Altered thoracic gas compression contributes to improvement in spirometry with lung volume reduction surgery.

BACKGROUND: Thoracic gas compression (TGC) exerts a negative effect on forced expiratory flow. Lung resistance, effort during a forced expiratory manoeuvre, and absolute lung volume influence TGC. Lung volume reduction surgery (LVRS) reduces lung resistance and absolute lung volume. LVRS may therefore reduce TGC, and such a reduction might explain in part the improvement in forced expiratory flow with the surgery. A study was conducted to determine the effect of LVRS on TGC and the extent to which reduced TGC contributed to an improvement in forced expiratory volume in 1 second (FEV1) following LVRS. METHODS: The effect of LVRS on TGC was studied using prospectively collected lung mechanics data from 27 subjects with severe emphysema. Several parameters including FEV1, expiratory and inspiratory lung resistance (Rle and Rli), and lung volumes were measured at baseline and 6 months after surgery. Effort during the forced manoeuvre was measured using transpulmonary pressure. A novel method was used to estimate FEV1 corrected for the effect of TGC. RESULTS: At baseline the FEV1 corrected for gas compression (NFEV1) was significantly higher than FEV1 (p<0.0001). FEV1 increased significantly from baseline (p<0.005) while NFEV1 did not change following surgery (p>0.15). TGC decreased significantly with LVRS (p<0.05). Rle and maximum transpulmonary pressure (TP(peak)) during the forced manoeuvre significantly predicted the reduction in TGC following the surgery (Rle: p<0.01; TP(peak): p<0.0001; adjusted R2 = 0.68). The improvement in FEV1 was associated with the reduction in TGC after surgery (p<0.0001, adjusted R2 = 0.58). CONCLUSIONS: LVRS decreased TGC by improving expiratory flow limitation. In turn, the reduction in TGC decreased its negative effect on expiratory flow and therefore explained, in part, the improvement in FEV1 with LVRS in this cohort.

Effects of smooth muscle activation on axial mechanical properties of excised canine bronchi.

This study tested the hypothesis that airway smooth muscle (ASM) activation produces an airway active axial force (AAAF). Bronchi (n = 10) immersed in a tissue bath containing 95% O2-5% CO2-equilibrated Krebs solution were subjected to passive axial lengthening and shortening at 0-20 cmH2O of transmural pressure. ASM was relaxed with isoproterenol and activated with methacholine. Axial tensile (epsilonx), transverse compressive (epsilony), and shear strains (epsilonxy) were computed from the displacements of four markers placed onto the specimen's surface. The AAAF was estimated by subtracting the control axial force (AF) values at a given epsilonx from those obtained after methacholine. epsilonx-AF relationships were curvilinear, with maximum epsilonx being approached at approximately 15 g of AF. The epsilony decreased during bronchial lengthening. Cholinergic stimulation produced 1) a decrease of both epsilonx and epsilony at a given AF relative to control, indicating ASM shortening, and 2) an AAAF that increased with increasing epsilonx and transmural pressure. A portion of the work of expanding the lungs is required to lengthen the airways; therefore, an AAAF would increase lung elastance and recoil.

Modeling the kinematics of the canine midcostal diaphragm.

The hypotheses that the chest wall insertion (CW) is displaced laterally during inspiration and that this displacement is essential in maintaining muscle curvature of the costal diaphragmatic muscle fibers were tested. With the use of data from three dogs, caudal, lateral, and ventral displacements of CW during both quiet, spontaneous inspiration and during inspiratory efforts against an occluded airway were observed and recorded. We have developed a kinematic model of the diaphragm that incorporates these displacements. This model describes the motions of the muscle fibers and central tendon; the displacements of the midplane, muscle-tendon junction (MTJ), CW, and center of the muscle fiber-central tendon arcs are modeled as functions of muscle fiber length. In the model, the center of the fiber arcs and MTJ both move caudally parallel to the midplane during inspiration, whereas CW moves both caudally and laterally. The observed lateral displacement of CW and the observed caudal displacement of MTJ, as functions of muscle fiber length, both approximate well the theoretical displacements that would be necessary to maintain curvature of the fiber arcs. In confirming our hypotheses, we have found that lateral displacement of CW is a mechanism by which changes in the shape of the costal diaphragm, as described by its curvature, are limited.

Desmin integrates the three-dimensional mechanical properties of muscles.

Striated muscle is a linear motor whose properties have been defined in terms of uniaxial structures. The question addressed here is what contribution is made to the properties of this motor by extramyofilament cytoskeletal structures that are not aligned in parallel with the myofilaments. This question arose from observations that transverse loads increase muscle force production in diaphragm but not in the hindlimb muscle, thereby indicating the presence of structures that couple longitudinal and transverse properties of diaphragmatic muscle. Furthermore, we find that the diaphragms of null mutants for the cytoskeletal protein desmin show 1) significant reductions in coupling between the longitudinal and transverse properties, indicating for the first time a role for a specific protein in integrating the three-dimensional mechanical properties of muscle, 2) significant reductions in the stiffness and viscoelasticity of muscle, and 3) significant increases in tetanic force production. Thus desmin serves a complex mechanical function in diaphragm muscle by contributing both to passive stiffness and viscoelasticity and to modulation of active force production in a three-dimensional structural network. Our finding changes the paradigm of force transmission among cells by placing our understanding of the function of the cytoskeleton in the context of the structural and mechanical complexity of muscles.

Shape and tension distribution of the passive rat diaphragm.

We developed an in vitro preparation to investigate shape and stress distribution in the intact rat diaphragm. Our hypothesis was that the diaphragm is anisotropic with smaller compliance in transverse fiber direction than along fibers, and therefore shape change may be small. After the animals were killed (8 rats), the entire diaphragm was excised and fixed into a mold at the insertions. Oxygenated Krebs-Ringer solution was circulated under the diaphragm and perfused over its surface. A total of 20-23 small markers were sutured on the diaphragm surface. At transdiaphragmatic pressure (P(di)) of 3-15 cmH(2)O, curvature was smaller in transverse direction than along fibers. Using finite element analysis we computed membrane tension. At P(di) of 15 cmH(2)O, tension in central tendon was larger than muscle. In costal region maximum principal tension (sigma(1)) is essentially along the fibers and ranged from 6-10 g/cm. Minimum principal tension (sigma(2)) was 0. 3-4 g/cm. In central tendon, sigma(1) was 10-15 g/cm, compared with 4-10 g/cm for sigma(2). The diaphragm was considerably stiffer in transverse fiber direction than along the fibers.

Inferences on force transmission from muscle fiber architecture of the canine diaphragm.

Functional properties of the diaphragm are mediated by muscle structure. Modeling of force transmission necessitates a precise knowledge of muscle fiber architecture. Because the diaphragm experiences loads both along and transverse to the long axes of its muscle fibers in vivo, the mechanism of force transmission may be more complex than in other skeletal muscles that are loaded uniaxially along the muscle fibers. Using a combination of fiber microdissections and histological and morphological methods, we determined regional muscle fiber architecture and measured the shape of the cell membrane of single fibers isolated from diaphragm muscles from 11 mongrel dogs. We found that muscle fibers were either spanning fibers (SPF), running uninterrupted between central tendon (CT) and chest wall (CW), or were non-spanning fibers (NSF) that ended within the muscle fascicle. NSF accounted for the majority of fibers in the midcostal, dorsal costal, and lateral crural regions but were only 25-41% of fibers in the sternal region. In the midcostal and dorsal costal regions, only approximately 1% of the NSF terminated within the fascicle at both ends; the lateral crural region contained no such fibers. We measured fiber length, tapered length, fiber diameters along fiber length, and the taper angle for 271 fibers. The lateral crural region had the longest mean length of SPF, which is equivalent to the mean muscle length, followed by the costal and sternal regions. For the midcostal and crural regions, the percentage of tapered length of NSF was 45.9 +/- 5.3 and 40.6 +/- 7.5, respectively. The taper angle was approximately 0.15 degrees for both, and, therefore, the shear component of force was approximately 380 times greater than the tensile component. When the diaphragm is submaximally activated, as during normal breathing and maximal inspiratory efforts, muscle forces could be transmitted to the cell membrane and to the extracellular intramuscular connective tissue by shear linkage, presumably via structural transmembrane proteins.

A model for influence of exercise on formation and growth of tissue bubbles during altitude decompression.

In response to exercise performed before or after altitude decompression, physiological changes are suspected to affect the formation and growth of decompression bubbles. We hypothesized that the work to change the size of a bubble is done by gas pressure gradients in a macro- and microsystem of thermodynamic forces and that the number of bubbles formed through time follows a Poisson process. We modeled the influence of tissue O(2) consumption on bubble dynamics in the O(2) transport system in series against resistances, from the alveolus to the microsystem containing the bubble and its surrounding tissue shell. Realistic simulations of experimental decompression procedures typical of actual extravehicular activities were obtained. Results suggest that exercise-induced elevation of O(2) consumption at altitude leads to bubble persistence in tissues. At the same time, exercise-enhanced perfusion leads to an overall suppression of bubble growth. The total volume of bubbles would be reduced unless increased tissue motion simultaneously raises the rate of bubble formation through cavitation processes, thus maintaining or increasing total bubble volume, despite the exercise.

Predicting time to decompression illness during exercise at altitude, based on formation and growth of bubbles.

For altitude decompressions, we hypothesized that reported onset times of limb decompression illness (DCI) pain symptoms follow a probability distribution related to total bubble volume [V(b.)(t)] as a function of time. Furthermore, we hypothesized that the probability of ever experiencing DCI during a decompression is associated with the cumulative volume of bubbles formed. To test these hypotheses, we first used our previously developed formation-and-growth model (Am J Physiol Regulatory Integrative Comp Physiol 279: R2304-R2316, 2000) to simulate Vb.(t) for 20 decompression profiles in which 334 human subjects performed moderate repetitive skeletal muscle exercise (827 kJ/h) in an altitude chamber. Using survival analysis, we determined that, for a controlled condition of exercise, the fraction of the subject population susceptible to DCI can be approximately expressed as a power function of the formation-and-growth model-predicted cumulative volume of bubbles throughout the altitude exposure. Furthermore, for this fraction, the probability density distribution of DCI onset times is approximately equal to the ratio of the time course of formation-and growth-modeled total bubble volume to the predicted cumulative volume.

Biaxial constitutive relations for the passive canine diaphragm.

Samples of the muscular sheet excised from the midcostal region of dog diaphragms were subjected to biaxial loading. That is, stresses in the direction of the muscle fibers and in the direction perpendicular to the fibers in the plane of the sheet were measured at different combinations of strains in the two directions. Stress-strain relations were obtained by fitting equations to these data. In the direction of the muscle fibers, for strains up to 0.7, stress is a modestly nonlinear function of strain and ranges up to approximately 60 g/cm. In the direction perpendicular to the fibers, the sheet is stiffer and more strongly nonlinear. At a strain in the perpendicular direction of approximately 0.35, stress increases abruptly. The stress-strain relation in the muscle direction is consistent with observations of passive muscle shortening in vivo. However, the stiffness in the perpendicular direction is not high enough to explain the observation that strains in the perpendicular direction in vivo are nearly zero. We conclude that, in the passive diaphragm in vivo, stress in the direction perpendicular to the muscle fibers is small.

Shape of the canine diaphragm.

In an earlier study (Angelillo M, Boriek AM, Rodarte JR, and Wilson TA. J Appl Physiol 83: 1486-1491, 1997), we proposed a mathematical theory for the structure and shape of the diaphragm. Muscle bundles were assumed to lie on lines that are simultaneously geodesics and lines of principal curvature of the diaphragm surface, and the class of surfaces that are formed by line elements that are both geodesics and lines of principal curvature was described. Here we present data on the shape of the canine diaphragm that were obtained by the radiopaque marker technique, and we describe a surface that fits the data and satisfies the requirements of the theory. The costal and crural diaphragms are fit by cyclides with radii of 3.7 and 2.3 cm, respectively. In addition, the theory is extended to include the description of a joint between cyclides, and the observed properties of the joint between the costal and crural diaphragms at the dorsal end of the costal diaphragm match those required by the theory.

Ratio of active to passive muscle shortening in the canine diaphragm.

Active and passive shortening of muscle bundles in the canine diaphragm were measured with the objective of testing a consequence of the minimal-work hypothesis: namely, that the ratio of active to passive shortening is the same for all active muscles. Lengths of six muscle bundles in the costal diaphragm and two muscle bundles in the crural diaphragm of each of four bred-for-research beagle dogs were measured by the radiopaque marker technique during the following maneuvers: a passive deflation maneuver from total lung capacity to functional residual capacity, quiet breathing, and forceful inspiratory efforts against an occluded airway at different lung volumes. Shortening per liter increase in lung volume was, on average, 70% greater during quiet breathing than during passive inflation in the prone posture and 40% greater in the supine posture. For the prone posture, the ratio of active to passive shortening was larger in the ventral and midcostal diaphragm than at the dorsal end of the costal diaphragm. For both postures, active shortening during quiet breathing was poorly correlated with passive shortening. However, shortening during forceful inspiratory efforts was highly correlated with passive shortening. The average ratios of active to passive shortening were 1.23 +/- 0.02 and 1.32 +/- 0.03 for the prone and supine postures, respectively. These data, taken together with the data reported in the companion paper (T. A. Wilson, M. Angelillo, A. Legrand, and A. De Troyer, J. Appl. Physiol. 87: 554-560, 1999), support the hypothesis that, during forceful inspiratory efforts, the inspiratory muscles drive the chest wall along the minimal-work trajectory.

Mechanical advantage of the canine diaphragm.

The mechanical advantage (mu) of a respiratory muscle is defined as the respiratory pressure generated per unit muscle mass and per unit active stress. The value of mu can be obtained by measuring the change in the length of the muscle during inflation of the passive lung and chest wall. We report values of mu for the muscles of the canine diaphragm that were obtained by measuring the lengths of the muscles during a passive quasistatic vital capacity maneuver. Radiopaque markers were attached along six muscle bundles of the costal and two muscle bundles of the crural left hemidiaphragms of four bred-for-research beagle dogs. The three-dimensional locations of the markers were obtained from biplane video-fluoroscopic images taken at four volumes during a passive relaxation maneuver from total lung capacity to functional residual capacity in the prone and supine postures. Muscle lengths were determined as a function of lung volume, and from these data, values of mu were obtained. Values of mu are fairly uniform around the ventral midcostal and crural diaphragm but significantly lower at the dorsal end of the costal diaphragm. The average values of mu are -0.35 +/- 0.18 and -0.27 +/- 0.16 cmH2O. g-1. kg-1. cm-2 in the prone and supine dog, respectively. These values are 1. 5-2 times larger than the largest values of mu of the intercostal muscles in the supine dog. From these data we estimate that during spontaneous breathing the diaphragm contributes approximately 40% of inspiratory pressure in the prone posture and approximately 30% in the supine posture. Passive shortening, and hence mu, in the upper one-third of inspiratory capacity is less than one-half of that at lower lung volume. The lower mu is attributed primarily to a lower abdominal compliance at high lung volume.

Muscle fiber architecture of the dog diaphragm.

Previous measurements of muscle thickness and length ratio of costal diaphragm insertions in the dog (A. M. Boriek and J. R. Rodarte. J. Appl. Physiol. 77: 2065-2070, 1994) suggested, but did not prove, discontinuous muscle fiber architecture. We examined diaphragmatic muscle fiber architecture using morphological and histochemical methods. In 15 mongrel dogs, transverse sections along the length of the muscle fibers were analyzed morphometrically at x20, by using the BioQuant System IV software. We measured fiber diameters, cross-sectional fiber shapes, and cross-sectional area distributions of fibers. We also determined numbers of muscle fibers per cross-sectional area and ratio of connective tissue to muscle fibers along a course of the muscle from near the chest wall (CW) to near the central tendon (CT) for midcostal left and right hemidiaphragms, as well as ventral, middle, and dorsal regions of the left costal hemidiaphragm. In six other mongrel dogs, the macroscopic distribution of neuromuscular junctions (NMJ) on thoracic and abdominal diaphragm surfaces was determined by staining the intact diaphragmatic muscle for acetylcholinesterase activity. The average major diameter of muscle fibers was significantly smaller, and the number of fibers was significantly larger midspan between CT and CW than near the insertions. The ratio of connective tissues to muscle fibers was largest at CW compared with other regions along the length of the muscle. The diaphragm is transversely crossed by multiple scattered NMJ bands with fairly regular intervals offset in adjacent strips. Muscle fascicles traverse two to five NMJ, consistent with fibers that do not span the entire fascicle from CT to CW. These results suggest that the diaphragm has a discontinuous fiber architecture in which contractile forces may be transmitted among the muscle fibers through the connective tissue adjacent to the fibers.

Kinematics and mechanics of midcostal diaphragm of dog.

Radiopaque markers were attached to the peritoneal surface of three neighboring muscle bundles in the midcostal diaphragm of four dogs, and the locations of the markers were tracked by biplanar video fluoroscopy during quiet spontaneous breathing and during inspiratory efforts against an occluded airway at three lung volumes from functional residual capacity to total lung capacity in both the prone and supine postures. Length and curvature of the muscle bundles were determined from the data on marker location. Muscle lengths for the inspiratory states, as a fraction of length at functional residual capacity, ranged from 0.89 +/- 0.04 at end inspiration during spontaneous breathing down to 0.68 +/- 0.07 during inspiratory efforts at total lung capacity. The muscle bundles were found to have the shape of circular arcs, with the three bundles forming a section of a right circular cylinder. With increasing lung volume and diaphragm displacement, the circular arcs rotate around the line of insertion on the chest wall, the arcs shorten, but the radius of curvature remains nearly constant. Maximal transdiaphragmatic pressure was calculated from muscle curvature and maximal tension-length data from the literature. The calculated maximal transdiaphragmatic pressure-length curve agrees well with the data of Road et al. (J. Appl. Physiol. 60: 63-67, 1986).

Effects of transverse fiber stiffness and central tendon on displacement and shape of a simple diaphragm model.

Our previous experimental results (A. M. Boriek, S. Lui, and J. R. Rodarte. J. Appl. Physiol. 75: 527-533, 1993 and A. M. Boriek, T. A. Wilson, and J. R. Rodarte. J. Appl. Physiol. 76: 223-229, 1994) showed that 1) costal diaphragm shape is similar at functional residual capacity and end inspiration regardless of whether the diaphragm muscle shortens actively (increased tension) or passively (decreased tension); 2) diaphragmatic muscle length changes minimally in the direction transverse to the muscle fibers, suggesting the diaphragm may be inextensible in that direction; and 3) the central tendon is not stretched by physiological stresses. A two-dimensional orthotropic material has two different stiffnesses in orthogonal directions. In the plane tangent to the muscle surface, these directions are along the fibers and transverse to the fibers. We wondered whether orthotropic material properties in the muscular region of the diaphragm and inextensibility of the central tendon might contribute to the constancy of diaphragm shape. Therefore, in the present study, we examined the effects of stiffness transverse to muscle fibers and inextensibility of the central tendon on diaphragmatic displacement and shape. Finite element hemispherical models of the diaphragm were developed by using pressurized isotropic and orthotropic membranes with a wide range of stiffness ratios. We also tested heterogeneous models, in which the muscle sheet was an orthotropic material, having transverse fiber stiffness greater than that along the fibers, with the central tendon being an inextensible isotropic cap. These models revealed that increased transverse stiffness limits the shape change of the diaphragm. Furthermore, an inextensible cap simulating the central tendon dramatically limits the change in shape as well as the membrane displacement in response to pressure. These findings provide a plausible mechanism by which the diaphragm maintains similar shapes despite different physiological loads. This study suggests that changes of diaphragm shape are restricted because the central tendon is essentially inextensible and stiffness in the direction transverse to the muscle fibers is greater than stiffness along the fibers.

Theory of diaphragm structure and shape.

The muscle bundles of the diaphragm form a curved sheet that extends from the chest wall to the central tendon. Each muscle bundle exerts a force in the direction of its curvature; the magnitude of this force is proportional to the curvature of the bundle. The contribution of this force to transdiaphragmatic pressure is maximal if the direction of bundle curvature is orthogonal to the surface and the curvature is maximal. That is, the contribution of muscle tension to transdiaphragmatic pressure is maximal if the muscle bundles lie along lines that are both geodesics and lines of maximal principal curvature of the surface. A theory of diaphragm shape is developed from the assumption that all muscle bundles have these optimal properties. The class of surfaces that are formed of line elements that are both geodescis and lines of principal curvature is described. This class is restricted. The lines that form the surface must lie in planes, and all lines must have the same shape. In addition, the orientation of the lines is restricted. An example of this class that is similar to the shape of the canine diaphragm is described, and the stress distribution in this example is analyzed.

Zone of apposition in the passive diaphragm of the dog.

We determined the regional area of the diaphragmatic zone of apposition (ZAP) as well as the regional craniocaudal extent of the ZAP (ZAPht) of the passive diaphragm in six paralyzed anesthetized beagle dogs (8-12 kg) at residual lung volume (RV), functional residual capacity (FRC), FRC + 0.25 and FRC + 0.5 inspiratory capacity, and total lung capacity (TLC) in prone and supine postures. To identify the caudal boundary of the ZAP, 17 lead markers (1 mm) were sutured to the abdominal side of the costal and crural diaphragms around the diaphragm insertion on the chest wall. Two weeks later, the dogs' caudal thoraces were scanned by the use of the dynamic spatial reconstructor (DSR), a prototype fast volumetric X-ray computer tomographic scanner, developed at the Mayo Clinic. The three-dimensional spatial coordinates of the markers were identified (+/- 1.4 mm), and the cranial boundary of the ZAP was determined from 30-40 1.4-mm-thick sagittal and coronal slices in each DSR image. We interpolated the DSR data to find the position of the cranial and caudal boundaries of the ZAP every 5 degrees around the thorax and computed the distribution of regional variation of area of the ZAP and ZAPht as well as the total area of ZAP. The ZAPht and area of ZAP increased as lung volume decreased and were largest near the lateral extremes of the rib cage. We measured the surface area of the rib cage cephaled to the ZAP (AL) in both postures in another six beagle dogs (12-16 kg) of similar stature, scanned previously in the DSR. We estimated the entire rib cage surface area (Arc = AZAP + AL). The AZAP as a percentage of Arc increased more than threefold as lung volume decreased from TLC to RV, from approximately 9 to 29% of Arc.

Inferences on passive diaphragm mechanics from gross anatomy.

The diaphragm is a relatively thin curved structure that is categorized in mechanics as a membrane. Tension in the membrane is given by the product of muscle thickness and stress parallel to the fiber bundles. If all muscle fibers were cylindrical and extended from origin to insertion, the ratio of thickness near the chest wall (CW) to thickness near the central tendon (CT) would vary inversely with the ratio of CW to CT perimeters. In freshly excised diaphragms of 36 mongrel dogs, the ratios of the perimeters (CT/CW) in the right and left costal diaphragm were 0.63 +/- 0.04 and 0.62 +/- 0.04, respectively. The means of the ratio of thickness near CW to that near CT in the right and left costal regions were 0.96 +/- 0.07 and 0.95 +/- 0.05, respectively, consistent with a nearly constant relationship between costal diaphragm membrane tension and muscle stress in the direction of the fibers. In the crural diaphragm, the average ratio of the perimeters of the insertions on CT to CW was 1.16 +/- 0.10. The average ratio of thickness of crural CW to CT was 1.25 +/- 0.11. The discrepancy between the perimeter ratio and thickness ratio in the costal diaphragm is incompatible with the muscle consisting of uniform fibers extending from CW to CT. Our data suggest that muscle fibers are either in series with a smaller number along the smaller perimeter or that they terminate by tapering within the muscle bundle. Both arrangements are consistent with previous anatomic studies (Gordon et al. J. Morphol. 201: 131-143, 1989). Having a nonuniform number of fibers mechanically in series is compatible with uniform stress in the fibers if the membrane is sufficiently curved as in a domed structure.

Displacements and strains in the costal diaphragm of the dog.

Radiopaque markers were attached at 1- to 2-cm intervals along three nearby muscle bundles to cover rectangular regions of the mid-costal diaphragms of seven dogs. The markers were tracked by biplane video fluoroscopy during spontaneous breathing (SB), mechanical ventilation with the same tidal volume (MV), and at inflation to total lung capacity (TLC) in the prone and supine positions. The three-dimensional positions of the markers at functional residual capacity (FRC), at end inspiration during SB and MV, and at TLC were determined, and the strains in the plane of the diaphragm relative to FRC were calculated. The principal strains were found to lie nearly along the muscle bundle direction and perpendicular to it. The principal strains along the muscle bundles, which describe muscle shortening, were uniform among the three bundles and uniform along the bundle for MV. For SB, in the prone and supine positions, shortening was approximately 30% greater in the middle of the bundle than near the central tendon and chest wall. Although the tidal volumes were the same for SB and MV, the shortening was larger for SB. The strains perpendicular to the bundle direction were not significantly different from zero. It appears that, for the loads that occur during tidal breathing, the diaphragm is inextensible in the direction perpendicular to the muscle direction. There is a very small displacement of the costal diaphragm at its insertion on the chest wall. The displacement at the central tendon is primarily a result of muscle shortening and rotation of the arc of the muscle around its insertion on the chest wall.

Costal diaphragm curvature in the dog.

The curvature of the midcostal region of the diaphragm in seven dogs was determined at functional residual capacity (FRC) and end inspiration during spontaneous breathing and mechanical ventilation and at total lung capacity in the prone and supine positions. Metallic markers were attached to muscle fibers on the abdominal surface of the diaphragm, and the dog was allowed to recover from surgery. The three-dimensional positions of the markers were determined by biplane videofluoroscopy. A quadratic surface was fit to the bead positions. The principal axes of the quadratic surface lie nearly along and perpendicular to the muscle fibers. In both the supine and prone positions, the values of the principal curvatures were similar at FRC and end inspiration during spontaneous breathing, when muscle tension and transdiaphragmatic pressure both increase with increasing lung volume, and during mechanical ventilation and passive inflation to total lung capacity, when both decrease relative to their magnitude at FRC. No abrupt change of curvature, which might be expected at the edge of the zone of apposition, was apparent. The curvature along the muscle fiber was 0.35 +/- 0.07 cm-1; the curvature perpendicular to the muscle fiber was much smaller, 0.06 +/- 0.01 cm-1. The costal region of the diaphragm displaces and shortens as lung volume increases, but its shape, as described by its curvatures, does not change substantially.