A new method for the determination of the characteristic shape of an isokinetic quadriceps femoris muscle torque curve.

It has been suggested that visual analysis of isokinetic quadriceps femoris muscle torque curve (TC) shapes may have potential use in the diagnosis and prognosis of knee pathologies. The primary purpose of this pilot study was to develop a method for analyzing the shape of an isokinetic TC. Our method norrealizes and averages the TC, and then uses curvilinear analysis of the TC shape to aid in diagnosis and prognosis. For demonstration, the method was applied to isokinetic quadriceps femotis muscle TC data collected using a fIDO(R) digital dynamometer from 25 healthy volunteer subjects and retrospectively acquired from the uninvolved limbs of 37 patients with unilateral knee pathologies. The preliminary results revealed (1) that a common quadricepsfemoris muscle TC shape existed for the volunteer group at 60 degrees and 18a'/s; (2) that the uninvolved limbs of the patient group exhibited the same shape at 60*/s, but not at 180*/s; and (3) that the quadncepsfemoris muscle TC shape demonstrated no significant differences with respect to limb dominance or gender for either group. Further testing of this quantitative method on a larger sample is needed to determine its usefulness in the analysis and implications of TC shape concerning pathology and diagnosis. [Afzali L, Kuwabara F, Zachazewski J,, et al. A new method for the determination of the characteristic shape of an isokinetic quadriceps femoris muscle torque curve. Phys Ther. 1992; 72:585-595.]

L Afzali, PT, ATC, is Staff Physical Therapist, Department of Physical Therapy, University of California at Los Angeles Medical Center, A2-226 CHS, 10833 LeConte Ave, Los Angeles, CA 90024-1704 (USA). Address all correspondence to Ms Afzali.

F Kuwabara, PT, is Staff Physical Therapist, Harbor-University of California at Los Angeles Medical Center, 1000 W Carson St, Torrance, CA 90509.

J Zachazewski, PT, SCS, ATC, is Coordinator, Sports Physical Therapy, Massachusetts General Hospital, and Assistant Professor, Post Professional Program in Physical Therapy, MGH Institute of Health Professions, 60 Staniford St, Boston, MA 02114. At the time of this research, he was Clinical Specialist, Sports Physical Therapy, Department of Physical Therapy, University of California, Los Angeles.

P Browne, PhD, PT, is Assistant Director, School of Physical Therapy, Childrens Hospital of Los Angeles/Chapman University, 4650 Sunset Blvd, Los Angeles, CA 90027.

B Robinson, PT, is Assistant Professor, School of Physical Therapy, Childrens Hospital of Los Angeles/Chapman University.

Ms Afzali and Ms Kuwabara were students in the School of Physical Therapy, Childrens Hospital of Los Angeles/Chapman University, when this study was completed in partial fulfillment of the requirements for their Master of Physical Therapy degrees.

This study was approved by the University of California, Los Angeles, Human Subject Protection Committee.

This article was submitted January 3, 1991, and was accepted March 27, 1992.

Isokinetic devices may be used to obtain measurements of torque, work, and power. 1,2 The isokinetic torque curve (TC) is created by plotting torque measurements in relation to either range of motion (ROM) or time. The shape of the quadriceps femoris muscle isokinetic TC has been reported to have various characteristics in different pathological conditions and may have potential diagnostic value.3-13 Some authors contend that the shapes of isokinetic TCs can be used to assist in identifying knee pathologies such as chondromalacia,5,7-9,12 anterior cruciate ligament deficiencies,5,10,13 and plica.3,5 In addition, it has been argued that muscle force production,5,8,11,12 pain,5,7,9,14 instability,10,13 and degree of effort15 can be evaluated by subjective analysis of the shape of the TC.

It has been suggested that by visually analyzing the shape of isokinetic TCs, one can determine the status of the involved limb following surgery12 or the progress of a patient during physical therapy.5,9 When isokinetic TCs are used to evaluate a patient's progress, the TC of the uninvolved limb often serves as the "normal" curve for the patient. Hazard et al16 and Sherman et al17 contend that the patient's rehabilitation may be considered complete when the TC of the involved knee approximates the TC of the uninvolved knee. This claim, however, is unsubstantiated[1,18 and disregards the following factors:

1. Contralateral comparison overlooks the possibilities of abnormalities in the uninvolved knee.

2. If there is bilateral involvement, there is no standardized normal TC shape for comparison in establishing a rehabilitation goal.

3. A specific normal TC in absolute torque measurements for one individual cannot be used as a guide for comparison with those of other individuals.

These interpretations of the shape of a quadriceps femoris muscle TC were based on the assumption of the existence of a normal quadriceps femoris muscle TC. No objective definition of a normal TC, however, has been documented. Only subjective interpretations of the shape of a TC have been reported.

The first purpose of this pilot study was to develop a quantitative method for analyzing the shape of an isokinetic TC. This method was used to generate preliminary results for the shapes of quadriceps femoris muscle TCs of healthy volunteers and patients who were tested on the LIDO(R) digital isokinetic dynamometer.* The volunteer data were obtained by the authors, whereas the patient data were retrieved from medical records. The second purpose was to demonstrate how to make quantitative comparisons of TC shapes for different test speeds and subject variables (ie, gender, limb dominance, healthy volunteers, uninvolved limbs of patients).

Method

Subjects

Isokinetic quadriceps femoris muscle TCs were analyzed from a group of 25 healthy volunteer subjects and a group of 37 patients. Both groups were tested on the LIDO(R) digital isokinetic dynamometer at the University of California at Los Angeles Outpatient Rehabilitation Center. The volunteers were physical therapy students and acquaintances who engaged in varying levels of physical activity. Volunteers were chosen based on a screening questionnaire to determine that they had no history of pathology of either lower extremity or of cardiac or pulmonary problems and that they were not participating in professional or semiprofessional sports. This group consisted of 14 men, aged 20 to 34 years (X=26, SD=4), and 11 women, aged 25 to 28 years (X=26, SD= 1) (Tab. 1). Each volunteer provided informed consent.

All patients had been tested from March through September 1987. Patient data were acquired retrospectively from physical therapy records from the University of California at Los Angeles Outpatient Rehabilitation Center. The criteria used for inclusion in this study were (1) physiciandiagnosed unilateral knee pathology with no history of injury of the uninvolved lower extremity and (2) available data from five cycles of concentric contractions of the quadriceps femoris and hamstring muscles at 60*/s and 10 continuous cycles at 180*/s. Records of 150 patients were screened, and all 37 patients who met the criteria of this study were included. This group consisted of 24 men, aged 17 to 32 years (X=25, SD=5), and 13 women, aged 19 to 40 years (X=26, SD=I) (Tab. 2). The dominant limbs of 13 men and 5 women and the nondominant limbs of 11 men and 8 women were uninvolved.

Procedure

All volunteers performed a 10-minute warm-up of cycling on a bicycle ergometer at a work load of 600 kpm followed by self-stretching of the hamstring and quadriceps femoris muscles. Each muscle group was stretched five times, and each stretch was held for 10 seconds. This warm-up session was used in an attempt to simulate the standard testing protocol of the patients at the University of California at Los Angeles Outpatient Rehabilitation Center. Both lower extremities were tested using the LIDO(R) digital isokinetic dynamometer. According to the manufacturer, the LIDO(R) is a selfcalibrating system with reported values for test-retest reliability of .82 to .93 for 20 healthy volunteers[19] .85 for 21 healthy subjects (10 men, 11 women) ranging in age from 22 to 53 years,20 and .99 for 25 healthy women aged 65 to 86 years21 for measurements of peak torque. This factor represents unknown potential error in the volunteer data.

Limb dominance was defined by each subject's handedness to simulate the testing procedures used on the patient group. Each volunteer was seated in the LIDO(R) chair with 80 degrees of hip flexion and the back of the calf touching the front of the seat. With the knee in 90 degrees of flexion, the lateral femoral epicondyle was used as the anatomical axis. This anatomical axis was aligned with the axis of rotation of the LIDO(R) dynamometer. Each volunteer was stabilized at the trunk and thigh utilizing Vekro(R)* straps and a thigh stabilization bar. The stabilization bar was adjusted to the subject's comfort. The test leg was strapped to the LIDO(R) input shaft by a sliding Velcro(R) ankle cuff placed on the distal tibia approximately 2.5 cm (1 in) superior to the lateral malleolus. Each volunteer subject was instructed to grasp the handgrips with both hands. To familiarize the subjects with isokinetic exercise and to further warm up the knee musculature, each subject performed three contractions of submaximal effort followed by three maximal contractions of the quadriceps femoris and hamstring muscles prior to actual testing at each test velocity. A l-minute rest period was provided between warm-up and actual testing. Standardized instructions were given to all volunteer subjects. Data were continuously acquired within the range of 90 to 100 degrees of knee flexion and maximum extension. Subjects were tested at velocities of 60* and 180*/s for comparison with the retrospective patient data. Subjects performed 5 continuous cycles of concentric contractions of the quadriceps femoris and hamstring muscles at 60*/s and 10 continuous cycles at 180*/s. A l-minute rest period was given after each test speed to simulate the test procedures used for the patient group. Dominant limbs were tested first in 50% of the subjects.

Patient data were retrieved from records that had been obtained in the clinical setting by 10 different physical therapists. Patient test velocities of 60* and 180*/s had been arbitrarly chosen by therapists in the clinical facility. A standard testing protocol was established at the facility, but we have no way of ensuring that the protocol was strictly followed by all of the therapists. This factor represents a potential source of error. One known difference in the testing protocol was that the patients' uninvolved lower extremity was always tested prior to the involved limb, regardless of limb dominance. For the purposes of this study, the TCs of the patients' involved limb were eliminated from the data analysis.

Data Analysis

Preliminary data reduction. The shape of the "normal" quadriceps femoris muscle TC was determined by analyzing the data collected experimentally from both limbs of the 25 volunteers. To make comparisons among different individuals, each quadriceps femoris muscle TC was normalized by calculating the percentage of peak torque produced throughout the sampled ROM. The average torque versus the ROM was then calculated from the normalized average TCs for each volunteer at uniform increments along the ROM. The individual normalized average torque curve (INATC) for each volunteer was computed as follows:

For TCs measured at 60*/s:

1. Repetitions two through four were sampled at 1-degree increments from 85 degrees of knee flexion to 10 degrees of knee flexion. Twopoint linear interpolation was used when a data point was not available at a sampled ROM.

2. Repetitions two through four were normalized and then averaged to the average peak torque.

For TCs measured at 180*/s:

1. Repetitions four through seven were sampled at 5-degree increments from 85 degrees of knee flexion to 10 degrees of knee flexion. Two-point linear interpolation was used when a data point was not available at a sampled ROM.

2. Repetitions four through seven were normalized and then averaged to the average peak torque.

The normalized average torques versus the ROM form an estimate of the normal quadriceps femoris muscle TC.

Point-by-point averaging. At 60* and 180*/s, the mean torque versus the ROM was computed by averaging the INATCs at 5-degree increments.

The standard deviation was calculated for each mean torque.

Curvilinear analysis. In an attempt to be more statistically rigorous, we applied curvilinear analysis22,25 to the INATCs. This technique is different from point-by-point analysis. Point-bypoint analysis treats a TC as a collection of uncorrelated measurements, whereas curvilinear analysis treats a TC as a collection of correlated measurements.

The curvilinear analysis procedure is outlined in the following steps:

Step 1. For the selected test speed and subject variables (ie, gender, limb dominance, volunteers, patients), we computed the INATCs as described in the "Preliminary Data Reduction" section.

Step 2. We selected a polynomial order (n) and then computed the bestfitting nth-order polynomial through all of the INATCs of step 1 using the method of least mean squares. We always started with order n= 1 and sequentially progressed to n=5 (Fig. 1).

Step 3. We computed the total sumsquared error between the polynomials of step 2 and all of the INATCs of step 1.

Step 4. We tested for the best-fitting polynomial among the different orders, n = 1 to n= 5, fitted to the INATCs. We then applied the F test to check for a significant reduction in the sum-squared error when order is increased from n = 1 to n = 2. If the reduction was not significant, the lower-ordered polynomial was chosen as the best fit. If a significant reduction in error was found, we repeated the F test for the next two polynomials of higher order (ie, n=2 and n=3).

Step 5. We determined whether the best-fitting polynomial found in step 4 was significant for all of the INATCs of step 1 as follows:

1. We computed the mean and the variance of the sum-squared error between all of the INATCs and the best-fitting polynomial of step 4.

2. We randomly divided the INATCs into three subgroups and computed the mean and the variance of the sum-squared error for each subgroup.

3. We used an analysis of variance (ANOVA) to test for significant differences in the mean and the variance of the sum-squared error between each subgroup and all of the INATCs. If no differences were found for any subgroup, then the polynomial was considered to be valid.

4. We performed items 1 through 3 at least 10 times.

RESULTS

Point-by-Point Analysis

The mean torques with standard deviations versus ROM for the volunteer group at test velocities of 60* and 180*/s are illustrated in Figures 2 and 3, respectively.

The ANOVA results revealed that the best-fitting polynomial for the volunteer group at the test velocity of 60*/s was the third-order polynomial (Fig. 4). This polynomial has the functional form:

(1) F(x) = 74.53 + 2.390x - 0.07166 + 0.000418x

where F represents the normalized average quadriceps femoris muscle torque and x represents the ROM values. The ANOVA results revealed that, at 180*/s, the best-fitting polynomial of the volunteer group was the secondorder polynomial (Fig. 5). This polynomial has the functional form:

(2) F(x) = 71.69 + 1.659x + 0.02766x

At each test velocity, the mean torque versus the ROM found with the pointby-point analysis technique was nearly identical to the best-fitting polynomial.

The ANOVA results for differences among the volunteer group are presented in Table 3. At 60*/s, no significant differences were demonstrated for 9 of the 10 random groupings (P|.05). At 180*/s, no significant differences were demonstrated for all 10 random groupings (P|.05). From these results, we can infer that the best-fitting polynomials were significant for the volunteers at both velocities.

A comparison was made between the shape of the quadriceps femoris muscle TCs of both limbs of the subjects in the volunteer group and the shape of the uninvolved limbs of the subjects of the patient group. For the test velocity of 60*/s, the TCs of both groups were referenced to the thirdorder polynomial in equation 1. At this velocity, no significant differences with respect to shape (P<.05) were demonstrated between these two groups (Tab. 4). Based on this result, the TCs of the two groups were combined to test for differences with respect to limb dominance and gender for 60*/s (Tab. 5). No significant differences (P< .05) attributable to limb dominance or gender were found at this velocity.

For the test velocity of 180*/s, the TCs of both groups were referenced to the second-order polynomial in equation 2. At this test velocity, there were significant differences with respect to shape (P< .05) between these groups Crab. 4). Thus, for 180*/s, only the TCs of both limbs of subjects in the volunteer group were tested for differences with respect to limb dominance and gender. No significant differences (P< .05) attributable to limb dominance or gender were found at this velocity Crab. 6).

Discussion

A "normal" isokinetic quadriceps femoris muscle TC has been described as "an inverted U-shaped curve,"24 and several examples at various velocities have been presented in the literature.4-7,11,14 These examples, however, were not derived quantitatively, but subjectively. Also, direct comparisons cannot be made between the shape of an individual's TC and these "normal" TCs because they are all based on absolute values of torque. In our method, the normalization of the dam allows for quantitative comparison of shape among all TCs.

Other investigators,7-9,11,13,14 have based findings on subjective observation of absolute TCs. This method is highly susceptible to error. Unusual characteristics seen on a graphed TC have often been described using terms such as "dips,"5 "plateaus,"5,9,13 "irregularities,"5,7,8,11 "flattened,"5,11 "double-humped,"5 and "breaks or unevenness."6,|14 These characteristics have not been operationally defined and are based on visual analysis of several individual TCs that had not been averaged or normalized. Rothstein and colleagues[1] have warned clinicians about assuming that visual interpretation of TC shapes is an objective measurement because no published data exist to support such practice. The advantage of our method is the ability to describe a TC with a mathematical model. With the model, a clinician can regenerate the TC and use it to conduct the same quantitative analysis with his or her own patient data.

Our method of analysis involved averaging over several cycles of the quadriceps femoris muscle TC. This method reduces the small, sporadic fluctuations, spikes, and oscillation that some authors attribute to machine artifact,[1] pain,5,7,9,14 instability,[10,13] and various knee pathologies.[5-9,11,13,15,14] The extent to which our method affects these small, sporadic fluctuations needs to be assessed on a group of torque curves that exhibit described visual abnormalities such as "dips," "plateaus," "double humps," and so forth. The effects of variables such as fatigue, motivation, and learning that may exist in individual repetitions also may not be seen in the INATC.

The normal quadriceps femoris muscle TCs derived by point-by-point averaging and by curvilinear analysis were nearly identical for each test velocity. This finding may be due to the preliminary data reduction (ie, normalizing and averaging) that was applied to the individual TC repetitions. Normalizing the individual TC repetitions is the key element for making objective comparisons of TC shape. Averaging the normalized TC repetitions allows the data to be consolidated while preserving the underlying shape of the TC. Even though the two analytical techniques produced nearly identical results, they must both be applied to a larger sample of data for a more thorough comparison.

This study utilized two types of data. The volunteer group data were obtained in an experimental setting, whereas the patient group data were obtained in a clinical setting. Retrospective patient data were used because it represented actual clinical data collected with a specific clinical protocol at a single facility. Volunteer test speeds of 60* and 180*/s were chosen to match the retrospective patient data. The clinical facility arbitrarily chose these test speeds after discussions with a number of other facilities. This quantitative method can be used on any digitized retrospective data for research into the shape of isokinetic TCs. It must be emphasized that the retrospective data should have been obtained with a documented protocol and should demonstrate test-retest reliability. The data also need to include specific subject characteristics, such as age, gender, athletic ability, and so forth, to categorize the isokinetic TCs.

The uninvolved limbs of the subjects in the patient group demonstrated the same normal quadriceps femoris muscle TC shape as did the uninvolved limbs of the subjects in the volunteer group at 60*/s, but not at 180*/s. This is an interesting result that may have some implications for the practice of using the uninvolved limb as a standard in determining rehabilitation goals for such patients. The fact that the two speeds demonstrated different findings indicates the need for evaluating other speeds. We did not assess the reliability of the measurements obtained with our test procedures, which may be the reason for these results. Thus, we cannot draw any general conclusions at this time, because the analysis method requires further testing, our data sample was small, and our data-collection method was potentially flawed by the lack of reliability testing. With respect to limb dominance and gender, there were no significant differences in quadriceps femoris muscle TC shape at 60* and 180*/s. For the reasons stated, however, therapists must be cautious in interpreting these results. Our findings and their implications for clinical practice indicate the need for additional studies.

Summary

This study demonstrated a quantitative method for determining the shape of an isokinetic TC. We applied this method to a volunteer group and a retrospective patient group at 60* and 180*/s on the LIDO(R) digital isokinetic dynamometer. Preliminary results for normal quadriceps femoris muscle TCs were found, but a larger data sample must be used before general conclusions can be drawn. This method will allow researchers and clinicians to perform further studies to determine whether the shape of a TC can provide valuable information about diagnosis and rehabilitation. By applying this method of statistical analysis, clinicians will be able to rely on objective data rather than subjective visual interpretations.

Acknowledgments

We wish to thank Tory Afzali for his invaluable computer assistance; the University of California at Los Angeles Outpatient Rehabilitation Center for the use of their facility and records; Loredan Biomedical Inc for graciously donating their LIDO(R) digital isokinetic dynamometer; and Jerry lank, PhD, for his consultation on statistical analysis.

References

1 Rothstein JM, Lamb RL, Mayhew TP. Clinical uses of isokinetic measurements. Phys Ther. 1987;67: 1840-1844.

2 Thistle H, Hislop HJ, Moffroid MT, Lowman EW. Isokinetic contraction: a new concept of resistive exercise. Arch Phys Med Rebabil. 1967; 48:279-282.

3 Blackburn T, Elland W, Bandy W. An introduction to the plica. Journal of Onhopaedic and Sports Physical Therapy. 1982;3:171-177.

4 Coplin T. Isokinetic exercise: clinical usage. Journal of the National Athletic Training Association. 1971;6:110-114.

5 Davies G. A Compendium of Isokinetics in Clinical Usage. La Crosse, Wis; S & S Publishers; 1984.

6 Grace T, Sweetser E, Nelson M, Skipper BJ. Isokinetic muscle imbalance and knee joint injuries. J Bone Joint Sung [Am]. 1984;66:734-740.

7 Hoke B, Howell D, Stack M. The relationship between isokinetic testing and dynamic patello-femoral compression. Journal of Ortbopaedic and Sports Physical Therapy. 1983;4: 150-153.

8 Hunter S, Cain T, Henry C. Preseason isokinetic knee evaluation in professional football athletes. Athletic Training. 1979;14:205-206.

9 Lennington K, Yanchuleff T. The use of isokinetics in the treatment of chondromalacia patellae: a case report. Journal of Orthopaedic and Sports Physical Therapy. 1983;4:176-178.

10 Malone T. Clinical use of the Johnson AntiShear device: how and why to use it. Journal of Orthopaedic and Sports Physical Therapy. 1986;7:304309.

11 Mira A, Carlisle K, Greet R. A critical analysis of quadriceps function after femoral shaft fracture in adults. J Bone Joint Sung [Am]. 1980;62:61--66.

12 Nordgren B, Nordesjo L, Rauschning W. Isokinetic knee extension strength and pain before and after advancement osteotomy of the tibial tuberosity. Arch Orthop Trauma Sung. 1983;102:95-101.

13 Timm K. Validation of the Johnson AntiShear accessory as an accurate and effective clinical isokinetic instrument. Journal of Ortbopaedic and Sports Physical Therapy. 1986;7: 298-303.

14 Elliot J. Assessing muscle strength isokinetically. JAMA. 1978;240:2408-2410. 15 Grace TG. Muscle imbalance and extremity injury: a perplexing relationship. Sports Med. 1985;2:7742.

16 Hazard R, Reid S, Fenwick J, Reeves V. Isokinetic trunk and lifting strength measurement s: variability as an indicator of effort. Spine. 1988;13:54-57.

17 Sherman W, Pearson D, Plyley M, et al. Isokinetic rehabilitation after surgery: a review of factors which are important for developing physiotherapeutic techniques after knee surgery. AmJ Sports Med. 1982;10:155-161.

18 Soderberg GL. Below-knee amputee knee extension force-time and moment characteristics. Phys Ther. 1978;58:966-971.

19 Aitkens S. Knee Flexton/Extension Reliability Study on the LIDO(R) Isokinetic Rehabilitation System. Davis, Calif. Loredan Biomedical Inc; 1987.

20 Francis K, Hoobler T. Comparison of peak torque values of the knee flexor and extensor muscle groups using the Cybex(R) 11 and LIDO@ 2.0 isokinetic dynamometers. Journal of Orthopaedic and Sports Physical Therapy. 1987;8: 480-483.

21 Cress M, Johnson J, Agre J. Isokinetic strength testing in older women: a comparison of two systems. Journal of Orthopaedic and Sports Physical Therapy. 1991;13:199-202.

22 Batson H. An Introduction to Statistics in the Medical Sciences. Minneapolis, Minn: Burgess Publication Co; 1956.

23 Snedecor G. Statistical Methods Applied to Experiments in Agriculture and Biology. 4th ed. Ames, Iowa: The Collegiate Press Inc; 1947.

24 Knapik JJ, Wright JE, Mawdsley RH, Braun J. Isometric, isotonic, and isokinetic torque variations in four muscle groups through a range of joint motion. Phys Ther. 1983;63:938-947.

The notion that the shape of a patient's isokinetic torque curve could be used to infer pathological conditions has been popular for many years. Numerous studies describe relationships between torque curve abnormalities such as "plateaus,"[1] "irregularities,''2 and "depressions"[3] and various pathologies usually involving the knee joint or musculature. Afzali et al correctly point out that these relationships were based on subjective visual observations and that there are no credible data supporting these claims. They cite an earlier review4 in which Rothstein et al caution clinicians that evidence is not yet available to support the use of this procedure in clinical decision making.

Afzali et al have developed a new quantitative method for analyzing the shape of isokinetic torque curves. They have described a procedure using normalization and mathematical modeling to construct a "normal" torque curve that allows for intersubject comparison. The authors have apparently developed a method for analyzing torque curves that eliminates some of the problems associated with visual inspection. I felt there were a number of problems and omissions in their methods, however, that reflect on their results and the replicability of their procedures.

The major point of contention that I have with the study by Afzali et al is that they did not test the reliability of their measurements. They are forthright about this error, but I do not believe that such an admission mitigates the responsibility of the investigators to perform such tests. I also feel that this omission is especially problematic in this case because Afzali et al are describing a new procedure. It is at this pilot stage that the investigators should discover potential threats to reliability and make changes in their procedures that would ensure the consistency of their measurements. Because the authors did not perform such tests, I believe their data may have been errorridden, which prevents the formation of sound conclusions. This is unfortunate because the authors have obviously put much effort into their procedure for quantifying torque curves.

The authors do not adequately justify the use of the retrospective patient sample. There is no evidence that the 10 different physical therapists who performed the patient testing 5 years ago adhered to any protocol, or that intratester or intertester reliability was adequate. The authors did provide a theoretical argument for analyzing the torque curves of the uninvolved limbs of patients. They should have developed a reliable procedure and prospectively tested their own patients.

The three references used by the authors to justify reliability are inappropriate. The first is from promotional literature,5 the second appears to have been conducted using a different machine,6 and the third was performed on an elderly female population.7

I was also surprised that the authors did not discuss the issue of gravity correction. Correction for the effects of gravity would seem to be particularly imporunt in this study because the authors normalized all of their torque data points to the peak torque for each curve. They therefore constructed a new curve for each subject composed entirely of percentages of the peak torque. In order to perform these calculations, their data would need to be ratio scaled. Ratio-scaled data can only be obtained if the authors corrected theft quadriceps femoris muscle torque curves for the effect of gravity acting on the limb segment. According to Winter et al,8 the failure to correct for the effects of gravity can lead to large errors in the calculation of torque values. This error is amplified at high isokinetic speeds, with concomitant lower torque values.9 This fact may partially explain their finding of a significant difference between their subject groups at the high isokinetic speed (180*/s). Even at the lower speed, however, it is possible that the authors normalized their torque data points, which were missing torque because of overcoming the weight of the limb, to an erroneously low peak torque. Using peak torque values not corrected for the effects of gravity might have resulted in an entirely different shape to the newly constructed "normalized" torque curve. The authors should have discussed the issue of gravity correction in their procedure.

The authors state that they "continuously acquired" data and that they "sampled at 1-degree [and 5-degree] increments." They do not, however, state how they sampled their data. Did they use the LIDO(R) data-acquisition and analysis software? If so, what was the sampling frequency of the system? What settings did they use? It would appear that the authors used an external recording system and perhaps their own data-analysis software in their procedures. Afzali et al did not provide any detafl about their recording or analysis system. Because the authors did not supply us with information about their instrumentation such as software name and version, sampling frequency, bench test data, and so forth, it would be impossible to replicate their study. This information is also necessary to judge the potential clinical usefulness of their procedure. Would this instrumentation be readily available to the clinic Jan?

In summary, Afzali et al have presented a potentially useful procedure for transforming isokinetic torque curves into quantitative measurements. I believe, however, that because the authors did not examine reliability and did not appear to correct for the effects of gravity, any conclusions drawn from their results would be premature. In addition, I believe the authors incompletely described their instrumentation, which affects the replicability of their study. They appropriately recognized and reported the potential threats to reliability in their study and cautioned the readers as to the meaningfulness and generalizability of their results. I would encourage the authors to test the reliability of their measurements and to consider some of the methodological issues that I have outlined. The idea that the shape of isokinetic torque curves may have diagnostic value remains an interesting, but unproven, concept.

Thomas P Mayhew, PbD, PT Assistant Professor Department of Physical Therapy School of Allied Health Professions Medical College of Virginia Virginia Commonwealth University PO Box 224, MCV Station Richmond, VA 23298-0224

References

1 Lennington KR, Yanchuloff Tr. The use of isokinetics in the treatment of chondromalacia patellae: a case report. Journal of Orthopaedic and Sports Physical Therapy. 1983;4:176-178.

2 Hoke B, Howell D, Stack M. The relationship between isokinetic testing and dynamic patellofemoral compression. Journal of Orthopaedic and Sports Physical Therapy. 1983;4: 150-153.

3 Mira AJ, Carlisle KM, Greer RB. A critical analysis of quadriceps function after femoral shaft fracture in adults. J Bone Joint Surg [Am]. 1980;62:6147.

4 Rothstein JM, Lamb RL, Mayhew TP. Clinical uses of isokinetic measurements. Phys Ther. 1987;67: 1840-1844.

5 Aitkens S. Knee Flexion/Extension Reliability Study on the LIDO(R) Isokinetic Rehabilitation System. Davis, Calif: Loredan Biomedical Inc; 1987.

6 Francis K, Hoobler T. Comparison of peak torque values of the knee flexor and extensor muscle groups using the Cybex(R) II and LIDO(R) 2.0 isokinetic dynamometers. Journal of Orthopaedic and Sports Physical Therapy. 1987;8: 480-483.

7 Cress M, Johnson J, Agre J. Isokinetic strength testing in older women: a comparison of two systems. Journal of Orthopaedic and Sports Physical Therapy. 1991;13:199-202.

8 Winter DA, Wells RP, Orr GW. Errors in the use of isokinetic dynamometers. EurJ Appl PhysioL 1981;46:397-408.

9 Fillyaw M, Bevins T, Fernandez L. Importance of correcting isokinetic peak torque for the effect of gravity when calculating knee flexor to extensor muscle ratios. Phys Ther. 1986;66:23-29.

Author Response

We would like to thank Dr Mayhew for reviewing the report of our pilot study and providing his insights. The issues that Dr Mayhew stated are similar to most of our concerns, which we mentioned in our study. We acknowledge that general conclusions about our preliminary data cannot be made because of the lack of reliability testing and the small data sample.

We feel, however, that the importance of our pilot study lies in the development of a mathematical model for average normalized isokinetic torque curves. We do not profess our method to be the best method, but we wanted to make an effort to eliminate the subjective nature of analyzing torque curve shape. Others have only assumed the existence of a normal quadriceps femoris muscle torque curve shape; we sought to develop a method of objectively defining the shape.

With respect to software, there were no software packages available that were appropriate for our data reduction and data analysis. We therefore had to work with a software programmer to implement the specific processing steps described in our "Method" section. All of the analysis software was written in FORTRAN and executed on a MicroVax II computer.* Data were recorded using Loredan's LIDO(R) software* on an IBM PC* and were later downloaded onto the MicroVax II computer. We would also like to point out that the HDO(R) digital isokinetic dynamometer* does correct for the effects of gravity. The procedure was used as part of the standard protocol for torque curve measurement as suggested by Loredan.

Our pilot study represents an attempt to develop a quantitative method for the analysis of isokinetic torque curve shape. Our goal was to develop a systematic and reproducible procedure to replace visual analysis, which relies on subjective descriptions of curve shape. We were aware of the flaws of our datacollection procedures and the potential for related criticism prior to submitting this article. We felt, however, that our method of analysis is a significant contribution to torque curve shape analysis. Although the results of our analysis of the normal quadriceps femoris muscle torque curve may be in question, the use of the data serves as a demonstration of the application of our analysis techniques. We feel it is important to allow the research and clinical communities a chance to debate, discuss, and scrutinize the potential use of this methodology for analyzing isokinetic torque curves.

Leslie Afzali, PT, ATC

Fumi Kuwabara, PT

James Zachazewski, PT, SCS, ATC

Phyllis Browne, PhD, PT

Bonnie Robinson, PT