Whole Muscle Length-Tension Properties Vary With Recruitment and Rate Modulation in Areflexive Cat Soleus

Thomas G. Sandercock and C. J. Heckman

Department of Physiology, Northwestern University Medical School, Chicago, Illinois 60611


    ABSTRACT
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
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Sandercock, Thomas G. and C. J. Heckman. Whole Muscle Length-Tension Properties Vary With Recruitment and Rate Modulation in Areflexive Cat Soleus. J. Neurophysiol. 85: 1033-1038, 2001. The length-tension relationship is a fundamental property of muscle. In its classic form, which is used in muscle models incorporated into studies of motor control, the length-tension relationship is measured during maximal activation via tetanic electrical stimulation in whole muscles or during high intracellular calcium levels in single muscle fibers. In this study, we measured the length-tension relationship of the cat soleus muscle during different levels of natural activation consisting of recruitment and rate modulation of motor units generated by the crossed extension reflex. The ipsilateral dorsal roots were cut to eliminate sensory feedback from the soleus. Length-tension was measured by large shortening steps that transiently allowed force to drop to zero. Force then recovered to a new steady value as the shorter length was maintained for several seconds. The effects of various levels of crossed extension activation on length-tension were compared with direct electrical stimulation of the muscle at 5, 10, 20, and 100 Hz. At all levels of crossed extension, the slope of the length-tension function was much steeper than the slope for tetanic stimulation at 100 Hz. Most slopes for crossed extension fell between the slopes seen with electrical stimulation at 10 and 20 Hz. There was a modest overall tendency for slope to decrease with the level of crossed extension activation. Because much of the normal movement repertoire requires submaximal activation, muscle models based on the tetanic length tension relationship will greatly underestimate the contribution of this relationship to force modulation at different muscle lengths.


    INTRODUCTION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

During maximal activation, the length-tension relationship of a sarcomere is well explained by changes in overlap of actin and myosin filaments (Gordon et al. 1966). At short sarcomere lengths, an increase in length brings an increase in force, giving a positive slope to the length-tension function. At medium lengths, filament overlap allows the largest number of crossbridges to form, and thus force is maximum and the slope is zero. At longer lengths, slope becomes negative in that force decreases with increasing length because available crossbridge sites decrease. The same model readily explains the length-tension relationship of tetanically stimulated single fibers and whole muscle, even though each fiber probably contains a distribution of slightly different sarcomere lengths.

When muscle is artificially stimulated at sub-tetanic rates, the length-tension relationship is altered; the peak shifts to longer lengths and the ascending limb of the length-tension curve becomes steeper. Rack and Westbury (1969) demonstrated this in cat soleus using asynchronous stimulation to smooth the unfused tetanus. At stimulation rates from 5 to 10 impulses per second, the length-tension curve shows little resemblance to that predicted from the sliding filament theory. Others have obtained similar results in stimulated whole muscle (Brown et al. 1999; Roszek et al. 1994) and isolated fibers (Balnave and Allen 1996; Stephenson and Wendt 1984). The effect is most likely to result from changing calcium sensitivity at different lengths (Balnave and Allen 1996).

The question addressed by this study is as follows: what is the length-tension relationship during normal movements? The natural activation pattern employed in movement is very different from the artificial stimulation used in single fiber preparations. Force is controlled by the recruitment and rate modulation of motor units (Binder et al. 1996). Motor unit firing rates rarely if ever reach the levels needed for sustained tetanus. If all motor units were recruited more or less simultaneously, the length-tension function seen during natural activation would be similar to that seen during whole muscle stimulation. This of course is not the case: motor units are recruited in order of the amount of force they generate (Binder et al. 1996). Units fire at relatively low rates at their recruitment thresholds, and then undergo rate modulation as additional units are recruited. Thus recently recruited units, firing at low rates, will have their peak in the length-tension relationship at longer fiber lengths. Previously recruited units, firing at higher rates, will produce peak force at shorter lengths. As a consequence, the length-tension function for the whole muscle, during natural activation, is likely to have a very different form than the tetanic length-tension function.

The specific goal of this work is to directly measure the length-tension functions that occur at various levels of recruitment and rate modulation in a muscle with a relatively simple architecture, the cat soleus muscle. The crossed extension reflex was used to activate the muscle while preserving normal recruitment and rate modulation. All reflexes from the soleus itself were eliminated by sectioning the ipsilateral dorsal roots. The results showed that the natural activation pattern generated by the crossed extension reflex produced length-tension relations that were much steeper than those produced with tetanic electrical stimulation.


    METHODS
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INTRODUCTION
METHODS
RESULTS
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REFERENCES

Data were collected from six animals. All procedures performed were approved by the Animal Care Committee at Northwestern University.

Surgical preparation

Initial surgical preparations were done under deep gaseous anesthesia (1.5-3.0% isoflurane in a 3:1 mixture of O2 and N2O), according to standard procedures in our lab (Lee and Heckman 1998; Sandercock and Heckman 1997). In the left hindlimb, the nerve to the soleus muscle was carefully isolated and left in continuity. All other nerves in the distal hindlimb were cut, as were the nerves to the semitendinosus, semimembranosus, and biceps femoris. The soleus tendon was attached to a computer-controlled muscle puller via a bone chip from the calcaneous. Before the tendon was freed, the foot was manually dorsiflected, and a small piece of suture was tied to the tendon and to the underlying shank of the lower leg. After the soleus was attached to the puller, alignment of the two threads was defined as maximum physiological length. The surgically exposed areas of the hindlimb were covered with a pool of mineral oil that was formed within the pulled-up skin flaps. A laminectomy of the spinal column was performed from L4 to S1. Ipsilateral dorsal roots from L4 to S2 were transected to eliminate sensory feedback from the soleus muscle. Contralateral dorsal roots were left intact, as were all ventral roots. A precollicular decerebration was performed by transecting the midbrain with an ophthalmic spatula and aspirating the entire forebrain. The calvarium was packed with saline-soaked cotton wool. The gaseous anesthesia was then discontinued, and the animal was allowed to breathe room air. Radiant heat was used to maintain hindlimb and core temperatures within physiological limits. At the end of the experiment, the animals were killed with a lethal dose (100 mg/kg iv) of pentobarbital sodium.

Experimental protocols

Measurement of the length-tension properties during the crossed-extension reflex required a technique different from traditional length-tension protocols. Various levels of steady force were generated in the soleus muscle by activating the crossed extension reflex from the contralateral leg. This was done by manual compression of the skin at the ankle and knee joints to evoke a steady noxious stimulus. The crossed extension reflex is by definition a natural form of activation (Powers and Rymer 1988), producing recruitment and rate modulation of soleus motoneurons. This will be referred to as CXR activation. Measurement of the length-tension relationship during CXR activation was done as follows. The muscle was held isometrically at an initial length. CXR activation was used to produce a desired level of force. If force remained steady for at least 1 s, then the computer initiated a step decrease in muscle length. Force rapidly recovered to reach a steady value at the new length (Fig. 1). This protocol allowed the measurement of force at two positions on the length-tension function, the start length and end length after the step (Fig. 1). Repeated trials at different initial forces, generated by varying levels of CXR, and different start lengths allowed us to map out the length-tension relationship as a function of recruitment and rate modulation of the soleus motor unit population. Passive muscle tension was measured by repeating the step when the muscle was inactive. The passive waveform was always subtracted from waveforms measured during muscle activity.



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Fig. 1. Method used to measure length-tension during the crossed extension reflex. Force is measured at 2 lengths: L1 and L2. Variable activation coupled with a necessary wait for tension to recover following the step change in length is a source of error. A 2nd source of error is the tension deficit observed when a muscle is actively shortened to a length (L2) compared with an isometric contraction at the same length. Making a step large enough to unload the muscle (force to zero) minimized this error. See text for details.

A potential problem with this approach is that CXR activation might not stay constant. After the step, at least 0.75 s are needed for tension rise to a steady level at the new muscle length. For accurate measurements, the drive to the motoneuron pool must remain constant over this period (see Fig. 1). Each trial had a 1.0-s isometric period before the step, and this period was used to judge the steadiness of activation. (One experiment had a 0.7-s isometric period.) Any trials with significant variations in force in this period (>10% of the force immediately preceding the step) were rejected. The normalized waveforms had approximately the same overall shape, with the variability between waveforms being due to the effect of different activation levels on the response to the step (see Fig. 3, middle plot). Any trial with an abnormal shape in the 1-s period following the step, indicative of a sudden increase or decrease in activation, was also rejected.

Direct muscle stimulation was used to measure traditional mechanical properties that could be compared with those from CXR activation. Fine stainless steel wires were inserted in the soleus; one in the distal portion of the muscle belly and one in the proximal portion. A stimulus intensity of 100-120 V produced repeatable and consistent forces. Further increases in intensity did not generate additional force. In two experiments this direct stimulation was shown to produce as much or more force than stimulation of the L7 and S1 ventral roots.

A second potential problem with using CXR activation to measure length-tension is that shortening an active muscle to a specific length can produce a tension deficit compared with an isometric contraction at that same length (Edman 1975; Edman and Reggiani 1984; Edman et al. 1993; Ekelund and Edman 1982). This problem was minimized by making all the steps large enough to unload the muscle. In cat soleus, a shortening step of 8 mm allowed force to transiently drop to zero (Fig. 1) and reduced the size of the deficit. The magnitude of the tension deficit was measured in six experiments. The 8-mm step change in length used during CXR was applied during steady electrical stimulation of the soleus muscle at 10, 20, and 100 Hz. Figure 2 shows results for one experiment. Note that for all frequencies, the 8-mm step allowed the force after step completion to match the force generated by passively shortening the muscle and then re-stimulating it. Similar results were obtained in all six experiments of this type. The mean tension deficit observed 1 s after the step was -2.2% of the isometric value.



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Fig. 2. Assessment of tension deficit following step change in length. Direct muscle stimulation at 100, 20, and 10 Hz. At each frequency the muscle contracted isometrically at 0 and -8 mm and during a step from 0 to -8 mm. The tension deficit following the step was small.

After the CXR measurements were completed, the traditional length-tension relationships resulting from direct electrical stimulation were measured. Length-tension curves were constructed at stimulation frequencies of 5, 10, 20, and 100 Hz. In each case, the muscle was moved passively to the desired length, and stimulation was applied for 1 s. Force was measured at lengths of 0, -4, -8, and -12 mm. Rest periods of 1 min were allowed between each electrical stimulation trial to avoid fatigue. The 100- and 20-Hz data were fit with a fourth-order polynomial with two free parameters (Sandercock and Heckman 1997). No attempt was made to fit the 10- and 5-Hz data.

Fatigue was monitored by measuring the muscle state before the CXR trials, midway through the CXR trials, and after the stimulated length-tension curves were measured. The force-frequency relationship of the muscle was measured using trains of 5, 10, 20, and 100 Hz. A three-point estimate of the tetanic (100 Hz) length-tension curve was also obtained. The soleus is a fatigue resistant muscle and did not show evidence of fatigue by either of these two measures.

Data analysis

The top graph in Fig. 3 shows a set of CXR trials for a single starting length in a single experiment. To compare the amplitude of the change in force across the two lengths as a function of recruitment and rate modulation, the ending force was normalized with respect to the starting force (middle graph, Fig. 3). During direct electrical stimulation, forces were measured 1.0 s after stimulation onset. Low stimulation frequencies (5 and 10 Hz) resulted in unfused tetanii. Here, force was averaged within each interpulse interval. (See DISCUSSION for possible differences between this force and that produced by distributed stimulation of ventral root filaments.) Statistical analyses assumed a significance level of alpha  = 0.05. 



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Fig. 3. Multiple trials from a single muscle measured at different crossed extension reflex (CXR) activation levels. Top graph: absolute force. Middle graph: the same data normalized by the average force between 0.59 and 0.60 s. Bottom graph: the length for all trials.


    RESULTS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The length-tension properties measured during CXR activation were substantially different from those during tetanic stimulation. Figure 4 shows the response of a muscle to a step release (0 to -8 mm) during CXR activation and direct muscle stimulation. All measurements were made from the same muscle. The waveforms were normalized by the force immediately preceding the step. The CXR waveforms had starting forces ranging from 15 to 81% of maximum tetanic tension at optimum length. First note that the CXR waveforms were different from the 100-Hz stimulated waveform. They had a slower rise time and did not recover as much force following the step. In all six experiments the CXR waveforms were different from the 100-Hz stimulated waveform. The average normalized force 1 s after the step was 0.69 for CXR activation (6 cats, 76 trials) compared with 0.95 for 100-Hz stimulation. This difference was statistically significant (t-test, P < 0.001). Second, note that in Fig. 4 all but one of the CXR waveforms fell between the 20- and 10-Hz stimulation curves. This was typical for five of the six experiments. In these five experiments, 87% fell below the 20-Hz stimulated waveform. In the atypical experiment, most of the CXR waveforms were above the 20-Hz stimulated waveform. No observed experimental abnormalities accounted for this difference.



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Fig. 4. Contrast between direct muscle stimulation and CXR activation during a step release. The muscle was stimulated at 100, 20, and 10 Hz. The 10-Hz trace is an average of 4 stimulus trials with the pulses consecutively delayed by 25 ms, to minimize the ripple in the unfused tetanus. The CXR data were collected from the same muscle. The isometric force before the step in the CXR trials ranged from 10 to 60% of maximum tetanic tension.

Figure 5 shows a comparison of the length-tension curves measured by direct electrical muscle stimulation to the two point length-tension measurements made during CXR activation. Activation levels up to 80% of maximal tetanic tension were achieved using the CXR. (Occasionally higher forces were produced but they were not steady enough to yield useful trials.) Note that even at the highest CXR activation the length-tension properties were steeper than observed during 20-Hz direct stimulation. For the most part, the slopes of the length-tension relations during CXR were similar to the slopes for 5- to 10-Hz direct stimulation. Similar results were obtained in five of six cats. One cat had slopes primarily between the 20- and 100-Hz stimulated curves.



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Fig. 5. Length-tension properties measured during direct stimulation compared with those measured during CXR activation.

The hypothesis that the steepness of the ascending portion of the length-tension curve is correlated with the activation level was tested by plotting the force before versus force after the step (Fig. 6). As force level increased, the percentage of force remaining after the step increased, which means that the slope of the two point length-tension relations decreased. A Spearman rank order test showed significant correlation (P < 0.05) in all six cats, supporting the hypothesis. An overall tendency for units recruited at low force levels to undergo rate modulation probably explains this correlation (see DISCUSSION). While statistically significant, it is apparent from Fig. 6 that the correlation between activation level and length-tension is not strong. The correlation results primarily from a change in length-tension properties at high CXR activations. If the data points with a starting force of >10 N were discarded in Fig. 6, the remaining points do not show significant correlation.



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Fig. 6. Correlation between activation level (force before step) and steepness of the length-tension curve (normalized force after step). These data are taken from Fig. 4 during the step from 0 to -8 mm. Each solid circle represents a single trial during CXR activation. The open circles were measured during direct stimulation.


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A method was developed to estimate the length-tension properties of cat soleus during CXR activation. CXR activation preserves normal recruitment and rate coding of the soleus motor units, so the measured length-tension properties are more likely to reflect the length-tension characteristics during normal use of the muscle. Because the level of CXR activation varied from trial to trial, a step method was employed, allowing the measurement of force at two lengths while activation remained constant. The length-tension properties measured during CXR activation were distinctly different from those measured during tetanic stimulation. In general they more closely matched the length-tension characteristics observed during 20- to 10-Hz stimulation; a steeper ascending slope with the peak shifted to longer lengths. The normalized force following a step showed statistically significant correlation with activation, although this relationship was not particularly strong and may be due primarily to changes in length-tension at high activation levels.

The mechanisms underlying the length-tension properties at low stimulation rates are poorly understood. At tetanic stimulus rates the length-tension characteristics of muscle are well explained by the sliding filament theory (Gordon et al. 1966). At low stimulus rates other mechanisms also become important. Rack and Westbury (1969) showed that in cat soleus the peak of the length-tension curve was shifted to longer lengths and the ascending limb of the length-tension curve was steeper at low rates of stimulation. Our stimulation results are similar. In amphibian muscle, Ca2+ release from the sarcoplasmic reticulum was reduced at longer lengths (Blinks et al. 1978). In contrast, in mouse muscle, calcium release was constant at different lengths, but the sensitivity of troponin to calcium binding is length dependent (Balnave and Allen 1996).

In this study the 5- and 10-Hz length-tension curves were measured using synchronous stimulation. Rack and Westbury (1969) demonstrated that at these frequencies synchronous stimulation lead to lower mean forces, particularly at short lengths, compared with asynchronous stimulation. Thus the 5- and 10-Hz length-tension curves shown in Fig. 5 are probably steeper and shifted to longer lengths than if measured using asynchronous stimulation. Clearly CXR activation is closer to asynchronous stimulation since little synchrony is observed between motor unit discharge patterns with this input (Powers and Rymer 1988).

Our results are consistent with the current understanding of rate coding and recruitment in cat soleus, although the details needed for a quantitative analysis are lacking. Cat soleus is a homogeneous muscle composed of type S motor units (Burke 1967, 1981). Therefore with increasing activation, motor units will be recruited with the same histological profile. A systematic study of the length-tension properties of individual soleus motor units has not been completed, but there is little reason to expect the length-tension characteristics of motor units recruited at high activation levels to be different from those at low levels. According to Henneman's size principle, motor units with small forces will be recruited before larger force motor units (Binder et al. 1996; Henneman and Mendell 1981). With increasing activation, small motor units already active will increase their firing rate, and new motor units will be recruited. Figure 6 shows that the normalized force following the step appears to remain relatively constant at force levels between 0 and 50% of maximum tetanic tension (Po). This indicates that the majority of the active muscle fibers are firing at relatively low rates: <20 Hz. There is insufficient information to determine whether the smallest early recruited units have reached higher rates and their effects are mitigated by larger units firing at lower rates. The relatively constant slope of the lines in Fig. 4 implies that there is a mixture of firing rates in the muscle. Because we were not able to steadily activate the muscle at more than 80% of Po, we were unable to determine whether the length-tension properties during CXR ever approach the tetanic stimulation length-tension profile.

CXR activation allows recruitment and rate modulation of the motoneuron pool and thus has distinct advantages over electrical stimulation in studying muscle properties during normal activation. The recruitment and rate modulation pattern is qualitatively similar to that seen in human subjects, in that this input had been shown to recruit units in an orderly fashion and to generate clear rate modulation of already-recruited units as force increases (Powers and Rymer 1988). It likely preserves normal recruitment and rate coding (Binder et al. 1996). Thus it seems reasonable to suppose that the length-tension properties in human subjects during submaximal contractions are similar to those seen during CXR in this study. However, it should be noted that firing rates in human subjects (reviewed in Binder et al. 1996) are generally lower than those in the cat (Cordo and Rymer 1982; Powers and Rymer 1988; Tansey and Botterman 1996). Human muscle is also slower (longer twitch contraction times and maximum velocity of shortening), which may balance the lower firing rates. Thus the net effect of the differences between length-tension slope during tetanic versus natural activation is probably comparable to the effects seen in the present study.

Substantial variability remains in the data that cannot be accounted for solely by the force preceding the step. This scatter is clearly seen in Fig. 6 for points with initial force between 0 and 10 N. Part of this noise may be accounted for by unsteady CXR activation (Fig. 1). In addition, the time between initiation of the CXR reflex and the step release may have affected the length-tension properties. The time varied from approximately 2 to 8 s. Force generally declined during this time. Normalized force following the step generally also decreased with time, which means there was an increased slope for the length-tension curve. This may have occurred consequent to a slow reduction in motoneuron firing rates. Motoneurons are known to exhibit long-term rate adaptation to steady inputs (Kernell and Monster 1982; Sawczuk et al. 1995). Further studies to simultaneously measure length-tension properties and motor unit firing rates are needed to address this issue quantitatively.

Tendon stretch plays a minor role in altering length-tension properties at low activation levels. When a muscle is only partly active, the tendon and aponeurosis will not be stretched as far as when the muscle is fully active. This means that, at a given length of the muscle-tendon complex, the muscle fibers will be longer when the muscle is partially active compared with when the muscle is fully active. In a typical cat soleus muscle, when the muscle is partially activated to a tension of 10 N, the fibers will be approximately 0.5 mm longer than at its tetanic tension of 20 N (Sandercock 2000). This effect is opposite of the observed change in length-tension and thus acts to mitigate the effects observed at low activation levels. This effect is relatively unimportant compared with the rather large shifts in length-tension.

Mathematical models of muscle generally either ignore the length-tension properties of muscle or employ the tetanic length-tension curve (Sandercock and Heckman 1997; Winters 1995; Zajac 1989), although recent models have incorporated the effects observed in this study (Brown and Loeb 2000; Brown et al. 1999). In cat soleus the muscle fibers are relatively long, so within the physiological range the length-tension properties do not have a profound effect on tetanic force. However, the results of this study indicate that during natural activation, length-tension may have a significant impact on the overall mechanical behavior of muscle.


    FOOTNOTES

Address for reprint requests: 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).

Received 15 May 2000; accepted in final form 17 November 2000.


    REFERENCES
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

0022-3077/01 $5.00 Copyright © 2001 The American Physiological Society