Vol. 94, Issue 3, 1084-1091, March 2003
Breath-by-breath measurement of the volume displaced by
diaphragm motion
Bhajan
Singh1,2,
Janine A.
Panizza1, and
Kevin E.
Finucane1
1 Department of Pulmonary Physiology, Sir Charles
Gairdner Hospital, and 2 Department of Physiology,
University of Western Australia, Nedlands, Western Australia 6009, Australia
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ABSTRACT |
To develop an accurate method to
measure the volume displaced by diaphragm motion (
Vdi) breath by
breath, we compared Vdi measured by a previously evaluated biplanar
radiographic method (Singh B, Eastwood PR, and Finucane KE.
J Appl Physiol 91: 1913-1923, 2001) at several
lung volumes during vital capacity inspirations in 10 healthy and nine
hyperinflated subjects with 1) Vdi measured from the same
chest X-rays by two previously described uniplanar methods
(Petroll WM, Knight H, and Rochester DF. J Appl
Physiol 69: 2175-2182, 1990; Verschakelen JA, Deschepper K,
and Demendts M. J Appl Physiol 72: 1536-1540,
1992) and a proposed method that considered actual cross-sectional
shape of the rib cage and spinal volume (VdiS); and
2) VdiS measured by lateral fluoroscopy in the same 10 healthy subjects. Relative to biplanar Vdi,
VdiS values from lateral chest X-rays and fluoroscopy
were not different, whereas Vdi values of Petroll et al. and
Verschakelen et al. were increased by (means ± SD) 1.98 ± 1.59 and 1.16 ± 0.82 liters, respectively (both P < 0.001). During quiet breathing, VdiS by lateral
fluoroscopy was 66 ± 16% of tidal volume and similar to that
between functional residual capacity and one-half inspiratory capacity
by the biplanar radiographic method. We conclude that accurate
breath-by-breath measurements of Vdi can be made by using lateral fluoroscopy.
respiratory muscles; respiratory mechanics; fluoroscopy
| |
INTRODUCTION |
OUR LABORATORY HAS
RECENTLY described a radiographic method for measuring inspired
volume attributable to diaphragm motion (Vdi) using matched
posteroanterior (PA) and lateral chest X-rays (CXRs) to quantify the
change in subphrenic volume during inspirations from residual volume
(RV) (9, 10). Vdi and the change in lung volume
attributable to expansion of the pulmonary rib cage, measured
independently, closely approximated inspired volume in healthy controls
and subjects with hyperinflation due to emphysema (9).
These results suggest that Vdi measured with the biplanar method is
accurate and defines the volume contribution of the diaphragm to inspiration.
Breath-by-breath measurements of Vdi would allow measurement of work
and power output of the diaphragm and may improve assessment of
diaphragm function. Measurement of Vdi during breathing cannot be
made by using CXRs but may be possible with the use of fluoroscopy, if
Vdi could be accurately measured from a single plane. Two such
methods have been proposed. Petroll et al. (7) measured Vdi in dogs using anteroposterior fluoroscopy and modeling the subphrenic space and dome of the diaphragm as a truncated cone with a
circular cross section and an oblate spheroid, respectively. Verschakelen et al. (11) measured Vdi in humans using
lateral fluoroscopy to measure sagittal rib cage diameter and the
surface area swept by the diaphragm during inspiration, modeling the
cross-sectional shape of the abdominal rib cage as a rectangle. The
cross-sectional shape of the rib cage used in these models differed
substantially from shapes based on studies in humans (4,
8), and neither method corrected the volume swept by the
diaphragm for the volume occupied by the spine and paraspinal tissues
(Vsp). For these reasons, the methods of Petroll et al.
(7) and Verschakelen et al. (11) are likely
to give inaccurate estimates of Vdi in humans. The accuracy of the
biplanar method previously reported by us depends in part on the
validity of the geometric shape used to calculate the cross-sectional
area of the abdominal rib cage from the coronal and sagittal diameters
measured from the PA and lateral CXRs, respectively. We adopted the
shape described by Pierce et al. (8) for the pulmonary rib
cage. To the extent that this shape may not apply to the abdominal rib
cage, our measurements would also be inaccurate.
The aim of this study was to develop a fluoroscopic method for
measuring Vdi breath by breath, which was accurate in both healthy
and hyperinflated subjects. To assess the relative accuracy of various
models for estimating the cross-sectional area of the abdominal rib
cage, we compared estimated and measured cross-sectional areas of
thoracic computed tomography (CT) scans. The accuracy of methods for
estimating Vdi from a single radiographic plane and lateral
fluoroscopy was assessed by comparing results with those obtained, in
the same subjects, with the previously validated biplanar method.
Methods used to estimate Vdi from a single plane were those
described by Petroll et al. (7), Verschakelen et al.
(11), and a new method that incorporated our findings on the cross-sectional shape of the abdominal rib cage and considered the
Vsp. We found that the cross-sectional shape of the
abdominal rib cage was accurately modeled as one-third the way between
an ellipse and a rectangle, as described by Pierce et al.
(8) for the pulmonary rib cage, and that the shape of the
rib cage changed little with lung volume. We hypothesized that Vdi
would be 1) overestimated by the methods of Petroll et al.
(7) and of Verschakelen et al. (11) because
these methods assumed thoracic shapes that overestimated the actual
cross-sectional area of the abdominal rib cage and did not consider the
volume occupied by spinal tissues, and 2) most accurately
estimated by the proposed new method. Our findings confirmed these hypotheses.
| |
METHODS |
Rib cage shape.
To examine the accuracy of various models used to estimate the
cross-sectional area of the rib cage (4, 7, 8, 11), CT
images of the thorax close to relaxed total lung capacity (TLC) were
obtained in 25 healthy subjects and 22 with pulmonary hyperinflation due to emphysema (Table 1). The CT scans
were obtained for clinical purposes with consent of the subjects. The
internal cross-sectional area of the rib cage at the levels of the
xiphoid process (abdominal rib cage) and the carina (pulmonary rib
cage) were 1) measured by planimetry and 2)
calculated by using the major sagittal and coronal diameters of the rib
cage. The following geometric models were used: circles, ellipse,
rectangle, a rectangle bounded by two semicircles ("athletic
track") as described by Chihara et al. (4), and
one-third the way between an ellipse and a rectangle as defined by
Pierce et al. (8). Separate cross-sectional areas were
calculated for circles with diameters equal to the major coronal and
sagittal diameters of the rib cage. All measurements were made by using
a digitizing palette (Accugrid, Numonics, Montgomeryville, PA).
Radiographic measurements of Vdi.
Vdi was measured by the biplanar method (9) in 10 healthy subjects and nine subjects with emphysema and severe pulmonary hyperinflation (Table 1). These results were then used to assess the
accuracy of Vdi estimated by various uniplanar methods using the
same CXRs. Subphrenic volume and the Vsp were estimated
from PA and lateral CXRs taken at active RV, functional residual
capacity (FRC), one-half inspiratory capacity (1/2IC), and TLC during a
slow vital capacity (VC) inspiration in the erect posture. At each lung
volume, Vdi was also measured with the method described by Petroll
et al. (7) applied to the right subphrenum on the PA CXRs
and to the lateral CXRs, the method of Verschakelen et al.
(11), and a new method described below
(VdiS). Informed consent was obtained from each subject,
and ethical approval was granted by the Committee for Human Rights,
University of Western Australia.
VdiS.
Lateral CXR images at RV, FRC, and 1/2IC were superimposed on images at
FRC, 1/2IC, and TLC, respectively, using the images of vertebral bodies
and radiopaque ball bearings adhered to the posterior chest wall. The
subphrenic space at the lower lung volume was defined by the silhouette
of the right hemidiaphragm, a straight line joining the anterior and
posterior costophrenic angles at the higher lung volume, a straight
line joining the anterior costophrenic angles at each lung volume, and
the posterior limit of the lung (Fig.
1A). This volume was divided
into a dome (Vdome,L) and a frustrum (Vfr), the
latter being represented by the area between the lines joining the
anterior and posterior costophrenic angles at each volume (Fig.
1A). The subphrenic space at the higher lung volume was
taken as the dome of the diaphragm (Vdome,H). The
Vsp within the volume swept by the diaphragm was defined by
the silhouettes of the diaphragm at each lung volume, the anterior
margin of the vertebral bodies, and the posterior limit of the lung
(Fig. 1A). The Vdi was calculated by using the following
equation
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(1)
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This equation can be represented as follows (see
APPENDIX)
|
(2)
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where Ddome,L and
Ddome,H are the length or sagittal diameter of
the base of the dome at the lower and higher lung volume, respectively;
Adome and Afr are the
areas projected by the dome and frustrum in the sagittal plane,
respectively; Adome,H and Adome,L are the Adome at
higher and lower lung volume, respectively; Dsp
is the sagittal width of the volume of spinal tissues at the level of
Ddome,L; and Asp is the
area of spinal tissues projected in the sagittal plane (Fig.
1A). Equation 2 is derived in the APPENDIX; it assumes that the ratio of coronal to sagittal
diameters does not change with lung volume and that the cross-sectional shape of the spinal tissues is circular.
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Fig. 1.
A: schematic illustration of proposed
uniplanar method for measuring the volume displaced by diaphragm motion
(VdiS) from a lateral chest X-ray (CXR) or fluoroscopy.
The silhouette of the diaphragm dome, sagittal diameter of the rib cage
at the base of the diaphragm dome, and the anterior and posterior walls
of the rib cage are represented by solid lines at the lower (L) lung
volume and dashed lines at the higher (H) lung volume.
VdiS was the difference in volume between
(DomeL + frustrum) and (DomeH + spine), which are represented by the respective areas bcdb,
abdea, ahea, and abcha. The sagittal
diameter of spinal tissues was taken as distance bg.
B: where the anterior costophrenic angle at the higher
volume is cephalad to the costophrenic angle at the lower volume, the
volume represented by area fdd'f was excluded from analysis,
and DomeL is represented by area bcd'b and
frustrum by area abd'a. See text for details.
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Cephalic movement of the anterior chest wall during inspiration
resulted in the anterior costophrenic angle at the higher lung volume
being cephalad of the anterior costophrenic angle at the lower volume
in 17 of the 46 volume pairs measured. To avoid overestimation of
VdiS in this circumstance, the anterior limit of
Vdome,L was defined by its intersection with the straight line joining the anterior and posterior costophrenic angles at the
higher volume (Fig. 1B).
Fluoroscopic measurement of VdiS.
To assess the accuracy of Vdi estimated from lateral fluoroscopy,
VdiS was measured by fluoroscopy in the 10 healthy
subjects in whom Vdi had been measured with the biplanar
radiographic method. The diaphragm and lower rib cage were imaged by
lateral fluoroscopy, with a field of vision 16 in. in diameter (Toshiba CAS 8000 DSA, Tokyo, Japan) at a frame rate of 15 per second. Images
and time of day were stored by using a super VHS video recorder and
cassette [Mitsubishi, HS-E82(A) and Fuji, Pro]. Radiopaque ball
bearings adhered to the chest wall allowed alignment of images at
different lung volumes. Each subject was seated with the left chest
wall as close as possible to the image intensifier with the arms
elevated and with hands resting on the head. Two sequences of two to
four tidal breaths followed by an exhalation to RV and an inspiration
to TLC were imaged. Inspiratory flow and volume were measured with a
pneumotachograph and recorded continuously on computer (Powerlab,
ADInstruments, Sydney, Australia). Posture was maintained constant; no
attempt was made to control chest wall configuration. Radiation
exposure was varied to optimize contrast of the diaphragm silhouette
and bony landmarks and was estimated at ~0.1 mSv.
Fluoroscopic images at end expiration and end inspiration during quiet
breathing and at RV, FRC, 1/2IC, and TLC during VC inspirations were
identified by interpolating images on video frames and inspired volume.
Images of the diaphragm and bony landmarks were traced onto transparent
paper. Distortion and magnification of the images were defined by using
a precise grid with radiopaque lines at 1-cm intervals placed at the
same distance from the image intensifier as the right midclavicular
line. The distorted image of the grid, also on transparent paper, was
used to replot the position of the diaphragm and chest wall on
Cartesian coordinates, thereby correcting for distortion and
magnification. VdiS was then measured from the replotted
images by using the method described above.
Data analysis and statistics.
All data are expressed as means ± SD. Characteristics of healthy
and hyperinflated subjects were compared by using the Student's t-test. Paired t-tests and the methods of Bland
and Altman (2) were used to examine the relationships
between 1) measured and calculated rib cage cross-sectional
area and 2) biplanar and uniplanar Vdi. Significance was
defined as P < 0.05.
| |
RESULTS |
Cross-sectional shape of the rib cage.
The measured cross-sectional areas of the abdominal and pulmonary rib
cage are compared with those calculated using the major sagittal and or
coronal diameters and various models of thoracic shape, in Fig.
2. In both healthy and hyperinflated
subjects, the cross-sectional areas of the rib cage were underestimated when modeled as an ellipse, overestimated when modeled as a rectangle, and either under- or overestimated when modeled as a circle, depending on whether the major sagittal or coronal diameter was taken to be the
diameter of the circle. The cross-sectional areas of the abdominal and
pulmonary rib cages were most accurately calculated when modeled as
one-third the way between an ellipse and a rectangle or as an
"athletic track" (Figs. 2 and 3). The
ratios of the major coronal-to-sagittal diameters of the abdominal rib
cage were 1.44 ± 0.11 in healthy subjects and 1.36 ± 0.13 in hyperinflated subjects. These results were similar to those obtained
with the biplanar method, where the ratios were 1.5 ± 0.08 at RV
and 1.36 ± 0.06 at TLC in controls and 1.38 ± 0.13 at RV
and TLC in emphysematous subjects (9).
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Fig. 2.
Difference between calculated cross-sectional (CS) area of the
abdominal and pulmonary rib cages with the use of a variety of
geometric models and actual CS area measured by digitizer, expressed as
a percentage of the measured value, in 25 healthy and 22 hyperinflated subjects. Values are means ± SD. Significant
difference from measured CS area: * P < 0.01,  P < 0.001 (paired t-test).
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Fig. 3.
Bland and Altman comparison of the calculated and measured CS areas
of the abdominal (A) and pulmonary (B) rib cages
in 25 healthy and 22 hyperinflated subjects. CS area was calculated
geometrically from the major coronal and sagittal diameters of the rib
cage and assuming a shape of one-third the way between an ellipse and a
rectangle and was measured from computed tomograms by digitizer. The
solid lines are the mean difference, and the dashed lines are the
limits of the 95% confidence intervals.
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Vdi.
Vdi estimated by the methods of Petroll et al. (7)
using PA CXRs, and of Verschakelen et al. (11) using
lateral CXRs, exceeded biplanar Vdi by 1.98 ± 1.59 and
1.16 ± 0.82 liters, respectively (both P < 0.001). These overestimates increased with volume, and, in many cases,
Vdi exceeded inspired volume (Table 2,
Fig. 4). Vdi by the method of
Petroll et al. (7) applied to lateral CXRs was reduced
(
0.47 ± 0.33 liter, P < 0.001) relative to
biplanar Vdi (Table 2, Fig. 4). There was no difference between biplanar Vdi and VdiS measured from lateral CXRs in
the healthy and hyperinflated subjects (mean difference 0.06 ± 0.24 liter, P = 0.08) or from lateral fluoroscopy in
healthy subjects (mean difference 0.06 ± 0.28 liter,
P = 0.30) (Table 2, Fig. 4). If the Vsp had
not been considered, VdiS measured from lateral CXRs would have exceeded biplanar Vdi by 0.29 ± 0.27 liter
(P < 0.001) and 0.15 ± 0.29 liter
(P = 0.03) in healthy and hyperinflated subjects,
respectively. Vdi measured fluoroscopically during tidal breathing
was 0.66 ± 0.16 relative to tidal volume. Vdi/tidal volume had
a coefficient of variation within subjects of 11.6 ± 5.7% (Fig.
5), and the mean value was similar to the
ratio of Vdi to the volume inspired between FRC and 1/2IC during VC
inspirations in the six subjects, in whom this information was obtained
with the biplanar method (0.71 ± 0.14 vs. 0.68 ± 0.12, P = 0.66).
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Table 2.
Ratio of Vdi to inspired volume for breaths between RV and FRC,
between RV and 1/2IC, and between RV and TLC, measured using the
biplanar and several uniplanar methods
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Fig. 4.
Bland and Altman comparisons of the volume displaced by diaphragm
motion (Vdi) in 10 healthy and 9 hyperinflated subjects for breaths
between residual volume (RV) and functional residual capacity, RV and
one-half inspired capacity, and RV and total lung capacity,
measured from matched posteroanterior (PA) and lateral (LAT) CXRs
(biplanar Vdi) and the uniplanar methods of Petroll et al.
(7) applied to PA [VdiPetroll(PA CXR);
A] and LAT CXRs [VdiPetroll(LAT
CXR); B] separately, Verschakelen et al.
(11) applied to LAT CXRs
[VdiVerschakelen(LAT CXR); C],
and our proposed method (VdiS) applied to LAT CXRs
[VdiS(LAT CXR); D]. In 10 healthy subjects, biplanar Vdi was compared with our proposed
method applied to LAT fluoroscopy [VdiS(LAT
Fluoroscopy); E]. The solid lines are the mean
difference, and the dashed lines are the limits of the 95% confidence
intervals.
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Fig. 5.
The volume contribution of the diaphragm to tidal volume
(VdiS/VT) measured by LAT fluoroscopy in 10 healthy subjects using our proposed method. The dashed line is the mean
value for the group.
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DISCUSSION |
This study found that the Vdi in healthy and hyperinflated
subjects was measured accurately from lateral CXRs by considering excursion of the diaphragm, sagittal diameter, and cross-sectional shape of the abdominal rib cage and the Vsp. The method
enabled accurate breath-by-breath measurements of Vdi in healthy
subjects by using fluoroscopy. Previously published methods for
measuring Vdi by fluoroscopy (7, 11) were found to be inaccurate.
Assumptions and limitations.
The accuracy of measuring Vdi from a single radiographic plane or
from fluoroscopy was examined by comparing, in the same subjects, the
results of three uniplanar methods with those of a biplanar method
using matched PA and lateral CXRs. The validity of our conclusions
relies on the accuracy of our biplanar method (9).
Although there is no direct validation of this method, several lines of
evidence support its accuracy. First, in healthy subjects at all
inspired volumes and in emphysema subjects at intermediate and high
lung volumes, the sum of Vdi and the change in lung volume
attributable to expansion of the pulmonary rib cage, both measured
independently by the biplanar method, accurately estimated inspired
volume measured by pneumotachograph (9). Second, the model
of the cross-sectional shape of the rib cage used to quantify
subphrenic volume was validated in healthy and hyperinflated subjects
in this study (Figs. 2 and 3). Third, the method assumes that the
coronal and sagittal planes determining the radiographic silhouette of
the diaphragm remain constant at different lung volumes so that the
change in position of the silhouette represents the overall change in
diaphragm position. These planes do move slightly as lung volume
increases (5, 13). However, the movements are unlikely to
significantly influence biplanar estimates of Vdi, because our
previous results showed that changes in the length of the diaphragm
over the VC measured radiographically (9) were consistent
with changes in length of the entire diaphragm measured by MRI
(5).
The method used by us for measuring Vdi from a single plane entails
a number of assumptions. First, we assumed that the cross-sectional shape of the abdominal rib cage remained constant during inspirations from RV and that spinal tissues had a circular rather than an elliptical cross section, as assumed in the previous biplanar study
(9). The ratio of major coronal to sagittal rib cage diameters, obtained during active inspirations from RV to TLC in the
erect posture with the use of biplanar CXRs (9), decreased by ~10% in healthy subjects and did not change in those with
emphysema. The constant ratio of 1.4 assumed in the expression used to
estimate Vdi from uniplanar images (APPENDIX) was within
the range of values found in healthy and emphysematous subjects and
unlikely to lead to errors of significant magnitude. The finding that,
for inspirations between RV and TLC, Vdi measured by the uniplanar
and biplanar methods were not different supported this conclusion. This
finding also suggests that our assumption of a circular cross section of spinal tissues did not cause significant error. On biplanar CXRs, we
found no consistent relationship between the coronal and sagittal
diameters of spinal tissues and, therefore, adopted the more simple
assumption of a circular cross section. Second, we assumed that the
change in position of the right hemidiaphragm silhouette in the
imaging plane is representative of the overall change in position of
the diaphragm. Excursion of the right hemidiaphragm usually exceeds
that of the left (3, 5, 9, 10, 13), and this could lead to
an overestimation of Vdi. The error is likely to be small in healthy
subjects in whom the mean difference in shortening of the
hemidiaphragms over the VC was only ~1% (9). In
subjects with hyperinflation, the mean difference was ~14%, and the
corresponding overestimation of Vdi over the VC would approximate 90 ml. Third, we assumed that the position of the costophrenic angles
around the circumference of the rib cage could be represented by a
straight line between the anterior and posterior costophrenic angles
(Fig. 1). Whitelaw (13) and Gauthier et al.
(5) have shown that, in the supine posture, the lateral costophrenic angle lies slightly above this line at low lung volumes and slightly below it at high lung volumes. However, the departure of
the costophrenic angles from a straight line around the circumference of the rib cage is small, and we expect the error associated with this
assumption to be small. Regarding the assumption that the anterior
costophrenic angle moves along a straight line during inspiration,
examination of the lateral CXRs showed that this assumption was
reasonable for the volume increments used. For larger volume changes,
e.g., VC inspirations, departures from this assumption are common,
resulting in overestimation of Vdi.
Vdi as measured in this study could underestimate the total
contribution of the diaphragm to inspired volume because it does not
include the effect of diaphragm tension in expanding and elevating the
rib cage, but this indirect contribution is believed to be small
(6, 9, 12). Diaphragm motion during inspiration is not
simply a function of diaphragm action but also of rib cage and
abdominal muscle activities and elastances and of the mechanical coupling between the diaphragm and chest wall (6). As
measured in this study, Vdi reflects the volume change of the lung
attributable to diaphragm motion, including motion due both to active
shortening and to the mechanical properties of the chest wall. Where
there is paradox of the pulmonary rib cage, Vdi reflects the volume change of the lung and pulmonary rib cage; such behavior was observed in two healthy subjects between RV and FRC.
Implications.
The ability to measure Vdi breath by breath is likely to be of
clinical value. Aliverti et al. (1) have shown that, in humans during exercise, the diaphragm contracts nearly isotonically and
acts mainly to generate inspiratory flow, whereas the increased pressures required to displace the rib cage and abdomen are developed largely by rib cage and abdominal muscles, respectively. These findings
suggest that the contribution of the diaphragm to inspiration depends
not only on its ability to develop tension, but also on its capacity to
shorten and displace volume. Using biplanar measurements of Vdi, we
have previously shown that decreases in VC in asbestos-related pleural
fibrosis were due mainly to reduced expansion of the lower rib cage
with relative preservation of Vdi (10) and revealed mechanisms by which the function of the diaphragm as a volume pump was
preserved in emphysema, despite severe pulmonary hyperinflation (9). The ability to measure Vdi from a single plane
using fluoroscopy enables dynamic study of the pump function of the diaphragm.
Vdi was not accurately measured by the methods of Petroll et al.
(7) or by those of Vershakelen et al. (11)
(Table 2, Fig. 4). Our data show that this was due, first, to
significant departures of actual cross-sectional shape of the abdominal
rib cage in humans from the circular and rectangular shapes,
respectively, assumed in these models (Fig. 2) and, second, to failure
to consider the volume occupied by spinal and paraspinal tissues. The
geometric model of Vershakelen et al. (11) assumes that
the cross-sectional shape of the abdominal rib cage was rectangular
with coronal dimensions 1.8 times the sagittal diameter; our data show
that this ratio was inappropriately high.
In contrast to these methods, Vdi measured from lateral CXRs and
fluoroscopy, using a method that considered excursion of the diaphragm,
actual shape of the abdominal rib cage, and the volume occupied by
spinal and paraspinal tissues, did not differ from that measured by the
biplanar method (Table 2, Fig. 4), despite the assumptions and
limitations discussed above. Vdi during tidal breaths in 10 healthy
subjects was relatively consistent from breath to breath (Fig. 5), and
the ratio of Vdi to inspired volume was similar to that during slow
inspirations between FRC and 1/2IC. These findings suggest that
this method allows accurate dynamic measurements of Vdi. In
combination with measurements of transdiaphragmatic pressure and the
duration of inspiration, fluoroscopic measurements of Vdi may allow
breath-by-breath estimation of work and power output of the diaphragm
and enable a clearer understanding of the role of the diaphragm in
pathogenesis of breathlessness, exercise limitation, and the
development of respiratory failure in chronic obstructive lung disease.
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APPENDIX |
Derivation of Proposed Method for Estimating Vdi From a
Lateral Radiographic/Fluoroscopic Image (VdiS)
Subphrenic volume was divided into Vdome,L and
Vfr and Vdome,H as described in
METHODS and Fig. 1. If the domes were elliptical in cross
section, their volumes (Vdome,ellipse) could be calculated from the equation
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(3)
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where DSag and
DCor are the sagittal and coronal rib cage
diameters at the base of the domes, respectively, and
Hdome is the height of the domes. The
Adome can be calculated from the equation
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(4)
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Combining Eqs. 3 and 4
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(5)
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We found that, in health and hyperinflation, the ratio of
DCor to DSag was ~1.4.
Therefore
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(6)
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Because the cross-sectional area of the rib cage is best
approximated by a shape one-third the way between an ellipse and a
rectangle (Figs. 2 and 3), and this area is 1.091 times the area of an
ellipse of the same dimensions
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(7)
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The Vfr can be calculated by dividing it into
multiple horizontal slices with a cross-sectional shape one-third the
way between an ellipse and a rectangle. The volume of each slice
(Vslice) can be calculated as follows
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(8)
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where Hslice is the height of each
slice. This can be simplified to
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(9)
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Assuming that a straight line can represent the lateral walls of
the frustrum, Vfr can be approximated by the following
equation
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(10)
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where Hfr is the height of the frustrum.
The area of each slice of the frustrum projected in the sagittal plane
(Aslice) is
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(11)
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and the Afr is approximated by
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(12)
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Combining Eqs. 10 and 12
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(13)
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As the ratio of DCor to
DSag is ~1.4, the equation can be expressed as
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(14)
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or
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(15)
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The Vsp within the volume swept by the diaphragm can
be estimated by assuming that this volume is cylindrical, i.e.
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(16)
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where Dsp is the diameter of the spinal
column, and Hsp is the height of spinal mass.
The Asp is
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(17)
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Combining Eqs. 16 and 17
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(18)
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The Vdi can be calculated from the equation
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(19)
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Combining Eqs. 7, 15, 18, and
19
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(20)
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ACKNOWLEDGEMENTS |
The authors thank P. R. Eastwood and W. J. Noffsinger for
technical assistance, Y. M. Lam for statistical advice, M. Crabbe for assistance with radiography, N. Hicks for assistance with fluoroscopy, and the Departments of Radiology and Radiotherapy, Sir
Charles Gairdner Hospital, for access to equipment and materials.
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FOOTNOTES |
This study was supported by grants from the Medical Research Fund of
Western Australia and the Sir Charles Gairdner Hospital Research Fund.
B. Singh is the recipient of an Australian Lung Foundation/Boehringer
Ingelheim Chronic Airflow Limitation Research Fellowship.
Address for reprint requests and other correspondence: B. Singh, Dept. of Pulmonary Physiology, Sir Charles Gairdner Hospital, Hospital Ave., Nedlands, WA 6009, Australia (E-mail:
Bhajan.Singh{at}health.wa.gov.au).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
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in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
First published November 15, 2002;10.1152/japplphysiol.00256.2002
Received 27 March 2002; accepted in final form 7 November 2002.
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ABSTRACT
INTRODUCTION
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