Abstract
To estimate diaphragm fiber length from thoracoabdominal configuration, we measured axial motion of the rightsided area of apposition by ultrasonography and volumes displaced by chest wall compartments [pulmonary, abdominal rib cage, and abdomen (Vab)] by optoelectronic plethysmography in four normal men during quiet breathing and incremental exercise without and with expiratory flow limitation. Points at the cephalic area of apposition border were digitized from echo images and mapped into threedimensional space, and the axial distance from the xyphoidal transverse plane (D_{ap}) was measured simultaneously with the volumes. Linear regression analysis between changes (Δ) in D_{ap} and the measured volume changes under all conditions showed that 1) ΔD_{ap} was linearly related more to ΔVab than to changes in pulmonary and abdominal rib cage volumes; and 2) this was highly repeatable between measures. Multiple stepwise regression analysis showed that ΔVab accounted for 89–96% of the variability of ΔD_{ap}, whereas the rib cage compartments added <1%. We conclude that, under conditions of quiet breathing and exercise, with and without expiratory flow limitation, instantaneous ΔD_{ap} can be estimated from ΔVab.
 chest wall volume
 diaphragm area of apposition
 echography
most of the available information on chest wall kinematics is based on the twocompartment chest wall model of Konno and Mead (12) composed of rib cage and abdomen (AB), with each behaving with a single degree of freedom, so that changes in volume of each compartment can be measured by a single dimension. Because the movable parts of the AB are the anterolateral abdominal wall and the diaphragm, the volume of abdominal contents (Vab) displaced from under the diaphragm must be equal and opposite to the volume displaced by the anterolateral abdominal wall (ΔVabw, where Δ is change). Thus diaphragmatic displacements are closely linked to abdominal wall displacements, and it had been assumed that diaphragm fiber length (L _{di}) would be simply related to displacements of the AB and nearly unrelated to rib cage displacements. This assumption was supported by the studies of Goldman et al. (8) and Grassino et al. (9), who found that lengthtension behavior of the diaphragm was much less sensitive to changes in rib cage diameter than to displacements of the abdominal wall.
Subsequent studies have shown that displacements of the abdominal contents under the diaphragm are more complex than those measured simply by displacements of the anterior abdominal wall. An analytic approach to these complexities was developed in an important paper by Mead and Loring (14). They put forward the concept that displacements of the lower part of the rib cage where the diaphragm is apposed to its inner surface, along with displacements of the AB, are important determinants of L _{di} and provided experimental evidence to support their theoretical analysis (14). However, in preliminary studies, our laboratory found that >80% of the variance in L _{di} in the area of apposition (A _{ap}) during exercise was accounted for by abdominal displacements (3). These findings are in agreement with those of Chen et al. (6), who found that twitch diaphragmatic pressure in response to supramaximal, transcutaneous, bilateral phrenic nerve stimulation was exquisitely sensitive to abdominal displacements and relatively insensitive to rib cage displacements. These studies suggest that L _{di} is more closely linked to abdominal displacements and less to rib cage displacements than has generally been thought. In this paper, we develop a method to assess factors determining L _{di} using optoelectronic plethysmography (OEP) (5) to measure volume displacements of the rib cage (ΔVrc) and ΔVabw, combined with ultrasound measurements of changes in L _{di} in theA _{ap} (ΔD_{ap}). We hypothesized that it would be possible to predict ΔD_{ap} from ΔVabw during quiet breathing and exercise, with and without expiratory flow limitation (EFL). To develop our ideas, it is necessary to review Mead and Loring's analytic paper (14) in some detail.
THEORY
In this section, we develop the relationship between abdominal and diaphragmatic displacements following the approach of Mead and Loring (14). To do so, we develop equations that are similar, but not identical, to those they used. They assumed, quite reasonably, that the Vab is constant and that it is composed of three compartments, all of which can change their contribution to the total volume during breathing. The three compartments are displaced during breathing by motion of the diaphragm dome apposed to the lung, by motion of the rib cage in A
_{ap}, and by displacement of the anterolateral abdominal wall. Thus
ΔVab,rc has two components: the first is ΔVab in theA
_{ap} of diaphragm to rib cage, and the second is ΔVab in the part of the rib cage caudal to the insertion of the costal part of the diaphragm (the obligatory ring). Mead and Loring (14) estimated the fraction of the internal surface of the rib cage at functional residual capacity occupied byA
_{ap} (fapp) to be ∼0.25, whereas the fraction occupied by the obligatory ring (fobr) was estimated to be ∼0.15. Mead and Loring assumed that “in the resting tidal range fapp decreases only modestly during inspiration, and 0.41 is a reasonable average value of (fapp + fobr).” Thus they estimated ΔVab,rc by
Substituting (fapp + fobr) Vrc for Vab,rc in Eq. 1
gives Vab at the beginning of inspiration
If one assumes a breath of 500 ml in which fapp decreases from 0.25 to 0.20, fobr remains constant at 0.15, ΔVrc = 375 ml, and ΔVabw = 125 ml, the ΔVab in A _{ap} becomes (150 − 0.05 Vrc − 6.25) ml. A reasonable value for the internal volume of the rib cage measured by OEP (5) (a new technology described in detail below) is 5 liters (A. Aliverti, personal communication). Thus the ΔVab in A _{ap}is a negative value of −106.25 ml compared with +150 ml calculated by using the Mead and Loring equation.
Thus the predictions arising from Eq. 6 are quite different from those arising from Eq. 3. Equation6 does not predict that the ΔVab in A _{ap}is necessarily positive. It can increase, decrease, or stay the same, depending on the relative magnitudes of rib cage expansion and decrease of the A _{ap}. The sum of ΔVab,l and ΔVab,rc gives the ΔVab contained within the diaphragm, and this sum is equal and opposite to ΔVabw. The assumption that the Vab contained within A _{ap} always increases with rib cage expansion cannot be correct when A _{ap} decreases. As a result, because fobr ΔVrc can be estimated, and to the extent that ΔVab,rc and ΔVab,l carry information about diaphragmatic shortening, ΔVabw can potentially be used to estimateL _{di}.
Clearly, how much fapp changes with a breath is crucial to the understanding of the diaphragm's contribution to breathing. Mead and Loring's (14) use of a constant average fapp must introduce substantial errors. Although it is true that their measurements (13) tended to support their theoretical analysis (14), not all measurements were made in all subjects, and some questionable assumptions tend to make their data open to reinterpretation (see Ref. 6 for further discussion). It would seem that Mead's earlier calculations of the effect of thoracoabdominal configuration on L _{di}[made with Goldman et al. (8) and Grassino et al. (9)] may have been closer to the truth than his later calculations.
METHODS
Subjects
We studied four healthy normal men 42 ± 3 (SD) yr old, with anthropometric and functional respiratory characteristics shown in Table 1. They were all laboratory personnel trained in respiratory maneuvers.
Protocol
Each subject was studied on two occasions while seated on a cycle ergometer with the arms supported away from the trunk. On both, the subjects breathed spontaneously for 3 min and then performed an incremental exercise test starting at 0 W and increasing by 25 W every 4 min until exhaustion. The incremental exercise tests were performed under control conditions (Ex,c) and with a Starling resistor in the expiratory line, which limited expiratory flow to ∼1 l/s (Ex,s). We measured maximal power output under Ex,c and Ex,s. Reports of the determinants of exercise limitation and dynamics of breathing during these experiments have previously been published (2, 10). During Ex,s, the subjects breathed through a mouthpiece, which was attached to a Hans Rudolph valve, which separated inspiratory and expiratory flow. Flow limitation was achieved by putting the Starling resistor on the expiratory port of the valve. A 2liter jar was placed in parallel with the Starling resistor, which acted as a capacitance, so that, at the beginning of expiration, flow was somewhat greater than 1 l/s, whereas, at the end, it was somewhat less (see Ref.10, Fig. 1). Data were gathered during the last 40 s of each workload. We randomized the order in which these two exercise tests were performed.
Measurements
OEP.
Figure 1 A shows a general overview of the measurement system. Chest wall kinematics and compartmental volumes were measured by OEP, as previously described, and validated at rest and during exercise (1, 5, 11). Eightynine reflecting markers were placed front and back over the chest wall from clavicles to pubis. Each marker was tracked in three dimensions (3D) by four video cameras: two in front of the subject and two behind. A dedicated image processor measured the position of each marker at 50 Hz. For volume computation, chest wall surface was approximated by 182 triangles connecting the markers. Then, using Gauss' theorem, the volume of the chest wall (Vcw) and of its compartments was calculated. We modeled the chest wall as a threecompartment system, comprised of the pulmonary or lungapposed rib cage (RCp), the abdominal or diaphragmapposed rib cage (RCa), and the AB (5, 15). The sum of the volume of each compartment equaled the Vcw: Vcw = Vrc,p + Vrc,a + Vab, where Vrc,p is pulmonary rib cage volume and Vrc,a is abdominal rib cage volume.
Ultrasonography of the diaphragm.
Diaphragm motion was visualized by a generalpurpose echo camera (Aloka Echo Camera), equipped with a linear probe (3.5 MHz, 128 mm). As the intrapulmonary air greatly attenuates the transmission of ultrasound waves, the resulting abrupt discontinuity in the image at the level at which the diaphragm reflects from the chest wall and the lung intervenes was used to identify the position of the cephalic margin of the zone of apposition (Fig. 1 B). The caudal border was measured by markers along the costal margin.
The probe was placed in a plastic frame fixed to the skin by adhesive tape and manually kept in a fixed position during the experiments. The probe was aligned approximately axially and placed between the two markers defining the right lateral border of the RCa. Three additional markers were placed on the probe and tracked by the OEP cameras to measure its position and orientation.
Ultrasonographic images were synchronized with the motion analyzer by generating a trigger signal that created a symbol at a frequency of 0.5 Hz on the ultrasonic image and that was recorded on a analogtodigital card (RTI800, Analog Devices, Norwood, MA) synchronized with the motion analysis system. The ultrasonic images were then recorded on a standard video recorder and successively digitized by a frame grabber (Screen Machine II, Fast Electronic) in motion JPEG format at 10 frames/s with a resolution of 320 × 240 pixels. When the first symbol and the first trigger appeared, respectively, on the image and the digitized signal, the sequence of echographic images and OEP volumes (downsampled at 10 Hz) was aligned to be in synchrony and automatically maintained synchronous for the duration of the measurement by a specifically developed software. Small movements of the margin of the zone of apposition could be easily detected, even if sometimes the margin was obscured by a rib at the initial or final position.
Data Analysis
L_{di} in the A_{ap}.
Changes in A _{ap} were estimated by measuring axial motion of its cephalic margin in the echographic images of the right hemidiaphragm. On each image, the cephalic extremity was manually selected. Successively, the twodimensional coordinates were mapped into 3D space by using the information on the position and orientation of the probe. For each image, the transverse plane at the level of the xiphisternum was estimated by computing the regression plane outlined by the markers placed at the xiphoid level. Finally, the D_{ap} to the upper border of A _{ap} was computed as reported in detail in the and in Ref.4.
Regression analysis.
For each test, four to five breaths were analyzed at a sampling rate of 10 Hz. Successively, a linear regression analysis between D_{ap} and Vrc,p, Vrc,a, Vab, and Vcw was performed, and the results were expressed as squared linear regression coefficient (r ^{2}) and slope of the regression line.
Analysis of variance.
To study the repeatability on different days and experiments and the differences between subjects on r ^{2} and slope values, we applied a oneway ANOVA on repeated measures to four different tests of quiet breathing. To study the effect of the presence of Starling resistor (factor 1), of different compartments (factor 2), and of different workloads (factor 3) on r ^{2} and slope values, we applied a threeway ANOVA on repeated measures to all of the tests.
For factor 3, we considered quiet breathing at rest, 25 W, maximum workload (Wmax) during exercise with EFL, and Wmax/2 (halfmaximal Wmax during Ex,c).
As r ^{2} values are all between 0 and 1, this parameter is not usually normally distributed. For this reason, we applied Fisher's transform, which allows acquisition of a statistical estimator (Y) of r ^{2}, defined as Y = arctanh (r ^{2}) = 1/2 ln(1 +r ^{2})/ (1 −r ^{2}). This estimator, calculated as the inverse hyperbolic tangent of r ^{2}, follows the normal distribution: all of the analyses of variance forr ^{2} were carried out by using Y instead ofr ^{2}. The fit to a normal distribution and homogeneity of variances were verified by KolmogorovSmirnov's test and univariate/Levene's test, respectively. Only when ANOVA was significant post hoc tests (Scheffé's test) were made to verify the statistical significance of the differences between all pairs of means. For all tests, the significance level was taken asP < 0.05. All results are reported as means ± SE.
Multiple stepwise linear regression analysis.
Variations of L
_{di} in theA
_{ap} are related to ΔVcw, which are determined by the displacement of the different compartments. To quantify the contribution of the different chest wall compartmental volumes to the ΔD_{ap}, we hypothesized the following linear relationship
RESULTS
Linear Correlation Analysis
Figure 2 A shows tracings of ΔVcw and its three compartments (Vrc,p, Vrc,a, and Vab) during quiet breathing. The bottom trace is the ΔD_{ap}. The time variations of the volumes of the different chest wall compartments were approximately in phase, and the inspiratory decrease of D_{ap} was in the order of 2.5 cm. Figure 2 Bshows the results of the linear regression analysis (slope andr ^{2}), computed between ΔD_{ap} and Vrc,p, Vrc,a, Vab, and Vcw, corresponding to the same data reported in Fig. 2 A. ΔD_{ap} was well correlated with the volume variations of each chest wall compartment and with those of the total chest wall. However, the highest value ofr ^{2} was obtained for ΔVab. The slopes of the linear regressions simply reflect the volume of each compartment because ΔD_{ap} is common to all.
Analysis of Variance
Figure 3 confirms the importance of abdominal wall displacements in predicting ΔD_{ap}. The r ^{2} values on the ordinate reveal how much of the variance in ΔD_{ap} is accounted for by the volume displacements of each of the three compartments and the whole chest wall during quiet breathing and as a function of exercise workload. Each bar contains pooled control and EFL breaths in all subjects. Mean r ^{2} values were again highest for the AB and were lower for the two rib cage compartments. The post hoc Scheffé test showed no significant differences between the r ^{2} of the two rib cage compartments (P > 0.95) or between the AB and the chest wall (P > 0.80), with significant differences for all other comparisons (P < 0.01 for all).
Table 2 gives the results of the onefactor analysis of variance in which we looked for possible differences among repeated measures and different subjects. The values of P level reported in Table 2 (r ^{2}and slope) demonstrate the repeatability of this method and the independence of r ^{2} from confounding variables, such as weight, height, age, etc., with the possible exception of D_{ap} vs. Vab, where the data approach statistical significance. In contrast, each subject had a characteristic slope as shown by the P values, all of which showed statistically significant differences in slope between subjects. In addition, differences between repeated measures approached statistical significance for D_{ap} vs. Vab.
As shown in Table 3, there were two significant effects for r ^{2}: the main effect for compartment and the interaction between compartment and workload. In contrast to the analysis of r ^{2}, Table 3 shows that there are many significant factors that affect slope: the main effect for compartment and workload, the interaction between compartment and workload, the interaction between presence of EFL and workload, and the interaction among presence of EFL, workload, and compartment.
The results of the post hoc Scheffé's test for the effect of workload on slope are shown in Fig. 4. As shown in this figure, the two rib cage compartments and the chest wall had higher slopes during exercise compared with quiet breathing, and the slope for the chest wall was significantly greater at maximal power output with EFL than at 25 W. Only the abdominal compartment showed no change in slope from quiet breathing to exercise.
The presence of EFL did not significantly affect eitherr ^{2} or slope within a compartment, as shown in Fig. 5. Table4 shows, as does Fig. 3, that there were no significant differences between the two rib cage compartments, or between the AB and the chest wall, but both r ^{2}and slope were significantly less for the rib cage than for the chest wall and AB. Therefore, Figs. 35 demonstrate that the correlation between ΔD_{ap} and the change of compartmental volumes is significantly better for the AB and total chest wall than for the rib cage compartments, and, considering both r ^{2} and slope, the AB is somewhat better than the chest wall in predicting ΔD_{ap}. Presumably, this is because the chest wall contains both rib cage compartments, which diminishes its ability to predict ΔD_{ap}.
Multiple Stepwise Linear Regression Analysis
Table 5 gives the results of the multiple stepwise linear regression analysis on all subjects at the different workloads. Between 89 and 96% of the variance in ΔD_{ap} was accounted for by the ΔVabw. Adding the displacements of the two rib cage compartments improved this by only 1%.
DISCUSSION
L _{di} is determined by thoracoabdominal configuration. Our results demonstrate that, under the conditions in which we measured ΔD_{ap} near the midaxillary line, abdominal displacement was its best predictor. Is ΔD_{ap} a measure of change of L _{di}? It may be possible with rib cage expansion for the diaphragm to peel away from the rib cage without a change in fiber length. However, Gauthier et al. (7) showed in humans that changes in the axial dimension of the A _{ap} were excellent estimates of fiber length in the supine position. No similar data exist in the upright posture in humans. Assuming that determinants ofL _{di} are the same upright and supine, our measurements of ΔD_{ap} are estimates of changes in costalL _{di}.
As illustrated in Fig. 2, we found substantial shortening of diaphragmatic fibers during quiet breathing, so that Mead and Loring's (14) use of an average value of theA _{ap} during quiet breathing does not seem justified either theoretically (as developed above) or from an experimental point of view.
One might expect that fiber length would be wellcorrelated with displacements of the RCa from which the costal fibers originate and with which they are in direct contact in theA _{ap}. In fact, Loring et al. (13) have provided evidence that this is the case, although we were unable to confirm their findings. However, it should be realized that we only measured the determinants of L _{di} when there was prominent abdominal motion. Before the rib cage can be excluded as an important determinant, it would be necessary to show that the diaphragm is quasiisometric during an inspiration without any abdominal displacement. We have not studied such breaths.
To further examine the relationship between the contributions of the RCp, RCa, and AB to tidal volume and their relationship to D_{ap}, we correlated the fractional contributions of these chest wall compartments to tidal volume on one hand and ΔD_{ap} on the other. The results are shown in Fig.6. The r ^{2} values for all chest wall compartments are small, and neither relationship is significant, although statistical significance is approached for the RCp (P = 0.54).
Loring et al. (13) showed that, when abdominal motion was minimal, the diaphragm could shorten. They studied three subjects to evaluate the dependence of L _{di} on lung volume and thoracoabdominal configuration and suggested thatL _{di} was closely coupled to rib cage displacement, as well as to ventral abdominal wall displacement. In their analysis, they considered the whole rib cage as a determinant of the L _{di}. They argued that, because the costal fibers originate at the costal margin, a diaphragmatic contraction should displace the rib cage cranially, entailing diaphragm shortening independent of abdominal motion. Nevertheless, the diaphragm and abdominal wall form a compartment of nearly constant volume. The volume swept by the abdominal wall must be equal and opposite to the volume swept by the diaphragm. If diaphragm fibers can shorten at constant Vab, then the diaphragm must decrease its surface area at constant volume. This can only occur if the diaphragm's configuration changes from a less spherical to a more spherical shape.
Despite the possibility of diaphragmatic shortening during a breath with no abdominal displacement, we have shown that abdominal displacements alone, measured by OEP, are sufficient to estimate changes in L _{di} in healthy subjects during quiet breathing and exercise, with and without externally applied EFL.
Before attempting such measurements, it would be necessary to calibrate the relationship between ΔD_{ap} and abdominal displacement in each subject on each occasion that measurements are made. The results of the ANOVA shown in Table 2 reveal highly significant differences in slope of the D_{ap}Vab regression between subjects. Therefore, the relationship between the two variables in each subject must be known before ΔVab can be used as a measure of ΔD_{ap}. Furthermore, the differences in D_{ap} vs. Vab between repeated measures approaches statistical significance. This probably reflects slight differences in posture and marker placement in different experiments. Nevertheless, it indicates the need to calibrate the D_{ap}Vab regression each time a subject is studied. Finally (again as shown in Table 2), the betweensubject difference inr ^{2} also approached statistical significance. Therefore, we cannot exclude the possibility that there are individuals in whom r ^{2} of the D_{ap}Vab regression is not sufficiently high to allow good estimates ofL _{di}.
Acknowledgments
We gratefully acknowledge E. Orsi for software development and G. Scano, R. Duranti, I. Iandelli, G. Misuri, and B. Kayser for valuable help in preparing and performing the experiments.
Footnotes

Address for reprint requests and other correspondence: A. Aliverti, Dipartimento di Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32, I20133 Milan, Italy (Email:andrea.aliverti{at}polimi.it).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

First published October 4, 2002;10.1152/japplphysiol.00329.2002
 Copyright © 2003 the American Physiological Society
D_{ap} Estimation
For each acquired frame, the position of the point P of coordinates x _{P},y _{P}, corresponding to the cephalic margin of the zone of apposition (see Fig. 1 B), was selected in the echographic image (plane of axes xy) and then geometrically transformed by a rototranslation into the point P′ of coordinatesX _{P′}, Y _{P′},Z _{P′} in the laboratory reference system (3D space of axes XYZ), in which the markers placed both on the chest wall surface and on the probe were acquired (Fig.7).
The coordinate system of the probe was defined by using the 3D coordinates of the markers placed on the probe (M_{1}, M_{2}, and M_{3}), and the three axes (x,y, z) were defined as follows: xaxis parallel to the straight line passing through points M_{1} and M_{2} at a distance d, equal to the distance between the markers M_{1} and M_{2} and the skin; thezaxis as the vector product between x and the straight line passing through M_{1} and M_{3}; finally, yaxis was obtained as the vector product betweenx and z.
Points P were then rototranslated into the 3D space by the following equation
The distance between the point P and the D_{ap} was computed as follows: 1) by estimating the regression plane π among the markers placed at the xiphoid level, of equation