Effects of inflation on the coupling between the ribs and the lung in dogs

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1 J Physiol pp Effects of inflation on the coupling between the ribs and the lung in dogs AndréDeTroyer 1,2 and Dimitri Leduc 1,3 1 Laboratory of Cardiorespiratory Physiology, Brussels School of Medicine, 1070 Brussels, Belgium 2 Chest Service, Erasme University Hospital, 1070 Brussels, Belgium 3 Intensive Care Unit, Saint-Pierre University Hospital, 1000 Brussels, Belgium The coupling between the ribs and the lung in dogs increases with increasing rib number in the cranial part of the rib cage and then decreases markedly in the caudal part. The hypothesis was raised that this non-uniformity is primarily related to differences between the areas of the lung subtended by the different ribs, and in the current study we tested this idea by assessing the effects of passive lung inflation. Thus, by causing a descent of the diaphragm, inflation would expand the area of the lung subtended by the caudal ribs and improve the coupling between these ribs and the lung. The axial displacements of the ribs and the changes in airway opening pressure ( P ao ) were measured in anaesthetized, pancuronium-treated, supine dogs while loads were applied in the cranial direction to individual rib pairs at functional residual capacity (FRC) and after passive inflation to 10 and 20 cmh 2 O transrespiratory pressure. In agreement with the hypothesis, inflation caused an increase in P ao for ribs 9 and 10. The most prominent alteration, however, was a marked decrease in P ao for ribs 2 8; at 20 cmh 2 O, P ao for these ribs was only 30% of the value at FRC. Additional measurements indicated that this decrease in P ao results partly from the increase in diaphragmatic compliance but mostly from the reduction in outward rib displacement. This alteration in the pattern of rib motion should add to the decrease in muscle length to reduce the lung expanding action of the external intercostal muscles at high lung volumes. (Received 21 October 2003; accepted after revision 15 December 2003; first published online 23 December 2003) Corresponding author A. De Troyer: Chest Service, Erasme University Hospital, Route de Lennik, 808, 1070 Brussels, Belgium. a detroyer@yahoo.fr The actions of the external and internal interosseous intercostal muscles have long been regarded according to the theory proposed 250 years ago by Hamberger (1749). This theory, based on the orientation of the muscle fibres and a two-dimensional model of the rib cage, predicts that the external intercostals throughout the rib cage raise the ribs and inflate the lung when they contract, and that the internal interosseous intercostals lower the ribs and deflate the lung. However, measurements of the changes in muscle length in dogs have indicated that the actions of these muscles on the lung vary markedly depending on their location along the rostrocaudal axis of the rib cage (De Troyer et al. 1999). Thus, the external intercostals in the rostral interspaces have a large inspiratory effect, and the internal interosseous intercostals in the rostral interspaces have a small inspiratory, rather than expiratory, effect. Conversely, both the external and the internal intercostals in the caudal interspaces have large expiratory effects. To assess the mechanism of this rostrocaudal gradient, we recently investigated the coupling between the different ribs and the lung by applying external loads to individual rib pairs in supine animals (De Troyer & Wilson, 2002). The rib displacement induced by a given load increased gradually with increasing rib number. However, the change in airway opening pressure ( P ao ) increased from the second to the fifth rib pair and then decreased markedly from the fifth to the eleventh rib pair. It was concluded therefore that the coupling between the ribs and the lung does vary from the top to the base of the rib cage, and it was further concluded that this coupling is indeed a primary determinant of the actions of intercostal muscles on the lung. Specifically, the coupling confers to both the external and the internal intercostal muscles an inspiratory action on the lung in the rostral interspaces and an expiratory action in the caudal interspaces. The mechanism of the non-uniform coupling between the ribs and the lung is uncertain, but the speculation was DOI: /jphysiol

2 482 A. De Troyer and D. Leduc J Physiol pp offered that the effect of a particular rib on the lung is directly related to the area of the lung subtended by the rib (De Troyer & Wilson, 2002). In the dog, the radii of the ribs in the rostral half of the rib cage increase gradually with increasing rib number (Margulies et al. 1989). In this half of the rib cage, therefore, the area of the lung subtended by a particular rib should be greater than that subtended by the rib above, so the fall in P ao produced by a cranial displacement of that rib would also be greater. On the other hand, the ribs in the caudal half of the rib cage are in part apposed through the diaphragm to the abdomen, rather than the lung (Mead, 1979). Consequently, a cranial displacement of these ribs should primarily result in an expansion of the ventral abdominal wall and a fall in abdominal pressure, and the fall in P ao would be only secondary, due to the (passive) caudal displacement of the diaphragm (De Troyer & Wilson, 2002). The fall in P ao produced by a given cranial displacement of the most caudal ribs, therefore, would be smaller than the fall in abdominal pressure and smaller than the fall in P ao produced by the same cranial displacement of more cranial ribs. In the present studies, we have tested these ideas by assessing the changes in both P ao and abdominal pressure during rib loading and by evaluating the effect of lung volume on the rib lung coupling. Thus, the zone of apposition of the diaphragm to the rib cage decreases when lung volume is passively increased above functional residual capacity (Mead, 1979). With inflation, therefore, the area of the lung subtended by the caudal ribs should increase, so it would be expected that the coupling between these ribs and the lung would be improved. Methods The studies were carried out on seven adult cross-breed dogs (11 18 kg), as approved by the Animal Ethics and Welfare Committee of the Brussels School of Medicine. The animals were anaesthetized with pentobarbitone sodium (initial dose, 30 mg kg 1 i.v.), placed in the supine posture, and intubated with a cuffed endotracheal tube. A venous cannula was inserted in the forelimb to give maintenance doses of anaesthetic (3 5 mgkg 1 h 1 i.v.) and a catheter was inserted in the right femoral artery to monitor blood pressure and heart rate, after which the rib cage and intercostal muscles were exposed on both sides of the chest from the first to the twelfth rib by reflection of the skin and the superficial muscle layers. Hooks were then screwed into the second right and left bony ribs, 1 cm lateral to the costochondral junctions. A long inextensible thread was attached to each hook and led cranially, parallel to the longitudinal body axis of the animal, over a pulley placed at the head of the table, and it was connected to a small basket in which weights could be placed later. An additional hook was screwed into the second right rib in the mid-axillary line and connected to a linear displacement transducer (Schaevitz Eng., Pennsauken, NJ, USA) to measure the craniocaudal (axial) rib displacement (De Troyer & Kelly, 1982), and a differential pressure transducer (Validyne Corp., Northridge, CA, USA) was connected to a side port of the endotracheal tube to measure airway opening pressure (P ao ). Fifteen minutes after instrumentation, the animal was injected with a neuromuscular blocking agent (2 mg pancuronium i.v.) and ventilated mechanically. After calibration of the displacement transducer, the ventilation was stopped and the chest wall was allowed to relax to equilibrium. The endotracheal tube was occluded, and 200 g lead balls were placed in both baskets attached to the second rib so that the load in each basket was increased by 0.2 kg increments from 0.2 to 0.6 kg. Two runs of loading were performed, after which a large syringe was connected to the endotracheal tube and the animal was inflated to a lung volume corresponding to a transrespiratory pressure of 10 cmh 2 O. Two runs of rib loading were also performed at this volume. The animal was finally inflated to a transrespiratory pressure of 20 cmh 2 O, and two runs of loading were also performed. The hookbasket system and the displacement transducer were then transferred to the third rib pair, and two runs of loading were obtained at 0, 10 and 20 cmh 2 O transrespiratory pressure. The procedure was repeated for every individual rib pair down to the eleventh pair. These measurements indicated that the coupling between the ribs and the lung is indeed markedly altered by inflation (see Results). After the initial procedure was completed, two additional protocols were therefore followed. (1) We first assessed the effect of rib loading on abdominal pressure (P ab ) and examined the potential role of diaphragmatic compliance in determining the alteration in rib lung coupling with inflation. In each animal, the abdomen was thus opened by a midline incision from the xiphisternum to the umbilicus, and a balloon-catheter system was positioned between the liver and the stomach to measure P ab. After the abdomen was closely sutured in two layers, the balloon was filled with 1.0 ml of air, and simultaneous measurements of P ao and P ab were obtained during loading first of the fourth rib pair, then of the tenth rib pair at 0, 10 and 20 cmh 2 O transrespiratory pressure; the axial displacement of the tenth rib during loading of

3 J Physiol pp Rib lung coupling during inflation 483 the fourth rib pair was also measured. A second ballooncatheter system filled with 0.5 ml of air was subsequently positioned in the middle third of the oesophagus to measure pleural pressure (P pl ), and the relaxed respiratory system was inflated twice by 100 ml increments from 100 to 1000 ml to establish the passive volume P ab and volume P pl relationships. (2) We next evaluated the role of the pattern of rib displacement in causing the alteration in rib lung coupling with inflation. In five animals, an additional thread was thus attached to the screw in the fourth rib and led laterally, perpendicular to the sagittal midplane to measure both the lateral and the axial displacement of the rib. After calibration of the two displacement transducers, the relaxed chest wall was inflated to a transrespiratory pressure of cmh 2 O, and the lateral and axial rib displacements were obtained during stepwise deflation to FRC. Two relaxation curves of the fourth rib were obtained, after which two runs of loading at 0, 10 and 20 cmh 2 O transrespiratory pressure were performed. The procedure was subsequently repeated for the seventh rib. Blood pressure and heart rate were monitored during the course of the experiments and no changes occurred. Also, the pupils in each animal remained constricted and unresponsive to light, thus indicating a deep level of anaesthesia. At the conclusion of the measurements, the animals were given an overdose (30 40 mg kg 1 i.v.) of anaesthetic. obtained was adjusted to yield a value of 0 cmh 2 Oat 1.0 litre above FRC. As for the data obtained during rib loading, the changes in P ab and P di during passive inflation were averaged over the animal group. All data are presented as means ± s.e.m. Comparisons between the slopes for the different rib pairs and between the slopes obtained for a given rib pair at the three different lung volumes were made by analysis of variance (ANOVA) with repeated measures, and multiple comparison testing of the mean values was performed, when appropriate, using Student Newman Keuls tests. The criterion for statistical significance was taken as P < Results The slopes of the relationships between X r and F obtained for all the ribs at the three different lung volumes in the seven animals are shown in Fig. 1. The cranial rib displacement induced by a given force at FRC increased progressively (P < 0.001) from the second to the seventh rib and then remained stable. The cranial rib displacement induced by a given force at 10 and 20 cmh 2 O transrespiratory pressure also increased from the second to the third rib and then remained unchanged from the third to the eighth rib. As lung volume was increased from FRC to Data analysis For each rib pair at each lung volume in each individual animal, the axial rib displacements (X r ) and the changes in P ao induced by each load (force, F)wereaveragedoverthe two runs. The relationships thus obtained between X r and F and between P ao and F were then calculated by using linear regression techniques (coefficient of correlation, r between and 0.999), and the slopes of these relationships (X r /F and P ao /F) were averaged over the animal group. The changes in P ab and the lateral rib displacements (Y r ) observed during rib loading were analysed similarly. The changes in P ab and P pl during passive inflation in each animal were also averaged over the two trials, and the alterations in (passive) diaphragmatic tension were evaluated by calculating the changes in transdiaphragmatic pressure (P di ) along the lines suggested by Agostoni & Rahn (1960). Thus, at each level of inflation, the change in P pl was subtracted from the change in P ab ( P di = P ab P pl ), and the P di thus Figure 1. Effect of lung volume on the relationships between rib displacement and force The data shown are the mean ± S.E.M. values of axial rib displacement per unit force (X r /F) obtained from seven animals during cranial loading of the individual rib pairs at functional residual capacity (FRC, ), 10 cmh 2 O transrespiratory pressure ( ), and 20 cmh 2 O transrespiratory pressure ( ).

4 484 A. De Troyer and D. Leduc J Physiol pp cmh 2 O, however, X r /F tended to decrease, particularly for ribs 7 9 (P < 0.001). The effects of lung volume on the slopes of the relationships between P ao and F are summarized in Fig. 2. In agreement with our previous observation (De Troyer & Wilson, 2002), P ao /F at FRC increased gradually from the second to the fifth rib pair and then declined from the fifth to the eleventh rib pair (Fig. 2A). This pattern was also observed during loading at 10 and 20 cmh 2 O transrespiratory pressure. With increasing lung volume, however, P ao /F for the second to seventh rib pairs decreased markedly (P < 0.001), such that at 10 and 20 cmh 2 O transrespiratory pressure, it amounted, respectively, to 55 ± 1 and 30 ± 1% of the FRC value (Fig. 2B). In contrast, P ao /F for the ninth rib pair was consistently greater at 10 cmh 2 O than at FRC (P < 0.05), and P ao /F for the tenth rib pair was greater at both 10 and 20 cmh 2 O than at FRC. The slopes of the relationships between P ab and F obtained during loading of the fourth and tenth rib pairs are compared with the slopes of the relationships between P ao and F in Fig. 3. When the tenth rib pair was loaded (Fig. 3, right), P ab /F was greater than P ao /F in every animal (P < 0.001), in particular at FRC. For the seven animals studied, the P ao / P ab ratioatfrcthus averaged 0.01 ± 0.12, and it increased (P = 0.03) to 0.22 ± 0.11 and 0.58 ± 0.27 at 10 and 20 cmh 2 O transrespiratory pressure, respectively. On the other hand, when the fourth rib pair was loaded (Fig. 3, left), P ab /F was consistently lower than P ao /F (P < 0.001) and the P ao / P ab ratio, which amounted to 3.12 ± 0.21 at FRC, decreased (P = 0.05) to 1.94 ± 0.26 at 20 cmh 2 O. Loading the fourth rib pair, however, also caused the tenth rib to move cranially at all lung volumes. Both at FRC and at 20 cmh 2 O, the slope of the relationship between the displacement of the tenth rib and F during the procedure was 22 ± 2% of the slope of the relationship obtained when the tenth rib pair Figure 3. Comparison between the changes in abdominal and airway opening pressure during rib loading The data shown are the mean ± S.E.M. values of the changes in abdominal pressure ( P ab, ) and airway opening pressure ( P ao, ) per unit force (F) obtained from seven animals during cranial loading of the fourth (left) and tenth (right) rib pairs at 0 (FRC), 10 and 20 cmh 2 O transrespiratory pressure. Note that during loading of the fourth rib pair, P ao is greater than P ab at all lung volumes. In contrast, during loading of the tenth rib pair, P ao is smaller. itself was loaded, and the P ab /F corresponding to this displacement represented 27 ± 2% of the total P ab /F. The changes in P ab and P di measured during passive inflation in the seven animals are shown in Fig. 4. Inflating the respiratory system from FRC to 1.0 l above FRC caused both P ab and P pl to rise. For any given increase in lung volume, however, the rise in P pl was greater than the rise in P ab. Consequently, P di was negative, thus indicating that tension in the diaphragm above FRC was reduced relative to FRC. In fact, although the rise in P ab was linearly related to lung volume, the relationship between P di and lung volume was curvilinear such that for a given volume increase, the reduction in P di decreased progressively as lung volume was greater. Figure 2. Effect of lung volume on the relationships between airway opening pressure and force The data in A are the mean ± S.E.M. values of the changes in airway opening pressure ( P ao ) per unit force (F) obtained from seven animals during cranial loading of the individual rib pairs. Same conventions as in Fig. 1. In B, the values of P ao /F at 10 ( ) and 20 cmh 2 O( ) are expressed as percentages of the values at FRC; values for the tenth and eleventh rib pairs are not shown because in several animals, P ao /F for these pairs at FRC was zero.

5 J Physiol pp Rib lung coupling during inflation 485 Figure 4. Changes in abdominal and transdiaphragmatic pressure during passive inflation The data are the mean ± S.E.M. values of the changes in abdominal pressure ( P ab, ) and transdiaphragmatic pressure ( P di, ) obtained from seven supine dogs during passive inflation from functional residual capacity (FRC) to 1.0 l above FRC. Note that P ab increases linearly with increasing lung volume, whereas P di decreases progressively. The lung volumes corresponding to 10 and 20 cmh 2 O transrespiratory pressure in these animals averaged, respectively, 0.4 and 0.8 l. The pattern of rib motion obtained in a representative animal during loading the fourth and seventh rib pairs at FRC is compared with the relaxation curve of the ribs in Fig. 5, and Fig. 6 shows the effect of lung volume on this pattern for the five animals studied. During loading at FRC, the ribs were displaced both cranially and outward, but the outward displacement was consistently smaller than the cranial displacement relative to the relaxation curve. Consequently, the pattern of rib motion during Figure 6. Effect of lung volume on the pattern of rib displacement during loading Data are the mean ± S.E.M. values of lateral (Y r ) and axial (X r ) rib displacement obtained from five animals during cranial loading of the fourth and seventh ribs with 0.2, 0.4 and 0.6 kg at FRC ( ), 10 ( ) and 20 cmh 2 O( ) transrespiratory pressure. Note that as lung volume is increased, the outward rib displacement associated with a given cranial displacement decreases markedly. loading was displaced to the right of the relaxation curve (Fig. 5). More importantly, when the ribs were loaded at 10 and 20 cmh 2 O, the outward rib displacement associated with a given cranial displacement decreased markedly and progressively (P < 0.001) as lung volume was increased (Fig. 6). At 20 cmh 2 O, the outward rib displacement was virtually abolished. Discussion The initial purpose of the current study was to test the hypothesis that the mechanical coupling between the most Figure 5. Pattern of rib displacement during cranial loading at functional residual capacity Records of lateral (Y r ) and axial (X r ) rib displacement obtained for the fourth (left panel) and the seventh rib (right panel) in a representative animal. The filled circles and continuous line in each panel correspond to rib loading with 0.2, 0.4 and 0.6 kg at FRC, and the dashed line corresponds to the relaxation curve. For a given cranial displacement, the outward displacement of the ribs was smaller during loading than during relaxation.

6 486 A. De Troyer and D. Leduc J Physiol pp caudal ribs and the lung is poor because these ribs act primarily on the abdomen, rather than the lung, and hence that this coupling is improved when the respiratory system is inflated and thediaphragm is displaced caudally. In agreement with this hypothesis, P ao / P ab was much smaller than 1 during loading of the tenth rib pair at FRC (Fig. 3, right), whereas during loading of the fourth rib pair, P ao / P ab was greater than 1 (Fig. 3, left). Also, P ao /F for ribs 9 11 increased with inflation in every animal (Fig. 2). This increase, however, was moderate, and P ao /F for these ribs remained smaller than that for ribs 5 7 at all lung volumes, including at 20 cmh 2 O transrespiratory pressure. The most prominent effect of inflation, in fact, was a decrease in P ao /F for all the ribs situated cranial to the zone of apposition of the diaphragm to the rib cage. The observation that X r /F in our animals decreased as lung volume was increased above FRC (Fig. 1) confirms our previous finding that in the dog, cranial rib compliance at high lung volumes is lower than at FRC (De Troyer et al. 1985). All other things being equal, such a decrease in X r /F should lead to a reduction in P ao /F for the ribs cranial to the zone of apposition. The decrease in X r /F should also reduce the increase in P ao /F for the caudal ribs that the increase in the area of the lung subtended by these ribs would cause otherwise. However, the decrease in X r /F with inflation was relatively small. For ribs 5 8, the change observed from FRC to 20 cmh 2 O transrespiratory pressure amounted to only 23% of the FRC value, whereas the corresponding reduction in P ao /F was 70% (Fig. 2B). Moreover, X r /F for ribs 2 4 was unaffected by inflation, yet P ao /F for these ribs was similarly reduced by 70%. The volume-induced reduction in P ao /F must therefore result primarily from other mechanisms. When forces are applied to a given rib pair in the cranial direction, the fall in airway opening (pleural) pressure elicits a cranial displacement of the passive diaphragm, and this displacement, in turn, causes a fall in abdominal pressure and reduces the fall in P ao. However, measurements of diaphragmatic muscle length (Sprung et al. 1990) and transdiaphragmatic pressure (Pengelly et al. 1971; Road et al. 1986; Hubmayr et al. 1990) have clearly established that in supine dogs and cats, the action of gravity on the abdominal visceral mass induces stretching and, with it, significant passive tension in the diaphragm at FRC. These measurements have also established that diaphragmatic compliance in such animals increases progressively as lung volume is passively increased above FRC, and indeed, during passive inflation, our animals demonstrated a gradual fall in transdiaphragmatic pressure with increasing lung volume (Fig. 4), and when the fourth rib pair was loaded, the P ao / P ab ratio decreased from FRC to 20 cmh 2 O transrespiratory pressure (Fig. 3, left). Because of this increase in diaphragmatic compliance, it would be expected that during rib loading at high lung volumes, a given P ao would lead to a greater cranial displacement of the diaphragm and therefore that the loss in P ao /F would also be greater. The role played by this mechanism in determining the reduction in P ao /F at high lung volumes is examined in Fig. 7. The filled and open circles in this figure indicate, respectively, the changes in P ao and P ab measured during loading of the fourth rib pair at different lung volumes and previously shown in Fig. 3 (left). If diaphragmatic compliance did not increase with increasing lung volume but instead remained unchanged, then a given fall in P ao would induce at all lung volumes the same fall in P ab as it does at FRC, and the P ao / P ab ratio would be constant. Using the values of P ab measured during loading at the different lung volumes in our animals and the P ao / P ab ratio measured at FRC, one can therefore calculate the values of P ao /F that would be obtained in this condition. The results of these calculations are represented by the Figure 7. Potential role of diaphragmatic compliance in the decrease in rib lung coupling at high lung volumes The filled circles are the mean values of P ao /F obtained from seven animals during cranial loading of the fourth rib pair at 0, 10 and 20 cmh 2 O transrespiratory pressure, and the open circles are the corresponding values of P ab /F (same data as in Fig. 3, left). If the compliance of the diaphragm at higher lung volumes were the same as at FRC, the P ao / P ab ratio would remain constant and P ao /F would decrease with increasing lung volume according to the dashed line. The hatched area between this line and the continuous line connecting the filled circles would thus correspond to the volume induced loss in P ao /F resulting from the increase in diaphragmatic compliance.

7 J Physiol pp Rib lung coupling during inflation 487 dashed line in Fig. 7. At the lung volume corresponding to 10 cmh 2 O transrespiratory pressure, the calculated P ao /F amounted to 2.6 cmh 2 O, whereas the measured value was 1.7 cmh 2 O. In other words, the increase in diaphragmatic compliance from FRC to 10 cmh 2 O transrespiratory pressure would yield a 25% reduction in P ao /F, i.e. it would account for about half of the total loss in P ao /F. Similarly, the greater diaphragmatic compliance at 20 cmh 2 O transrespiratory pressure would account for a 15% reduction in P ao /F, representing 20% of the total loss. These calculated values can only be approximate for several reasons. First, the greater diaphragmatic compliance at high lung volumes would result not only in a greater loss in P ao /F during rib loading but also in a greater fall in P ab. Consequently, to the extent that the calculated values of P ao /F were computed on the basis of the measured P ab values, they tend to overestimate the effect of the increase in diaphragmatic compliance. Second, the analysis in Fig. 7 rests on the assumption that loading of the fourth rib pair has no effect on P ab other than via the diaphragm. In fact, loading of these ribs also led to a cranial displacement of the most caudal ribs, and this displacement must have affected the abdominal wall and P ab in much the same way as it does when the caudal ribs themselves are loaded. This displacement, however, was small at all lung volumes and corresponded to a relatively small fraction of the total P ab measured during loading of the fourth rib pair, thus suggesting that it was not a key factor. Finally, the analysis in Fig. 7 also rests on the assumption that the compliance of the abdominal wall remains constant with increasing lung volume. The observation in our animals that the relationship between lung volume and P ab during passive inflation is linear (Fig. 4) supports this assumption; a linear volume P ab relationship during passive inflation has also been reported in supine cats (Pengelly et al. 1971). Yet, because we measured lung, rather than abdominal volume, the possibility still exists that as in humans (Grimby et al. 1976; Hill et al. 1984), the abdominal wall in supine dogs would be stiffer at high lung volumes than at FRC. Such a change, however, would only impede the cranial displacement of the diaphragm at high lung volumes, and this would also reduce the loss in P ao /F. Thus, even though the losses in P ao /F attributed to the increase in diaphragmatic compliance in Fig. 7 are approximate, the conclusion can safely be drawn that this increase is not the main determinant of the volume-induced reduction in the rib lung coupling. On the other hand, the ribs in the dog are slanted caudally at FRC and move primarily through a rotation around the axis defined by their vertebral articulations (Margulies et al. 1989). It would be expected therefore that as the ribs rotate cranially with inflation and become orientated more transversally relative to the sagittal midplane, a given cranial rib displacement would be associated with a smaller outward displacement, as shown in Fig. 8. Furthermore, in a previous study of the patterns of rib motion produced by the actions of the canine parasternal and external intercostal muscles, it was shown that a given outward displacement of the ribs during breathing is much more effective in increasing lung volume than the same rib displacement in the cranial direction (De Troyer & Wilson, 2000). Consequently, the speculation was also raised that a decrease in outward rib displacement at high lung volumes would play a major role in causing the observed reduction in rib lung coupling. In agreement with this prediction, the outward rib displacement associated with a given cranial displacement decreased markedly and gradually as lung volume was increased (Fig. 6). In fact, at 20 cmh 2 O transrespiratory pressure, the outward rib displacement was virtually abolished, and these measurements allow the quantitative contribution of this mechanism to be estimated. Thus in the dog, the increase in lung volume per unit rib displacement is known to be about four times greater for outward than for cranial displacement (De Troyer & Wilson, 2000). If the P ao produced by an axial rib displacement of 1 mm is denoted a, the relationship between rib displacement and P ao /F during loading at a given lung volume can therefore be expressed, to a good approximation, by the following equation: P ao /F = a(x r /F + 4Y r /F) (1) Figure 8. Diagram of the pattern of rib motion at different lung volumes Dorsal view of the spine and one rib in its position at FRC and its position at 20 cmh 2 O transrespiratory pressure. Because the rib at FRC is slanted caudally, it moves both cranially (X r ) and outward (Y r ) during cranial loading. However, at 20 cmh 2 O transrespiratory pressure, the rib is almost horizontal. Therefore, loading the rib should cause a cranial displacement with little or no outward displacement.

8 488 A. De Troyer and D. Leduc J Physiol pp The data obtained for X r /F and Y r /F in our animals then lead to the result that P ao /F at 10 cmh 2 O transrespiratory pressure would amount to 75% of the FRC value. In other words, at this lung volume, the reduction in P ao /F due to the alteration in rib displacement alone (i.e. independent of any concomitant increase in diaphragmatic compliance) would be 25% of the FRC value. At 20 cmh 2 O transrespiratory pressure, the isolated alteration in rib displacement would also yield a 47% reduction in P ao /F, and these two values are close to those predicted on the basis of the measured changes in P ab /F. Indeed, the analysis developed in Fig. 7 suggested that the reduction in P ao /F unrelated to diaphragmatic compliance was 26% of the FRC value at 10 cmh 2 O and 55% at 20 cmh 2 O. Overall the measurements of P ab and rib displacement, while based on independent techniques, thus lead to the conclusion that the decrease in rib lung coupling at high lung volumes results partly from the increase in diaphragmatic compliance but mostly from the reduction in outward rib displacement. As a corollary, to the extent that the bucket-handle rotation of the human ribs during passive inflation (Wilson et al. 2001) is similar in magnitude to that observed in the dog (Margulies et al. 1989), one would further predict that the coupling between the ribs and the lung in humans would also decrease markedly with increasing lung volume. When the ribs in our animals were loaded, their cranial displacement was consistently greater than their outward displacement relative to the relaxation curve (Fig. 5). The pattern of rib motion induced by loading thus closely reproduced the pattern of rib motion caused by an isolated contraction of the external intercostal muscles (De Troyer & Wilson, 2000), and it is well known that the pressuregenerating ability of these muscles decreases markedly as lung volume is increased above FRC (Di Marco et al. 1990). This decrease has conventionally been attributed to the length tension characteristics of the muscles, and indeed the external intercostals, particularly those in the rostral interspaces, shorten gradually as lung volume is increased (Di Marco et al. 1992; De Troyer et al. 1999). The current findings, however, have established that the pattern of rib motion would result in a marked decrease in the pressuregenerating ability of these muscles even though the length of the muscles was kept constant and the force generated by them was preserved. References AgostoniE&RahnH(1960). Abdominal and thoracic pressures at different lung volumes. 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Effect of body position on regional diaphragm function in dogs. J Appl Physiol 69, Wilson TA, Legrand A, Gevenois PA & De Troyer A (2001). Respiratory effects of the external and internal intercostal muscles in humans. J Physiol 530, Acknowledgements This study was supported in part by a grant ( ) from the Fonds National de la Recherche Scientifique (FNRS Belgium) and by a Research grant from the Brussels School of Medicine.