Muscle architecture and force-velocity relationships in humans THOMAS L. WICKIEWICZ, JAMES J. PERRINE, AND
ROLAND R. ROY, PERRY V. REGGIE EDGERTON
L. POWELL,
The Hospital for Special Surgery, New York, New York 10021; and Department of Kinesiology and Brain Research Institute, University of California, Los Angeles, California 90024
WICKIEWICZ, THOMAS L., ROLAND R. ROY, PERRY L. PowELL, JAMES J, PERRINE, AND V. REGGIE EDGERTON. MU& architecture and force-velocity relationships in humans. J. Appl.
Physiol. Respirat. Environ. Exercise Physiol. 57(Z): 435-443, 1984.-The in vivo torque-velocity relationships of the knee extensors (KE), knee flexors (KF), ankle plantarflexors (PF), and ankle dorsiflexors (DF) were determined in 12 untrained subjects using an isokinetic testing device (Cybex II). These data were then matched to the predicted maximum forces and shortening velocities derived from muscle architectural determinations made on three hemipelvectomies (36). The torquevelocity curves of all muscle groups resembled that predicted by Hill’s (19,20) equation except at the higher forces and lower velocities. The peak torques occurred at mean velocities ranging from 41-62 rads-l for the KE, KF, and PF. Although the peak torque of the DF occurred at the isometric loading condition, it was also lower than that predicted by Hill’s equation. The muscle fiber length and physiological cross-sectional area measurements indicate that the architecture of the human leg musculature has a major influence on the torque-velocity characteristics. These data corroborate previous findings (24) that some neural inhibitory mechanism exists in the control of the leg musculature, which limits the maximum forces that could be produced under optimal stimulating conditions. force/torque velocity relationships; human; skeletal muscle architecture; specific tension; isokinetics
SKELETAL MUSCLE from a Variety Of Species, including humans, functions in a predictable way with respect to its force-velocity relationship when maximally stimulated (9, 11, 12, 29). Hill (19) raised the question as to whether the same force-velocity relationship exists in humans when muscles are voluntarily activated. The consensus of opinion seems to be that the same hyperbolic relationship between force and velocity exists for shortening contractions in humans whether the muscle is activated by the central nervous system or by artificial stimulation (13, 14, 32, 37). This conclusion has been challenged using isokinetic testing methods where the velocity of muscle shortening is controlled, at least at the lower velocities, and when angle specificity is taken into account (8, 17, 24). If the force-velocity relationship of a maximally and identically stimulated isolated muscle is similar under a variety of load conditions to that of an intact muscle group activated by the central nervous system, then an ISOLATED
0161-7567/84
$1.50
Copyright 0 1984 the American Physiological
Society
identical level of activation would presumably exist at all velocities in vivo (25). Conversely, if the relationship is not similar to that predicted by Hill’s equation, then the implication is that the ability of the nervous system to maximally and identically activate a muscle group over a variety of load conditions is velocity dependent. It should be noted that the force-velocity relationship could be similar to Hill’s (19) predictions under in vivo and in situ conditions whether or not the stimulation is maximum as long as it is constant under each loading condition (25). A second issue addressed in this paper is to what extent the architectural features of flexor and extensor muscles of the lower limb influence the force-velocity properties of those muscle groups. Although the histochemical parameters related to the contractile properties are similar in the flexors and the extensors of the knee and ankle of a range of species (2), including humans (10, 21, 28, 31), the actual torque-velocity relationships of these muscle groups in humans clearly differ. It is hypothesized that these physiological differences can be explained in large part by the architectural design of the muscles within each muscle group (6, X,27). The third point addressed is that the absolute torquevelocity data can be converted to force-velocity values expressed per cross-sectional area and number of sarcomeres in series. This permits a more acceptable comparison between human and other species that are independent of muscle volume, fiber number, fiber length, and so on. Preliminary results have been published elsewhere (26,35). METHODS
Twelve untrained human subjects, eight males and four females ranging from 20 to 38 years of age, were tested on an isokinetic dynamometer (Cybex II, Lumex). Two to four trials, each occurring on a different day for a given subject, were carried out to familiarize the subjects with the test methods before the recording session. Angle-specific force-velocity curves were generated for the following functional muscle groups: knee extensors (KE), knee flexors (KF), ankle plantarflexors (PF), and ankle dorsiflexors (DF). The recording speeds ranged from 0 rad s-l (isometric) to 5.03 rad s-‘. To assure that the readings of the torque were angle specific, a switch l
l
435
436 momentarily drove the recorder pen to full scale when the lever arm reached the test angle. Recordings for the knee and ankle muscles were made on different test days to minimize fatigue. The angles at which the torques were measured were sufficiently distal in the arc of motion to allow for rise time to peak tension in the muscle group. This was important at the higher recording speeds (B3.49 rads-‘) (24). The KE and KF were tested with the subject seated with the backrest at a 100” angle. The recording angles for the muscle groups were 30” of knee flexion relative to full extension for the KE, 70” of knee flexion relative to full extension for the KF, 10” of plantarflexion relative to a 90” angle for the foot and lower leg for the PF, and a 90” angle for the foot and lower leg for the DF. The ankle recordings were made with the subject in a completely supine position with the knee and hip at -90’. Recordings were made during singular maximum efforts through approximately the same range of motion for each speed. The subjects were encouraged to make a maximum effort at the specific recording angle for each movement. When testing at the lower speeds (0.83 rad. s-l or slower), maximum effort was delayed until a point in the arc was reached that would still allow sufficient time for peak tension development at the recording angle. This technique was necessary because the distal recording angle requires prolonged (l-2 s) efforts that are “fatiguing” if held maximally throughout the arc of motion. To relate the in vivo force-velocity characteristics with the architectural differences between functional muscle groups, the moment arm variations of the musculature to the skeletal system must also be known. To determine these features, two cadaver hemipelvectomy sections used in a previous study (36) were stripped of musculature, leaving the tendons and retinacular structures undisturbed along with intact capsular and ligamentous structures at the hip and knee joints. Metal hooks were placed on the pelvis and femur at the proximal site of attachment of the various muscles. Thread was attached to the tendon ends and passed through the hooks and held taut with lead weights. Lead markers were placed on the thread. Tendon excursions for the knee musculature (see Table 3 for a listing) were measured from full extension to 90” flexion. Recordings were made with the hip at maximal extension and at 90” from full extension. Calculations of the changing moment arm for the knee musculature were made from tendon displacements for each 10” arc. Although the knee has a continually changing center of rotation, we assumed that for a short arc of rotation about the point at which the torque was measured, the knee acts as a simple hinge. This allowed the average moment arm over that short arc length to be calculated from the linear displacements of the tendon. Data for tendon excursions for ankle musculature was obtained from Ambagtsheer (l), who used procedures similar to that described above. Predicted maximum torque (P,) and maximum velocity of shortening ( Vmax) were calculated using Hill’s equation and constants (19) and assuming V = 0.42 (PO k P)/P + 0.26, where in the equation (P + a) V = b (PO - P), a = 0.26 when P, is
WICKIEWICZ
ET
AL.
normalized to 1.0, and b = 0.42 when Vmax is in fiber lengths per second. The constant of 0.42 was originally derived in a muscle preparation in which the muscle length and fiber lengths were essentially the same. The 0.42 constant is appropriate when it reflects fiber length. If muscle and fiber length differ as they do in all major muscles of the leg, then a Vmaxcalculated using the constant of 0.42 cannot be expressed meaningfully in muscle lengths per second. Thus fiber lengths and changes in fiber length must be known to use Hill’s constants. RESULTS
hlean torque values at selected test speeds are shown in Fig. 1. The peak of the mean torques occurred at speeds slightly greater than 0 rad. s-l (isometric) for the KE, KF, and-PF. The DF was the only group in which mean peak torque occurred at 0 rad. s-l. The mean peak torque (angle specific) produced by the KF was 79% of that observed for the KE, and the DF produced only 26%
2
n E i
Angular
Velocity
b-ads- 1)
Mean torque-velocity curves (n = 12) for knee extensors (A), knee flexors (A), plantarflexors (0), and dorsiflexors (0). Dashed line represents predicted peak torques using Hill’s equation (16). FIG.
1.
HUMAN
TABLE
MUSCLE
ARCHITECTURE
1. Mean torque-velocity
AND
437
FORCE-VELOCITY
relationships
for flexor and extensor groups of knee and ankle rad . s-l
0.21
0
0.41
0.62
0.83
149rt61 116t23
147237 116*28
1.26 Torque
KE KF PF DF Values
123t44 96,t28 57216 19t6
128+46 114t25
are means
&SD.
142t57 117t19 72t15 18~16 KE,
knee
132t70
1.68 (N- m)/velocity
KF,
knee
flexors;
2.51
2.93
3.35
3.77
4.19
4.61
’ 5.03
(rad- s-l)
125t35 103t24
38tll 1323 extensors;
2.09
loo-t31 841k24 25t8 10*3
PF, plantarflexors;
83k29 69,t23 16t7 7k2
DF,
67t28 54t20 llt6 4t2
46k21 40t17 6k5 3*1
dorsiflexors.
FIG. 2. Normalized (% peak torque) torque-velocity curves for 4 muscle groups. Notice that only ankle dorsiflexors had its peak torque at isometric (0 rad. s-l) velocity. Change in velocity for a 10% change in torque (60-70% peak torque) is also shown. (see DISCUSSION).
Angular
Velocity
bad-s - ‘1 of the mean peak torque of the PF (Table 1). The maximum torque-velocity relationship at the higher speeds was either linear or slightly concave for all muscle groups (Fig. 2). The data points at the higher velocities of the maximum torque-velocity curve could be fitted reasonably&well to Hill’s equation (19, 20). However, the torques at the lower velocities were less than would be predicted from the torques measured at the higher velocities (Fig. 3). Proportionately, there was a greater loss of torque per unit change in velocity above 0.41 rad& in the PF, followed by DF, KE, and KF (Fig. 2). There was more similarity in the absolute torque-velocity curves of agonist and antagonist pairs of muscle groups than between either the agonists or the antagonists of the two joints studied. This relationship was apparent whether the torque-velocity curves were expressed in absolute values (Fig. 1) or normalized with respect to peak torque (Fig. 2) . The mean force value transmitted by the tendon was calculated for the four muscle groups using the average moment arms as determined by the tendon excursions (Table 2). For simplification, the action of both the PF and the DF were assumed to act at right angles to the joint axis, even though there was a 10" difference in joint position at the point of measurement. To estimate the force potential of the knee musculature, a correction was made for the peak torque (Table 2) based on the fact
that -26% higher torque can be produced by the quadriceps at 60” compared with 30” from full knee extension (23). When this 26% correction factor for the mechanical disadvantage at 30” was used to represent the quadriceps’ full force potential, tension production at the tendon for the KF was 72% of the force for the KE. The DF produced 29% of the force observed in the PF. Tensions normalized to the KE are also shown in Table 2. Specific tensions for the KE, KF, PF, and DF were 53, 79, 30, and 47 N. cmB2, respectively. Estimates of the maximum angular shortening velocity for each muscle group tested were obtained by matching the torques observed at the higher velocities to a normalized in vivo force-velocity curve (24) reported by Hill (19) and generated by a velocity-specific afterloading method (Fig. 3). The high-speed portion of our experimental torque-velocity curves could be scaled to closely match Hill’s predicted curve. There is, however, a marked departure of the experimental curve at the lower speeds. Average knee extensor and flexor tendon excursions of the two cadaver limbs were similar relative to muscle length when the knee moved through a 90” arc (Table 3). The relative displacement for the KF was semitendinosus > semimembranosus > biceps femoris, femoral head > biceps femoris, ischial head. All muscles of the quadriceps had similar excursions. The distance between the points of attachment of the sartorius were displaced the least of any muscle.
438
WICKIEWICZ
ET
AL.
08
KE
KF
0.2
0.0
2.0
4.0
6.0
8.0
10.0
0.0
12.0
0.0
2.0
4.0
* 0
0
40 4-O
1 0
0
8-O 80
. 16b 160
GO 120 mm.s'l . 40
20 2-o
200
. 280
240
. 32-O 320
0.8-
12.0
4-o
S’O
1 2-o
160
20-o
24-O
28-o
320
mm3'1 60 6b
80 8-O
100
10
1.0 8 \
10.0
fad&l
20
mms-l.lOOOsarc.-1 c
8.0
6.0
rad*s - '
. 30 40 mmzi-l~lOOOsarc.-l
50
60
70
II 8 \\
0.8
PF
DF
0.6;
0.6
0.0
1.0
2.0
3.0 rad-s
. 0 t 0
20 . 10
40 . 20
4.0
5.0
6.0
0.0
7.0
1.0
2.0
3.0
4.0 rads-1
-1 60
mm& . 30
. 100
80
1 110
0
2’0
40
i0
5.0
8’0
6.0
7.0
ld0
8.0
1;o
140
1;o
mm& . 40
. 50
1 60
I 0
1
70
mm.s-l.lOOOsarc.-1
1 10
1 20 mms-l
I 30 lOOOsarc9
1 40
1 50
3. Normalized torque-velocity curves for A, knee extensors (A); B, knee flexors (A); C, plantarflexors (0); and D dorsiflexors (0) fitted to experimentally predicted force-velocity curve (x) generated using Hill’s equation (16). Torque is expressed as a percent of maximum (P/
P,) and velocity of shortening is expressed as rad. s-l, mm s-‘, and mm s-l. 1,000 sarcomeres-? KE, knee extensors; KF, knee flexors; PF, ankle plantarflexors; DF, ankle dorsiflexors.
Although there was a large difference in cadaver limb size (36), the relative tendon excursions, when expressed as a percent change of whole muscle length, enabled us to approximate linear displacements of muscles in vivo. Table 4 lists the observed and estimated maximal angular and linear rates of shortening velocity for each muscle group. Based on the architectural data from a previous report (36) and the muscle length changes shown in Table 3, angular velocities were converted to linear velocities. This data was further normalized per 1,000 sarcomeres to eliminate the variable of the number of sarcomeres in series for each muscle group. The general shapes of the torque-velocity curves at the higher velocities are similar (Fig. 2). The estimated Vmax (rads-‘) of the KE and KF is twice as much as that of the PF and DF (Table 4). When these predicted Vmax values are converted from angular to linear velocities, the differ-
ences between these muscle groups are even greater. The linear velocity differences can be accounted for, at least to a large degree, by the differences in the number of sarcomeres in series (Fig. 4). To avoid using the predicted Vmax to compare the velocity potential of each muscle group, the observed difference between the velocity at 70 and 60% of the maximum measured torque was determined (Fig. 2). The relationship between this change in velocity in radians per second and in millimeters per second suggests that a major determinant of the velocity potential of the muscle groups studied is the number of sarcomeres arranged in series typical for each muscle group (Fig. 4). A similar conclusion was evident when the velocities measured over a range of percents of maximal torques were compared. In general, these data illustrate that the reduction in force potential of a muscle as a result of increasing
FIG.
l
l
HUMAN
MUSCLE
ARCHITECTURE
439
AND FORCE-VELOCITY
2. Observed and estimated torques and forces of knee and ankle extensor and fkxor muscle groups
TABLE
2
1
CSA, cm2
KEa
3
Estimated Moment Am, cm
87
4
Observed Maximum Torque, N-m
4.0
5
Relative Maximal Torquesd
147 (186)’ 116 72 19
1.00
6
7
Observed Maximum Force, N
Specific Tension,’ N cmm2
Expected Force: N
3675 (4631)’ 3314 2769 792
42.2 (53.2)’ 78.9 30.1 46.6
1958
l
8 Expected Force Observed Force,h % 53
9 Relative Force’
1.00
KF 42 3.5 0.62 945 29 0.72 PF 92 2.6 0.39 2070 75 0.60 DF 17 2.4 0.10 383 48 0.17 a KE, KF, PF, and DF are same as in Table 1. b CSA, mean cross-sectional area for each muscle group from 3 cadaver limbs calculated as described in METHODS (from Ref. 36). ’ Values corrected for reported 26% greater torque at 60 than at 30” of knee flexion from 180” (23). Actual torque measurements were made at 30’. d Values normalized to corrected maximal torque of KE (see *). For comparison, values reported by Fugl-Meyer (13) were 1.00, 0.52, 0.60, and 0.19, respectively. e Column 3 divided by column 2, with column 2 converted from centimeters to meters. f Column 5 divided by column 1. g Calculated assuming a specific tension of 22.5 N crnv2 (29) and CSA shown in row 1 of this table (i.e., column 1 X 22.5 N-cm-“). h Ratio of expected force divided by observed force (i.e., column 7 divided by column 5). i Column
8 normalized
to relative
force
of KE.
3. Muscle and fiber length changes in knee extensors and flexors for 90* of knee excursion
TABLE
Muscle Length,* cm
Rectus femoris Vastus medialis Vastus intermedius Vastus lateralis Semimembranosus Biceps femoris Ischial head Femoral head Semitendinosus Sartorius Gracilis
Absolute Muscle Length 4S cm
Fiber Lw$h,t cm
Relative Muscle Length A,$ %
I
II
I
II
I
II
I
II
32.1 33.4
31.2 36.5
26.0 25.4
6.4 7.1 7.0 6.5 .6.5
6.1 7.4 7.0 7.8 4.8
4.7 4.8 4.9 4.9 5.0
5.8 5.7 5.6 5.8 5.0
14.6 14.4 15.9 14.9 19.3
18.5 15.6 14.8 22.8 19.6
31.9 21.6 28.7 40.7 25.3
7.4 10.3 12.6 33.7 17.8
7.9 11.8 15.1 38.2 20.4
3.9 3.9 6.9 3.8 4.0
4.3 3.5 6.3 4.5 5.0
12.4 18.1 24.1 9.3 15.7
11.5 12.6 20.6 10.8 20.0
30.9 37.4 32.9
25.3
37.0 27.7 30.8 41.7 24.9
Data obtained from 2 (I, II) cadaver specimens. * Distance between most proximal and most distal points at which muscle fibers can be observed. Limbs were fixed in a position such that knee was fully extended, ankle was plantarflexed, and hip was in an extended posit Lengths of small fiber bundles (see METHODS). Normalized tion. to a sarcomere length of 2.2 pm (16, 22) as described by Wickiewicz et $ See METHODS for description. al. (36).
velocities will be less in muscles having longer fibers (more sarcomeres in series). DISCUSSION
General features of torque-velocity relationships. Using a velocity-specific afterloading method to test human subjects, Hill (19) concluded that skeletal muscle in vivo performs in virtually the same predictable way as in maximally stimulated muscle preparations. Other reports have supported this conclusion (13, 32, 37). .However, Perrine and Edgerton (24) found that when the variables of muscle length (angle specificity) and duration of effort were controlled, at least for the quadriceps muscle group, the in vivo force-velocity curve was not hyperbolic over the entire range of velocities. That is, the torques at the lowest velocities and under isometric conditions were considerably less than what would be predicted. In addition, the peak torques that occurred at
low velocities were often higher than those generated isometrically. The data in this report demonstrate that lower than expected torques at the lower velocities are also characteristic of the KF, PF, and DF muscle groups. One possible reason for this difference in results at the lower velocities may be the technique of data collection. Ideally, all torques would be recorded at the same muscle length. The recording of the angle-specific torque must be sufficiently distal in the test range so that the maximal tension may be obtained at high test speeds. Because rise time to peak tension in the muscle is relatively constant regardless of the test speeds, the arc length covered in that time must therefore differ at varying velocities. To use the peak torque measure at each speed without considering angle specificity induces the variables of length tension and activation time to the force-velocity curve. The inability to maintain a peak effort for the duration of a relatively long contraction must also be considered as noted previously in METHODS. Two points should be noted regarding the .torquevelocity relationship at the lower velocities. First, inertia can affect the torque-velocity measures (37). However, the torques that differ the greatest from Hill’s (19) predictions occur at the lower velocities when the inertial factors are minimal. A second point concerning the torques at the lower velocities is whether or not the peak torque occurs at 0 rad. s-l or at some low shortening velocity (24). The velocity at which the peak torque occurs appears to be correlated to the percentage of fibers with a high or low alkaline myofibrillar adenosine Ytriphosphatase (ATPase) activity as shown histochemitally (17, 25, 32, 33). Subjects that have the higher proportion of alkaline dark ATPase fibers (type II) tend to produce the highest torques at 0 rads-‘, whereas the maximum torques at 0 rad. s-l are commonly below those that can be produced at speeds slightly greater than 0 rad s-’ if type I fibers predominate (17, 32). Factors related to peak torque. One objective of this study was to determine the role of muscle design in influencing the in vivo maximum torque-velocity relationship. Knowledge of the muscle architecture is necessary to make valid muscle-to-muscle comparisons even within the same subject. Fiber lengths (number of sarl
440
WICKIEWICZ
4. Predicted
TABLE
maximum
1
rates of shortening
2
Longest
No. Sarcomeres, x 10’
Length, mm
3
Fibers b
velocities for knee and ankle extensors and flexors 4
5
6
7
Avg Fibers’ Length, mm
ET AL.
Hill’s Predicted v g rady”
No. Sarcomeres, x 10’
Conversion Factor,’ mm. rad-’
Predicted v mani mm 8-l l
8
Predicted Lx Longest Fibers’ mm4?4,000 sarcomeres-’
9
Predicted KrJu Average Fiber$ mm.s+J,OW sarcomeres-’
77 3.5 69 3.1 12.5 25.2 315 90 102 KE” KF 137 6.2 96 4.3m 11.9 26.9 320 52 74 51 2.3 37 1.7 6.8 16.0 109 48 64 PF 69 3.1 64 2.9 8.1 17.8 144 46 50 DF a KE, KF, PF, and DF are same as in Table 1. bMean fiber lengt h of muscle of each functional muscle group that had longest fibers. c Average of mean fiber lengths for all muscles within functional group. d Fiber lengt h s are normalized to a sarcomere length of 2.2 pm (16, 22) as described by Wickiewicz et al. (36). ’ Column 1 divided by 2.2 pm. f Column 3 divided by 2.2 pm. gSee METHODS and Fig. 3. b KE and KF data were taken from mean values of each muscle group from 2 cadaver samples shown in Table 3 where fiber excursions over a 90” range are shown. Similar data on KF and DF was taken from Ref. 1. i Column 5 X column 6. j Column 7 divided by column 2. ’ Column 7 divi ded by column 4. ’ Average fiber length for KF is 91 mm if femoral head of biceps femoris is included (36). m Average number of sarcomeres (X 10’) for KF is 4.1 if femoral head of biceps femoris is included* (36).
0 CFIG. 4. Difference in observed (rad. s-l) and derived (mm. s-l) velocities of shortening between 60 and 70% peak torque is plotted relative to average fiber length (no. of sarcomeres per fiber) of each muscle group. KE, knee extensors; KF, knee flexors; PF, ankle plantarflexors; DF, ankle dorsiflexors.
KF
0.0
1.0
2.0
# of sarcomereslfiber
3.0
4.0
5.0
(x 10S4)
comeres arranged in series) and mechanical factors must be considered when comparing the in vivo properties of various muscle groups. As noted by Close (9), a common error is to assume that fiber length is similar to muscle length and express velocities in muscle lengths per second. A comparison of the V max of two muscles of equal length but having unequal fiber length would incomctly suggest that the intrinsic V max of the muscle with the shorter fibers would be less than for the muscle with the longer fibers (6, 15, 27). The predicted maximum torque that a muscle can produce is proportional to its physiological cross-sectional area (CSA). In turn, the CSA is proportional to the number of cross bridges arranged in parallel. Based on the architectural data from a previous study (36), the KE muscle group should be capable of producing twice as much force as the KF (Table 2). The PF should produce almost six times the force that the DF can
produce.
In a&&ion,
the PF should have the greatest
potential for tension production of all four muscle groups tested. Because ofthe different joint biomechanics for each muscle group, the observed or predicted maximal torques must be converted to forces using assumed or measured moment arms. An indication of the overall relative effect of these mechanical factors on each muscle group can be seen if it is assumed that the musculature of each group has fundamentally similar tension-producing capabilities when normalized to CSA, i.e., 22.5 N crns2 (29). If the relative assumed CSA and the specific tension of each muscle group were accurate, then the relative moment arms for the KE, KF, PF, and DF would be %8,12.8,3.6, and 5.1 cm, respectively. These values exceed those measurements reported previously (1, 18, 30) and those of the knee flexors and extensors reported here by about twofold. l
HUMAN
MUSCLE
ARCHITECTURE
AND
FORCE-VELOCITY
Measurements from the two cadaver limbs studied and data from the literature (7) predict ~13% longer KE than KF moment arms at the test positions, 30 and 70” of knee flexion, respectively. The mechanical advantage in the knee flexors for producing torques is nearest its optimal at 70”, whereas that for the knee extensors is at 60" (23). Another possibility for the disproportionately high torque observed in the KF could be an overestimation of its moment arm. The observed peak torques (angle specific) reflect the torques that would be expected, given a similar force potential per CSA of the muscle groups and the average moment arms shown in Table 2. If human skeletal muscle has the same force potential as other mammalian muscle, i.e., 22.5 N crnB2 (29), then the forces observed for all four muscle groups were about twice the predicted value (Table 2). This might be expected because the CSA’s were derived from cadaver materials obtained from older subjects and were undoubtedly reduced in volume by the fixative solutions. In contrast, the torque measurements were obtained from young healthy subjects: In spite of the probability that the explanation above can account for a significant part of the difference between the observed and predicted forces, a more extensive assessment of CSA and moment arms will be necessary to determine the specific tension of human muscle voluntarily activated and that activated in situ by maximal stimulation. Given that at the moderate velocities the torque-velocity relationships in the lower limb are similar to Hill’s prediction (19), then the predicted peak torques should be perhaps as much as double the observed peak torques at the lower velocities (Fig. 3). Whether the same force can be produced by neural activation or by artificial electrical stimulation of human skeletal muscle is unknown. Recently, Belanger and McComas (4) concluded on the basis of various combinations of voluntary effort and’electrical stimulation that under isometric conditions, the DF (but not the PF) can be maximally activated by the nervous system. Although our data suggests that the activation at zero velocity is less than maximum for both muscle groups, the percent of maximum activation is higher in the DF in comparison to the PF. Therefore, the ability to approach the maximum force potential when neurally activated may differ among muscles or muscle groups (4,5). One important assumption that must be made to relate the in vivo and in situ force-velocity data is that the level of activation of the antagonistic muscle group is not seriously affecting the net torque. Our intuitive impression is that this is not the explanation for the unexpectedly low torques recorded at the slow velocities because 1) the peak torque is similar whether the maximum effort is brief (Cl s) or more sustained (a few seconds), and 2) the level of activation by the CNS is basically determined before the leg is moved at a high or low velocity. Although Wilkie (37) attempted to gain some insight into this problem using surface electromyography, he was well aware of its limitations as a measure of ,assessing the level of activation, particularly when the duration of the electromyographic signal necessarily varied with the speed.
441 Factors related to peak velocity. Assuming similar intrinsic biochemical properties, the shortening velocities of different muscles should reflect their fiber lengths, i.e., the number of sarcomeres in series (6). Based on this data (Table 4), the KF should have the highest, and the PF, the lowest maximum linear velocities. A relationship between the number of sarcomeres arranged in series and the calculated Vmal is suggested in Fig. 4. The Vmax of the knee extensors appears to be disproportionately high. Because the calculated Vmax is projected considerably beyond that observed, the change in velocity between torques of 70 and 60% of the observed maximum were also related to the number of sarcomeres in series (Fig. 3). In this region of the curve, the torquevelocity relationship is in the most predictable range, i.e., it is far enough from the lower velocities to be unaffected by the apparent “inhibitory” factors present at less than about 0.80 rad. s-’ and it is at an observed rather than an extrapolated velocity. The change in velocity from 70 to 60% peak torque is closely related to the number of sarcomeres in series and thus further supports the idea that fiber length is a major factor in dictating shortening velocity (Fig. 4). To determine the intrinsic velocity characteristics, i.e., independent of architectural features, Vmax values were standardized per 1,000 sarcomeres (Table 4). To compare the velocities for each muscle group, some assumptions were made and certain constraints were accepted. Theoretically, the Vmax should be a function of the longest fibers of a muscle group, but practical considerations, such as the large mass of the rotating segment and joint constraints, may result in an average fiber length being the more accurate choice as a standard of comparison. Therefore, the predicted Vmax was calculated based on both standardizing procedures as shown in Table 4. Another underlying assumption in the calculation of the intrinsic Vmax is in determining which muscles contribute to the movement studied. This is particularly true in the DF where the mechanics of the muscle-to-bone attachments appear to be the most complex. The tibialis anterior comprises half of the CSA of the muscle group but is primarily an inverter of the ankle. Similarly, the posterior calf musculature is complex. Muscles that normally produce inversion (supination) and eversion (pronation) torques may assist in plantarflexion in the confines of the bilateral rigidity of the footplate. For simplicity, only the triceps surae was considered in the calculation of maximum torques, forces, and velocities for the PF group. It must also be assumed that the involved muscles of a group act as a single functional unit. Finally, the conversion from angular to linear velocities by examining the joint mechanics and changes in muscle length in a few cadaver samples further limits the accuracy of the velocity estimates. In spite of these assumptions and limitations, the linear velocities of the KF, DF, and PF are similar when expressed per 1,000 sarcomeres and based on the muscle of each muscle group with the longest fibers (Table 4). The intrinsic velocity of the KE was much greater than for the other muscle groups. The Vmax of the longest fibers expressed in millimeters per second per 1,000
442 sarcomeres for the four groups are 90, 52, 48, and 46 compared with 13 and 36 for cat slow and fast muscle (29) and 30 for human elbow flexors (3). Practical considerations. The shape of the force-velocity curve for the ankle plantarflexors is of particular interest. Animal studies (29,34) have shown the inability of the soleus to contribute significant tension to highspeed shortening. Although human studies preclude direct in vivo measurements of simple muscle function, it is interesting to note that dramatically less tension is produced during high-speed contractions. At 2.1 rad. s-l, an angular velocity less than that incurred at a usual walking pace (30), the PF have lost 65% of their peak torque potential (Fig. 2). At the same speed, the DF, KE, and KF have lost 45,20, and 30%, respectively. The large decrease in PF torque at these velocities may be related to the extremely short fibers (6% of muscle length) (36) and relatively high slow-twitch fiber composition (10) of the soleus. That is, the soleus appears to be designed to maximize force production at very slow shortening velocities and in lengthening contractions. The 90” flexed position of the knee places the PF at some mechanical disadvantage due to its shortened length. However, in this position, the gastrocnemius is shortened only 6.4% of its length relative to full extension (0’) (18). In the present study, three subjects were tested for peak torque-velocities of the PF with the knee in full extension and at 90” of flexion. The mean peak
WICKIEWICZ
ET AL.
torque of the PF was 113 N*m when the knee was extended and 126 N*m when it was flexed. Consequently, knee position appears to have a small effect on the forceproducing properties of the ankle plantarflexors, at least in the confines of our testing method. In addition, the relative torque -vel .ocity relationship of the ankle musculature would be minimally affected by the knee position because the muscle length at which the torque was taken was constant for all tests of a particular muscle
grOUP*
In summary, it is apparent, at least at slow speeds of shortening in the human lower limb, that skeletal muscle contraction in vivo does not follow the force- 8velocity relationship that would be predicted when the level of stimulation is held constant under varying loading conditions. Some inhibitory or disfacilitating mechanism may be responsible for the difference in response from isolated muscle preparations (24). Muscle fiber length and CSA appear to determine the performance potential of a functional muscle group to a major extent. These results permit the expression of forces and velocities in units that permit a valid comparison across muscles within the same or other species. We thank Sylvia Goodwin for typing the manuscript. This work was supported in part by National Institutes of Health Grant NS-16333 and Biomedical Grant 5-507RR7009-13. Received 26 August 1983; accepted in final form 5 March 1984.
REFERENCES 1. AMBAGTSHEER, J. B. T. The function of the muscles of the lower leg in relation to movements of the tarsus. An experimental study in human subjects. Acta Orthop. Stand. Suppl. 172: l-196,1978. 2. ARIANO, M. A., R. B. ARMSTRONG, AND V. R. EDGERTON. Hindlimb muscle fiber populations of five mammals. J. Histochem. Cytochem. 21: a-55,1973. 3. BARANY, M. ATPase activity of myosin correlated with speed of muscle shortening. J. Gen. Physiol. 50: 197-218,1967. 4. BELANGER, A. Y., AND A. J. MCCOMAS. Extent of motor unit activation during effort. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 51: 1131-1135,198l. 5. BIGLAND-RITCHIE, B. EMG and fatigue of human voluntary and stimulated contractions. In: Human Muscle Fatigue: Physiological Mechanisms. London: Pitman, 1981, p. 130-156. 6. BODINE, S. C., R. R. ROY, D. A. MEADOWS, R. F. ZERNICKE, R. D. SACKS, M. FOURNIER, AND V. R. EDGERTON. Architectural, histochemical, and contractile characteristics of a unique biartitular muscle: the cat semitendinosus. J. Neurophysiol. 48: 192201,1982. 7. BRUUNSTROM, S. Clinical Kinesiology. Philadelphia, PA: Davis, 1966. 8. CAIOZZO, V. J., J. J. PERRINE, AND V. R. EDGERTON. Traininginduced alterations of the in vivo force-velocity relationship of human muscles. J. Appl. Physiol.: Respirat. Environ. Exercise Physid. 51: 750-754,198l. 9. CLOSE, R. I. Dynamic properties of mammalian skeletal muscles. Physiol. Rev. 52: 129-197,1972. 10. EDGERTON, V. R., J. L. SMITH, AND D. R. SIMPSON. Muscle fiber type populations of human leg muscles. Histochem. J. 7: 259-266, 1975. li. FAULKNER, J. A., D. R. CLAFLIN, K. K. MCCULLY, AND D. A. JONES. Contractile properties of bundles of fiber segments from skeletal muscles. Am. J. Physiol. 243 (CeZZPhysiol. 12): C66-C73, 1982. 12. FENN, W. O., AND B. S. MARSH. Muscular force at different speeds of shortening. J. Physiol. London 85: 277-297,1935. 13. FUGL-MEYER, A. R. Maximum isokinetic ankle plantar and dorsal
14. 15. 16. 17.
18. 19. 20. 21. 22. 23.
24. 25.
flexion torques in trained subjects. Eur. J. Appl. Physiol. Occup. Physiol. 47: 393-404,198l. FUGL-MEYER, A. R., K. H. MILD, AND J. HORNSTEN. Output of skeletal muscle contractions. A study of isokinetic plantar flexion in athletes. Acta Physiol. Scand. 115: 193-199,1982. GANS, C., AND W. J. BOCK. The functional significance of muscle architecture: a theoretical analysis. Ergeb. Anut. Entwicklungsgesch. 38: 115-142, 1965. GORDON, A. M., A. F. HUXLEY, AND F. J. JULIAN. The variation in isometric tension with sarcomere length in vertebrate muscle fibers. J. Physiol. London 184: 170-192,1966. GREGOR, R. J., V. R. EDGERTON, J. J. PERRINE, D. S. CAMPION, AND C. DEBUS. Torque-velocity relationships and muscle fiber composition in elite female athletes. J. Appl. Physid.: Respirat. Environ. Exercise Physiol. 47: 388-392, 1979. GRIEVE, D. W., P. R. CAVANAGH, AND S. PHEASANT. Prediction of gastrocnemius length from knee and ankle joint posture. In: Biomechanics IV. Baltimore, MD: University Park, 1978, p. 405-412. HILL, A. V. The heat of shortening and the dynamic constants of muscle. Proc. R. Sot. London Ser. B 126: 136-195,1938. HILL, A. V. First and Last Experiments in Muscle Mechanics. London: Cambridge Univ. Press, 1970. JOHNSON, M. A., J. POLGAR, D. WEIGHTMAN, AND D. APPLETON. Data on the distribution of fiber types in thirty-six human muscles. An autopsy study. J. Neural. Sci. 18: ill-129,1973. JULIAN, F. J., AND M. R. SOLLINS. Regulation of force and speed of shortening in muscle contraction. Cold Spring Harbor Symp. Quunt. Biol. 37: 635-646,1973. MURRAY, M. P., J. M. BALDWIN, G. M. GARDNER, S. B. SEPIC, AND W. J. DOWNS. Maximum isometric knee flexor and extensor muscle contractions: normal patterns of torque versus time. Phys. Ther. 57: 637-643,1977. PERRINE, J. J., AND V. R. EDGERTON. Muscle force-velocity and power-velocity relationships under isokinetic loading. Med. Sci. S’rts 10: 159-166,1978. PHILLIPS, C. A., AND J. S. PETROFSKY. Velocity of contraction of skeletal muscle as a function of activation and fiber composition:
HUMAN
MUSCLE
ARCHITECTURE
AND
FORCE-VELOCITY
a mathematical model. J. Z&hem. 13: 549-558,1980. 26. POWELL, P. L., T. L. WICKIEWNZ, R. R. ROY, J. PERRINE, AND V. R. EDGERTON. Torque-velocity and architectural relationships of knee and ankle flexors and extensors in humans. Sot. Neurosci. Abstr. 8: 330,1982. 27. SACKS, R. D., AND R. R. ROY. Architecture of the hindlimb muscles of cats: functional significance. J. Mo@oL 173: 185-195,1982. 28. SALTIN, B., J. HENRIKSSON, E. NYCAARD, P. AND-EN, AND E. JANSSON. Fiber types and metabolic potentials of skeletal muscles in s&ntary man and endurance runners. Ann. NY Ad. Sci 301329,1977. 29. SPECTOR, S. A., P. F. GARDINER, R. F. ZERNICKE, R. R. Rev, AND V. R. EDGERTON. Muscle architecture and the force-velocity characteristics of the cat soieus and medial gastrocnemius: Implications for motor control. J. Neurophysid. 44: 951-960,198O. 30. SUTHFZUAND, D. H., L. COOPER, AND D. DANISL. The role of the ankle plantarflexors in normal walking. J. Bone Jt. Surg. 62k 354-363,mo. 31. THORSTENSSON, A. Muscle strength, fibre types and enzyme ac-
443 tivities in man. Acta Physid Scand. Supple 443: l-45,1976. 32. THORSTENSSON, A., G. GRIMBY, AND JXULSSON. Force-velocity relations and fiber composition in human knee extensor muscles. J. AppL Physid 40: 12-16,1976. 33. TUWNYI, J., P. AFOR, AND G. FEKETE. Force-velocity-power characteristics and fiber composition in human knee extensor muscles. Eur. J. Ap& Physiol. &cup. Physid 48: 3319343,1982. 34. WALMSLEY, B., J. A. HODGSON, AND R. E. BURKE. FOWS pmduced by medial gastrocnemius and soleus muscles during locomotion in freely moving cats. J. Neumphysiol. 41: 1203-1216,1978. 35. WICKIEWICI, T. L., V. R. EDGERTON, R. R. ROY, J. F%RRINE, AND P. POWELL. Human leg muscle architecture and force-velocity properties. A&&. Sci Sports Exercise 14: 144,1982. 36. WICKIEWICZ, T. L., R. R. ROY, P. L. POWELL, AND V. R. EDGERTON. Muscle architecture of the human lower limb. C&a. Orthup. Reiat. Res. 179: 317-325,1983. 37. WILKIE, D. R. The relation between force and velocity in human muscle. J. Physid London 110: 249-280,195O.
