Tracheal slowly adapting stretch receptors: Theoretical models

.I. theor. Biol. (1980) 83,3 13-320

Tracheal Slowly Adapting Stretch Receptors: Theoretical Models J.P. MORTOLA Department

of Physiology, McGill University, 3655 Drummond Street, Montreal, Quebec, Canada AND S. A. MORTOLA

Department

of Mathematics,

University of Minnesota, MN, U.S.A.

(Received

Minneapolis,

10 October 1979)

Experimental findings indicate that the response of pulmonary stretch receptors (PSR) is better related to the circumferential tension developed in the airways than to transpulmonary pressure or lung volume. Whether the absolute value in tension and its rate of change (T + dT/dt) or only the variation in tension (dT/dt) should be considered the most appropriate stimulus for PSR is here discussed. Some experimental findings seem to

imply that the former is more appropriate, since the receptor seems to have a “static” response. However, if the PSR’s response were alinearly related to the stimulus, as some experimental results indicate, it is possible to conceive a model where the PSR’s activity is only determined by dT/dt. This would also imply that the so called “static” response is actually a dynamic one since dT/dt is greater than zero.

1. Introduction Two groups of receptors with myelinated fibers are classically described in the airways, the slowly adapting stretch receptors (SR) and the rapidly adapting irritant receptors (IR) (Widdicombe, 1964). The stimulus appropriate for their activation is not well established. In fact, though many physiological studies have provided information on their gross localization in the airways (Widdicombe, 1954; Miserocchi, Mortola & Sant’Ambrogio, 1973; Mortola, Sant’Ambrogio & Clement, 1975; Bartlett, etal., 1976a; Sant’Ambrogio, et al., 1978), the fine structure of the airways receptors unknown.

and their relation to the tissues in which they are embedded is Furthermore, lack of precise information on the intrinsic proper-

ties of the airways receptors makes the study of the mechanisms responsible for their adapting properties very arduous. 313

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It is of interest to note that the mechanisms determining the adaptation of a sensory ending to a suddenly applied mechanical stimulus are probably very similar to those which cause the receptor to be sensitive to the velocity of application of the stimulus (Pringle & Wilson, 1952; Partridge & Glasser, 1960), such that the two phenomena may be looked on “as facets of the same thing” (Matthews, 1964). In the case of the muscle spindles, many arguments are in favor of a mechanical origin for the dynamic response of the primary ending (Matthews, 1964; Houk, Cornew & Stark, 1966). Similarly, the viscoelastic properties of the muscle are important in the response of the Golgi tendon organs (Houk, 1967). The rapidly adapting behavior of the Pacinian corpuscle has been shown to be driven by its mechanical properties (Hubbard, 1958). In frog skin, Lowenstein (1956) showed that rapidly adapting receptors become slowly adapting when the skin was stretched, and he suggested that the adaptation was most likely dependent on mechanical factors. These analogies, the strong link between SR behavior and mechanical properties of the airways (Sant’Ambrogio 8 Mortola, 1977; Mortola & Sant’Ambrogio, 1979) and the fact that the tracheal SR are uniquely located in the trachealis muscle (Bartlett et al., 1976~) while IR are placed all over the tracheal circumference (Sant’Ambrogio et al., 1978) suggests that a mechanical origin could be an important factor in determining the behavior of the airways receptors, as appears to be the case of other more successfully studied mechanoreceptors. In this study, we try to approach the problem of the appropriate stimulus of the SR on the basis of the experimental findings available in the literature and theoretical considerations. 2. Airways Slowly Adapting

Receptors: the “Appropriate”

Stimulus

In the first studies of airways receptors, it was shown that the SR activity increases with the lung volume (Adrian, 1933; Knowlton & Larrabee, 1946). Davis, Fowler & Lambert (1956) showed that the SR response had a better correlation with transpulmonary pressure than with lung volume. Other following studies supported this idea (Taglietti & Casella, 1966; Miserocchi & Sant’Ambrogio, 1974; Herzynski & Karczewski, 1975; Bartlett, Sant’Ambrogio & Wise, 19766). Bartlett et al. (1976a) separated the effects of the transmural pressure (PTM) from those of the circumferential tension on the receptor’s discharge. In an isolated in situ water filled trachea, they applied a small negative Pm and then stimulated the trachealis smooth muscle. This isometric contraction determined a further

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reduction in PTM but an increase in receptor discharge showing that in static conditions the receptor response is better related to circumferential tension than to transmural pressure. In dynamic conditions, however, the tension per se cannot be the appropriate stimulus of the airway mechanoreceptors. In fact, at any given PTM the volume of the airways and hence their radius of curvature is lower during inflation than during deflation (Martin & Proctor, 1958), hence at any given PrM also the cicumferential tension is lower during inflation than during deflation. In dynamic conditions the receptor activity leads PTM (Widdicombe, 1954; Bartlett et al., 19766) and therefore it is expected to lead tension also. This appears from the records presented by Bradley & Scheurmier (1977) in which transversal tension and receptor activity are simultaneously recorded during transverse stretch of the trachealis muscle in vitro. It is therefore evident that the SR have a dynamic response which, similarly to other mechanoreceptors (Matthews, 1964), appears to be related to the velocity of application of the stimulus. Whether the tension and its first derivative T + (d T/dt) or simply the variation of the stimulus dT/dt might explain the SR behavior is the object of the following analysis. 3. Theoretical

Models

In Fig. 1 at the left, is a schematic representation of a change in tension (T), its first derivative (dT/dt) = T’ and the sum of the two (T + T’) when the muscular tissue is elongated as indicated in (a) and (b). In the panels at the right the smooth muscle is pictured as a model composed of a viscous component represented by a dashpot and an elastic component represented by a spring, arranged in parallel (schema at the top). In the other schemas from top to bottom, the location where a stretch receptor (SR) should be functionally positioned in order to sense only T, T’ or T+ T’ is shown. We will consider first the case in which the receptor’s activity is linearly related to the stimulus. If SR is in series with an elastic element (case l), its activity will be proportional to the displacement, and independent of the rate of the stimulus; a pure static response will be obtained. If SR is arranged in series with pure viscous elements (case 2) the response of the receptor will be proportional to the speed of elongation and no activity will be present in static condition, therefore a purely dynamic response will be obtained. In case 3, where SR is sensing both the static and dynamic components, no adaptation will occur once the elongation stops. In experiments where the lung is inflated at different rates and then maintained inflated (Adrian, 1933; Knowlton & Larrabee, 1946;

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Sf?

-

c2 L

T’

SR

2

3

f‘ Time

FIG. 1. Schematic representation of the variation in tension (I’), its rate of change IdT/drl = T’ and the sum of the two (T + T’) for a stretch applied at two different rates to a viscoelastic model, as indicated in (a) and in (b). The model is composed by elastic elements (spring) and viscous elements (dashpot). SR indicates the location where a stretch receptor should be functionally positioned in order to sense only T(l), T’(2) or T+ T’(3). If the receptor’s activity were linearly related to the stimulus, in the first case its response would be only “static”, in the second only “dynamic”, in the third, both “static” and “dynamic.”

Widdicombe, 1954; Davis &al., 1956), the SR response seems to mimic the behavior described in the case 3 of Fig. 1. However, once the volume is maintained, differently to what the model implies, the SR activity does show an adaptation, the magnitude of which is probably dependent on the experimental conditions. As previously mentioned, the lung volume does not uniquely reflect the stimulus at the receptor’s level; in experiments in vitro, it was found (Bradley & Scheurmier, 1977) that a square wave increase in tension produces a rapid increase in SR activity which then declines even if the tension is maintained, and vice versa, a sudden reduction in tension is usually associated with cessation of discharge. Miserocchi & Sant’Ambrogio (1974), by measuring the quasi static response of SR to transpulmonary pressure, found mainly two kinds of behavior. One group of receptors sharply increased its activity at low pressures and then the response progressively decreased until a plateau was reached. The receptors of the second group increased their activity in an almost linear fashion up to 30 cm Hz0 of transpulmonary pressure. Since

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most of these latter receptors were placed in the intrapulmonary airways, where the radius of curvature increases with lung volume (Hyatt & Flath, 1966), it is likely that all the SR would have shown a progressively smaller increase in activity if, instead of transpulmonary pressure, circumferential tension was considered. More recently, it has been shown that the activity of tracheal stretch receptors reaches a plateau when the trachealis muscle where they are located is transversally stretched (Mortola & Sant’Ambrogio, 1979). Due to the characteristics of the tension-length relationship of the trachealis muscle (Mortola & Sant’Ambrogio, 1979), the quasi static response of the SR to tension should be an alinear one, with a concavity toward the tension axis. We will now consider the adaptation of a SR to a maintained stretch when its response is alinearly related to the stimulus in the way that the experimental data mentioned above seem to suggest. 4. Alinear Response of the Receptor to the Variation

in Tension

After the stretching of a smooth muscle, the tension (T) does not stay constant, but decreases toward a static value according to an exponential decay (Remington, 1957). For t > to, where to is the time at which the tension begins to decay according to an exponential function, this can be described by T(t) = e-’ + T,, where T,, represents the static value of tension for that elongation. T’ = (dT/dtl, it follows that T’(t) = e-‘.

Since (1)

This is graphically represented in the panel at the right of Fig. 2. The response of a receptor (SR,) which is linearly related to T’ [Fig. 2(a)] and that of a receptor (SR,) which is alinearly related to T’ [Fig. 2(a)] are described by SRI (T’) = KT

(2)

SR2 (T’) = K( T’)’

(3)

and

where a is between 0 and 1, and K is a proportionality constant. In order to have SRI and SR2 at different times, we substitute (1) in (2) and obtain SRI (t) = K e-’

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Jp

Time

FIG. 2. (a) Relationship between receptor’s activity (ordinate) and variation in tension ldT/drl = T' (abscissa) in the case of linear (SR,) and alinear (SR,) response to T’. (b) Schematic representation of the decay in tension (T) and of its first derivative (dT/dr = T’) to a maintained elongation, in a viscous elastic model as that represented in Fig. 1. At the bottom the theoretical decay in activity of the two receptors (SRI and SR2) described in the panel at the left is shown. At any given time SR2 will fire more than SRI and will approach zero activity later than SRI.

and substituting

(1) in (3) we obtain SR2 (t) = K eC .

Since a is between 0 and 1, K ear c K e’, and therefore hence at any time t > to: SR;? > SRI

K eear > K e-‘;

as graphically visualized in Fig. 2(b). It is also apparent that the lower the a the greater the SRz/SR1 ratio, and that SRI will approach zero faster than SR2; in fact, at any time t, SR1/SR2 = eCnV1)‘,and this tends to zero. The constant K in (2) and in (3) is assumed to be the same for simplicity. If the two constants were different it would not be true that, for t > to, k eea’> k’ eeL, but it would still be true that, for t > tl, SR1/SR2 = klk’ e’“-“I. t can be calculated from k e-’ < k’ eda*, k/k’ < e(‘-‘)‘; (1 - a)t > logklk’therefore t>tl=(l/l-a)logk/k’. 5. Conclusion The transduction properties of the slowly adapting stretch receptors will remain an obscure aspect of the airway receptor’s physiology until their morphology and relations with the smooth muscle is elucidated.

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Experimental data support the idea of a “dynamic” and “static” component in the activity of the stretch receptors. Most of the experiments however, consider the response of the receptor to changes in lung volume or transpulmonary pressure, which are not always reflecting the variations in tension at the receptor’s location. Furthermore, the “static” activity in most of the cases is measured a few seconds after the application of the stimulus when the dynamic properties of both the receptor and the smooth muscle are very likely still operating. In conclusion, the so called “static” response of stretch receptors does not seem necessarily to imply that the receptor has to sense the absolute value of tension T. The characteristic nature of the breathing act, with oscillations between inspiration and expiration, should imply two periods of constant tension (i.e. dT/dt = 0), in each respiratory cycle, which should stop the receptor’s firing (even if this does not have to be exactly at zero airflow). In some cases, however, the receptors do not cease completely their activity. This can be explained considering that, on one side, the periods of constant tension during breathing are probably very short, and, on the other side, if the response of the receptors to dT/dt is similar to that proposed in Fig. 2(b) (dotted line) it would be sufficient a very small variation in tension for maintaining the receptor’s firing. If the appropriate stimulus of pulmonary stretch receptors were indeed dT/dz, then their “slowly adapting properties” can be interpreted as the effect of the mechanical properties of the tissue in which they are located. Since the rapidly adapting properties of the other group of airway receptors (the so called “rapidly adapting irritant receptors”) are currently attributed to their ability to sense only dT/df, it would follow that the two main groups of airways receptors behave similarly as far as the appropriate stimulus is concerned, both sensing dT/dt. The very different adapting properties of “stretch receptors” and “irritant receptors” could therefore be due not to differences in intrinsic transduction properties but more likely to differences in the mechanical properties of the tissues in which they are located. Supported by the MRC of Canada. REFERENCES ADRIAN, E. D. (1933). J. Physiol., Lond. 79, 332. BARTLETT, D. JR., JEFFREY, P., SANT'AMBROGIO, Physiob,

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