INTRODUCTION

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THE SERIES ELASTIC STIFFNESS (SES) of active muscles has a significant influence on both the control and the economy of movement. For making a quantitative evaluation of the functional significance of SES during human movement, accurate and reliable quantitative measures of SES in vivo in humans have to be developed.

The mechanical properties of the tendinous tissue in the human tibialis anterior measured in vivo by use of a method based on ultrasonography have recently received a lot of attention (5, 6, 10-13). This has given important new information about this muscle in vivo. However, for a functional evaluation of the SES of the human dorsiflexors, the ultrasonography method is not sufficient. The ultrasonography method has limitations that do not allow for studies of whole muscles and muscle groups but only of parts of muscles and superficial muscle structures. Therefore, only distal tendon and aponeurosis parts of superficial muscles have been investigated so far with this method.

During natural movement, however, joint moment is generated by muscle synergies, i.e., more than one muscle, and both proximal and distal series elastic component (SEC) structures are involved. Therefore, to get a more functional measure of SES in a muscle synergy controlling a joint, it is necessary to include all the involved series elastic tissue in the synergy in the measurement. It is possible to achieve this in vivo with the fast controlled release method (4, 7). This method is based on muscle shortening at a very high but constant speed. The shortening should be completed before the first reflexes arrive at the antagonist muscles, and the speed should be well above the maximum shortening speed of the muscle to minimize muscle fiber shortening. By recording the decline in moment as a function of joint rotation corresponding to shortening of the active synergy, the SES can be measured and expressed in newton-meters per radian, which we consider to be a useful functional measure for evaluation of the influence of series elasticity in human movement. This measure does not require knowledge about the lengths of the tendon moment arms of the individual muscles, which is a methodological advantage because it simplifies the measurement procedures. However, to translate the rotational measures of SES into linear measures of SES of the individual muscles, detailed information about tendon/aponeurosis dimensions, tendon moment arms, and force sharing is needed.

The aim of this study is to quantify the SES in the human ankle dorsiflexors by using the fast controlled release method with a custom-designed high-pressure hydraulic actuator. In addition to voluntary activation of the dorsiflexors, we also applied electrical stimulation to the tibialis anterior. This allowed us to measure the SES of tibialis anterior alone and to compare our results with data from the literature, especially the study by Maganaris and Paul (11).

	METHODS

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Equipment. A Servo-controlled custom-designed high-pressure hydraulic actuator (MTS-systems 215.35, 230 Bar) was used for the fast controlled-release experiments (16). The foot of the subject was firmly strapped to a foot adapter with large cable ties. The position of the foot adapter was adjusted such that the anatomical axis of the ankle coincided as well as possible with the center of rotation of the actuator. The releases were imposed over a 30° angular excursion between 20° plantar flexion and 10° dorsiflexion with an angular velocity of about 15 rad/s. For the calculation of the ankle joint angular accelerations and joint moments, the foot adapter was instrumented with linear load cells (Kistler, Slimline) to measure the force components parallel and vertical to the footplate of the foot adapter and accelerometers (Kistler, K-SHEAR Piezotron) to measure the corresponding acceleration components (see Fig. 1). The position of the rotary actuator was monitored with an angular displacement transducer (Transtek DC ADT series 600). Surface electromyograms were recorded from the tibialis anterior and soleus muscles. The signals were sampled at 4,000 Hz.

View larger version (24K): [in this window] [in a new window]   Fig. 1.   A schematic view of the foot-actuator interface and the forces and accelerations measured. The three forces Fa, Fb, and Fc were measured with linear load cells (Kistler, Slimline). These forces act on the adapter where the adapter was attached to the hydraulic actuator. The moment around the center of rotation (COR) was calculated by multiplying Fc with the moment arm L, and Fa and Fb with the moment arm (H) and adding them together. The accelerations Aa and Ab were measured with accelerometers (Kistler, K-SHEAR Piezotron). The angular acceleration was calculated by using these 2 linear accelerations and the geometry. The position of the adapter was adjusted such that the anatomical axis of the ankle coincided as well as possible with the COR of the actuator.

Experimental procedure. The experimental protocol and procedures were approved by the local ethical committee. Three women and five men gave their informed consent to participate in the experiments. They sat in a chair with a knee angle of ~160° and a hip angle of ~100°. After two recordings necessary for correction (see below), two sets of 20 releases were performed. In the first set of 20 releases, the subject produced a steady level of voluntary dorsiflexion moment before each release. The subject could see the produced moment level on an oscilloscope. The initial moment was varied between ~5 Nm and maximum effort, which was presented as a mark on the oscilloscope. In the second set of 20 releases, the moment was produced by electrical stimulation of the tibialis anterior at different levels (stimulator: Isolator 11, Axon Instruments). Electric activation of the tibialis anterior was produced by 1 s of percutaneous stimulation at a frequency of 100 Hz using pulses with a duration of 100 µs. Electrodes (Medicotest neurostimulation electrodes) were placed over the tibialis anterior muscle. The current was varied between the motor threshold and the point at which the subject could tolerate no higher current.

Correction for inertia and passive stiffness. The moment signal had to be corrected for inertia and passive stiffness of the antagonists. The correction method is described in detail in De Zee and Voigt (4). In short, the correction for inertia was based on the assessment of the angular acceleration plus two additional recordings. The first extra recording was a slow release with an angular velocity of 0.1 rad/s with the muscle passive, which gave the passive moment-angle curve. The second extra recording was a fast release (15 rad/s) also with the muscle passive. From this recording, a transfer function H was obtained with the angular acceleration as input and the moment as output. The fast controlled release measurements were then first corrected for inertia by using the acceleration signal. Subsequently the passive moment was subtracted from the total moment. Figure 2 gives an impression of the correction procedure applied.

View larger version (18K): [in this window] [in a new window]   Fig. 2.   Moment as a function of ankle angle. a: Raw moment-angle curve. b: Moment-angle curve after correction for inertia and passive stiffness. c: Moment-angle curve b, also with correction for the shortening of the contractile component. 0 rad, actuator position where the ankle joint was in neutral position.

Correction for CC shortening. If the force decreases below the initial isometric moment, the contractile component (CC) starts to shorten with a certain speed. The speed of shortening (expressed in rad/s) can be calculated from the Hill's force velocity relation (2, 7)

(1)

where _cc is the CC shortening speed, M_cc is the measured moment after correction, and M₀ is the initial isometric moment just before the release. The values for the parameters have been adopted from the literature (8, 17), where b = 1.2 and n = 0.12. The shortening speed was integrated to obtain the angular excursion corresponding to CC shortening, and this number was subtracted from the measured ankle angle (see also Fig. 2).

Shift of release curves and curve fitting. Because the individual releases start at different initial moment levels, but at the same joint angle, the moment and angle are shifted between the measurements. Therefore, in line with our previous study on plantar flexor SES (4), the corrected, submaximal release curves were angle shifted so the initial moment level corresponded to the moment level on the trial with the highest (M_0,max) initial moment (see Fig. 3). The shifted curves were averaged and fitted with the following nonlinear function (14)

(2)

where  is angle and M is moment. A nonlinear function gives good fits because tendinous tissue shows nonlinear behavior up to stresses of 30 MPa (1, 15). The values of the constants a, b, and c were obtained by a nonlinear regression using the Marquardt-Levenberg algorithm.

View larger version (17K): [in this window] [in a new window]   Fig. 3.   Shift of a submaximal release curve to the left (as indicated by the arrow) so the curve coincides with curve of the moment level on the trial with the highest initial moment (M0,max). a: M0,max curve. b: Submaximal release curve before shift. c: Submaximal release curve after shift. 0 rad, actuator position where the ankle joint was in neutral position.

Statistics. A paired t-test was used to compare between the voluntary muscle activation and electrical stimulation. A value of P < 0.05 was considered significant. Average values are presented as means ± SD.

	RESULTS

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The mean age of the 8 subjects was 35 ± 6 yr, body mass 76 ± 17 kg, and height 174 ± 8 cm. The maximum measured M_0,max just before the release was 66 ± 17 Nm with the voluntary isometric muscle activation and 34 ± 16 Nm with electrical stimulation (P < 0.001). See for individual values Table 1. An example of an electromyogram recording during a voluntary contraction is presented in Fig. 4. It shows that the stretch reflex of the soleus is too late to influence the stiffness calculation.

View larger version (20K): [in this window] [in a new window]   Fig. 4.   A: angle of ankle joint during a fast controlled release recorded with the angular displacement transducer. 0 rad, actuator position where the ankle joint was in neutral position. B: electromyogram (EMG) of the soleus during a fast controlled release. C: EMG of the tibialis anterior with a voluntary contraction of the dorsiflexors. Note the stretch reflex in soleus around 60 ms, which occurred after the end of the fast controlled release. Hence, the stretch reflex will not influence the stiffness measurement.

Figure 5A presents 20 release curves obtained during voluntary activation from one subject. The signals are corrected for inertia, passive stiffness, and CC shortening. Figure 5B presents the results of the shift of the release curves. Finally, an average of the curves in 5B is presented in Fig. 5C (solid line).

View larger version (16K): [in this window] [in a new window]   Fig. 5.   A: 20 release curves of subject 1 with different initial moments produced with voluntary activation. B: release curves in A are shifted to the left in such a way that they coincide with the release curve with the highest initial moment. C: solid line is the average of the curves in B, and dashed line is the nonlinear fit. 0 rad, angular position where the ankle joint was in neutral position.

The average curves of Fig. 5C were fitted with Eq. 2. The dashed line in Fig. 5C is an example of the fit. For all subjects, good fits were obtained (voluntary muscle activation, R² = 0.98 ± 0.025; electrical stimulation, R² = 0.91 ± 0.051). To calculate the SES for the situation with voluntary muscle activation and the situation with electrical stimulation, Eq. 2 was differentiated. SES is moment dependent, so for the sake of comparison the SES had to be calculated at the same moment for the two situations. The moment of 34 Nm was chosen, which was the average maximum in the case of electrical stimulation. The SES at this moment of 34 Nm was significantly different between the trials, with voluntary muscle activation and electrical stimulation (voluntary muscle activation, SES_{34 Nm} = 219 ± 54 Nm · rad¹; electrical stimulation, SES_{34 Nm} = 149 ± 54 Nm · rad¹; P < 0.001).

Figure 6 shows families of dorsiflexor SES vs. moment curves (0  M_0,max) from all the subjects during voluntary (Fig. 6A) and electrical (Fig. 6B) activation, respectively, obtained by differentiation of the fitted series elastic release curves. It is clearly seen that the stiffness of SEC between 0 and M_0,max never reaches an asymptote, i.e., a constant stiffness.

View larger version (33K): [in this window] [in a new window]   Fig. 6.   Stiffness of series elastic component vs. moment from all the subjects during voluntary (A) and electrical (B) activation obtained by differentiation of the fitted series elastic release curves.

	DISCUSSION

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Comparing voluntary muscle activation with electrical stimulation. The maximum measured moment during voluntary dorsiflexion was much higher than during electrical stimulation. This is most probably because during voluntary dorsiflexion not only the superficial tibialis anterior was active but also the toe extensors, i.e., extensor digitorum longus and extensor hallucis longus. In the case of electrical stimulation, the moment was produced solely by the tibialis anterior. This also implies that during voluntary activation of the dorsiflexors more elastic tissue lying parallel is involved than during electrical stimulation, which should be reflected in the measured stiffness. Our results indeed showed a significantly higher stiffness during voluntary activation compared with electrical stimulation at a certain moment. The total SES at a certain moment is, however, not just proportional with the total cross section of the elastic tissue, but also dependent on the stress. In case of electrical stimulation, the whole moment is taken up by the elastic tissue in series with the tibialis anterior muscle fibers, whereas in the case of voluntary activation the moment is distributed over the elastic tissue of more than one muscle. Hence, during electrical stimulation, the involved elastic tissue is working at a higher stress in the nonlinear stress-strain curve than the involved elastic tissue during voluntary contraction. Although the involved elastic tissue during voluntary contraction is working at lower stresses with lower stiffnesses, the total stiffness increases because of the larger total cross-sectional area of the elastic tissue. This implies that in vivo the total SES of the human dorsiflexors is dependent not only on which muscles are active but also on where on the stress-strain curve the involved elastic tissue is working.

Comparing stiffness values with those from the literature. A recent article written by Maganaris and Paul (11) gives a platform for comparison. They used a combination of the ultrasound technique and magnetic resonance imaging to measure tendon stiffness in the human tibialis anterior in vivo. Electrical stimulation was used to activate the tibialis anterior to make sure that only this muscle was active. This makes it possible to make a comparison with our data obtained with electrical stimulation. Maganaris and Paul (11) found an average tendon stiffness of 161 N/mm at a maximum average moment of 25 Nm. We can convert this stiffness value to a rotational stiffness by using the average moment arm of the tibialis anterior, measured by Maganaris and Paul, of 36 mm.

1

1

Nonlinearity of angle-moment curve. If the different curves with different M₀ originate from the same amount of elastic tissue, one would expect the curves to coincide when shifting the curves to the left as shown in Fig. 3. As can be seen from Fig. 5B, this indeed was the case. This phenomenon is further supported by research done on animals; the aponeurosis is already totally involved at low forces because of the lateral shear transmission of force (9), and the muscle fibers active at low forces are not concentrated in one part of the muscle but are distributed (3). Because of this, we believe that the average curve in Fig. 5C expresses the total moment-angle curve of the SEC for a particular muscle synergy.