A model of spindle afferent response to muscle stretch

1. A unified model of the properties of stretch responses of mammalian spindle endings is proposed. This model encompasses the disparity between sensitivity of spindle endings to small and to large stretch of the muscle as well as the disparity in their dynamic responsiveness for different amplitudes of stretch. 2. In the model the mechanical properties of intrafusal fibers include a property akin to friction, which is hypothesized on the basis of reported observations on amphibian muscle. Transducer and encoder processes are modeled in the light of recent observations on isolated spindles. The model involves five unknown parameters whose values are selected by reference to certain reported observations on deefferented primary and secondary endings. The model can be used to predict responses to length changes of arbitrary time course. 3. Predicted responses to large ramp-and-hold stretch are quantitatively comparable to observations over a wide range of stretch velocities. The quantities compared include the increment in response during ramp stretch as well as the dynamic index, which is a measure of adaptation at stretch plateau. 4. At a fixed frequency of sinusoidal stretch, the relation between amplitudes of stretch and response is predicted in quantitative agreement with measurements. As the frequency of stretch is decreased, the predicted phase lead decreases and then increases, while the sensitivity decreases monotonically, in accord with observations. 5. In the model the high sensitivity for small stretch is not specific to any particular length of the muscle. When stretch is large, the region of high sensitivity is gradually reestablished at the new length, a phenomenon referred to as resetting. The dynamic response to a large stretch can be seen as arising, for the most part, from the dynamic process of resetting. 6. The influences of static or dynamic fusimotor activation on stretch responses of the primary ending are simulated by modifying the parameter values in the model. The modifications are such that static (dynamic) fusimotor activity speeds up (slows down) the resetting of the high-sensitivity region. The predictions mimic qualitatively the observed fusimotor effects not only on the response to large ramp stretch but also the contrasting effects seen with smaller, sinusoidal stretch.     

The regularity of primary and secondary muscle spindle afferent discharges

1. The patterns of nerve impulses in the afferent fibres from muscle spindles have been studied using the soleus muscle of the decerebrate cat. Impulses from up to five single units were recorded simultaneously on magnetic tape, while the muscle was stretched to a series of different lengths. Various statistics were later determined by computer analysis.2. After the ventral roots were cut to eliminate any motor outflow to the muscle spindles, both primary and secondary spindle endings discharged very regularly. At frequencies around 30 impulses/sec the coefficient of variation of the interspike interval distributions had a mean value of only 0.02 for the secondary endings and 0.058 for the primary endings. The values obtained for the two kinds of ending did not overlap.3. When the ventral roots were intact, the ;spontaneous' fusimotor activity considerably increased the variability of both kinds of endings. Secondary endings still discharged much more regularly than primary endings, even when the fusimotor activity increased the frequency of firing equally for the two kinds of endings. At frequencies around 30/sec the average coefficient of variation of the interval distributions was then 0.064 for the secondary endings and 0.25 for the primary endings.4. When the ventral roots were intact there was usually an inverse relation between the values of successive interspike intervals. The first serial correlation coefficient often had values down to - 0.6 for both kinds of ending. Higher order serial correlation coefficients were also computed.5. Approximate calculations, based on the variability observed when the ventral roots were intact, suggested that when the length of the muscle was constant an observer analysing a 1 sec period of discharge from a single primary ending would only be able to distinguish about six different lengths of the muscle. The corresponding figure for a secondary ending was twenty-five lengths.6. The increase in variability with fusimotor activity, and the pattern of serial correlations, were probably caused by static fusimotor fibres firing at rates below the fusion frequency of the intrafusal muscle fibres that they supply.     

After-effects of fusimotor stimulation on the response of muscle spindle primary afferent endings

1. The experiments were performed on the soleus muscle of the anaesthetized cat in which the ventral roots had been cut.2. A short period of repetitive stimulation of a single fusimotor fibre which influenced a particular spindle primary ending invariably caused a characteristic alteration in the response of the same ending to a subsequently applied ramp stretch of the muscle. The change consisted in the appearance of a burst of impulses at the beginning of the stretch where none had been present before. Occasionally, such an ;initial burst' was spontaneously present; it was then enhanced following fusimotor stimulation.3. This after-effect of fusimotor stimulation was abolished by a subsequent stretch of the muscle, but otherwise persisted for over a minute.4. When the muscle was released to below the length at which the spindle had been facilitated and a testing stretch applied from the new initial length there was no burst of impulses at the beginning of stretch. There was, however, a burst as the muscle was stretched through the length at which the fusimotor fibre had been stimulated.5. These effects are suggested to be due to the persistence of stable bonds between the actin and myosin filaments of the intrafusal fibres, so that their previously activated regions were ;stuck' at the length they were when the fusimotor stimulation was applied.6. Such effects were produced both by static and by dynamic fusimotor fibres. The effects of the two kinds of fusimotor fibre, however, appeared to be mediated by different intrafusal muscle fibres. This was shown by stimulating one kind of fibre with the muscle slightly stretched, then releasing the muscle a few mm and stimulating the other kind of fibre to the same spindle. A subsequent testing stretch then elicited two bursts, one at the beginning and one in the middle of the stretch.     

A determination of static mechanical properties of intrafusal muscle in isolated cat muscle spindles.

The sensitivity of mammalian muscle spindles to stretch is greater in a stretched muscle than in a slack one. We have investigated this behavior in isolated muscle spindles removed from cat tenuissimus muscle. We measured the steady-state strain of intrafusal muscle in sensory and non-sensory regions and found that there is a proportional relationship between sensory strain and receptor sensitivity; both increase with spindle length. By comparing intrafusal strain of sensory and non-sensory areas with and without an intact spindle capsule, we conclude that capsule does not contribute to the non-linear sensitivity. Measurements of steady-state tension indicate that the striated portions of the intrafusal muscle exhibit a non-linear stiffness which can quantitatively account for the observed behavior.     

Sensory terminal responses of frog muscle spindle recorded across vaseline gap onto intrafusal muscle fibre.

When electrical activities of the sensory terminal in the frog muscle spindle were recorded across a vaseline gap which was oriented transversely to the intrafusal muscle bundle (IFM-gap), large and small spikes occurred in coincidence with propagated and abortive spikes respectively recorded across the axon-gap. The IFM-gap placed on the receptor region displayed triphasic spikes in which the first small positive deflection occurred approximately 0.2 ms prior to the propagated and abortive spikes. No such deflection was observed when the IFM-gap was placed more than 50 mum away from the receptor region. Increasing the distance from the receptor region to the IFM-gap resulted in an exponential decay in the amplitudes of both the large and small spikes. Regardless of the position of the IFM-gap relative to the receptor region, bimodal distributions in the amplitude histograms of the large spikes, and large variations in the shapes of the small spikes were observed. These results indicate that the IFM-gap responses may represent electrical activity of the non-myelinated branches, along which propagated impulses may arise from at lest two separate origins, while abortive spikes arise from many more sites.     

Interaction of recurrent inhibitory and muscle spindle afferent feedback during muscle fatigue.

Mammalian skeletal motor units have differing properties including their different susceptibility to fatigue. The question discussed in this paper is whether and to what extent proprioceptive feedback via muscle spindles can contribute to shape the firing patterns of motor units so as to minimize their loss of force during fatiguing contraction. The firing of a skeleto-motoneuron dispatches signals which are fed back to the same and homonymous as well as synergistic motoneuron. Two feedback pathways are of concern here: one via the related muscle unit and muscle spindle afferents (proprioceptive path), and one via recurrent motor axon collaterals and Renshaw cells (recurrent inhibitory path). It is suggested that the contraction of a motor unit or a small group of adjacent ones is signalled to the homonymous alpha-motoneurons via proprioceptive afferents, the signal being filtered and enhanced by spinal recurrent inhibition. This is effected by timed correlation of the signals which are propagated through the two feedback loops. The effects of the correlation can be strengthened by (i) topographical order of the feedback connections, (ii) heterosynaptic interaction, and (iii) tendencies towards synchronous discharge between motoneurons. These mechanisms render the possibility more likely that information about the unfused contractions of a muscle unit (or a small group of them), mediated via proprioceptive afferents, play a role in shaping the precise discharge pattern of the innervating motoneuron(s). These mechanisms could be used to optimize the force output of large fatiguing motor units during long activation, during which their activation rates normally decrease (adapt) over time. Our results show that during adapting motoneuron firing Renshaw cells and muscle spindle afferents may show discharge patterns which at least in part are in keeping with such an hypothesis.     

The complex architecture and innervation of intrafusal muscle fibers in the sensory region of a muscle spindle in the adult Chinese hamster.

A particular muscle spindle was encountered which consisted of intrafusal muscle fibers taking a complex three-dimensional architecture and innervation pattern along the equatorial to the juxtaequatorial region in the tenuissimus muscle of the adult Chinese hamster. These intrafusal fibers formed pairings not only between nuclear bag fibers but also between nuclear chain fibers, and decreased in number from the equatorial region toward the juxtaequatorial region in order that the chain fibers might freely terminate within the inner capsule without a cellular attachment. In addition, a bag fiber and a chain fiber were innervated by multiaxonal nerve endings located adjacent to the annulospiral sensory endings and considered to be autonomic in nature. These findings suggest that the intrafusal fibers may fail to accomplish differentiation at an early stage of development, retaining immature features into adulthood.     

A new grouping of intrafusal muscle fibers based on developmental studies of muscle spindles in the cat

The development of muscle spindles was studied using the tenuissimus muscle of the cat. Observations show that the intrafusal muscle fibers develop as two separate groups: one group represented by a single nuclear bag fiber while the second group comprises the second nuclear bag fiber in association with all the nuclear chain fibers. This grouping is most pronounced in the fetus and is clearly seen in neonatal kittens (i.e., up to 2 weeks of age). As the intrafusal fibers begin to separate from each other, the groupings become less noticeable, although this basic pattern is often retained in the adult. The pattern of intrafusal fiber grouping is most noticeable in the equatorial regions of the spindle and least noticeable in the polar regions. This is not the grouping of fibers which would have been expected from a consideration of existing reports on muscle spindles. The implications for spindle form and function are considered.     

Electrical threshold of the sensory nerve terminal of the frog muscle spindle: a role of spindle potential for generating afferent impulses

The threshold at the terminal node in the capsule of frog muscle spindle, where afferent impulses are initiated, was calculated to be 2 nA on average, from data of intracellularly recorded threshold depolarization of the node against antidromic stimulation and of a mean attenuation ratio of the stimulation current from the stimulation site to the recording site. Using a similar procedure, the absolute value of orthodromically generating current at the node during static stretch of the spindle from the in situ length was calculated to be approximately 0.9 nA. It thus is supposed that at the terminal node the afferent impulses may be triggered by abortive spikes of 1.1 nA or more in amplitude, which are generated along non-myelinated filaments, being superimposed on the generating current.     

Evidence for fusimotor drive in stroke patients based on muscle spindle thixotropy.

To study fusimotor function in stroke patients, we compared the amplitude of stretch reflexes elicited in flexor carpi radialis (FCR) after contraction of FCR with the wrist held flexed ('hold-short') or extended ('hold-long'). Seven subjects with impaired hand function and spasticity due to stroke, and seven healthy subjects were investigated. Surface electrodes recorded electromyographic activity of wrist flexors and extensors while subjects performed isometric wrist flexions with the wrist alternately in 15 degrees of flexion or extension. After contractions the wrist was moved passively to the mid-position, and stretch reflexes were elicited via controlled mechanical taps delivered over the FCR tendon. For both groups, the amplitude of the stretch reflex was greater after 'hold-short' than 'hold-long' contractions. This finding is consistent with the 'after-effects' of intrafusal fibre activation, and suggests that fusimotor neurones are activated during voluntary contractions of the paretic limb, just as in the limb of a healthy subject.     

The influence of extrafusal muscle activity on discharge patterns of primary muscle spindle endings

The influence of extrafusal muscle activity in anaemically decerebrate cats upon discharge patterns of primary spindle endings was ascertained by simultaneously recording spike trains from several Ia afferents and muscle tension fluctuations of the triceps-surae muscle. 1. Tension fluctuations were averaged with respect to spikes from primary endings yielding tension "trajectories" of specific shape for each spindle and probably reflecting frequently recurring mechanical events in the spindles' surroundings. 2. Spindles situated in close vicinity and influenced by similar mechanical events as evidenced by similar average tension trajectories are correlated in their discharge patterns to a degree depending on the strength of their mechanical coupling. 3. The modulation of spindle discharge frequency in response to average tension changes at the muscle tendon is very different in amplitude for different spindles; this response may show a high sensitivity. It is usually phase advanced by 90-180 degrees with respect to the "internal length" changes; between spindles ther may be phase differences of up to 180 degrees. 4. It is concluded that primary endings react very sensitively to local extrafusal events. The CNS receives much more accurate information about these events in the correlation of several Ia afferents than in the discharge of a single fibre.     

Cinematographic analysis of contractile events produced in intrafusal muscle fibres by stimulation of static and dynamic fusimotor axons.

1. Muscle spindles with an intact blood supply and uninterrupted connexions with ventral and dorsal spinal roots (Bessou & Pagés, 1967, 1972) have been prepared in cat's tenuissimus muscles with the aim of cinephotographically recording intrafusal movements induced by the stimulation of single static or dynamic gamma axons; the time cours of these movements and the morphological kind of activated intrafusal muscle fibres have been established. 2. Displacements of spindle guiding marks in the equatorial region elicited by stimulating single static gamma axons are 4-20 times greater in amplitude than the ones elicited by stimulating dynamic gamma axons at the same frequency. 3. The dynamic gamma axons induced a contraction only in nuclear bag fibres which, in addition, never received any static gamma innervation. The static gamma axons evoked contractions either in nuclear bag fibres alone, or in nuclear chain fibres alone, or in both types of intrafusal fibres. Two thirds of static gamma axons supplied nuclear bag fibres. For various reasons, one half only of static gamma axons innervating nuclear bag fibres could be shown to simultaneously innervate nuclear chain fibres. Consequently, about one third of static gamma axons supplied both nuclear bag fibres and nuclear chain fibres, but it is highly probable that this latter figure is an underestimate. One third of static gamma axons produced contraction in nuclear chain fibres only. In this work, the distribution of fusimotor axons has been established in only one muscle spindle of the cluster of muscle spindles that each fusimotor axon is generally innervating. 4. Generally speaking, a static gamma axon elicits contraction of several intrafusal fibres whereas a dynamic gamma axon innervates only one intrafusal fibre and frequently only one pole of the fibre. 5. One third of static gamma axons evoked contractions in nuclear chain fibres that seemed to involve the whole pole. The other static gamma axons and all dynamic gamma axons produced, in the intrafusal fibres that they supplied, one or several foci of localized contractions. 6. The nuclear chain fibres contract and relax faster than nuclear bag fibres. The contractions of nuclear bag fibres supplied by static gamma axons are stronger and faster than those of nuclear bag fibres innervated by dynamic gamma axons. Nearly all nuclear bag fibres innervated by static gamma axons, like the nuclear chain fibres, show transient contractions at each pulse of a stimulation at low frequency (2-20/sec). 7. The results are discussed taking into account the available anatomical and physiological data on the muscle spindle. Their consequences with regard to intrafusal working are briefly considered.     

A continuum mechanical model of mechanoreceptive afferent responses to indented spatial patterns

Information about the spatial structure of tactile stimuli is conveyed by slowly adapting type 1 (SA1) and rapidly adapting (RA) afferents innervating the skin. Here, we investigate how the spatial properties of the stimulus shape the afferent response. To that end, we present an analytical framework to characterize SA1 and RA responses to a wide variety of spatial patterns indented into the skin. This framework comprises a model of the tissue deformation produced by any three-dimensional indented spatial pattern, along with an expression that converts the deformation at the receptor site into a neural response. We evaluated 15 candidate variables for the relevant receptor deformation and found that physical quantities closely related to local membrane stretch were most predictive of the observed afferent responses. The main outcome of this study is an accurate working model of SA1 and RA afferent responses to indented spatial patterns.