and Back Squats

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Here is the full paper of my Master’s project. Unfortunately I wasn’t able to figure out how to resize the photos I had for the first 4 figures. Also, I couldn’t figure out how to get the graphs on here either. They wouldn’t copy and paste from word, so I apologize for that. But, hey, you still have the results! Enjoy!

Activation of Lower-Extremity Musculature during Squat Variations; Comparing Front and Back Squats

Douglas A. Berninger and Brian M. Campbell, Ph.D.

Introduction

Strength and conditioning coaches can benefit from including compound, multi-joint movements in their programs (16,33). These types of movements simultaneously work multiple muscle groups over multiple joints. It benefits these coaches because of the limited time and/or resources available to them. Performing these movements saves time because of working multiple muscles at once, while allowing the athlete to use more weight than single joint movements. This allows the athletes to further adapt to heavier loads by way of increased muscle recruitment, rate coding, and synchronization (3), escalating their strength and power production to a higher level in their given sport.

One of the most well-known multi-joint movements is the squat. The squat can be performed with many implements such as kettlebells, dumbbells, and medicine balls. The most common implement used for squats is the barbell. Squats can be used in many different ways within a strength and conditioning program (30). One can perform the squat with accommodating resistance (1,17), which adds resistance to the barbell by way of chains or elastic bands. Ebben et al. (11) have also shown that the squat can be used to predict loads for other compound, lower extremity exercises such as the deadlift, lunge, and step-up. This would make initial sessions easier for strength coaches who are unaware of their new athlete’s current strength capabilities in these exercises, but have squatted prior to attempting them.

It has been shown that an acute, high-intensity squat protocol resulted in improved 40m sprint performance (27). A program such as this would include lower volume, mixed with heavier loads. Cronin et al. (8) reviewed sprint performance and discovered, out of the eight studies showing running speed and maximal strength improvements, seven had used the squat to assess maximal, lower-body strength. Given that there was an 87.5% improvement rate from these studies, it is no wonder why most strength coaches believe the squat greatly enhances athletic ability.

Tricoli et al. (31) found similar results to this when they compared short-term effects of heavy resistance training, in physically active subjects, combined with either a vertical jump (VJ) or weightlifting (WL) program. They established that the WL group significantly improved in the 10m sprint and squat jump. They concluded the WL exercises (high pull, power clean, clean and jerk, half-squat) seemed to produce greater performance outcomes than the VJ exercises (double-leg hurdle hops, alternated single-leg hurdle hops, single-leg hurdle hops, 40-cm drop jumps, half-squat). Therefore, it has been proven that these multi-joint movements improve many aspects of performance, including sprinting and jumping.

To the author’s knowledge, the two most common variations of barbell squats used by strength coaches are the back and front squat. There is a high level of difficulty involved in perfecting the back squat, and the amount of achievable muscular development of the lower extremity is also substantial (32). There are two variations of the back squat that are known to be used by strength coaches. The first is the high-bar back squat (Figure 1), which is characterized by placing the bar above the posterior deltoids at the base of the neck. Hands are closed and pronated, with a width slightly wider than the shoulders (3).

The second variation is the low-bar back squat, represented in Figure 2, which is characterized by placing the bar on top of the posterior deltoids at the middle of the trapezius. Hands are also closed and pronated, with a width wider than the shoulders (3). Errors that should be avoided in the back squat are improper head position (9,13), lack of range of motion, excessive forward lean, misalignment of the spine, and uneven bar grip (13).

The front squat is characterized by the barbell being held on the anterior deltoids and clavicles. The hands are held in a pronated grip on the barbell, slightly wider than shoulder-width. The elbows are pointed straight forward (Figure 3) and held high to create a shelf for the barbell at the deltoids (15). The arms can also be crossed (Figure 4) to create a shelf for the barbell, if the athlete’s wrists are not flexible enough to hold the barbell with the straight forward method. Some errors that should be avoided in the front squat are lowering the elbows, raising the hips too early during the ascent, and raising the heels from the floor (7).

Squatting produces many significant benefits. These benefits range from increased speed (8,19,27), power (22,33) and strength (8). Squatting is also an excellent exercise for injury prevention and rehabilitation of the knee (24). Gullett et al. (14) stated that “squats can safely and effectively be used to strengthen the leg muscles that surround and support the knee for ACL patients, and for the general population as well”. Therefore, squats should be an integral part of any strength coach’s training program to improve performance, while simultaneously increasing the prevention of injury.

As mentioned, squats are a big part of developing the complete athlete and are used throughout all levels of sport for weight training. There has been an abundant amount of research exploring electromyography (EMG) during the squat (10,18,20,28) examining the changes that take place during different mechanical variations of foot rotation (4), stance width (2,21,25), and depth (6) during the back squat.

There have also been kinetic and kinematic examinations of back squats (9,12,23), and comparisons of front and back squats (5,14). However, there is limited information available comparing changes in muscle activity of the front and back squat exercises. This is especially true when both variations of the back squat are compared with the front squat.

Significance

The problem that may arise is that different squats may elicit different muscle activation levels due to varying bar placement. The possible differences in muscle activation levels may change the way strength coaches train their athletes and/or rehabilitation professionals train their patients. Discovering the muscle activity elicited from the selected muscles during the differing squat variations will help the strength coach, personal trainer, and physical therapist design rehabilitation/sport performance protocols, which include the appropriate type of squat to elicit specific muscular responses.

Purpose

The purpose of this study was to determine the differences in select lower extremity muscle activity between the high-bar back squat (HBS), low-bar back squat (LBS), and front squat (FS) while being performed with 75% of bodyweight loaded on a barbell. Some questions we looked to answer include 1) Does bar position change EMG activity during parallel squatting, and 2) Are front and back squats equally effective at activating the examined musculature of the lower body, or is one variation better than the other?

Methods

Experimental Approach to the Problem

A within-subject randomized comparison was used to investigate which muscles were the most active during each of the squat variations; and whether one of the squat types was better for overall muscle activation between subjects. Therefore, the subjects served as their own controls. The muscles used were chosen because they are considered to be targeted for their development through squatting movements (21,25). We hypothesized that 1) Bar position would not change overall EMG activity of the examined musculature between the squat variations, 2) The back squat would promote more activity of the posterior lower extremity musculature, and 3) The front squat would promote more activity of the anterior lower extremity musculature. The first hypothesis was due to findings by Gullett et al. (14).

 

Subjects

Eleven recreationally trained individuals (8 males and 3 females) were recruited to participate in this study. Their information can be found in Table 1. They must have had at least one year of regular experience squatting to be considered recreationally trained. Prior to each individual being included in the study, they must have been able to reach 90° of knee flexion, been squatting consistently within the year of the study, and been able to perform at least five repetitions with 75% of their bodyweight loaded on a barbell. The subjects read and signed informed consent forms, and the Bowling Green State University Human Subjects Review Board approved all the procedures.

Age (years) 22.2 ± 1.9
Height (cm) 172.3 ± 10.3
Weight (kg) 71.6 ± 14.4
Back Squat Experience (months) 32.8 ± 22.7
Training Age (months) 82.4 ± 33.2

Table 1. Subject Information

 

 

 

 

 

Instrumentation

EMG System and Software

An eight channel telemetered EMG system (Noraxon, INC. USA, Scottsdale, AZ) was used to measure muscle activity during the squat variations. MyoResearch XP version 1.07.01 (Noraxon, INC. USA, Scottsdale, AZ) was used to collect and analyze the EMG data.

Weight Equipment

The barbell used was a standard, Olympic barbell (Eleiko Sport, Sweden).  The squat stand (Sorinex, Irmo, SC) was a free-standing squat stand that could be easily moved. The weight plates (Cap Barbell, Houston, TX) were standard, Olympic style plates that fit on the barbell sleeves.

Electronic Beepers

Electronic beepers (Safety Squat, Scottsdale, AZ) were attached to the non-dominant thigh and used as an auditory aid for the subjects to know when they reached parallel (90° of knee flexion) during their squat trials.

Procedures

The subjects were recruited from the undergraduate student body at Bowling Green State University. Volunteers were given an information letter that contained a questionnaire which was designed to question the potential participants’ squatting experience and preferred squatting technique.

The subjects were instructed to leave the completed squat questionnaire in the office of the principle investigator for examination before they could be included in the study. The questionnaire was necessary to determine whether these subjects had the appropriate experience with squatting to participate in the study. If they had the appropriate experience, they were contacted by the principal investigator by e-mail to confirm a time to meet in the laboratory for data collection. They were also instructed to refrain from any lower-extremity activity outside of normal activities of daily living within 24 hours prior to data collection. This was to make sure muscle activity was not altered by soreness of any kind.

When they arrived for data collection at their scheduled time, the subjects were asked to perform a few bodyweight squats so the investigators could physically determine if their technique was congruent with their questionnaire answers. Their informed consent was obtained along with age, height, and weight before the data collection began.

The investigators prepared the skin over muscles of the thigh and placed two EMG electrodes on the skin over each of the selected muscles of the dominant leg. Perotto (26) was utilized to ensure the electrodes were in the proper position on each muscle. The muscles examined were the rectus femoris, biceps femoris, gluteus medius, and vastus medialis. These muscles were chosen because it is believed that they make up some of the prime movers for squatting (21,25). The proncipal investigator prepared each muscle by shaving the area to remove any hair and then cleaned it with an alcohol prep pad, followed by electrode placement.

Once anthropometrics were measured and electrodes placed, the subjects were instructed to warm-up for approximately 5 minutes with general, dynamic stretches including 20 butt kickers, 12 traveling lunges on each leg, 5 trunk rotations to each side, 10 frankensteins (tin-mans) on each leg, 20 jumping jacks, and 12 bodyweight squats. These dynamic stretches were done for two sets each, and overseen by the principal investigator throughout the study.

EMG data were collected during one session and consisted of each participant performing a set of bodyweight squats, as well as 75% of the subjects’ bodyweight loaded on a barbell for each of the squat variations (front squat, high-bar back squat, and low-bar back squat). The load used was determined from similar loads used in previous studies (6,23) and to limit the chance of injury to the subjects because of the lighter load. Squat depth (90 degrees of knee flexion) was controlled by electronic beepers (Safety Squat, Salt Lake City, UT), and was chosen to match the range of motion most coaches have their athletes perform. There was no guidance or encouragement given to the subjects once data collection was initiated. The principal investigator was certified through the National Strength and Conditioning Association as a Certified Strength and Conditioning Specialist and, therefore, is very familiar and qualified to supervise and teach these lifting techniques.

Three minutes of rest was provided between the end of the warm-up and the beginning of data collection. Weight belts were not permitted during the study. The participants were asked to perform five bodyweight squats to provide a baseline EMG reading of which to compare the weighted squat variations (front squat, low-bar back squat, and high-bar back squat). Next, the subjects were asked to complete five repetitions of each squat variation with 75% of their bodyweight loaded on a standard Olympic barbell (Eleiko Sport, Sweden), making sure that they achieved 90 degrees of knee flexion during each repetition. Two minutes of rest was provided between each squat variation and the subjects were permitted to pace in a small area or stand still during each rest period, but were not allowed to sit. The order of loaded squat variations performed were randomized, while each subject began all trials with the bodyweight variation first for normalization. In order to randomize the loaded squats, the investigators rotated the order so the last squat variation of the previous participant would be the first squat variation for the current participant, and so on.

Trials were discarded if the parallel beepers did not beep, the subjects lost balance, their backs rounded, or if their heels lost contact with the floor. Each session lasted approximately 60 minutes. Once all the squat trials were performed and data was recorded, the session was complete. All electrodes were removed and subjects were done with their contribution to the study.

Data Analysis

Mean EMG data was gathered using the MyoResearch XP software from each of the squatting variations. The raw EMG signals were smoothed and rectified using a 50ms RMS method. The first and fifth repetitions of each squat variation were thrown out to eliminate any possible variation in activity due to the subjects starting the set with an improper repetition, or thinking about racking the weight before the repetition was fully completed. Once this was done, the EMG values for the three middle repetitions were averaged to minimize the possible variation from repetition to repetition, according to similar methods from previous studies (6). The mean EMG data for the three weighted squat variations were compared as a percentage change from the squat trials with no weight. This allowed the investigator to use the squat trials that were performed with no weight to serve as the control for the loaded squat variations.

 

 

Results

Again, I’m sorry that there are no figures to go along with the words, but you can use your imagination, right?!

An analysis of each muscle during each loaded squat type was compared to those same muscles during bodyweight squats. This analysis was done to answer the question we had about which squat type was best at activating each of the examined muscles. With this analysis, we also looked to answer if bar position changed EMG activity during parallel squatting. The front squat (FS) elicited the highest mean activity for the biceps femoris and the gluteus medius. The low-bar squat (LBS) elicited the highest mean activity for the rectus femoris and the vastus medialis. Figure 5 represents how each squat type affected the individual muscles.

Figure 6 illustrates the percent change in muscle activity from the bodyweight squat to each of the loaded squat types (FS, HBS, LBS). The largest percent change in the vastus medialis and rectus femoris was caused by the LBS (76% and 85.6%, respectively), while the FS caused the largest changes in the biceps femoris (102.8%) and gluteus medius (101.7%).

Figure 7 illustrates the percent change in muscle activity from the FS to LBS and FS to HBS, which was another aspect of EMG examined in the current study. This was analyzed to find how the muscle activity changed between the front and back squats, and compare which was better at activating the examined musculature. We found that there was an increase in activity of 7.7% and 6.1% in the vastus medialis from the FS to LBS and FS to HBS, respectively. The biceps femoris experienced a decrease in both cases, declining by 11.5% from the FS to HBS and 7.2% from the FS to LBS. The gluteus medius experienced decreases of 21.7% and 17.9% from the FS to HBS and FS to LBS, respectively. The rectus femoris experienced a 14.1% and 4.1% increase from the FS to LBS and FS to HBS, respectively.

Figure 7 also shows the differences in EMG activity of the two back squat variations, demonstrating which one might be better for activating specific leg musculature. The LBS elicited 1.45%, 4.8%, 9.6%, and 4.8% higher activity in the vastus medialis, biceps femoris, rectus femoris, and gluteus medius, respectively, compared to the HBS.

Figure 8 compares the overall mean EMG activity of the selected lower-extremity musculature during each of the squat variations. It appears that the LBS activated the musculature the best out of the four variations (BWT, FS, HBS, and LBS). However, there was not much difference between the three loaded variations.

Discussion

The purpose of this study was to determine the differences in select lower extremity muscle activity between the high-bar back squat (HBS), low-bar back squat (LBS), and front squat (FS) while being performed with 75% of bodyweight loaded on a barbell. We sought to answer if bar position changes EMG activity during parallel squatting; and if front and back squats are equally effective at activating the examined musculature of the lower body.

We hypothesized that 1) Bar position would have no affect on overall EMG activity of the examined musculature between the squat variations, 2) The back squat would promote more activity of the posterior lower extremity musculature, and 3) The front squat would promote more activity of the anterior lower extremity musculature.

Our primary finding was that the LBS promoted greater overall activity than the HBS or FS (Figure 7, 8). The LBS also elicited greater activity of all four muscles when switching from the FS to either the LBS, or HBS. Our results show that the LBS is superior in recruiting the vastus medialis, rectus femoris, gluteus medius, and biceps femoris when examining the percentage change from the FS, BWT, and HBS.

The higher activity in the LBS in relation to the HBS was also found in a study done by Wretenberg et al. (35). Eight weightlifters (high-bar) and six powerlifters (low-bar) participated in the study. All of whom were Swedish national class lifters in their age and weight categories. Two depths were studied, parallel and deep. A stop bar was set under the lifters’ buttocks to determine parallel depth, while the authors described deep squats as a squat to full knee flexion. The bar weight used was based on the subjects’ all-time maximum for a deep squat. Muscle activity of the vastus lateralis (VL), rectus femoris (RF), and long head of the biceps femoris (BF) were recorded, with an isometric contraction of 3 seconds at parallel depth using 65% 1RM as a reference. The subjects were allowed to choose their own foot width, much like the current study.

They found that the powerlifters put relatively more load on the hips than the knees, while the weightlifters had a more equal distribution of the load between the hips and knees. This could be an effect of the bar placement being either higher or lower, which would alter the torque on the body. The muscle activity was higher for the powerlifters during both squat depths, with the only significant difference found in the RF. Figure 1 of the current study shows similar results of the RF. Also like the current study (Figure 6), the highest activity for both groups, compared to baseline, was found in the BF, with the relative activity of about three times the reference level. The activity of the BF also showed the greatest individual difference out of the examined musculature. They also reported that the low-bar technique resulted in a hip moment almost two times as large as the knee moment, while the high-bar technique resulted in more equally distributed moments of force between the hip and knee joints. It can be seen from this study, much like the current study, that the use of the LBS is more advantageous from a muscle recruitment point of view.

An abundant amount of research in the past has explored electromyography (EMG) during the squat (10,18,20,28). Many coaches believe that squatting benefits hamstring development, especially if performed at greater depths. However, previous research (6,10, 35, 36) and the current study report conflicting results to these prominent coaching beliefs.

Wright et al. (36) described the hamstrings’ role in squats as more of a stabilizer of the knee than a prime mover. They go on to say “the hamstrings show maximum activity during hip extension when the knee is either stabilized or flexed simultaneously. They are minimally active, however, during simultaneous hip and knee extension, such as rising from a squatting position”. Caterisano et al. (6) also states that “increasing depth has no significant effect on the relative contribution of the biceps femoris to the total electrical activity of the major muscles involved in the lift”.

Wright et al. (36) additionally compared the EMG activity of the hamstrings during the leg curl (LC), stiff-leg deadlift (SLDL), and back squat movements. They discovered that peak EMG activity showed half of the subjects peaking in the concentric LC, while the other half peaked in the concentric SLDL. Ebben et al. (10) performed a similar study, examining hamstring muscle activity during the performance of the deadlift, step-up, lunge, squat, and leg extension. They discovered that the squat does elicit some hamstring activity, but this activity is less than some of the other exercises tested. For example, the step-up showed significantly greater biceps femoris activity than the squat. If hamstring activation is desired, Wright et al. (36) recommend the deadlift.

The study shows comparable findings to that of previous studies (10,36). The back squat movement was not effective in eliciting hamstring muscle activation. Out of the three loaded squats, the front squat caused more posterior muscle recruitment, including the biceps femoris and gluteus medius, than either the high-bar or low-bar back squat. This may be due to the increased distance of the resistance arm due to the anterior bar placement, which would increase the torque that the hamstrings and gluteus medius have to overcome to assist the gluteus maximus in hip extension.

Examining the changes that take place during different mechanical variations of foot rotation (4) and stance width (2,21,25) are important for how squats may be performed. Unfortunately this study did not take stance width or foot rotation into account, but used what was comfortable for the subjects.

Boyden et al. (4) investigated the effects of smaller degrees of foot rotation on the EMG activity of the quadriceps femoris muscles (rectus femoris, vastus medialis, and vastus lateralis) of six, male college students during the performance of the parallel back squat. One-repetition maximum was tested with each subject’s preferred foot position. For data collection, 3 repetitions at 80-90° of knee flexion were performed with 65 and 75% of 1RM. This was done with four different foot positions (10° medial rotation, neutral, 10° lateral rotation, and 20° lateral rotation) in a random order.

A comparison of relative EMG activity in the three muscles was recorded, and found that the highest overall mean EMG, compared with all the foot positions, occurred at 65% 1RM with the feet rotated 20° laterally. However, the overall peak activity was greater at 75% 1RM than 65% 1RM. This is common, as muscle activity/recruitment increases with increasing resistance (3). There were no statistically significant differences in the level of peak activity with foot rotation at either the 65 or 75% 1RM conditions.

Anderson et al. (2) investigated if modifying foot placement of 15 physical therapy students during the squat would significantly alter EMG of the vastus medialis (VMO) when compared to the vastus lateralis (VL). The subjects had to remove their shoes and squat to a chair, using their own rate of movement, at knee angles of 30°, 60°, and 90°.

They found a trend for the VMO to be more active with more external rotation (wider stance). They also discovered that VMO:VL ratios increased with increasing knee flexion angles. This is not surprising, considering the amount of difficulty to rise from a squat increases as one gets deeper into the movement. What can be taken from this is that widening the squat stance shows a trend toward targeting more VMO activity. Also, the VMO seems to be active through the entire range of motion of the squat. However, there was no significant difference in muscle activity when comparing respective ranges of narrow and wide-stance squats; and the width of stance does not seem to significantly alter VMO or VL activity.

Based on what Boyden et al. (4) and Anderson et al. (2) found, we believed that controlling for specific foot positioning was not important and would not have any significant impact on our findings. This method may have actually been a control in itself for each subject’s foot positioning between squat variations, as individuals seem to use the same foot width and rotation for whichever type of squat they are performing.

EMG activity during different squat depths has also been studied. Caterisano et al. (6) tested the effect of partial, parallel, and full back squats on the EMG activity of the biceps femoris, gluteus maximus, vastus lateralis, and vastus medialis. Their subjects performed three repetitions with a load between 100-125% of their bodyweight. They did report similar activity to what we found for the biceps femoris. They found that there was a low level of biceps femoris activity, and squatting depth had no significant effect on the activity of this muscle. Again, this is probably due to the simultaneous hip and knee extension and the hamstrings’ prominence as a knee stabilizer during the squat (36).

Back and front squats are regularly used by strength coaches. Comparisons of front and back squats have been made previously (5,14,29). However, there is limited information available comparing changes in muscle activity of the front and back squat exercises. This is especially true when both variations of the back squat are compared with the front squat.

Gullett et al. (14) compared and quantified the net compressive and shear forces of the tibiofemoral joint and extensor moments, as well as comparing the muscle activation of front and back squats. They used 15 healthy individuals, who had at least one year experience in both variations of squatting and assessed EMG data from the rectus femoris, biceps femoris, vastus lateralis, vastus medialis, erector spinae, and semitendinosus. They hypothesized that the back squat would result in increased loads on the knee joint compared with the front squat; and the front squat would result in increased knee extensor and decreased back extensor muscle activity when compared to the back squat.

They found that the muscle activity was relatively low during the eccentric phase and reached maximal levels during concentric phase, with bar position not influencing the muscle activity. An interesting note to consider is the fact they found that shear forces did not vary between the two squat variations. Therefore, they believe that front squats may be more advantageous for people with knee problems and for general long-term joint health because of the similar muscle activity and lower compression forces on the knee.

Similar to other hypotheses (14), we hypothesized that the two variations of the back squat would result in increased EMG of the posterior musculature compared to the front squat; and the front squat would result in increased EMG of the anterior musculature compared to the back squat. However, we found identical results to Gullett et al. (14); the front squat resulted in increased EMG of the posterior musculature and the back squats resulted in increased EMG of the anterior musculature. This is most likely because of the increased resistance arm in relation to the musculature, due to the change in bar position.

The current study is comparable to previous studies (14), considering that the purpose was to compare the lower-extremity muscle activity of varying squats to each other. They discovered that the bar position did not significantly influence muscle activity, which is what we had hypothesized in our study. The current study resulted in similar activity levels of each muscle within each of the loaded squat variations (Figures 5, 6). By comparing the percent change from the bodyweight squat to the loaded variations (Figure 6) and the difference between the FS and LBS, FS and HBS, and HBS and LBS (Figure 7), this showed that there was not much difference in EMG between variations. From these results, it can be suggested that whichever squatting variation is most comfortable for each athlete is the variation that should be performed.

However, it should be noted that these results were discovered with recreational athletes and light loads (75% of body weight), which may not be applicable to higher level athletes and higher loads. Having stricter requirements for the experience of the front squat and hand position would have made the study stronger as well. The subject’s squat experience was obtained by their word, so there was no real way of knowing if these numbers were true.

Practical Applications

This study was a concerted effort to determine what changes take place as bar position changes. Strength and conditioning coaches can benefit from including compound, multi-joint movements in their programs (16,33). It has been reported that the use of squats within a strength program can result in improved athletic performance (27,34). For this reason alone, the way squats are performed should be examined more closely in the future for more application to performance programs.

The problem that we thought may arise is that different squats may elicit different muscle activation levels due to varying bar placement. Our results show that, at least with lighter loads, this is not the case. We believed the possible differences in muscle activation levels may change the way strength coaches train their athletes. In reality, the fact that we found that there is not much difference between the squat types may allow more flexibility for strength coaches to develop a protocol that adheres to each athlete’s squat preference. This, of course, is strictly from a muscle activation standpoint. When other parameters are considered, such as compressive and shear forces (14), being able to choose the squat type utilized based on preference may not be the case.

Future research should focus on examining the differences in muscle activation with higher level athletes, using heavier loads that are more realistic to training, for greater application. Also, future studies should include hip, knee, and ankle joint angle examinations, as well as multiple squat depths to go along with EMG. This will allow more comparisons to be made between muscle activation differences at different positions within the squat movement.

 

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