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Responses of muscle spindles in feline dorsal neck muscles to electrical stimulation of the cervical sympathetic nerve

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Abstract

Previous studies performed in jaw muscles of rabbits and rats have demonstrated that sympathetic outflow may affect the activity of muscle spindle afferents (MSAs). The resulting impairment of MSA information has been suggested to be involved in the genesis and spread of chronic muscle pain. The present study was designed to investigate sympathetic influences on muscle spindles in feline trapezius and splenius muscles (TrSp), as these muscles are commonly affected by chronic pain in humans. Experiments were carried out in cats anesthetized with alpha-chloralose. The effect of electrical stimulation (10 Hz for 90 s or 3 Hz for 5 min) of the peripheral stump of the cervical sympathetic nerve (CSN) was investigated on the discharge of TrSp MSAs (units classified as Ia-like and II-like) and on their responses to sinusoidal stretching of these muscles. In some of the experiments, the local microcirculation of the muscles was monitored by laser Doppler flowmetry. In total, 46 MSAs were recorded. Stimulation of the CSN at 10 Hz powerfully depressed the mean discharge rate of the majority of the tested MSAs (73%) and also affected the sensitivity of MSAs to sinusoidal changes of muscle length, which were evaluated in terms of amplitude and phase of the sinusoidal fitting of unitary activity. The amplitude was significantly reduced in Ia-like units and variably affected in II-like units, while in general the phase was affected little and not changed significantly in either group. The discharge of a smaller percentage of tested units was also modulated by 3-Hz CSN stimulation. Blockade of the neuromuscular junctions by pancuronium did not induce any changes in MSA responses to CSN stimulation, showing that these responses were not secondary to changes in extrafusal or fusimotor activity. Further data showed that the sympathetically induced modulation of MSA discharge was not secondary to the concomitant reduction of muscle blood flow induced by the stimulation. Hence, changes in sympathetic outflow can modulate the afferent signals from muscle spindles through an action exerted directly on the spindles, independent of changes in blood flow. It is suggested that such an action may be one of the mechanisms mediating the onset of chronic muscle pain in these muscles in humans.

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Acknowledgements

We thank Monica Edström, Stina Langendoen, and Margareta Marklund for valuable assistance in the experiments; Lars Bäckström and Göran Sandström for implementing the data processing routines and for technical support; and Professor Uwe Windhorst for enlightening and fruitful comments on the manuscript. This study was supported by grants from The Swedish Council for Work Life Research, IngaBritt and Arne Lundbergs Forskningsstiftelse, and the Italian Ministry of Scientific Research (MIUR).

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Correspondence to S. Roatta.

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F. Hellström and S. Roatta equally contributed to this work.

Appendix

Appendix

According to a widely used procedure, the stretch-evoked MSA activity may be quantitatively characterized by constructing a cycle histogram of spike density to which a 1-Hz sine function is fitted by means of a least-square algorithm (e.g., Matthews and Stein, 1969; Hulliger et al. 1977). A modified version of this procedure is described here that grants improved performance in case the number of spikes in the histogram is low, such as when the discharge rate is low and/or the spike sequence is collected from only a few consecutive cycles. Although this algorithm does not require the construction of the histogram, this approach is nevertheless described because it helps explain how the algorithm works.

The sinusoidal length stimulus applied to the (neck) muscles was the following:

$${\text {Stimulus}}=L\,{\text {sin}}(\theta),$$
(1)

where θ is the radian angle: θ=ω t=2π ft, with ω being the angular velocity, f being the frequency of the sine wave (f=1 Hz in our case), and t the time. The range 0<θ<2π (radians) corresponds to a single cycle.

Consider the cycle divided into n bins, the center of the ith bin being located at the angle θ i (1 ≤ i ≤ n) and the bin width being Δ θ=2π/ n radians. A cycle histogram is generated from the spike activity of a single MSA collected over four consecutive cycles. The jth spike occurs at a time t j , which corresponds to a specific angle θ j =2πf t j within the cycle, 1≤ jm, with m being the total number of spikes collected from the current sample. The number of spikes collected into the ith bin, Y i , divided by the number of cycles (n c =4) and the bin width in seconds (Δt=1/(nf)), yields bin contents in terms of spike densities.

The histogram thus obtained is fitted with a sine wave whose amplitude, phase, and offset are to be determined by the fitting algorithm. For mathematical convenience, we defined this sine wave by the sum of three terms: a sine (in phase with the length stimulus), a cosine (90° in advance of the length stimulus), and a constant term, C, corresponding to the mean firing rate (bias):

$$F(\theta)=A\,{\text {sin}}(\theta)\,+\,B\,{\text {cos}}(\theta)\,+\,C$$
(2)

The three unknown variables (A, B, and C) are determined by solving the system of n equations, defined in matrix terms as

$${\mathbf {Mx}} = {\mathbf Y},$$
(3)

where M is a numerical matrix, Y is the array of spike densities from the above histogram, and x contains the variables to be estimated:

$${\mathbf M}=\left[{\,\begin{array}{*{20}c} {\sin (\theta_1)} & {\cos (\theta_1)} & 1 \\ {\sin (\theta_2)} & {\cos (\theta_2)} & 1 \\ {\sin (\theta_3)} & {\cos (\theta_3)} & 1 \\ \vdots & \vdots & \vdots \\ {\sin (\theta_n)} & {\cos (\theta_n)} & 1 \\ \end{array}} \right]\;\quad {\mathbf{x}}=\left[{\begin{array}{*{20}c} A \\ B \\ C \\ \end{array}} \right]\quad \hbox{Y} = \frac{nf}{n_{\text {c}}}\left[{\begin{array}{*{20}c } {Y_1} \\ {Y_2} \\ {Y_3} \\ \vdots \\ {Y_n} \\ \end{array}} \right]$$
(4)

This system is solved by means of the least-square algorithm (LSA), which involves multiplying both sides with the transpose of M:

$${\mathbf M}^{\mathbf T}{\mathbf {Mx}} = {\mathbf M}^{\mathbf T}{\mathbf Y},$$
(5)

where MT is the transpose of the matrix M, and then solve for x:

$${\mathbf x} = ({\mathbf M}^{\mathbf T} {\mathbf M})^{-1} {\mathbf M}^{\mathbf T}{\mathbf Y}$$
(6)

The following matrices are generated in Eq. 5:

$${\mathbf{M}}^{\mathbf{T}} {\mathbf{M}}=\left[{\begin{array}{*{20}c} {\sum\limits_1^n {\sin ^2 (\theta _i)}} & {\sum\limits_1^n {\sin (\theta _i)\cos (\theta _i)}} & {\sum\limits_1^n {\sin (\theta _i)}} \\ {\sum\limits_1^n {\sin (\theta _i)\cos (\theta _i)}} & {\sum\limits_1^n {\cos ^2 (\theta _i)}} & {\sum\limits_1^n {\cos (\theta _i)}} \\ {\sum\limits_1^n {\sin (\theta _i)}} & {\sum\limits_1^n {\cos (\theta _i)}} & n \\ \end{array}} \right]$$
(7)
$${\mathbf M}^{\mathbf T}{\mathbf Y}=\frac{nf}{n_{\rm c}}\left[{\begin{array}{*{20}c} {\sum\limits_1^n {Y_i \sin (\theta _i)}} \\ {\sum\limits_1^n {Y_i \cos (\theta _i)}} \\ {\sum\limits_1^n {Y_i}} \\ \end{array}} \right]$$
(8)

Now, by letting the width of the histogram bins approach zero (Δt →0), i.e., n→∞, the elements in the MTM matrix (Eq. 7) become definite integrals computed over one cycle (0≤ θ ≤2π); for instance, for the element in row 1, column 1 we get the following:

$$\sum\limits_1^n {\sin^2 (\theta _i)}=\frac{1}{\Delta\theta}\sum\limits_1^n {\sin ^2 (\theta _i)\Delta \theta} \mathop{\longrightarrow}\limits^{n \rightarrow \infty}\frac{n}{{2\pi}}\int_0^{2\pi} {\sin ^2 (\theta _i){\rm d}\theta},$$
(9)

and expression Eq. 7 becomes

$${\mathbf{M}}^{\mathbf{T}} {\mathbf{M}}=\frac{n}{{2\pi}}\left[{\begin{array}{*{20}c} {\int {\sin ^2 (\theta){\text {d}}\theta}} & {\int {\sin (\theta)\cos (\theta){\text {d}}\theta}} & {\int {\sin (\theta)} {\text {d}}\theta} \\ {\int {\sin (\theta)\cos (\theta){\text {d}}\theta}} & {\int {\cos ^2 (\theta)} {\text {d}}\theta} & {\int {\cos (\theta){\text {d}}\theta}} \\ {\int {\sin (\theta)} {\text {d}}\theta} & {\int {\cos (\theta){\text {d}}\theta}} & {2\pi} \\ \end{array}} \right]$$
(10)

Therefore, excluding the common factor n (n→∞), the nine elements in the matrix can be exactly solved for θ, resulting in simple constant (numeric) values.

As for the MTY vector (Eq. 8), its elements now contain an infinite number of terms, corresponding to the infinite number of bins, but only m terms will be different from zero, m being the total number of spikes collected into the histogram. In fact, because the bin width approaches zero (Δt→0), any bin will contain either one or zero spike. It is therefore convenient to maintain the discrete form of the MTY matrix and only sum the nonzero terms:

$${\mathbf M}^{\mathbf T}{\mathbf Y}=\frac{nf}{n_{\text {c}}}\left[{\begin{array}{*{20}c} {\sum\limits_1^m {\sin (\theta _j)}} \\ {\sum\limits_1^m {\cos (\theta _j)}} \\ {\sum\limits_1^m 1} \\ \end{array}} \right],$$
(11)

where θ j is the angular occurrence of each spike.

Expressions in Eqs.10 and 11 are then inserted in Eq. 5, and the nonfinite term n is eliminated from both sides. The resulting numerical equation is the one that is used by the algorithm and solved for x according to Eq. 6. Estimates A, B, and C as defined in Eq. 2 are finally obtained.

Empty bins

This second part deals with the method applied to exclude empty bins in the “silent period,” which, if not excluded, would tend to lower the amplitude of the fitted sine (Hulliger et al. 1977).

After the sine had been fitted, the code checked whether the amplitude was greater than the baseline (=negative swing). The part of the sine with negative values was then excluded in the integral of the sine, and spikes occurring in the “silent period” were also excluded. So, MTM and MTY were recalculated and solved as before.

Finally, MDR, AMP, and PHASE (see Methods) were computed from A, B, and C:

$${\text {MDR}}\,=\,C,\quad {\text {AMP}}\,=\,\sqrt{A^{2} + B^{2}}, {\text {PHASE}}={\text {Atan}}\left({{A}\over{B}}\right)$$
(12)

Validation

Comparisons of the classical 24-bin method and the present algorithm were performed by fitting a simulated (artificially generated) spike train with the following characteristics: average discharge rate=30 Hz, amplitude of modulation=10 Hz, frequency of modulation=1 Hz, Phase=0°. The better performance of the present algorithm is apparent from Table 1, which shows the results of the fitting in two examples with different sample sizes.

Table 1 Comparisons of the estimates produced by the fitting of an artificially generated spike train with sinusoidal modulation of the firing frequency (average discharge rate: 30Hz, amplitude of the sinusoidal modulation: 10 Hz, frequency of the sinusoidal modulation: 1 Hz)

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Hellström, F., Roatta, S., Thunberg, J. et al. Responses of muscle spindles in feline dorsal neck muscles to electrical stimulation of the cervical sympathetic nerve. Exp Brain Res 165, 328–342 (2005). https://doi.org/10.1007/s00221-005-2309-7

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