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J Physiol (2003), 550.1, pp. 263-278
© Copyright 2003 The Physiological Society
DOI: 10.1113/jphysiol.2002.031930
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ABSTRACT |
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Static-motor activity is strongly modulated by a particular phase relationship to the cyclic movements of locomotion, and this has a profound effect on the firing patterns of muscle spindle afferents. Whilst primary afferents are affected by both static and dynamic
(Received 6 September 2002; accepted after revision 15 April 2003; first published online 23 May 2003)
Corresponding author A. Taylor: Department of Sensorimotor Systems, Division of Neuroscience and Psychological Medicine, Imperial College London, Charing Cross Campus, St Dunstans Road, London W6 8RP, UK. Email: t.taylor{at}ic.ac.uk
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INTRODUCTION |
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During natural movements, muscle spindle primary afferents provide a feedback signal that contains two main components. The discharge during lengthening is dominated by a component that is related to velocity (Prochazka & Gorassini, 1998), for which the sensitivity is determined by the level of gamma dynamic (d) motor output directed to the bag1 intrafusal fibres. The discharge at rest or during shortening is determined mainly by the firing of gamma static (s) motoneurons, acting through the bag2 and chain fibres. It has been shown that a substantial part of the s motor output during locomotion in the cat fluctuates with a smoothly modulated pattern that resembles the profile of muscle shortening (Murphy et al. 1984; Taylor et al. 2000a, b) and acts to oppose the unloading effect of shortening. For this reason it may be better to regard the s pattern as a signal that is algebraically summed with muscle length to determine the afferent firing, rather than as a means of controlling the sensitivity of the spindle to stretch (see Taylor et al. 2000a,b). With this in mind, the primary afferents have been studied recently by stimulating s axons with sinusoidally frequency-modulated pulse trains with the muscle held at a constant length (Durbaba et al. 2001b) after identifying which intrafusal fibres were activated by random stimulation (Taylor et al. 1998). The transfer of the s signal was found to depend in a predictable way upon the extent to which bag2 and chain fibres were involved. Since the only significant fusimotor influence on the secondary afferents is via the bag2 and chain fibres, it is clearly important to explore the properties of the s action on secondary afferents in a similar way.
Histological studies have shown that all mammalian muscle spindle secondary afferents terminate on chain intrafusal muscle fibres and that most (89 % mean for cat hindlimb muscles) also terminate on bag2 type fibres (Banks et al. 1982). Axons from s motoneurons supply these two types of intrafusal muscle fibre either singly or jointly, so that the terminations of a given s axon in a particular spindle can be designated as bag2, chain or bag2-chain. In the case of primary afferents it has proved possible to identify which intrafusal fibres are activated by each s axon by a detailed study of the afferent firing patterns elicited by various patterns of efferent stimulation. The methods depend on the fact that chain fibres have fast-twitch characteristics and a tetanic fusion above 100 Hz (Boyd, 1976). The primary endings are sensitive enough to respond to the small fluctuations in force that consequently accompany s stimulation at lower frequencies. Bag2 fibres are more tonic in their properties and have a lower tetanic fusion frequency (Boyd, 1976; Dickson et al. 1993; Celichowski et al. 1994b) and so produce smoother contractions. A particularly convenient means of identification has been described using a completely random stimulus train (with intervals exponentially distributed) and to cross-correlate this with the resulting afferent impulses (Taylor et al. 1998). Secondary afferents, however, appeared to respond much less directly to s stimulation (Celichowski et al. 1994a), and consequently they have not previously been studied by cross-correlation techniques. In the present paper we consider how spindle secondary responses may depend on the activation of bag2 or chain fibres. Since we recognised that much less information is available on secondaries than on primaries and that it would be unwise to extrapolate directly from primary to secondary properties, we have gathered together the results of a number of tests in a way that has not been done before. It appears that similar basic principles apply as in primary afferents, but in a proportion of cases the random stimulation method failed to detect chain fibre activation. In these cases, valuable additional information was provided by the afferent response during a linearly rising frequency of stimulation, because afferent frequency increases due to bag2 fibre contraction saturate at a lower frequency than those due to chain fibre contraction. The classification of the s effects based on the joint use of the various methods was then used to explore the relative parts played by the two fibre types in modulating the afferent discharge, using sinusoidally frequency-modulated stimulation.
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METHODS |
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All experiments were carried out in full accordance with the United Kingdom Home Office Animals (Scientific Procedures) Act of 1986.
The experiments were performed on female cats in the weight range 2.3-3.5 kg. Most of the results were gathered during the course of experiments that were concerned mainly with primary afferents and the methods have been described fully elsewhere (Taylor et al. 1998; Durbaba et al. 2001b), but there were an additional five experiments. Animals were fully anaesthetised throughout with sodium pentobarbitone (60 mg kg-1). In the earlier experiments, induction of anaesthesia was by this dose given I.P., followed by supplements of 12 mg kg-1 in 1 ml of 0.9 % saline I.V. In later experiments, induction was by halothane vapour (5 % in 10 l min-1 of 50 % nitrous oxide and oxygen delivered into a 30 l box) and followed by pentobarbitone given I.V. as above. The level of anaesthesia was maintained by monitoring by arterial blood pressure, respiration, end-tidal PCO2, pupil diameter and depression of reflex responses (see below re monitoring in the presence of neuromuscular blockade). Rectal temperature and muscle temperature were monitored and maintained at 36-38 °C by means of a heated blanket and radiant heat. The animals were killed by intravenous overdose with pentobarbitone at the end of the experiment.
Briefly, the preparation involved denervation of the left hindlimb, save for the medial gastrocnemius (MG) or soleus muscles, and isolating up to 12 dorsal-root filaments to record single muscle spindle afferents. The afferents were tested for their responses to muscle stretch, muscle twitch and by conduction velocity and their response to succinylcholine (SCh). The purpose of the SCh was to determine for each afferent the presence or absence of terminations on bag1 and bag2 fibres (Price & Dutia, 1989; Taylor et al. 1992). On each occasion of using SCh, the level of anaesthesia was first checked carefully through observation of the blood pressure, pupil diameter and response to paw pinch. Ventral roots L7 and S1 were cut, and functionally single axons were isolated and characterised by the conduction velocity measured to the muscle nerve.
In most cases the muscle was stretched as described previously (Taylor et al. 1998; Durbaba et al. 2001b). Muscle length was set to L0 + 4 mm, with L0 defined as the length at which the muscle just became slack, and ramp stretches were of 5.0 mm from this point. In the last five experiments, which were on the soleus muscle, the LG muscle was removed to expose the soleus nerve and the soleus tendon was left attached to the calcaneum. Muscle stretching was effected by rotation of the ankle joint with a servo apparatus, as described previously (Taylor et al. 2000a,b). This had the advantage of maintaining the normal relationships and length of the muscle. The normal resting muscle length was then taken as that existing when the ankle joint angle was at 90 deg. Ramp and hold rotations were scaled to stretch the soleus by 5 mm from this point. Stretches were repeated regularly at 5.8 s intervals, with the rise lasting 1 s, the plateau of stretch lasting 1.5 s and the fall 0.8 s. Responses to cyclically repeating ramp and hold stretches can be separated into different phases, defined as in Fig. 1. The frequency in the period immediately before each stretch commences is known as the initial frequency (IF). With the onset of the ramp stretch there is a rapid increase in frequency, referred to by Boyd (1981) as the initial fast component (FC). This is followed by a steady rise during the stretch, with a well-defined slope, referred to as the slow stretch slope (SS). Following the peak frequency (PF) at the end of the stretch phase, there is an adaptation of the discharge frequency to a value called the static index (SI) 0.5 s after the end of stretch. The maximal response to stretch is the dynamic difference (DD), which is given by PF - IF. The adaptation is measured by the difference PF - SI and is referred to as the dynamic index (DI; Crowe & Matthews, 1964). The maintained response to stretch is called the static difference (SD), which is given by SI - IF. The frequency changes of secondary afferents during the release phase closely resemble an inverted version of the responses to stretch, especially in the presence of s stimulation. To characterise changes caused by stimulation, it is convenient to take the changes in the above values, symbolised by the prefix 
. Thus, for example, DI is DI during s stimulation minus control DI (see Taylor et al. 1992).
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Figure 1. Definition of the various components of the afferent response to ramp stretch The instantaneous frequency of a secondary afferent is shown above and the stretch waveform below. Note that the line labelled SS is a linear regression of the slow slope response during stretch. Abbreviations: IF, initial frequency; FC, fast component; PF, peak frequency; SS, slow slope; SI, static index. Derived values are shown in the inset: DD, dynamic difference; DI, dynamic index; SD, static difference. | ||
For each s-secondary afferent pairing, three tests procedures were applied: (1) the effect of continuous s stimulation at 100 Hz on the afferent response to ramp and hold stretches was recorded, ignoring the first stretch cycle after the onset of stimulation; (2) the effect of ramp frequency stimulation was also recorded at constant muscle length of L0 + 4 mm with the stimulus frequency rising to 150 Hz in 2.0 s and maintained for 1.0 s; (3) the response to random stimulation was studied. Random stimulation was provided by triggering the stimulator from a Geiger counter excited to a mean of 50 pulses s-1 by a radioactive source of natural uranium acetate. This ensured Poisson statistics with an exponential distribution of interpulse intervals (see Taylor et al. 1998). Records of afferent response pulses and s stimuli were gathered for the duration of approximately 5000 stimuli, using Spike 2 software (Cambridge Electronic Design, Cambridge, UK). Cross-correlograms for simple analysis in the time domain were constructed using bin widths of 1 ms and pre- and poststimulus periods of 125 ms (Durbaba & Taylor, 1996). Cross-correlograms were assessed objectively by fitting with a log-normal curve using 'Kaleidagraph' (Abelbeck , USA). The equation used was:
P(t) = Aexp(-(1/2
2)ln2((t - ts)/(tp - ts))) + B,
where P(t) is the probability density, A is the amplitude, is the standard deviation of the underlying normal distribution, ts is the time to the start of the curve, tp is the time of peak and B is the baseline value (modified from Evans et al. 1993). In other cases, correlograms were fitted with the sum of two log-normal curves, according to the formula:
in which A1 and A2 are their amplitudes, 1 and 2 are the standard deviations of the underlying normal distributions, ts1 and ts2 their start times, tp1 and tp2 their peak times, respectively, and B the base line value.
The cross-correlograms were also converted into cross-spectra by subtracting the baseline value and then applying a fast Fourier transform routine. In this case the cross-correlograms were computed with bin widths of 1/1024 s and pre- and poststimulus periods of 500 ms. The spectra are expressed in terms of amplitude as a function of frequency and are plotted with a resolution of 2 Hz. The system gain as a function of frequency was computed for each corresponding frequency point by taking the cross-spectrum and normalising it by dividing by the autospectrum of the stimulus signal. The gain function could then be fitted by curves using Kaleidagraph to obtain objective estimates of the gain of the system (G0) and the speed of activation in terms of the corner frequency value (fc). The basic curve used was derived from the expression for gain as a function of frequency in a lag system, namely:
Gf = G0/
(1 + (f/fc)2n),
where G0 = gain at zero frequency, fc = corner frequency and n = order of the system. All curves were initially fitted with n set to 1. In some cases it was necessary to fit curves as the sum of two such first-order functions to represent a system with two such paths in parallel. It was then essential to allow for different propagation times in the two pathways. The expression for describing the gain function for a single input/output model with two pathways that have different dynamic characteristics is then given by:
G = [G12 + G22 + 2G1G2cos(2
ftd)]1/2,
where td is the difference in propagation times between the two pathways and G1 and G2 are the gain functions for the independent pathways and are given by the expression for gain as a function of frequency as above (see Bendat & Piersol, 1993, which also gives a valuable account of the relationships between the time- and frequency-domain analysis).
Finally, all s-secondary pairings were tested with stimulus trains in which the mean frequency of 50 Hz was sinusoidally frequency-modulated to a depth of ± 30 Hz at a modulating frequency 1.0 Hz. This frequency was chosen because it lies within the range of natural stepping. During all of the observations on the effects of random, ramp frequency and sinusoidally modulated stimuli, the muscle was maintained at a constant length. Responses of spindle afferents to modulated s axon stimulation were assessed by constructing cycle-averaged frequency plots from 10 or more cycles using 32 bins per cycle. These were then fitted with sine waves by the method of least sum of squares error to give objective measures of amplitude and phase of response for comparison with similarly computed fits to the sinusoidally modulated stimulus trains. The use of these methods of testing have been reviewed by Matthews (1972).
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RESULTS |
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Data were derived from experiments on 16 cats (nine MG and seven soleus muscles). The total number of muscle spindle afferents recorded was 195, of which 52 were designated as secondary since their conduction velocity was < 65 m s-1. Of these 52 secondary afferents, 30 received contacts from the axons isolated and are the subject of this report. The total number of axons isolated was 213, of which 134 acted upon at least one afferent, primary or secondary. Conventional classification showed that the axons that had a contact could be divided into 114 s and 18 d. Thirty-seven s axons were found to influence at least one of the secondary afferents. Since five of the s axons affected more than one of the secondary afferents recorded, and 11 secondary afferents received innervation from more than one s axon, there were altogether 42 pairings between the 37 s axons and the 30 secondary afferents. No systematic differences were found between the results for the MG and soleus spindles and they have therefore been pooled.
Range of static -motor effects on secondary responses to stretch
The effects of static gamma stimulation vary considerably from one example to another, and this variation must presumably be related to the extent to which bag2 and chain fibres are excited by a given axon. In the case of primary afferents, methods have been worked out for distinguishing the contribution of these two intrafusal fibre types (Celichowski et al. 1994a; Taylor et al. 1998), but, as explained in the introduction, the same analyses have not been attempted for secondary afferents. It is therefore worth looking afresh at all of the various tests that might help to distinguish between bag2 and chain effects. Figure 2 shows four examples of secondary afferent responses to ramp and hold stretches with and without s-axon stimulation at a constant frequency of 100 Hz, representing the range of effects observed. In Fig. 2A there is merely a small increase in afferent frequency throughout, with no significant increase in the amplitude of the stretch response. This is referred to as biasing. The same, but more marked effect is seen in Fig. 2B. It is noticeable that s stimulation leads to a more precise following of the length changes by the frequency changes, especially by making the slow response to stretch and release more linear and by preventing periods of silencing during release. The records in Fig. 2C and D show in addition to biasing as in A and B, marked increases in SS and consequently also in DD and SD, there being no increase in DI. Previous studies in which contraction of individual intrafusal fibres was observed in isolated muscle spindles (Boyd et al. 1985a, b) led to the general conclusion that contraction of bag2 fibres caused biasing with little effect on SS. Chain fibre contraction caused biasing and increased the amplitude of stretch response (due to increases in SS), when sufficient chain fibres were activated (Jami et al. 1980; Boyd, 1986). On this basis, the changes seen in Fig. 2A and B suggest contraction of bag2 fibres, whilst those in C and D suggest chain-fibre contraction. The latter two cases may also involve bag2 fibres, especially in Fig. 2D. Values of DI were affected very little by s stimulation. The cause of the increased irregularity of afferent firing seen in Fig. 2C and D may be competition between two separate impulse initiation sites for bag2 and chain fibres. Chain fibre activation alone with regular high-frequency stimulation would not be expected to have this result (see Celichowski et al. 1994a).
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Figure 2. Range of effects of Panels A-D each show two cycles of the response of a different MG secondary afferent to ramp and hold stretches before ( | ||
The functionally important effects of s stimulation on secondary responses to stretch can therefore be expressed essentially as changes in IF and SS. Figure 3B and C and shows how values of SS were estimated by fitting straight lines to the main part of the response during ramp stretch. Figure 3A shows for all the data how stimulation at 100 impulses s-1 changed the value of SS. It is immediately evident that one group of responses with control values above 100 impulses s-2 is quite distinct from the rest with control values less than 65 impulses s-2. Comparison of the two groups, from which examples are shown in Fig. 3B and C, show that the high control values of slope are associated with a frequency rise with stretch occurring in two phases, which could have resulted from slack in the chain fibres in the control state. The first phase of the rise would then be due to stretch of the bag2 fibre, which does not go slack (Boyd & Ward, 1975). The delayed second phase would be expected to dominate when the slack in the chain fibres is taken up. A review of the data showed that all of these cases were from experiments in which the muscles were left attached to the calcaneum and the resting length was defined by the position of the ankle joint at 90 deg. Most of the other cases occurred when the tendon was detached from the calcaneum and the muscle length set to L0 + 4 mm. Evidently, in the absence of s stimulation the chain intrafusal muscle fibres tend to be slack when the muscle length corresponds to an ankle angle of 90 deg. The data in which the initial SS was greater than 100 impulses s-2 were therefore excluded from consideration when assessing the effects of s stimulation on the responses to stretch. They were, however, retained in the remaining tests in which slack was assumed to be taken up by continuous s stimulation.
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Figure 3. Recognition of two different types of response to A, the values of SS during control stretches for each | ||
Considering the rest of the data, it is seen that in most cases 100 Hz s stimulation caused an increase in SS and; the distribution of values is shown in Fig. 4A. Stimulation also always caused an increase in IF, as shown in the distribution in Fig. 4B. These two variables, however, were not correlated (Fig. 4C) and this is consistent with the idea that they arise largely from different sources. Although increases in IF and SS would thus be expected to provide some guide as to bag2 and chain fibre effects, the fact that their values are unimodally distributed shows that no clear separation of bag2 and chain fibre innervation can be achieved in this way.
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Figure 4. The effects of A, distribution of values of increase in slow slope ( | ||
Afferent driving and random stimulation
In primary afferents, stimulation of s axons that make contact with chain fibres often results in entrainment of the afferent firing by the stimuli. This is called 'driving' (Crowe & Matthews, 1964) and may be strong (1:1) or weaker, at a subharmonic such as 1:2 or 1:3. The effect has been noted to occur in secondary afferents (Jami et al. 1980; Boyd, 1986), but assumed to be unusual. However, signs of driving have been seen in nine out of the 42 pairings in the present data. Figure 5 (left hand column) shows three examples of 'ramp frequency' stimulation with the frequency rising linearly to 150 Hz. In Fig. 5A the afferent follows the stimulus generally 1:2 until the stimulus frequency reaches 60 Hz. By contrast, the s-afferent pairs shown in Fig. 5D and G show no sign of driving. When we look at the effects of random stimulation in the middle column of Fig. 5, it is seen that the firing frequency of the driven unit (B) is highly irregular and the cross-correlogram (C) consists of a single narrow peak. This correlogram is shown fitted with a single log-normal curve and, following the arguments made previously in connection with primary afferents (Taylor et al. 1998), seems likely to represent an effect that is mediated through chain fibres acting alone. In Fig. 5E the effect of random stimulation is much less marked and the correlogram in Fig. 5F is small and prolonged, but could also be fitted with a single log-normal curve. Again, by analogy with the behaviour of primary afferents, this would be interpreted most simply as an effect due purely to bag2 action. The third example in Fig. 5G, although showing no sign of driving, is strongly affected by the random stimulation (Fig. 5H). The correlogram (Fig. 5I) in this case has a large brief peak followed by a small, prolonged one. This plot could be well fitted with the sum of two log-normal curves, shown superimposed, as explained in Methods. The obvious suggestion here is that the effect is due to the combined action of bag2 and chain fibres. The alternative explanation for the second component of Fig. 5I, that it is due to the underlying regular firing of the afferent (Petit et al. 1999) seems very unlikely since the separation of the two peaks is 18 ms. This would correspond to rhythmic firing at 55.6 Hz, whereas the basal firing rate seen in Fig. 5H is actually 19.6 Hz.
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Figure 5. Effects of ramp frequency and random Panels A, D and G show three examples of the response of secondary afferents to increasing the frequency of | ||
A confident recognition of these three types of correlogram was possible for three cases of a single narrow peak (half-peak width 3.4-6.7 ms) and 14 cases of a single broad peak (half-peak width > 8.2 ms). In the seven cases in which two peaks could be clearly distinguished, the half-peak widths were 5.2-8.8 ms and 11.1-78.1 ms. The overlap of one case of a fast effect at 8.8 ms was considered to be acceptable. This left 18 cases uncertain, either because the response was too small to be fitted reliably or because the correlogram suggested two components but the fitting routine could only detect one. In the following section we therefore use an additional method to investigate them further.
Frequency-domain analysis
It has been shown previously in connection with a study of primary afferents that there is some advantage in computing Fourier transforms of the cross-correlograms to obtain 'gain' as a function of frequency (Taylor et al. 1998), thus representing the effects of random stimulation in the frequency domain. In Fig. 6, data are shown from two cases of s-secondary pairings that appear to act through chain fibres alone. In the correlogram shown in Fig. 6A there is a single relatively narrow peak (well fitted by a single log-normal curve) and the frequency domain plot is shown as the dotted points in Fig. 6B and C. In conformity with what had previously been helpful with primaries, the plot of gain as a function of frequency (Fig. 6B) was then fitted with a curve appropriate to first-order lag dynamics. A difference from the findings for the primary afferents is seen in this case, in that the observed frequency response function falls more rapidly than expected and the fit is much improved by proposing that there are two first-order filters cascaded (Fig. 6C). The fit was found to be best when the two corner frequencies were the same, and in this case this had the relatively high value of 48.4 Hz, appropriate to the behaviour expected of the fast-twitch chain fibres. The possible reasons for the need for two cascaded first-order lags to fit some of the secondary frequency response plots are considered in the discussion. An interesting variant is seen in the case illustrated by Fig. 6D, E and F. Here the correlogram (Fig. 6D) has a small narrow peak, consistent with a weak chain effect, but there are also subsequent successively smaller peaks spaced at a mean interval of 20 ms. Notice that these are quite distinct from the first peak, which is well fitted with a single log-normal curve. The later peaks are clearly due to a tendency to regular firing of the afferent, for which the modal firing interval during the stimulation was 20 ms. The regular firing component stands out very clearly in Fig. 6E in the form of peaks at 50 Hz and at successive harmonics. It is a striking feature of the frequency domain plots that any element of regular firing can be distinguished, as in this case, from the main part of the response due to the action of the random stimuli on the secondary afferent firing. Presumably the regular component is evident in the lower example in Fig. 6, but not in the upper one because the much stronger chain action in the upper one ensures that the random stimulation completely disrupts the regular firing. The main part of the frequency response for the lower example in Fig. 6 is better fitted by the single lag curve (Fig. 6E) than by two cascaded lags (Fig. 6F). The estimated gain and corner frequency were 0.11 and 21.4 Hz, respectively.
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Figure 6. Frequency-domain analysis of responses to the random stimulation chain effect A and D are cross-correlograms of random | ||
Figure 7 shows two further examples, in this case thought to be characteristic of pure bag2 effects, due to a single s axon acting on two different secondary afferents. The effects were weak, as shown by the cross-correlograms in Fig. 7A and D (plotted at higher sensitivity that in previous figures). The correlogram in Fig. 7A could be fitted well with a log-normal curve, but that in Fig. 7D was too weak for this to be attempted, although the presence of a genuine effect was confirmed by the superimposed cumulative sum plot. Despite the small amplitude of the response in these two cases, their Fourier transforms in Fig. 7B and E are well defined. In both cases, in addition to the principal component with a low corner frequency, there were also peaks at high frequencies due to regular afferent firing. The first of these high-frequency peaks corresponds to the regular firing frequency and the subsequent peaks to harmonics. The data points affected by this regular firing were not included in computing the best fit single-lag curves drawn in Fig. 7B and E. Note that in Fig. 7B this curve fits well, but in Fig. 7E it does not. In Fig. 7C and F we see the same data with curve fits computed for two cascaded single-lag filters with the same corner frequencies, showing a marked improvement in goodness of fit for Fig. 7F, but not for Fig. 7C. The corner frequencies estimated were 6.3 and 6.8 Hz for Fig. 7B and F, respectively. The close similarity of these two values is consistent with motor innervation to bag2 intrafusal fibres. The possible reasons for requiring two cascaded lag elements in some cases will be considered later.
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Figure 7. Frequency-domain analysis of responses to random stimulation-bag2 effects A and D are cross-correlograms of random stimuli of a single | ||
Figure 8A shows one example that is readily interpretable as a mixed effect, since the correlogram could be fitted with the sum of two log-normal curves. The Fourier transform in Fig. 8B has a complex shape that required the sum of two first-order lag curves for a satisfactory fit. The inflection in the curve at around 20 Hz arises because of different time delays affecting the two components. The gains and corner frequencies of the fast and slow components were 0.21 and 7.2 Hz and 0.54 and 29.7 Hz, respectively. The lower example in Fig. 8 (C) is one in which the correlogram showed clear evidence of a fast component, fitted with a log-normal plot, but with an additional late component, which was more difficult to interpret. However, the true situation is clarified by the Fourier plot in Fig. 8D. A very satisfactory fit was obtained by summing two first-order lags with a small Gaussian pulse at 40 Hz. This pulse represented the effect of a small tendency to regular firing. The gains and corner frequencies of the fast and slow components were 0.28 and 46.1 Hz and 0.17 and 6.5 Hz, respectively. The presence of the slow component and its separation from the effects of repetitive firing would not have been evident without the analysis of the Fourier transforms.
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Figure 8. Frequency-domain analysis of responses to random stimulation-bag2 and chain effects A and C are two further examples of cross-correlograms of random | ||
Making use of the above interpretations of the random correlograms and the Fourier transforms, the s stimulation effects were classified according to the apparent involvement of bag2 and chain fibres. The numbers found amongst 42 pairings were: bag2 alone 26, chain alone three, bag2 and chain together 10, and three cases undecided. This represents a higher proportion of pure bag2 effects than expected from the data derived from primary afferents (Taylor et al. 1998) or from histological studies (Banks, 1994a, b). It appears likely that chain effects are being missed in a proportion of cases. The reason for this and ways of dealing with it will best be explained after describing the responses to sinusoidal frequency-modulated stimuli.
Sine modulation responses
In Fig. 9 are shown the effects in three s-secondary pairings of frequency-modulating the s stimulation rate with a sine wave at 1 Hz. The mean frequency was 50 Hz and the depth of modulation ± 30 Hz (shown by open circles). In Fig. 9A, which was believed to be a pure chain effect, the afferent is seen to be modulated quite strongly, although with some non-linearity. From the cycle average derived in Fig. 9B the gain was estimated as 0.46 and the phase lag as 1.8 deg. In Fig. C, which is a case of a pure bag2 effect, the afferent modulation is weak (gain = 0.05) and the phase lag large (46.5 deg). In Fig. 9E and F, which is a case of a mixed bag2 and chain effect, the modulation is strong (gain = 0.58) and essentially linear with a small phase lag (1.6 deg). The behaviour in these three examples of different s effects was very similar to those reported previously for primary afferents (Durbaba et al. 2001b). In particular, pure bag2 effects give a relatively weak modulation with large values of phase lag, as might be expected from the slow characteristics of bag2 fibres, whilst mixed bag2 and chain effects caused the strongest and most linear modulation of secondary afferent discharge.
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Figure 9. Effects of sinusoidally frequency-modulated stimuli A, C and E show three examples of the effects of | ||
Hidden chain effects
As described above, the random stimulation method indicated that the proportion of s axons with no apparent effect on chain fibres was larger than that expected from the data derived from effects on primary afferents. A possible explanation for this is that in the case of secondary afferents, relatively strong bag2 effects may obscure chain effects. Evidently some additional way of detecting a contribution from chain fibres is needed and this may be provided by a more detailed examination of the response to the ramp frequency stimulation in relation to the response to sinusoidal modulation. It is important to recall the direct observation of Boyd (1976) that the average frequency for maximal contraction of 'fast bag fibres' (now identified as bag2) was 75 Hz, whilst that for chain fibres was 150 Hz. Figure 10 shows data from a case in which random stimulation produces a marked effect (A), but the correlogram (B) has only a small prolonged deflection, characteristic of a bag2 effect. This is confirmed by the frequency domain plot (C), which is best fitted by a single lag curve with the low corner frequency of 4.1 Hz. Despite these indications of a pure bag2 effect, the sinusoidal modulation plots (D and E) show an ability to follow with the high gain of 0.95 and the relatively small phase lag of 18.5 deg. From the data presented in Fig. 9, these are features that are characteristic of the presence of a chain effect. The response to ramp frequency stimulation shown in Fig. 10F also shows that there must indeed be a contribution from chain innervation. The essential point to observe is that the afferent firing frequency rises steeply until the stimulation frequency reaches 44 Hz (arrow), but then continues to rise less steeply up to the maximum stimulation frequency of 150 Hz. Presumably the force output of the bag2 fibre does not increase further with stimulation above 44 Hz, whereas the chain fibres continue to do so to their much higher tetanic fusion frequency of about 150 Hz. Returning to Fig. 10C, it is true that the observed gain falls below the curve fitted to a single slow component and this suggests that there was a small chain contribution. However, the fitting routine for two components could not detect this because of the high-frequency noise.
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Figure 10. Example of a hidden chain effect A, effect of random | ||
A very clear contrast is presented by the data of Fig. 11 for another s-secondary pairing. Here the afferent firing pattern (A), the correlogram (B) and the frequency domain plot (C) are all very similar to the equivalents in Fig. 10. However, with sinusoidal modulation (Fig. 11D and E) the gain is seen to be only one-third of that in Fig. 10 and the phase lag nearly twice as great. When we consider the ramp frequency response (Fig. 11F), it is seen that the afferent frequency ceases to increase when the stimulation frequency reaches 71 Hz, whereas in Fig. 10F it continued on to 150 Hz. The compelling explanation is that there is a chain effect in Fig. 10, but not in Fig. 11. The presence of a chain effect (hidden in the random stimulation testing, but revealed by the ramp frequency test) accounts for the high gain and low phase lag during sinusoidal frequency modulation seen in Fig. 10. It should be pointed out that this use of the ramp frequency test is distinct from the conventional one, which seeks to reveal signs of afferent driving.
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Figure 11. Example of a pure bag2 effect A, effect of random | ||
Revised classification of s effects on secondary afferents
Making use of this additional criterion the identification of the involvement of bag2 and chain fibres in each s-secondary pairing was revised and related to the gain and phase lag found with sinusoidal frequency modulation. The values for modulation gain and phase lag at 1 Hz are shown for the 37 pairings that could be confidently measured in Fig. 12, categorised accordingly. Figure 12A and B confirms that pure bag2 effects (n = 9) generally show low gain (mean = 0.28) and large phase lags (mean = 37.0 deg). Mixed effects (n = 25) are most common and have mean gain = 0.47 and mean phase lag 19.9 °. Only three pure chain effects were observed, with a mean gain of 0.37 and mean phase lag of 4.1 deg.
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Figure 12. Summary of the modulating effects of bag2 and chain intrafusal fibres A and B, distributions of the values of modulation gain and phase lag, respectively: filled bars, chain; open bars, bag2; hatched bars, mixed. C, scatter plot of phase lag against gain: filled circles, chain; open circles, bag2; crosses, mixed. Note that in C the mixed effects appear to fall into two groups. | ||
The relationship between the estimates of modulation gain and phase lag is shown in Fig. 12C, with different symbols for the three types of effects. Pure bag2 effects (open circles) were confirmed as having low gains with large phase lags. Pure chain effects (filled circles) had small phase lags even though their gain estimates covered a similar range to those of pure bag2 effects. The mixed bag2-chain effects (crosses) dominated and appear to fall into two groups according to the values of modulation phase lag (Fig. 12C). The first group shows a significant linear regression of phase lag with gain. The other group overlies the points associated with the pure bag2 effects.
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DISCUSSION |
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In this study, the methods of analysis of the effects of s stimulation on afferent firing, which had been developed previously for primary afferents (Taylor et al. 1998), have been applied to secondary afferents. At first it was suspected that the effects of bag2 and chain fibre activity would not be readily distinguishable, because of the lower sensitivity of secondary endings than primary endings to small and rapid mechanical disturbances. However, in many cases the results were similar, in that the correlograms computed between random s stimuli and the secondary afferent impulses could be divided into three types, just as in the case of primary afferents. A single, relatively large and brief peak of increased probability of firing following a stimulus is therefore reasonably interpreted as being due to chain fibres acting alone. A single small and broad peak is probably due to bag2 fibres acting alone. In those cases in which two such peaks occurred together, we suppose that there was joint innervation of both fibre types. The alternative interpretation of the second peak as being due to rhythmic firing of the afferent was eliminated, because the time interval between the correlogram peaks did not correspond to the period of the rhythmic component of firing. In support of this conclusion was the observation that the occurrence of rhythmic firing was very clearly revealed by the presence of a peak at the appropriate frequency in the Fourier transforms, often followed by harmonics.
It should be emphasised that the special advantages of the use of the random stimulation method, which permit these interpretations, are only realised if the stimulus train is a Poisson process with exponentially distributed interpulse intervals. The autocorrelogram of such a process is a pulse at the origin and a constant value on either side. This is the point process equivalent of white noise. If the pulse sequence is modified by scaling or by some other smoothing process (Petit et al. 1999) then an element of regularity is introduced and this is revealed by features of the autocorrelogram. The effect of this modification is to cause the generation of spurious peaks in the cross-correlogram.
The present study has served to emphasise the value of the Fourier transforms as an extension of the random stimulation method. We have already referred to the way in which the disturbance of the correlograms due to an element of regular firing can be recognised in the Fourier transforms. The other advantage stems from their superior smoothing properties in the detection of small signals in the presence of noise. Construction of cross-correlograms by counting the occurrence of events in short time intervals (1 ms bins in the present case) provides some smoothing on a short time scale, referred to by Lanczos (1957) as 'smoothing in the small'. The residual noise may make it impossible to distinguish some features in the time domain, such as small contributions from bag2 fibres. However, the whole data set from the correlogram is used in the estimation of each element in the frequency domain and this is referred to as 'smoothing in the large' (Lanczos, 1957). It is this superior smoothing characteristic that has permitted in the present study not only the detection of fast and slow components in cases in which they were otherwise unclear, but also to estimate their amplitude ('gain') and their equivalent corner frequencies. The corner frequencies of the frequency response functions were similar for the two afferent types. Thus, the mean values for primaries were 46.0 and 4.6 Hz and for secondaries 30.8 and 5.7 Hz, respectively. This implies that it is the properties of the intrafusal fibres contacted which determine the response to s stimulation, rather than the afferent type.
In recent work on s effects on primary spindle afferents (Taylor et al. 1998), it was found that the frequency response functions could all be well fitted as first-order lag functions. The same observation has now been made in the case of most secondary afferents. However, in a minority of cases (8/42) good fits were only obtained by assuming that each component was modelled by two first-order lag systems in series, with the same corner frequencies. It is proposed that this difference may arise because, whilst the majority of secondary endings lie in the juxta-equatorial (S1) region (defined by Boyd, 1962), a minority lie further from the centre (S2-5). Histological studies of the soleus muscle (Banks et al. 1982) have in fact revealed that in nine out of 42 spindles the secondary ending was in the S2-5 regions. A modelling study reported elsewhere (Durbaba et al. 2001a) has shown that if these regions are characterised by having a higher viscosity than the S1 region (due to the greater concentration of myofibrils in the former; Banks et al. 1982), then it is to be expected that two first-order lag elements will exist between the force generator and the sensory ending in the S2-5 regions.
One reason for developing the random stimulation analysis method in the case of the primary afferents was to use it to look for specificity of innervation of bag2 and chain fibres by distinct groups of s motoneurons. In MG the proportions of effects found by this means were: pure chain 23.5 %, pure bag2 25 % and joint chain and bag2 51.5 %. The equivalent proportions estimated from secondary afferents based on random stimulation alone were: chain 7.1 %, bag2 61.9 % and mixed 23.8 % (with three out of 42 unidentified). The chief difference between these two sets of figures appears to be due to failure to detect chain fibre innervation in a significant number of secondary afferents. This may arise because the falling part of the gain curve for chain fibres may run into the high-frequency noise. The additional examination of the way in which secondary afferents responded to sinusoidally modulated and to ramp frequency s stimulation showed that some of the cases thought to be pure bag2 actually also had chain contacts. Taking this into account, the proportions then became pure chain 7.7 %, pure bag2 23.0 % and mixed 64.1 %, which is closer to the values reported for the primary afferent study. The main residual difference is a greater apparent incidence of pure chain innervation in the primary group. Despite the introduction of the various methods of analysis described here, it may still not be possible to be as certain of the contribution of chain and bag2 fibres using physiological tests in the case of secondary afferents as it is with primaries. The basic difficulty may lie in the differences in the structure of the two types of ending (Banks et al. 1982). It appears that whereas the primary afferent branch innervating the chain and bag2 fibres provides them each with relatively separate innervation, in the case of secondary afferents, most of the terminal branches appear to contact both fibre types.
One additional reason why some chain effects on secondary afferents do not show up with random stimulation testing may be that individual secondary endings do not necessarily contact all of the chain fibres in a spindle capsule. This certainly seems to be a reasonable conclusion from histological studies (Barker & Cope, 1962; Banks et al. 1982; Kucera, 1982; Thornell et al. 1995). Another observation that is likely to be important is that secondary afferents commonly have much higher resting firing frequencies than do primaries. If this resting discharge depends largely on sensory endings on the bag2 fibres, then this could well occlude effects due to chain fibres. In experiments in which histology confirmed that a s axon innervated both bag2 and chain fibres, it was also demonstrated that the effects of the chain innervation may not be evident (Halliday et al. 1988; Gladden & Matzusaki, 2002).
From a practical standpoint it is evident that no one physiological test can reliably detect bag2 and chain fibre contributions to the firing of secondary afferents. The random stimulation and correlation method combined with Fourier transformation gives a clear result in many cases. However, it is desirable also to check the responses to ramp frequency stimulation and to sinusoidally frequency-modulated stimuli to reveal cases of hidden chain effects. The ramp frequency test in this case is not being used in its usual form to detect driving, but rather to look for a continuing increase in the afferent response above 75 Hz, at which bag2 contraction would be expected to reach its maximum (Boyd, 1976). Chain effects that are hidden may also be revealed by a greater amplitude of response and smaller phase shift with sinusoidal stimulation than expected for bag2 fibres. This test can also suggest the presence of a bag2 effect, which is otherwise uncertain, by the presence of a larger phase shift than expected for chain fibres.
The present work has confirmed that the effect of s activity applied with the muscle at constant length is to produce an essentially linear modulation of the secondary afferent discharge, and that this is most effective when expressed via bag2 and chain fibres acting together. Previous work has shown that sinusoidally modulated s activity can summate linearly with sinusoidal length changes to determine primary afferent firing (Appenteng et al. 1982), and this observation has been extended to natural movements and to secondary afferents (Taylor et al. 2000a,b; Durbaba et al. 2001a,b). Classically, s activity has been found to reduce primary afferent sensitivity to stretch and to have an ill-defined effect on secondary sensitivity. Such effects on sensitivity do not make themselves apparent in the examples of natural or experimentally induced modulation of s activity quoted above. It is therefore concluded that the importance of the s system is to be seen not as a control of the spindle parameters of response to stretch, but rather as a source of a signal to be summed algebraically with the length changes, to determine the signal fed back to the central nervous system (see also Taylor et al. 1999). The important consequence of this is the simplification of the interpretation of the recordings of s activity. Hence, the functional effect is that because the phasing of the static fusimotor drive is such as to minimise unloading during active shortening, the dynamic range of the spindle afferents is greatly increased.
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Acknowledgements
This research was supported by a grant from the UK Medical Research Council. Our thanks are due to the late Mrs O.D. Taylor for technical assistance.
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) and during (
) stimulation of a