A model of the respiratory pump

The interaction of forces that produce chest wall motion and lung volume change is complex and incompletely understood. To aid understanding we have developed a simple model that allows prediction of the effect on chest wall motion of changes in applied forces. The model is a lever system on which the forces generated actively by the respiratory muscles and passively by impedances of rib cage, lungs, abdomen, and diaphragm act at fixed sites. A change in forces results in translational and/or rotational motion of the lever; motion represents volume change. The distribution and magnitude of passive relative to active forces determine the locus and degree of rotation and therefore the effect of an applied force on motion of the chest wall, allowing the interaction of diaphragm, rib cage, and abdomen to be modeled. Analysis of moments allow equations to be derived that express the effect on chest wall motion of the active component in terms of the passive components. These equations may be used to test the model by comparing predicted with empirical behavior. The model is simple, appears valid for a variety of respiratory maneuvers, is useful in interpreting relative motion of rib cage and abdomen and may be useful in quantifying the effective forces acting on the rib cage.     

Coupling between rib cage and abdominal compartments of the relaxed chest wall

The volume displacements of the rib cage and abdomen of relaxed seated subjects were measured as functions of pleural pressure with the chest wall expanded by airway pressure and with the chest wall distorted by an external force applied to the rib cage. From the measured displacements for the two independent loads, the three compliances that describe the mechanical properties of the relaxed chest wall modeled as a linear elastic system with two degrees of freedom were obtained. The cross compliance that describes the coupling between the rib cage and abdomen was found to be small and positive, 0.01-0.02 1/cmH2O. The displacement of the rib cage by the external force was consistent with the displacement predicted by use of standard methods for calculating the mechanical advantage of the force.     

Mechanical coupling of the rib cage, abdomen, and diaphragm through their area of apposition

Although volumetric displacements of the chest wall are often analyzed in terms of two independent parallel pathways (rib cage and abdomen), Loring and Mead have argued that these pathways are not mechanically independent (J. Appl. Physiol. 53: 756-760, 1982). Because of its apposition with the diaphragm, the rib cage is exposed to two distinct pressure differences, one of which depends on abdominal pressure. Using the analysis of Loring and Mead as a point of departure, we developed a complementary analysis in which mechanical coupling of the rib cage, abdomen, and diaphragm is modeled by a linear translational transformer. This model has the advantage that it possesses a precise electrical analogue. Pressure differences and compartmental displacements are related by the transformation ratio (n), which is the mechanical advantage of abdominal over pleural pressure changes in displacing the rib cage. In the limiting case of very high lung volume, n----0 and the pathways uncouple. In the limit of very small lung volume, n----infinity and the pathways remain coupled; both rib cage and abdomen are driven by abdominal pressure alone, in accord with the Goldman-Mead hypothesis. A good fit was obtained between the model and the previously reported data for the human chest wall from 0.5 to 4 Hz (J. Appl. Physiol. 66:350-359, 1989). The model was then used to estimate rib cage, diaphragm, and abdominal elastance, resistance, and inertance. The abdomen was a high-elastance high-inertance highly damped compartment, and the rib cage a low-elastance low-inertance more lightly damped compartment. Our estimate that n = 1.9 is consistent with the findings of Loring and Mead and suggests substantial pathway coupling.     

Chest wall mechanics: effects of acute and chronic lung disease

Data from the literature show that lung tissue properties affect the chest wall compliance, Ccw, which is the change in lung volume, Vl, with respect to the pleural pressure, Ppl. to analyze the difference between acute and chronic lung tissue changes, we used a mathematical model that describes the static, nonlinear mechanics of the ventilatory system in terms of its major elements: rib cage; abdomen; diaphragm and lung. With this model we derived the relationship between chest wall, rib-cage and diaphragm compliances. Although the Vl-Ppl relation is independent of lung mechanics, the volume operating point (FRC) of the ventilatory system depends on lung tissue properties. This accounts for the effect of acute lung abnormalities. In the presence of chronic lung abnormalities, the properties of the rib-cage are changed which shifts the entire Vl-Ppl curve. In general, valid comparisons of (extra-pulmonary) chest wall mechanics can only be made using the entire Vl-Ppl relation, or at least a sufficiently large part of the relation about FRC. Differentiation of the rib-cage and diaphragm mechanics requires additional measurements of the rib-cage A-P distance and the relative position of the diaphragm.     

Relative strengths of the chest wall muscles

We hypothesized that during maximal respiratory efforts involving the simultaneous activation of two or more chest wall muscles (or muscle groups), differences in muscle strength require that the activity of the stronger muscle be submaximal to prevent changes in thoracoabdominal configuration. Furthermore we predicted that maximal respiratory pressures are limited by the strength of the weaker muscle involved. To test these hypotheses, we measured the pleural pressure, abdominal pressure (Pab), and transdiaphragmatic pressure (Pdi) generated during maximal inspiratory, open-glottis and closed-glottis expulsive, and combined inspiratory and expulsive maneuvers in four adults. We then determined the activation of the diaphragm and abdominal muscles during selected maximal respiratory maneuvers, using electromyography and phrenic nerve stimulation. In all subjects, the Pdi generated during maximal inspiratory efforts was significantly lower than the Pdi generated during open-glottis expulsive or combined efforts, suggesting that rib cage, not diaphragm, strength limits maximal inspiratory pressure. Similarly, at high lung volumes, the Pab generated during closed-glottis expulsive efforts was significantly greater than that generated during open-glottis efforts, suggesting that the latter pressure is limited by diaphragm, not abdominal muscle, strength. As predicted, diaphragm activation was submaximal during maximal inspiratory efforts, and abdominal muscle activation was submaximal during open-glottis expulsive efforts at midlung volume. Additionally, assisting the inspiratory muscles of the rib cage with negative body-surface pressure significantly increased maximal inspiratory pressure, whereas loading the rib cage muscles with rib cage compression decreased maximal inspiratory pressure. We conclude that activation of the chest wall muscles during static respiratory efforts is determined by the relative strengths and mechanical advantage of the muscles involved.     

Analysis of human chest wall motion using a two-compartment rib cage model.

We present a model of chest wall mechanics that extends the model described previously by Macklem et al. (J. Appl. Physiol. 55: 547-557, 1983) and incorporates a two-compartment rib cage. We divide the rib cage into that apposed to the lung (RCpul) and that apposed to the diaphragm (RCab). We apply this model to determine rib cage distortability, the mechanical coupling between RCpul and RCab, the contribution of the rib cage muscles to the pressure change during spontaneous inspiration (Prcm), and the insertional component of transdiaphragmatic pressure in humans. We define distortability as the relationship between distortion and transdiaphragmatic pressure (Pdi) and mechanical coupling as the relationship between rib cage distortion and the pressure acting to restore the rib cage to its relaxed configuration (Plink), as assessed during bilateral transcutaneous phrenic nerve stimulation. Prcm was calculated at end inspiration as the component of the pressure displacing RCpul not accounted for by Plink or pleural pressure. Prcm and Plink were approximately equal during quiet breathing, contributing 3.7 and 3.3 cmH2O on average during breaths associated with a change in Pdi of 3.9 cmH2O. The insertional component of Pdi was measured as the pressure acting on RCab not accounted for by the change in abdominal pressure during an inspiration without rib cage distortion and was 40 +/- 12% (SD) of total Pdi. We conclude that there is substantial resistance of the human rib cage to distortion, that, along with rib cage muscles, contributes importantly to the fall in pleural pressure over the costal surface of the lung.     

Chest wall motion during spontaneous breathing and mechanical ventilation in dogs

We measured the volume change of the thoracic cavity (delta Vth) and the volumes displaced by the diaphragm (delta Vdi) and rib cage (delta Vrc) in six pentobarbital-anesthetized dogs lying supine. A high-speed X-ray scanner (dynamic spatial reconstructor) provided three-dimensional images of the thorax during spontaneous breathing and during mechanical ventilation with paralysis. Tidal volume (VT) was measured by integrating gas flow. Changes in thoracic liquid volume (delta Vliq, presumably caused by changes in thoracic blood volume) were calculated as delta Vth - VT. Absolute volume displaced by the rib cage was not significantly different during the two modes of ventilation. During spontaneous breathing, thoracic blood volume increased during inspiration; delta Vliq was 12.3 +/- 4.1% of delta Vth. During mechanical ventilation, delta Vliq was nearly zero. Configuration of the relaxed chest wall was similar during muscular relaxation induced by either pharmacological paralysis or hyperventilation. Expiratory muscle activity produced 50 +/- 11% of the delta Vth during spontaneous breathing. We conclude that at constant VT the volume displaced by the rib cage is remarkably similar during the transition from spontaneous breathing to mechanical ventilation, while both diaphragmatic volume displacement and changes in intrathoracic blood volume decrease by a similar amount.     

Mechanical analysis of extrapulmonary volume displacements in the thorax and abdomen

Currently, the effect of intrathoracoabdominal, extrapulmonary volume displacements (Vep) are not well understood. Various clinical conditions can lead to volume displacements caused by gas or liquid accumulations. To analyze the pressure and volume changes that occur by Vep, we used a mathematical model of chest wall and lung mechanics that accounts for static changes associated with rib cage, diaphragm, abdomen, and lungs. By solving the model equations, we obtained simulations of the pleural and abdominal displacements that clearly differentiate the mechanisms involved. When abdominal displacement occurs, the reduction in lung volume is less than that caused by an equal displacement in pleural space. Abdominal displacement produces an increased pressure that expands the rib cage significantly, whereas pleural displacement does not produce a comparable action. Furthermore, our model predicts the conditions under which the work of inspiration is expected to increase as a consequence of these displacements. Finally, an important distinction is predicted between abdominal displacements caused by gas or liquid accumulation. Although an abdominal gas displacement tends to decrease the resting lung volume, the weight effect of a liquid displacement tends to increase the resting lung volume by pulling down the diaphragm.     

Theoretical analysis of chest wall mechanics

A mathematical model of the chest wall partitioned into rib cage, diaphragmatic and abdominal components is developed consistent with published experimental observations. The model describes not only the orthodox chest wall movements (rib cage and abdomen expand together during inspiration) of the quietly breathing standing adult, but also Mueller maneuvers (inspiration against an occluded airway opening) and the paradoxical breathing patterns (rib cage contracts while abdomen expands during inspiration) observed in quadriplegia and in the newborn. The abdomen is inferred to act as a cylinder reinforced by the abdominal muscles functioning similarly to bands around a barrel. The rib cage and abdominal wall are inferred to act not as though they were directly attached to one another, but as though they were being pressed together by the skeleton. Furthermore, transabdominal pressure is visualized as acting, not across the rib cage isolated from the diaphragm, as has been suggested previously, but instead, across the combined rib cage and diaphragm acting as a deformable unit containing the lungs.     

Chest wall kinematics and respiratory muscle action in walking healthy humans.

We studied chest wall kinematics and respiratory muscle action in five untrained healthy men walking on a motor-driven treadmill at 2 and 4 miles/h with constant grade (0%). The chest wall volume (Vcw), assessed by using the ELITE system, was modeled as the sum of the volumes of the lung-apposed rib cage (Vrc,p), diaphragm-apposed rib cage (Vrc,a), and abdomen (Vab). Esophageal and gastric pressures were measured simultaneously. Velocity of shortening (V(di)) and power [Wdi = diaphragm pressure (Pdi) x V(di)] of the diaphragm were also calculated. During walking, the progressive increase in end-inspiratory Vcw (P < 0.05) resulted from an increase in end-inspiratory Vrc,p and Vrc,a (P < 0.01). The progressive decrease (P < 0.05) in end-expiratory Vcw was entirely due to the decrease in end-expiratory Vab (P < 0.01). The increase in Vrc,a was proportionally slightly greater than the increase in Vrc,p, consistent with minimal rib cage distortion (2.5 +/- 0.2% at 4 miles/h). The Vcw end-inspiratory increase and end-expiratory decrease were accounted for by inspiratory rib cage (RCM,i) and abdominal (ABM) muscle action, respectively. The pressure developed by RCM,i and ABM and Pdi progressively increased (P < 0.05) from rest to the highest workload. The increase in V(di), more than the increase in the change in Pdi, accounted for the increase in Wdi. In conclusion, we found that, in walking healthy humans, the increase in ventilatory demand was met by the recruitment of the inspiratory and expiratory reserve volume. ABM action accounted for the expiratory reserve volume recruitment. We have also shown that the diaphragm acts mainly as a flow generator. The rib cage distortion, although measurable, is minimized by the coordinated action of respiratory muscles.     

Determinants of transdiaphragmatic pressure in dogs

We measured the transdiaphragmatic pressure (Pdi) during bilateral phrenic nerve stimulation and evaluated the determinants of its change with lung volume, chest wall geometry, and respiratory system impedance in supine dogs. Four rows of radiopaque markers were sewn onto muscle bundles of the costal and crural diaphragm between their origin on the central tendon and their insertion on the rib cage and spine. The length of the diaphragm (L) was determined from the projection images of marker rows using biplane fluoroscopy. Measurements were made at lung volumes between total lung capacity and functional residual capacity before and after the infusion of Ringer lactate solution into the abdominal cavity. In contrast to relaxation, during tetanic stimulation the active lengths of the muscle bundles were similar at all volumes, but the diaphragm assumed different shapes. Although the small differences in active muscle length with volume and liquid loads are consistent with only small changes in muscle force output, Pdi varied by a factor of greater than or equal to 5. There was no single L/Pdi curve that fitted all data during 50-Hz stimulations. We conclude that under these experimental conditions Pdi is not a unique measure of the force produced by the diaphragm and that lung volume, chest wall geometry, and respiratory system impedance are important determinants of the mechanical efficiency of the diaphragm as a pressure generator.     

Chest wall impedance partitioned into rib cage and diaphragm-abdominal pathways

We measured chest wall "pathway impedances" (ratios of pressure changes to rates of volume displacement at the surface) with esophageal and gastric balloons and inductance plethysmographic belts around the rib cage and abdomen during forced volume oscillations (5% vital capacity, 0.5-4 Hz) at the mouth of five relaxed, seated subjects. Volume displacements of the total chest wall surface, measured by summing the rib cage and abdominal signals, approximated measurements using volume-displacement, body plethysmography over the entire frequency range. Resistance (R) and elastance (E) of the diaphragm-abdomen pathway were several times greater than those of the rib cage pathway, except at the highest frequencies where diaphragm-abdominal E was small. R and E of the diaphragm-abdomen pathway and of the rib cage pathway showed the same frequency dependencies as that of the total chest wall: R decreased markedly as frequency increased, and E (especially in the diaphragm-abdomen) decreased at the highest frequencies. These results suggest that the chest wall can be reasonably modeled, over the frequency range studied, as a system with two major pathways for displacement. Each pathway seems to exhibit behavior that reflects nonlinear, rate-independent dissipation as well as viscoelastic properties. Impedances of these pathways are useful indexes of changes in chest wall mechanical behavior in different situations.     

Structural change of the thorax in chronic obstructive pulmonary disease.

This study examines structural changes of the thorax in hyperinflated subjects with chronic obstructive pulmonary disease (COPD). Age-matched normal subjects were used for comparison. Thoracic dimensions were determined using anteroposterior and lateral chest radiographs performed at total lung capacity, functional residual capacity, and residual volume. Rib cage dimensions (lateral diameter, rib angle, anteroposterior diameter) and diaphragm position were determined at each lung volume. There were no significant differences in rib cage dimension between the COPD and normal subjects for all lung volumes. In contrast, the diaphragm was significantly lower in the COPD subjects. The change of rib cage dimensions in the COPD subjects (for a similar volume change) was not different from that in normal subjects, whereas the change of diaphragm position in the COPD subjects (for a similar volume change) was reduced. In conclusion, the primary structural change of the thorax in COPD with chronic hyperinflation is confined to the diaphragm, with no appreciable structural change in the rib cage.     

The effect of carbon dioxide inhalation on phase characteristics of breathing movements in healthy newborn infants

Chest wall distortion (inward motion of the rib cage on inspiration) has been found recently to reduce the tidal volume during active sleep in the neonatal period. To determine some of the factors that relate to the chest wall distortion and the decreased tidal volume seen in active sleep, a quantification of the phase differences between the movements of the chest wall and those of the abdominal wall, and of the relation of their phase differences to tidal volume was performed on data obtained before and during carbon dioxide stimulation in 15 newborn infants sleeping in the prone position. In quiet sleep, the breathing movements were congruent and regular, and the tidal volume and the mean inspiratory flow increased during carbon dioxide stimulation. In active sleep during exposure to carbon dioxide, the chest wall distortion decreased, the breathing movements were incongruent and the degree of the chest wall distortion was negatively correlated with the tidal volume, while the tidal volume and the mean inspiratory flow was increased. Chest wall distortion did not appear in quiet sleep and was decreased in active sleep in spite of increased ventilation during CO2 stimulation. This study favours the idea that chest wall distortion is caused by a well regulated change in neuromuscular activity and not by the strength of diaphragmatic movements overcoming the mechanical stability of the rib cage.     

Relationships between abdominal and diaphragmatic volume displacements

We investigated the relationship between the volumes displaced by the diaphragm and the abdominal wall during spontaneous breathing in supine anesthetized dogs. Diaphragmatic volume displacement (Vdi) was calculated from measurements taken from anteroposterior fluoroscopic images employing a previously described geometric model. The volume displacement of the abdominal wall (Vabd) was measured with a calibrated Respitrace. Shortening of single diaphragm muscle bundles in costal and crural regions was measured as the distance between radiopaque beads sutured to the peritoneal surface of the muscle. We found that Vdi always exceeded Vabd, but Vabd/Vdi was larger in animals in which the abdominal wall was more compliant. In this preparation, Vdi is better correlated with costal than with crural shortening. Vabd did not correlate with either costal or crural shortening. We infer that the difference between Vdi and Vabd reflects the volume displacement of the lower rib cage caused by diaphragm contraction. This volume difference was tightly correlated with costal shortening. We conclude from these data that coupling between Vdi and Vabd is influenced by the relative compliances of the chest wall and abdomen. Shortening of regions of the diaphragm may have variable relationships to the measured volume displacement, but costal shortening is intimately related to expansion of the lower rib cage.     

Effect of position on the mechanical interaction between the rib cage and abdomen in preterm infants.

To determine the influence of body position on chest wall and pulmonary function, we studied the ventilatory, pulmonary mechanics, and thoracoabdominal motion profiles in 20 preterm infants recovering from respiratory disease who were positioned in both the supine and prone position. Thoracoabdominal motion was assessed from measurements of relative rib cage and abdominal movement and the calculated phase angle (an index of thoracoabdominal synchrony) of the rib and abdomen Lissajous figures. The ventilatory and pulmonary function profiles were assessed from simultaneous measurements of transpulmonary pressure, airflow, and tidal volume. The infants were studied in quiet sleep, and the order of positioning was randomized across patients. The results demonstrated no significant difference in ventilatory and pulmonary function measurements as a function of position. In contrast, there was a significant reduction (-49%) in the phase angle of the Lissajous figures and an increase (+66%) in rib cage motion in prone compared with the supine position. In addition, the degree of improvement in phase angle in the prone position was correlated to the severity of asynchrony in the supine position. We speculate that the improvement in thoracoabdominal synchrony in the prone position is related to alterations of chest wall mechanics and respiratory muscle tone mediated by a posturally related shift in the area of apposition of the diaphragm to the anterior inner rib cage wall and increase in passive tension of the muscles of the rib cage. This study suggests that the mechanical advantage associated with prone positioning may confer a useful alternative breathing pattern to the preterm infant in whom elevated respiratory work loads and respiratory musculoskeletal immaturity may predispose to respiratory failure.     

Effect of respiratory muscle tension on lung volume.

The chest wall is modeled as a linear system for which the displacements of points on the chest wall are proportional to the forces that act on the chest wall, namely, airway opening pressure and active tension in the respiratory muscles. A standard theorem of mechanics, the Maxwell reciprocity theorem, is invoked to show that the effect of active muscle tension on lung volume, or airway pressure if the airway is closed, is proportional to the change of muscle length in the relaxation maneuver. This relation was tested experimentally. The shortening of the cranial-caudal distance between a rib pair and the sternum was measured during a relaxation maneuver. These data were used to predict the respiratory effect of forces applied to the ribs and sternum. To test this prediction, a cranial force was applied to the rib pair and a caudal force was applied to the sternum, simulating the forces applied by active tension in the parasternal intercostal muscles. The change in airway pressure, with lung volume held constant, was measured. The measured change in airway pressure agreed well with the prediction. In some dogs, nonlinear deviations from the linear prediction occurred at higher loads. The model and the theorem offer the promise that existing data on the configuration of the chest wall during the relaxation maneuver can be used to compute the mechanical advantage of the respiratory muscles.     

Effect of mechanical loading on displacements of chest wall during breathing in humans

Using a respiratory inductive plethysmograph (Respitrace) we studied thoracoabdominal movements in eight normal subjects during inspiratory resistive (Res) and elastic (El) loading. The magnitude of loads was chosen so as to produce a fall in inspiratory mouth pressure of 20 cmH2O. The contribution of rib cage (RC) to tidal volume (VT) increased significantly from 68% during quiet breathing (QB) to 74% during El and 78% during Res. VT and breathing frequency did not change significantly. During loading a phase lag was present on inspiration so that the abdomen led the rib cage. However, outward movement of the abdomen ceased in the latter part of inspiration, and the RC became the sole contributor to VT. These observations suggest greater recruitment of the inspiratory musculature of the RC than the diaphragm during loading, although changes in the mechanical properties of the chest wall may also have contributed. Indeed, an increase in abdominal end-expiratory and end-inspiratory pressures was observed in five out of six subjects, indicating abdominal muscle recruitment which may account for part of the reduction in abdominal excursion. Both Res and El increased the rate of emptying of the respiratory system during the ensuing unloaded expiration as a result of a reduction in rib cage expiratory-braking mechanisms. The time course of abdominal displacements during expiration was unaffected by loading.     

Respiratory mechanical effects of abdominal distension

We develop a theory to predict the partitioning of a change in volume of the abdominal contents into the end-expiratory volume changes of the lung, rib cage, and anterior abdominal wall. First, we calculate the distribution of such a volume change using the relative compliances of the three compartments. We then consider the inspiratory influence of abdominal pressure on the rib cage and its effect on the distribution of this volume. We test our theory by inducing gastric distension in three experienced laboratory personnel. We instilled and subsequently withdrew 1 liter of water from a gastric balloon and examined the effects of this change in gastric volume on the relaxation characteristics of the respiratory system. The distribution of the volume change that would be expected from the observed relative compliances of the three compartments would be approximately 66% into change in lung volume, 25% into change in rib cage volume, and 9% into change in abdominal volume. Instead, in line with our predictions for acute gastric distension, approximately 33% went into decrease in lung volume, 40% into increase in rib cage volume, and 26% into increase in abdominal volume. These results suggest that the interactions among the rib cage, abdomen, and diaphragm are such as to defend against large changes in end-expiratory lung volume in the face of abdominal distension.     

Shape and size of the human diaphragm in vivo

Serial computerized tomograph (CT) sections at 5-mm intervals of a human diaphragm in relaxed and contracted states were obtained in one subject while he held his breath and lay supine in a CT scanner. All sections for one state were scanned at the same chest wall configuration as monitored by rib cage and abdominal dimensions, using magnetometers. Sections were scanned at relaxed functional residual capacity and after inspiring approximately 1 liter in such a way that rib cage dimensions increased only slightly. Models of the diaphragm dome in the two states were constructed from the sets of serial sections. Diaphragm length and volume displaced were measured, the zone of apposition of diaphragm to rib cage was mapped, and the line of the diaphragm silhouette in anteroposterior and lateral X-rays identified. Coronal and sagittal sections were constructed. In the inspiration studied, the diaphragm movement displaced 680 ml. Meridian lines in sagittal, coronal, and transverse directions over the right hemidiaphragm dome shortened by 6.7-7.2 cm, but over the left dome by only 4.0-4.3 cm. Lines of X-ray silhouettes were close to meridian lines, and estimates of shortening were similar to those made previously from X-rays. The peculiar saddle shape of the muscle may help the hemidiaphragms to operate independently, the fibers of the saddle acting as an anchor for midline directed fibers of the hemidiaphragm domes. The shape of the diaphragm also has implications for the distribution of transdiaphragmatic pressure and for the kind of distortion of the lower rib cage margin that is seen during inspirations at high lung volume.