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1 Baylor College of Medicine, Houston, Texas 77030; and 2 Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
ABSTRACT 
Boriek, Aladin M., Joseph R. Rodarte, and Theodore A. Wilson. Kinematics and mechanics of midcostal diaphragm of dog. J. Appl. Physiol. 83(4):
1068-1075, 1997.
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).
respiration; chest wall; muscle; transdiaphragmatic pressure
INTRODUCTION THE MUSCLE BUNDLES of the diaphragm lie along curved
lines, and the sheet of muscle bundles together with the central tendon (CT) form a curved membrane. The pressure difference across this membrane, transdiaphragmatic pressure (Pdi), is given by the product of
two factors, tension and curvature, and failure to generate Pdi could
be caused by loss of either tension or curvature. Both of these
mechanisms seem plausible. The muscles of the diaphragm shorten
significantly as lung volume increases (3), and active muscle tension
decreases with decreasing length (5). It also seems likely
that diaphragm curvature would decrease as the diaphragm descends. In
humans with emphysema and hyperexpanded lungs, the diaphragm is
depressed and in lateral X-rays the curvature appears to be smaller
than normal (14, 16). Experimental evidence for both mechanisms has
been reported. Road et al. (13) measured Pdi and muscle length during
phrenic nerve stimulation in dogs. In their preparation, the rib cage
was open, and the abdomen was encased in a cast with adjustable volume.
As abdominal volume was displaced and the diaphragm descended, Pdi at
maximal muscle stimulation decreased. The shape of the relation between
Pdi and muscle length matched the shape of the force-length curve of
diaphragm muscle, and Road et al. concluded, in agreement with earlier
work of Kim et al. (11), that curvature remained constant and that the
decrease of Pdi was caused by decreasing tension due to muscle shortening. On the other hand, Hubmayr et al. (9) measured Pdi and
muscle length during phrenic nerve stimulation in intact animals at
different lung volumes and reached a different conclusion. For maximal
stimulation, the Pdi vs. muscle-length curve was steeper than the
muscle force-length curve, and they concluded that change of shape
contributed to decreasing Pdi at high lung volume.
Both the experiments of Road et al. (13) and the experiments of Hubmayr
et al. (9) were not physiological. In both, the diaphragm was activated
by maximal phrenic nerve stimulation. As a result, the diaphragm was
maximally active, whereas other inspiratory muscles were silent. In the
experiment of Road et al., the shapes of the abdomen and lower rib cage
were constrained by the cast, and the lower chest wall (CW) was
probably less distorted than in the experiments of Hubmayr et al., but
muscle length could not be related to lung volume because the rib cage
was open. In the experiment of Hubmayr et al., the CW was distorted,
because the muscles of the rib cage were silent, and the rib cage
displaced paradoxically inward during diaphragm contraction.
In this paper, we report data on the relations among muscle shape,
muscle length, and lung volume for physiological states of inspiratory
muscle activation in prone and supine anesthetized dogs. In previous
studies (1, 3), we measured shape and muscle shortening in the
midcostal diaphragm during quiet breathing and passive lung inflation.
The current study extends that work to measurements of diaphragm shape
and muscle shortening during forceful inspiratory efforts (IEs) at lung
volumes from functional residual capacity (FRC) to total lung capacity
(TLC). The methods are the same as those used in the previous study.
Radiopaque markers were placed along three muscle bundles in the
midcostal diaphragm, and the length and shape of these fibers were
determined from biplanar videofluoroscopic images of marker locations.
Airway opening pressure and esophageal and gastric pressures (Pes and Pg, respectively) were measured. Data were obtained for
FRC during quiet spontaneous breathing (SB) and for four
active inspiratory states: end inspiration (EI) during SB, and during
maximal spontaneous IE with the airway occluded at three lung volumes:
FRC, FRC + 1/2 inspiratory capacity (IC), and TLC. Muscle lengths for
the five maneuvers ranged from length at FRC
(LFRC) to
~0.7 LFRC.
Our results are similar to our earlier results for quiet breathing and
passive inflation (1). We find that these muscle bundles of the
midcostal diaphragm have the shape of circular arcs. The muscles
shorten, and the arc of the muscles rotates around the line of
insertion on the CW as the diaphragm descends, but curvature remains
nearly constant. We incorporated these observations into a kinematic
model that describes muscle shortening with constant curvature. From
muscle curvature and values of muscle tension taken from the maximal
tension-length curve reported by Farkas and Rochester (5), we
calculated Pdi for maximal tension
(Pdimax). As lung volume
increases and the diaphragm descends, muscle curvature remains nearly
constant and Pdimax decreases,
because maximal muscle tension decreases with decreasing length.
However, the kinematic model predicts that diaphragm curvature depends
strongly on the diameter of the ring of insertion of the diaphragm on
the CW. If the rib cage and the ring of insertion were enlarged,
diaphragm curvature would be reduced and curvature would decrease as
the muscle shortens. In that case,
Pdimax and the range of diaphragm displacement would be reduced.
METHODS Four bred-for-research beagle dogs, weighing between 9.9 and 10.5 kg,
were surgically prepared, using the same methods that we have used
previously (1, 3). The abdomen was opened by midline laparotomy, and
2-mm silicon-coated lead spheres were stitched to the peritoneal
surface of muscle bundles in the midcostal region of the left
diaphragm. The locations of the markers are shown in Fig.
1. Four markers were placed along each of
three nearby muscle bundles: one at the origin of each muscle bundle on
the CT, one at its insertion on the CW, and two at equal intervals along the muscle bundle. The animals were allowed to recover for at
least 3 wk.
The animals were anesthetized with pentobarbital sodium (30 mg/kg),
intubated with a cuffed endotracheal tube, and placed in the supine or
prone position in a radiolucent body plethysmograph that was situated
in the test field of a biplanar fluoroscopy system. Balloon-tipped
catheters were inserted in the stomach and esophagus. The positions of
the catheters were checked by fluoroscopy and by demonstrating that
abdominal pressure increased and Pes decreased during a spontaneous
breath and that Pes and airway pressures decreased equally during an
occluded IE at FRC. The animal was inflated to TLC, defined as
30-cmH2O inflation pressure, and a
passive deflation pressure-volume curve was obtained. Biplanar images
were recorded at TLC and at steps of 1/3 IC down to FRC. Next, biplanar
images were recorded continuously during five spontaneous breaths. The
airway was then occluded at FRC, or the lungs were inflated to either
FRC + 1/2 IC or TLC, and the airway was occluded until the animal made
inspiratory efforts against the occluded airway. Biplanar images were
recorded when the change of airway pressure reached a plateau, usually
during the fifth or sixth IE at each volume. The animal was rotated to the opposite posture, and the procedure was repeated.
For each dog and each posture, frames at FRC and at EI were selected
from the recordings made during SB, and frames were selected from the
recordings made during IE at the three lung volumes. The coordinates of
the markers in the two biplanar images were determined, and the three
dimensional coordinates of the markers were computed. The lengths of
each muscle bundle in each state were determined by adding the
distances between markers on each bundle, and the average length of the
three bundles was computed.
An example of a lateral view of the data is shown in Fig.
2. The geometrical relations between the
muscle bundles and the diaphragm surface were determined by the
following procedure. A plane was fit through the locations of the 12 markers. The perpendicular distance of each marker from the best-fit
plane was computed, a quadratic surface was fit to the perpendicular
distance values, and the directions of the principal curvatures of the
quadratic surface were determined. A second plane was fit through the
locations of the four markers on the middle muscle bundle, and the
angle between this plane and the plane fit to the 12 markers was
determined. This is the angle
The data for all lung volumes for a given dog in a given posture were
then viewed in a single-coordinate system, the local coordinate system
at occluded TLC. That is, the plane fit to the locations of the 12 markers at occluded TLC was used as the basis for a local
RESULTS
Fig. 1.
Locations of metallic markers on abdominal surface of left midcostal
diaphragm. Four markers were sutured along each of 3 muscle bundles
from origins of bundles on central tendon (CT) to their insertions on
rib cage.
[View Larger Version of this Image (16K GIF file)]
shown in Fig. 2. Finally, the angle
between the line of maximal principal curvature and the line of the
middle muscle bundle (the angle 
shown in Fig. 2) was computed.
Fig. 2.
Lateral view of 12 markers, 4 along each of 3 muscle bundles, in
dog 4 in prone posture at end
inspiration (EI). A quadratic surface was fit to 12 markers, and a
plane was fit to 4 markers on the middle muscle bundle. Dashed line,
line of maximal principal curvature of surface. Angle , angle
between plane of muscle bundle and tangent plane of surface; angle ,
angle between line of muscle bundle and line of maximal curvature of
surface.
[View Larger Version of this Image (12K GIF file)]
-
-
coordinate system, defined as follows. The axis was chosen as a
line in the best fit plane in the direction of the smaller principal
curvature. The - plane, which contains the direction of maximal
principal curvature, was rotated to align the axis parallel to the
midplane of the dog. The data for all volumes for the given dog and
posture were then transformed to -- coordinates and viewed in
the - plane. Examples of these projections of the data onto the
- plane are shown in Fig. 3. The
locations of the 12 markers in the - plane for each volume were
fit by a circle.
Fig. 3.
Examples of data on marker locations projected onto - plane, a
plane parallel to planes of muscle bundles in prone
(A) and supine
(B) dogs. Locations of 12 markers, 4 markers in each of 3 neighboring muscle bundles, are shown (solid
symbols) for each of 5 states: functional residual capacity (FRC), EI
during spontaneous breathing, and during inspiratory effort (IE)
against an occluded airway at FRC (IE at FRC), 1/2 inspiratory capacity
(IC) above FRC (IE at FRC + 1/2 IC), and total lung capacity (TLC).
Lines, circular arcs fit to data at each state; open symbols, locations of centers of arcs.
[View Larger Version of this Image (12K GIF file)]
30 to 60 cmH2O during IE at FRC, 10
to 30 cmH2O at FRC + 1/2
IC, and +10 to 20 cmH2O
during IE at TLC. Changes in Pes during occluded maneuvers were about
the same as changes in airway opening pressure.
Pes, and the active component
of Pdi was taken as the difference between Pdi during IE and in the
passive animal at the same volume. These values were also variable,
ranging from 10 to 35 cmH2O and 55 cmH2O in one case. On average, Pdi
during IE decreased with increasing volume, but this accounted for a
small part of the variability.
Geometry.
Values of the angles and are shown plotted against muscle
length in Fig. 4. These angles, as shown in
Fig. 2, are the angle between the plane of the muscle bundle and the
tangent plane of the diaphragm surface and the angle between the lines
of maximal curvature of the surface and the line of the muscle bundle,
respectively. The average value of among the four dogs was
~90° at all volumes and both postures. That is, on average, the
plane of the muscle bundle lies perpendicular to the tangent plane of
the surface. However, the SD of at the higher volumes is large. In
dogs 2 and
3, the muscle bundle tilted away from
the perpendicular to the surface at high volume. The directions of tilt
were opposite in the two dogs. In the prone posture, the angle was
near zero. Thus, in the prone posture, the muscle bundles lie along the
line of maximal principal curvature. In the supine posture, the
direction of the muscle bundle consistently differed from the direction of maximal curvature by ~20°.
(squares) and angle (circles), as shown
in Fig 2, for prone (solid symbols) and supine (open symbols) dogs, vs.
muscle length (L) as fraction of
length at FRC
(LFRC). Bars,
SD.
Kinematics. Examples of the data projected onto the
- plane are shown in Fig.
3. In this figure, the 12 points that describe the locations of the 12 markers are shown for FRC and for each of the four inspiratory states.
The data for the three muscle bundles lie along nearly the same line in
the - plane. This superposition shows that, in this region, the
curvature of the diaphragm surface in the direction orthogonal to the
- plane is negligible, and the displacements of the three muscle
bundles are nearly the same.
The average length of the three muscle bundles for each dog and each
posture at FRC and the average length, as a fraction of the
LFRC, for each
maneuver are listed in Table 1. The lengths were consistently greater in the supine than in the prone position, and
the displacements of the markers on the CT were also greater. However,
the greater displacement, and hence greater muscle shortening, compensated for the greater original length, and the values of muscle
lengths at higher volumes, as a fraction of
LFRC, were not
significantly different in the two postures. Also, values of fractional
length were reasonably consistent among dogs despite the fact, noted
above, that the pressures that were generated were variable.
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. The full angle of
the arc between point CW and the intersection of the arc with
line AB is denoted
, and the angle of the extension of the arc from CT to
AB, which presumably is formed by the
CT, is denoted 
.
; angles A-O-CW and A-O-CT are denoted and , respectively. Perpendicular from CW to AB of length
d meets AB at P, and
CD intersects perpendicular at a distance
a from P. As point O moves through P,
r decreases to minimal value and then
increases. Thus r remains nearly
constant as O passes through P.
The data were cast in terms of the variables of the kinematic model. A line was drawn through the centers of the circles, corresponding to line AB in Fig. 5. The value of d was obtained by measuring the perpendicular distance from this line to the center of the cloud of points on the CW for all states. A second line corresponding to line CD was drawn through the locus of points that marked the origin of the muscle at the CT at different states. The angle corresponding to
in Fig. 5 and the distance
corresponding to were measured. The angles and
at each volume were measured. Values of these parameters, obtained from the plots of the data, are
listed in Table 2.
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are larger for
dogs 1 and
4 than for dogs
2 and 3. The data
shown in Fig. 3 contain an example of each group. For
dogs 1 and
4, the values of
at FRC
(FRC) are larger, and they
decrease to ~90° at TLC. That is, point O lies well above point P
at TLC and moves down to a position near point P at TLC. For
dogs 2 and
3, the values of
FRC are smaller and decrease to
<90° at TLC. In these dogs, point O lies lower at FRC, and point
O moves through point P to a position below point P at TLC.
DISCUSSION
In the present study, we report data on the length and curvature of muscle fibers of the midcostal diaphragm of the dog during SB and during forceful IE at different lung volumes. These data extend our previous observations on the geometry and kinematics of the midcostal canine diaphragm to more forceful diaphragm contractions and greater muscle shortening. In both studies, the shape of the midcostal diaphragm was found to be nearly a right circular cylinder. In this study, we found a small difference between the direction of the muscle fiber and the direction of maximal curvature in the supine posture, and in two dogs, the plane of the muscle bundle tilted away from the perpendicular to the surface during IE at the highest volumes. However, the main conclusions about the geometry of the midcostal canine diaphragm are consistent with our earlier results. In this region, the muscle bundles lie in planes that are orthogonal to the surface, and the lines of the muscle bundles lie along the lines of maximal curvature of the surface. The r of curvature of the bundle does not change as the diaphragm descends and the muscle shortens.
As in the previous study, we found no break in the curve of the muscle that would indicate a margin between a lung-apposed zone and the zone of apposition to the CW. In addition, we found that the motion of the muscle could be pictured as a rotation around the line of insertion with no change in shape. Thus the zone of apposition, which is narrow in this region, had no apparent effect on muscle geometry and kinematics.
In the following sections, the observations on muscle geometry and kinematics will be used to develop quantitative models for the kinematics and mechanics of the midcostal canine diaphragm.
Kinematics. The model shown in Fig. 5 can be used to obtain relations among the variables, r,
d, and
L. The variables
r, , and
d are related by the equation
|
(1) |
and , measured in radians, and r by
the equation
|
(2) |
that is occupied by CT with
subtended angle is different in different dogs. However, in each
dog, the ratio / remains nearly constant as lung volume changes.
Rewriting Eq. 2 as
L = (1 /)r, where the factor (1 /) is independent of volume, and substituting for
r from Eq. 1 yields the following equation for the ratio of muscle
lengths L/LFRC
|
(3) |
with d and
FRC as parameters. For given
values of d and
FRC, values of
r and
L/LFRC
for each value of can be combined to obtain a plot of
r vs.
L/LFRC.
The average values of d and
FRC from the data were chosen
as parameter values, and the curve of r vs.
L/LFRC
shown by the solid line in Fig. 6 was
constructed from Eqs. 1 and 3. The curve is consistent with our
observations; it shows very little change of
r with
L/LFRC.
FRC, shown in Fig.
3, equal to 120° (solid line). Curves are also shown for values of
d that are 30% larger (dotted-dashed
line) and 30% smaller (dashed line) than base case.
The kinematic model shown in Fig. 5, and described by Eqs. 1 and 3 and Fig. 6, is similar to an older, and now discarded, model of alveolar mechanics. In that model, the alveolus was pictured as a spherical bubble blown on a rigid circular ring that represented the alveolar opening, and the model was used to relate the curvature of the alveolar surface to alveolar volume. According to that model, if the center of the sphere lay above the plane of the ring, the r of the sphere would be larger than the r of the ring. As the alveolus deflated and the center descended, the r of the sphere would decrease to a minimum value equal to the r of the ring and then increase again as the center moved below the ring and the bubble became shallow. The model shown in Fig. 5 is the cylindrical analogue of the alveolar model. The cylindrical shell is imagined to extend from the line of insertion on the CW up to a peak in the CT and presumably back down, perhaps through the crural diaphragm, to another line of insertion near the spine. If the center of the cylinder lies above the lines of insertion, the r of the cylinder is larger than d. As the diaphragm descends, the r decreases to a minimum equal to d and then increases again as the center descends further. The values of the model parameters differed among different dogs, but on average, the center of the muscle arc began at a point above the line of insertion at FRC and descended to a point slightly below the line of insertion at TLC. For this range of positions, the value of r is nearly constant as it passes through its minimum value. Thus this model provides a kinematic explanation for the observations, reported here and in our previous paper (1), that muscle curvature is independent of muscle length. Mechanics. Previous studies have provided qualitative information about the relation between muscle length, muscle shape, and Pdi, but the data were insufficient for a quantitative analysis. Kim et al. (11) measured Pdi and muscle tension during phrenic nerve stimulation in dogs and found that the ratio of the two remained approximately constant over a range of muscle length. They concluded that shape remained nearly constant. They also calculated a r of curvature from their data for Pdi and tension, but in the absence of any information about shape, they assumed that the diaphragm was a spherical membrane with equal tensions and curvatures in two orthogonal directions. Road et al. (13) measured Pdi and muscle length and compared the shape of the curves of Pdi vs. length with the shape of the muscle tension-length curve, but without information about curvature, they could not make a quantitative comparison between measured values of Pdimax and values calculated from the muscle tension-length curve. Similarly, Hubmayr et al. (9) measured Pdi and muscle length, but not shape. The data reported in this paper provide the first information about curvature of the active diaphragm at different lung volumes and muscle length, and these data provide the information that is needed to calculate Pdimax. Two features of the data are essential to this calculation. First, data for active states are required as a basis for an analysis of diaphragm mechanics. At lung volumes above FRC, the passive diaphragm is a minor mechanical component of the abdominal pathway, and its shape is determined by the shapes and elastances of the lung, abdominal contents, and abdominal wall. To be sure, the shapes of the lung and abdomen may impose a shape on the passive diaphragm that is similar to its active shape, but the diaphragm's passive shape is not directly determined by its mechanical properties. In our experiments, Pdi were 20-30 cmH2O greater during the IE against an occluded airway than were passive Pdi. The diaphragm is the major mechanical element that balances this additional pressure difference. In addition, these pressure differences are large compared with regional pressure differences caused by gravitational gradients, and local variations in Pdi are relatively small. Therefore, our data can justifiably be used to compute Pdi from tension and curvature. Second, the particular shape of the midcostal diaphragm is crucial to obtaining a relation between Pdi and muscle tension. In regions with significant curvatures in two directions, both curvatures and both components of tension would be required to calculate Pdi. Maximal muscle tension has been measured as a function of muscle length, but in the intact diaphragm, tension in the direction transverse to the muscle is a result of diaphragm shape and loading and is unknown. However, in the midcostal region, the diaphragm has the shape of a circular cylinder with the muscle bundles lying in the direction of maximal curvature. Curvature in the direction transverse to the fibers is small, and although the membrane undoubtedly carries tension in the transverse direction, this unknown tension contributes little to Pdi because the curvature in that direction is small. Therefore, in this region, Pdi can be computed from muscle tension and muscle curvature. The curve of Pdimax vs. L/Lo, where Lo is the optimal force-generating length of the muscle, was computed by the following procedure. Maximal stress in the direction of the muscle bundles was obtained from the data reported by Farkas and Rochester (5). Farkas and Rochester measured the maximal stress-length curve of excised diaphragm muscles under uniaxial loading, and we assume that the stress-length curve of the intact muscle under biaxial loading is the same as the in vitro curve. Stress was multiplied by a muscle thickness of 0.25 cm (2, 12) to obtain membrane tension. Values of r were taken from the solid curve shown in Fig. 6. The ordinate of Fig. 6, L/LFRC was taken to be equal to L/Lo, because our values of LFRC are the average of the values for the prone and supine postures and thus are near Lo. Finally, membrane tension was divided by values of r to obtain Pdimax. The resulting curve of Pdimax vs. L/Lo is shown by the solid line in Fig. 7. The shape of the calculated curve of Pdimax vs. L/Lo is nearly the same as the shape of the muscle stress-length curve because, as shown in Fig. 6, r varies by only ~10% for
FRC = 120° and
L/Lo
in the range from 1 to 0.5.
The values of Pdi that we measured during IE are considerably smaller than the values of Pdimax shown in Fig. 7. Thus we conclude that the diaphragm was not maximally activated during maximal IE in these dogs. This is consistent with the conclusion of Hershenson et al. (8) that the diaphragm is less than maximally activated during maximal voluntary IE in humans. It appears that the force exerted by the diaphragm is adjusted to match the force exerted by the muscles of the rib cage. If the forces exerted on the abdominal and rib cage compartments were matched and the CW were not distorted during IE, airway and pleural pressures would fall, but Pg would remain unchanged. In our experiments, the changes in Pg were quite variable and included both positive and negative changes. Hershenson et al. (8) observed relatively small changes in Pg during IE in upright humans, and the changes of Pg also included changes of both signs. Some of the parasternal internal intercostals of the dog are maximally activated during SB against resistive loads (4). Thus, if the forces on the two compartments are matched, it appears that the intercostals limit the activation of the diaphragm. If the diaphragm were fully activated, the diaphragm would overwhelm the intercostals, rib cage volume would decrease, abdominal volume would increase, and Pg would increase. Instead, it appears that the diaphragm is less than maximally activated, so that its force nearly matches the force exerted by the maximally activated parasternals. In the experiments of Road et al. (13), the diaphragm was maximally activated by phrenic nerve stimulation, but the lower rib cage was constrained by a cast. It seems plausible that the cast preserved a physiological configuration of the lower rib cage and ring of insertion of the diaphragm despite the unphysiological muscle activation. The values of Pdimax reported by Road et al. are replotted in Fig. 6. These agree with the calculated Pdimax curve very well. We would like to emphasize that the comparison shown in Fig. 7 is not a comparison of curve shapes. Neither curve has been normalized, and Fig. 7 shows a quantitative comparison between experimental values and values calculated from the kinematic model. The data of Hubmayr et al. (9) are also plotted in Fig. 7. Hubmayr et al. report Pdimax as a function of L/LFRC, and the values of L/Lo shown in Fig. 7 are shifted slightly from the reported values of L/LFRC because of the difference between Lo and LFRC in the supine dog. As noted by Hubmayr et al. the values of Pdimax that they measured have a steeper dependence on L/Lo than would be expected from the force-length curve. Although the variability in these data is large, the mean values are 50% larger than predicted, and if the data were extrapolated, following the shape of the muscle tension-length curve, a value of Pdimax at L = Lo of ~160 cmH2O would be predicted. We hypothesized that the larger values of Pdimax observed by Hubmayr et al. were the result of CW distortion. To test this hypothesis, the kinematic model was used to predict values of r for a smaller diameter of the ring of insertion. The parameter d in Eq. 1 was reduced by 30%, and
FRC was increased to 136°
to maintain the value of
Lo, and the
computations of r and
Pdimax were repeated. The results
are shown by the dashed lines in Figs. 6 and 7. The calculated curve of
Pdimax vs.
L/Lo is steeper simply because r is
smaller, not because r is changing significantly with
L/Lo
in the range of
L/Lo
covered by the data. This seems to be a plausible explanation for the
difference between the data of Hubmayr et al. (9) and the data of Road
et al. (13).
Similarly, the model can be used to predict the effect of rib cage
expansion and a corresponding increase in the diameter of the ring of
insertion. The computations of r and
Pdimax were repeated for a value
of d that was 30% larger than the
base case and for the corresponding value of 104°
for FRC. The results are shown
by the dashed and dotted lines in Figs. 6 and 7. For this case,
r is minimum for
L/Lo = 0.85, and r increases sharply as
L/Lo
decreases below 0.7. As a result, the dependence of
r on
L/Lo
has a significant effect on the values of
Pdimax for
L/Lo <0.7. That is, although d was
increased by only 30%, the values of
Pdimax lie >30% below the
values for the base case for
L/Lo < 0.7.
The results for the enlarged ring of insertion may be pertinent to
understanding diaphragm function in patients with chronic obstructive
pulmonary disease (COPD) and enlarged lungs and rib cages. Although it
is widely believed that the CW is enlarged in COPD, attempts to measure
the effects of COPD on rib cage dimensions or rib inclinations have
yielded conflicting results. In the study in which no difference
between rib angles of COPD patients and normal subjects was found (17),
the ages of the COPD and control groups were the same. However, in the
other two studies, it was found that the COPD patients had larger rib
cage dimensions (7) or more elevated ribs (15) than younger control
groups.
The diaphragm is depressed in COPD patients (14, 16). Our model, in
which FRC is decreased to
maintain Lo
constant as d increases, mimics a
depression of the diaphragm accompanying CW enlargement. Our adjustment
of the value of FRC may be
conservative, because estimates of diaphragm
L indicate that
LFRC is, in fact, smaller in COPD patients than in normal subjects. Studies of
elastace-induced emphysema in hamsters have shown that the diaphragm
remodels and that
Lo becomes
smaller in animals with enlarged lungs (6, 10). Remodeling to a smaller
value of Lo would
change the shape of the calculated values of
Pdimax shown in Fig. 6. The peak
of the curve would be shifted to the left. However, the lower limit of
the interrupted curve (the point at which
Pdimax = 0) would not move,
because this limit is the result of the geometry of the diaphragm. At
L = 0.55 Lo, the diaphragm
is flat. Thus diaphragm remodeling may increase
Pdimax at the remodeled
Lo, but the range of diaphragm shortening and displacement would be less than normal.
In summary, we report data on the configuration of the midcostal region
of the canine diaphragm for active inspiratory states at lung volumes
from FRC to TLC. From these data, we developed a model for the
kinematics of this region of the diaphragm. Although the model was
generated from data in which the diaphragm was not maximally activated,
it was used to calculate Pdi for maximal activation. The computed
curves agree well with the data of Road et al. (13) for
Pdimax during maximal diaphragm
activation with the lower rib cage constrained by a cast. We conclude,
however, that the computed Pdimax
vs. muscle L curve never is realized during physiological inspiratory maneuvers because the diaphragm is not
maximally activated during spontaneous IE, and if it were, the lower
rib cage and ring of insertion of the diaphragm would be distorted,
thereby changing the relation between diaphragm shape and muscle
L. Therefore, although the calculated
Pdimax vs. muscle
L curve may be pertinent to maneuvers,
such as the expulsive maneuver, in which the diaphragm is maximally
activated (8), it is not pertinent to breathing. However, the kinematic model provides the information that is needed to relate Pdi to muscle
tension for lower levels of diaphragm activation. It also describes the
reduced Pdi and reduced range of shortening that accompanies rib cage
enlargement.
ACKNOWLEDGEMENTS
We thank Mike Kerzee, Ann Marie Doneski, Yang Rui, and Deshen Zhu for technical assistance.
FOOTNOTES
Address for reprint requests: T. A. Wilson, 107 Akerman Hall, 110 Union St. SE, Minneapolis, MN 55455.
Received 3 February 1997; accepted in final form 23 June 1997.
REFERENCES
| 1. |
Boriek, A. M.,
S. Liu,
and
J. R. Rodarte.
Costal diaphragm curvature in the dog.
J. Appl. Physiol.
75:
527-533,
1993 |
| 2. |
Boriek, A. M.,
and
J. R. Rodarte.
Inferences on passive diaphragm mechanics from gross anatomy.
J. Appl. Physiol.
77:
2065-2070,
1994 |
| 3. |
Boriek, A. M.,
T. A. Wilson,
and
J. R. Rodarte.
Displacements and strains in the costal diaphragm of the dog.
J. Appl. Physiol.
76:
223-229,
1994 |
| 4. |
De Troyer, A.,
and
A. Legrand.
Inhomogeneous activation of the parasternal intercostals during breathing.
J. Appl. Physiol.
79:
55-62,
1995 |
| 5. |
Farkas, G. A.,
and
D. F. Rochester.
Functional characteristics of canine costal and crural diaphragm.
J. Appl. Physiol.
65:
2253-2260,
1988 |
| 6. |
Farkas, G. A.,
and
C. Roussos.
Diaphragm in emphysematous hamsters: sarcomere adaptability.
J. Appl. Physiol.
53:
1263-1272,
1982 |
| 7. | Gilmartin, J. J., and G. J. Gibson. Abnormalities of chest wall motion in patients with chronic airflow obstruction. Thorax 39: 264-271, 1984[Abstract]. |
| 8. |
Hershenson, M. B.,
Y. Kikuchi,
and
S. H. Loring.
Relative strengths of the chest wall muscles.
J. Appl. Physiol.
65:
852-862,
1988 |
| 9. |
Hubmayr, R. D.,
J. Sprung,
and
S. Nelson.
Determinants of transdiaphragmatic pressure in dogs.
J. Appl. Physiol.
69:
2050-2056,
1990 |
| 10. | Kelson, S. G., T. Wolanski, G. S. Supinski, and U. Roessmann. The effect of elastase-induced emphysema on diaphragmatic muscle structure in hamsters. Am. Rev. Respir. Dis. 127: 330-334, 1983. [Medline] |
| 11. |
Kim, M. J.,
W. S. Druz,
J. Danou,
W. Machnack,
and
J. T. Sharp.
Mechanics of the canine diaphragm.
J. Appl. Physiol.
41:
369-382,
1976 |
| 12. |
Margulies, S. S.
Regional variation in canine diaphragm thickness.
J. Appl. Physiol.
70:
2663-2668,
1991 |
| 13. |
Road, J.,
S. Newman,
J. P. Derenne,
and
A. Grassino.
In vivo length-force relationship of canine diaphragm.
J. Appl. Physiol.
60:
63-70,
1986 |
| 14. | Rochester, D. F., and N. M. T. Braun. Determinants of maximal inspiratory pressure in chronic obstructive pulmonary disease. Am. Rev. Respir. Dis. 132: 42-47, 1985[Medline]. |
| 15. |
Sharp, J. T.,
G. A. T. Beard,
M. Sunga,
T. W. Kim,
A. Modh,
J. Lind,
and
J. Walsh.
The rib cage in normal and emphysematous subjects: a roentgenographic approach.
J. Appl. Physiol.
61:
2050-2059,
1986 |
| 16. | Sharp, J. T., J. Danon, W. S. Druz, N. B. Goldberg, H. Fishman, and W. Machnach. Respiratory muscle function in patients with chronic obstructive pulmonary disease: its relationship to disability and to respiratory therapy. Am. Rev. Respir. Dis. 110: 154-167, 1974[Medline]. |
| 17. |
Walsh, J. M.,
C. L. Webber,
P. J. Fahey,
and
J. T. Sharp.
Structural change of the thorax in chronic obstructive pulmonary disease.
J. Appl. Physiol.
72:
1270-1278,
1992 |
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