Action of the isolated canine diaphragm on the lower ribs at high lung volumes.

The normal diaphragm has an inspiratory action on the lower ribs, but subjects with chronic obstructive pulmonary disease commonly have an inward displacement of the lateral portions of the lower rib cage during inspiration. This paradoxical displacement, conventionally called 'Hoover's sign', has traditionally been attributed to the direct action of radially oriented diaphragmatic muscle fibres. In the present study, the inspiratory intercostal muscles in all interspaces in anaesthetized dogs were severed so that the diaphragm was the only muscle active during inspiration. The displacements of the lower ribs along the craniocaudal and laterolateral axes and the changes in pleural pressure (∆Ppl) and transdiaphragmatic pressure were measured during occluded breaths and mechanical ventilation at different lung volumes between functional residual capacity (FRC) and total lung capacity. From these data, the separate effects on rib displacement of ∆Ppl and of the force exerted by the diaphragm on the ribs were determined. Isolated spontaneous diaphragm contraction at FRC displaced the lower ribs cranially and outward, but this motion was progressively reversed into a caudal and inward motion as lung volume increased. However, although the force exerted by the diaphragm on the ribs decreased with increasing volume, it continued to displace the ribs cranially and outward. These observations suggest that Hoover's sign is usually caused by the decrease in the zone of apposition and, thus, by the dominant effect of ∆Ppl on the lower ribs, rather than an inward pull from the diaphragm.

Effects of the insertional and appositional forces of the canine diaphragm on the lower ribs.

The diaphragm has an inspiratory action on the lower ribs, and current conventional wisdom maintains that this action is the result of two mechanisms, namely, the force applied by the muscle fibres on the ribs into which they insert (insertional force) and the transmission of abdominal pressure through the zone of apposition (appositional force). The magnitude of the diaphragmatic force and the relative contributions of the insertional and appositional components, however, are unknown. To assess these forces, the inspiratory intercostal muscles in all interspaces were severed in anaesthetized dogs, so that the diaphragm was the only muscle active during inspiration, and the displacements of the lower ribs along the craniocaudal and laterolateral axes were measured during quiet breathing, during occluded breaths and during passive lung inflation. From these data, the isolated effects of pleural pressure and transdiaphragmatic pressure on rib displacement were determined. Then external forces were applied to the ribs in the cranial and the lateral direction to simulate, respectively, the effects of the insertional and appositional forces, and the rib trajectories for these external forces were used as the basis for a vector analysis to obtain the relative magnitudes of the insertional and appositional contributions to the rib displacement driven by transdiaphragmatic pressure. The results show that, per unit pressure, the inspiratory effect of the diaphragmatic force on the lower ribs is equal to the expiratory effect of pleural pressure, and that the insertional force contributes 60% of that inspiratory effect.

Effect of acute inflation on the mechanics of the inspiratory muscles.

When the lung is inflated acutely, the capacity of the diaphragm to generate pressure, in particular pleural pressure (Ppl), is impaired because the muscle during contraction is shorter and generates less force. At very high lung volumes, the pressure-generating capacity of the diaphragm may be further reduced by an increase in the muscle radius of curvature. Lung inflation similarly impairs the pressure-generating capacity of the inspiratory intercostal muscles, both the parasternal intercostals and the external intercostals. In contrast to the diaphragm, however, this adverse effect is largely related to the orientation and motion of the ribs, rather than the ability of the muscles to generate force. During combined activation of the two sets of muscles, the change in Ppl is larger than during isolated diaphragm activation, and this added load on the diaphragm reduces the shortening of the muscle and increases muscle force. In addition, activation of the diaphragm suppresses the cranial displacement of the passive diaphragm that occurs during isolated intercostal contraction and increases the respiratory effect of the intercostals. As a result, the change in Ppl generated during combined diaphragm-intercostal activation is greater than the sum of the pressures generated during separate muscle activation. Although this synergistic interaction becomes particularly prominent at high lung volumes, lung inflation, either bilateral or unilateral, places a substantial stress on the inspiratory muscle pump.

Length and curvature of the dog diaphragm.

Transdiaphragmatic pressure is a result of both tension in the muscles of the diaphragm and curvature of the muscles. As lung volume increases, the pressure-generating capability of the diaphragm decreases. Whether decrease in curvature contributes to the loss in transdiaphragmatic pressure and, if so, under what conditions it contributes are unknown. Here we report data on muscle length and curvature in the supine dog. Radiopaque markers were attached along muscle bundles in the midcostal region of the diaphragm in six beagle dogs of approximately 8 kg, and marker locations were obtained from biplanar images at functional residual capacity (FRC), during spontaneous inspiratory efforts against a closed airway at lung volumes from FRC to total lung capacity, and during bilateral maximal phrenic nerve stimulation at the same lung volumes. Muscle length and curvature were obtained from these data. During spontaneous inspiratory efforts, muscle shortened by 15-40% of length at FRC, but curvature remained unchanged. During phrenic nerve stimulation, muscle shortened by 30 to nearly 50%, and, for shortening exceeding 52%, curvature appeared to decrease sharply. We conclude that diaphragm curvature is nearly constant during spontaneous breathing maneuvers in normal animals. However, we speculate that it is possible, if lung compliance were increased and the chest wall and the diameter of the diaphragm ring of insertion were enlarged, as in the case of chronic obstructive pulmonary disease, that decrease in diaphragm curvature could contribute to loss of diaphragm function.

Action of the diaphragm on the rib cage.

When the diaphragm contracts, pleural pressure falls, exerting a caudal and inward force on the entire rib cage. However, the diaphragm also exerts forces in the cranial and outward direction on the lower ribs. One of these forces, the "insertional force," is applied by the muscle at its attachments to the lower ribs. The second, the "appositional force," is due to the transmission of abdominal pressure to the lower rib cage in the zone of apposition. In the control condition at functional residual capacity, the effects of these two forces on the lower ribs are nearly equal and outweigh the effect of pleural pressure, whereas for the upper ribs, the effect of pleural pressure is greater. The balance between these effects, however, may be altered. When the abdomen is given a mechanical support, the insertional and appositional forces are increased, so that the muscle produces a larger expansion of the lower rib cage and, with it, a smaller retraction of the upper rib cage. In contrast, at higher lung volumes the zone of apposition is decreased, and pleural pressure is the dominant force on the lower ribs as well. Consequently, although the force exerted by the diaphragm on these ribs remains inspiratory, rib displacement is reversed into a caudal-inward displacement. This mechanism likely explains the inspiratory retraction of the lateral walls of the lower rib cage observed in many subjects with chronic obstructive pulmonary disease (Hoover's sign). These observations support the use of a three-compartment, rather than a two-compartment, model to describe chest wall mechanics.

Smooth muscle dynamics and maximal expiratory flow in asthma.

A computational model for maximal expiratory flow in constricted lungs is presented. The model was constructed by combining a previous computational model for maximal expiratory flow in normal lungs and a previous mathematical model for smooth muscle dynamics. Maximal expiratory flow-volume curves were computed for different levels of smooth muscle activation. The computed maximal expiratory flow-volume curves agree with data in the literature on flow in constricted nonasthmatic subjects. In the model, muscle force during expiration depends on the balance between the decrease in force that accompanies muscle shortening and the recovery of force that occurs during the time course of expiration, and the computed increase in residual volume (RV) depends on the magnitude of force recovery. The model was also used to calculate RV for a vital capacity maneuver with a slow rate of expiration, and RV was found to be further increased for this maneuver. We propose that the measurement of RV for a vital capacity maneuver with a slow rate of expiration would provide a more sensitive test of smooth muscle activation than the measurement of maximal expiratory flow.

Compartmental models of the chest wall and the origin of Hoover's sign.

First, one- and two-compartment models of the chest wall are reviewed. Then, a three-compartment model is described, and the predictions of the model are compared with data on pressure and volume relationships for different breathing maneuvers in dogs. Finally, the three-compartment model is scaled to apply to humans, and dynamic solutions for periodic breathing are obtained. To model COPD, the area of the zone of apposition is decreased, and to model COPD patients who show Hoover's sign, pulmonary resistance and abdominal compliance are increased. The resulting traces match those reported by Binazzi et al. (2008. Respir. Physiol. Neurobiol. 160: 325-333) for controls and patients with COPD, both without and with Hoover's sign. We conclude that Hoover's sign is a dynamic phenomenon that results from the decrease in the area of the zone of apposition that occurs in COPD and a larger pulmonary resistance and abdominal compliance in those patients who show Hoover's sign.

Mechanism of the increased rib cage expansion produced by the diaphragm with abdominal support.

When the abdomen in quadriplegic subjects is given a passive mechanical support, the expansion of the lower rib cage during inspiration is greater and the inward displacement of the upper rib cage is smaller. These changes have traditionally been attributed to an increase in the appositional force of the diaphragm, but the mechanisms have not been assessed. In this study, the inspiratory intercostal muscles in all interspaces were severed in anesthetized dogs, so that the diaphragm was the only muscle active during inspiration, and the displacements of the ribs 10 and 5 and the changes in pleural and abdominal pressure were measured during unimpeded breathing and during breathing with a plate applied on the ventral abdominal wall. In addition, external forces were applied to the 10th rib pair in the cranial and lateral directions, and the rib trajectories thus obtained were used as the basis for a vector analysis to estimate the relative contributions of the insertional and appositional forces to the rib 10 displacements during breathing. Application of the abdominal plate caused a marked increase in the inspiratory cranial and outward displacement of rib 10 and a decrease in the inspiratory caudal displacement of rib 5. Analysis of the results showed, however, that 1) the insertional and appositional forces contributed nearly equally to the increased inspiratory displacement of rib 10 and 2) the decrease in the expiratory displacement of rib 5 was the result of both the greater displacement of the lower ribs and the decrease in pleural pressure.

The two mechanisms of intercostal muscle action on the lung.

The mechanisms of respiratory action of the intercostal muscles were studied by measuring the effect of external forces (F) applied to the ribs and by modeling the effect of F exerted by the intercostal muscles. In five dogs, with the airway occluded, cranial F were applied to individual rib pairs, from the 2nd to the 11th rib pair, and the change in airway opening pressure (Pao) was measured. The ratio Pao/F increases with increasing rib number in the upper ribs (2nd to 5th) and decreases in the lower ribs (5th to 11th). These data were incorporated into a model for the geometry of the ribs and intercostal muscles, and Pao/F was calculated from the model. For interspaces 2-8, the calculated values agree reasonably well with previously measured values. From the modeling, two mechanisms of intercostal muscle action are identified. One is the well-known Hamberger mechanism, modified to account for the three-dimensional geometry of the rib cage. This mechanism depends on the slant of an intercostal muscle relative to the ribs and on the resulting difference between the moments applied to the upper and lower ribs that bound each interspace. The second is a new mechanism that depends on the difference between the values of Pao/F for the upper and lower ribs.

Empirical model for dynamic force-length behavior of airway smooth muscle.

An empirical mathematical model that describes the relation between force and length for dynamic loading of maximally activated airway smooth muscle is described. The model consists of three first-order, ordinary differential equations: one for muscle shortening, one for lengthening, and a third that describes the evolution of an internal variable that depends on muscle history. The model fits data on the dynamic force-length behavior of maximally activated trachealis muscle for a range of amplitudes and rates of shortening and lengthening. The muscle model is incorporated into a model for an intact airway tethered to the surrounding parenchyma. As an example of its use, the model airway is subjected to the loading that occurs during a deep breath. After the breath, the rate of muscle shortening is determined by the interaction between muscle dynamics and the elastic load that is imposed by interdependence forces.

Impedance, gas mixing, and bimodal ventilation in constricted lungs.

To evaluate the effect of increasing smooth muscle activation on the distribution of ventilation, lung impedance and expired gas concentrations were measured during a 16-breath He-washin maneuver in five nonasthmatic subjects at baseline and after each of three doses of aerosolized methacholine. Values of dynamic lung elastance (El,dyn), the curvature of washin plots, and the normalized slope of phase III (S(N)) were obtained. At the highest dose, El,dyn was 2.6 times the control value and S(N) for the 16th breath was 0.65 liter(-1). A previously described model of a constricted terminal airway was extended to include variable muscle activation, and the extended model was tested against these data. The model predicts that the constricted airway has two stable states. The impedances of the two stable states are independent of smooth muscle activation, but driving pressure and the number of airways in the high-resistance state increase with increasing muscle activation. Model predictions and experimental data agree well. We conclude that, as a result of the bistability of the terminal airways, the ventilation distribution in the constricted lung is bimodal.

Parenchymal mechanics, gas mixing, and the slope of phase III.

A model of parenchymal mechanics is revisited with the objective of investigating the differences in parenchymal microstructure that underlie the differences in regional compliance that are inferred from gas-mixing studies. The stiffness of the elastic line elements that lie along the free edges of alveoli and form the boundary of the lumen of the alveolar duct is the dominant determinant of parenchymal compliance. Differences in alveolar size cause parallel shifts of the pressure-volume curve, but have little effect on compliance. However, alveolar size also affects the relation between surface tension and pressure during the breathing cycle. Thus regional differences in alveolar size generate regional differences in surface tension, and these drive Marangoni surface flows that equilibrate surface tension between neighboring acini. Surface tension relaxation introduces phase differences in regional volume oscillations and a dependence of expired gas concentration on expired volume. A particular example of different parenchymal properties in two neighboring acini is described, and gas exchange in this model is calculated. The efficiency of mixing and slope of phase III for the model agree well with published data. This model constitutes a new hypothesis concerning the origin of phase III.

Ventilation-perfusion distribution in normal subjects.

Functional values of LogSD of the ventilation distribution (σ(V)) have been reported previously, but functional values of LogSD of the perfusion distribution (σ(q)) and the coefficient of correlation between ventilation and perfusion (ρ) have not been measured in humans. Here, we report values for σ(V), σ(q), and ρ obtained from wash-in data for three gases, helium and two soluble gases, acetylene and dimethyl ether. Normal subjects inspired gas containing the test gases, and the concentrations of the gases at end-expiration during the first 10 breaths were measured with the subjects at rest and at increasing levels of exercise. The regional distribution of ventilation and perfusion was described by a bivariate log-normal distribution with parameters σ(V), σ(q), and ρ, and these parameters were evaluated by matching the values of expired gas concentrations calculated for this distribution to the measured values. Values of cardiac output and LogSD ventilation/perfusion (Va/Q) were obtained. At rest, σ(q) is high (1.08 ± 0.12). With the onset of ventilation, σ(q) decreases to 0.85 ± 0.09 but remains higher than σ(V) (0.43 ± 0.09) at all exercise levels. Rho increases to 0.87 ± 0.07, and the value of LogSD Va/Q for light and moderate exercise is primarily the result of the difference between the magnitudes of σ(q) and σ(V). With known values for the parameters, the bivariate distribution describes the comprehensive distribution of ventilation and perfusion that underlies the distribution of the Va/Q ratio.

Diagrammatic analysis of the respiratory action of the diaphragm.

During isolated phrenic nerve stimulation, the muscles of the diaphragm shorten by 40-50% of their optimal length, and the force in the muscle and transdiaphragmatic pressure (Pdi) depend on the final muscle length. The muscle shortening depends on the load imposed on the diaphragm by pleural and abdominal pressures during a particular maneuver. The mechanics of the interaction between the diaphragm and the load is well understood, but the force-length properties of the diaphragm are nonlinear, and an algebraic analysis of the interaction is clumsy. Here we describe a graphical analysis of the interaction. The variable muscle length is transformed into an equivalent variable, i.e., volume displaced by the diaphragm (Vdi), to obtain the characteristic line for the diaphragm, a graph of Pdi vs. Vdi for a given level of activation. The load is described by the same variables. Therefore, load lines can be drawn on the same graph, and the equilibrium point for the diaphragm is given by the intersection of the load line with the characteristic line of the diaphragm. Graphical analyses of the volume dependence of the respiratory effects of diaphragm and intercostal muscle activation and for the interaction between them are shown.

History dependence of vital capacity in constricted lungs.

Measurements of dynamic force-length behavior of maximally activated strips of smooth muscle during oscillatory length changes show that force decreases well below the isometric force during the shortening phase of the oscillation. The magnitude of the decrease depends on the rate of shortening; for slower shortening, the decrease is smaller and force is larger. Modeling of expiratory flow, based on these data, predicts that vital capacity in constricted lungs depends on the rate of expiration. In maximally constricted lungs, forced vital capacity (FVC) is predicted to be 16% smaller than control, and vital capacity for a very slow expiration (SVC), 31% less than control. These predictions were tested by measuring FVC and SVC in constricted normal subjects. In the first group of 9 subjects, four maneuvers were made following the delivery of two doses of methacholine in the order: SVC, FVC, FVC, SVC. In a second group of 11 subjects, two maneuvers were performed at each dose in the order: FVC, SVC. At the highest dose of methacholine, FVC for both trials in group 1 and for the one trial in group 2 were all approximately 13% less than control, a slightly smaller decrease than predicted. SVC for the 1st trial in group 1 was 27% less than control, also slightly smaller than predicted. The difference between FVC and SVC for this trial, 13%, was close to the predicted difference of 15%. However, SVC for the 2nd trial in group 1 (preceded by 3 vital capacity maneuvers) and for group 2 (preceded by 1) were no different from FVC. We conclude that vital capacity in constricted lungs depends on the dynamic force-length properties of smooth muscle and that the history dependence of the dynamic properties of smooth muscle is more complicated than has been inferred from oscillatory force-length behavior.

Mechanisms of the inspiratory action of the diaphragm during isolated contraction.

The lung-expanding action of the diaphragm is primarily related to the descent of the dome produced by the shortening of the muscle fibers. However, when the phrenic nerves in dogs are selectively stimulated at functional residual capacity, the muscle insertions into the lower ribs also move caudally. This rib motion should enhance the descent of the dome and increase the fall in pleural pressure (DeltaPpl). To quantify the role of this mechanism in determining DeltaPpl during isolated diaphragm contraction and to evaluate the volume dependence of this role, radiopaque markers were attached to muscle bundles in the midcostal region of the muscle in six animals, and the three-dimensional location of the markers during relaxation at different lung volumes and during phrenic nerve stimulation at the same lung volumes was measured using computed tomography. From these data, accurate measurements of muscle length, dome displacement, and lower rib displacement were obtained. The values of dome displacement were then corrected for lower rib displacement, and the values of DeltaPpl corresponding to the corrected dome displacements were obtained using the measured relationship between DeltaPpl and dome displacement. The measurements showed that phrenic stimulation at all lung volumes causes a caudal displacement of the lower ribs and that this displacement, taken alone, contributes approximately 25% of the DeltaPpl produced by the diaphragm. To the extent that this lower rib displacement is itself caused by DeltaPpl, the lung-expanding action of the diaphragm during isolated contraction may therefore be viewed as a self-facilitating phenomenon.

Respiratory action of the intercostal muscles.

The mechanical advantages of the external and internal intercostals depend partly on the orientation of the muscle but mostly on interspace number and the position of the muscle within each interspace. Thus the external intercostals in the dorsal portion of the rostral interspaces have a large inspiratory mechanical advantage, but this advantage decreases ventrally and caudally such that in the ventral portion of the caudal interspaces, it is reversed into an expiratory mechanical advantage. The internal interosseous intercostals in the caudal interspaces also have a large expiratory mechanical advantage, but this advantage decreases cranially and, for the upper interspaces, ventrally as well. The intercartilaginous portion of the internal intercostals (the so-called parasternal intercostals), therefore, has an inspiratory mechanical advantage, whereas the triangularis sterni has a large expiratory mechanical advantage. These rostrocaudal gradients result from the nonuniform coupling between rib displacement and lung expansion, and the dorsoventral gradients result from the three-dimensional configuration of the rib cage. Such topographic differences in mechanical advantage imply that the functions of the muscles during breathing are largely determined by the topographic distributions of neural drive. The distributions of inspiratory and expiratory activity among the muscles are strikingly similar to the distributions of inspiratory and expiratory mechanical advantages, respectively. As a result, the external intercostals and the parasternal intercostals have an inspiratory function during breathing, whereas the internal interosseous intercostals and the triangularis sterni have an expiratory function.

Coupling between the ribs and the lung in dogs.

In contrast to the conventional theory, the external and internal intercostal muscles show marked rostrocaudal gradients in their actions on the lung. We hypothesized that these gradients are the result of a non-uniform coupling between the ribs and the lung. Rib displacements (X(r)) and the changes in airway opening pressure (P(a,o)) were thus measured in anaesthetized, pancuronium-treated, supine dogs while loads were applied in the cranial direction to individual pairs of odd-numbered ribs and in the caudal direction to individual pairs of even-numbered ribs. During cranial loading, X(r) induced by a given load increased gradually with increasing rib number. The decrease in P(a,o) also increased from the third to the fifth rib pair but then decreased markedly to the eleventh pair. A similar pattern was observed during caudal loading, although X(r) and DeltaP(a,o) were smaller. These results were then combined to calculate the net X(r) and the net DeltaP(a,o) that a hypothetical intercostal muscle lying parallel to the longitudinal body axis would produce in different interspaces. The net X(r) was cranial in all interspaces. However, whereas the net DeltaP(a,o) was negative in the cranial interspaces, it was positive in the caudal interspaces. These observations confirm that the coupling between the ribs and the lung varies from the top to the base of the ribcage. This coupling confers to both the external and the internal intercostal muscles an inspiratory action on the lung in the cranial interspaces and an expiratory action in the caudal interspaces.