INTRODUCTION

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ALTHOUGH THE ACTIONS of most respiratory muscles on the chest wall have been qualitatively described, the question of how much lung expansion (or deflation) each of these muscles can produce has not been answered. This is a difficult question because a number of muscles cannot be maximally activated in isolation, but recent theoretical studies by Wilson and De Troyer (16, 17) have proposed an indirect approach. Thus, by using a standard theorem of mechanics, the Maxwell reciprocity theorem, these investigators have 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-sectional area (), and the fractional change in muscle length per unit volume increase of the relaxed chest wall [L/(LVL)]_Rel, such that

(1)

Studies in anesthetized dogs have shown that the internal intercostal muscles of the parasternal region of the rib cage (the so-called parasternal intercostals), the sternomastoids, and the scalenes behave in agreement with this equation (3, 10, 11). Indeed, for these three sets of inspiratory muscles, Pao values obtained per unit muscle mass (Pao/m) during maximal stimulation were closely related to the fractional changes in muscle length during passive inflation, such that a greater fractional shortening was associated with a greater fall in Pao per gram of muscle mass. If this relationship could be extended to other muscles, in particular some expiratory muscles, then one would have strong evidence for estimating the respiratory effect of any particular muscle simply on the basis of its fractional change in length during passive inflation.

The present study was therefore undertaken to assess the extent to which Eq. 1 also applies to the canine triangularis sterni, a well-established expiratory muscle of the rib cage (4). We initially measured the change in length of this muscle during gradual, passive inflation of the chest wall in a group of anesthetized, paralyzed animals. As anticipated, passive inflation caused muscle lengthening, but the amount of lengthening, although variable among animals, was much larger than the shortening of the parasternal intercostals. To understand this large muscle lengthening and the variability among animals, we subsequently developed a geometric model of the ventral area of the rib cage and obtained a relationship between muscle lengthening and the angles describing the orientation of the muscle and costal cartilage. We then measured these angles in another animal group. Last, as a direct test of Eq. 1, we measured the pressure-generating ability of the muscle.

	METHODS

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Experiment 1. The relationship between lung volume and the length of the triangularis sterni muscle was examined in four adult mongrel dogs (15-29 kg). The animals were deeply anesthetized with pentobarbital sodium (initial dose = 30 mg/kg iv), placed in the supine posture, and intubated with a cuffed endotracheal tube, after which the parasternal region of the rib cage was exposed on the right side of the sternum from the first through the eighth interspaces. Two interspaces between the third and the sixth were studied in each animal. In each interspace, the triangularis sterni was exposed by sectioning the caudal insertion of the parasternal intercostal from the lateral border of the sternum to the chondrocostal junction. The orientation of the triangularis sterni fibers could therefore be carefully defined, and a pair of small screws was inserted into the sternum in the midline and into the lateral portion of the costal cartilage at the points of insertion of the muscle bundle. The animal was then paralyzed with an intravenous injection of 2 mg pancuronium and ventilated mechanically.

Model. Figure 1 shows a simple model of the geometry of the triangularis sterni; the model is similar to the one we have previously developed for the parasternal intercostals (3). Triangularis sterni muscle length L is related to the distance d along the costal cartilage between the sternum and the muscle attachment, the distance s along the sternum between the attachments of the muscle and cartilage, and the angle  between the sternum and the costal cartilage by the law of cosines

(2)

The values of d and s are constant with changes in lung volume. Therefore, if the values of L and  before and after a 1.0-liter passive inflation are denoted by subscripts 1 and 2, respectively

(3)

and the fractional change in muscle length, L/L₁ = L₂/L₁  1, is given by the following equation

(4)

If  denotes the angle between the sternum and the muscle fibers, simple trigonometric relationships yield the results d/L₁ = sin /sin ₁ and s/L₁ = sin (  ₁)/sin ₁. With these substitutions, Eq. 4 becomes

(5)

View larger version (17K): [in this window] [in a new window]   Fig. 1.   Model of geometry of triangularis sterni muscle. L, muscle length;  and , angles between sternum and costal cartilage and between sternum and muscle fibers, respectively; 1 and 2, L and angle  before and after a 1.0-liter passive inflation, respectively; s, distance along sternum between attachments of muscle fibers and cartilage; d, distance along cartilage between sternum and muscle attachment. With cartilage rotation, d and s remain constant.

Experiment 2. Nine adult mongrel dogs (15-22 kg) were subsequently studied to identify the factors responsible for the amount and variability of muscle lengthening observed in experiment 1 and to assess the muscle's pressure-generating ability. As in experiment 1, the animals were deeply anesthetized with pentobarbital sodium (30 mg/kg iv), placed in the supine posture, and intubated with a cuffed endotracheal tube, and the rib cage and intercostal muscles in the parasternal area were exposed on both sides of the chest from the first through the eighth interspaces. The triangularis sterni in this study was investigated in one interspace between the third and the sixth in six animals and in both the third and the sixth interspaces in three animals. For the 9 animals, a total of 12 interspaces were thus studied. All measurements were obtained while the animals were made apneic by mechanical hyperventilation.

Data analysis. The length of each muscle bundle at each lung volume was averaged over the three measurements that were performed. The angles describing the orientation of the muscle fibers and costal cartilage relative to the sternum and Pao obtained during nerve stimulation were also averaged over the three measurements. To allow comparison among the different animals, the changes in muscle length induced by passive inflation (deflation) were subsequently expressed as percent changes relative to the muscle length at FRC, and Pao values were divided by muscle mass to yield specific Pao (spec Pao). Data were finally averaged for the animal group, and the values are presented as means ± SE. Statistical comparison between Pao measured at the different lung volumes was made by analysis of variance with repeated measures and Student-Newman-Keuls tests. The criterion for statistical significance was taken as P < 0.05.

	RESULTS

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Relationship between lung volume and muscle length (experiment 1). The triangularis sterni lengthened with passive inflation above FRC and shortened with passive deflation below FRC in the four animals (8 interspaces) studied. As shown in Fig. 2, the relationship thus obtained between lung volume and muscle length was curvilinear, such that, for a given volume change, the amount of muscle shortening associated with deflation was about one-half the amount of lengthening caused by inflation. Above FRC, however, even though the amount of muscle lengthening induced by a given increase in volume also decreased at high lung volumes, the relationship was virtually linear; on average, the departure from linearity was only 10-15%.

View larger version (13K): [in this window] [in a new window]   Fig. 2.   Relationship between lung volume and changes in triangularis sterni L (L) during passive inflation. Values are means ± SE of 8 interspaces in 4 animals. L is expressed as %changes relative to L at relaxed end expiration (functional residual capacity; %LFRC); positive values indicate muscle lengthening, and negative values indicate muscle shortening.

Muscle and cartilage orientation (experiment 2). The changes in triangularis sterni muscle length during passive inflation in the 9 animals (12 interspaces) studied were similar in all respects to those observed in experiment 1. With a 1.0-liter inflation, the amount of muscle lengthening thus averaged 17.9 ± 1.6% of the muscle length at FRC but varied from 5.7 to 25.3%. These extreme values were obtained in two animals with the same body mass, thus confirming that animal size was not the primary determinant of this variability.

View larger version (11K): [in this window] [in a new window]   Fig. 3.   Comparison between measured and calculated values of fractional change in triangularis sterni L during a 1.0-liter passive inflation (L/L1). Individual data from 12 interspaces in 9 animals are shown. Solid line, line of identity. Calculated values were obtained by substituting angles , 1, and 2 in Eq. 5.

Pressure-generating ability (experiment 2). The Pao values recorded during maximal, tetanic stimulation of the triangularis sterni at different lung volumes are shown for one representative animal in Fig. 4. In this example, the rise in Pao generated at FRC was 0.54 cmH₂O. However, when lung (chest wall) volume was increased by 0.5 liter above FRC, the rise in Pao caused by the same stimulation amounted to 1.49 cmH₂O. Increasing lung volume by an additional 0.5 liter accentuated this effect such that the rise in Pao was 2.02 cmH₂O.

View larger version (7K): [in this window] [in a new window]   Fig. 4.   Changes in airway opening pressure (Pao) recorded during bilateral, tetanic stimulation of triangularis sterni in 3rd interspace in a representative animal. EMG activity recorded from muscle is also shown. Stimulation at FRC resulted in a small rise in Pao. However, rise in Pao increased substantially when lung volume was passively increased by 0.5 and 1.0 liter above FRC. Small, gradual decline in baseline pressure at these 2 lung volumes results from stress relaxation of respiratory system (12, 14).

View larger version (11K): [in this window] [in a new window]   Fig. 5.   Effect of lung volume on Pao produced by tetanic, supramaximal stimulation of triangularis sterni in 1 intercostal space. Values are means ± SE of 12 interspaces in 9 animals.

View larger version (10K): [in this window] [in a new window]   Fig. 6.   Relationship between fractional L of triangularis sterni and Pao per unit muscle mass (spec Pao). Individual data from 12 interspaces in 9 animals are shown. Dashed line, linear relationship (r = 0.88). Fractional L values were measured during a 1.0-liter passive inflation and are expressed as %LFRC, and values of spec Pao are expressed as cmH2O/g muscle mass.

	DISCUSSION

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The triangularis sterni in dogs and cats is invariably active during the expiratory phase of the breathing cycle, and this contraction pulls the ribs caudally to deflate the rib cage compartment of the chest wall (4, 9, 13). Therefore, one would anticipate that this muscle would lengthen during inflation of the relaxed chest wall, and indeed passive inflation caused lengthening of the triangularis sterni in all animals. Our study of the geometry of the rib cage in individual animals (Fig. 3) also indicated that this change in muscle length is determined by three factors, namely, the orientations of the muscle fibers and costal cartilage relative to the sternum and the rotation of the cartilage during inflation.

We have previously shown that these three factors also determine the changes in length of the parasternal intercostals (3). However, whereas the canine parasternal intercostals shorten by 5-10% with a 1.0-liter passive inflation (3), the triangularis sterni for the same inflation lengthened, on average, by 17.9%. The mechanism of this difference in magnitude is illustrated in Fig. 7. In this figure, the fractional changes in muscle length during passive inflation, calculated from Eq. 5 for the average values of angle ₁ (54°) and angle ₂ (65°) measured in the present study , are plotted as a function of angle  (). According to Eq. 5, the values of L/L₁ are negative for angle  < angle ₁ and positive for angle  > angle ₁. Therefore, all muscle fibers with angle  < 54° shorten during passive inflation, and all muscle fibers with angle  > 54° lengthen. However, the curve is clearly asymmetric, such that the potential maximum shortening is only 6%, whereas the potential maximum lengthening amounts to 18%. These values are similar to the parasternal shortening measured in our previous studies (3) and to the triangularis sterni lengthening measured in this study, respectively, which indicates that the orientations of both the parasternals and the triangularis sterni in dogs are close to the orientations for maximum length changes. On the other hand, if the costal cartilage extended out from the sternum at a right angle (angle ₁ = 90°), then the curve () would be antisymmetric about  = 90°, and the magnitudes of maximum shortening and lengthening would be equal. In other words, the lengthening of the canine triangularis sterni during passive inflation is two to three times greater than the shortening of the parasternal intercostals because, in dogs, the costal cartilages slope downward from the sternum.

View larger version (15K): [in this window] [in a new window]   Fig. 7.   Relationship between L/L1 and angle . , Curve calculated from Eq. 5 for measured mean values of angles 1 (54°) and 2 (65°); , curve calculated for angle 1 = 90° and a similar cartilage rotation (angle 2 = 101°). Because costal cartilage in dogs slopes downward from sternum, potential lengthening of a muscle that attaches to cartilage from below (triangularis sterni) is larger than potential shortening of a muscle that attaches to cartilage from above (parasternal intercostals). On the other hand, if cartilage met sternum at a right angle (angle 1 = 90°), potential muscle lengthening and shortening would be about equal. Measured values of angle  for canine parasternal intercostals (26°; Ref. 3) and triangularis sterni (126°) are also shown (arrowheads).

Previous studies have shown that in supine dogs the length of the triangularis sterni at FRC corresponds to ~75% of the muscle's in vitro optimal length (L_o) (8). In view of the large increase in muscle length during passive inflation, one would therefore expect that an increase in lung volume would displace the muscle toward L_o and, hence, would induce a gradual increase in the muscle's pressure-generating ability. As shown in Figs. 4 and 5, this is exactly what we observed. With a 1.0-liter passive inflation, the muscle lengthened, on average, by 18% of its FRC length. Consequently, at this lung volume, the muscle was at 0.75 × 1.18 or 90% of L_o. However, we measured muscle length as the linear distance between two screws implanted in the costal cartilage and the sternum. These measurements, therefore, encompassed a portion of cartilage and the tendinous attachments of the muscle to the sternum. These attachments are 5-10 mm in length. As a result, our values of L₁ were greater than the actual muscle length, and our measured values of L/L₁ underestimated the fractional muscle lengthening by 10-15%. Thus, when lung volume was increased by 1.0 liter above FRC, the triangularis sterni was very close to its L_o. Presumably, therefore, its pressure-generating ability was then maximal or near maximal.

Our previous theoretical studies have led to the prediction, summarized in Eq. 1, that the maximal Pao produced by a given respiratory muscle per unit muscle mass (i.e., spec Pao) is equal to the product of the fractional change in length of the muscle during a 1.0-liter passive inflation and  (16, 17). In agreement with this prediction, we have previously shown that the spec Pao values for the parasternal intercostals, the sternomastoids, and the scalenes in dogs are proportional to the fractional changes in muscle length during passive inflation (3, 10). Furthermore, the coefficient of proportionality () between spec Pao and the fractional change in length for these three sets of inspiratory muscles was ~3.0, and this provided further evidence in support of Eq. 1; indeed, when measured in vitro, maximal active tension in both limb and respiratory muscles is 2.2-3.5 kg/cm² (1, 6, 15). Similarly, spec Pao for the triangularis sterni in the different animals of this study was closely related to the fractional muscle lengthening during passive inflation (Fig. 6), and when the data obtained for this muscle in the animal group were averaged and plotted together with the data previously obtained for the parasternal intercostals and the neck inspiratory muscles (3, 10), it appeared that a line with a slope of 3.0 fits all data remarkably well (Fig. 8).

View larger version (13K): [in this window] [in a new window]   Fig. 8.   Relationship between the fractional L of different respiratory muscles and spec Pao. Values are ± SE. , Data previously obtained for parasternal intercostals (PS) in 3rd, 5th, and 7th interspaces (3) and for sternomastoids (Stm) and scalenes (Scal) (10); , data obtained for triangularis sterni (TS) at 1.0 liter above FRC. Units of measure for L and spec Pao are as described in Fig. 6. Solid line, linear relationship between L and spec Pao (slope = 3.0).

The observation that the coefficient of proportionality between spec Pao and the change in muscle length is 3.0 (i.e., similar to the values of maximal muscle tension measured during isometric contractions in vitro) for both the parasternal intercostals and the triangularis sterni is somewhat surprising. To induce a fall in Pao, the contracting parasternal intercostals require that the ribs be displaced cranially. There is, therefore, a shortening of the muscles. In supine dogs, however, the length of these muscles at FRC is ~115% of L_o (7, 8). As a result, during a maximal stimulation at FRC, the canine parasternal intercostals should still operate on the most advantageous portion of their length-tension relationship such that the force developed should be close to the optimal force generated during isometric contractions in vitro. Although the changes in triangularis muscle length during stimulation were not measured in the present studies, the observed rise in Pao also implies a significant (caudal) displacement of the ribs and a significant muscle shortening. However, as previously emphasized, a 1.0-liter passive inflation places this muscle in the immediate vicinity of L_o, rather than beyond it. A maximal stimulation of the triangularis sterni at this lung volume should therefore have displaced the muscle to a less advantageous portion of its length-tension relationship, leading to a reduction in . Our failure to detect such a reduction suggests that when the rib cage muscles contract, the loss of force due to muscle shortening plays a relatively small role in the translation of muscle tension into rib displacement and Pao.

Although this issue requires further study, the present findings have three important conclusions and implications. First, for a machine, such as a lever, "mechanical advantage" is the ratio of the force delivered at the load to the force applied at the handle, and by analogy, we have previously defined the mechanical advantage of a respiratory muscle as Pao/m (17). On the basis of the present findings, we therefore conclude that the expiratory mechanical advantage of the triangularis sterni in dogs is substantially greater than the inspiratory mechanical advantage of the parasternal intercostals. Second, because this difference results from the downward orientation of the canine costal cartilages, we speculate that in humans, in whom the costal cartilages are nearly perpendicular to the sternum, the mechanical advantage of the triangularis sterni is almost similar to the mechanical advantage of the parasternal intercostals (Fig. 7). Finally, the findings summarized in Fig. 8 establish that there is a unique relationship between the spec Pao values of the respiratory muscles, both inspiratory and expiratory, and their fractional changes in length during passive inflation. As a corollary, the spec Pao of a particular muscle can be estimated simply by measuring its fractional change in length during passive inflation. If the mass of the muscle is also measured, then the Pao that the muscle would produce during a maximal contraction at L_o can be computed. With this procedure, one could therefore assess the actions of muscles with respiratory effects that cannot be studied directly, such as the respiratory muscles in humans.