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Department of Physiology, Northwestern University Medical School, Chicago, Illinois
Submitted 12 December 2005; accepted in final form 31 May 2006
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ABSTRACT |
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INTRODUCTION |
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; Joyce et al. 1969; Rack and Westbury 1969) examined the mechanical properties of cat soleus under physiological stimulus and movement patterns. In some of these experiments, they activated the soleus using asynchronous stimulation. The ventral roots were divided into five bundles, each stimulated with the same frequency but with different time delays. Using this technique, they could activate the muscle such that each fiber was stimulated at a low frequency yet the overall force from the muscle was quite steady, that is, with about one-fifth the variation or ripple in force seen in a synchronous unfused stimulus (see Fig. 2 vs. Fig. 1) Surprisingly, they showed not only was the force smoother, but force was greater compared with synchronous stimulation. They suggested that asynchronous stimulation prevented internal movement of the muscle fibers. Because the muscle fibers are connected in series with the external tendon and the external tendon can be expected to stretch by an amount proportional to force, a variation in external force can be expected to translate into internal movement.
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recently examined the summation of force between two parts of cat soleus. The ventral roots were divided into two bundles each innervating approximately half of the muscle. Under all conditions, the summation of force was quite linear. The small nonlinearities could be attributed to stretch of the common elastic elements. No assumption was made about the location of the elasticity, which probably resides throughout the external tendon, aponeurosis, and connective tissue links in the muscle itself. This suggested that the difference in force during asynchronous and synchronous stimulation noted by Rack and Westbury could also be explained by the stretch of the common elastic elements. The purpose of this study was to test the hypothesis that in cat soleus, the difference in force between synchronous and asynchronous stimulation can be attributed to the stretch of the common elastic elements.
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METHODS |
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Preliminary results showed that the greatest difference between asynchronous and synchronous stimulation occurred at relatively low frequencies and at relatively short muscle lengths. Therefore short lengths and low frequencies were studied. Each muscle was stimulated at 5, 7.5, and 10 Hz. The muscles were generally studied at –6 and 0 mm (a length of 0.0 mm is defined as the length producing peak tetanic tension). Muscles in this study ranged in weight from 3.5 to 5.1 g with a mean of 4.4 g. Sacks and Roy (1982) reported that cat soleus muscles with mean weight of 4.03 g had a mean fascicle length of 41.7 mm and pennation angle of 7°. Hence a length of –6 mm represents a fascicle length of 86% of Lo.
At each frequency and muscle length the soleus was stimulated four different ways: asynchronous, synchronous, individually and summed, and individually and summed with puller compensation. Figures 1–4 depict each of the stimulus methods. During asynchronous stimulation, the four parts of the muscle are stimulated together. Each part is stimulated at the same frequency, but the stimulus trains are delayed sequentially by 1/4 of the interpulse interval, see Fig. 1. During synchronous stimulation, each of the four parts are stimulated together without any delay between the impulse trains (Fig. 2). Individual stimulation is defined as stimulation of each of the parts alone with the forces digitally summed. To allow easy comparison between the individual and asynchronous results, the trains are delayed by the same intervals used in asynchronous stimulation (Fig. 3). Individual stimulation with puller compensation is similar, in that each part is stimulated alone, except here, rather than hold the muscle at a fixed length, the puller is used to mimic tendon stretch predicted to occur when all parts of the muscle are stimulated together (Fig. 4). The method used to estimate tendon stretch is detailed in the following paragraph.
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The common elasticity, K, was estimated using quick releases during both partial and full stimulation of the muscle. The difference in measured stiffness can be solved algebraically to determine K (Sandercock 2000).
Fatigue is a potential problem with this analysis. To minimize its effects, the stimulations were repeated in a different order. Determination of the compensatory movements (Fig. 4, step 1) were not repeated because the fatigue effects were small.
The preceding procedure was repeated in seven cats. Force was integrated between 0.0 and 1.4 s. Each of the four methods was normalized by the integrated asynchronous force. An ANOVA with repeated measures was used to test statistical significance of the integrated force.
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RESULTS |
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Similar results were seen in all seven muscles tested at this length. The data are summarized in Fig. 6. While the difference between force from different stimulation protocols was small, they are statistically significant because of consistent differences from muscle to muscle. The most striking feature is that the largest difference between synchronous and asynchronous stimulation was about 30% at –6 mm and 5 Hz. Figure 6B shows the data at a length of 0 mm. Puller compensation was not tested at this length because there was already little difference in integrated force at this longer length. The difference between synchronous and asynchronous was even less than before.
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DISCUSSION |
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1/4 of the soleus. The muscle was stimulated by asynchronous stimulation, synchronous stimulation, summation of force with each part stimulated individually, and summation with each part stimulated individually and the servomechanism mimicking tendon stretch during asynchronous stimulation. Muscle length was isometric except for the last protocol. Surprisingly, the observed differences were small. The difference between synchronous and asynchronous stimulation were substantial only at low frequencies and only when the muscle was on the ascending limb of the length-tension curve. Here (ascending limb, fascicle length 15% shorter than at Lo) a maximum difference of 27% was observed. At all frequencies and lengths, synchronous stimulation produced the least force. This is when the greatest stretch of the common elasticity is expected and, due to the force-velocity properties of the muscle, the least force. Summation of force from the individual parts produced the greatest force, slightly larger than that resulting from asynchronous stimulation. This is when the least stretch of the common elasticity is expected. Compensatory puller movements (Fig. 4) reduced the force from the individual parts, closely matching the force from asynchronous stimulation. These results are consistent with the hypothesis that the common -elasticity can explain the difference between synchronous and asynchronous stimulation.
The extra average tension during asynchronous stimulation was first noted by Rack and Westbury (1969). Similar results have been obtained by others in cat caudofemoralis (Brown et al. 1999). Their work has often been cited as a reason why motor units must fire asynchronously (Maltenfort et al. 1998; Merletti et al. 1992). However, in this study, the effects were quite small. At Lo, even at 5 Hz there was only a 16% difference. At 5 Hz and a length of –6 mm, the difference was 28%, which is substantial, but 5 Hz is a very low frequency, probably below what is physiologically significant. The results of this study are in full agreement with Rack and Westbury, who also studied cat soleus. The large differences they reported occurred at short lengths and low frequencies. So, although asynchronous firing may be important in assuring smooth force generation, the extra force produced probably has little physiological significance.
The extra force during asynchronous stimulation is a special case of the more widely studied problem of nonlinear summation. Nonlinear summation has been demonstrated in whole muscle (Brown and Mathews 1960; Hunt and Kuffler 1954) and in single motor units (Clamann and Schelhorn 1988; Emonet-Denand et al. 1990; Powers and Binder 1991). In whole muscle, the force from the sum of the parts has always been reported to be greater than the force from the synchronous stimulation of the whole. Initially this difference was thought to be evidence for polyneuronal innervation (Hunt and Kuffler 1954), but later Brown and Mathews (1960) argued that it was due to stretch of the tendon. Different results have been obtained in single motor units where generally greater than linear summation has been observed, but single motor units are probably subject to measurement errors not seen during activation of larger parts of the muscle.
It is not fully understood what happens to the fibers within a muscle when only part of the muscle contracts. The connective tissue structure between muscle fibers is complex. Muscle fibers are contained within a collagenous meshwork that cross-links the fibers (Trotter 1993). These links are capable of transmitting the full force of a fiber to its neighbors (Street 1983). The meshwork may also serve to transmit force around local damage to a fiber (Patel and Lieber 1997). Because the diameters of fibers varies along their length (Eldred et al. 1993), the collagen network may help to distribute the force to prevent localized strain. If the force transmission between fibers is significant, then force measured from different parts of the muscle may sum nonlinearly. The aponeurosis and tendon may also show nonuniform strain when different portions of the muscle are active (Bojsen-Moller et al. 2003). The aponeurosis often forms a broad sheet so activation of a single motor unit can result in localized strain. Proske and Morgan (1984) showed that activation of single motor units can result in nonuniform strain of the tendon. The tendon and aponeurosis may also show different stress-strain properties (Lieber et al. 1991; Maganaris and Paul 2000). Treating the aponeurosis and tendon as a single elastic element may lead to errors in understanding how motor units interact.
Despite the complex connective structure of muscle, in cat soleus its behavior is well described by a simple model-independent fibers connected to a common elasticity (Sandercock 2000). In this study, the soleus was divided into two large pseudo-motor units by splitting the ventral roots into two bundles, thus allowing each portion of the muscle to be stimulated independently. No assumption was made about the exact location of the elasticity—it may reside in any combination of tendon, aponeurosis, and intramuscular collagen matrix. The extent to which one part of the muscle stretched the elasticity of the other part was measured. Results indicate approximately one half of the total elasticity should be viewed as common-stretched by both parts of the muscle. Under all conditions, nonlinear summation was small (<5% of maximal tetanic tension) and most could be accounted for by stretch of the common elasticity. Although the data were fit quite well by a linear elastic element (70% of the error was accounted for), different values of K were measured with different protocols. The common elasticity also showed evidence of hysteresis—it is stiffer during stretch than relaxation.
The common-elasticity model can explain the results seen here. The model assumes the different parts of the muscle interact only through the common elasticity. Thus part of a muscle can effect the force from its neighbors in two ways: stretching them so they operate on a different point on the length-tension curve (Gordon et al. 1966) or changing their velocity and therefore force via the force-velocity relationship (Hill 1938). Assuming a linear common elasticity, when the whole muscle is stimulated, compared with a quarter of the muscle, the common elasticity stretches four times as much. So during an unfused tetanus on the ascending limb of the length tension curve (Figs. 2, 3, and 5), synchronous stimulation leads to reduced force because of higher velocities and an unfavorable position of the length tension curve. At higher stimulation rates, the tetanus becomes more fused and velocity becomes an issue only on the rising and falling edge of the train (Fig. 6C). Thus Fig. 6A shows that at 10 Hz, there is little difference between asychronous and synchronous stimulation. At 10 Hz, there is still a small advantage to summation because of the shift in the position on the length-tension curve. This disappears when the operating length is Lo as shown in Fig. 6B. Compensatory movements with the puller are able to reduce the summation of the parts so it is almost identical to asynchronous stimulation. However, because there was already little difference in force between the asynchronous and summation treatments, this is not a rigorous test of the hypothesis.
McDonnall et al. (2004a,b) have recently used asynchronous stimulation to produce ripple free muscle force at low stimulation frequencies. They were able to stimulate parts of the muscle using intrafascicular electrodes in the peripheral nerve. They demonstrated low-frequency stimulation provided greater fatigue resistance, suggesting the technique might be useful for FES. The results here suggest that part of the improvement in fatigue resistance may result from less shortening of the individual motor unit fibers, resulting in less cross-bridge cycling, and hence greater force and fatigue resistance (Sandercock and Heckman 1997).
In summary, there is little difference between synchronous and asynchronous stimulation in cat soleus except for very low stimulation rates when the muscle is positioned on the ascending limb of the length-tension curve. Summation of the force when each part is stimulated by itself produces slightly more force than asynchronous stimulation. Using the puller to make compensatory movements predicted by the common-elasticity model results in a close match to the asynchronous stimulation trials. This is consistent with the hypothesis that the difference results from stretch of the common-elastic elements.
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GRANTS |
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FOOTNOTES |
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Address for reprint requests and othercorrespondence: T. G. Sandercock, Dept. of Physiology, M211, Ward 5-295, Northwestern University School of Medicine, 303 E. Chicago Ave., Chicago, IL 60611 (E-mail: t-sandercock{at}northwestern.edu)
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REFERENCES |
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ABSTRACT
INTRODUCTION
