Journal of Applied Physiology
Vol. 83, No. 4,
pp. 1123-1132,
October 1997
EXERCISE AND MUSCLE
Patterns of shortening and thickening of the human
diaphragm
J. L.
Wait and
R. L.
Johnson
Department of Internal Medicine, Dallas Veterans Affairs Medical
Center, and University of Texas Southwestern Medical Center, Dallas,
Texas 75230
ABSTRACT
- INTRODUCTION
- METHODS
- RESULTS
- DISCUSSION
- APPENDIX
- FOOTNOTES
- REFERENCES
ABSTRACT 
Wait, J. L., and R. L. Johnson. Patterns of shortening
and thickening of the human diaphragm. J. Appl.
Physiol. 83(4): 1123-1132, 1997.
To study how the human diaphragm changes
configuration during inspiration, we simultaneously measured diaphragm
thickening using ultrasound and inspired volumes using a
pneumotachograph. Diaphragm length was assessed by chest radiography.
We found that thickening and shortening were greatest during a breath
taken primarily with the abdomen. However, the degree of thickening was
greater than expected for fiber shortening, assuming parallel muscle
fibers and no shear. So, to clarify this unexpected finding, we
considered geometric models of the diaphragm. How a muscle thickens as
its fibers shorten is critically dependent on geometry. Thus, if a flat
rectangular sheet of muscle shortens along one dimension, surface
area-to-length ratio along this dimension should remain constant, and
thickness would be inversely proportional to length during shortening.
The simplest model of the diaphragm, however, is a cylindrical sheet of
muscle in the zone of apposition capped by a dome; the ratio of surface
area to radial fiber length in the dome is substantially less than the
ratio of area to length of the cylindrical zone of apposition; hence,
as the zone of apposition shortens while the dome radius remains
constant, the ratio of total surface area to combined length (i.e.,
dome + zone of apposition) must decrease and thickening of the muscle
correspondingly must increase more than expected for a simple
rectangular strip. A similar relationship can be derived between
thickening and length in a muscle sheet with a wedge-shaped insertion
into a thin flat tendon. Comparison of calculations with these types of
models to data from human subjects indicates that the unexpected
thickening in the zone of apposition is explained by the peculiar
geometry of the diaphragm. The greater thickening of the diaphragm in
the zone of apposition suggests that more of the muscle mass and more sarcomeres are retained in the zone of apposition as the dome descends.
Physiologically, this greater thickening may have importance by
reducing wall stress in the zone of apposition and reducing the work or
energy requirements per sarcomere.
diaphragm geometry; thickening ratio; wall stress
INTRODUCTION
TO STUDY HOW the human diaphragm changes configuration
during inspiration, we previously imaged the thickness changes of the upright diaphragm using ultrasound (19). Our studies and others have
shown that the diaphragm thickens in the zone of apposition proportionally to inspired volume and inspiratory force, but the thickening is often greater than threefold (17, 19). This was more than
expected on the basis of the assumptions of a fixed muscle volume and
simple shortening along parallel muscle fibers. Previous studies
indicate that the human diaphragm normally shortens maximally to
between 0.7 and 0.6 of its initial length
(l/l0) (3, 11).
If thickness is inversely proportional to length, we would have
expected maximum thickening ratios
(h/h0) ranging from 1:0.7 to 1:0.6 (1.42-1.67).
We reasoned that the relationships among diaphragm thickening,
diaphragm length, and lung volume should depend in part on the pattern
of ventilation, i.e., greater thickening and shortening with respect to
inspired volume when the rib cage is constrained to induce abdominal
breathing. Therefore, in this study, we compared these relationships
during normal and abdominal inspirations in human volunteers. The
results follow the expected patterns qualitatively, but we still could
not explain the magnitude of thickening based on the assumption that
the dome-shaped diaphragm behaves as if it were made of simple
rectangular strips of muscle. In fact, one cannot reconstruct the
topology of a three-dimensional dome-shaped diaphragm by pasting
together rectangular strips of paper without folding some of the strips
to create the dome; the problem is the same as that of reconstructing a
globe from multiple small two-dimensional map projections. Once the
latter problem is recognized, our results can be approximated by models
that assume relatively simple interactions among the muscle in the zone
of apposition, the muscle in the ellipsoidal dome, and the shape of the
muscle insertion into the central tendon (CT).
Thus we also compared four different geometric models of diaphragm
configuration with our measurements taken from volunteers under
conditions of different breathing patterns. Diaphragm thickness increased out of proportion to shortening based on a rectangular strip
of muscle but best fit models that address the reduction of the curved
surface area of the dome or the taper of the muscle as it inserts into
the CT.
METHODS
Subjects
All eight subjects (ages 23-39 yr, 6 men and 2 women) were
nonsmokers, had no history of pulmonary disease, and gave informed consent. Before the study, all had simple spirometry performed to
ensure normal pulmonary function, and inspiratory capacity (IC) was
measured at the onset of the studies. Respiratory inductance plethysmography was measured in all subjects to determine the relative
breathing patterns during the physiological measurements. Chest
radiographs were taken in seven subjects at end expiration to
approximate functional residual capacity (FRC) and at a specified lung
volume >20% of the IC.
Chest Radiographs
The chest radiographs were taken in the chest radiology room (Siemens
dedicated chest unit), with each set of films taken at 6 ft. from the
camera. The subjects were seated with their backs resting against the
film plate; the position of the arms was the same as that when the
ultrasound and physiological parameters were recorded. Lateral films
were also taken with the subjects seated, with the right chest against
the film plate, and with back support. The radiographs were taken at
FRC and at a specified lung volume representing the largest tidal
volume studied. The inspired volume for each subject was selected from
the studies using ultrasound measurements of thickness. By use of a
volume-calibration syringe, the volume was injected into an
anesthesia bag fitted with a mouthpiece on a three-way valve attached
to the end of a flexible tube. The subject practiced inhaling this
volume from end expiration before the radiographs were taken. When the
subject was ready, he/she signaled that the radiograph be taken at the instant he/she felt and saw the anesthesia bag empty.
For three of the eight subjects, radiographs were taken during
inspiration with the abdomen; for the other five subjects, radiographs
were taken with a normal inspiration. All radiographs were taken at
inspired volumes to match those taken with ultrasound. One subject
(PS) declined chest radiographs.
Adjustments were made in the radiographic measurements for
magnification (1). Dimensions from the radiographs were used to
determine the height of the dome, the length of the zone of apposition,
and the radial axes of the thorax (Fig. 1);
the length of the diaphragm was measured from the chest radiographs
using a flexible tape measure, as described by Braun et al. (3). In our
study the lowest point of the zone of apposition was taken at the point
of the lead marker (see below). Adjustments were made for the presence
of the CT on the basis of necropsy studies (0.25 × FRC length) so
that only diaphragm muscle lengths were approximated and compared (3).
The transverse axis (D) was one-half
the measured diameter of the anteroposterior chest radiograph, which
was determined by measuring straight across the inside margins of the
ribs at the right costophrenic angle (from point
1 to 2). A line was
drawn across the lateral roentgenogram from the point where air and
diaphragm are seen to join behind the sternum to the posterior angle
formed by diaphragm and air (from point
3 to 4). One-half of
this distance is the minor axis (A)
for an ellipsoid model. The height of the dome
(d) was determined as the length of
a line drawn perpendicular to the lateral axis line extending to the
highest portion of the dome. The length of the zone of apposition
(z) was determined as the distance
from the right costophrenic angle to the lead marker
(point 1 to
x). So that these values could be
used in theoretical calculations for models of the diaphragm, they were
normalized to z for each individual
(see Table 2). Thus the transverse axis was expressed as
D/z, the lateral axis as
A/z, and the height of the dome as d/z, and the mean of these values for
the subjects was used.
Fig. 1.
Determination of variables from chest radiographs. Transverse axis
(D) was one-half measured diameter
of anteroposterior (AP) chest radiograph (from point
1 to 2). A lateral
axis line was drawn across lateral roentgenogram from point where air
and diaphragm are seen to join behind sternum to posterior angle formed
by diaphragm and air (from point 3 to
4). Height of dome
(d) was determined as length of a
line drawn perpendicular to lateral axis line extending to highest
portion of dome. Length of zone of apposition
(z) was determined as distance from
right costophrenic angle to lead marker (point
1 to x).
[View Larger Version of this Image (10K GIF file)]
|
Table 2.
D/z, d/z, and A/z for each subject
|
| Subject |
D/z |
d/z |
A/z |
|
| CS |
1.72 |
0.59 |
0.98 |
| LS |
2.07 |
0.62 |
1.28 |
| LC |
2.34 |
0.95 |
1.51 |
| CO |
1.31 |
0.58 |
0.85 |
| JW |
2.13 |
0.7 |
1.29 |
| TD |
2.42 |
0.63 |
1.29 |
| JL |
2.16 |
0.57 |
0.97 |
| TB |
2.01 |
0.57 |
1.18 |
|
| Mean |
2.02 |
0.65 |
1.17 |
|
|
Transverse axis (D), height of dome (d),
and lateral axis (A) normalized to length of zone of
apposition (z).
|
|
Ultrasound Images
Ultrasound recordings of diaphragm thickness were made with a 10-MHz
transducer and an analog M-mode echocardiograph (IREX). Details of the
ultrasound technique have been reported by us previously and used by
others (17, 19). Because ultrasound cannot pass through the air in the
lung, the diaphragm often cannot be visualized throughout the entire
vital capacity. Instead, the largest breaths possible producing
acceptable ultrasound images of the diaphragm were used (19). Only
tracings showing complete, unbroken lines from the pleural and
peritoneal surfaces of the diaphragm were used. The ultrasound
transducer was held perpendicular to the diaphragm immediately above
the lowest rib that afforded the best and consistent view of the
diaphragm in the midaxillary or anterior axillary line. This was the
10th or 11th rib in all individuals, and none of the diaphragm could be
visualized by ultrasound below that level. All diaphragm images for
each individual were taken from the same location. Before the
radiographs were obtained (see Chest
Radiographs), a lead marker was taped to the chest
walls of the subjects to mark the point of ultrasound measurements and to indicate the lowest margin of the zone of apposition for the purposes of this study. Measurements of diaphragm thickness were taken
at 200-ms intervals from the hard copy of the ultrasound recording.
Respiratory Inductance Plethysmography
The relationship of the rib cage and abdominal contributions to
inspired volume were determined with respiratory inductance plethysmography (Non-Invasive Monitoring Systems, Miami Beach, FL). The
instrument was calibrated by the least-squares method using a fixed
inspired volume (4). The signals from the respiratory inductance
plethysmograph on an oscilloscope were used as visual feedback to the
subjects for changing breathing patterns. Values were expressed as the
relationship of the rib cage component to the total expansion (RC + Ab,
where RC is rib cage and Ab is abdomen) measured in arbitrary units.
Inspired Volumes
Timed expiratory volume and forced vital capacity were measured in each
subject (Apex DS, Collins, Braintree, MA). During the studies, each
subject was seated with a noseclip in place, and tidal volume was
recorded with a Fleisch pneumotachograph connected to a low-dead-space
one-way Hans Rudolph valve. The flow signal was electrically integrated
for volume on a multichannel physiological recorder (Honeywell
Electronics for Medicine). IC was determined using the
pneumotachograph. To provide measurement of diaphragmatic thickness
over a continuous range of increasing lung volume, we performed dynamic
assessments of single large breaths.
The physiological and ultrasound recorder paper speeds differed
slightly, producing small differences in events after several seconds.
To exactly match data from two recorders, a timer calibrated for 200 ms
sent simultaneous signals to both recorders through in-line connections
with the event markers.
Protocol
Ultrasound images and all physiological recordings were performed with
the subjects seated with back support and arm rests. Ultrasound images
were taken from the right side in all subjects. The subjects were asked
to breathe normally through the pneumotachograph, but with
larger-than-normal tidal breaths. They were instructed to use the most
comfortable breathing pattern and rate. A series of breaths taken in
this fashion were recorded from all subjects. Five subjects were also
instructed to vary their breathing pattern so that they were breathing
"with their abdomens." This was determined by changes in the
respiratory inductance plethysmography tracings showing a reversal of
the predominantly rib cage expansion such that RC/(RC + Ab) was <0.6.
Three subjects were able to accomplish this. One subject
(TD) was unable to significantly
change his breathing pattern, since his native pattern was
predominantly abdominal, and the diaphragm of another subject
(CS) thickened so much that the
peritoneal surface moved out of the resolution range of the transducer
and no usable diaphragm images were obtained.
All reported measurements of thickness are the means of at least three
independent measurements from the ultrasound tracings. Measured
thickening was expressed as a ratio of the thickness (h) at that point in time to the
thickness at end expiration preceding the breath
(h/h0).
Models of Diaphragm
Four simple models representing the in situ diaphragm are used to
examine the relationships of costal diaphragm length to thickening. All
these models make the same a priori assumptions: 1) the mass (or volume) of the
diaphragm muscle remains constant; 2) the diaphragm is separated into
two compartments, the dome and the zone of apposition, which change
relative surface areas and volumes during contraction; and
3) the dimensions of the CT are
constant. All models use relative geometric dimensions based on FRC
radiographs from our subjects. These dimensions are the transverse
radius of the thorax (D), the height
of the dome (d), the lateral axis of
the diaphragm (A), and the length of
the zone of apposition (z).
D, A, and
d were normalized to
z for each subject, and the mean of
these values was used for calculations in the models.
Model A is a simple linear strip of
muscle; the volume (V) of the muscle is
![V = <IT>hw</IT>[(<IT>D</IT> − CT) + <IT>z</IT>]](/content/vol83/issue4/fulltext/1123/img001.gif)
|
(1)
|
where
D is the radial axis, CT is the length
of the central tendon, z is the length
of the zone of apposition, h is the
thickness of the diaphragm, and w is
the width of the muscle strip.
Model B is a hollow cylinder with
thickness h. The volume of the muscle
is
|
(2)
|
Model C is also a strip, but the
thickness in the dome tapers toward the insertion to the CT. The volume
of the muscle is
|
(3)
|
Model D is a combination of
models B and
C. The base is an elliptical cylinder
topped by an ellipsoid for the dome. The thickness at the base of the
structure is the same, but it tapers in the dome toward the insertion
into the CT. The volume of the muscle is
|
(4)
|
Models A-D are illustrated in
Fig. 2, and derivation of the formulas is
given in the APPENDIX.
Fig. 2.
Four geometric models of costal diaphragm. Model
A is a rectangular costal diaphragm strip.
Model B represents diaphragm as a
cylinder with radius equal to transverse diameter of thorax (D), and height is length of zone of
apposition (z).
Model C represents a costal diaphragm
strip that tapers toward central tendon (CT) in dome region.
Model D is an elliptical cylinder with
an ellipsoidal dome that also tapers to its insertion in CT.
Y, length of segment in dome;
h, thickness; A, lateral
axis of diaphragm.
[View Larger Version of this Image (11K GIF file)]
Data Analysis
All data samples were taken at 200-ms intervals from the onset of
inspiration as determined by the onset of airflow. Three measurements
of thickness at each timed interval were taken in a series, and the
mean of the three was used for analysis. Similar-sized breaths from
each subject, varying within 10% of the subject's IC, were compared
with those taken with a different thoracoabdominal configuration. Mean
values of h/h0,
l/l0, and
inspired volumes were compared by Student's
t-test, with significance at
P < 0.05.
RESULTS
Subjects
The physical characteristics and spirometry for each subject are shown
in Table 1. The transverse radius of the
thorax (D), lateral axis
(A), and height of the dome
(d), normalized with respect to
length (z) of the zone of apposition
at FRC, are given for each subject in Table
2.
|
Table 1.
Subject characteristics
|
| Subject |
Sex |
Age, yr |
Wt, kg |
Ht, cm |
FEV1,
l/s |
FVC,
ml |
|
| CS |
M |
19 |
75 |
183 |
4.75 |
5.94 |
| LS |
F |
27 |
59 |
170 |
3.69 |
4.65 |
| PS |
M |
32 |
70 |
178 |
4.87 |
5.59 |
| LC |
M |
28 |
68 |
175 |
4.55 |
5.89 |
| CO |
M |
27 |
84 |
188 |
4.11 |
5.61 |
| JW |
F |
39 |
55 |
174 |
3.06 |
3.65 |
| TD |
M |
36 |
75 |
183 |
4.96 |
6.29 |
| JL |
M |
26 |
60 |
173 |
4.29 |
4.93 |
| TB |
M |
34 |
75 |
183 |
4.41 |
5.32 |
|
|
M, male; F, female; FEV1, forced expiratory volume in
1 s; FVC, forced vital capacity.
|
|
Different Breathing Patterns
The effects of different breathing patterns on diaphragm configuration
were assessed by two independent methods with two different breathing
patterns: diaphragm thickening was determined by ultrasound throughout
inspiration (Tables 3 and
4, subjects LS,
PS, and JW), and
shortening was determined from radiographs matched to specific inspired
volumes (subjects JW, TB, and
JL, Table
5). In Tables 3 and 4 the normal vs.
abdominal breathing pattern is reflected by the fraction of total
expansion attributed to the rib cage by inductance plethysmography
[RC/(RC + Ab)]: 0.8 ± 0.08 vs. 0.38 ± 0.12 (SE).
The size of the breaths is shown in milliliters and expressed as a
percentage of each subject's IC (50.7 ± 7.7 and 38.3 ± 8.2%
for normal and abdominal, respectively, P < 0.01). The end-inspiratory
fractional thickness
(h/h0) for each
breath is also shown: 2.17 ± 0.5 and 3.12 ± 0.7 for normal and
abdominal, respectively (P < 0.01).
Abdominal breaths were measured radiographically from three subjects
(Table 5). The mean
l/l0 from the
three subjects with abdominal breaths was less than the mean from the
other six normal inspiratory radiographs: 0.75 ± 0.01 vs. 0.88 ± 0.03 (P < 0.001).
|
Table 3.
Inspiratory volume and thickening for normal breathing pattern
|
| Subject |
RC/(RC + Ab) |
h/h0 |
Inspired
Volume
|
| ml |
%IC |
|
| CS |
0.71 |
1.8 |
1,337 |
45 |
|
0.68 |
1.72 |
1,375 |
46 |
|
0.7 |
1.8 |
1,312 |
44 |
| Mean ± SE |
0.7 ± 0.01 |
1.77 ± 0.04 |
|
45 ± 0.8 |
| LS |
0.85 |
1.7 |
1,363 |
62 |
|
0.93 |
1.7 |
1,400 |
63 |
|
0.93 |
1.5 |
1,287 |
59 |
| Mean ± SE |
0.9 ± 0.04 |
1.63 ± 0.09 |
|
61.3 ± 1.7 |
| PS |
0.75 |
2.3 |
1,450 |
42 |
|
0.74 |
2.2 |
1,300 |
38 |
|
0.81 |
2.9 |
1,675 |
49 |
| Mean ± SE |
0.77 ± 0.02 |
2.46 ± 0.31 |
|
43 ± 4.5 |
| JW |
0.86 |
2.7 |
888 |
53 |
|
0.87 |
2.8 |
900 |
54 |
|
0.82 |
3.0 |
88 |
53 |
| Mean ± SE |
0.85 ± 0.02 |
2.83 ± 0.12 |
|
53.3 ± 0.47 |
|
|
RC, rib cage; Ab, abdomen; h/h0, fractional
thickening; IC, inspiratory capacity.
|
|
|
Table 4.
Inspiratory volume and thickening for abdominal breathing pattern
|
| Subject |
RC/(RC + Ab) |
h/h0 |
Inspired
Volume
|
| ml |
%IC |
|
| LS |
0.49 |
2.1 |
938 |
43 |
|
0.56 |
2.5 |
1,150 |
52 |
|
0.58 |
2.5 |
1,100 |
50 |
| Mean ± SE |
0.54 ± 0.04 |
2.37 ± 0.19 |
|
48 ± 3.9 |
| PS |
0.32 |
3.9 |
1,195 |
35 |
|
0.37 |
3.8 |
1,357 |
39 |
|
0.31 |
4.4 |
1,325 |
38 |
| Mean ± SE |
0.33 ± 0.03 |
4.0 ± 0.26 |
|
37.3 ± 1.7 |
| JW |
0.27 |
2.8 |
512 |
31 |
|
0.27 |
3.1 |
477 |
29 |
|
0.29 |
3.0 |
475 |
28 |
| Mean ± SE |
0.28 ± 0.01 |
2.97 ± 0.12 |
|
29.3 ± 1.3 |
|
|
Mean values are significantly different from those in Table 3,
P < 0.01.
|
|
|
Table 5.
Radiographic diaphragm length
|
| Subject/Condition |
Inspired
Volume, ml |
DML,
cm |
l/l0 |
h,
cm |
h/h0 |
|
| CS |
| FRC |
|
15.53 |
|
0.26 |
|
| Normal |
1,000 |
13.82 |
0.89 |
0.36 |
1.4 |
| LS |
| FRC |
|
14.1 |
|
0.16 |
|
| Normal |
800 |
12.85 |
0.91 |
0.19 |
1.2 |
| LC |
| FRC |
|
15.53 |
|
0.17 |
|
| Normal |
800 |
13.19 |
0.85 |
0.21 |
1.2 |
| CO |
| FRC |
|
18.16 |
|
0.2 |
|
| Normal |
2,000 |
15.28 |
0.84 |
0.43 |
2.2 |
| JW |
| FRC |
|
14.31 |
|
0.11 |
|
| Normal |
500 |
12.87 |
0.9 |
0.16 |
1.5 |
| Abdominal |
500 |
10.62 |
0.74 |
0.37 |
3.4 |
| TD |
| FRC |
|
16.2 |
|
0.19 |
|
| Normal |
1,250 |
13.96 |
0.86 |
0.3 |
1.6 |
| JL |
| FRC |
|
14.85 |
|
0.13 |
|
| Abdominal |
500 |
11.07 |
0.75 |
0.33 |
2.5 |
| TB |
| FRC |
|
15.53 |
|
0.14 |
|
| Abdominal |
750 |
11.83 |
0.76 |
0.31 |
2.2 |
|
|
DML, diaphragm muscle length adjusted for length of central tendon
(0.25 × FRC length, where FRC is functional residual capacity); l/l0, fractional length;
h, thickness.
|
|
Length-Thickening Relationship
Figure 3 shows the measured relationships
of l/l0 to
h/h0 from Table 5
compared with theoretical relationships derived from the different
models using data from Table 2. Calculated relationships from
models B and
C deviate significantly from the
measured data, although both are closer than model
A. Model D, with a
hypothetical 10% decrease in the height of the dome and a 10%
increase in the transverse axis of the thorax at total lung capacity
(TLC) taken into account, causes the predicted relationship of
l/l0 to
h/h0 to approach
that measured. The height of the dome decreased by 0-25%, and the
transverse axis of the thorax increased by 5-8% in our subjects
for the range of inspired volumes studied here. The 10% increase for
transverse axis at TLC is an approximation based on measurements from
residual volume to TLC (3).
Fig. 3.
Fraction of diaphragm muscle length
(l/l0) vs.
fractional thickening
(h/h0) for each
geometric model. Solid line, model A; long dashed line, model B; short
dashed line, model C; dashed-dotted line, model D
, with height of
dome reduced by 10% and transverse axis increased by 10%. 
,
Measured values of
h/h0 and
l/l0 from each
subject. Thickening was determined from ultrasound measurements, and
lengths were from chest radiographs matched to same inspired lung
volumes.
[View Larger Version of this Image (13K GIF file)]
Relationship of h/h0 to Inspired Volume
The measured patterns of thickening in relation to inspired volume for
three representative breaths from the subjects who completed ultrasound
studies with both breathing patterns are shown in Fig.
4. For the same degree of diaphragm
thickening, the inspired volumes for the abdominal breaths were less
than those for the normal breathing patterns, indicating that for the same diaphragm shortening, less volume expansion of the lung is accomplished.
Fig. 4.
Fractional diaphragm thickening
(h/h0) vs.
inspired lung volumes throughout breaths with normal and abdominal
breathing patterns. Three similar-sized breaths for each subject
(A: subject JW; B: subject
LS; C: subject PS), expressed as percentage
of inspiratory capacity (IC), are shown. Each point is a measurement at
200-ms intervals. 
, Normal breathing pattern; 
, abdominal
breathing pattern.
[View Larger Version of this Image (11K GIF file)]
Models C and
D better approximated the measured
relationship of
l/l0 to
h/h0 than
model B or
A (Fig. 3). Because
model B is mathematically the
simplest, it was used to demonstrate the change in
h/h0 in relation
to inspired volume with the two different breathing patterns. The
volume under the cylinder approximates the theoretical IC, and the
change in volume as z decreases is the
inspired volume. When z = 0, IC is
100%. Changes in
h/h0 and lung
volume are determined as shown in the
APPENDIX (Eqs.
A7-A10). The results are shown in Fig.
5, which demonstrates the same curvilinear relationship of
h/h0 to inspired
volume in the normal subjects in Fig. 4, indicating that this
relationship is determined by geometry.
Fig. 5.
Relationship of
h/h0 to inspired
volume expressed as percentage of inspiratory capacity based on
model B. , Normal breathing pattern; , abdominal breathing pattern.
[View Larger Version of this Image (10K GIF file)]
DISCUSSION
Three statements can be made with regard to these studies:
1) for a given inspired volume,
diaphragm shortening and thickening are greater during an abdominal
breath; 2) for a single breath, the
relationship between inspired volume and thickening is curvilinear; the
rate of rise in
h/h0 increases as
inspired volume increases; and 3)
relative diaphragmatic thickening for a given inspired volume is
greater than expected for fiber shortening, assuming parallel muscle
fibers and no shear. Statements 1 and
2 are expected results, but
statement 3 requires considerations of
the geometry of the human diaphragm and its attachments.
Diaphragm Shortening and Abdominal Breathing
The measured diaphragm muscle lengths from the chest radiographs show
almost twice as much shortening with abdominal breaths (Table 5). This
was also evident in the ultrasound studies of three subjects
(JW, LS, and
PS) examined with normal and
abdominal breathing patterns (Fig. 4). Figure 4 also shows that greater inspired volumes are achieved for the same diaphragm shortening when
the rib cage expands normally. Thus, as expected, inspiration primarily
with the diaphragm is less effective in expanding the lung.
The abdominal breathing pattern presumably caused near-maximal
shortening of the diaphragm in our studies, as demonstrated previously
by others (6). Although not measured here, simultaneous paradoxical
motion of the upper rib cage was found with abdominal breathing by De
Troyer and Estenne (6). This occurs because the scalenes and
intercostal muscles that elevate the rib cage are minimally activated
with the abdominal breathing pattern (6). Similarly, radiographs from
two subjects showed inward movement of the lower rib cage (data not
shown), suggesting an expiratory effect. Thus inspiration primarily
with the abdomen may cause even less expansion of the lung.
Furthermore, this supports the concept that maintenance of
thoracoabdominal configuration enhances the efficiency of respiratory
muscular action (9).
Curvilinear Relationship of h/h0 to
Inspired Volume
The relationship of thickness to length for a rectangular strip during
shortening must be curvilinear if the volume of the strip and the width
do not change; the rate of thickening increases exponentially as length
approaches zero. Because lung volume increases proportionally to
diaphragm shortening (3, 11), thickening should be proportional to
inspired volume, and this relationship is also expected to be
curvilinear. Thus, as expected, the relationship of
h/h0 to inspired
volume is curvilinear, as shown in Fig. 4. The same phenomenon was
demonstrated by using the simple cylinder of model
B to determine the relationship of
h/h0 to inspired
volume for the abdominal and normal breathing patterns (Fig. 5) and
indicates that this curvilinear relationship is set by geometry.
Considerations of Geometry
Although we have good evidence that the diaphragm thickens
significantly in the middle costal region at the attachment to the rib
cage (17-19), it is not known how this thickening occurs. The
principle is that the regional shape change of the diaphragm during
inspiration is reflected by thickness increases in the zone of
apposition. This is supported by three of the geometric models here and
similar previous considerations (14, 15). Only in
model A (see
APPENDIX) is
h/h0 inversely
proportional to l/l0, and
h/h0 = l0/l;
i.e., at maximal shortening,
l/l0 = 0.56 and
h/h0 = 1/0.56 = 1.8, which is less than the maximal degree of thickening we observed
(Fig. 4). Studies of the biological constraints of muscle fibers reveal
that >30% shortening requires greater stimulation, yielding less
tension and more tendency for fiber damage or fatigue (12), which
suggests that this model does not apply in vivo.
Models B, C, and
D predict much greater thickening for
shortening in the range of 40 and 30%. Model
D, which incorporates features of
models B and
C, yields predictions much closer to
measured relationships when mean changes in height of the dome and
thoracic diameter are considered, as was seen in most of our subjects.
The common features of the models are as follows.
1) Because the geometry of the
diaphragm includes a dome of relatively fixed muscular surface area and
a zone of apposition that decreases its surface area with muscle
shortening, a change must occur in distribution of the muscle between
these regions as the zone of apposition disappears. In the cylindrical
model (model B) the muscle mass must
be redistributed from a state of a large surface area-to-muscle mass
ratio to a state with a relatively small surface area-to-muscle mass
ratio. This causes a greater thickening ratio than expected if a muscle
strip maintained a simple rectangular shape (model
A). 2) The
addition of a variable taper of the muscle from the zone of apposition
to its insertion into the CT (model C) causes nonuniform distribution of the muscle mass
and has been demonstrated in canine diaphragms (18). This is magnified
with the redistribution of muscle mass from the zone of apposition to
the dome with muscle shortening (creating a wedge), generating greater
thickening in the zone of apposition than expected if the shape change
occurred uniformly.
Techniques and Potential Sources of Error
LS, LC, and
CS were naive subjects who had limited
understanding of the nature of the study. The other subjects, however, were physicians who understood the purpose of the study, which may have
subconsciously affected their "native" breathing patterns. Nevertheless, we think that useful information was obtained, since significant differences were noted even though the bias most likely increased the subject's diaphragmatic contribution to each breath. Furthermore, all subjects' breathing patterns remained consistent throughout each run of breaths, which allowed comparisons between breathing patterns.
Chest radiographs were used to determine the length of the diaphragm as
well as the relative values of A, D,
d, and z for the
equations. The inspired volumes used for the chest radiographs were
based on the ultrasound images; i.e., they were matched. However, we
were concerned about errors from matching the two studies to determine
length and thickness at the same inspired volume. Extreme care was
taken to position the subjects for the chest radiographs as they were
when the physiological parameters were measured and to ensure that the
inspired volumes and breathing patterns were consistent. Accordingly,
the FRC is not likely to have changed significantly between the
ultrasound studies and the radiographs for these subjects, because they
were normal subjects studied on the same day and in the same seated
posture (including arm support) each time. Other studies have shown a
difference in FRC of at most only 3% in seated subjects studied
without arm support and with arm support (5). In addition, the
ultrasound thickness measurements at end expiration did not vary during
the runs, which also suggests that the FRC was not changing
significantly. Although it is possible that the subjects may have
varied the inspiratory efforts slightly during the radiographic
procedures, they were instructed to not "pull" against the empty
anesthesia bag to minimize that effect, and we have determined that
ultrasound diaphragm thickness does not change during a simple breath
hold (unpublished observations).
Significance of Resting Diaphragm Thickness in the Zone of
Apposition
For the same level of stimulation and the same resting length, the
maximal inspiratory force that can be generated by muscle in the zone
of apposition is determined by the number of fibers in parallel,
represented by resting thickness of the diaphragm. This maximal force
can be estimated by the maximal transdiaphragmatic pressure
(Pdimax) and resting
cross-sectional area of the muscle in the zone of apposition.
Diaphragmatic wall stress or tension in the zone of apposition
(
di) × cross-sectional
area of the muscle
(Adi) in the
zone of apposition must balance the transdiaphragmatic pressure (Pdi) × cross-sectional area of the thorax
(Ath) in the same region;
i.e.
|
(5)
|
Maximal
tension can be estimated using a rearrangement of Eq. 5
|
(6)
|
where
dimax is the estimated
maximal tension per unit cross-sectional area that can be
developed by the diaphragm contracting isometrically (26 N or
2.65 kg/cm2) (16). We assume
that Pdimax is produced from
relatively isometric contractions, neglecting effect from decompression
of gas in the thorax and deformation of the rib cage in performing the
maneuvers. For each subject,
Adi was
determined by using dimensions from radiographs at FRC and at
inspiration.
Significance of Enhanced Thickening in the Zone of Apposition
During Inspiration
Minimizing wall stress.
On the basis of Eq. 5, the greater the
thickness of the diaphragm in the zone of apposition during
inspiration, the greater will be
Adi and the
smaller di. This may have a
beneficial effect on regional blood flow by minimizing pressure
surrounding the microvasculature. For example, predicted values of wall
stress at peak inspiration for 10 cmH2O Pdi on the basis of
radiographic dimensions and matched diaphragmatic thickness for each of
our subjects are shown in Table 6. If
inspiratory Pdi becomes high during exercise or in a patient with lung
disease, muscle tension at a given thickness must correspondingly
increase, and the higher wall tension potentially may increase
intramuscular pressure to levels that would collapse capillaries and
impede blood flow, leading to impaired function (13). As the ratio of
inspiratory time to total time of a breath increases at a high wall
stress, further constraints on blood flow are added which may increase the susceptibility to diaphragmatic fatigue (2). Enhanced thickening of
the diaphragm in the zone of apposition during inspiration may help
maintain adequate blood flow.
|
Table 6.
Calculated Pdi and
|
| Subject |
D,
cm |
A, cm |
h, cm |
z,
cm |
Pdimax, cmH2O |
,
g/cm2
|
| Pdi = 10 cmH2O |
Pdi = 20 cmH2O |
|
| CS |
12.55 |
7.16 |
0.26 |
7.29 |
154 |
|
|
|
13.23 |
7.5 |
0.36 |
3.96 |
|
130 |
260 |
| LS |
11.2 |
7.2 |
0.16 |
5.4 |
101 |
|
|
|
11.66 |
7.16 |
0.19 |
4.05 |
|
230 |
460 |
| LC |
12.87 |
8.28 |
0.17 |
5.49 |
90 |
|
|
|
13.14 |
9.36 |
0.21 |
3.06 |
|
258 |
516 |
| CO |
12.96 |
8.42 |
0.2 |
9.9 |
105 |
|
|
|
14 |
9.59 |
0.43 |
4.77 |
|
132 |
264 |
| JW |
11.52 |
6.97 |
0.11 |
5.4 |
68 |
|
|
|
12.11 |
7.06 |
0.16 |
2.88 |
|
272 |
544 |
| TD |
13.73 |
7.25 |
0.19 |
5.67 |
109 |
|
|
|
13.86 |
7.42 |
0.3 |
2.88 |
|
158 |
316 |
| JL |
13.05 |
5.58 |
0.13 |
6.03 |
89 |
|
|
|
12.24 |
5.76 |
0.33 |
1.53 |
|
114 |
228 |
| TB |
13.41 |
7.83 |
0.14 |
6.66 |
76 |
|
|
|
13.86 |
7.74 |
0.31 |
2.52 |
|
156 |
312 |
|
|
Pdi, transdiaphragmatic pressure; Pdimax, maximum Pdi;
, wall stress. JL and TB were studied with
abdominal breath only.
|
|
Distribution of work requirements.
The zone of apposition in the diaphragm is primarily responsible for
the inspiratory pressure-volume work by the diaphragm. The models
employed assume uniform shortening of muscle fibers; hence, greater
thickening than conventionally predicted for the muscle in the zone of
apposition means that more sarcomeres are retained where the work
requirements are highest, thereby distributing the work in the zone of
apposition among more contractile units. Diffusing capacity in red
muscle is primarily determined by the number of capillaries per muscle
fiber rather than muscle thickness (7, 10). Hence, if oxygen
requirements per sarcomere are minimized by enhanced thickening during
inspiration while capillaries and diffusing capacity per sarcomere
remain fixed, work efficiency and oxygen extraction could be
significantly enhanced by the mechanism.
Summary and Speculations
In summary, these studies show a link between the three-dimensional
shape of the diaphragm and the unusual thickness changes in the zone of
apposition. Furthermore, the resting thickness and thickness increases
during inspiration may have substantial physiological significance for
diaphragm muscle performance.
Measurements of diaphragm length and thickening were compared with
geometric models of the costal diaphragm. Although these models make no
assumptions about the alignment of muscle fibers, previous assumptions
were that all fibers are parallel and shorten along the axis of
diaphragm descent. However, if it is assumed that all thickening is
muscle mass and excessive fiber shortening does not occur, one
explanation for the magnitude of observed thickening would be to
consider the spatial attachments of the muscle fibers between the CT
and the rib cage. Fiber alignments in situ may cause shear to occur
during inspiration, creating greater axial descent than fiber
shortening. This supposition would be consistent with the observed
behavior of the diaphragm, and the biological constraints of fiber
shortening would be within the constraints of model B,
C, or D.
Despite these speculations, the mechanism of diaphragm thickening is
not known. Further studies are needed to determine how this is
accomplished and its potential effect on the regional force output of
the diaphragm. Understanding how the thickness changes of the diaphragm
occur is important not only for completely understanding the in situ
structure-function relationship of the diaphragm but also for
developing better mathematical models for predicting behavior of the
respiratory pump.
FOOTNOTES
Address for reprint requests: J. L. Wait, Suite B-202, 7777 Forest
Ln., Dallas, TX 75230.
Received 28 May 1996; accepted in final form 30 May 1997.
APPENDIX
Where indicated, the values used in the equations are based on the mean
values determined from chest radiographs of our subjects taken at FRC.
The height of the dome (d), the
transverse axis of the thorax (D),
the lateral axis of the thorax (A),
and the length of the zone of apposition
(z) were determined as relative mean
values (Table 1). Thickness at FRC is assigned an arbitrary value;
i.e., h0 = 0.1. In summary, the relative values from our subjects are as follows:
w = 1, z0 = 1, d = 0.65, CT = 0.75 (for models A and
B),
h0 = 0.1, D = 2.02, and
A = 1.17.
Model A.
The simplest relationship of thickness to relative length can be
determined for a straight, untapered strip of muscle with constant
volume (V) and the dimensions of length
(l), thickness (h), and width
(w)
![V = [(<IT>D</IT> − CT) + <IT>z</IT>]<IT>hw</IT>](/content/vol83/issue4/fulltext/1123/img007.gif)
|
(A1)
|
where
D is the transverse dimension of the
thorax, CT is the length of the central tendon, and
z is the length of the zone of
apposition. The width of the strip remains constant
(w = 1), and this is rearranged to
determine thickness during inspiration
![<IT>h</IT> = V/[(<IT>D</IT> − CT) + <IT>z</IT>]<IT>w</IT>](/content/vol83/issue4/fulltext/1123/img008.gif)
|
(A2)
|
Also,
on the basis of previous studies, CT may be estimated from the length
of the hemidiaphragm at FRC (3)
|
(A3)
|
Thickness
change is expressed as the ratio of the mean thickness at that point
(h) to the mean thickness at end
expiration preceding that breath
(h0), i.e.,
h/h0, and the
fractional length changes are expressed as a fraction of the initial
length (l/l0). Thus, by use of the dimensions from our subjects and the assumed value
for h0, the
thickness at TLC becomes h = 0.225/1.25 = 0.18 or
h/h0 = 0.18 and
l/l0 = 0.56.
Model B.
Model B assumes that the diaphragm's
shape is that of a cylinder with the radius the same dimension as the
transverse axis of the thorax (D).
The height of the cylinder is the length of the zone of apposition
(z). The volume of this structure is
the volume in the dome (the area of the circle × the thickness)
plus the volume in the zone (the area of the cylinder × the
thickness)
![V = &pgr;<IT>h</IT>[(<IT>D</IT><SUP>2</SUP> − CT<SUP>2</SUP>) + (2<IT>Dz</IT>)]](/content/vol83/issue4/fulltext/1123/img010.gif)
|
(A4)
|
So
The
length is the radius (D) minus CT
plus z
|
(A5)
|
![<IT>h</IT> = V/&pgr;[(<IT>D</IT><SUP>2</SUP> − CT<SUP>2</SUP>) + (2<IT>Dz</IT>)]](/content/vol83/issue4/fulltext/1123/img013.gif)
|
(A6)
|
at
TLC h/h0 = 2.1 and l/l0 = 0.56. The inspired volume of the hypothetical lung inflated by this model is
the volume displaced by the descent of the diaphragm. We also assume
that as the rib cage expands with the normal breathing pattern, the
hemithorax increases by 10% at TLC but the same value of
D remains for abdominal breathing, so
|
(A7)
|
where
D0 is
D at FRC and
DIC is
D at IC. Also, the IC with normal
breathing (ICN) is
|
(A8)
|
where
z0 is
z at FRC. With abdominal breathing,
rib cage expansion does not occur, so
|
(A9)
|
where
ICA is IC with abdominal
breathing. Inspired volumes between FRC and TLC are determined by the
change in z during inspiration (zI), and
|
(A10)
|
where
zI is the value
of z substituted for
z0 in
Eq. A8 or
A9 to determine inspired volume with
normal breathing or abdominal breaths, respectively. Therefore, the IC
with normal breathing (using rib cage and abdomen) is IC = (2.22)2
= 15.48; with the
abdomen alone it is 12.6 or 81%.
Model C.
A segment of diaphragm extending from a certain thickness at the rib
cage should taper toward its insertion into the extremely thin CT.
Theoretically, this section in the dome can be represented as a wedge,
and the section extending along the zone of apposition can be
represented as a cube. The volume of a wedge is equal to one-half its
base times the height. The volume of the whole structure is the sum of
the volume of the wedge
(1/2hwd) plus the volume of the cube (hwz)
|
(A11)
|
so
and
|
(A12)
|
As
inspiration approaches TLC, the length of the zone of apposition
approaches 0, and so does the relative volume in the cube. So, if
d and
w remain constant, the thickness
quadruples. Thus, h = 0.133/0.33 or
0.4, and h/h0 = 4. However, to adjust for the CT, the length of the segment in the dome
(Y) becomes
|
(A13)
|
and
|
(A14)
|
and
|
(A15)
|
at
FRC and
|
(A16)
|
So,
using the above values for D, z, and
d and combining Eqs.
A13 and A16 to solve
for CT
|
(A17)
|
On
the basis of the principle of Cavalieri (8), the volume of a wedge
remains the same if dimensions of base and height do not change
regardless of the length of the surface. So, by combining
Eqs. A12-A14,
l as the fraction of initial length
can be estimated from the thickening ratio
(h/h0),
assuming that D and
d remain constant
![<IT>l</IT> = [1.37 − 0.325 + 0.1325/(<IT>h</IT>/<IT>h</IT><SUB>0</SUB>)(0.1)]](/content/vol83/issue4/fulltext/1123/img027.gif)
|
(A18)
|
Model D.
Model D is an elliptical cylinder
representing the diaphragm in the zone of apposition, and the dome is
one-half of an ellipsoid. The formula for the volume of the cylinder is
the difference between two similar structures that differ by the
thickness (h). Because the dome is
based on two concentric ellipsoids that must intersect at the CT, the
thicknesses along the major and minor axes in the base are not equal.
The relationship between the axes and thickness of these concentric
ellipses can be defined as such
and
where
A is the minor axis,
h is thickness in the minor
axis, D is the major (transverse)
axis, and h is thickness in the major
axis (costal thickness). Because the relationship between the axes also
holds for the zone of apposition, substitutions are made for the
determination of the volume of the elliptical cylinder in the zone of
apposition (Vz)
|
(A19)
|
|
(A20)
|
The
volume for the dome (Vd) is
|
(A21)
|
Combining
Eqs. A20 and A21 gives the formula for the volume
of the whole diaphragm
|
(A22)
|
and
![<IT>h</IT> = <FR><NU>−(2<IT>D</IT>) + <RAD><RCD>[(−2<IT>D</IT>)2 − (4<IT>E</IT>)]</RCD></RAD></NU><DE>2</DE></FR>](/content/vol83/issue4/fulltext/1123/img034.gif)
|
(A23)
|
where
|
(A24)
|
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![V = 0.314[(3.52) + 2<IT>Dz</IT>] = 2.37](/content/vol83/issue4/fulltext/1123/img011.gif)
