Isometric, Isotonic, and Isokinetic Torque Variations in Four Muscle Groups Through a Range of Joint Motion

JOSEPH J. KNAPIK, JAMES E. WRIGHT, ROBERTA H. MAWDSLEY, and JOANNE BRAUN

The purpose of this investigation was to describe and examine variations in maximal torque produced by knee extension, knee flexion, elbow extension, and elbow flexion through a range of joint motion. Subjects were young, healthy men (n = 16) and women (n = 15). Torque was measured isometrically and isokinet-ically using a modified Cybex® apparatus. Isotonic torque was calculated from a one-repetition maximum using a modified N-K® device. Joint angles were moni­tored with an electrogoniometer. Torque-joint angle curves were constructed for both men and women for each muscle group. Isometric torque was highest, followed by isotonic and isokinetic torque. Torque declined with increasing isokinetic velocity. The angle of peak torque was found to be highly variable in individual subjects. Variations in torque curves were explained in terms of mechanical characteristics of the musculoskeletal system. Muscle group capa­bility was generally found to be well matched to the mechanical requirements of the movement.

Key Words: Elbow joint, Knee joint, Musculoskeletal System, Torque.

A description of the relationship between the torque exerted by a muscle group and the joint angle is useful both in clinical settings and in human factors engineering. Knowledge of normal variations can alert the clinician to abnormal conditions, and the human factors engineer can use these variations in the design of various apparatuses. The relationship between the torque and the body segment position (joint angle) is determined by three major factors: the cross-sectional area of muscle, the length-tension re­lationship of the muscles, and the mechanical char­acteristics of the lever system. The greater the cross-

sectional area of the muscle, the greater the amount of contractile protein (actin and myosin), and conse­quently the more force that can be developed.1 The length-tension relationship of human triceps brachii muscles has been studied in amputees.2 Total tension (force at the tendon) increased up to about 1.2 times the resting length, then decreased slightly, and finally increased and continued to increase. In the intact human subject, individual muscles usually act within a narrow range of lengths estimated to be between 0.7 to 1.2 times the resting length.3 Individual muscles act on one or more levers (bones) to produce move­ment in a body segment. Muscles are attached to bones at various locations, and thus each muscle produces a different torque around the joint axis. Consequently, plots of torque versus joint angle for various body segments represent the sum of the torques of the individual muscles (dependent on the muscles' lever lengths and cross-sectional area) and the lengths of these individual muscles at a particular joint position.

A number of investigators have described the torque-joint angle relationship in isometric,4-15 iso­tonic,7,13,14 or isokinetic12,16 testing for a number of muscle groups. No study, however, has attempted to describe this relationship for all three modes of test­ing. The purpose of this study was to describe and

Mr. Knapik and Dr. Wright are physiologists, Exercise Physiology Division, US Army Research Institute of Environmental Medicine, Natick, MA 01760 (USA).

Dr. Mawdsley was Assistant Professor of Physical Therapy, Sar­gent College of Allied Health Professions, Boston University, when the study was conducted. She is now Assistant Professor, Program in Physical Therapy, School of Allied Health Professions, Northern Illinois University, Dekalb, IL 60115.

Ms. Braun was Research Assistant, Exercise Physiology Division, US Army Research Institute of Environmental Medicine, Natick, MA, when this study was conducted.

This study was conducted at the US Army Research Institute of Environmental Medicine. The views and findings contained in this report are those of the authors and should not be construed as an official Department of the Army position, policy, or decision unless so designated by other official documentation.

This article was submitted December 21,1981; was with the authors for revision 18 weeks; and was accepted for publication September 7, 1982.

PHYSICAL THERAPY 938

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TABLE 1 Physical Characteristics of Subjects ( ± s)

Men (n = 16) Women (n = 15)

Age (yrs)

26.1 ± 3.8

24.9 ± 4.1

Weight (kg)

73.5 ± 13.8

61.4 ± 10.1

Height (cm)

174.6 ± 7.3

164.3 ± 7.1

Body Fat (%)

16.2 ± 3.8

28.5 ± 3.5

Lean Body Mass (kg)

61.3 ± 9.7

43.7 ± 5.8

examine the variations in torque through a range of joint motion in knee extension, knee flexion, elbow extension, and elbow flexion. These four muscle groups were tested isometrically, isokinetically, and isotonically in both men and women. For the pur­poses of this study the definitions of the words iso­metric, isokinetic, and isotonic were those used by Hislop and Perrine.17

METHODS

Subjects

Healthy men (n = 16) and women (n = 15), most of whom were soldiers, volunteered to participate in this investigation after being informed about the study and the requirements. The physical character­istics of the subjects at the start of the study are shown in Table 1. Percent body fat (% BF) was estimated from four skinfolds using the equations of Durnin and Womersley.18 Lean body mass was calculated from % BF and weight.

Apparatus

Subjects were tested for knee extension (KE), knee flexion (KF), elbow extension (EE), and elbow flexion (EF). For the isometric and isokinetic measurements, a modified Cybex® apparatus* was used. The modi­fications, which have been described in a previous study, were designed to provide adequate body sta­bilization and prevent the occurrence of synkinetic movement patterns.19 The lever arms were modified so that they were attached near the distal end of the body segment involved in the contraction, that is, just proximal to the ankle or wrist. The wrist was fixed midway between supination and pronation.

The isotonic apparatus was similar to the N-K® table described by Noland and Kuckhoff20 and was commercially available from Preston Corporation.† Modifications on the commercial device included a more secure subject-machine coupling identical to the one on the isokinetic device and the attachment of

the device to a fabricated stand so that it could be adapted to use in the Cybex® chair. The movable portion of the unit consisted of two arms connected by an axle. The subject was coupled to one arm, and weights were placed on the other arm. The axle allowed the two arms to move together, and the position of the arms were adjustable with respect to one another. The weight arm was positioned so that the subject experienced the maximal load at 60 de­grees for KE, 20 degrees for KF, and 90 degrees for both EE and EF.

An electrogoniometer (elgon)‡ was used to record the joint angles using methods similar to those of Karpovich and co-workers.21 Extensive experimenta­tion with the positioning of the elgon indicated that attachment of the device to the body segment with a fabricated elastic and Velcro strap provided the least possibility of misalignment during a contraction and consequently the most consistent measurements. The position of the elgon was verified on each subject by using a manual goniometer.

Design and Procedures

Subjects were tested over a five-week period. Dur­ing the first week, physical characteristics were ob­tained, and subjects were familiarized with the testing protocol. Familiarization included practice contrac­tions in all three modes of testing. Subjects returned one day a week over the next four weeks and were tested as closely as possible at the same time of day. In each of these sessions, subjects completed all test­ing on one of the four muscle groups. This involved approximately 18 contractions in both KE and KF and about 16 contractions in both EE and EF.

For isometric KE and KF, subjects performed one contraction every 10 degrees in the range of motion (ROM) from 90 degrees to 20 or 10 degrees. For EE and EF, subjects were given one isometric contraction at 60 and 70 degrees and every 20 degrees thereafter. Isokinetic velocities were 36°/sec, 108°/sec, and 180°/sec for all four motions. Isotonic measurements were made using a one-repetition maximum (1RM) procedure. The 1RM procedure was a trial and error

* Cybex Division of Lumex, Inc, 2100 Smithtown Ave, Ronkon-koma, NY 11779.

† J A Preston Corp, 60 Page Rd, Clifton, NJ 07012. ‡ Karpovich Instruments, 57 Wyndward Rd, Longmeadow, MA

01106.

Volume 63 / Number 6, June 1983 9 3 9

Fig. 1. Torque-joint angle curves for knee extensor mus­cles of the men.

technique, but the number of trials was reduced by preliminary estimates of the 1RM made during the familiarization session. Isotonic torque was calculated by multiplying the 1RM by the length of the lever arm on the N-K® device. This value represented the isotonic torque at 60 degrees of KE, 20 degrees of KF, and 90 degrees of EE and EF. The isotonic torque values at the other angles of interest were calculated trigonometrically. Included in the 1RM load was the estimated weight of the body segment22

and the effective weight of the isotonic apparatus. The lever arm length was recorded as the distance from the axis of rotation of the isotonic unit to the center of the arm or leg cuff.

In each of the sessions, the elgon was attached to the appropriate body segment while the subject was seated in the Cybex® chair. The subject was strapped and properly positioned in the chair. The joint angles before the start of an isokinetic or isotonic contraction were approximately 100 degrees for KE, 5 degrees for KF, 135 degrees for EE, and 5 degrees for EF. The three testing modes were administered in a system­atically counterbalanced order, and within each test­ing mode, the isometric angles or isokinetic velocities were also counterbalanced. Several submaximal iso­kinetic and isometric contractions were allowed be­fore the testing began, and at least two minutes of rest was allowed between each contraction.

On the isometric tests the subject was directed to build up to his maximal strength as rapidly as possible without jerking and to hold it until told to relax, usually three to five seconds. On the isokinetic tests the subject was instructed to move as hard and as fast as possible through the entire ROM. For the isotonic tests the subject was instructed to push or pull the lever arm as hard as possible in an attempt to move the weight through the entire ROM. For the isotonic tests the subject was considered to have completed

the ROM when the body segment was brought to approximately 30 degrees for KE, 90 degrees for KF, 20 degrees for EE, and 120 degrees for EF.

The two voltage signals from the Cybex® recorder were fed through the driver amplifier of a Grass Polygraph** and simultaneously displayed on the polygraph recorder as torque-time and angle-time curves. For the isokinetic tests the data were manually reduced by aligning the angle of interest with the torque curve and recording the torque at that angle. On the isometric tests the highest torque value ob­tained during a contraction at a particular joint angle was recorded.

Data were analyzed using standard statistical tech­niques. Mean values of all subjects were used to construct torque-joint angle curves. Differences in torque within a particular test and muscle group were examined using a one-way repeated measures analysis of variance.23 If the F ratio was significant, the differ­ences between means were tested using the Tukey test.23 Significance level was set at p < .01.

RESULTS

Torque-joint angle curves for the men and the women for each of the four muscle groups are de­picted in Figures 1 through 8 and plotted from the start to the completion of the movement. The vertical lines denote the standard error; because the variances were relatively homogeneous, only a few points were selected for illustration. Some commonalities among the curves can be seen. Generally, the isometric torque was the highest throughout the recorded ROM. The isotonic torque, with some exceptions, demonstrated the second highest torque. As the iso­kinetic velocity increased, the torque decreased; this relationship was generally consistent in all muscle groups throughout the recorded ROM. The isometric and isokinetic curves were generally similar in shape with a few exceptions.

The KE curves for the men and women are pre­sented in Figures 1 and 2, respectively. Because sub­jects were only required to move the isotonic load to about 30 degrees of extension, the isotonic torque was not calculated beyond this point. At 180°/sec, sub­jects often did not reach the preset speed of the dynamometer by 90 degrees (depending on their ac­celeration), so this point was not included in the data analysis. As shown in Figures 1 and 2, both the isometric and isokinetic curves rose somewhat more sharply than the isotonic curve from about 90 degrees to about 60 degrees. Beyond about 60 degrees the amount of isometric and isokinetic torque that could be generated by the KE muscle group decreased at a much more rapid rate than the isotonic torque. Peak

** Grass Instrument Co, 101 Old Colony Ave, Quincy, MA 02169.

PHYSICAL THERAPY 9 4 0

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Fig. 2. Torque-joint angle curves for knee extensor mus­cles of the women.

torque for KE of the men as a group occurred at 70 degrees both isometrically and at 36°/sec (Fig. 1). At 108°/sec and 180°/sec, peak torque occurred at 60 degrees. For the women as a group, peak torque for KE occurred at 60 degrees both isometrically and at 36°/sec (Fig. 2). Peak torque shifted to 50 degrees at 108°/sec and 180°/sec.

Figures 3 and 4 depict the torque-joint angle curves for KF of the men and the women, respectively. The isometric and isotonic curves demonstrated an ap­proximately linear decrease in torque throughout the ROM. After about 60 degrees, however, the decline in isotonic torque was more rapid than that in iso­metric torque. The isokinetic curves followed the same general pattern as the isometric curves after a slight initial rise at some velocities. As a group, men demonstrated peak torque at the earliest recorded

Fig. 3. Torque-joint angle curves for knee flexor muscles of the men.

Fig. 4. Torque-joint angle curves for knee flexor muscles of the women.

point in the ROM (20 degrees) both isometrically and at 180°/sec (Fig. 3). Peak torque occurred at 30 degrees during the 36°/sec movement and at 40 degrees during the 108°/sec movement. For the women as a group, peak torque occurred at 20 degrees isometrically and at 36°/sec but shifted to 30 degrees at 108°/sec and 180°/sec (Fig. 4).

The torque-joint angle curves for EE of the men and the women are presented in Figures 5 and 6, respectively. For the men as a group, the pattern of isometric and isotonic torque was almost identical: the curves rose to a peak at about 90 degrees and then dropped off (Fig. 5). Although the isokinetic curves followed the same general pattern, the angle of peak torque was shifted to 70 degrees. Figure 6 shows that women as a group demonstrated a sharp linear rise in isometric torque of EE and reached a peak at 70

Fig. 5. Torque-joint angle curves for elbow extensor mus­cles of the men.

Volume 63 / Number 6, June 1983 941

Fig. 6. Torque-joint angle curves for elbow extensor mus­cles of the women.

Fig. 7. Torque-joint angle curves for elbow flexor mus­cles of the men.

Fig. 8. Torque-joint angle curves for elbow flexor mus­cles of the women.

degrees. Torque declined beyond this point in the same sharp linear fashion. The three isokinetic curves rose somewhat more gradually to 70 degrees and then declined in the same gradual fashion. The isotonic apparatus was set so that the maximal load would be achieved at 90 degrees. Because peak isometric and isokinetic torque actually occurred at 70 degrees, the isotonic curve appeared somewhat offset.

Figures 7 and 8 depict the torque-joint angle curves for EF of the men and the women, respectively. For the men as a group, isometric torque rose from 30 degrees to 50 degrees, plateaued from 50 degrees to 90 degrees, and declined thereafter (Fig. 7). The three isokinetic curves gradually increased, reached a peak at 70 degrees, and gradually declined thereafter. The isotonic curve appeared offset because the load was selected to produce maximal torque at 90 degrees when, in actuality, the torque changed very little from 50 degrees to 90 degrees. For the women as a group, the isometric and isotonic curves for EF were similar, but the isotonic torque started at a much lower level and rose somewhat more rapidly up to 70 degrees (Fig. 8). Beyond this point the two curves appeared to mirror one another, with the isotonic curve some­what lower. The isokinetic curves rose gradually from 30 to 90 degrees and declined thereafter.

Table 2 shows the range in which peak torque occurred in individual subjects. Some of the widest

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TABLE 2 Ranges (°) for the Occurrence of Peak Torque in Four Muscle Groups for the Isometric and Isokinetic Tests

Subjects

Men

Women

Test

ISOM ISOK (36°/sec) ISOK(108°/sec) ISOK(180°/sec) ISOM ISOK (36°/sec) ISOK (108°/sec) ISOK(180°/sec)

KE

9 0 - 5 0 9 0 - 5 0 9 0 - 5 0 8 0 - 5 0 7 0 - 4 0 9 0 - 4 0 8 0 - 4 0 7 0 - 4 0

KF

2 0 - 4 0 2 0 - 4 0 2 0 - 4 0 2 0 - 4 0 2 0 - 4 0 2 0 - 4 0 2 0 - 5 0 2 0 - 4 0

EE

1 1 0 - 5 0 1 1 0 - 5 0

9 0 - 5 0 9 0 - 5 0 9 0 - 5 0 9 0 - 5 0 9 0 - 5 0 9 0 - 5 0

EF

5 0 - 9 0 3 0 - 9 0 3 0 - 9 0 3 0 - 1 1 0 5 0 - 1 1 0 5 0 - 9 0 3 0 - 1 1 0 5 0 - 9 0

ranges occurred in the isometric mode. For KE, peak torque occurred in greater than half the ROM, any­where from 90 degrees to 40 degrees. Knee flexion demonstrated some consistency, with peak torque occurring between 20 degrees and 40 degrees in all but one instance. For EE and EF, peak torque in individual subjects occurred in almost the entire ROM. For EE, the range was between 110 degrees and 50 degrees, with the men slightly more variable than the women. Elbow flexion ranged from 30 de­grees to 110 degrees. Because of the positioning of the isotonic apparatus, peak isotonic torque occurred at only one joint angle for all subjects: 60° of KE, 20° of KF, and 90° of EE and EF. Table 3 shows the angles adjacent to the angles of peak isometric or isokinetic torque at which there were no statistically significant differences.

DISCUSSION

Comparison of Isometric and Isokinetic Torque Curves

Although there have been a plethora of investiga­tions on isometric force or torque variations in the ROM of KE and EF, few have evaluated the other two motions in this study. For KE and KF, the discussion is limited to those studies that used subject postures similar to those of this study, because differ­ent postures will markedly influence the shape of the curve.9,12 For EE and EF, torque was measured with the forearm midway between supination and prona­

tion, whereas in most other studies the forearm was supinated. Jorgensen and Bankov demonstrated that there is little difference in the shape of the isometric torque curve regardless of whether a pronated or a supinated forearm is tested.24

Studies on KE were in general agreement with this study.4,8-12,14-16 All reported the same general inverted U-shaped curve. Peak isometric torque has been re­corded from 85 degrees11 to 130 degrees,8 with most studies indicating 60 degrees.9,10,12,15,16 Campney and Wehr performed a statistical analysis similar to the one in this study and reported no significant differ­ences in the isometric force exerted between 90 de­grees and 60 degrees.5 The present study found no significant differences between 80 and 50 degrees for men and between 70 and 50 degrees for women. Clarke et al reported a similar finding.4 The isometric and isokinetic KF curves in this study were similar in shape and in angle of occurrence of peak torque to those presented by Scudder.12 Houtz et al, however, found an inverted U-shaped curve for KF with peak torque at 60 degrees.9

For EE, Singh and Karpovich reported very little change in isometric or concentric force from 40 to 90 degrees, unlike the findings of this study.13 The two studies agreed, however, in that force (or torque) seems to decline after 90 degrees. Studies on isometric EF4,7,13,15 demonstrated curves similar to the ones in this study with peak force occurring between 9015 and 140 degrees.4 Generally, there were little isometric4,7,13 or concentric7,13 force differences in the range between 90 degrees and 60 degrees. Komi

TABLE 3 Angles (°) Not Significantly Different From One Another That Surround the Angle of Peak Torque

Subjects

Men

Women

Test

ISOM ISOK (36°/sec) ISOK(108°/sec) ISOK(180°/sec) ISOM ISOK (36°/sec) ISOK (108°/sec) ISOK (180°/sec)

KE

8 0 - 5 0 8 0 - 6 0 7 0 - 6 0 8 0 - 5 0 7 0 - 5 0 7 0 - 5 0 6 0 - 4 0 8 0 - 4 0

KF

2 0 - 4 0 2 0 - 4 0 2 0 - 4 0

a

2 0 - 3 0 2 0 - 3 0 2 0 - 5 0 2 0 - 5 0

EE

9 0 - 7 0 9 0 - 5 0 9 0 - 7 0 9 0 - 7 0 9 0 - 7 0 7 0 - 5 0 7 0 - 5 0 7 0 - 5 0

EF

5 0 - 9 0 5 0 - 9 0 5 0 - 9 0 3 0 - 9 0 9 0 - 1 1 0 7 0 - 9 0 7 0 - 9 0 7 0 - 9 0

a All angles around angle of peak torque were significantly different.

Volume 63 / Number 6, June 1983 9 4 3

TABLE 4 Estimates of Forces Produced by Knee Extension (KE) and Knee Flexion (KF) Muscle Groups and a Comparison of

the Present Study with a Study by Smidt14

Muscle Group

KE

KF

Angle (°)

90 60 30 30 60 90

MAma

(M)

.0380

.0467

.0486

.0387

.0394

.0256

Present Study

Torque (Nm)

206.3 250.6 155.9 137.9 106.3

71.1

Fm b

(N)

5428.9 5366.2 3201.2 3563.3 2698.0 2777.3

Torque (Nm)

101.6 116.8 105.0

55.6 49.4 35.4

Smidt14

Fm b

(N)

2712.6 2524.5 2168.7 1484.7 1273.0 1475.9

a MAm = moment arm of the muscle group. b Fm = force in the muscle group.

measured the isokinetic force of EF and found force-muscle length curves that were similar in shape to the torque-joint angle curves reported here.25

Mechanical Factors Accounting for Torque Variations

The variations in isometric and isokinetic torque through the ROM can be accounted for by using some of the mechanical principles noted in the intro­duction. The forces in the active muscle group and the lever arm length must be known. For an isometric contraction, these factors can be obtained using the formula Muscular Moment = Resisted or Measured Moment.26 In this study the muscular moment was the moment produced about the knee by the muscle group. The resisted or measured moment was the moment produced about the knee by the external force at the Cybex® lever arm. Thus,

Fm.MAm = Fx.MAx, (1)

where Fm was the force in the muscle group, MAm was the moment arm of the muscle group, Fx was the external force, and MAX was the moment arm for the external force. The factor FX.MAX is actually the torque recorded on the Cybex® apparatus. Estimates of the MAm can be obtained from a study by Smidt.14

In his study, the moment arms of the patellar ligament and the hamstrings were obtained by taking serial roentgenograms on 26 male subjects while they per­formed isometric KE and KF contractions at various joint angles.14 With these moment arms, the estima­tion of Fm becomes a simple task. It should be noted that Fm for KE was actually the force in the patellar tendon, because the MAm measured by Smidt was actually the moment arm for the patellar tendon. Assuming there is little or no friction between the patella and the femur, Fm could be better estimated by accounting for the angles of pull of the individual muscles attached to the patella as well as the percent­age of cross-sectional area each contributes to the muscle group.

Table 4 shows the estimated values for Fm in this study at the joint angles where it was possible to apply Smidt's data.14 Smidt's data are also compared with the present study in the table. The torque gen­erated by the subjects in Smidt's study was only 40 to 67 percent of that of the male subjects in this study. This may be accounted for by differences in testing posture9,12 or in strength differences in the popula­tions. Of more interest, however, is that the changes in the isometric torque curves in Figures 1 and 3 can be accounted for in terms of the Fm and MAm. For KE (Fig. 1), the increase in isometric torque from 90 to 60 degrees could be attributed to an increase in the MAm, because the Fm changed very little (1.2%). From 60 to 30 degrees the MAm increased slightly, but the 67 percent decline in Fm resulted in a decrease in torque. The same general trend could be seen in Smidt's data. For the KF, the decline in torque from 30 to 60 degrees was accounted for by a 32 percent decrease in Fm, because the MAm was relatively con­stant (Fig. 3). Also in consonance with Smidt's obser­vations, from 60 to 90 degrees the torque continued to decline because of a decrease in MAm, although the Fm actually increased 3 percent. It should be emphasized that the Fm was calculated (rather than obtained directly) from torque and MAm data and that the MAm was acquired from subjects other than those in the present study. With these qualifications in mind it is possible to estimate the variation in the isometric torque of other muscle groups in a similar fashion.

For an isokinetic or isotonic contraction, the for­mula Muscular Moment = Resisted or Measured Moment + I° a could be used to calculate the Fm.26

In this equation, I° = moment of inertia and α = angular acceleration. The equation expands to

Fm.MAm = Fx.MAx + I° α. (2)

In an isokinetic contraction, acceleration is approx­imately equal to zero because the velocity of the Cybex® dynamometer is relatively constant. The fac­tor I° α becomes zero. Thus, variations in the isoki-

Fm∙MAm = Fx∙MAx + Io α. (2) In an isokinetic contraction, acceleration is approx­

imately equal to zero because the velocity of the Cybex® dynamometer is relatively constant. The fac­tor Io α becomes zero. Thus, variations in the isoki-

PHYSICAL THERAPY 944

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netic torque curves for KE and KF were due to the same factors as were the variations in the isometric curve. The curves were generally similar in shape, substantiating this suggestion. It was not possible to mechanically analyze the isotonic curves because they were calculated rather than measured directly, and the acceleration was not recorded or controlled.

Rationale for Inclusion of Isotonic Measures

Isometric, isokinetic, and isotonic strength meas­ures can all be used to assess the functional capacity of a muscle group or to rehabilitate muscle groups that have suffered functional loss. The purpose of the present study was to determine whether these three modes of testing were comparable in terms of the torque generated and the shapes of the functional torque curves. Isotonic torque measures differ consid­erably in a mechanical sense from isometric and isokinetic measures, however. The factors of acceler­ation and deceleration alone could account for either very high or very low values at any point in the ROM.

In the early portions of our studies strain gauges were applied to the isotonic torque units (modified N-K® devices), but we found that the torque readings from this device were so variable as to not be of any practical use in making a comparison with the iso­metric and isokinetic curves.19 The more theoretical approach of calculating torque from the 1RM was therefore chosen. This removed the acceleration-de­celeration factor so that a theoretical constant velocity was achieved and the isotonic curves could be com­pared with the other two torque curves.

Muscle Group Capability and Mechanical Requirements

Muscle groups are capable of exerting the greatest amount of torque in an eccentric muscular contrac­tion.7, 13 As this type of contraction was not measured in this study, the isometric torque curve best repre­sented the maximal voluntary capability of the muscle group. The isotonic torque curve, on the other hand, is a mechanical representation of the torque that the muscle group was called on to exert in order to move the load (the 1RM) through the ROM. Thus, it is possible to compare muscle capability (isometric torque) with the external mechanical requirement (isotonic torque) by comparing the shapes of the two torque curves.

For KE of both the men and the women the isometric torque curves rose more sharply than the isotonic curves from 90 to 70 or 60 degrees (Figs. 1 and 2). After 70 or 60 degrees, the isometric torque declined much more rapidly than the isotonic torque. This rapid drop-off in muscle capability when the mechanical requirement decreases at a much less

rapid rate may account for the frequent clinical ob­servation that the latter portion of the ROM in KE is the most difficult to complete. Because, as shown earlier, the MAm was relatively constant from 60 to 30 degrees, it must be assumed that excessive shorten­ing of the muscle group (the length-tension relation­ship) accounted for the sharp decrease in isometric torque. For KF of the men and women, the isotonic and isometric torque curves showed an almost iden­tical linear decline from 20 to 60 degrees (Figs. 3 and 4). This indicated that muscle group capability was well matched to the mechanical demands in this ROM. Beyond 60 degrees the isotonic torque declined more rapidly than the isometric torque, which dem­onstrated that the muscle group had more capability than it was being called on to use. Because the MAm decreased from 60 to 90 degrees, it was the mainte­nance of the Fm that resulted in the slower decline.

For EE of the men, the isometric and isotonic curves were almost identical in shape (Fig. 5). When examining the isotonic EE curve of the women, one must remember that the magnitude and shape of this curve (with respect to the isometric curve) was de­pendent on both the selection of the 1RM and the determination of where the maximal load was applied in the ROM (Fig. 6). Peak isometric torque occurred at 70 degrees, and maximal isotonic loading occurred at 90 degrees; therefore, the two curves appeared considerably different. At 110 degrees, the isotonic torque exceeded the isometric torque, which may be the result of excessive acceleration of the load or a measurement error. If the 1RM was decreased slightly in magnitude and the maximal loading was applied at 70 degrees (this can be done graphically), the isotonic torque curve would approximate the isomet­ric curve, though the peak torque would not rise or decline as rapidly. Thus it would appear that the capabilities and mechanical requirements for EE were matched well for both men and women.

For EF of the men and the women, more isometric torque was generated than isotonic torque up to about 70 degrees, which indicated that capability exceeded the requirement (Figs. 7 and 8). Although the women appeared comparable in their isometric and isotonic torque beyond 70 degrees, the men appeared to de­cline in isometric torque more rapidly than in isotonic torque. Doss and Karpovich found results similar to those for the men in this study when they measured isometric and concentric force in EF.7

Shift in Angle of Peak Isokinetic Torque

For KE and KF, it was found that as the isokinetic velocity increased, the angle at which peak torque occurred was shifted to a point later in the ROM. An exception was during KF of the men at 180°/sec. When the shift did occur, the torque value at this new

Volume 63 / Number 6, June 1983 945

point was not significantly different from the torque at the same joint angle where peak isometric torque was found. Several other investigations have reported a similar phenomenon.11,12,16,27 Although most dis­cussions of the topic have been vague, the phenome­non has been attributed to 1) a lag in the excitation of the contractile elements in the muscle,27 2) momen­tum overcoming some of the inertia of the leg,11 and 3) a protective dampening of the series elastic com­ponents of the muscles at high speeds.12 An alternate explanation may lie in some inherent mechanical characteristics of the Cybex® and the subject-machine coupling. At higher isokinetic velocities the limb com­pleted a certain portion of the ROM as it accelerated to achieve the preset velocity. When the preset veloc­ity was reached, the torque developed by the muscle group was lower than that which could be achieved at the preset velocity. While additional torque was being developed, the leg completed a further portion of the ROM. Thus, the combination of the lag time as the limb accelerated to the preset velocity and the time required for the muscle group to develop addi­tional torque may have accounted for the shift in the angle of peak torque. This shift occurred less often in EE and EF and in fact only occurred in EE of the men (Fig. 5). Torque was measured only in intervals of 20 degrees in these muscle groups, and the shift in peak torque was seldom greater than 10 degrees in KE and KF.

Decline in Torque with Increasing Velocity and Differing Methodology

In all muscle groups measured in this study, the isometric torque was greater than the isokinetic torque, and the isokinetic torque decreased system­atically with increasing velocity of contraction. This relationship was relatively consistent throughout the range of motion and generally agreed with the find­ings of Thorstensson et al,16 Osternig,11 and Scud-der.12 Moffroid et al27 and Perrine and Edgerton,28

however, reported a biphasic torque-velocity curve with low velocity torque being slightly higher than isometric torque and with the torque decreasing with further increases in velocity. These latter findings were not in accord with in vitro force-velocity rela­tionships.29 More important, there were a number of methodological differences between the present study and that of Perrine and Edgerton. Perrine and Ed­gerton instructed subjects not to exert a maximal contraction at the lower isokinetic velocities until they had passed part way through the ROM. They meas­ured the torque in KE at 30 degrees. In testing KE in our study, subjects were instructed only to kick as hard and as fast as possible and to complete the entire ROM. There were also differences between the two studies in subject-machine coupling (foot vs ankle) and in stabilization (none vs extensive). It seems most

likely that methodological differences account for the dissimilarity in the findings. In some individual cases in this study, however, the isokinetic torque at 36°/ sec did exceed the isometric torque. Considering each measured point in the ROM and each subject as an individual case, this occurred in one case for KE, in 21 percent of the cases for KF, in 18 percent for EE, and in 14 percent for EF. These exceptions generally occurred near the ends of the movements.

Gregor et al suggested that isokinetic torque meas­urements of KE at angles less than 30 degrees are invalid because inadequate time is available to reach the maximal force possible at the later angle.30 If it is again assumed that the isometric torque represented the maximal capability of the muscle, this assumption can be examined. In all muscle groups tested there was a tendency for the torque curves to show the largest isometric-isokinetic differences at the begin­ning of the range of motion and the smallest differ­ences at the end of the range of motion, which provided some support for this assumption. Scudder, however, found the smallest isometric-isokinetic dif­ferences at the start of the range of motion.12

Clinical Relevance

The discussion of the comparison of isometric and isokinetic torque curves demonstrated the variability reported in the literature with regard to a single angle in the ROM where peak torque can be said to occur. Even in our own study, individuals varied widely in the angle at which peak torque occurred (Tab. 2), and this resulted in no statistically significant difference within a certain ROM (Tab. 3). It would seem that in evaluating patients for therapeutic exercise, individ­uals should be tested for their own unique torque curves if possible. The individual isometric torque curve could be used to estimate the 1RM and also the angle where maximal isotonic loading should occur. If it is not possible to evaluate a patient individually, the torque curves presented here may serve as a general guide.

Our torque curves were obtained from a group of healthy men and women. The shapes of these curves can be taken as the shapes of usual isometric, isotonic, and isokinetic torque curves. In patient assessment, large variations from the general shapes of these curves may indicate functional loss from injury or disease.

The isometric and isokinetic torque curves were similar both in shape and in the related fact that the same mechanical factors could account for the changes in torque through the ROM. This suggests that the physical therapist can assess the patient with either mode of testing and can anticipate that pro­gressively lower torque values will be obtained as the isokinetic velocity increases. Further, moderate to

PHYSICAL THERAPY 9 4 6

RESEARCH

high correlations have been found between isometric and isokinetic torque measures, suggesting that if a patient scores high on an isometric test, he will also score high on an isokinetic test.31 Thus, isometric testing through a ROM will probably provide as much information as isokinetic testing. Isometric test­ing in this manner would offer this disadvantage of being more time-consuming but would certainly be less expensive in terms of equipment. The greater degree of muscle tension in isometric testing may be disadvantageous in some situations.

SUMMARY Torque variations through a ROM of KE, KF, EE,

and EF were presented. The angle at which peak torque occurred was found to be highly variable in individual subjects, although the shape of the curves were similar. It was suggested that patients be assessed individually for their own unique torque curves and that isometric torque curves may provide as much information as isokinetic curves. Torque variations

were discussed in terms of the mechanical character­istics of the musculoskeletal system. In most cases, the maximal capability of the muscle groups (isomet­ric torque) was found to meet or exceed the mechan­ical demands of moving a weight through the ROM (isotonic torque). This was not true at the end of the ROM of KE, however. The shift in the angle of peak isokinetic torque with increasing velocity of contrac­tion may be attributed to both of the following: 1) the time lag between the onset of limb movement and the achievement of the preset dynamometer velocity and 2) the time required to develop additional torque once the preset velocity is achieved. Torque was found to decrease with increasing velocity of contrac­tion.

Acknowledgments. Appreciation is expressed to David Priser and Margaret Kinney, who served as technicians during the data collection phase of this study, and to Pat Basinger, Cynthia Bishop, and Elaine Lampert for their technical assistance in pre­paring the manuscript.

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