BRAGG, RICHARD W.; MACMAHON, JOHN M.; OVEROM, ERIN K.; YERBY, SCOTT A.; MATHESON, GORDON O.; CARTER, DENNIS R.; ANDRIACCHI, THOMAS P.
Various methods exist for the prevention and treatment of joint ligament and other soft tissue injuries among athletes. Typically, these techniques attempt to stabilize joint movement. Athletic tape is the primary tool used to restrict excessive joint motion for athletes in a wide range of sports, from football to gymnastics. Despite its widespread use, its effectiveness in preventing injuries is still unknown. Although the ankle is the most commonly taped part of the body, the lateral ligament complex of the ankle is still the single most frequently injured structure in the body during athletic activity (5,13).
Although ankle taping seems to be initially quite effective in limiting range of motion (ROM) and reducing excessive inversion (the primary mechanism of injury (9)), it loses most of these effects after about 20 min of exercise (1,5,6,8,10–17,19,25). Twenty minutes is less time than most precompetition warm-ups, and thus the majority of the ROM control provided by the tape is lost by game time.
There are two commonly cited mechanisms of injury prevention provided by athletic tape. It can act as an external ligament through direct mechanical support (1–3,5,6,8,10–19,21,25), or it can increase the sensitivity of the proprioceptive feedback mechanism (7,20,23). With respect to direct mechanical support, since muscle reaction time is not adequate during sudden inversion to contribute any reduction in load to the lateral ligaments (1,16), tape may act as an external ligament (2,3). On the other hand, there are arguments that tape can enhance proprioception (7) and increase joint control (5,13). The mechanical properties of tape may be a key indicator in both cases.
Although many studies have assessed the functional capabilities of tape using performance tests (e.g., ROM limits (1,6,8,11,15–17,25), electromyography (1,16), torque measurements (5)), very few studies address the mechanical properties of athletic tapes (1,2). The primary objective of this study was to mechanically test commonly used athletic tapes to determine differences in their individual rheological properties. Failure tests were used to determine failure strength, elongation at failure, and stiffness values for each tape, as well as to define load parameters for subsequent fatigue tests. Fatigue testing under load control measures the increasing length of the tape while it is cyclically pulled to a given force. This provides useful information concerning the ability, or inability, of athletic tape to maintain its structural characteristics after repeated loading. Similarly, fatigue testing under displacement control measures the decreasing force resistance of the tape while it is cyclically pulled to a given length. This provides information concerning the ability, or inability, of tape to resist external forces after repeated stretching.
It is proposed that these relevant time-dependent mechanical properties of current commercially available athletic tapes are dictated by their microstructure. The mechanical tests will then provide two types of useful information. First, the results will indicate the current state-of-the-art mechanical behavior of athletic tape. Second, these measurements can be used as benchmarks in the future development and evaluation of better athletic tapes.
A Web-based survey (originally available at http://www.foo-bar.com/tape/tape.html) was compiled and administered to athletic trainers in the National Football League (NFL), National Hockey League (NHL), Major League Baseball (MLB), and schools in the Pacific 10 Athletic Conference (Pac-10), in order to obtain feedback from athletic trainers regarding commonly used athletic tapes. Trainers were asked which brands of adhesive, elastic-adhesive, and self-adhesive tapes were most commonly used by their organization, in addition to the most common widths for each tape used.
On the basis of this survey, the most popular adhesive and elastic-adhesive tapes were chosen for inclusion. Zonas (Johnson & Johnson, Inc., Arlington, TX) was chosen as the most common adhesive athletic tape. The elastic-adhesive tape of choice was Jaylastic (Jaybird & Mais, Inc., St. Lawrence, MA).
The third tape chosen for the study, Leukotape (Beiersdorf, Inc., Norwalk, CT), was chosen because a few trainers that were interviewed suggested that it was one of the strongest tapes available. It is typically used for medical purposes such as patellar tracking and arch support, and is not typically used for everyday taping because of its abrasive nature. However, since a wide range of tapes was desired for inclusion in the study, Leukotape was selected as a possible “high-performance” tape.
Surveys also revealed that 1.5 inches (3.81 cm) is the most common width of tapes used, so this was the width chosen for all three of the tapes used. To ensure randomness of sample selection, the tapes were obtained from a number of sources, and batch and roll numbers were recorded for each tape tested.
Using an MTS-810 hydraulic material testing machine (MTS, Minneapolis, MN), three types of mechanical tests were performed on each of three different athletic tapes. The first test was load to failure. The second was a fatigue test under load control, with peak loads of 90%, 70%, and 50% of the mean failure load determined from the load-to-failure tests. The third and final test was a fatigue test under displacement control. The peak displacements for these tests were those displacements initially corresponding to 90%, 70%, and 50% failure load at the peak of the first cycle. Eight samples of each tape were subjected to each test. This was the sample size necessary to detect a 10% difference between the properties of any two tapes, assuming a standard deviation of 5%, a level of significance of 0.05, and a power of 0.95.
To begin each test, the tape was mounted in the loading frame (Fig. 1) by wrapping each end three times around an aluminum cylinder measuring 15 cm long and 7 cm in diameter. The axis of the tape was aligned with the axis of the load frame cross head. Each tape was loaded in a manner such that the initial length for each run was approximately 10 cm. Load was monitored using a Sensotec (Columbus, OH) load cell, capable of withstanding forces up to 445 N. All tests were run at room temperature (22°C).
For the load-to-failure test, the tape was preloaded to 5 N in tension. This value was chosen after previous trials with smaller preloads were not successful in breaking the elastic tape (Jaylastic) because of stroke length limitations of the system. Following this preload, the tape was loaded at a rate of 1 mm·s−1 until failure. Tensile load and elongation were recorded every 0.1 s.
Both modes of fatigue testing (load control and displacement control) (Fig. 2) began by preloading the tape to 20 N, and the tape was subsequently cycled between either a maximum load or a maximum displacement and this preload tension (or its corresponding displacement). The 20-N preload, approximately the load that would be expected from a typical ankle taping, is based on the force limit analysis performed by Andreasson and Edberg (3). In the load control fatigue testing, the maximum load was 90%, 70%, or 50% of the failure load obtained in the load-to-failure tests. In the displacement control fatigue testing, the maximum displacement corresponded to the same maximum loads as in the load control tests (90%, 70%, or 50% of the failure load) at the top of the first cycle, but instead of returning to the same load at the second cycle, the tape returned to the same displacement. Each fatigue test was cycled at 1 Hz, which is typically accepted to simulate the frequency of human movement. Each trial was terminated after meeting either of the following criteria: failure or 20 min of elapsed time (1200 cycles).
Twenty minutes of testing time was chosen because it has been widely reported that tape loses most of its force resistance capabilities during the first 20 min of exercise (5,10,11,13). If any of the trials were terminated before tape failure, the tape was then stretched at a rate of 1 mm·s−1 until failure. These postcycling load-to-failure results were then compared to the original failure tests in order to determine differences that may be analogous to tape load-elongation properties before and after 20 min of exercise.
Each tape was mounted in the loading frame and two images were obtained. The first image was obtained with the tape loaded to 5 N, and the second was obtained with the tape loaded to 50% of its failure load. Acquisition was performed using a CCD camera mounted on a dissecting microscope. Images were acquired at 20× magnification and the field of view was consistent for all images.
Load-to-failure tests were used for the determination of failure load, percent elongation at failure, and tape stiffness. Failure was defined by a dramatic decrease in load. The maximum load reached during each run was recorded as the failure load. Percent elongation as a function of time was calculated using %elongation(t) = (length(t) − length at 20 N preload)/(length at 20 N preload). Stiffness values were calculated by measuring the slope of the resulting load versus elongation curve using a linear least-squares fit. For tapes with nonlinear stiffnesses, separate stiffness values were calculated for each distinct region using the same method.
The results of the fatigue tests were analyzed and interpreted in several ways. Cycles to failure were recorded in the trials in which the tape failed before 1200 cycles. Failures in the load control tests were obvious, characterized by the first cycle that did not reach the nominal peak load. Failures in the displacement control tests were less obvious, and were characterized by the first discontinuity in the curve connecting the peaks of the output loads.
Additionally, the time-dependent behavior of the tape during cycling was characterized by fitting the output peaks during each run to a logarithmic function using a transformed least-squares regression model. R2 values were used to assess the goodness of the fits. This approach is similar to that used by Andreasson and Edberg to fit tape relaxation data (3). All runs were processed using every peak during cycling up to, but not including, the peak at which failure occurred.
In the load control testing (Fig. 2A), the peak displacements after each loading cycle were extracted, and fit to the function (%elongation (t))/(%elongation at failure) = (ALCF ln t + 1) × (%elongation at first cycle)/(%elongation at failure), in which t is the number of cycles (or time in seconds, since the tests were run at 1 Hz), and ALCF is the curve fitting constant. In this equation, ALCF is indicative of the logarithmic rate at which the tape stretches during cycling under load control, and is the principal variable to characterize the time-dependent behavior of the tapes in this testing mode.
In the displacement control testing (Fig. 2B), the peak load after each displacement cycle was extracted, and fit to the function F(t)/Ffailure = (ADCF ln t + 1) × Finitial/Ffailure, in which t is the number of cycles (or seconds), Finitial is the peak force during the initial cycle, Ffailure is the mean failure load of the tape from the load-to-failure experiments, and ADCF is the curve fitting constant. In these experiments, Finitial is prescribed in the experimental procedure to be a given percentage of failure load (50%, 70%, or 90%) and thus, the constant ADCF is sufficient to characterize the time-dependent characteristics of the tapes in this testing mode. In this case, ADCF is indicative of the logarithmic rate at which the load decreases during displacement controlled cycling. Note that under load control, the percent elongation increases, but under displacement control, the load decreases. Therefore, values of ALCF are typically positive and values of ADCF are typically negative. For those trials in which the tape did not fail during the cycling phase of the fatigue tests, and were subsequently loaded to failure, failure strengths, elongations at failure, and stiffnesses were recorded after cycling to compare with those measured in the earlier failure tests.
For the failure tests, a one-way analysis of variance (ANOVA) was used to determine significant differences between group mean failure strengths, elongations, and stiffness values (primary and secondary) obtained from the failure tests (P < 0.05). Bonferroni’s multiple comparison test (P < 0.05) was then used to compare between any pair of tapes.
For the fatigue tests, mean cycles to failure at 90% of failure load for each tape were tested for significant differences using a two-tailed t-test (P < 0.05). The logarithmic rate constants obtained from the curve fits (ALCF and ADCF) were compared in two ways: 1) The mean values obtained at each of the three cycling amplitudes were compared for each individual tape using a one-way ANOVA (P < 0.05) and Bonferroni’s multiple comparison test (P < 0.05); and 2) the values were compared between tapes at each cycling amplitude using the same method. Each parameter obtained from the postcycling failure tests were compared with the corresponding parameter from the precycling failure tests again using a two-tailed t-test (P < 0.05).
Load to failure.
Leukotape had the greatest mean load to failure, followed by Zonas, then Jaylastic (Fig. 3 and Table 1). Jaylastic had the greatest elongation at failure, followed by Leukotape, then Zonas (Fig. 3 and Table 1). The failure loads and percent elongation at failure values for the three tapes were all significantly different from one another (P < 0.01) and consistent with reported values (Table 1). Each tape had a different characteristic load-to-failure curve (Fig. 3). The curve for Zonas is fairly linear, indicating one uniform stiffness throughout loading. The Leukotape and Jaylastic curves have distinct regions of differing stiffness. Leukotape has two such regions: the initial stiffness (the stiffness of the tape before yielding) and the secondary stiffness (the stiffness of the tape subsequent to yielding and before failure of the tape). Jaylastic appears to have three such linear regions. The middle region, which indicates elongation without an associated increase in load, has a slope very near zero, and in some trials this value was even slightly negative. Thus, for comparative purposes, the “secondary” stiffness reported for Jaylastic is the stiffness value associated with the final linear region just before failure. Zonas does not have a secondary stiffness because its curve seems to be linear throughout loading. The initial stiffness values for all three tapes are significantly different from one another (P < 0.01). The secondary stiffness values of the Leukotape and Jaylastic are significantly different as well (P < 0.0001).
Fatigue testing: load control.
The values for ALCF were significantly different (P < 0.001) between all three tapes in the 90% load group, with Jaylastic having the highest ALCF value, and Zonas having the lowest (Table 2). In the 50% and 70% load groups, significant differences were found between Zonas and Leukotape (P < 0.001), although neither were significantly different from Jaylastic in the same load groups (Table 2).
Comparing between load groups for each tape, there were no significant differences between the values of ALCF at 50%, 70%, and 90% failure load for either Zonas or Jaylastic. However, the value at 70% failure load for Leukotape was significantly different from both its value at 90% (P < 0.01) and its value at 50% (P < 0.001) (Table 2).
When cycling at 90% failure load for the load control fatigue testing, each tape failed before reaching 1200 cycles. Jaylastic took significantly (P < 0.05) more cycles to fail than did the other two tapes.
Fatigue testing: displacement control.
The values for ADCF were significantly different (P < 0.001) between all three tapes in the 70% load group, with Jaylastic having the ADCF value of highest magnitude, and Zonas the lowest (Table 3). Similar trends between the three tapes were seen under the other loading conditions, but not to the same level of significance, although the magnitude of ADCF for Jaylastic was greater than that for both Leukotape and Zonas in every load group. This indicates that, for Jaylastic, the load decreases much more quickly during cycling between displacements than it does for Zonas or Leukotape (Fig. 4). There were no significant differences between ADCF values calculated for different load groups of the same tape.
When cycling at 90% failure load for the displacement control fatigue testing, not all subjects failed before reaching 1200 cycles, as was the case in the load control tests. Out of eight trials, two Zonas and five Leukotape trials failed before achieving 1200 cycles. None of the Jaylastic trials failed prematurely during any of the displacement control tests.
Postcycling failure tests.
In most cases, failure load values and percent elongation at failure do not significantly change after cycling compared to values obtained before cycling (P > 0.05) (Table 4). However, for every tape and every loading condition, the initial stiffness increased significantly (P < 0.01). Meanwhile, the secondary stiffness for both Leukotape and Jaylastic either did not change (all Jaylastic tests and post-50% load control Leukotape tests) or significantly decreased (three of four loading conditions for Leukotape, P < 0.01). The characteristic load-elongation curves also had important differences.
From the microscopic analysis (Fig. 5), a qualitative assessment can be performed. Zonas is a relatively homogeneous tape, with one type of fiber in the direction of loading, another type perpendicular to loading, and a uniform distribution of fibers throughout the area of the tape. Leukotape is also homogeneous in terms of number of fibers per unit area, but the orientation of the fibers is a bit different than that for Zonas. Leukotape has one type of fiber in the direction of loading, similar to Zonas, but in addition has a secondary fiber running at an angle of approximately 45 degrees. Compared with the other two tapes, Jaylastic is inhomogeneous, with two to three different types of fibers in the direction of loading and at least one type perpendicular. In addition, the fibers are not arranged as tightly as for the other two tapes—there are fewer fibers per unit area. Finally, although it cannot be seen in the photographs, Jaylastic is composed partly of elastic fibers, hence the classification of this tape as “elastic.”
Properties of athletic tape have typically been examined using performance studies (1,5,6,8,11,15–17,24). Gait analysis was used to examine kinematics of walking subjects in studies by Laughman et al. (15). Gait tests were run before taping, immediately after taping, and after 15 min of exercise on a course of running and jumping. The initial taping resulted in a 26.7% reduction in ROM. After exercise, the ROM had increased by 12.1% relative to the initial taping. This is bit shy of the 40% loss of initial support reported by Rarick et al. (19) after 10 min of exercise. Both of these studies, however, examined only the effects of one type of tape, without considering differential effects between tapes. Alt et al. (1) and Lohrer et al. (16) performed functional tests for two identified types of tape, and reported ROM and proprioceptive response before and after exercise.
Few recent studies directly address the mechanical properties of the tapes. In 1983, Andreasson and Edberg (3) investigated 10 “elastic” tapes and 15 “stiff” tapes, and reported breaking strength, breaking elongation, Young’s modulus, relaxation parameters, and fatigue properties. The breaking strengths and elongations reported for the stiff tapes compare favorably with our results for Zonas and Leukotape (Table 1), suggesting that stiff tapes may not have changed considerably since these results were obtained. The average breaking strength for Jaylastic, however, was not in the range of breaking strengths reported for “elastic” tapes, indicating that, on average, the “elastic” tapes analyzed by Andreasson and Edberg were stronger than Jaylastic. This study was of limited use, however, in that the brands of the individual tapes tested were not disclosed.
In our study, failure loads and percent elongation at failure values for three different types of tape were all significantly different (Fig. 3 and Table 1). The microstructure of the tapes can be used to interpret these differences (Fig. 5). Both Zonas and Leukotape have approximately the same number of fibers per width oriented in the direction of loading. Leukotape, however, has secondary fibers oriented at about 45 degrees to the loading direction, which also contribute a force resistance component in the direction of loading. This may explain the higher failure load for Leukotape than for Zonas. Jaylastic has considerably fewer fibers per width in the direction of loading than either Zonas or Leukotape, which is consistent with its significantly lower failure load. The fact that Jaylastic stretches considerably more than the other two tapes before failure is consistent with the fact that, unlike the other tapes, Jaylastic is composed partly of elastic fibers.
Differences in the characteristic load-elongation curves (Fig. 3) of the three tapes can also be interpreted by examining their microstructure. Zonas has just one type of fiber in the direction of loading, and therefore one stiffness. The secondary fibers of Leukotape may be the reason behind the fact that this tape yields, thereby creating two different linear stiffness regions. Perhaps one of these two fibers breaks first, leaving behind the other fiber, but creating a second, lower stiffness equal to that of the intact fiber. Jaylastic is inhomogeneous in composition, and contains as many as three or four different types of fibers. Comparing the image of Jaylastic at 50% of failure load to those of Zonas and Leukotape, it is evident that the structure of Jaylastic during loading does not deform in a repeatable, well-organized manner as do the other tapes. The fact that the force elongation curve of this tape has several stiffness regions is possibly attributable to both its variable composition and its inhomogeneous microstructural deformation characteristics.
A tape that performs well physiologically in the case of sudden inversion will provide external ligamentous support coinciding with the anterior talofibular ligament. This ligament fails at a mean force of 138.9 ± 23.5 N (4). Also, when skin deformation exceeds 10% in an inverted ankle, this is enough to induce pain (3). Thus, the external support of the tape should be resistant to loads greater than 139 N, whereas its percent elongation should be smaller than 10%. However, no direct comparison can be made between our results obtained from a single strip of tape, but we do expect that the differences between the mechanical properties of the tapes could be extrapolated to their physiological behavior.
The stiffness of the tape is an indication of how much ankle support the tape will give as it is stretched during physical activity. Clearly, the considerably smaller stiffness of Jaylastic indicates that it would not offer much support as it is stretched. Zonas and Leukotape, on the other hand, have higher stiffnesses, and would therefore possibly offer better support during physical activity. The yield region present in the Leukotape curve could be interpreted in two ways. First, it may be undesirable to have a lower stiffness at high loads, since more support is needed as load on the ankle reaches dangerous levels. On the other hand, more total energy can be absorbed by the Leukotape before it fails (compared with Zonas), on the basis of the area beneath its load-elongation curve. It is not clear which is more important in ultimately preventing injury.
Fatigue tests offer information supplemental to that of the failure tests. Arguments can be made for the physiological relevance of both load control and displacement control fatigue testing modes. In running, for instance, it seems that the ankle may cycle between specific displacements, with the tape providing less external support after more cycles—this would suggest displacement control. On the other hand, in sports that involve cutting, it is possible that the tape is subjected to similar loads during each cut, but after several cuts, the tape relaxes and allows more ankle motion—this would suggest load control.
Under load control at 90% failure load, the values for ALCF were significantly different for each tape, with Jaylastic having the largest ALCF value, and Zonas the lowest (Table 2). A similar trend was observed at both 50% and 70%, although statistical significance was masked by the large standard deviations in the Jaylastic parameter values. The ALCF parameter indicates the logarithmic rate at which the tape stretches during cycling. By examining the values of ALCF for each of the three tapes (Table 2), we can see that Zonas has the smallest ALCF value, and would therefore stretch least quickly during physical activity. A tape with a comparatively small ALCF value would stretch less over time and cycling, and would be most beneficial to an athlete who needs support over an extended period of time and activity.
Under displacement control, the ADCF values for each load group were significantly different between the three tapes (Table 3), with the ADCF value for Jaylastic having the highest magnitude, and Zonas the lowest, similar to the results of the load control tests. This is an indication of the fact that, for Jaylastic, the load decreases much more quickly over cycling time than it does for the other two tapes. By the end of 1200 cycles, the load in Jaylastic has decreased from 70% failure load to approximately 30% failure load (Fig. 4). The loads in Leukotape and Zonas, however, only decrease approximately 20% and 15%, respectively, after 1200 cycles. These results indicate that, similar to the load control tests, displacement controlled cycling does the most structural damage to Jaylastic, and the least amount of damage to Zonas. If the desired quality of a tape is to maintain structural support during a cyclic activity such as running, where the ankle may cycle between specific displacements, clearly, it would be beneficial if the load in the tape did not decrease over time. Thus, a small ADCF magnitude would be desirable for a cyclic activity such as running.
An additional benefit of the ADCF parameter is that, unlike ALCF, ADCF was successful in distinguishing between the tapes under each loading condition (Tables 2 and 3). These results suggest that ADCF is a material parameter independent of the cyclic loading conditions, whereas the value of ALCF depends on both the tape and the test amplitude. As such, ADCF could be a useful measure of time-dependent behavior to compare with other tapes, and may also be a stronger candidate for correlation with physiological performance data.
Comparisons of the parameters obtained from the failure tests before and after cycling can provide additional information regarding the loss of structural support that a tape undergoes as a result of cyclic activity (Table 4). These “postcycling” failure tests could be thought of as analogous to a sudden inversion after 20 min of rigorous exercise. On the basis of the results, we observed that cycling induces some plastic deformation, causing the postcycling curve to begin at a greater elongation than its corresponding precycling curve (Fig. 6). For a tape with a single stiffness (i.e., Zonas), the postcycling curve increases with a greater slope in order to achieve failure at the same load and elongation as the precycling curve. For a tape with two stiffness regions, the initial stiffness region of the postcycling curve intersects with the secondary stiffness region of the precycling curve, consistent with the observation that the transition between the two stiffness regions occurs at both a higher load and elongation after cycling. Energy considerations reveal that, because of the plastic deformation region, after cycling the tapes absorb less energy before failure, indicating that some energy was irreversibly absorbed during cycling. This is also demonstrated by comparing the relative areas under the load-elongation curves before and after cycling (Fig. 6).
Despite the fact that the findings of this research are unprecedented, there are certain limitations of the study that should be addressed. For instance, the tape in this study was loaded as individual pieces of tape in pure tension. In a typical ankle taping, however, the tape is wound many times around the ankle, resulting in a layering effect, with the layers running in different directions. Andreasson and Edberg showed that a layer of three strips of tape in pure tension has a higher failure load, less elongation, and higher stiffness than a single strip of tape (3). Thus, even if tape applied to the ankle was loaded purely in tension, the lamination effect would still create an obstacle in directly comparing the mechanical findings to the desired characteristics for athletic activity. Another limitation is that changes in tape width during elongation were not considered. Since a taped ankle has many layers of tape that are loaded in many directions, the properties of the tape in all directions contribute to the overall stability of the taped ankle. Another factor that may be important, but is not considered, is the effect of tape adhesion. Differences in peel adhesion for six different tapes have been recently reported (22). Finally, all of the tests in this study were run at room temperature and ambient humidity. In a truly physiological environment, the tape would be introduced to factors such as body heat and perspiration. It is quite possible that increased body heat and perspiration during athletic activity may be added factors leading to the loss of structural support in the tape, and some tapes may be more sensitive to these factors than others.
Despite these limitations, the mechanical tests performed in this study were successful in distinguishing between time-dependent parameters of three existing tapes. The ability of athletic tape to maintain its strength and function under stress over time is a crucial property that is lacking in current athletic tape designs. The results of these tests can now be used as benchmarks by which future mechanical tests of athletic tapes can be compared. These benchmarks, along with continued research toward the identification of the injury prevention mechanism of tape, should lead to the development of higher performance tapes. Ultimately, these tapes should reduce the incidence of ankle injury in athletics.
We thank Dale Rudd, Head Trainer, Stanford Athletic Department, and Todd Toriscelli, Head Trainer, Tampa Bay Buccaneers, for their invaluable expert advice in taping issues pertaining to elite athletes. We thank Micro Bio-Medics, Inc., for help in randomizing the Zonas and Leukotape, and to Jaybird & Mais, Inc., for donating the Jaylastic tape. In addition, we gratefully acknowledge the help of Ajit Chaudhari, Ann Caslin, Kevin Rennert, Nick Wharton, and our ME282 classmates during this project. We also thank all of the NFL, Pac-10, MLB, and NHL athletic trainers who so graciously took the time to fill out our survey. Finally, we thank the Palo Alto Veterans Affairs Rehabilitation Research and Development Center for funding this project.
Address for correspondence: Thomas P. Andriacci, Ph.D., Department of Mechanical Engineering, Durand 227, Stanford University, Stanford, CA 94305-4038; E-mail: email@example.com.