Role of tendon properties on the dynamic performance of different isometric muscles K. ROELEVELD,

R. V. BARATTA,

M. SOLOMONOW,

A. G. VAN SOEST,

AND P. A. HUIJING

Bioengineering Laboratory, Department of Orthopaedic Surgery, Louisiana State University Center, New Orleans, Louisiana 70112; and Vakgroep Funktionele Anatomic, Faculteit Beulegingswetenschapperz, Vrije Universiteit, Amsterdam, The Netherlands ROELEVELD, K.,R.V. BARATTA, M. SOLOMONOW, A.G. VAN SOEST,ANDP. A. HUIJING.RC& ~ftendonp~~~pertieson thedy-

Medical

coelastic stiffness on the dynamic performance of the tibialis anterior (TA) by comparing the frequency renamic performance of different isometric muscles. J. Appl. Physsponse of the muscle with and without tendon. Such a iol. 74(3): 1348-1355, 1993.-The effect of the tendon’s viscocomparison was made during isometric contraction at elastic stiffness on the dynamic performance of muscleswith the muscle’s optimum length with electrical stimulation different architecture was determined using the cat's medial as input and force as output. The force was varied begastrocnemius and extensor digitorum longus. Dynamic retween 20 and 80% of the muscle’s maximal isometric sponse models were derived under sinusoidal contraction-reby orderly recruitment of molaxation in the range of 0.4-6.0 Hz and between 20 and 80% of force and was manipulated the muscles’ maximal isometric tension, manipulated by or- tor units together with firing rate increase. Because no derly recruitment-derecruitment of motor units together with difference was found in the response of the muscle with firing rate increase-decrease.It was shown that, for isometric and without tendon, Baratta and Solomonow concluded contractions at the muscle’s optimum length, the dynamic rethat for these conditions the tendon acts as a stiff force sponseof the muscleswasnot significantly different before and transmission linkage without significantly modifying the after dissectionof the tendon. Therefore the conclusion that muscle’s performance. under these conditions the tendon acts like a stiff force transNevertheless, it is unknown to what extent those remitter without significantly modifying the muscle’s perforsults can be generalized, because different muscles have mance was confirmed and extended to muscleswith different different dynamic responses (3) and differ in tendon mearchitecture. chanical properties (extensibility, hysteresis, elasticity, and elastic storage capability) because frequency response; cat; medial gastrocnemius; extensor digi- tensile strength, torum longus of variability in tendon thickness, length, and material properties (collagen cross-linking) (19,21,22). Although digital flexor and extensor tendons in the forelimbs of domestic pigs have nearly identical properties in the TEIE TENDON, THE APONEUROSIS, the intersarcomere newborn, they exhibit large differences at maturity (22). membranes, and the cross bridges of a muscle are known The digital flexor and extensors of mature specimens to have viscoelastic properties (12, 13). The compliance show similar dry weight (36.8 and 35.3%, respectively), of the tendon has frequently been determined to be tension dependent; in these cases compliance is high at low yet their elastic modulus is 1.66 GPa for the flexors and 0.76 GPa for the extensors. The hysteresis of their stress tensions and diminishes as the applied tension increases vs, strain curves in a stretch-relaxation cycle also differs (18, 21, 22). Several ideas have been formulated regarding the appreciably, 9.2% for the flexors and 17.5% for the extensors. The elastic strain energy recovered from a 3% functional significance of the tendon’s viscoelastic pruperties. However, its exact rule in different movements of strain is 415 J/kg for the digital flexor tendon compared daily living functions is still unclear. A stretch in the with only 164 J/kg in the extensors. Similarly, the maximum strain energy at failure (rupture) is 4,500 J/kg in viscoelastic structures during the course of a contraction the flexors and only 1,400 J/kg in the extensors. The does not prevent filaments from overlapping each other failure strain is 9% in the flexors and only 7% in the so that the muscle can maintain its force-generation properties (21). Furthermore, the elastic structures are extensors (22). The large differences in the mechanical properties of able to act as a mechanical buffer to protect muscle fibers from damage during eccentric contractions (14, 18, 21). mature tendons are believed to be the functional manifestations of each muscle. Specifically, high ground reacThe tendon can store energy and be used to obtain shorttion forces influence the growth and structure of the ening velocities and instantaneous muscle powers higher than can be achieved by the muscle fibers themselves (1, flexors to sustain higher strains and stresses and store more energy compared with the extensor tendon, which 8, 16, 21). is exposed to much lower external forces. In contrast, in a recent study by Baratta and Solomonow (4) the effect of tendon properties on the dySuch differences in the mechanical properties of tennamic behavior of the muscle-tendon complex could nut dons can lead to different contributions of certain muscle be found. These authors studied the effect of tendon vis- tendons to dynamic response, as supported by a recent 1348

0161-75671'93

$2.00

Copyright 0 1993 the American Physiological Society

TENDON

AND

MUSCLE

study (van Soest, Huijing, and Solomonow, unpublished data) that employs a Hill-type model. By modeling of the TA, the medial gastrocnemius, and the soleus muscles, differences in the effect of tendon dynamics were predicted to exist between muscles and hypothesized to depend on the ratio between tendon and fiber length and on the maximal fiber-shortening velocity. The discrepancy between the functions of tendons as formulated by many authors and the results obtained by Baratta and Solomonow (4) was believed by van Soest et al. to be the result of the specific muscle preparation used by Baratta and Solomonow. In this study, the hypothesis that the effect of the tendon varies from muscle to muscle on the basis of its architecture is put to an experimental test by performance of the same experiment on two other muscles, the extensor digitorum longus (EDL) and the medial gastrocnemius (MG) of the cat. These two muscles differ appreciably from the TA in tendon length, thickness, and mechanical/material properties, and they have different dynamic responses (3) relative to fiber length. METHODS

Preparation. Four adult cats were anesthetized with intraperitoneal injection of chloralose (60 mg/kg). From the left leg, the medial part (head and tendon) of the MG was isolated from the rest of the triceps surae muscles. The tendons of the MG and the EDL were freed from their surrounding tissues, but the muscle origin, belly, blood supply, and innervation were left intact. After the calcaneus was cut, the tendons of the MG (with a piece of the calcaneal bone still attached) and the EDL (cut close to its separation to the digits) were fixed in separate metal clamps for later connection to a force transducer. The sciatic nerve was exposed, and a tripolar cuff stimulation electrode (2) was placed on it for later connection to two stimulators. A pin was inserted through the distal condyle of the femur and clamped to a rigid platform in addition to a pelvic clamp to fix the preparation in isometric stability, with the hip and knee joints in angles of 90°. The ankle joint was amputated to allow direct anatomic line of connection of all muscle-tendon units to the force transducer. A skin flap was sutured uver the muscle-tendon complexes to prevent them from drying, and the tendons were kept under a layer of isotonic saline solution to further ensure that sufficient moisture was available to them. In the second part of the experiment, the distal tendon of each muscle was dissected in such a way that the metal clamp held the distal end of the aponeurosis (muscle-tendon junction). instrumentation. A computer-controlled electrical nerve stimulation system was used to study the dynamic performance of isometric muscles. The details of this system were described (5, 28) and validated (2, 25). Briefly, a sinusoidal voltage wave of a given frequency and amplitude, generated by an IBM-XT computer, was delivered via two output channels to a linear voltagecontrolled oscillator and a pulse modulator, respectively (Fig. 1A). The voltage-controlled oscillator converted the input voltage to lOO-ps pulses of suprathreshold amplitude and a rate that was proportional to the voltage in-

DYNAMICS

1349

put. Pulse rates from O-100 pulses/s were available and were delivered to the nerve via the proximal and middle poles of the sleeve electrode to constitute the firing rate stimulus. The middle pole was used in common for both stimuli. The second sinusoidal voltage wave was first inverted and then multiplied by unit pulse train of 100~ps pulses at a rate of 600 pulses/s. The amplitude of the pulses was governed by the sinusoidal voltage wave amplitude that could be varied via the computer keyboard as necessary. Normally, the pulse amplitude was calibrated experimentally to vary between the “just-above-excitation” threshold of the smallest axon and the “just-below-excitation” threshold of the largest motor axon (2, 7, 28). Because such high frequency (600 pulses/s) blocks muscular excitation (23, 26, 27), as its pulse amplitude is decreased from the “above” threshold of the smallest nerve axon, that unit escapes the stimulus inhibition and becomes active to induce contraction in the muscle fibers it innervates. Further reduction in the pulse amplitude allows progressively larger motor units to become active in an orderly fashion, according to the “size principle” recruitment (15). This recruitment stimulus was applied to the distal pole of the sleeve electrode while the middle pole served as the common, as mentioned above. Figure 1B provides a schematic of the stimulation system and its functional effect on the muscle. Muscle force was measured by a Grass FT-10 transducer attached firmly to the tendon clamp via a metal turn-buckle. The stiffness of this transducer is 100 N/ mm. Because the maximal force generated from any muscle in this study did not exceed 30 N and the maximal muscle length from insertion to insertion was 7 cm, the maximal error due to the transducer compliance was 0.43%, a rather negligible value. The resonance frequency of the transducer is 700 Hz, well above the frequency-response range of skeletal muscles (3, 25). Muscle force and the sinusoidal input control voltage were sampled and stored on an IBM-AT computer via a data acquisition card with a sampling rate of 64 Hz. The force and the two stimuli voltage envelopes were also displayed on a Gould 260 polygraph. Protocol. Initially, the muscle’s optimum length was set by determining the maximal isometric force while its length was modified by turning a turn-buckle between the tendon clamp and the force transducer. At the muscle’s optimal length some calibration trials were conducted to obtain the desired sinusoidal force output of the muscle. These initial calibration trials consisted of four trials of 6 s each. The first and second trials were conducted to identify the stimulation rate at which the muscle developed a maximal force and the firing rate of fusion of the smallest motor unit. The third and fourth calibration trials were conducted to define the recruitment stimulus voltage limits corresponding to the justabove-excitation threshold of the smallest motor axon and the just-below-excitation threshold of the largest motor axon. Further attempts were made at an oscillation frequency of 0.4 Hz to calibrate the upper and lower voltages of sinusoidal stimulation in such a manner that the force response provided ~60% peak-to-peak swings around the midforce value of the muscle’s maximal iso-

1350

TENDON

AND MUSCLE

A ----e--e-----fl I I I I 1 t I IBM-XT I I------w----m

f

d--s-

B

AXONS

F i3 Q: co P

F-R. STiMULUS

DYNAMICS FIG. 1. A: schematic of experimental system used to elicit sinusoidal contraction-relaxation of muscle. Functions inside broken rectangle depict computer control elements that generate a sinusoid of a given frequency. Arrows to -K1 and Kzt capabilities to calibrate peak-topeak voltage of each stimulus as necessary via computer keyboard; -K, 180” phase shift of recruitment stimulus; PM, pulse modulator in which sinusoid voltage modulates amplitude of lOO-ps pulses at 600 pulses/s; VCO, linear voltage-controlled oscillator that constitutes firing rate stimulus. Modifications of stimuli waves by each component are also shown. B: simplified schematic illustrating effect of firing rate (FR) and recruitment (REC) stimuli on sample population of motor units of increasing size with corresponding increase in innervation ratios. Spikes, 100-p pulses. Stimuli are simultaneous. Note sinusoidal decrease in interpulse interval of FR stimulus, indicating increase in FR that is occurring concurrently with release of progressively larger motor units from high-frequency block as REC stimulus amplitude decreases sinusoidally. Net effect is sinusoidal recruitment of motor units according to size principles, with each larger motor unit activated at a slightly higher FR.

REC.SflMULUS

metric force (e.g., force was varied from 20 to 80% of the maximal isometric force). Data recordings were started once calibration trials were terminated. The sinusoidal input voltage was set at a frequency of 0.4 Hz for a period of 6 s. Additional 6-s trials were also obtained for voltage input frequencies of 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.5,3.0, 4.0, 5.0, and 6.0 Hz to provide sufficient data points for the analysis. Three-minute intertrial intervals were observed to prevent fatigue and possible posttetanic potentiation (6) . from influencing the data. To make sure that fatigue did not have any influence on the response, a 0.4-Hz trial was obtained at the end of the series and compared with the 0.4-Hz trial at the start of the series. If the maximal and minimal forces were not similar, the data were rejected and the experiment was repeated. Once the data for the whole muscle-tendon unit were collected, the distal tendon was removed and a metal clamp was attached at the approximate distal border of the aponeurosis. The test procedure described above was then repeated. Analysis. Only the last 4 s of the trials were used for analysis to fully eliminate the effect of the initial transient response, which lasts - 1 s (23). Longer recordings were excluded because of the possible intrusion of fatigue. Four-second samples of recording at a given oscillation frequency allowed the inclusion of several force cycles in the analysis and increased its accuracy. A shorter recording duration would include only one or two cycles, and at low frequencies less than a cycle. This would not properly represent the data and might also decrease their accuracy. On the basis of these restraints (fatigue and accuracy), a 4-s trial was considered an optimal sample duration without limiting the significance of the results. The transfer function representing the sinusoidal steady-state behavior of a system is a function of frequency (jw) and is itself a complex function that possesses a magnitude and a phase angle (10). The difference in magnitude and phase angle of the output (force)

with respect to the stimulus input (voltage) is governed by the gain and phase, respectively. To yield the gain and phase of each trial, the force output and stimulus input voltage of each trial were multiplied by a Hamming window before their fast-Fourier transform (FFT) was taken by software programmed on the IBM-AT computer and manipulated by the following equation

where F is the FFT of the force at the trial’s fundamental frequency, v is the FFT of the stimulus voltage, 1F I/ 1v 1 is the gain, and Q, is the phase. F and V are complex functions, each including a magnitude and a phase. To allow direct comparison of the data traces from the different preparations, the gain of each trial was normalized with respect to the gain obtained in the trial, with oscillation frequency of 0.4 Hz for each muscle tested and then represented in decibels (dB) according to the following equation

IWI~I

gain (dB) = 20 log

/wI%.4Hz

The means and SDS of the gain and phase data before and after the tendon was dissected, as well as the change in gain and phase as the result of tendon dissection, were then plotted on the conventional gain vs. frequency plot and on the companion degrees vs. frequency Bode plot for both muscles. Previous studies (3,4) using the same protocol resulted in best-fit transfer functions with two identical real poles and a pure time delay. The dynamic properties of the muscles [MCjw)] were then described by the following equation Ke-Tdjw MCiw)

=

(1

+

ajw)Z

where K is constant model gain, a is l/w, = l/(%f), w is oscillation frequency (rad/& Td is pure time delay (s), and j is IJ-1.

TENDON

AND

MUSCLE

1 §0C I

n

n

FIG. 2. Typical force traces recorded from 1 medial gastrocnemius preparation and at several frequencies.

The best-fit models lay via

method of least squares was used to test for the transfer function- characterizing the data using with two identical real p ales and a pure time dethe following equations model gain =

(w” ; w;)

2 model ADhase = -2 arctan i - \ - wTd \ WO I

Td represents well-known physiological delays, such as conduction time of action potentials in the nerve and along the muscle fibers, neuromuscular junction transmission, and excitation-contraction coupling. On the basis of these a priori requirements, candidate test models that resulted in a pure time lead were not considered. To identify any possible changes in the model parameters obtained before and after dissection of the tendon, model parameters (poles and time delay) were derived for the data of each preparation at each condition (with and without tendon), and a paired t test (P < 0.05) was applied. For each frequency, the paired t test was also applied to the obtained gains (relative to 0.4 Hz) and phases. To determine whether nonlinearities associated with the hysteresis (related to the sinusoidal stretch-relaxation) of the tendon were present (18, 19), the harmonic distortions of the preparation with and without the tendon were calculated at all the oscillation frequencies, and paired t tests (P < 0.05) were applied. RESULTS

Figure 2 represents several typical force traces at various frequencies recorded from one preparation of the MG. Visual inspection of the traces confirms the expected decline in t,he peak-to-peak force as the oscillation frequencies increased. Similar traces were obtained from the other seven preparations. Figure 2 also shows the typical drift in the baseline of each force trace as well as a slight decrease in the force peak-to-peak value that is the manifestation of the various series elastic components of

DYNAMICS

1351

the muscle (tendon, aponeurosis, intersarcomere membrane) as it adjusts to the new oscillatory condition of the muscle at a given force range and muscle length (3,4,23, 28). These features did not influence the analysis, because the FFT takes into account only the fundamental frequency of the given oscillation, disregarding the drift. Also, the minor decrease in the peak-to-peak amplitude of the force oscillations was averaged over the several cycles of each trial before the gain was calculated. Figure 3 illustrates the pooled data from the four preparations of the MG and the EDL, both with tendon (WT) and after dissection of the tendon (NT). The top and bottom panels represent the mean and SD of the gain and phase values, respectively. The continuous lines through the data points represent the best-fit model for each test category, with the pole values P (because P, = P,, only one pole is represented), correlation coefficient R, and SE of the estimate in the inset of each plot. The phase plot’s inset also contains Td and the associated R and SE. Furthermore, the model parameters of the pooled data resulted in pole values and a Td for the MG of 1.99 Hz and 20 ms, then 2.11 Hz and 25 ms before and after removing the tendon, respectively. The parameters for the EDL with and without tendon were exactly the same: poles 2.26 Hz, and Td 7.75 ms. The R values were >0.93, indicating a high-quality fit. Paired t tests for the models developed for the MG and EDL with and without tendon resulted in no significant differences between the poles and Tds. The mean and SDS of the gain and phase changes of the muscles as the result of tendon dissection are plotted in Fig. 4. Paired t tests for each muscle and every frequency for the gain and phase data resulted in significant differences (P -C 0.05) only for the gain of the MG at oscillation frequencies of 0.8, 1.0, and 1.2 Hz. At these frequencies the gain of the MG without tendon was lower than that with the tendon. Table 1 summarizes the means t SDS of the percent total harmonic distortion for the force output signals of every trial (0.4-6 Hz) from the MG and the EDL with and without tendon. It shows that the percentage of harmonic distortion was ~5% in most of the trials; only a few trials with low sinusoidal frequencies had higher values. This confirms the linearity of the muscle’s dynamic response model in isometric conditions with forces in the range of 20-80% of the maximal isometric force. Paired t tests (P < 0.05) for each muscle and every frequency showed that the harmonic distortion of the muscles with and without tendon did not differ significantly and furthermore that the tendon did not modify the muscle’s dynamic response. The only exception was the harmonic distortion of the EDL at 0.4 and 0.6 Hz. Table 2 shows calculated poles and time delays for the same preparations. DISCUSSION

The dynamic response parameters (poles and time delay) of the MG and the EDL, like the TA, did not change significantly after the tendon dissection; in other words, the tendon did not affect the dynamic response of the

1352

TENDON

WT

MO

AND MUSCLE

DYNAMICS

NT

cl MEAN AND SD .+.MEAM. .AMD..SD.

.I......

MODEL GAIN WT ........, MODEL GAIN NT .......................*....1......*.......*.....l....l..*.......*.... +r. . ......*......**... P

-20

o~EAN..AND.‘SCS.WT

.

.

.

.

.

+ MEAN AND SD NT MCKEL

GAIN

WT

0

cl +

0 . . . . . . . . . . . . . . . . . . . . . . . . ..f........~.....................................

-2u

-a0

+ 1

I

I

IItIilI

I

..*,.......................,......

d? . . . . . . . . . . . . . . . . . .

1

. . ..)..........

.

. . I.

..._*. . . .

IIIIII

mo

1

FREQUENCY (WW8Ec)

dh,

WT NT P=1,99Hr P-2111Hr .............*.....*....*.....*.*.........*......_.... Td-2Oms Td=25ms El R-01987 R-O.984 SE-7046 SE-876 .........~....l*.......*..*.*..~.~~.*‘...*.~~ .*......,..****.,...*.......*....*..~I.

aMEAN AND SD WT P................. + f+EAN. ..AND ...... ..*80. ...NT .......... MODEL PHASE WT --.*+.--.. MODEL

PHASE

x

m

WT P-2,2&k

y1 P ................. .......\........% . . .Q

EDL

NT P-2026Hz

.,.....,. .

oMEAN AND SD WT 4’ b ........*........ + MEAN .....*.... AW ... ...SR . s..,...... NT ... ........... ...................I \’ MCX3EL PHASE WT d3 m-MODEL PHASE NT 8,

NT

~.....................*.......,....*...,*...............*.....*.....,......*................. 6

1

lo

loo

FREQUENCY (MW8EC) FIG. 3. Gain (top) and phase (bo&m) data (means -F SD) obtained from medial gastrocnemius (MG) and extensor digitorum long-us (EDL) before (WT) and after (NT) whole tendon dissection represented in gain vs. frequency and phase vs. frequency Bode plots, respectively. Td, time delay. Note that for EDL, models WT and NT are superimposed, because best-fit models are identical.

muscles. However, for the oscillation frequencies between 0.8 and 1.2 Hz, the gain of the MG was significantly smaller without the tendon. However, because this represents only a very small part of the total dynamic response, one can confirm the conclusion of Baratta and Solomonow (4) that during isometric contraction in the midrange of the maximal isometric force of the muscle, the tendon acts like a stiff force transmitter. Because the three muscles (TA, MG, and EDL) differ

appreciably in tendon and fiber properties and dynamic responses, this conclusion may be generalized to other muscles as well. The EDL has a longer tendon and a lower maximal isometric force than the TA. The MG has a thicker and shorter tendon than the TA, whereas the maximal isometric force is much higher for the MG. Furthermore, because the MG is a plantar flexor and the TA a dorsi flexor and because flexors and extensors differ in tendon

TENDON

AND MUSCLE

1353

DYNAMICS

...I*...*.......*....*.........*.......*..... *...........**..*...*......*..*..., I

10

- 10

e

- 16

FIG. 4. Change (means t SD) in gain (top) and phase (bottom) as result of tendon dissection obtained from MG and EDL, plotted in gain vs. frequency and phase vs. frequency Bode plots. *Frequency at which significant difference existed.

material properties (22), it is probable that the MG also differs from the TA in tendon material properties. These differences can cause differences in compliance and stress of the tendon (9, 19, 21, 22) and therefore differences in the effect of the tendon on the dynamic response. Furthermore, the MG and the EDL also differ from the TA in their dynamic responses. The MG has the lowest poles and the TA the highest; the EDL has the lowest time delay and the MG the highest (3). Because those differences existed not only for the whole muscletendon complexes but also for the muscles without the tendon, the tendons of the different muscles will not receive the same inputs, which can cause changes in the contribution of the tendon to the dynamic response of the muscle. These expectations are supported by the Hill-type model study of van Soest et al. (unpublished data). By a model of the TA, the MG, and the soleus, 1. Percent harmonic distortion of MG and EDL at each frequency, with und without tendon TABLE

MG Frequency, HZ

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 4.0 5.0 6.0

WT

7.34k8.00 4.97t2.29 3.31t2.58 3.4322.68 2.76k1.75 3.96k2.62 2.56kl.85 1.99kl.53 1.92tl.39 1.52tl.07 1.45t1.21 1.14tl.08 0.93t0.55 0.68-sO.10

EDL NT

5.62k4.04 3.9023.98 2.30t2.90 2.53t2.92 2.17k2.35 3.02t3.19 2.13t2.00 1.4WO.98 1.64kl.35 1.38kl.05 1.16kl.11 0.98,+0.83 0.86kO.55 0.7lrkO.38

WT

13.75tl.75 4.38t0.67 2.64kO.39 2.81t0.67 2.07~0.45 3.36t0.35 2.58t0.24 2.07_tO,27 2.09t0.30 1.671~0.41 1.49t0.54 1.44t0.75 1.4OkO.83 0.98t0.54

NT

7.33-to.44 1.92t0.80 1.42tO.48 1.60t0.65 1.53t0.75 2.33kO.95 1.68t0.67 1.29t0.48 1.30t0.37 1.22t0.41

differences in the effect of tendon dynamics were predicted to exist between muscles and hypothesized to depend on the ratio between tendon and fiber length and on the maximal fiber shortening velocity. The maximal fiber shortening velocity will influence the dynamic response and so, indirectly, the contribution of the tendon. None of the above expectations was manifested in the data.

A compliant tendon is expected to impact the dynamic performance of the muscle as the sinusoidal contraction frequency is increased. Then dissecting out the tendon

would result in a change in phase angle and gain, manifesting a change in the model parameters time delay and poles relative to those obtained from the whole muscletendon complex. A compliant tendon can change the gain in two ways. Because stiffer units have higher resonance frequencies, dissecting out the tendon (making the muscle-tendon complex stiffer) is expected to lead to higher poles. This, however, was not shown in the results of these studies, further asserting that tendon stiffness is much higher compared with the muscle. In addition to the dynamic parameters, the effect of tendon compliance can also be detected by the percent harmonic distortion, which reflects the (non)linearity of a system. If the tendon had shown its nonlinear viscoelasTABLE

2. Culculu~edpoles and time delays with and without tendun

for all preparations

MG Poles,

EDL

Hz

Td, ms

Poles, Hz

Td, ms

Cat No.

WT

NT

WT

NT

WT

NT

WT

NT

I

1.7 2.1 2.0 2.2

2.5 2.2 1.8 2.1

15.0 30.0 17.5 17.5

22.5 30.0 22.5 22.5

2.7 2.5 1.9 2.2

3.1 2.4 1.7 2.3

2.5 2.5 20.0 12.5

2.5 2.5 15.0 15.0

1.37kO.94 1.27t0.90 1.1920.83 0.69t0.44

Values are means + SD of medial gastrocnemius (MG) and extensor digitorum longus (EDL) muscles from 4 cats. WT and NT, with and without tendon, respectively.

2 3 4

Values are means 2 SD of 14 trials from MG and EDL muscles. Td, time delays.

1354

TENDON

AND MUSCLE

tic properties, thus causing hysteresis (18), we would have expected the force of the preparation with the tendon to be less linear and to have been detected by the percent harmonic distortion. However, aside from the distortion of the EDL at 0.4 and 0.6 Hz, for each muscle and every oscillation frequency the percent harmonic distortion was not significantly lower after tendon removal with respect to the whole muscle-tendon complex, and because the dynamic parameters also did not change, one can safely conclude that the tendon behaved as a very stiff component. Simple inspection of the harmonic distortion data of Table 1 yields a different picture. The harmonic dI stortion is consistently lower for the preparations of the MG and EDL after the tendons have-been removed. This implies that the linearity of the muscle’s input/output relationships has increased after the removal of the tendon. In other words, the tendon had a minor contribution to the dynamic response by increasing its nonlinearity. Although this minor nonlinear contribution of the tendon was not statistically significant, it should be considered, inasmuch as it is the manifestation of the nonlinear viscoelastic properties of its collagen substrate. The conclusion that the dynamic response is independent of the tendon is in agreement with the results of a study in which the dynamic response of nine different muscles was studied in the same way (4). Although the nine muscles had large variability in tendon length, muscle-tendon ratio, and poles of the dynamic response, statistical analysis failed to identify tendon length or muscle-tendon ratio as a factor that directly influenced the model poles. This also confirms the conclusion of Mannard and Stein (20) that synaptic transmission failures and mechanical (viscoelastic) properties of the muscle could not be the responsible processes for the secondorder dynamic response of a muscle. That the tendon appears stiff in the midrange of its maximal isometric force confirms the observation of Proske and Morgan (21) that the stiffness of the tendon is high with forces >25% of the maximal isometric force. However, it must be kept in mind that the tendon could have a different function with lower forces acting on it because, when low forces are acting on the tendon, an increase of these forces will cause the tendon to lose its wavy appearance so that its tension does not change much and stiffness will remain low. Forces applied to the tendon in excess of 25% of its maximal isometric force, however, meet with high stiffness (21). Furthermore, the probability that an isometric force 90% of the maximal is used in daily functions is small also, because with such high forces there is the probability of generating ruptures, and large fatigue effects will show. Several authors stated that the tendon is able to save energy by storing it in one part of a movement and releasing it in another (1,8,21). Because these are nonisometric contractions (partly eccentric, partly concentric) and in our study only the behavior of the tendon during isometric contractions is determined, this tendon function can still be valid. Further research is necessary to delineate clearly the exact conditions in which the tendon contributes to movement functions in the manner described in these studies. Furthermore, the tendon was l

DYNAMICS

believed to have an important protection function during eccentric contractions (14, 17). Although eccentric contractions meet with high forces acting on the tendon and thus with high tendon stiffness, the possibility of a length change of the tendon during such contractions cannot be excluded. Using a Hill-type model, van Soest et al. (unpublished data) predicted an effect of the series elastic component (SEC) on the dynamic response of some muscles during isometric contractions in the midforce range of the muscle’s maximum. This can be explained by the fact that, in our experiments, only a part (tendon) of the SEC was removed, inasmuch as the aponeurosis, intersarcomere membranes, and the cross bridges also contain viscoelasticity (11, 13). Therefore it is possible that the muscle is not totally stiff in its midforce range, so that the linear shortening of the muscle fibers during the development of isometric force, found by Griffiths (l4), could be taken up by the other viscoelasticity-containing structures. In conclusion, during isometric contraction in the midrange of the maximal isometric force of the muscle, the tendon acts like a stiff force transmitter without significantly modifying the muscle’s performance. This conclusion could be extended to various common skeletal muscles of different muscle-tendon architecture, as determined in this study. This work was supported by National Science Foundation Grants EET-8820772 and BCS-9006639. Address for reprint requests: M. Solomonow, Dept. of Orthopaedics, LSU Medical Center, 2025 Gravier, New Orleans, LA 70112. Received 7 February 1992; accepted in final form 20 October 1992. REFERENCES 1. ALEXANDER, A. M., AND H.C. BENNET-CLARK. Storage ofelastic strain energy in muscle and other tissues. Nature Land. 265: 114117,1977. 2. BARATTA, R.,M. ICHIE,~. K. HWANG,AND M. SOLOMONOW. Orderly stimulation of skeletal muscle motor units with tripolar nerve cuff electrode. IEEE Trans. Biomed. Eng. 36: 836-843, 1989. 3. BARATTA, R., AND M. SOLOMONOW. The dynamic response model of nine different skeletal muscles. IEEE Trans. Biomed. Eng. 37: 243-251, 1990. 4. BARATTA, R., AND M. SOLONONOW. The effect of tendon viscoelastic stiffness on the dynamic performance of isometric muscle. J. Biomech. 24: 109-116, 1991. 5. BARATTA, R,,B. ZHOU,AND M. SOLOMONOW. Frequencyresponse model of skeletal muscle: effect of perturbation level, and control strategy. Med. Biol. Eng. Comput. 27: 337-345, 1989. 6. BIGLAND-RITCHIE, B. EMG and fatigue of human voluntary and stimulated contraction. In: Human Muscle Fatigue: Physiological Mechanism. London: Pitman, 1981, p. 130456. (Ciba Found. Symp. 82) 7. BLAIR, E. A., AND J. ERLANGER. A comparison of the characteristics of axons through their individual electrical responses. Am. J. Physiol. 106: 524-564, 1933. 8. BOBBERT, M.F.,P.A. HUIJING,ANDG. J. VANINGENSCHENAU. An estimation of power output and work done by human triceps surae muscle-tendon complex in jumping. J. Biomech. 19: 899-906,1986. 9. CLOSE, R. I. Dynamic properties of mammalian skeletal muscle. Physiol. Rev. 52: 129-197, 1972. 10. DORF, R. Modern Control Systems (3rd ed.). Menlo Park, CA: Addison-Wesley, 1983. 11. ETTEMA, G. J. C., AND P. A. HUIJING. Properties of the tendinous structures and series elastic component of EDL muscle-tendon complex of the rat. J. Biomech. 22: 1209-1215,1989. 12. FUNG, Y. Biomechanics: Mechanical Properties of Living Tissue. New York: Springer-Verlag, 1981. 12 GOUBEL, F., AND J. F. MARINI. Fibre type transition and stiffness Iu.

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