INTRODUCTION

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USING A STANDARD THEOREM of mechanics, the Maxwell reciprocity theorem, Wilson and De Troyer (17, 18) have recently postulated that the potential change in airway opening pressure (Pao) produced by a muscle contracting alone against a closed airway is related to the mass (m) of the muscle, the maximal active muscle tension per unit cross section (), and the fractional change in muscle length (L/L) per unit volume increase of the relaxed chest wall (VL)_Rel, such that

(1)

where L is muscle length, VL is volume of the chest wall, and Rel is relaxation.

The validity of this conclusion has then been demonstrated experimentally for a number of canine inspiratory and expiratory muscles, including the parasternal intercostals (10, 13), the neck inspiratory muscles (12), and the triangularis sterni (9). Thus, for all these muscles, a close relationship was found between the change in airway pressure produced by unit muscle mass (Pao/m) during isolated, maximal contraction and the fractional change in muscle length during passive inflation. Furthermore, the slope of this relationship () was ~3.0 kg/cm², in close agreement with values of maximal active muscle tension measured in vitro (1, 11, 16). The major implication of these observations is that the maximal pressure-generating ability of any respiratory muscle contracting alone can be computed from two simple measurements, namely, the mass of the muscle and its fractional change in length during passive inflation.

However, the act of breathing involves a number of muscles contracting in concert, and the validity of Eq. 1 for coordinated activity of a number of muscles remains uncertain. The Maxwell reciprocity theorem and Eq. 1 are obtained by modeling the chest wall as a linear elastic system, and, in such a system, the resultant effect of different forces acting simultaneously is simply the sum of the effects of the individual forces. If the model is reasonably accurate, the effects of active forces in several muscles on Pao should therefore be additive. However, the chest wall is neither perfectly linear nor perfectly elastic. In addition, the force developed by a particular respiratory muscle depends on its length, its length depends on the configuration of the chest wall, and the chest wall configuration depends on the forces developed by other muscles. Thus, depending on the interactions between a particular muscle and the other muscles that contract at the same time, the pressure-generating ability of this muscle during coordinated muscle contraction might be different from its pressure-generating ability predicted by Eq. 1. The present study was therefore undertaken to evaluate the interactions between various sets of rib cage muscles in the generation of airway pressure.

	MATERIALS AND METHODS

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The experiments were performed in 13 adult mongrel dogs (15-35 kg) anesthetized with pentobarbital sodium (initial dose: 30 mg/kg iv). The animals were placed in the supine posture, intubated with a cuffed endotracheal tube, and connected to a mechanical ventilator (Harvard pump, Chicago, IL). The level of anesthesia was maintained so that the corneal reflex was abolished throughout. Two experimental protocols were followed.

Experiment 1. Eight animals were first studied to assess the interactions between 1) the parasternal intercostals in different interspaces; 2) the sternomastoids and the parasternal intercostals; 3) the scalenes and the parasternal intercostals; and 4) different segments of the triangularis sterni. In each animal, the mandible was firmly secured parallel to the floor, and the sternomastoids were exposed through a long midline incision in the neck. The cervical accessory nerve, which provides motor supply to the sternomastoid, was then isolated bilaterally at the deep aspect of the muscle about midway between the manubrium and the mastoid process (12), and a loose ligature was placed around it so that it could be easily identified later. In each animal, the rib cage was also exposed on both sides of the chest from the first through the tenth rib by deflection of the skin and underlying muscle layers, and the parasternal intercostals in two or three interspaces between the third and the seventh interspace were prepared for investigation by using the procedure previously described (8, 10). In each interspace, the ventral portion of the external intercostal muscle was thus severed bilaterally, and the internal intercostal nerve was isolated 1-2 cm lateral to the chondrocostal junction and sectioned. In four animals, rib cage exposure was made to keep the medial head of the scalenes (pars supracostalis) intact, and the motor nerve of the muscle (i.e., a superficial branch of the second internal intercostal nerve) was also isolated and sectioned near its points of emergence from the second external intercostal muscle (2).

Experiment 2. Five animals were then studied to examine the interaction between the interosseous intercostal muscles in different interspaces. In preliminary experiments, we used a procedure similar to that described in experiment 1. Thus, after denervation of the parasternal intercostals at the chondrocostal junction, we exposed the external or internal intercostal nerves in the dorsal portion of the intercostal spaces in the vicinity of the rib angle, and we stimulated the nerves to achieve isolated contraction of the external or internal interosseous intercostal muscles. However, exposure of the nerves was difficult and required that the animal's trunk be twisted toward the contralateral side. Muscle contraction, therefore, was induced on only one side of the chest. In addition, isolation of the external intercostal nerve was associated with significant muscle damage over ~2 cm ventral to the rib angle, i.e., the area in which the external intercostal muscle is thickest and has the greatest inspiratory mechanical advantage (17). The pressure changes thus recorded were small (<1 cmH₂O), and the interaction between these muscles could not be evaluated with confidence.

Data analysis. The Pao values obtained in each animal during nerve (experiment 1) or muscle (experiment 2) stimulation in any given condition were averaged over the three stimulations performed in that condition. To assess the mechanical interaction between two sets of muscles, the Pao obtained during stimulation of the first set alone was then added to the Pao measured during isolated stimulation of the second set; the value thus calculated will be referred to here as the predicted Pao. This value was finally compared with that measured during simultaneous contraction of the two sets of muscles. Statistical comparison between the predicted and measured Pao was made by using a t-test for paired observations; correlations between predicted and measured Pao values were also carried out for individual muscle combinations by standard linear regressions. The criterion for statistical significance was taken as P < 0.05.

	RESULTS

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Interaction between the parasternal intercostals. The effects on airway pressure of stimulating the parasternal intercostals in two interspaces separately and then simultaneously are shown for one representative animal in Fig. 1. In this example, stimulating the parasternal intercostals in the fourth interspace (A) produced a 4.50-cmH₂O fall in Pao. Stimulating the parasternal intercostals in the sixth interspace (B) also resulted in a fall in Pao; in agreement with our previous finding that in dogs the respiratory effect of these muscles is greatest in the third interspace and decreases gradually in the caudal direction (10), the fall in Pao, however, amounted to only 2.50 cmH₂O. Therefore, the predicted Pao for these two interspaces was 7.00 cmH₂O (dashed line in Fig.1C). The Pao measured during combined stimulation of these parasternal intercostals was, in fact, 6.25 cmH₂O.

View larger version (8K): [in this window] [in a new window]   Fig. 1.   Changes in airway opening pressure (Pao) during bilateral tetanic stimulation of internal intercostal nerve in 4th interspace alone (A), in 6th interspace alone (B), and in both 4th and 6th interspaces (C) in 1 representative animal. EMG activity recorded from parasternal intercostal muscles is also shown. Dashed line in C, Pao that would be obtained during simultaneous contraction of 2 muscles if their effects were perfectly additive.

3

View larger version (14K): [in this window] [in a new window]   Fig. 2.   Comparison between measured and predicted Pao for parasternal intercostals in 2 interspaces. Individual data were obtained in 8 animals (16 data pairs). Solid line, line of identity; dashed line, linear relationship (r = 0.979; slope = 0.90).

Interaction between the parasternal intercostals and the neck inspiratory muscles. Stimulating the sternomastoids or the scalenes and the parasternal intercostals in one interspace produced essentially similar results, as shown in Fig. 3. Thus the measured Pao was smaller than the predicted value in 13 of the 16 sternomastoids-parasternal intercostals pairs and in 6 of the 8 scalenes-parasternal intercostals pairs. The measured Pao was also closely related to the predicted Pao (r = 0.993; P < 0.001), and the slope of the linear relationship thus calculated for both muscle combinations was 0.87 (confidence interval = 0.002).

View larger version (15K): [in this window] [in a new window]   Fig. 3.   Comparison between measured and predicted Pao during stimulation of sternomastoid () or scalene () muscles and parasternal intercostal in 1 interspace. Individual data were obtained in 8 animals (24 data pairs). Lines are defined as in Fig. 2 (r = 0.993; slope = 0.87).

Interaction between segments of the triangularis sterni. Although the triangularis sterni caused a rise rather than a fall in Pao, the Pao measured during stimulation of two interspaces together was also slightly smaller than the sum of the Pao values generated individually (Fig. 4). The slope of the linear relationship (r = 0.992) calculated between the measured and predicted values for the triangularis sterni was 0.90 (confidence interval = 0.01).

View larger version (14K): [in this window] [in a new window]   Fig. 4.   Comparison between measured and predicted Pao for triangularis sterni in 2 interspaces. Individual data were obtained in 7 animals. Lines are defined as in Fig. 2 (r = 0.992; slope = 0.90).

Interaction between the interosseous intercostal muscles. A representative example of the Pao measured during stimulation of the external and internal interosseous intercostals in two contiguous interspaces separately and then simultaneously is shown in Fig. 5. Stimulating the interosseous intercostals in one interspace between the third and the sixth interspace always resulted in a fall in Pao, whereas stimulating these muscles in the seventh interspace caused little or no Pao; these results are consistent with the previous studies of Ninane et al. (15). Depending on the interspaces studied, therefore, the predicted Pao values ranged between 1.08 and 7.23 cmH₂O. However, the measured Pao values were very close to the predicted values, as shown in Fig. 6. The slope of the linear relationship thus calculated between these values was 1.14 (confidence interval = 0.02).

View larger version (5K): [in this window] [in a new window]   Fig. 5.   Pao during bilateral tetanic stimulation of interosseous intercostal muscles in 4th interspace alone (A), in 5th interspace alone (B), and in both interspaces (C) in 1 representative animal. Stim, stimulator. Dashed line is defined as in Fig. 1.

View larger version (13K): [in this window] [in a new window]   Fig. 6.   Comparison between measured and predicted Pao for interosseous intercostal muscles in contiguous interspaces. Individual data were obtained in 5 animals (10 data pairs). Lines are defined as in Fig. 2 (r = 0.993; slope = 1.14).

	DISCUSSION

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The Maxwell reciprocity theorem is valid for any linear elastic system. According to this model for the chest wall, the change in airway pressure produced by two muscles contracting simultaneously should therefore be equal to the sum of the changes in pressure produced by the muscles contracting individually (18). However, contraction of the parasternal intercostals in one interspace may have various effects on the length and, with it, the force exerted by the parasternal intercostals in another interspace. On one hand, when these muscles are activated in a single interspace, they probably shorten more than they do when the muscles in other interspaces are also activated. The Pao generated by the parasternal intercostals contracting simultaneously in two interspaces might therefore be greater than the sum of the Pao produced individually. On the other hand, contraction of the parasternal intercostals in a single interspace causes a caudal displacement of the sternum and a cranial displacement of the ribs situated caudally (5), such that the parasternal intercostals in the more caudal interspaces shorten passively (4). This change in length is qualitatively similar to that produced by a passive inflation of the chest wall above FRC, and this is known to elicit a marked reduction in the parasternal pressure-generating ability (14). In addition, contraction of the parasternal intercostals in a single interspace produces a local distortion from the natural displacement of the rib cage. The additional work done by the muscle to induce such a distortion might result in some pressure dissipation. Finally, previous experiments in dogs have shown that when weights are applied cranially on a pair of ribs at FRC, the relationship between force and rib displacement is linear but the relationship between force and airway pressure is commonly alinear, such that at high forces Pao induced by a given increase in force or a given rib displacement is smaller (17). When the parasternal intercostals in two interspaces contract simultaneously, the ribs may therefore operate on an alinear portion of the force-Pao relationship, and this would also make the resultant Pao smaller than the sum of the Pao produced individually.

Stimulating the parasternal intercostals in two interspaces simultaneously yielded a Pao that was usually smaller than the sum of the individual Pao values (Figs. 1 and 2). The loss of force because of the passive muscle shortening and/or the pressure losses related to the distortion of the rib cage and the alinearity of the respiratory system appeared, therefore, to predominate over the decreased active muscle shortening. However, the slope of the relationship between the measured and predicted airway pressure was 0.90, thus indicating that the average difference was only 10%. Similarly, the rise in airway pressure measured during contraction of the triangularis sterni in two interspaces was smaller than the predicted value, but the difference also amounted to only 10% (Fig. 4). Thus, even though maximal contraction of the parasternal intercostals and triangularis sterni in several interspaces is associated with some pressure loss, their effects on the lung are essentially additive.

Contraction of the neck inspiratory muscles might also have altered the pressure-generating ability of the parasternal intercostals. When the sternomastoids contract alone in dogs, they produce a marked cranial displacement of the sternum and a smaller cranial displacement of the ribs (6). In so doing, the muscles induce passive lengthening of the parasternal intercostals (4), which might lead to an increase in parasternal pressure-generating ability. Conversely, the primary action of the pars supracostalis of the scalenes is to pull the ribs cranially (6). It is likely, therefore, that contraction of these muscles causes passive shortening of the parasternal intercostals, such that their pressure-generating ability might be reduced. Furthermore, both the sternomastoids and the scalenes cause distortion of the rib cage (6), and the cranial rib displacement associated with their contraction could also make the parasternal intercostals operate on an alinear portion of the rib displacement-airway pressure relationship. Yet, when either the sternomastoids or the scalenes were maximally stimulated with the parasternal intercostals, here again the measured Pao was only 13% smaller than the sum of the Pao values produced by the two sets of muscles individually (Fig. 3). Therefore, as was the case for the parasternal intercostals and the triangularis sterni in several interspaces, there was no major complicating effect of length and force interdependence and no significant pressure loss.

A greater length (and force) interdependence might have been anticipated during contraction of the interosseous intercostal muscles in contiguous interspaces. Indeed, when the external intercostal, or the internal interosseous intercostal, or both intercostals in a single interspace are selectively stimulated at FRC, there is a cranial displacement of the rib making up the caudal boundary of the interspace and a caudal displacement of the rib making up the rostral boundary (7, 15). Consequently, when these muscles contract simultaneously in two contiguous segments, they have opposite effects on the rib in between; therefore, they might shorten less than they do when contracting in a single segment, and so the Pao might be greater than the sum of the individual Pao values. In fact, the differences between the measured and predicted airway pressure were observed to be very small (Figs. 5 and 6). This finding thus strengthens our conclusion that when several inspiratory or expiratory muscles of the rib cage contract together, the resultant effect on the lung is about equal to the sum of their individual effects.

These observations have two important implications. The first is that the validity of Eq. 1 is not restricted to isolated muscle contraction. Thus measurements of the fractional change in length of a particular muscle during passive inflation and measurements of its mass can also be used to estimate, to a good approximation, the potential pressure-generating ability of the muscle in the presence of coordinated muscle contraction. The second implication is that there is no significant synergism or antagonism among the rib cage muscles with respect to airway pressure. As a corollary, because all inspiratory intercostals have the same function of expanding the chest wall, no muscle has as its function to "stabilize" the rib cage. It is true that some muscles, such as the canine external intercostals in the third and fourth interspaces, may be electrically active during inspiration and yet remain constant in length (3). Such muscles do not perform any external work, but we postulate that they contribute to a fall in pleural pressure that adds to the pressure changes exerted by the other intercostal muscles.