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Individual muscle contributions to the in vivo achilles tendon force
Clinical Biomechanics 13 (1998) 532-541
Individual muscle contributions to the in vivo achilles tendon force A. N. Arndt”“, P. V. Kom?‘, G.-P. Briiggemann”, J. Lukkariniem? ~‘Institute for Athletics and Gymnastics, German Sport University Cologne, Germuny hDepatiment of Biology of Physical Activiry University of Jyviiskyl&Jyviiskylii, Finland
Received 5 September 1997; accepted 24 March 1998
Abstract Objective. To ascertain the possibility of non-uniform stress within the achilles tendon due to individual force contributions of the triceps surae. Design. Calculation of non-uniform stress through discrepancies in moments about the ankle joint. Background. Non-uniform stress over the cross-sectional area have been implied in the etiology of achilles tendon injury and may influence functional aspects.However, this has not been empirically demonstrated. Methods. In vivo achilles tendon forces were measured with an optic fibre technique during isometric plantarflexions at systematically varied knee angles and contraction intensities. A comparison to the plantar force measured underneath the metatarsal heads permitted the calculation of the achilles tendon contribution to the resultant plantarflexion moment. The achilles tendon force was further differentiated into gastrocnemius and soleus contributions. Individual muscle activation patterns were described. Results. The average achilles tendon contribution to the resultant moment was 67.4%. Variations were found at different knee angles and contraction intensities. A force discrepancy of 967 N occurred between gastrocnemius and soleus over a gastrocnemius length change of 2.67 cm. This corresponded to a stress discrepancy of 21 N/mm’ over the tendon cross-sectional area. Separate muscles showed individual activation patterns. Conclusions. Non-uniform stress in the achilles tendon can occur through modifications of individual muscle contributions. Relevance
Non-uniform stress in the achilles tendon has been implied in its injury etiology. This study demonstrated such loading resulting from discrepancies in individual muscle forces. 0 1998 Elsevier Science Ltd. All rights reserved. Keywords: Achilles tendon; Triceps surae; In vivo force; Ankle joint moments; Force-length relationship; Non-uniform stress
1. Introduction Non-uniform stress has frequently been described as an etiological factor in achilles tendon injury. Stress (force/cross-sectional area) concentrations within the tendon are assumed to precede microtears [l-4] or to result in frictional forces between fibres leading to fibre damage and tendinitis [3,5,6]. There has, however, been a tendency for epidemiological and clinical studies to describe this possibility in a symptom oriented manner with no direct evidence of non-uniform stresses within the tendon. A theoretical simulation study of a dynamic starting movement involving a topple-over effect at the ankle joint [7] is at *Corresponding author: Dept of Orthopaedics K54, Huddinge University Hospital, 141 86 Huddinge, Sweden. 026%0033/98/$19.00+ 0.00 0 1998 Elsevier Science Ltd. All rights reserved PII: SO268-0033(98)00032-l
this stage the only quantification of such loading patterns. In the described specific movement it was shown that forces in a lateral compartment of the tendon will considerably exceed those in other parts. A recent investigation of human achilles tendon morphology [8] demonstrated that collagen fibres interchange between fascicles. This indicates that non-uniform muscle forces may be mechanically distributed across the tendon cross-sectional area. Conversely, however, non-uniform in vitro loading of muscle components results in variability of the functional effects upon the calcaneus and the forces measured in medial and lateral tendon compartments [91. Achilles tendon forces calculated by a moment arm approach with the input of plantarflexion forces must be treated with caution as they will not demonstrate
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any variations in the achilles tendon contribution to the plantarflexion force with a varying force-length relationship of the triceps surae. Human achilles tendon forces have been measured in viva in a number of studies [l&12] including one in which the achilles tendon moment and residual muscle moment were described during cycling [13]. The anatomical configuration of the triceps surae presents the opportunity to alter the gastrocnemius muscle length by modifications of the knee angle while maintaining constant lengths of all synergists in plantarfiexion [14-l 61. A controlled static experimental determination of the gastrocnemius force-length relationship through in vivo force measurements has not been conducted. Recent developments in in vivo measuring techniques have provided us with the essentially non-invasive optic fibre technique [17] which was applied in this study. Although it has been shown that in viva and mathematically derived forces of the ankle plantarflexors in kangaroo rats are essentially the same during dynamic movements [ 181,a more precise differentiation of this relationship could be applied to a description of discrepancies dependent upon the plantarflexor force-length relationship. The accuracy of static mathematical assumptions across various joint configurations could thus be shown. The intention of this study was to investigate muscle force-length properties, their influence upon the achilles tendon force and to subsequently quantify the tendon stress. Furthermore, it was an attempt to establish the achilles tendon contribution to the resultant plantarflcxion moment and the specific contribution of the gastrocncmius to the achilles tendon force.
2. Methods 2. I. Experimental design
The assessment of stress inconsistencies across the cross-sectional area of the tendon followed a three step design. Firstly the gastrocnemius (GAST) force-length relationship was derived utilizing the in vivo achilles tendon force (ATF) as input. This relationship was acquired by calculating the force difference to that occurring at x = 90”. GAST muscle length changes ( AIC+,,,~~) were established through regression equations [19]. As the ankle angle at the sagittal plane (/?) was constant, only the equation utilizing knee angle at the sagittal plane (x) as input was required. In a second step the contribution of the achilles tendon (MA) to the resultant plantarflexion moment (MR) was obtained from the discrepancies in the moments about the ankle joint. Finally MA was separated into soleus (SOL) and GAST contributions and the differences described.
PFF
LM
Fig. 1. The measured forces and moment arms. PFF: Plantarflexion force. ATF: In viva achilles tendon force. LM: Center of the lateral maleolus (the assumed axis of plantarflexion about the ankle). 1: Head of metatarsal V. 2: Insertion point of the optic fiber. P: Moment arm of the PFF about the ankle. S: Moment arm of the ATF about the ankle.
MR is the moment about the ankle joint contributed by all active and passive structures (muscles, tendons, ligaments and skin). MR and MA were calculated with eqns (1) and (2). The variables required for these equations are presented in Fig. I. The static design eliminated acceleration and inertial parameters. The plantaris muscle was assumed to have negligible force production potential. MK was calculated with eqn (l), M, with eqn (2):
MK=PFFxP
VI
M,\=ATFxS
(4
If non-muscle structures arc neglected, then: (3) MR = M,t++Mtqq
(4)
According to eqn (3) and (4), the GAST contribution (M,,,,) to M, can be determined from changes in MA and MR if the assumption is made that the forces produced by the SOL (FSOL) and the remaining plantarflexors (FPIFI)remain constant at all knee angles. An increase in MA is equivalent to an increase in MCAST.It was assumed that FGAsT= 0 N at a = 90” as it has been mentioned previously that this muscle will produce little or no force at such short lengths [15]. With known moment arms about the ankle joint centre the relative increase of FGAsTto FsoL and consequently an indication of non-uniform stress of the achilles tendon can be obtained. The distribution of such loads over the cross-sectional area (the stress acting upon the tendon) was approximated by determining this area for one subject with ultrasound. SOL, GM (medial head of the gastrocnemius) and GL (lateral head of the gastrocnemius) activity at varying plantarflexion intensities and knee angles were recorded with electromyography
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(EMG). Additional validation recordings were made on the vastus lateralis and gluteus maximus muscles to control their activity and consequently the possibility of their contributing indirectly to the measured PFF (plantarflexion force measured under the metatarsals). 2.2. Data acquisition The subjects lay in a supine position on a specifically constructed plantarflexion machine (Fig. 2). This machine was designed to eliminate the influence of gravity upon the moments about the ankle at different knee angles. The lower leg was set in a horizontal position. Length changes of the SOL, PlFl* or the achilles tendon moment arm were avoided by setting the ankle angle at 90” (neutral position). The greater trochanter (GT), lateral knee joint centre (KJ) and lateral maleolus (LM) were marked for definition of segment end points to determine the knee angle. This was defined as the internal angle between an extension of the thigh (GT-KJ) and the lower leg (KJ-LM), the ankle angle was defined as the angle between the lower leg and the sole of the foot. Knee angles were set with a manual goniometer. A one dimensional strain gauge force sensor was installed under the metatarsal heads to determine the normal component of the plantarflexion force. A change in the resistance of the strain gauge resulting *The remaining plantarflexors (peroneus longus, peroneus brevis, tibialis posterior, flexor digitorum longus, flexor hallucis longus).
from compression of the strain gauge carrier was transformed into a voltage signal proportional to the force. The output was amplified by a standard strain gauge amplifier prior to analog to digital conversion. The ATF was measured with an optic fibre technique [17]. The advantage of this methodology in comparison to previous techniques of in vivo force measurement on human anatomical structures [11,13] is that it facilitates an essentially non-invasive procedure for implanting the force sensor. This considerably reduces the injury risk (especially that of infection) to the subject. A static load test of this technique has demonstrated a linearity of the measured values to the input force of r = 0,999 [17]. Details of this procedure have been described elsewhere [17]. Scaling of the PFF and ATF signals into Newtons was conducted with the data analysis software 22 (C. Steppat, Kiiln, Germany). The forces were obtained from the raw data by defining a 1 s interval in which the curves approximated a plateau (Fig. 3). The average value was calculated for this interval. As opposed to animal experiments in which force sensors can be calibrated in terminal experiments [18], the calibration in human in vivo experiments must proceed directly on the tendon. In this study the optic fibre was calibrated through the PFF. The distance from the point of application of the PFF under the metatarsals and the point of the tendon insertion to the centre of the lateral maleolus were measured. Assumptions required for this calibration procedure were:
Straingauge force !iemor Qptic fiber Light transmitter andreceiver
Fig. 2. Experimental setup. Execution of an isometric plantarflexion at a defined knee angle (a). The ankle angle (0) was set at 90”.
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PFF[V] 4
4900
--1O”cal.
6
100
Fig. 3. An example of raw force data for one trial. The dotted vertical lines define the one second interval in which all data points were averaged for the determination of the variables ATF and PFF.
1. The knee and ankle are frictionless joints. 2. The line of force application of the achilles tendon on the calcaneus is constant at varying knee angles. 3. The axis about which plantarflexion occurs passes through the centre of both maleoli. 4. The greatest GAST proportion of the plantarflexion torque is produced when the leg is extended [15,16]. Therefore, the most accurate representation of the PFF by the optic fibre signal occurs at LX=10”. On the basis of this assumption the calibration proceeded across various plantarflexion contraction intensities at c(= lo”. 5. Although variations in the knee angle change the length of the complete muscle tendon complex, the passive force in the achilles tendon can be neglected. Differences in the fibre output result from variations in muscle force only. Other authors [15,20,21] observed only minimal passive muscle forces at the length changes used in this study. Consequently the passive tendon force is also minimal. The ATF calculation required for the optic fibre calibration was performed with eqn (5). Moment arms are as illustrated in Fig. 1: ATF = (PIS)xPFF
200
300 ATF[mv]
Time [s]
(5)
One of the aims of this study was to establish differences between the ATF and PFF resulting from modified muscle lengths. Such differences would not be observed if the ATF had been calibrated with the PFF (eqn (5)) at all angles. Relatively high ATF values recorded by the optic fibre would remain consistently proportional to the PFF. Figure 4 illustrates the relationship between ATF and PFF at all knee angles for subject EL (subject details are presented in Table 1). This data is illustrated as the optic fibre signal (x-axis) against the strain gauge signal.
Fig. 4. Calibration of the optic tibre. Subject EL. Dotted line: PFF = 6.68 x ATF[mV], i.e. ATF = 6.68 N/mV.
Figure 4 provides an indication of the GAST forcelength relationship, as lower optic fibre signals were obtained at the same PFF values. This effect would have been removed if the scaling factor had been determined by averaging all knee angles for calculating the ATF from the PFF (eqn (5)). Calibration of the optic fibre across four plantarflexion intensities at only M= lo” permitted the identification of such discrepancies between ATF and PFF in the results. The regression line for c(= lo” was used for calibrating the optic fibre. The cross-sectional area of the achilles tendon of subject EL was obtained with a 7.5 MHz real-time ultrasound scanner (model SSD 28OLS, Aloka, Helsinki, Finland). The measurement proceeded approximately 40 mm above the point of insertion of the tendon, at about the same height at which the optic fibre was inserted. The tendon circumference was digitized with a cursor and the area calculated. Two 4 mm diameter miniature EMG surface electrodes (model 650437, Beckmanns, Illinois, USA) were positioned 2 ems apart on the centre of the muscle bellies of SOL, GM and GL and connected to a telemetry system for data capture (Glonner, Germany). The EMG signal of each complete trial was rectified and time base integrated (20 ms intervals) and the integral of this signal (IEMG) was calculated over the same 1 s interval for which the force values were Table 1 Subject details. The moment arms S and P are defined in Fig. 2 Subject
Height
Weight
Age
Moment arms
bl
[kg1
[Yl
[mm1 S
P
150 125 128
EL(m)
194
96.5
26
55
Ww)
170 176
58.0 77.0
23 44
46 45
HT(m)
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Biomechanics 13 (1998) 532-541
determined for each trial (Fig. 3). The highest IEMG of each subject across every trial was set as 100% and the integrals of all other trials were normalized to this maximum. The synchronized recording and storage of all analog signals was conducted with a 12 bit analog to digital converter on a PC with the data collection software Codas (Dataq Instruments, Akron, USA). The sampling rate was 1000 Hz. 2.3. Experimental procedure
The posterior surface of the right lower leg was disinfected and treated with EMLA skin anesthetic creme (Astra, Sodertalje, Sweden; active ingredients: Lidocain and Prilocain). After approximately 15 min the achilles tendon was palpated 20-60 mm above the point of insertion to determine the location of the optic fibre. A disinfected cannula (0 = 1.1 mm, length = 40 mm) was inserted into the tendon centrally in the frontal plane perpendicular to the long axis of the tendon. The disinfected optic fibre was threaded through the cannula after which this was removed and the two fibre ends were attached to the transmitter and receiver. An optic fibre inserted in the achilles tendon is shown in Fig. 5. The subjects performed maximum isometric plantarflexion contractions at nine different knee angles (a = lo”-90” in 10 increments). The most extended angle was lo” as no subject could extend to 0”. In each trial the subjects were instructed to maintain the maximum force for at least 1 s whereby no feedback of the obtained force was received to minimize motivational factors. The order of angles was randomized. Plantarflexions at different intensities were executed at knee angles lo”, 30”, 60” and 90” to provide a description of the influence of these variations on the force contribution and activation patterns of the triceps
surae components. The sub-maximal intensity levels were achieved by reading the strain gauge signal from an analog dial. The subjects were instructed to control the plantarflexion contractions at the intensities 25% (PFF,,), 50% (PFF,,,) and 75% (PFFT5) of the maximum via feedback from the analog dial. Fatigue effects were minimized by allocating two minute rests between trials at the same angle and at least five minutes between different angles. Each subject performed one trial for each angle-intensity combination. 2.4. Subjects
Three subjects participated in the study (Table 1) after being informed of the risks and purposes involved. 3. Results 3.1. Force-length relationship
The optic fibre technique was proven to be more sensitive to interference than expected. Only four data points could be utilized for subjects TL and HT. The optic fibre of subject TL received a kink and the baseline of that of subject HT drifted after the data was obtained. A complete data set was therefore, only obtained for subject EL. The PFFrvlAX(plantarflexion force at maximum voluntary contraction) data acquired for all subjects at varying GAST lengths is illustrated in Fig. 6. The example of subject EL in Fig. 6 demonstrates that the force-length relationship of the gastrocnemius lies upon the ascending limb. AATF [N] 2000
0
1500 i
1000 -
o&a. 08
Fig. 5. An optic fibre inserted in the achilles tendon. The cannula has been removed and the fibre ends connected to the transmitter and reciever.
Fig. 6. Force TL and HT. points of 716.262 xx-
I. OS
I.I.1. 14
195
2,0
’ 2,5
*
J.0 3,0
n EL OTL AHT %.4sT-1 lengh relationship of the gastrocnemius. Subjects EL, The polynomial regression curve fitted to the data subject EL has the equation: y = 60.345 + 136.976 XX’@ = 0.923~ = 0.003).
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The value of the in viva technique was illustrated by comparing the ATF as measured by the optic fibre to the ATF calculated through a moment arm and PFF approach. A comparison of the results obtained by these two techniques at the angles 30” and 90” is shown in Fig. 7. At 90” the in vivo ATF deviated considerably from the calculated force: from 76.5% at 25% maximum intensity to 62.0% at maximum contraction intensity. At 30” the corresponding values were 92.5% and 90%. The calculated results do not reveal that at more extended knee angles (i.e. greater muscle lengths) a greater proportion of the resultant moment about the ankle joint is derived from forces transferred through the achilles tendon. 3.2. Resultant and achilles tendon moments After the force-length relationship had been established, the moment arms P (PFF to the ankle joint centre) and S (ATF to the ankle joint centre) could be Am IN A -
3500 3000
2500
used to calculate the moments MR and MA through eqns (2) and (3). This was performed with the complete data set of subject EL. The contribution of MA to MR was determined at PFF,,, (Fig. 8a) and at the varying intensities (Fig. Sb). The data shown in Fig. 8 was used to describe the percent contribution of MA to MR. The results are presented in Table 2. 3.3. The contributions of GAST and SOL to the achilles tendon moment The force production potential of SOL and CAST at varying muscle lengths were investigated in order to explore the possibility of a non-uniform stress of the achilles tendon. This was quantified by means of the data from the MA - MR relationship at PFFMm under the previously described assumptions. Equations (4) and (5) yielded the results presented in Table 3. The information concerning the calculated moments and the achilles tendon moment arm of subject EL (55 mm) was used to show that across the complete range of muscle lengths of 2.67 cm, FGASTvaried by 967 N. The cross-sectional area of the achilles tendon of this subject was 92 mm’. If this area is equally divided into collagen fibres transferring FsoL and FFAsT (i.e. 46 mm’ each) then the demonstrated force increase would result in an increased loading of the GAST fibres of 21 N/mm*. According to these calculations MPIFl (moment produced by remaining plantarflexors) was 44.3 Nm lower at a = lo” than at a = 90”. 3.4. Electromyography
dc. 3o” -o- meas.30” -e &c. 900 -x3 meas.!w --m-
% max.int.
Fig. 7. Comparison of calculated and measured achillers tendon forces. Of special interest is the large deviation at flexed knee and high contraction intensity.
The normalized IEMG results for the SOL, GM and GL at the four angles for which the intensities were varied are illustrated in Fig. 9. This data includes the results of all three subjects. B
A
W?W
WW t
PFF-
200‘
PFF
15
-I
150 ---____-A l@) -
A/-------
____ --.----.,’ ,/.’
PFF
25
50 0’
I
I
,
0,5
1
1,5
I
I
2 2,5 AL cxdcml
0,5
Fig. 8. Resultant and achilles tendon moments. A. MR and M,, at PFF MAXand different and PFF,S of the same subject over the same muscle length changes.
1
1,5
2 2,5 AL G*sr[cml
muscle lengths (AILoAsT) for subject EL. B. PFFS5. PFFs,,
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Table 2 MA proportions of MR. All values prsented as pecentages of MR. Note the tendancy to decreasing contributions with increasing intensity and more
flexed knee. The mean for PFFhnAxover all angles was 67.4& 13.0%. The last column shows the mean + SD at each knee angle and the last row shows the same values for each intensity. The bottom right entry shows the overall means and standard deviations first of the last row then of the last column (in parentheses) Plantarflexion intensity
Knee angle
[“I 10 20 30 40 50 60 70 80 90 Mean
PFFzr[%I
PFFso [%I
PFFn[%I
121.4
114.4
103.3
106.3
94.8
77.6
104.8
93.7
74.7
68.2 100.2 (SD22.6)
67.2 92.5 (SD19.4)
56.4 78.0 (SD19.3)
-
Table 3 Variations in the moments produced by different muscles. Calculated at knee angles of 90” and 10 MGAST
u=90 u= 10”
[Nml
0 53.2
MsoLWI
MPIFl [Nml
60.3 60.3
84.3 40.0
PFhx [%I
Mean[%](SD)
74.0 87.0 76.7 57.2 73.0 67.9 68.0 60.8 41.7 67.4 (SD13.0)
103.3 (SD20.9) 88.9 (SD14.3) 85.3 (SD17.0) 58.4 (SD12.3) 84.5 (84.0)
Of major interest in Figs 9 and 10 is the SOL and GM data. At a = 10” GM activity was clearly higher than that of the other muscles. SOL activity was the lowest of the three muscles at lo”, similar at 30” and 60” and highest at 90”. At 60” the curves are all similar and the values at PFFMAx are higher for all muscles than at 30” (SOL: 90%, 71%; GM: 85%, 74%; GL: 87%, 67%). At 90” both GAST components were clearly less active than SOL. Fig. 10 further clarifies the
% max. IEMG loo
-
b
I
0 25
50
7s
100
“25
50
25
SO
75
100
“25
50
SOL+
GM+
GL +
15
100
75
100
% max. Intensity
Fig. 9. Muscle activation patterns at increasing intensity. IEMG of SOL, GL and GM at lo”, 30”, 60” and 90” knee angles. Average values for three subjects.
A. N. Arndt et al./Clinical
Biomechanics 13 (1998) 532-541
% max. IEMG
“10
30
60
90
a [“I SOL+
GM++
GLt
Fig. 10. Normalized IEMG at maximum intensity. The results at maximum intensity and increasing knee flexion. As each illustrated data point only incorporates three values, no tests for significant differences were conducted.
relative activity of the three muscles at varying knee angles by showing only the data for PFFMUIAX. The inverse pattern of SOL and GM is again noticeable. The data presented in Fig. 10 are in general agreement with those found in the literature [16]. These similarities are described in greater detail in the discussion. 4. Discussion The present study followed a case study design with a complete data set for one subject. No statistical tests were conducted and further research with a greater database is required for confirmation of the significance of the presented results. The advantageous anatomical features of the human GAST utilized in this study have been used previously for modifying the length of this muscle [14-16,221. Only one group has applied this phenomenon directly to the experimental determination of the gastrocnemius force-length relationship [15]. By varying both the knee and ankle angles muscle length, changes considerably greater than those of this study were achieved (hLcAsT = 4.0 cm and 2.67 cm, respectively). It appeared inappropriate for the aims of this study to incorporate variations in ankle angle as the GAST length was to be varied at constant SOL and PlFl lengths. The force-length relationship for the GAST was described from M.= lo”-90” (Fig. 6) and confirmed that over this range of motion the force production increased with increasing muscle length [15]. The passive force increase for the muscle length changes studied here can be assumed to be negligible [15] and they were not considered in the results. Various studies have calculated the achilles tendon to contribute between 62% and 77% to the plantar-
539
flexion moment [13,23,24]. A study in which the achilles tendon force was measured in vivo during ergometer cycling to determine the contribution of MA to MR indicated a constant 65% contribution by the achilles tendon at all stages of the pedal cycle and at three different work loads [13]. In this study the average contribution of MA to MR of 67.4% agrees with those mentioned in the literature. However, it was found that the contribution varies with muscle length and contraction intensity. In cycling, muscle activity of knee and hip extensors or a flexion of the upper body over the leg in the early stage of the pedal cycle may cause a non-proportional increase of MR relative to MA. An EMG control of the gluteus maximus and vastus medialis conducted in this study showed that with this static experimental setup the activity of these muscles was minimal at both extreme angles of a = lo” and 90”. At PFFzs and knee angles of lo”, 30” and 60” MA contributions to MR of over 100% were calculated (Fig. 8 and Table 2). A possible explanation for this is that in controlling the sub-maximal intensities antagonists such as the tibialis anterior were active and thus produced an opposing moment about the ankle. The achilles tendon would therefore, transfer more force relative to MR. This interpretation is supported by the fact that contributions of over 100% were calculated for all sub-maximal intensities when the leg was extended (a = 100). Many animal experiments have indicated different amplitudes of gastrocnemius and soleus force production during different movements [25-281. The extent to which these results can be applied to humans is unknown and furthermore, it is not possible to separate the tendons of the individual triceps surae components for the application of force sensors [9]. In vivo force measurements conducted during isometric plantarflexion permitted an estimation of the GAST and SOL contributions to MA. This represented the primary aim of this study in that it presented the possibility of assessingand quantifying non-uniform stress of the achilles tendon. MCAsT increased by 53.2 Nm over the complete range of muscle lengths. At the given achilles tendon moment arm (S = 55 mm) this represented a GAST force increase of 967 N. MsoL (moment produced by the soleus muscle) was assumed to be constant and was calculated to be 60.3 Nm (a SOL force of 1100 N if both GAST and SOL have the same achilles tendon moment arm). MPIFl was calculated to be 84.3 Nm at u = 90”. The assumption of a constant MsoL and MPIFIwas, however, proven not to hold as the increase in MR was less steep than that of MA. Consequently a decreased Mpln of 40 Nm was calculated for the extended knee condition although the less steep MR curve may also have resulted from decreased SOL force. An explanation for this is that an increase in GAST force with an extended leg incorporates a short-
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erring of the SOL muscle tendon complex and consequently exerts a negative influence upon the SOL force-length relationship [14]. This would result in decreased stress in SOL portions of the tendon at simultaneously increasing GAST stress. The tendon cross-sectional area of one subject was measured as 92 mm’. Under the assumption that SOL and GAST fibres each occupy half of this area (i.e. 46 mm* each) a stress discrepancy of 21 N/mm2 was calculated. Such a difference in forces originating solely from static muscle activity represents a considerable factor in etiological theories concerning achilles tendon injuries and function. The electromyographical results showed that the relationship of muscle activation between different components of the triceps surae vary if the length of the GAST and plantarflexion contraction intensity are modified. As the absolute SOL activity increased it is postulated that unfavourable force length characteristics of the GAST are compensated by increased neuromuscular activation of the SOL. A sigmoidal curve was obtained for the activation of both GAST components whereas a flatter curve resulting from knee flexion has been reported for GM elsewhere [ 161. A lower relative normalized GM activation has also been reported to occur with plantarflexed ankles [14]. The results presented in Fig. 10 support these data with decreased activity at decreased muscle lengths which has been attributed to impaired neuromuscular transmission or a reduction in the neural impulse of the spinal motor neurons [16,29]. Previous studies have posed the question whether tendon morphology permits stress to be evenly distributed over the tendon cross-sectional area [8] or conversely if different moments are transferred to the calcaneus dependent upon which triceps surae component is loaded [9]. The present study supports the occurrence of non-uniform forces in v&o. It can therefore, be concluded that non-uniform force input to the achilles tendon is not evenly distributed over the tendon and will lead to stress concentrations within the tendon and varying functional effects upon the calcaneus. 5. Conclusions
The study demonstrated that different muscle characteristics of the triceps surae components can cause non-uniform influences upon the force production and muscle activation patterns and consequently the loading of the achilles tendon. A discrepancy in GAST and SOL forces was established over an 80 range of knee motion. Such a quantification of nonhomogenous tendon loading resulting from non-uniform muscle forces has not been presented to
date. The data indicates an important factor in the etiology of tendon injury in the form of load concentrations within the tendon and also frictional forces between individual collagen fibres. Both mechanisms may subject the tendon to localized fibre damage and subsequently inflammation, partial ruptures or even total rupture. A further implication introduced by the results is that a non-uniform force production of the various components of the triceps surae may lead to different functional effects of the achilles tendon on the calcaneus. It is suggested that future research based upon biomechanical models of the human achilles tendon takes the possibility of non-uniform stress into account. References [l] Clement DB, Taunton JE, Smart GW. Achilles tendinitis and peritendinitis: etiology and treatment. The American Journal of Sports Medicine 1984;13(3):179-184. der [2.] Hawe W, Klecker N, Bernett P. Uberlastungssyndrome unteren Extremitlt bei Ausdauersportlern. Sportmedizin 1990;41:420-425. [3] Biedert R. Beschwerden im Achillessehnenbereich. Unfallchirurg 1991;94:531-537. [4] Lohrer H. Die achillodynie Eine Ubersicht. Sportorthopadie-Sporttraumatologie 1996;12( 1):36-42. [5] Segesser B, Nigg BM, Morel1 F. Achillodynie and tibiale Insertionstendinosen. Medizin und Sport 1980;20:79-83. [6] Segesser B. Atiologie von reversiblen and irreversiblen Sportschlden. Schweizerische Zeitschrift fiir Sportmedizin 1983;31:81-86. [7] Wallenbock E, Lang 0, Lugner P. Stress in the achilles tendon during a topple-over movement in the ankle joint. Journal of Biomechanics 1995;28(9):1091-1101. [8] Arndt AN, Notermans H-P, Koebke J, Briiggemann G-P. Zur Fasertextur der menschlichen Achillessehne Eine Analyse durch Mazeration. Der Praparator 1997;43:63-70. [9] Arndt AN. Entstehung und Auswirkungen asymmetrischer Belastung der menschlichen Achillessehne unter besonderer Berucksichtigung ihrer Morphologie. Doctoral Dissertation, German Sport University Cologne, Germany, 1997. [lo] Gregor RJ, Komi PV, Jarvinen M. Achilles tendon forces during cycling. International Journal of Sports Medicine 1987;8:9-14. [ll] Komi PV, Salonen M, Jarvinen M, Kokko 0. In viva Registration of Achilles tendon forces in man. I methodological development. International Journal of Sports Medicine 1987$:3-g. [12] Komi PV, Fukashiro S, Jarvinen M. Biomechanical loading of achilles tendon during normal locomotion. Clinics in Sport Medicine 1992;11(3):521-531. [13] Gregor RJ, Komi PV, Browning RC, Jlrvinen M. A comparison of the triceps surae and residual muscle moments at the ankle during cycling. Journal of Biomechanics 1991;24(5):287-297. [14] Sale D, Quinlan J, Marsh E, McComas AJ, Belanger AA. Influence of joint position on ankle plantarflexion in humans. Journal of Applied Physiology 1982;52(6):1636-1642. [15] Herzog W, Read LJ, ter Keurs HEDJ. Experimental determination of force-length relations of intact human gastrocnemius muscles. Clinical Biomechanics 1991;6:230-238. [16] Cresswell AG, Loschner WN, Thorstensson A. Influence of gastrocnemius muscle length on triceps surae torque develop-
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[17]
[18]
[19]
[20]
[21]
[22]
[23]
ment and electromyographic activity in man. Experimental Brain Research 1995;105:283-290. Komi PV. Belli A, Huttunen V, Bonnefoy R, Geyssant A, Lacour JR. Optic fibre as a transducer of tendomuscular forces. European Journal of Applied Physiology 1996;72:278-280. Biewener AA, Blickhan R, Perry AK, Hegland NC, Taylor CR. Muscle forces during locomotion in kangaroo rats: Force platform and tendon buckle measurements compared. Journal of Experimental Biology 1988;137:191-205. Grieve DW, Pheasant S, Cavanagh PR. Prediction of gastrocnemius length from knee and ankle joint posture. In: Asmussen E, Jorgensen K, editors. Biomechanics VI-A. Baltimore: University Park Press. 1978. p.405-12. Woittiez RD, Huijing PA, Rozendal RH. Influence of muscle architecture on the length-force diagram. A model and its verification. Pfliigers Archiv. European Journal of Physiology 1983;397:73-74. Woittiez RD, Huijing PA, Rozendal RH. Influence of muscle architecture on the length-force diagram of mammalian muscle. Pfliigers Archiv. European Journal of Physiology 1983;399:275-279. Fugl-Meyer AR, Custafsson L, Burstedt Y. Isokinetic and static plantar flexion characteristics. European Journal of Applied Physiology 1980;45:221-234. Murray MP, Guten GN, Baldwin JM, Gardner GM. A
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comparison of plantar flexion torque with and without the triceps surae. Acta Orthopaedica Scandinavica 1976;47:122-124. [24] Fukunaga T, Roy RR, Shellock FG., Hodgson JA, Day MK, Lee PL. Kwong-Fu H, Edgerton VR. Physiological crosssectional area of human leg muscles based on magnetic resonance imaging. Journal of Orthopaedic Research 1992;10(6):926-934. [25] Fowler EC, Gregor RJ, Roy RR. Differential kinetics of fast and slow ankle extensors during the paw-shake in the cat. Experimental Neurology 1988;99:219-224. [26] Fowler EG, Gregor RJ, Hodgson JA, Roy RR. Relationship between ankle muscle and joint kinetics during the stance phase of locomotion in the cat. Journal of Biomechanics 1993;26(415):465-483. [27] Herzog W, Leonard TR, Renaud JM, Wallace J, Chaki G, Bornemisza S. Force-length properties and functional demands of cat gastrocnemius, soleus and plantaris muscles.. Journal of Biomechanics 1992:25(11):1329-1335. [28] Herzog W. Leonard TR, Guimares ACS. Forces in gastrocnemius, soleus and plantaris tendons of the freely moving cat. Journal of Biomechanics 1993;26(8):945-953. 1291 Lewis DM, Luck JC, Knott S. A comparison of isometric contractions of the whole muscle with those of motor units in a fast-twitch muscle of the cat. Experimental Neurology 1972;37:68-85.
Individual muscle contributions to the in vivo achilles tendon force A. N. Arndt”“, P. V. Kom?‘, G.-P. Briiggemann”, J. Lukkariniem? ~‘Institute for Athletics and Gymnastics, German Sport University Cologne, Germuny hDepatiment of Biology of Physical Activiry University of Jyviiskyl&Jyviiskylii, Finland
Received 5 September 1997; accepted 24 March 1998
Abstract Objective. To ascertain the possibility of non-uniform stress within the achilles tendon due to individual force contributions of the triceps surae. Design. Calculation of non-uniform stress through discrepancies in moments about the ankle joint. Background. Non-uniform stress over the cross-sectional area have been implied in the etiology of achilles tendon injury and may influence functional aspects.However, this has not been empirically demonstrated. Methods. In vivo achilles tendon forces were measured with an optic fibre technique during isometric plantarflexions at systematically varied knee angles and contraction intensities. A comparison to the plantar force measured underneath the metatarsal heads permitted the calculation of the achilles tendon contribution to the resultant plantarflexion moment. The achilles tendon force was further differentiated into gastrocnemius and soleus contributions. Individual muscle activation patterns were described. Results. The average achilles tendon contribution to the resultant moment was 67.4%. Variations were found at different knee angles and contraction intensities. A force discrepancy of 967 N occurred between gastrocnemius and soleus over a gastrocnemius length change of 2.67 cm. This corresponded to a stress discrepancy of 21 N/mm’ over the tendon cross-sectional area. Separate muscles showed individual activation patterns. Conclusions. Non-uniform stress in the achilles tendon can occur through modifications of individual muscle contributions. Relevance
Non-uniform stress in the achilles tendon has been implied in its injury etiology. This study demonstrated such loading resulting from discrepancies in individual muscle forces. 0 1998 Elsevier Science Ltd. All rights reserved. Keywords: Achilles tendon; Triceps surae; In vivo force; Ankle joint moments; Force-length relationship; Non-uniform stress
1. Introduction Non-uniform stress has frequently been described as an etiological factor in achilles tendon injury. Stress (force/cross-sectional area) concentrations within the tendon are assumed to precede microtears [l-4] or to result in frictional forces between fibres leading to fibre damage and tendinitis [3,5,6]. There has, however, been a tendency for epidemiological and clinical studies to describe this possibility in a symptom oriented manner with no direct evidence of non-uniform stresses within the tendon. A theoretical simulation study of a dynamic starting movement involving a topple-over effect at the ankle joint [7] is at *Corresponding author: Dept of Orthopaedics K54, Huddinge University Hospital, 141 86 Huddinge, Sweden. 026%0033/98/$19.00+ 0.00 0 1998 Elsevier Science Ltd. All rights reserved PII: SO268-0033(98)00032-l
this stage the only quantification of such loading patterns. In the described specific movement it was shown that forces in a lateral compartment of the tendon will considerably exceed those in other parts. A recent investigation of human achilles tendon morphology [8] demonstrated that collagen fibres interchange between fascicles. This indicates that non-uniform muscle forces may be mechanically distributed across the tendon cross-sectional area. Conversely, however, non-uniform in vitro loading of muscle components results in variability of the functional effects upon the calcaneus and the forces measured in medial and lateral tendon compartments [91. Achilles tendon forces calculated by a moment arm approach with the input of plantarflexion forces must be treated with caution as they will not demonstrate
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any variations in the achilles tendon contribution to the plantarflexion force with a varying force-length relationship of the triceps surae. Human achilles tendon forces have been measured in viva in a number of studies [l&12] including one in which the achilles tendon moment and residual muscle moment were described during cycling [13]. The anatomical configuration of the triceps surae presents the opportunity to alter the gastrocnemius muscle length by modifications of the knee angle while maintaining constant lengths of all synergists in plantarfiexion [14-l 61. A controlled static experimental determination of the gastrocnemius force-length relationship through in vivo force measurements has not been conducted. Recent developments in in vivo measuring techniques have provided us with the essentially non-invasive optic fibre technique [17] which was applied in this study. Although it has been shown that in viva and mathematically derived forces of the ankle plantarflexors in kangaroo rats are essentially the same during dynamic movements [ 181,a more precise differentiation of this relationship could be applied to a description of discrepancies dependent upon the plantarflexor force-length relationship. The accuracy of static mathematical assumptions across various joint configurations could thus be shown. The intention of this study was to investigate muscle force-length properties, their influence upon the achilles tendon force and to subsequently quantify the tendon stress. Furthermore, it was an attempt to establish the achilles tendon contribution to the resultant plantarflcxion moment and the specific contribution of the gastrocncmius to the achilles tendon force.
2. Methods 2. I. Experimental design
The assessment of stress inconsistencies across the cross-sectional area of the tendon followed a three step design. Firstly the gastrocnemius (GAST) force-length relationship was derived utilizing the in vivo achilles tendon force (ATF) as input. This relationship was acquired by calculating the force difference to that occurring at x = 90”. GAST muscle length changes ( AIC+,,,~~) were established through regression equations [19]. As the ankle angle at the sagittal plane (/?) was constant, only the equation utilizing knee angle at the sagittal plane (x) as input was required. In a second step the contribution of the achilles tendon (MA) to the resultant plantarflexion moment (MR) was obtained from the discrepancies in the moments about the ankle joint. Finally MA was separated into soleus (SOL) and GAST contributions and the differences described.
PFF
LM
Fig. 1. The measured forces and moment arms. PFF: Plantarflexion force. ATF: In viva achilles tendon force. LM: Center of the lateral maleolus (the assumed axis of plantarflexion about the ankle). 1: Head of metatarsal V. 2: Insertion point of the optic fiber. P: Moment arm of the PFF about the ankle. S: Moment arm of the ATF about the ankle.
MR is the moment about the ankle joint contributed by all active and passive structures (muscles, tendons, ligaments and skin). MR and MA were calculated with eqns (1) and (2). The variables required for these equations are presented in Fig. I. The static design eliminated acceleration and inertial parameters. The plantaris muscle was assumed to have negligible force production potential. MK was calculated with eqn (l), M, with eqn (2):
MK=PFFxP
VI
M,\=ATFxS
(4
If non-muscle structures arc neglected, then: (3) MR = M,t++Mtqq
(4)
According to eqn (3) and (4), the GAST contribution (M,,,,) to M, can be determined from changes in MA and MR if the assumption is made that the forces produced by the SOL (FSOL) and the remaining plantarflexors (FPIFI)remain constant at all knee angles. An increase in MA is equivalent to an increase in MCAST.It was assumed that FGAsT= 0 N at a = 90” as it has been mentioned previously that this muscle will produce little or no force at such short lengths [15]. With known moment arms about the ankle joint centre the relative increase of FGAsTto FsoL and consequently an indication of non-uniform stress of the achilles tendon can be obtained. The distribution of such loads over the cross-sectional area (the stress acting upon the tendon) was approximated by determining this area for one subject with ultrasound. SOL, GM (medial head of the gastrocnemius) and GL (lateral head of the gastrocnemius) activity at varying plantarflexion intensities and knee angles were recorded with electromyography
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(EMG). Additional validation recordings were made on the vastus lateralis and gluteus maximus muscles to control their activity and consequently the possibility of their contributing indirectly to the measured PFF (plantarflexion force measured under the metatarsals). 2.2. Data acquisition The subjects lay in a supine position on a specifically constructed plantarflexion machine (Fig. 2). This machine was designed to eliminate the influence of gravity upon the moments about the ankle at different knee angles. The lower leg was set in a horizontal position. Length changes of the SOL, PlFl* or the achilles tendon moment arm were avoided by setting the ankle angle at 90” (neutral position). The greater trochanter (GT), lateral knee joint centre (KJ) and lateral maleolus (LM) were marked for definition of segment end points to determine the knee angle. This was defined as the internal angle between an extension of the thigh (GT-KJ) and the lower leg (KJ-LM), the ankle angle was defined as the angle between the lower leg and the sole of the foot. Knee angles were set with a manual goniometer. A one dimensional strain gauge force sensor was installed under the metatarsal heads to determine the normal component of the plantarflexion force. A change in the resistance of the strain gauge resulting *The remaining plantarflexors (peroneus longus, peroneus brevis, tibialis posterior, flexor digitorum longus, flexor hallucis longus).
from compression of the strain gauge carrier was transformed into a voltage signal proportional to the force. The output was amplified by a standard strain gauge amplifier prior to analog to digital conversion. The ATF was measured with an optic fibre technique [17]. The advantage of this methodology in comparison to previous techniques of in vivo force measurement on human anatomical structures [11,13] is that it facilitates an essentially non-invasive procedure for implanting the force sensor. This considerably reduces the injury risk (especially that of infection) to the subject. A static load test of this technique has demonstrated a linearity of the measured values to the input force of r = 0,999 [17]. Details of this procedure have been described elsewhere [17]. Scaling of the PFF and ATF signals into Newtons was conducted with the data analysis software 22 (C. Steppat, Kiiln, Germany). The forces were obtained from the raw data by defining a 1 s interval in which the curves approximated a plateau (Fig. 3). The average value was calculated for this interval. As opposed to animal experiments in which force sensors can be calibrated in terminal experiments [18], the calibration in human in vivo experiments must proceed directly on the tendon. In this study the optic fibre was calibrated through the PFF. The distance from the point of application of the PFF under the metatarsals and the point of the tendon insertion to the centre of the lateral maleolus were measured. Assumptions required for this calibration procedure were:
Straingauge force !iemor Qptic fiber Light transmitter andreceiver
Fig. 2. Experimental setup. Execution of an isometric plantarflexion at a defined knee angle (a). The ankle angle (0) was set at 90”.
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PFF[V] 4
4900
--1O”cal.
6
100
Fig. 3. An example of raw force data for one trial. The dotted vertical lines define the one second interval in which all data points were averaged for the determination of the variables ATF and PFF.
1. The knee and ankle are frictionless joints. 2. The line of force application of the achilles tendon on the calcaneus is constant at varying knee angles. 3. The axis about which plantarflexion occurs passes through the centre of both maleoli. 4. The greatest GAST proportion of the plantarflexion torque is produced when the leg is extended [15,16]. Therefore, the most accurate representation of the PFF by the optic fibre signal occurs at LX=10”. On the basis of this assumption the calibration proceeded across various plantarflexion contraction intensities at c(= lo”. 5. Although variations in the knee angle change the length of the complete muscle tendon complex, the passive force in the achilles tendon can be neglected. Differences in the fibre output result from variations in muscle force only. Other authors [15,20,21] observed only minimal passive muscle forces at the length changes used in this study. Consequently the passive tendon force is also minimal. The ATF calculation required for the optic fibre calibration was performed with eqn (5). Moment arms are as illustrated in Fig. 1: ATF = (PIS)xPFF
200
300 ATF[mv]
Time [s]
(5)
One of the aims of this study was to establish differences between the ATF and PFF resulting from modified muscle lengths. Such differences would not be observed if the ATF had been calibrated with the PFF (eqn (5)) at all angles. Relatively high ATF values recorded by the optic fibre would remain consistently proportional to the PFF. Figure 4 illustrates the relationship between ATF and PFF at all knee angles for subject EL (subject details are presented in Table 1). This data is illustrated as the optic fibre signal (x-axis) against the strain gauge signal.
Fig. 4. Calibration of the optic tibre. Subject EL. Dotted line: PFF = 6.68 x ATF[mV], i.e. ATF = 6.68 N/mV.
Figure 4 provides an indication of the GAST forcelength relationship, as lower optic fibre signals were obtained at the same PFF values. This effect would have been removed if the scaling factor had been determined by averaging all knee angles for calculating the ATF from the PFF (eqn (5)). Calibration of the optic fibre across four plantarflexion intensities at only M= lo” permitted the identification of such discrepancies between ATF and PFF in the results. The regression line for c(= lo” was used for calibrating the optic fibre. The cross-sectional area of the achilles tendon of subject EL was obtained with a 7.5 MHz real-time ultrasound scanner (model SSD 28OLS, Aloka, Helsinki, Finland). The measurement proceeded approximately 40 mm above the point of insertion of the tendon, at about the same height at which the optic fibre was inserted. The tendon circumference was digitized with a cursor and the area calculated. Two 4 mm diameter miniature EMG surface electrodes (model 650437, Beckmanns, Illinois, USA) were positioned 2 ems apart on the centre of the muscle bellies of SOL, GM and GL and connected to a telemetry system for data capture (Glonner, Germany). The EMG signal of each complete trial was rectified and time base integrated (20 ms intervals) and the integral of this signal (IEMG) was calculated over the same 1 s interval for which the force values were Table 1 Subject details. The moment arms S and P are defined in Fig. 2 Subject
Height
Weight
Age
Moment arms
bl
[kg1
[Yl
[mm1 S
P
150 125 128
EL(m)
194
96.5
26
55
Ww)
170 176
58.0 77.0
23 44
46 45
HT(m)
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determined for each trial (Fig. 3). The highest IEMG of each subject across every trial was set as 100% and the integrals of all other trials were normalized to this maximum. The synchronized recording and storage of all analog signals was conducted with a 12 bit analog to digital converter on a PC with the data collection software Codas (Dataq Instruments, Akron, USA). The sampling rate was 1000 Hz. 2.3. Experimental procedure
The posterior surface of the right lower leg was disinfected and treated with EMLA skin anesthetic creme (Astra, Sodertalje, Sweden; active ingredients: Lidocain and Prilocain). After approximately 15 min the achilles tendon was palpated 20-60 mm above the point of insertion to determine the location of the optic fibre. A disinfected cannula (0 = 1.1 mm, length = 40 mm) was inserted into the tendon centrally in the frontal plane perpendicular to the long axis of the tendon. The disinfected optic fibre was threaded through the cannula after which this was removed and the two fibre ends were attached to the transmitter and receiver. An optic fibre inserted in the achilles tendon is shown in Fig. 5. The subjects performed maximum isometric plantarflexion contractions at nine different knee angles (a = lo”-90” in 10 increments). The most extended angle was lo” as no subject could extend to 0”. In each trial the subjects were instructed to maintain the maximum force for at least 1 s whereby no feedback of the obtained force was received to minimize motivational factors. The order of angles was randomized. Plantarflexions at different intensities were executed at knee angles lo”, 30”, 60” and 90” to provide a description of the influence of these variations on the force contribution and activation patterns of the triceps
surae components. The sub-maximal intensity levels were achieved by reading the strain gauge signal from an analog dial. The subjects were instructed to control the plantarflexion contractions at the intensities 25% (PFF,,), 50% (PFF,,,) and 75% (PFFT5) of the maximum via feedback from the analog dial. Fatigue effects were minimized by allocating two minute rests between trials at the same angle and at least five minutes between different angles. Each subject performed one trial for each angle-intensity combination. 2.4. Subjects
Three subjects participated in the study (Table 1) after being informed of the risks and purposes involved. 3. Results 3.1. Force-length relationship
The optic fibre technique was proven to be more sensitive to interference than expected. Only four data points could be utilized for subjects TL and HT. The optic fibre of subject TL received a kink and the baseline of that of subject HT drifted after the data was obtained. A complete data set was therefore, only obtained for subject EL. The PFFrvlAX(plantarflexion force at maximum voluntary contraction) data acquired for all subjects at varying GAST lengths is illustrated in Fig. 6. The example of subject EL in Fig. 6 demonstrates that the force-length relationship of the gastrocnemius lies upon the ascending limb. AATF [N] 2000
0
1500 i
1000 -
o&a. 08
Fig. 5. An optic fibre inserted in the achilles tendon. The cannula has been removed and the fibre ends connected to the transmitter and reciever.
Fig. 6. Force TL and HT. points of 716.262 xx-
I. OS
I.I.1. 14
195
2,0
’ 2,5
*
J.0 3,0
n EL OTL AHT %.4sT-1 lengh relationship of the gastrocnemius. Subjects EL, The polynomial regression curve fitted to the data subject EL has the equation: y = 60.345 + 136.976 XX’@ = 0.923~ = 0.003).
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The value of the in viva technique was illustrated by comparing the ATF as measured by the optic fibre to the ATF calculated through a moment arm and PFF approach. A comparison of the results obtained by these two techniques at the angles 30” and 90” is shown in Fig. 7. At 90” the in vivo ATF deviated considerably from the calculated force: from 76.5% at 25% maximum intensity to 62.0% at maximum contraction intensity. At 30” the corresponding values were 92.5% and 90%. The calculated results do not reveal that at more extended knee angles (i.e. greater muscle lengths) a greater proportion of the resultant moment about the ankle joint is derived from forces transferred through the achilles tendon. 3.2. Resultant and achilles tendon moments After the force-length relationship had been established, the moment arms P (PFF to the ankle joint centre) and S (ATF to the ankle joint centre) could be Am IN A -
3500 3000
2500
used to calculate the moments MR and MA through eqns (2) and (3). This was performed with the complete data set of subject EL. The contribution of MA to MR was determined at PFF,,, (Fig. 8a) and at the varying intensities (Fig. Sb). The data shown in Fig. 8 was used to describe the percent contribution of MA to MR. The results are presented in Table 2. 3.3. The contributions of GAST and SOL to the achilles tendon moment The force production potential of SOL and CAST at varying muscle lengths were investigated in order to explore the possibility of a non-uniform stress of the achilles tendon. This was quantified by means of the data from the MA - MR relationship at PFFMm under the previously described assumptions. Equations (4) and (5) yielded the results presented in Table 3. The information concerning the calculated moments and the achilles tendon moment arm of subject EL (55 mm) was used to show that across the complete range of muscle lengths of 2.67 cm, FGASTvaried by 967 N. The cross-sectional area of the achilles tendon of this subject was 92 mm’. If this area is equally divided into collagen fibres transferring FsoL and FFAsT (i.e. 46 mm’ each) then the demonstrated force increase would result in an increased loading of the GAST fibres of 21 N/mm*. According to these calculations MPIFl (moment produced by remaining plantarflexors) was 44.3 Nm lower at a = lo” than at a = 90”. 3.4. Electromyography
dc. 3o” -o- meas.30” -e &c. 900 -x3 meas.!w --m-
% max.int.
Fig. 7. Comparison of calculated and measured achillers tendon forces. Of special interest is the large deviation at flexed knee and high contraction intensity.
The normalized IEMG results for the SOL, GM and GL at the four angles for which the intensities were varied are illustrated in Fig. 9. This data includes the results of all three subjects. B
A
W?W
WW t
PFF-
200‘
PFF
15
-I
150 ---____-A l@) -
A/-------
____ --.----.,’ ,/.’
PFF
25
50 0’
I
I
,
0,5
1
1,5
I
I
2 2,5 AL cxdcml
0,5
Fig. 8. Resultant and achilles tendon moments. A. MR and M,, at PFF MAXand different and PFF,S of the same subject over the same muscle length changes.
1
1,5
2 2,5 AL G*sr[cml
muscle lengths (AILoAsT) for subject EL. B. PFFS5. PFFs,,
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A. N. Amdt et al.IClinical Biomechanics 13 (1998) 532-541
Table 2 MA proportions of MR. All values prsented as pecentages of MR. Note the tendancy to decreasing contributions with increasing intensity and more
flexed knee. The mean for PFFhnAxover all angles was 67.4& 13.0%. The last column shows the mean + SD at each knee angle and the last row shows the same values for each intensity. The bottom right entry shows the overall means and standard deviations first of the last row then of the last column (in parentheses) Plantarflexion intensity
Knee angle
[“I 10 20 30 40 50 60 70 80 90 Mean
PFFzr[%I
PFFso [%I
PFFn[%I
121.4
114.4
103.3
106.3
94.8
77.6
104.8
93.7
74.7
68.2 100.2 (SD22.6)
67.2 92.5 (SD19.4)
56.4 78.0 (SD19.3)
-
Table 3 Variations in the moments produced by different muscles. Calculated at knee angles of 90” and 10 MGAST
u=90 u= 10”
[Nml
0 53.2
MsoLWI
MPIFl [Nml
60.3 60.3
84.3 40.0
PFhx [%I
Mean[%](SD)
74.0 87.0 76.7 57.2 73.0 67.9 68.0 60.8 41.7 67.4 (SD13.0)
103.3 (SD20.9) 88.9 (SD14.3) 85.3 (SD17.0) 58.4 (SD12.3) 84.5 (84.0)
Of major interest in Figs 9 and 10 is the SOL and GM data. At a = 10” GM activity was clearly higher than that of the other muscles. SOL activity was the lowest of the three muscles at lo”, similar at 30” and 60” and highest at 90”. At 60” the curves are all similar and the values at PFFMAx are higher for all muscles than at 30” (SOL: 90%, 71%; GM: 85%, 74%; GL: 87%, 67%). At 90” both GAST components were clearly less active than SOL. Fig. 10 further clarifies the
% max. IEMG loo
-
b
I
0 25
50
7s
100
“25
50
25
SO
75
100
“25
50
SOL+
GM+
GL +
15
100
75
100
% max. Intensity
Fig. 9. Muscle activation patterns at increasing intensity. IEMG of SOL, GL and GM at lo”, 30”, 60” and 90” knee angles. Average values for three subjects.
A. N. Arndt et al./Clinical
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% max. IEMG
“10
30
60
90
a [“I SOL+
GM++
GLt
Fig. 10. Normalized IEMG at maximum intensity. The results at maximum intensity and increasing knee flexion. As each illustrated data point only incorporates three values, no tests for significant differences were conducted.
relative activity of the three muscles at varying knee angles by showing only the data for PFFMUIAX. The inverse pattern of SOL and GM is again noticeable. The data presented in Fig. 10 are in general agreement with those found in the literature [16]. These similarities are described in greater detail in the discussion. 4. Discussion The present study followed a case study design with a complete data set for one subject. No statistical tests were conducted and further research with a greater database is required for confirmation of the significance of the presented results. The advantageous anatomical features of the human GAST utilized in this study have been used previously for modifying the length of this muscle [14-16,221. Only one group has applied this phenomenon directly to the experimental determination of the gastrocnemius force-length relationship [15]. By varying both the knee and ankle angles muscle length, changes considerably greater than those of this study were achieved (hLcAsT = 4.0 cm and 2.67 cm, respectively). It appeared inappropriate for the aims of this study to incorporate variations in ankle angle as the GAST length was to be varied at constant SOL and PlFl lengths. The force-length relationship for the GAST was described from M.= lo”-90” (Fig. 6) and confirmed that over this range of motion the force production increased with increasing muscle length [15]. The passive force increase for the muscle length changes studied here can be assumed to be negligible [15] and they were not considered in the results. Various studies have calculated the achilles tendon to contribute between 62% and 77% to the plantar-
539
flexion moment [13,23,24]. A study in which the achilles tendon force was measured in vivo during ergometer cycling to determine the contribution of MA to MR indicated a constant 65% contribution by the achilles tendon at all stages of the pedal cycle and at three different work loads [13]. In this study the average contribution of MA to MR of 67.4% agrees with those mentioned in the literature. However, it was found that the contribution varies with muscle length and contraction intensity. In cycling, muscle activity of knee and hip extensors or a flexion of the upper body over the leg in the early stage of the pedal cycle may cause a non-proportional increase of MR relative to MA. An EMG control of the gluteus maximus and vastus medialis conducted in this study showed that with this static experimental setup the activity of these muscles was minimal at both extreme angles of a = lo” and 90”. At PFFzs and knee angles of lo”, 30” and 60” MA contributions to MR of over 100% were calculated (Fig. 8 and Table 2). A possible explanation for this is that in controlling the sub-maximal intensities antagonists such as the tibialis anterior were active and thus produced an opposing moment about the ankle. The achilles tendon would therefore, transfer more force relative to MR. This interpretation is supported by the fact that contributions of over 100% were calculated for all sub-maximal intensities when the leg was extended (a = 100). Many animal experiments have indicated different amplitudes of gastrocnemius and soleus force production during different movements [25-281. The extent to which these results can be applied to humans is unknown and furthermore, it is not possible to separate the tendons of the individual triceps surae components for the application of force sensors [9]. In vivo force measurements conducted during isometric plantarflexion permitted an estimation of the GAST and SOL contributions to MA. This represented the primary aim of this study in that it presented the possibility of assessingand quantifying non-uniform stress of the achilles tendon. MCAsT increased by 53.2 Nm over the complete range of muscle lengths. At the given achilles tendon moment arm (S = 55 mm) this represented a GAST force increase of 967 N. MsoL (moment produced by the soleus muscle) was assumed to be constant and was calculated to be 60.3 Nm (a SOL force of 1100 N if both GAST and SOL have the same achilles tendon moment arm). MPIFl was calculated to be 84.3 Nm at u = 90”. The assumption of a constant MsoL and MPIFIwas, however, proven not to hold as the increase in MR was less steep than that of MA. Consequently a decreased Mpln of 40 Nm was calculated for the extended knee condition although the less steep MR curve may also have resulted from decreased SOL force. An explanation for this is that an increase in GAST force with an extended leg incorporates a short-
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erring of the SOL muscle tendon complex and consequently exerts a negative influence upon the SOL force-length relationship [14]. This would result in decreased stress in SOL portions of the tendon at simultaneously increasing GAST stress. The tendon cross-sectional area of one subject was measured as 92 mm’. Under the assumption that SOL and GAST fibres each occupy half of this area (i.e. 46 mm* each) a stress discrepancy of 21 N/mm2 was calculated. Such a difference in forces originating solely from static muscle activity represents a considerable factor in etiological theories concerning achilles tendon injuries and function. The electromyographical results showed that the relationship of muscle activation between different components of the triceps surae vary if the length of the GAST and plantarflexion contraction intensity are modified. As the absolute SOL activity increased it is postulated that unfavourable force length characteristics of the GAST are compensated by increased neuromuscular activation of the SOL. A sigmoidal curve was obtained for the activation of both GAST components whereas a flatter curve resulting from knee flexion has been reported for GM elsewhere [ 161. A lower relative normalized GM activation has also been reported to occur with plantarflexed ankles [14]. The results presented in Fig. 10 support these data with decreased activity at decreased muscle lengths which has been attributed to impaired neuromuscular transmission or a reduction in the neural impulse of the spinal motor neurons [16,29]. Previous studies have posed the question whether tendon morphology permits stress to be evenly distributed over the tendon cross-sectional area [8] or conversely if different moments are transferred to the calcaneus dependent upon which triceps surae component is loaded [9]. The present study supports the occurrence of non-uniform forces in v&o. It can therefore, be concluded that non-uniform force input to the achilles tendon is not evenly distributed over the tendon and will lead to stress concentrations within the tendon and varying functional effects upon the calcaneus. 5. Conclusions
The study demonstrated that different muscle characteristics of the triceps surae components can cause non-uniform influences upon the force production and muscle activation patterns and consequently the loading of the achilles tendon. A discrepancy in GAST and SOL forces was established over an 80 range of knee motion. Such a quantification of nonhomogenous tendon loading resulting from non-uniform muscle forces has not been presented to
date. The data indicates an important factor in the etiology of tendon injury in the form of load concentrations within the tendon and also frictional forces between individual collagen fibres. Both mechanisms may subject the tendon to localized fibre damage and subsequently inflammation, partial ruptures or even total rupture. A further implication introduced by the results is that a non-uniform force production of the various components of the triceps surae may lead to different functional effects of the achilles tendon on the calcaneus. It is suggested that future research based upon biomechanical models of the human achilles tendon takes the possibility of non-uniform stress into account. References [l] Clement DB, Taunton JE, Smart GW. Achilles tendinitis and peritendinitis: etiology and treatment. The American Journal of Sports Medicine 1984;13(3):179-184. der [2.] Hawe W, Klecker N, Bernett P. Uberlastungssyndrome unteren Extremitlt bei Ausdauersportlern. Sportmedizin 1990;41:420-425. [3] Biedert R. Beschwerden im Achillessehnenbereich. Unfallchirurg 1991;94:531-537. [4] Lohrer H. Die achillodynie Eine Ubersicht. Sportorthopadie-Sporttraumatologie 1996;12( 1):36-42. [5] Segesser B, Nigg BM, Morel1 F. Achillodynie and tibiale Insertionstendinosen. Medizin und Sport 1980;20:79-83. [6] Segesser B. Atiologie von reversiblen and irreversiblen Sportschlden. Schweizerische Zeitschrift fiir Sportmedizin 1983;31:81-86. [7] Wallenbock E, Lang 0, Lugner P. Stress in the achilles tendon during a topple-over movement in the ankle joint. Journal of Biomechanics 1995;28(9):1091-1101. [8] Arndt AN, Notermans H-P, Koebke J, Briiggemann G-P. Zur Fasertextur der menschlichen Achillessehne Eine Analyse durch Mazeration. Der Praparator 1997;43:63-70. [9] Arndt AN. Entstehung und Auswirkungen asymmetrischer Belastung der menschlichen Achillessehne unter besonderer Berucksichtigung ihrer Morphologie. Doctoral Dissertation, German Sport University Cologne, Germany, 1997. [lo] Gregor RJ, Komi PV, Jarvinen M. Achilles tendon forces during cycling. International Journal of Sports Medicine 1987;8:9-14. [ll] Komi PV, Salonen M, Jarvinen M, Kokko 0. In viva Registration of Achilles tendon forces in man. I methodological development. International Journal of Sports Medicine 1987$:3-g. [12] Komi PV, Fukashiro S, Jarvinen M. Biomechanical loading of achilles tendon during normal locomotion. Clinics in Sport Medicine 1992;11(3):521-531. [13] Gregor RJ, Komi PV, Browning RC, Jlrvinen M. A comparison of the triceps surae and residual muscle moments at the ankle during cycling. Journal of Biomechanics 1991;24(5):287-297. [14] Sale D, Quinlan J, Marsh E, McComas AJ, Belanger AA. Influence of joint position on ankle plantarflexion in humans. Journal of Applied Physiology 1982;52(6):1636-1642. [15] Herzog W, Read LJ, ter Keurs HEDJ. Experimental determination of force-length relations of intact human gastrocnemius muscles. Clinical Biomechanics 1991;6:230-238. [16] Cresswell AG, Loschner WN, Thorstensson A. Influence of gastrocnemius muscle length on triceps surae torque develop-
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comparison of plantar flexion torque with and without the triceps surae. Acta Orthopaedica Scandinavica 1976;47:122-124. [24] Fukunaga T, Roy RR, Shellock FG., Hodgson JA, Day MK, Lee PL. Kwong-Fu H, Edgerton VR. Physiological crosssectional area of human leg muscles based on magnetic resonance imaging. Journal of Orthopaedic Research 1992;10(6):926-934. [25] Fowler EC, Gregor RJ, Roy RR. Differential kinetics of fast and slow ankle extensors during the paw-shake in the cat. Experimental Neurology 1988;99:219-224. [26] Fowler EG, Gregor RJ, Hodgson JA, Roy RR. Relationship between ankle muscle and joint kinetics during the stance phase of locomotion in the cat. Journal of Biomechanics 1993;26(415):465-483. [27] Herzog W, Leonard TR, Renaud JM, Wallace J, Chaki G, Bornemisza S. Force-length properties and functional demands of cat gastrocnemius, soleus and plantaris muscles.. Journal of Biomechanics 1992:25(11):1329-1335. [28] Herzog W. Leonard TR, Guimares ACS. Forces in gastrocnemius, soleus and plantaris tendons of the freely moving cat. Journal of Biomechanics 1993;26(8):945-953. 1291 Lewis DM, Luck JC, Knott S. A comparison of isometric contractions of the whole muscle with those of motor units in a fast-twitch muscle of the cat. Experimental Neurology 1972;37:68-85.