CopyrIght

PII: SOO21-9290(96)00094-2

.I. Bmnechanics, Vol 30. No. 1. pp 63-70. 1997 !:s 1996 Elsewer Science Ltd. All rights reserved Printed in Great Britain 0021-9290:97 $17.00 + 00

ELSEVIER

MUSCLE

AND TENDON FORCE-LENGTH PROPERTIES THEIR INTERACTIONS IN I/IV/o

AND

David Hawkins*? and Michael Beyt *Department of Exercise Science, tBiomedica1 Engineering Graduate Group, University of California, Davis, CA 95616, U.S.A. Abstract-Many attempts have been made to model muscle and/or muscleetendon (MT) behavior for the purpose of predicting muscle forces in viuo. One important parameter often considered in such models is muscle length. This study was conducted to evaluate (1) the force-length properties of a MT complex and the range of these properties over which the muscle operates in uiuo, and (2) the effect that tendon compliance has on a muscle’s forct4ength behavior. The rat tibialis anterior (TA) MT complex was used as the experimental model. Muscle and tendon lengths as they occurred in the body during ankle joint motion ranging from 20” to 90” of flexion were determined for both passive and active muscle. Force-length (FL) properties for the tendon, passive muscle, and active muscle were determined from a partially isolated MT preparation. Results suggest that during movement involving a normal range ofjoint motion, the TA muscle operates within an optimal region of its FL relationship, generating minimal passive force and nearly constant active force. However, the passive force increases rapidly for extreme foot extension while the active force decreases for both extreme foot flexion and extension. For the rat TA muscle, the effect of tendon compliance does not alter the active force generated by the muscle over a normal joint range of motion. However, tendon compliance does effect the muscle’s ability to generate force at the extremes of joint motion. Copyright cc) 1996 Elsevier Science Ltd. Keywords:

Muscle; Tendon; Interactions.

the muscle, its inherent rest length, the orientation of the joints over which the muscle crosses, and the compliance of its associated tendon. Relatively few studies have been conducted which define the range of lengths over which muscles operate in vivo (Banus and Zetlin, 1938; Lieber and Boakes, 1988; Herzog et al., 1991; Herzog et al., 1992a, b; Stolov, 1966; Zuurbier et al., 1994), and the effects that tendon and/or aponeurosis compliance have on muscle length in vivo (Ettema et al., 1990; Ettema and Huijing, 1989; Griffiths, 1991; Lieber et al., 1992; Morgan et al., 1978; Rack and Westbury, 1984; Zuurbier et al., 1994). The objectives of this study were (1) to determine the force-length (FL) properties of a muscle-tendon (MT) complex and the normal range of these properties over which the complex operates in vim, and (2) to evaluate the effects of tendon compliance on muscle length in vivo. These objectives were achieved through testing of the rat tibialis anterior (TA) MT complex.

INTRODUCTION

Studies conducted over the past century have shown that both the passive and active forces generated by a muscle are affected by the muscle’s relative length. Passive force increases in an exponential fashion as the muscle is stretched beyond its unstressed length (Buchthal, 1942; Buchthal and Kaiser, 1951; Buchthal and Lindhard, 1939; Ramsey and Street, 1940; Woittiez et al., 1983). An active muscle elicits a parabolic force-length (FL) relationship. The force generated by the active contractile material is greatest over a limited range of muscle lengths and decreases for lengths outside this range (Banus and Zetlin, 1938; Buchthal, 1942; Buchthal and Kaiser, 1951; Buchthal and Lindhard, 1939; Evans and Hill, 1914; Gareis et al., 1992; Gordon et al., 1966; Herzog et al., 1992; Huxley, 1969; Huxley and Hanson, 1954; Huxley and Niedergerke, 1954; Lieber et al., 1992; Ramsey and Street, 1940; Woittiez et al., 1983). Based on the results from these studies and in an effort to predict muscle forces in vivo, many attempts have been made to model the FL behavior of muscle (Bahler, 1968; Gordon et al., 1966; Huijing and Woittiez, 1985; Otten, 1988; Pell and Stanfield, 1972; Woittiez et al., 1984; Zajac, 1989). However, to predict the static force generating potential of a muscle in vivo it is necessary to know not only the FL properties of the muscle, but also the range of lengths over which the muscle operates in viva This range of lengths is dependent on the force generated by

METHODS

The work station used to collect the data for this study consisted of several components described in detail elsewhere (Hawkins and Bey, 1994). Briefly, the hardware included an arbitrary waveform generator (Model 75 supplied by WaveTek), an ergometer lever system (Model 305B supplied by Cambridge Technologies), a videobased motion analysis system (Motion Analysis Corporation), and a microcomputer containing a Lab Master DMA data acquisition board (Scientific Solutions). Software developed with Turbo Pascal 6.0 and ASYST 4.0 controlled the nerve stimulator, ergometer and simultaneously acquired muscle force data.

Receioed in jinalform 17 April 1996. Address correspondence to: David Hawkins, Ph.D., Department of Exercise Science, University of California-Davis, Davis, CA 95616, U.S.A. 63

63

D. Hawkins

The work station provided a robust environment for controlling and sampling the variables of interest. The Cambridge lever system provided suitable resolution and accuracy for force and position detection. The lever system has a resolution of 1 pm with a linearity of 0.1%. The force transducer has a resolution of 100 mg with a linearity of f 0.2%. The analog to digital converter was the limiting factor in quantifying force and length. It provided a force and length resolution of 250 mg and 5 pm, respectively. The Wave Tek arbitrary function generator was appropriate because it provided a physiological signal for stimulating the muscle’s nerve. The optical motion analysis system provided both advantages and disadvantages compared to other length detection approaches. Two advantages of this approach were that it detected length changes along the muscle complex rather than just across the gross MT complex, and it was a noncontact method which provided a digital signal that was stored and manipulated within a computer. One disadvantage of the Motion Analysis System was that small black silicone markers had to be secured to the surface of the MT complex, thus, only surface strains could be quantified. The work station described above was used to test the tibialis anterior (TA) MT complex of 15 female Holtzman rats having an average mass of 310 f 24 g. The animals were maintained in a room at 24 $ 2°C in which the light was artificially controlled (12 h light, 12 h dark). They were provided food (rat chow) and water ad libitum. Prior to conducting this study, all experimental procedures were approved by an animal testing review board. The rat was anesthetized by an intraperitoneal injection of pentobarbitone sodium (50 mg kg- ’ body weight). Tissue covering the TA was carefully removed so as not to disturb the nerve supply provided to the TA. The nerve innervating the TA was exposed and a small electrode cuff was attached to it approximately 1 cm proximal from the neuromuscular junction. The nerve was crushed near the hip to prevent afferent responses. The signal used to stimulate the nerve innervating the TA consisted of a bipolar 5 V peak-to-peak amplitude of 50 11s dura-

I

and M. Bey

tion repeated every 4 ms. The stimulation signal was initiated 10 ms prior to the recording force. An illustration of the muscle force profile associated with a given 250 ms stimulus is shown in Fig. 1. Three small black silicone markers were located on the MT complex. one at the proximal end of the muscle, another over the MT junction, and the third over the tendon-bone junction. The entire leg, with all muscles and primary connective tissue intact, was held in front of a video camera with the foot in both a fully extended position (approximately 20’ of flexion with 0” being full extension) and then in a 90 flexed position. For both joint angles the TA was recorded on video tape in both a passive state and an active state. An illustration of the markers and foot positions used in this procedure is given in Fig. 2. Next, the distal end of the TA was dissected free with a small section of bone retained for use in attaching the MT complex to the lever arm. The partially intact TA was again positioned in front of the video camera and the tibia secured to a fixture to minimize movement of the limbs during testing. A saline drip system was used to maintain the TA moist at all times. All mechanical tests were conducted at room temperature, 24 ) 2’.C. The force generated by the partially intact TA was determined during a passive test and a series of active tests. During the passive test, the non-active MT complex was stretched 10 mm at a lever arm rate of 2.0 mm s- ‘. Force, lever arm position, and video data were collected at 60 Hz. During the active test, the muscle was stimulated isometrically for 250 ms at 0.2 mm increments over the same 10 mm range used in the passive test. Each stimulation was separated by a 10 s delay. The video data were collected continuously at 60 Hz over the entire series of active tests. The force and lever arm position data were collected at 60 Hz for 300 ms at each lever arm position. The muscle stimulation signal characteristics were the same as those described for the tests conducted on the intact muscle. The distances between contrast markers located on the muscle and tendon were determined and used to evaluate the relative stiffness of the passive muscle, active muscle, and tendon.

time (ms) I

0.15

Time

(s)

Fig. 1. An illustration of the signal used to stimulate the nerve along with for a 250 ms stimulation period. The force profile is shown in the larger profile given as the inset. The nerve was stimulated 10 ms prior to the stimulation signal consisted of a bipolar 5 V peak-to-peak amplitude of 50

the resulting muscle force profile illustration with the stimulation recording of muscle force. The ps duration repeated every 4 ms.

Muscle and tendon force-length properties

Rat Lower

65

Limb

Tibialis

Anterior

Muscle

90’

20’

of flexion

of flexion

Fig. 2. An illustration of the tibialis anterior muscle-tendon complex with contrast markers in place during in uioo testing with the ankle flexed 90” and fully extended to 20” of flexion.

MT units often perform eccentric contractions during daily usage and because the force generated during such contractions depends on the interaction of the muscle and the tendon a series of eccentric contractions were conducted on the rat TA muscles. The muscle was contracted isometrically from a length less than the optimal length (defined as the muscle length at which maximum active force was developed) and then stretched. Four stretch amplitudes (1, 2, 3, and 4 mm) were imposed on the MT complex at rates of 1, 10, and 100 mms- ‘. Muscle and tendon length changes associated with each stretch were determined using the video system. The two primary steps involved in the data analysis included the determination of muscle and tendon length from the video data and the consolidation of these data with the muscle force data. Muscle length was defined as the distance between the center of the markers located over the MT junction and the proximal muscle. Tendon length was defined similarly as the distance between the center of the markers located over the MT junction and the tendon-bone junction. Passive and active muscle lengths for the intact TA were determined for both the fully extended foot position (approximately 20” of flexion) and the 90” flexed position. These data were used as reference lengths to identify the range of muscle lengths over which the muscle operates in vivo. The FL characteristics of the muscle were determined from the results of the passive and active tests conducted on the partially intact MT complex.

RESULTS

The average mass of the TA muscles was 531 + 69 mg. The average gross length of the muscles measured from

the proximal bony attachment to the distal myotendon junction was 2.12 + 0.25 cm. The distance between contrast markers located on the muscle belly varied between 1.4 and 2.0 mm. Because the distance between contrast markers varied and did not represent true muscle or tendon length, muscle and tendon strain were determined [as shown in Equation (l)] to provide a means of comparing data between MT units. Tissue strain = (L - J&)/L,,

(1)

where L is the instantaneous muscle or tendon length (calculated from the distance between contrast markers) and LO the muscle or tendon length associated with the onset of passive force development (calculated from the distance between contrast markers). The average passive muscle strain in uivo ranged from 39% for the foot in full extension (approximately 20” of flexion) to 18% for the foot flexed to 90”. The average active muscle strain in vivo ranged from 3 1 to 18% for full extension and 90” of flexion, respectively. The normal range of ankle motion observed for the rats moving in their cages was between 35” and 135” of flexion, determined based on simple angle measurements taken from sagittal plane video images (the 35” value corresponded to the rat standing on its hind limbs while attempting to climb the cage wall, the 135” value corresponded to the rat laying with its feet positioned under its body). In a separate study involving rat gait the average ankle range of motion was reported to be between 50” and 140” (Gruner et al., 1980). Thus, the length data taken from the intact MT complex in this study represents a very extended position and only a partially flexed position relative to the normal joint range of motion (ROM). Muscle length changes associated with this greater ROM are considered in the discussion.

66

D. Hawkins

Average results from the intact MT complexes, and the partially intact passive and active tests are illustrated in Fig. 3. Shown in A are force-strain results for the tendon obtained from the passive tests. The strain level at which the tendon force began to increase rapidly for increased strain levels varied between 2 and 12% approximately. Passive forces in excess of 500 mN were recorded over this strain range. Shown in B are force-strain results for the muscle obtained from the passive tests. The strain level at which the muscle force began to increase rapidly for increased strain levels varied between 25 and 35% approximately. These strain values were 2-10 times greater than those of the tendons. Shown in C are the results from the active and passive series of tests. Nerve damage or stimulation problems were evident in four specimens and hence were not included in this part of the analysis. Total, active, and passive force profiles follow the expected trends with the active force increasing for small strains, remaining fairly constant for higher strains and then decreasing for even higher strains. Active force was calculated by subtracting the passive force from the total force. The total muscle force had a plateau for muscle strains between 10 and 30%. The intact muscle’s passive and active muscle strains are identified with small vertical lines, for both the foot fully extended and flexed to 90” (passive muscle strains are shown in B and active muscle strains in C). An illustration of the interaction between muscle and tendon lengths (for a single muscle) as a function of MT length and the mode of action of the muscle is given in Fig. 4. The total MT length during stimulation was less than that prior to stimulation due to deformation of the bone and insertion sites. The important point to observe in Fig. 4 is that the TA tendon acts as a rigid structure as indicated by the fact that its length changed very little as the muscle went from a passive to an active state. Further, its length changed very little during the eccentric contractions in which the force nearly doubled. This implies that as the muscle is activated and begins to develop force the tendon stretches a small amount but then becomes quite stiff and resists further deformation. Illustrated in Fig. 5 are the average length changes incurred by the muscle and tendon during eccentric contractions of different stretch amplitude and stretch velocities. The imposed MT stretch amplitudes are shown along the horizontal axis and grouped according to the MT stretch rate. The average stretch amplitudes incurred by the muscles and tendons are indicated along the vertical axis. In every trial the stretch induced in the MT complex was taken up primarily by the muscle (considering all the trials, approximately 96% of the MT length change occurred in the muscle). Illustrated in Fig. 6 are the effects that a compliant tendon have on the force generating potential of one TA muscle in uivo. For purposes of comparison, a rigid tendon was modeled with a length equal to the tendon length under zero load. The force generated by a muscle having a rigid tendon is similar to that of a muscle with a compliant tendon over the normal ROM experienced in vivo, however, the force profiles are different at the extremes of motion. During full extension, the compliant tendon allows greater motion prior to the rapid increase in passive force. During extreme flexion. the compliant

and M. Bey

tendon reduces the force generating muscle.

potential

of the

DISCUSSION

The total force generated by a skeletal muscle is the result of both passive and active force components. The passive force component is primarily dependent on the muscle’s length while the active component is dependent on the muscle’s length, shortening velocity and level of neural activation. To understand how a muscle functions within the body, and to predict its behavior, the relationships between muscle force and each quantity mentioned above must be known along with reasonable values for each quantity experienced in vivo. The objectives of this study were to study one of these quantities (muscle length) and (1) to determine the FL properties of a MT complex and the normal range of these properties over which the complex operates in viva and (2) to evaluate the effects of tendon compliance on muscle length in GPO. Experimental

model and limitations

The experimental model used in this study was the rat TA muscle. This model allowed the determination of both passive and active muscle and tendon lengths during physiological limb movements. It also allowed the structural properties of the partially isolated muscle and tendon to be determined. Such testing is not practical in humans and can only be achieved through the use of an animal model. The limitation of the model is that it represents a single muscle which may elicit mechanical responses which are not representative of other muscles from the same species or from humans. The use of video to determine muscle and tendon strains had a few limitations. One limitation was that only surface strains could be monitored. Another limitation involved the determination of marker centroids. During a contraction the muscle belly would move causing the contrast marker to distort slightly and/or its illumination to change. Associated with these changes could be a 0.2 mm error in identifying the centroid of the marker (one pixel fluctuation with a calibration factor of 0.20 mm per pixel gives an error of 0.2 mm). In the worst case condition muscle or tendon length estimations could be in error by a total of 0.4 mm (if both markers centroids

Fig. 3. Muscle and tendon force-strain properties. The passive force-strain curves for the tendons are shown in A. The passive force-strain curves for the muscles are shown in B. The total, passive, and active muscle force-strain curves are shown in C. The passive components of the force-strain curves were obtained from the passive tests, the total force curves from the active tests, and the active component of the curves were calculated by subtracting the passive force from the total force. The intact muscle’s passive strains are identified by the vertical lines in B. The intact muscle’s active strains are identified by the vertical lines in C. In both B and C the vertical lines represent both the foot fully extended (20” of flexion) and flexed to 90”. The normal range of rat ankle motion is roughly 35”P135” of flexion. The additional 45” of flexion would cause the vertical lines representing passive and active in uiuo lengths to shift to the left approximately 6% and 1 1 %, respectively. Under normal physiological conditions the TA operates along the toe-region of the passive force-strain curve and the plateau region of the active force-strain curve.

Muscle and tendon force-length properties

N=lS

strain

67

(% )

A.

15 N=15

-5 N=ll

c.

m

strain

5

10

(Oh)

15

muscle

m

strain

25

(%)

30

35

40

D. Hawkins and M. Bey

2.4

.

4cm l .

_I-3.2

I _-._.

_--

-- 1.2

---

~ m-m I -m-T’3.4 3.5

3.3

.

-Cl 3.7

3.6

passive MT length (cm) -passive force 0 total force o passive Mscle A a&e

#endon

+ active force l eccentric force o tendon length for passive muscle x tendon length for active muscle

kngth length length after active

nuSCk?

stretch

Fig. 4. An illustration of muscle and tendon lengths along with muscle-tendon (MT) force for passive, isometric and eccentric MT action. Plotted along the horizontal axis is the MT length at the initiation of muscle stimulation. The total MT length during stimulation was less than prior to stimulation due to deformation of the bone and insertion sites. It is evident that for this MT complex the tendon acted as a very stiff structure for all modes of MT action.

4-

strvel

= 1 mm/s

strvel=

str WI = 100 mmk

10mmls

T

3.5 3 2.5 2 1.5 1 0.5 0

-0.5 wa

1

2

3

4

5

6

7

a

9

10

11

12

MT stretch amp (mm)

Fig. 5. Muscle and tendon length changes during stretch of an active MT complex. Stretch amplitudes varying from I to 4 mm were imposed on a MT complex at rates of 1, 10, and 100 mm s- ‘. The stretch amplitude was accommodated primarily by the muscle in all cases. The negative length changes obtained for some of the trials are a result of the marker movement artifact. There were no apparent strain-rate differences across the three stretch rates used.

were in error by 0.2 mm). Errors of this type are evident in Fig. 5 for the trials in which the tendon was found to shorten by O-O.2 mm while the MT complex lengthened. The activation protocol did not elicit the maximum force expected for the muscles tested, but the forces recorded were probably representative of the forces that might be developed by these muscles during daily activities. Though the force profiles illustrated in Fig. 3 followed the expected trends the stimulation procedures did not elicit the maximum force potential predicted for a given muscle based on its muscle mass and architecture. It was estimated that the TA muscles used in this study should generate a maximum isometric force of approximately 8 N (based on a specific tension of 22.5 N cm-‘, an

average fiber length equal to 70% of the muscle length, and an average muscle volume of 0.54 cm3). The maximum forces actually recorded ranged from 2 to 4 N or 25-50% of the maximum expected. Thus, the stimulation procedure did not elicit complete motor unit recruitment. These results were consistent and repeatable throughout an experiment. Several isometric force checks were performed throughout the testing to ensure that fatigue was not a factor. Any muscles that demonstrated force changes were not included in the analysis. We believe that the nerve cuff did not make appropriate contact with the nerve to elicit complete motor unit recruitment. The incomplete motor unit recruitment created maximum muscle forces (25-50% of the expected isometric

69

Muscle and tendon force-length properties

2

2.2

2.4

2.6

2.8

3

3.2

3.4

MT length (cm) Fig. 6. The effectsof tendon compliance on the force generating potential of a single tibialis anterior muscle in I%O. For purposes of comparison, a rigid tendon was modeled with a length equal to the tendon length under zero load. Tendon compliance does not affect the muscle force over the normal range of ankle motion, however, it does have an effect at the extremes of motion. During full extension, the compliant tendon allows greater motion prior to the rapid increase in passive force. During extreme flexion. the compliant tendon reduces the force generating potential of the muscle.

maximum) that were probably representative of the forces that these muscles would actually generate in uivo during daily usage. Force-length properties in vivo

The foot ROM examined in this study was 20”-90” of flexion, however, as mentioned earlier the normal ROM of the rat ankle is approximately 35”-135” of flexion. The additional range of flexion angles could not be monitored in this study because the foot obscured the markers from the video camera for flexion angles greater than 90”. However, based on manual measurements of intact MT complexes the additional flexion from 90” to 135” would cause the average minimum passive and active muscle strains in vivo to be 6% and 11% less, respectively. It is evident from Fig. 3 and the normalized lengths just cited, that very little passive force and nearly constant total force is developed over the normal ROM. Outside of this range, the force decreases for joint flexion, and increases rapidly for joint extension. The total force generated by the TA muscle remains near its maximum value over the foot’s normal ROM. The nearly constant total force maintained as the foot approached full extension resulted from a decrease in the active force which was offset by an increase in the passive force. Similar results were found by Lieber and Boakes (1988) for frog semitendinosus muscles, however, different results were found by Banus and Zetlin (1938) for the gastrocnemius muscle of the cat and frog, and Herzog et al. (1992a, b) for the cat soleus, gastrocnemius, and plantaris muscles. These muscles were reported to operate along the ascending and plateau portions of the active FL curve in viuo. The differences in the in uiuo FL operating range of these muscles compared to the rat TA and frog semitendinosus may be due to differences in muscle architecture and the functional utilization of these muscles.

Eficts of tendon compliance to force-length properties in vivo

The benefit of tendon compliance to muscle function is not readily apparent from the results of this study. For the rat TA muscle, tendon compliance does not alter the force generated by the muscle over a normal joint ROM. However, it does effect the muscle’s ability to generate force at the extremes of joint motion; allowing greater joint extension before large passive muscle forces are developed, and reducing the muscle force potential for extreme joint flexion (similar conclusions were drawn by Lieber et al., 1992, for the frog semitendinosus muscle). During eccentric contractions initiated from an isometric contraction, the tendon acted as a very stiff structure and any imposed MT length change was accommodated primarily by a length change in the muscle. These data suggest that tendon compliance plays a minimal role in muscle function for isometric or simple eccentric contractions of the rat TA. It should be noted that only gross muscle and tendon compliance were considered. No attempts were made to quantify aponeurosis compliance. The TA muscle has a relatively distinct myotendinous junction without a large aponeurosis, thus, the effects of aponeurosis compliance should be minimal. The ratio of tendon slack length to muscle rest length has been used by Zajac (1989) to characterize the compliance of MT units. The larger this ratio, the more compliant the MT unit. Though fiber lengths were not directly measured in this study, assuming them to be 60-70% of the muscle length (based on data from larger male Wistar rats-personal communication, P. A. Huijing, 1995) yields an average tendon length to muscle fiber length ratio for the TA of about 1.2. These ratios for the frog semitendinosus, cat soleus, cat gastrocnemius, and kangaroo gastrocnemius are 1.5,2.4,4.1, and 6.5, respectively. Thus, the rat TA MT stiffness is greater than the

D. Hawkins and M. Bey

70

stiffness associated with the muscles considered in other studies of MT interactions. CONCLUSIONS

Force-length properties of rat TA muscle and tendon were investigated. It was found that the TA muscle operates over an optimal region of its force-length curve under normal physiological conditions; the TA tendon was relatively stiff causing the muscle to incur most of the stretch imposed during plantar flexion; relatively large passive force (25% of the maximum measured isometric force) was induced for extreme plantar flexion; and relative to eccentric-type muscle action, the tendon acted as a rigid structure independent of the stretch rate. MT behavior can be quite variable depending on the MT unit. thus, it is important to understand the force-length behavior of both the muscle and the tendon when attempting to model muscle behavior and to predict muscle forces in uivo. Acknowlrdyernents-The author is grateful to James Vannes for his technical assistance. This project was supported in part by the Whitaker Foundation. REFERENCES

Biomed.

Engng

BME-H(4),

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249-251.

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