Biomechanical analyses are often conducted to provide insight into human performance, with the aim of either improving that performance or mitigating injury risk. At one end of the spectrum, elite performances illustrate how people who are extremely proficient accomplish a task (e.g., Usain Bolt's 100-m sprint performances (16)). This approach may be limited in that those individuals may have a unique constellation of anatomical features and intrinsic dynamics (e.g., mobility, strength, power, endurance) that may allow for distinctive movement patterns. On the other side of the performance spectrum, additional insights may be gleamed from examining individuals who fail to perform a certain task. The literature concerning slips and falls has numerous examples of people who fail to arrest themselves from a fall (e.g., see Ref. 12). This approach is not without its limitations as well: if the task is simply too demanding for an individual, it may be impossible to determine what would prevent her from completing the task under less demanding circumstances. A third approach might be to examine a task that an individual can complete, but on some occasion failed to do so. However, capturing and analyzing such situations are rare. We were fortunate enough to capture data on 5 individuals who both completed, and fail to complete, a repetition with the same load while performing the back squat. Examining these data may provide insight as to what limited performance of the squat and thus provide a road map for the prescription of exercises that may help improve it.
The bilateral back squat is used both as a training modality and is a sporting event in and of itself. Like most human activities, it involves multiple joints (predominately, the hip, knee, and ankle (8)). As both load and volume determine the training effect, it would be important to understand what would limit the performance of the squat activity so that assistive exercises could be prescribed that would allow for increased load, volume, and training effect over time.
The muscles around a joint create a net joint moment (NJM), which can be thought of as the net rotational effect of all muscles crossing that joint (23,24). Assuming a failure would occur during the concentric (as opposed to eccentric) portion of the lift, successful completion of the squat requires the muscles around the acting joints to generate sufficient energy, through the NJMs, to raise the system's (body plus barbell) center of mass (10). Thus, there are 2 possible causes for failure: either a complete system failure or a cascading failure. With a complete system failure, all of the NJMs deliver an insufficient amount of energy to the segments and the lower extremity simply collapses (or does not rise). In such a case, no one joint could be singled out as limiting performance.
With a cascading failure, there is lower energy generated by one (or fewer than the total) of the NJMs (the limiting joint(s)). If this occurs, another NJM, at a compensating joint, could increase its energy contribution and still lift the center of mass (COM), and/or prevent collapse of the lower extremity (22). If the increased demand is within the capacity of the compensating joint, then the lift may still be completed. If not, the load will either shift to yet another joint within the system or the person will be unable to complete the lift. In network parlance, this phenomenon is known as a cascading failure (1). It would seem plausible that cascading failures are responsible for the inability to complete a task that is otherwise within the capability of the human movement system (they may also be responsible for certain types of injuries). If this occurs, the joint that initiated the cascading failure could be considered the limiting joint. Although studied extensively within the realm of computer science, little is currently known about cascading failures during multijoint human movements.
For example, if the knee was the limiting joint during the squat, then exercises targeting the knee extensors would lead to improved performance over time. Targeting the hip extensors, if not the limiting joint, would probably not have the desired effect. Similarly, larger contributions from a compensating joint could lead to increased stresses on that joint and injure it, although that joint was not an original source of impairment. Interventions that do not target the impairment would be less than optimal in preventing injury or reinjury to the compensating joint.
Furthermore, the limiting joint may not be the same for each individual. If an increased contribution from the hip compensates for a decreased contribution from the knee for 1 individual, but the opposite occurs for another individual, then their differences will cancel and not appear in the aggregate data (9,14). This may limit the applicability of traditional statistics in such instances, and it may be necessary to examine each subject individually.
The primary purpose of this investigation was to determine whether a failed attempt during the concentric phase of a barbell squat exercise was the result of a complete system failure or a cascading failure. With a complete system failure, the contribution of each joint's NJM would decrease nearly simultaneously, and there would be no compensatory increase in the contribution of another joint's NJM. With a cascading failure, the decreased contribution of 1 joint would be compensated by an increase in the contribution of another joint. However, the increased contribution would not be enough to raise the system's COM and failure would ultimately occur. If a cascading failure were detected, it could incriminate a specific joint as being the “weak link” in the chain. Such findings could have potential applications for training and injury prevention.
Experimental Approach to the Problem
We examined subjects who were part of a larger study that required participants to perform 3 repetitions of a barbell squat with a 3 repetition maximum (RM) load atop force platforms while instrumented for biomechanical analyses. Five of the subjects were able to complete at least 1, but not all 3, repetitions. This was quite serendipitous because subjects demonstrated the capacity to perform the task initially, yet still failed subsequently—allowing for comparisons between the unsuccessful repetition and the preceding successful repetition to determine why biomechanically they failed to complete the set. These comparisons included the energy generated at the hip, knee, and ankle during the same time period. We hypothesized that these unsuccessful repetitions were the result of a limiting joint that produced a cascading failure and that the limiting joint may differ across individuals.
Eighteen young healthy adults (mean age: 26.6 ± 4.29 years) were recruited from the university campus and the surrounding community to take part in the larger study (10). Each subject completed a medical screening questionnaire to rule out existing medical conditions that would preclude them from squatting with a heavy load and provided their informed written consent to participate in this study. All subjects had at least 1 year of resistance training experience. The protocol required subjects to perform 3 sets of 3 repetitions of a barbell squat to a linear depth that was 45% of their leg length with a load that was equivalent to their previously established 3RM. During testing, 5 subjects could not complete all 3 repetitions for at least one of the sets. Those 5 subjects were used for this analysis, and their characteristics are presented in Table 1. For comparison purposes, the subjects who successfully completed all 3 repetitions of all 3 sets had a mean (±SD) 3RM of 119.58 (±39.03) kg and a strength-to-mass (3RM per kilogram body mass) ratio of 1.55 (±0.41).
The larger study was approved by the university's Institutional Review Board. On day 1, a 3RM full-squat resistance was determined for each subject using the protocol established by Stone and O'Bryant (21). A linear depth of 45% of leg length was chosen because it approximated a 90° knee flexion angle, yet allowed the subjects to attain that depth with the control strategy (i.e., combination of hip, knee, and ankle flexion) of their choice. The depth of the squat was ensured by having each subject touch safety supports with the barbell before beginning the ascent (Figure 1). On day 2, which occurred 1 week after day 1, subjects began with a self-selected warm-up. Subjects then performed 3 repetitions each, using 25, 50, 75, and 100% of their 3RM.
Biomechanical Instrumentation and Analyses
Subjects performed each repetition with markers attached to the specified bony prominences required for a modified Helen Hayes lower extremity marker set to create a model with 7 segments: a pelvis, 2 feet, 2 shanks, and 2 thighs (15). A Vicon 370 motion analysis system (Oxford Metrics, Oxford, United Kingdom) was used to collect coordinate data and 2 AMTI (Model OR6-6-1; AMTI, Watertown, MA, USA) force plates (one under each foot) were used to collect ground reaction force and center of pressure data.
During the 100% condition, each of the 5 subjects was unable to complete all 3 repetitions of a given set (Table 1). During the ascent, they failed to generate enough energy to return to the upright position and then descended back to the barbell safety supports. Analyses were limited to the concentric (upward propulsive) phase of the movement. The unsuccessful repetition was deemed the “failed” repetition. The repetition immediately preceding it was deemed the “successful” repetition. Inspection of the kinematic data was used to determine the beginning (bar ascent; t1) and the point at which failure (bar descent; t2) occurred on the failed repetition; positive (upward) velocity of the COM indicated t1 and negative (downward) velocity indicated t2. A corresponding start and time interval was then determined for the successful repetition. For example, if the failure occurred 1,400 milliseconds after the beginning of the repetition, the successful repetition was cropped 1,400 milliseconds after the beginning of the movement.
A reference frame was imbedded in each segment, with the positive directions for X, Y, and Z oriented anteriorly, laterally (left), and superiorly, respectively. A Cardan (YXZ) sequence was used with the proximal segment used as the reference segment. Standard inverse dynamic calculations were used to determine the instantaneous joint angles, NJMs (in Newton-meters per kilogram), and NJM powers (in Watts per kilogram) at the hip, knee, and ankle. The NJM energy (NJME) was calculated by integrating the NJM power curve using a 0.417 milliseconds time interval. The NJME represents the total amount of energy engendered to the system up to that point in time.
Vertical ground reaction force data (correlation of multiple coefficient [CMC] = 0.995 ± 0.003) and joint moment data (CMC = 0.945 ± 0.035) determined through inverse dynamics have been demonstrated to be highly reliable (15) and have been used to study squat mechanics in previous investigations (8–10).
Group mean data were used to compare peak NJM power and NJM work. Because of the small sample size, group mean values were compared using a Wilcoxon matched-pair signed-rank test. This test addresses small sample sizes by removing the assumption of normality associated with the t-test. Statistical significance was set at 0.05.
For NJME, the failed values were subtracted from the successful trials. In this way, a positive value represented a greater value than the successful trial and a negative value represented a smaller value than the successful trial. Based on our operational definition, a compensation occurred if a negative value of 1 DOF was compensated for by a positive value at another DOF. A compensation was considered negligible if the increase was less than 10% of the total work of that joint: slight if the increase was between 10 and 20%, modest if the increase was between 20 and 50%, and large if the increase was >50%.
Squats were classified as a total system failure if all NJME measures fell below zero within 10% of the movement time and as a cascading failure if 1 joint failed at least 10% of the movement time before another joint. Subjects were grouped according to these failure modes.
The group mean data are presented in Table 2. For peak NJM power, there were significant differences only at the left and right hip (71 and 74%, respectively, p = 0.043). For NJM work, there were also significant differences only at the left and right hip (63 and 69%, respectively, p = 0.043).
The difference in energy vs. time graphs for all 5 subjects are presented in Figures 2–6. For all subjects, the difference in energy between trials generated by the ankle NJME was negligible compared with the knee and hip, and none of the subjects could be classified as ankle failures. Three of the 5 subjects (subjects 1–3; Figures 2–4) were classified as hip failures and the remaining 2 (subjects 4 and 5; Figures 5 and 6) were classified as knee failures (Table 3).
Compensations were seen between the hip and knee albeit at different amounts for the individual subjects. For the hip failures, subject 1 (Figure 2) had a modest increase in energy generated by the knee; subject 2 (Figure 3) had a slight increase in energy generated at the knee; and subject 3 (Figure 4) had a negligible increase in energy generated at the knee. For the knee failures, subject 4 had a negligible increase in energy generated at the hip, whereas subject 5 had a slight increase in energy generated by the hip, followed by a modest increase in energy generated at the knee.
This study examined the reasons for task failure during a bilateral back squat. The subjects were taken from a larger sample used in a previous investigation where subjects were asked to complete 3 sets of a 3 RM (10). These subjects did not seem remarkable compared with those who could complete all 3 sets; 2 of the subjects did have 3RM strength values that were below 1 SD of the mean of the successful group but strength-to-mass ratios were all within 1 SD of the mean. Therefore, we thought this would be an interesting study to see if we could determine why biomechanically they failed to perform the prescribed number of repetitions.
Group mean data suggest that the failure was a result of the inability to produce sufficient work/power of the lower-extremity NJMs, although only the hip was significantly lower during the failed trial. Furthermore, the group mean data did not reveal a compensatory increase in work/power by any joint. However, using energy analysis and an individual approach, negligible to modest compensatory dynamics were uncovered in the lower extremity during the squat exercise, particularly between the hip and knee.
Furthermore, in the sample studied during this investigation, it seems as though failure was a result of a limiting joint causing a cascading failure. For 3 of the subjects, the hip was the limiting joint; for the other 2, the knee was the limiting joint. One of the more interesting examples of this was subject 5 (Figure 6). The energy compensation is more striking if the hip and knee on 1 side appears in the same graph (Figure 7). Initially, both the hip and knee produced less energy during the failed trial; however, at ∼300 milliseconds, the knee actually started generating more energy during the failed repetition—in an apparent attempt to continue raising the body's COM. About the time the knee peaks in its energy generation, the hip compensates by generating a larger amount of energy during the failed trial. However, this compensation by the hip is not large (or possibly soon) enough to allow the subject to successfully complete the lift. These findings highlight the need to examine individual data in addition to group mean values, to make appropriate interpretations.
Another important finding of this study was that failure of the multijoint squat activity did not occur because the entire system failed simultaneously, but because 1 joint limited the movement. A previous investigation demonstrated that the hip NJM was the dominant contributor to the squat movement, and this contribution increased as the external load increased (10). Moreover, although many different combinations of NJM contributions were used with lower resistances, the system converged on a tighter grouping of contributions as the load approached maximum (10). However, that investigation was not able to determine which NJM(s) limited the movement. Each of the 5 subjects in this investigation demonstrated that there was a single joint that initiated the failure and that the other joints followed after varying amounts of time. This is analogous to a cascading failure of networks or power grids (1).
It is also interesting to note the bilateral similarity of the NJMs, as there are likely differences in strength between the dominant and nondominant limbs (19). This certainly leaves open the possibility that a single joint (left or right) may have been the limiting one, but it is impossible to make such a determination in the context of this investigation. The bilateral similarities noted here may be related to central factors (11), which may be necessary for postural control (18). As the different NJMs affect the direction of the ground reaction force (13), and thus the trajectory of the center of mass of the system, these bilaterally kinetic findings may have occurred simply to maintain balance.
Furthermore, this investigation highlights the importance of examining single subject data over group mean data. James et al. (14) highlighted this point by identifying 2 distinct statistically significantly different landing strategies in response to increases in drop height. The authors caution that the “presence of different strategies can result in a conclusion of no significant differences for the aggregate group (p. 117).” Our findings echo that caution. Group mean data findings suggest that the hip was the limiting DOF. Coupled with earlier findings that the hip NJM was the largest contributor during the squat (10), one would conclude that the hip extensors must be strengthened to improve squat performance. However, for 2 of the subjects, the knee extensors limited performance. An intervention targeting the hip extensors for these individuals may not have the desired effect.
These findings suggest that strength and conditioning professionals may wish to use specific assistive exercises to address the weak link in the chain and improve multijoint performance; having an individual “just squat more” to improve the squat may be analogous to telling a sprinter to “just run faster.” For example, studies have found that patients can shift the demand away from the quadriceps during multijoint movement after anterior cruciate ligament (ACL) reconstruction surgery (17,20), and these, sometimes dramatic, compensatory motions may not be noticeable (6). Enocson et al. (7) found greater shifts in MRI signal intensity (a measure of muscle involvement) of the quadriceps during a knee extension compared with a leg press exercise. Taken together, these studies suggest that patients after ACL reconstructive surgery need to perform knee extensions and squats. We posit that healthy individuals may make similar compensations away from the limiting joint, and specifically targeted isolation exercises as an adjunct to multijoint exercises may be more beneficial than performing multijoint exercises alone, even in healthy individuals. The methodology used in this study may identify which exercises (hip extension, knee extension) the trainee needs to prioritize. Further studies, using these types of interventions, are needed to validate this strategy.
Like all investigations, the findings of this study need to be interpreted in light of its limitations. First, we chose to use work-energy methods to examine this task. It worked well, particularly for this movement, because the powers of the NJMs during the concentric phase of the squat were all positive. Difficulties may arise for other tasks if certain NJM powers are positive, whereas others are negative (2,3), or if there was a large isometric demand at a particular joint.
Second, the failures incurred are specific to the parameters of the squat exercise used. Bryanton et al. (5) found that the relative muscular effort of the knee extensors increased with squat depth but not with an increase load, whereas increases in the hip relative muscular effort occur with increases in both depth and load. Our findings support the notion that the hip is the dominant contributor to the squat when the loads are relatively heavy and the depth relatively shallow. However, we found the hip is not necessarily the limiting joint in each case (we identified 2 cases where the limiting factor was the knee). It could be hypothesized that there may have been a greater incidence of knee failures had the squat been deeper, but this requires further investigation.
Third, we chose a 10% difference in movement time to determine that a cascading failure occurred. As evidenced by Table 3, had that difference been averaged bilaterally and increased to 15%, 4 of the 5 subjects would have been characterized as such; with a 20% difference, only 1 subject would have experienced a cascading failure. Similarly, had other percentages been chosen to characterize the magnitude of the compensations (negligible, slight, modest), different interpretations may have been warranted. As this is the first study that we know of to examine cascading failures and compensations in this way, further investigation (most probably through computer simulations) is also necessary to examine these timing and compensatory effects.
Fourth, there was a small sample size (N = 5). However, as mentioned earlier, the number of subjects was based on the number of subjects who failed to complete a task they could otherwise do. Although we could have designed an experiment that would have forced a task failure (through either a load that was too heavy or a repetition range that would have ensured fatigue), our rationale for this study was to examine a movement that the subject was capable of safely completing. Had a design been chosen that would have forced a task failure, there is possibility that a cascading failure may not have occurred. This is a topic for future investigations. A larger sample size would not have changed another premise summarized by Bates: individuals are unique, no 2 subjects are alike (4). Although we may have found more subjects with hip or knee failures (and possibly some with ankle failures), when studying task failure, each subject must be considered individually rather than collectively. This may require new experimental designs and statistical methods.
Finally, we did not have an opportunity to follow-up with these individuals and see if an intervention based on these data would have corrected their issues and improved their squat performance. This study was an important first step in identifying a potential limiting factor in performance. Future investigations should examine how interventions, based on deficiencies identified by this methodology, would improve squat performance over more general strengthening programs.
Error compensation and cascading failure may be important features of human movement. Energy analyses provide insight into these 2 features. Because of the individual nature of task failure, each subject should be examined individually in addition to group mean aggregated data. However, this type of analysis holds promise for determining the limiting joint for a particular movement and how other joints may compensate. This was demonstrated for the squat movement, with the hip or knee acting as the limiting joint during failure. Future investigations should focus on expanding this analysis to different activities that involve multiplanar movements and investigate the efficacy of this approach for designing tailored interventions to correct the issues necessary to complete a task.
Although the hip extensors were the dominant contributor to mechanical energy during the concentric phase of a barbell squat, it was not necessarily the limiting joint during the lift. Group mean data can mask these individual effects. A limiting joint, or “weak link,” may explain failure to complete a lift. Interventions should address the limiting joint on an individual-specific basis and incorporate assistive exercises that target these deficiencies.
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