measurement of the separate volume changes of rib cage and ......degrees of freedom of a closed...

Measurement of the separate volume

changes of rib cage and abdomen during breathing

KIM10 KONNO AND JERE MEAD Department of Physiology, Harvard School of Public Health, Boston, Massachusetts

KONNO, KIMIO, AND JERE MEAD. Measurement of the separate volume changes of rib cage and abdomen during breathing. J. Appl. Physiol. 22(3) : 407-422. I 967 .-Changes in the anteroposterior diameters of the rib cage and abdomen were recorded on the axes of a direct-writing X-Y recorder both during relaxation against a closed airway at different lung volumes, and while, at fixed lung volumes, displacements of volume were made voluntarily back and forth between the rib cage and abdomen in both the standing and supine postures. The family of isovolume lines was used to construct the volume-motion relationships for the rib cage and abdomen, and this in turn was used to estimate the separate volume changes of these parts during breathing. A high degree of volume dependence between the rib cage and abdomen was demonstrated under isovolume conditions, while a high degree of volume independence between these parts was demonstrated when total volume change was unconstrained. During breathing the chest wall deviated substantially from its passive configuration. In six subjects the abdomen accounted for about half or more of the tidal volume, but much less than half of the vital capacity, in both postures.

mechanics of breathing; chest-wall mechanics

C OMPARED TO PRESENT KNOWLEDGE of pulmonary mechanics relatively little is known about the mechanics of the chest wall. The major difficulties have been two: first, the problem of measuring the volumes displaced by motions of different parts of the chest wall, and second, the problem of measuring the pressures applied to and by these parts. Recently, Agostoni and Rahn (2) showed that esophageal and gastric pressures could be used to estimate the pressure differences across the major structures of the chest wall-the rib cage, diaphragm, and abdominal wall. As yet, however, there has been no comparably satisfactory method for estimating the volume displacements of these parts. This paper presents a method for measuring separately the volume changes of two of them: the rib cage and abdominal wall.

The “chest wall,” in respiratory terms, includes all

Received for publication 7 March 1966.

parts of the body outside the lung which share changes in the volume of the lungs. Its surface is coextensive with that of the torso. Anatomically, this surface has two sub- divisions: the “rib cage” and the “abdomen’‘-the di- viding line between them being the costal margin. Viewed in terms of motion of the surface, the chest wall appears to have functional separation between the rib cage and abdomen as well. Each appears to move as a unit, while as between them there appears to be consid- erable independence of motion. For example, it is easy to inspire mainly with the rib cage or with the abdomen, and even to cause outward displacements of one while moving the other inward. It occurred to us that we could take advantage both of the apparently unitary behavior of the rib cage and abdomen and of the ability to move one or the other independently, to measure their volume changes separately.

THEORY

Our method is based on the relationships between linear motion and volume displacement. These are com- mon to all mechanical systems in which volumes are displaced. We begin by defining some terms.

Dejnition of Terms

The number of degrees of freedom is defined by the number of independent variables. A single independent variable corresponds to a single degree of freedom.

A ‘cpart” is a mechanism which displaces volume as it moves and for which volume change is the only independent variable with respect to its motion. A part has I df.

A CC system” is an arrangement of parts. An open system can exchange volume with its surroundings. A closed system is an arrangement of parts which together have a constant volume so that all volume changes take place among the parts.

Relationshz) between number of parts and number of degrees of freedom in open and closed systems. The number of degrees of freedom in a particular system depends on how its parts are arranged an on whether it is closed or open.

407

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K. KONNO AND J. MEAD

VOLUME

PART I

3

OF

0

0 C VOLUME OF TOTAL SYSTEM: 5 *UNITS

MOTION OF 3

PART I

MOTION OF

FART l.i

First concerning the arrangement, parts interconnected so that their volume changes are equal are said to be arranged in series. All such serial arrangements have a single degree of freedom.

The number of degrees of freedom of an open system equals the number of serial arrangements it is made up of which operate independently. The number of degrees of freedom in a closed system is equal to the number of degrees of freedom in the same system when open, less I. This may be seen from the following:

A closed system with a single part, or a single arrangement of parts in series, cannot move; accordingly, it has no independent variable and o df.

A closed system with two parts can have no more than I df. Any volume change of one part must be equal and opposite to that of the other. There is, at most, one independent variable and I df.

PART I

MOTION

PART a

0 I 2

VOLUME

3

MOTION

2

I

FIG. I. A. volume relationships of a system with two parts, I and II, operating as a closed system at various total volumes. The total volume within the system, shown by the diagonal lines with the negative slope of I, varies from o to 5 arbitrary volume units. The volume change of each part also varies from o to 5. B. hypothetical relationships between volume changes of parts I and II and some aspect of their motions. The volume change of part I varied from o to 3 and that of part II from o to 2, so that the total potential volume change of the system is 5 units. The motion of each part varies from o to 5 arbitrary units of motion. The lines are seen to be continuous monotonic increasing functions. These functional relationships are arbitrary. C: relative motion relationships between parts I and II at different total volumes of the closed system.

A closed system with three parts can have no more than 2 df. Once the volume of one part is determined only a single degree of freedom remains. The same reasoning leads to the conclusion that the number of degrees of freedom of a closed system is one less than that of the same system when open.

Degrees of Freedom of the Chest Wall

We have assumed that, to a useful approximation, the chest wall has two moving parts-the rib cage and abdomen. During ordinary breathing the system is open and has 2 df. When one breathes from a spirometer the system is closed, but a part, the spirometer, has been added and the system again has 2 df. When the tubing leading to the spirometer is closed, however, the chest wall becomes a closed system with two parts, and hence, a single degree

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SEPARATE VOLUME CHANGES OF RIB CAGE AND ABDOMEN 409

TO SPIROMETER

TRANSDUCERd-

PING-PONG BALL

TO VACUUM PUMP

L I

FIG. 2. Method for measuring the anteroposterior motion of the anterior wall of the rib cage and abdomen in standing subjects. The changes in anteroposterior diameters were transmitted by means of threads to the cores (823-3PI, Sanborn) within linear differential transducers (535 DT 1000 Bm, Sanborn). The end of the thread was fixed to the body surface by means of a partially evacuated Ping-Pong ball which had been dented in from opposite sides and which was sealed to the skin with clay, as shown in B. The outside end of the thread was connected to a weight (ca. IO g). The distortion of anteroposterior motion due to the soft tissue at the point where the Ping-Pong ball was fixed was avoided by sealing with clay. The length of the thread was chosen (IOO cm, from body surface to the transducer) so that distortion due to vertical motion was negligible. The measurements were made midway between the right nipple line and midline at the nipple level for the rib cage and midway between the same lines at the level of the umbilicus for the abdomen. The pulley and the transducer were placed together on a plastic plate. Transducers were linear in response over a range of &5 cm from the midposition, and the response characteristics of the measuring system were adequate for our purpose. The signal from the rib cage was displayed on the I’ axis and that from the abdomen on the X axis of a direct-writing X-Y recorder (Autograph model # 135, Mosley). An aneroid manometer was used for monitoring mouth pressure. Changes in lung volume were measured with a spirometer (9 liters, Collins).

of freedom. In this instance any volume change of the rib cage must be equal and opposite to that of the abdomen.

Relationships Between Volume Cflange of Parts and Other Aspects of Their Motion

Since, as defined, all motions of parts are expressed with a single independent variable, it follows that all motions of points within parts must bear fixed relationships to volume change. When such a relationship is known, volume change can be estimated from measurements of motions of a single point within the part in question. A recording spirometer is an instance of this: its recording pen moves in fixed relationship to its change in volume.

There are two ways to arrive at the relationship between motion and volume change: theoretically, by analysis of the geometry of the part, and experimentally, by displacing known volumes into the part. We have used

the second approach in conjunction with ideas developed in the first part of this section, along the following lines.

Figure IA presents volume relationships of an open system with two parts and 2 df. It may be closed at different total volumes, in which case the system has a single degree of freedom and the relationships between the volumes of the parts are single straight lines with slopes of - I, as shown.

Figure I B presents hypothetical relationships between the volume of the parts and some aspect of their motions. The functional relationships are arbitrary but share these characteristics : each is a monotonic increasing function, i.e., volume and motion are represented as increasing together.

Figure I C describes the relationships between the motions of the two parts when the system is closed at different total volumes. The isovolume lines were constructed by plotting pairs of points from Fig. IB which had volumes summing to the total volume in question. These lines are seen to be monotonic decreasing functions.

Our approach is essentially the inverse of the process just described. We obtain relationships corresponding to those in Fig. I C experimentally. From these we construct the functional relationships between motion and volume change. We then use these to estimate the separate volume changes of the parts.

Volume-motion relationships are derived from graphs such as the one shown in Fig. I C as follows : displacements between the isovolume lines along one of the coordinates correspond to motions of one part with the other part fixed. This is also graphically equivalent to removing one part and, hence, to reducing the number of degrees of freedom to one. The total volume change, as measured by spirometer, corresponds to the volume change of the part in question, which, in turn, corresponds to the motion measured along the coordinate between the two lines. By repeating this process at known increments of total vol-

FIG. 3. The isovolume maneuver. At constant lung volume the subject shifts as much volume as possible from rib cage to abdomen in the picture in the left and from abdomen to rib cage in the right. In the middle picture the subject is relaxed.

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4’0

TABLE I. Physical characteristics, values of vital capacity, and total lung capacity

Vital Total Lung

Subj Capacity, Capacitf,

Age, yr Height, cm Weight, kg liters BTPS liters BTPS

EB - 3’ I65 7= 4.87 5.80 KK 32 I73 56 4.40 5*70 DL 32 785 73 6.10 7.32 PM 33 ‘75 82.2 5*23 7.40 JM 42 ‘87 86 6.80 8.97 FS 32 773 59.3 4.90 6.19

ume the relationships between the volume change of the part and its motion can be derived. The same process can be repeated along the other coordinate to derive a similar relationship for the other part. (It should be noted that this additional step is redundant. Since the total volume change is known, once that of one of the two parts is known as well, the volume change of the other part may be obtained by subtraction. The second volume-motion relationship adds nothing new-it merely serves to check the estimate made by subtraction.)

I f the rib cage and abdomen behave as parts, the volume of one should not affect the volume-motion relationship of the other. This can be tested experimentally since the volume-motion relationship of a part can be derived at different fixed volumes of the other part (i.e., along different coordinates of the relative motion diagrams).

The graphs of relative motions of the rib cage and abdomen at different fixed total volumes will be used for three purposes : r) to test our assumption that the chest wall has, basically, two moving parts (this will be re- flected in the extent to which volume isopleths are single-valued) ; 2) to test the independence of the volume- motion relationships, along lines described in the pre- ceding paragraph; and 3) to estimate the separate volume contributions of the rib cage and abdomen during breathing.

METHODS

We intended initially to measure motion in terms of changes in circumference. We were unsuccessful in de-

FIG. 4. Relative anteroposterior motions within the rib cage in the standing and supine posture. The small open circles indicate the end-expiratory level (FRC) and the continuous lines and the broken lines indicate the tracings during isovolume maneuver and vital capacity maneuver, respectively. The motion of the reference point (midway between the right nipple line and midline at the nipple level) is along the Y axis.


vising a pneumograph adequately free from artifacts, presumably due to soft tissue distortion, and chose instead to measure changes in anteroposterior diameters. These have the advantage of being among the most prominent motions of breathing and the further advantage of being easy to record without distortion.

Our method of recording is shown in Fig. 2. The output of the transducers ran to the axes of a direct- writing X-Y recorder. We used a spirometer to measure volumes and these we expressed as percent of the vital capacity (VC). During the isovolume maneuver, which is described in the next paragraph, mouth pressure was indicated on an aneroid manometer in the view of the subject. He was instructed to maintain mouth pressure between rt20 cm Hz0 during the maneuver.

Isovolume Maneuver

With the tubing to the spirometer closed off, the subject moved as much volume as possible back and forth between the rib cage and abdomen without flexing or extending the spine. Figure 3 shows an example of this. Lung volume is the same in the three pictures. In the middle one the subject is relaxed. On the right, he had shifted as much volume as possible into his rib cage, while on the left, he has shifted as much volume as possible from his rib cage into his abdomen. This maneuver was accomplished slowly, taking about 5-10 set to

complete one “cycle.” The subject first practiced the maneuver while watch-

ing the X-Y recording. All subsequent recordings were obtained with the recorder out of the subject’s field of view. During the isovolume maneuver, and during all other measurements of chest-wall diameters, the subjects tried to maintain contact at fixed points along the spine and in this way reduced flexion and extension of the spine. Vital capacities were thereby reduced approximately 5 %. Some subjects were able to perform the maneuver satisfactorily at their first try. Others could do so after a little practice. All had been subjects in respiratory experiments many times. Some of their physical characteristics are given in Table I.

STANDING

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SEPlWATE VOLUME CHL4NGES OF RIB CAGE AND ABDOMEN

STANDING SUPINE

FIG. 5. Relative anteroposterior motions within the abdomen in the standing and supine posture. The reference point is midway between the same lines as for the rib cage at the level of the umbilicus.

RESULTS

Relative Motions Within Parts

According to our assumption that the rib cage and abdomen each have single degrees of freedom, all anteroposterior motions within these parts should be single- valued functions of their volumes, and, accordingly, should be single-valued functions of each other. We made simultaneous measurements of anteroposterior motions at different points on the surface of the anterior chest wall during quiet breathing, vital capacity maneuvers and isovolume maneuvers at resting end-expiratory lung volume, both in the standing and supine postures in all of our subjects. The distribution of the points of measurement is shown in Figs. 4 and 5. For all measurements of the rib cage the reference point was rnidway between the right nipple line and midline at the nipple level and for all measurements of the abdomen the reference was midway between the same lines as for the rib cage, at the level of the umbilicus. An upward deflection along the Y axis occurred with anterior movement of the reference point; deflection to the right along the .X axis occurred with anterior movement at the test site.

Anteroposterior motions of the rib cage. Figure 4 shows a representative example of tracings of relative anteroposterior motions at different points on the anterior wall of the rib cage in the standing and supine posture. The tracings are centered at the point sampled. The motion of the reference point is along the Y axis. The tracings are representative in the following respects: Over the mid rib cage points moved relative to the reference point along nearly single lines for both vital capacity and isovolume maneuvers. These lines very nearly superimposed and had slopes of approximately + I. We conclude that a substantial part of the anterior rib cage not only operated with a single degree of freedom, but moved equally, in the manner of a piston. Near the upper and lower margins the tracings tended to be more looped and the two maneuvers were less nearly superimposed. To-

ward the neck the motions were decreased relative to these of the reference point while the opposite was the case near the costal margin, particularly below FRC.

Anteroposterior motions of abdomen. Figure 5 shows a representative example of tracings of relative anteroposterior motions of the abdomen. The scale is identical to that of Fig. 4, and again, motion of the reference point is along the Y axis. It is apparent that the abdomen moves less as a unit than the rib cage. This was strikingly the case for all the subjects. The only points which move nearly as single-valued functions of the reference point are those at the same level (b3 and c3). The points nearest the costal margins moved much less during the isovolume maneuvers than during a vital capacity. These points were very nearly at the border line between the rib cage and abdomen. Such points would be expected to stay nearly fixed during the isovolume maneuver but to move when both regions changed volume in the same direction, as during the vital capacity maneuver.

Antero;Dosterior and transverse motions of the rib cage during relaxation at the extremes of lung volumes. A single degree of freedom dictates a fixed shape at a particular volume. We anticipated that changes in the mechanical properties of the walls of the rib cage and abdomen attending changes in the degree of muscular contraction, and changes in the pressure differences across their walls, would produce changes in the shape of these structures and, hence, introduce additional degrees of freedom. Under the conditions of our experiments these changes would be greatest at the extremes of lung volume as subjects passed from the active state-airways open-to relaxation against a closed glottis. At both IOO 70 of vital capacity and at residual volume (RV), in the active state, muscular contraction is nearly maximal. At IOO 70

of VC pleural pressure is about -30 cm Hz0 and at RV, approximately atmospheric. With relaxation against a closed airway, pleural pressure rises some 40 cm Hz0 at IOO 7c VC and falls by almost the same amount at RV. Thus at high lung volume as the subject relaxes

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A-P(a), cm Trans (a), cm A-P(r), cm Trans (r), cm AA-P, cm ATrans, cm A (a), cm2 A (r), cm2 AA, cm2 Subj

Nipple Level TLC EB 25.6 33.6 25.2 34-o - 037 +.32 675 669 +6

KK lg.6 28.5 19.0 28.8 - .56 +*30 439 430 +9 DL 24.0 32.6 23.0 33.1 -1 .o +.50 615 596 +19 PM 25.3 33.6 24-7 34.1 - .60 +.52 667 660 +7 JM 28.7 37-o 28.0 37.2 - .63 +.25 835 816 +19 FS 23.2 31.5 22.0 32.2 -1 .I2 +*77 572 556 +16

Mean

RV

24.40 32.80 23 -65 33.23 - .71 +a44 633 -8 621.2 +12.6

EB 24-4 33-o 23.9 33.3 - -47 +*37 632 621 +I1 KK 17.4 27.8 17.0 28.0 - -37 +.22 380 374 +6 DL 20.6 32. I I9*3 32.6 -I .31 +.52 520 49’ +29 PM 23.0 33-o 22. I 33.2 - -94 +.21 596 575 +21 JM 25.1 34.5 24.7 34-7 - -37 +.21 677 673 +4 FS 20.5 30.7 lg.8 31.3 - .65 +.65 492 486 +6

Mean 21.83 31.85 21.13 32.21

Xiphoid Level

3’ 97 30.0

33.4 32.2 33.3 31.2

- .685 + -363 549.5 536.4 +12.g

TLC EB 25.1 31-4 24.6 KK ‘9.9 29.0 18.7 DL 24.0 32.7 23.5 PM 26.0 31.6 25.4 JM 29.0 35.2 28.6 FS 23.0 31 .o 22.6

- -43 - . 18 - .50 - .62

- -37 - -37

+*3 616 612 +4 +.10 456 445 +I1 +a75 616 615 +I +*57 645 634 +I1 +.12 804 790 +14 +.21 560 554 +6

Mean

RV

24.50 31.81 23.90 31.96 - .411 + -341 616. I 608.3 -f-7.8

ER 23.4 30.5 22.9 31.1 - -45 +.60 560 556 +4 KK 17.8 27.1 ‘7.3 27-4 - 05 +.25 383 369 +I4 DL 20.7 31.5 19.9 32.5 - I .81 +1 .o 513 506 +7 PM 23.8 29*7 22.5 30.2 -I .25 +*5o 553 533 +20 JM 24.0 33.6 24.3 33.8 + -25 +.20 646 644 +2 FS lg.8 30.0 ‘9.9 29.7 + .I2 -.25 466 462 +4

Mean 21.58 30.40 21.13 30.78 - .6go -t-.38 520. I 511.6 He5

. 1. . A ma open)

icares cross-sectional area and relaxed state (airway

1 A-P indicates anteroposterior diamerer. I rans lnalcates transverse diameter. lated assuming the rib cage as an ellipse. (a) and (r) indicate active state (airway tively. A indicates difference between active and relaxed state.

and was calcu- closed), respec-

the rib cage is subjected to an increase in transmural pressure while at low volumes it is subjected to a decrease in transmural pressure. To the extent that the cross section of the rib cage is elliptical, and to the extent that the influence of changing muscle forces can be neglected, one would expect relaxation at high lung volumes to be associated with an increase in the ratio of the minor to the major diameter, i.e., an increase in the anteroposterior diameter relative to the transverse diameter. Relaxation at RV should produce the opposite change.

ner shown in Fig. 2. For transverse motions we used two such devices- one at each side-and added their outputs with a mixing circuit.

Table 2 presents individual values and Fig. 6 averages for anteroposterior and transverse diameters of the rib cage at the extremes of the vital capacity, both as maintained with airways open and after relaxation against a closed airway. The pattern was similar, with minor exceptions, in all individuals. Over the vital capacity range both diameters increased as lung volume increased -the anteroposterior diameters approximately 3 cm and the transverse diameters about one-third that amount. During relaxation at both maximum and minimum volumes the diameters changed in the opposite sense; the anteroposterior diameter decreased while the transverse diameter increased.

The changes at RV were in the direction to be ex- petted on the basis of the fall in pleural pressure ac- companying relaxation : a decrease in transmural pressure would be expected to reduce the anteroposterior

To examine these possibilities we measured transverse and anteroposterior diameters at two levels of the rib cage at the extremes of lung volume in the standing posture. We measured absolute diameters in the active state with anthropometrist’s calipers (means of three determinations were used) and changes in diameters electrically with linear transducers. For anteroposterior motions the contralateral poi nt w ‘as fixed a nd only the motion of th e anterior surface was measured in the man-

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NIPPLE LEVEL XIWOID LEVEL

25

RV

20

FIG. 6. Anteroposterior and transverse diameters of the rib cage during relaxation at the extremes of lung volume in the standing posture. Closed and open circles indicate the active state (airway open) and the relaxed state (airway closed), respectively.

TRANSVERSE DIAMETER 1 cm

1 191 , , 1 30 31 32 33 34 30 31 32 33

is JM .................. ~-T@~,“:,.:

$s&&y _

QF”~fsFRc[i.l \\>zi$i$i ‘: ... ..... *. c. .............. ........ ......... 4 a

ir DL

A-P MOTION OF ABDOMEN I NSP, FS

PM h-- 0 KK

Y JM

4

FIG. 7. Individual relative motion isovolume diagrams for six subjects in the standing and supine postures. The anteroposterior motion of the rib cage was measured from the reference point shown in Fig. 4 and was displayed on the Y axis. Abdominal motion was measured from the reference point shown in Fig. 5 and was displayed on the X axis. Open circles indicate the active state with airway open at the extremes of the lung volume and closed circles indicate the relaxed state. The dashed lines show the

diameter relative to the transverse diameter. At TLC pleural pressure rises during relaxation and the rib cage is subjected to relative expansion. We reasoned that this would tend to make the rib cage more circular in cross section. We observed the opposite, which suggests that changes in muscle forces operating within the wall of the rib cage or directly on the wall through tissue attachments override the influence of transmural pressures.

The results given up to this point demonstrate that

DL

A-P MOTION OF ABDOMEN

INSP FS

PM

0 0

L/&222$ \ \

/ 0’ 0

KK 0

relaxed configuration of the chest wall in terms of its anteroposterior diameters and the continuous lines indicate isovolume lines at different fixed lung volumes. The light dotted outermost envelope in one subject (JM) shows the maximum range of deviation from the relaxed configuration in terms of anteroposterior diameter. The heavy dotted lines indicate the tracings during quiet breathing including the end-expiratory level (FRC).

the chest wall does have more than a single degree of freedom in particular circumstances. We think that we have probably examined the furthest departures from a single degree of freedom on the part of the rib cage that existed under the conditions of our experiments: namely, the condition in which maximum change in the activity of the respiratory muscles and the maximum change in transmural pressures occurred. Changes in shape of the rib cage as great or greater than these must take place

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414 K. KONNO AND J. MEAD

FIG. 8. ,4verage relative motion isovolume diagrams for six subjects; anteroposterior motions of the rib cage and abdomen are displayed on the Y and X axis, respectively. All motions are expressed as a percent of the total excursions observed during a vital capacity maneuver. The solid lines indicate the isopleths at 8oy0, 607& 4oy0, and 2oyo of VC, based on averages of three points each: the two extremes of the isopleth and the relaxation point. Open circles indicate the relaxed state at the different fixedlung volumes. The dashed lines indicate the theoretical isopleths at IOO% and RV. The intercepts (closed triangles) of the dashed line on the horizontal line indicate theoretical points corresponding to 100% VC and RV at the active state with the airway open. Notice that the deviations of the closed triangles from the closed circles corresponding to the observed point at 100% VC and RV are marked in the supine posture as compared to those in the standing posture. The dotted lines indicate the theoretical isopleths which correspond to volumes obtaining during relaxation at 100%

VC and RV with volume changes due to compression or expansion taken into account. Open squares indicates theoretical points during relaxation at the extremes of lung volume. Note the close correspondence between observed (open circles) and theoretical points.

STANDING

A - P MOTION OF ABDOMEN

SUPINE

when pleural pressure is changed beyond the limits of ordinary breathing, as during muscular efforts produced against a closed airway or during forced breathing.

Relative Motions of Rib Cage and Abdomen

All comparisons of the anteroposterior motions of the rib cage and abdomen were made between the reference points shown in Figs. 4 and 5. For the rib cage the point was midway between the right nipple line and the midline at the nipple level. For the abdomen the point was midway between the right nipple line and the midline at the level of the umbilicus. Rib cage motion was displayed on the Y axis (diameter increasing in the upward direction) and abdominal motion on the X axis (diameter increasing to the right) of the X-Y recorder.

Procedure for obtaining isopleths at diferent fixed lung volumes.* relative motion isovolume diagram. After several quiet breaths the subject inspired room air slowly and maximally and relaxed against an obstructed airway. After a few seconds he was allowed to breathe out into the spirometer until he reached a volume which corresponded to 80 % VC, where he again relaxed against the closed airway, and following a pause of a few seconds performed the isovolume maneuver. The same sequence was repeated at 60 %, 40 %, and 20 ci: of VC. The subject then expired maximally to residual volume and relaxed

A - P MOTION OF ABDOMEN

against an obstructed airway. Each run was repeated more than three times on a given occasion, and the measurements were repeated on a separate occasion with an interval of several months. All data presented here were based on the latest run.

Figure 7, A and B, represent relative motion isovolume diagrams for the six subjects in the standing and supine postures. The scales are the same for both axes.

A comparison of the area enclosed by single isopleths with the over-all areas contained by the extremes of all isopleths (indicated by the dotted line in one of the examples) gives an idea of the validity of our assumption that the chest wall has basically two moving parts. When lung volume is fixed, the relative motions of the rib cage and abdomen are greatly confined and could be reason- ably well approximated with single lines.

The dashed line is drawn through points of relaxation. Departures from this line indicate the extent to which voluntary action distorts the chest wall from the relaxed configuration. (The potential for this distortion is only partially exhibited inasmuch as the subjects were con- strained to the extent of maintaining mouth pressure within rt20 cm HzO-except during relaxation at the volume extremes.)

In general th e isopleths have similar slopes. In all cases motion of the abdomen is greater than that of the

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0 A STANDING

A- P 14OTION OF ABDOMEN

SUPINE

- 40 -20 0 & 20 40 60 80 loo- 120 140 160 l8(

A- P MOTION OF ABDOMEN

rib cage as volume is shifted between them. The total range of anteroposterior motion of the abdomen is somewhat greater than that of the rib cage, and is considerably greater than the excursion occurring between the extremes of lung volume. This is in contrast to the rib cage where the excursion during the vital capacity is very nearly equal to its maximal range of motion.

The isopleths are somewhat curved and, in several instances, distinctly so in the supine posture. The relationship between motion of a surface and the volume displaced by it as it moves is constant only if the surface moves like a piston, i.e., without change in shape. Al- though this may be approximately true for the rib cage it is clearly not the case for the abdominal wall. The abdominal wall may be more appropriately likened to a loosely stretched elastic membrane. At low lung volumes it is nearly flat or even slightly concave, while as it is displaced outward it becomes increasingly convex. In such a membrane the ratio of linear motion of points at the surface to the volumes displaced by the surface tends to be smallest when the surface is most nearly flat and to increase as the surface becomes more highly curved. On this basis one would expect the anteroposterior motion of the abdominal wall to increase relative to that of

FIG. g. Corrected average relative motion isovolunle diagrams (for basis of “correction,” see text). Open circles indicate the relaxed states at the different fixed lung volumes.

the rib cage as volume is shifted from the rib cage to abdomen and for the isopleths to be curved in the sense observed.

When one adds to these considerations the influence of gravity, an explanation for the greater degree of curvature of the isopleths in the supine posture may be given. In the standing posture pressures within the abdomen at the reference level will, in general, be greater than atmospheric and will tend to push the wall outward and increase its convexity. In the supine the pressure within the wall at the reference point will be closer to atmospheric and the abdominal wall will tend to become more nearly flat. One would expect on these grounds that the ratio of anteroposterior motion to volume change would be greater in standing than in supine subjects. I f one assumes that the rib cage is less influenced by posture, an increased ratio of motion to volume changes for the abdomen would result in an increased ratio of abdominal to rib cage motion as volumes are shifted between them. The decreased slopes of the isopleths in standing as compared to supine subjects is then to be expected. Furthermore, to the extent that the degree of curvature of the abdominal wall changes more with volume change in the supine posture, which is reasonable, one would

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STANDING : RI6 - CAGE I

80

60

40

0 A

f

g m a

1 L 60 80 100

A - P MOTION OF RIB - CAGE

SUPINE: ABDOMEN

FIG. IO. A; volume-motion relationship of the rib cage in the dotted line indicates a linear approximation of the relationship. B. standing posture. Volume is expressed as percent of VC and motion volume-motion relationship of the abdomen in the standing as percent of total excursion observed during a VC. Closed circles posture. Closed circles correspond to “fixation” of the rib cage at indicate the volume-motion relationship with abdominal motion 40~3 of its total excursion during a VC and open circles to fixation “fixed” at 0% of its total motion, i.e., at RV, and open circles at 60% of its total motion. The dotted line indicates a linear that with abdominal motion fixed at 807~ of its total motion. The approximation of the relationship.

expect greater curvilinearity of isopleths, with a tendency for the slopes to approach those seen in the standing posture as abdominal volume increases. Again, Fig. 7, A and B, appear to be consistent with this prediction.

The isopleths at different lung volumes are nearly parallel and the spacing of the isopleths is quite uniform. This is strikingly the case for diagrams based on averages for the six subjects. These are shown in Fig. 8, A and B. The solid lines are based on averages of three points each: the two extremes of the isopleths and the point during voluntary relaxation. All points are expressed as percent of the total excursions observed during a vital capacity mane1 Aver. The isopleths are very nearly equidistant. This will be more clearly seen when the volume- motion relationships are developed. At the extremes of the vital capacity no isopleths can be obtained. The dashed lines are theoretical isopleths which would obtain at RV and IOO % VC if the spacing of the isopleths were maintained at these levels, or, in other words, if the volume-motion relationships were the same at these volumes as at intermediate ones. The dotted lines are theoretical isopleths corresponding to volumes that would be obtained during relaxation at IOO % VC and at RV. (During relaxation against a closed airway at TLC, volume decreases due to gas compression, while during relaxation against a closed airway at RV, volume increases due to gas expansion.) We have assumed that deviations of the observed points from the theoretical isopleths (i.e., of the solid circles from the dashed isopleth and of the open circles from the dotted isopleth) reflect changes in shape of the rib cage and abdomen associated with maximal muscular contraction in the active state and the substantial transmural pressures in the relaxed state. In general, the distortions are small with the ex-


ception of RV in the supine posture. We feel that the discrepancy at RV in the supine posture is due mainly to contraction of the rectus abdominus, although we have nothing more substantial than direct observation of the contour of the abdomen on which to base this.

To include the extremes of lung volume in our analysis of relative volume changes we h theoretical isopleths obtained by

ave assumed that the extrapolation are cor-

rect and that deviations from these isopleths reflect abdominal rather than rib cage distortion. This iS

reasonable on the grounds of the relative rigidity of the rib cage. It should be borne in mind that all estimates of relative volumes of the rib cage and abdomen beyond the range of the directly measured isopleths represent extrapolations. All estimates between 20 % and 80 70 of VC are, in essence, interpolations. Figure g, A and B, presents the isopleths replotted on the basis of the “corrected” abdominal excursion between the volume extremes.

Volume-motion relationsi@ of rib cage and abdomen. The relative motion isovol ume diagram .s were used struct volume-motion rela tionships in the man

to ner

con- de-

scribed in connection with Fig. I. Figure IO, A and B, shows volume-motion relationships of the rib cage and abdomen in the standing posture, derived from the corrected relative motion isovolume diagram (Fig. gA). Volume-motion relationships were obtained at two different fixed positions of the other part. Volumes are expressed as percent of VC and motion as percent of the total excursion between the maximal inspiratory and expiratory levels. Figure IO A shows volume-motion relationships of the rib cage with abdominal motion at o % and 80 70 of its total excursion. The volume-motion relationships are closely similar and nearly linear. The

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SEPARATE VOLUME CHANGES OF RIB CAGE AND ABDOMEN 4=7

SUPINE : RIB - CAGE STANDING : ABDOMEN

100 0 A 0 8 80

t 80

60

A-P MOTION OF RIB -CAGE

FIG. I I. Volume-motion relationships of the rib cage and abdomen in the supine posture. Closed circles in A indicate “fixation” of abdominal motion at 0% (RV) and open circles at 600/o of its

similarity of the volume-motion relationships reflects the fact that the isopleths are nearly parallel which, in turn, indicates that the volume-motion relationships of the rib cage are independent of the volume of the abdomen. Linearity of the volume-motion relationships reflect the fact that isopleths are nearly equidistant for equal increments of lung volume. The geometrical basis for this linearity is twofold: I) changes in diameter are small compared to the absolute diameters (and the changes in volume correspondingly small compared to the absolute volume of the chest wall) so that the segment of the over- all volume-motion relationship is small enough to approach linearity, and 2) changes in anteroposterior diameters are large compared to changes in transverse or vertical diameters, so that the over-all relationship between anteroposterior diameters and volume itself should be nearly linear. The dotted line is a straight line fitted to the data by eye.The equation of this line is

Vrc = 0.7 Mrc ( 1 I

where V indicates changes in volume, expressed as percent of the vital capacity, and M indicates changes in motion, expressed as percent of the total excursion between the maximal inspiratory and expiratory levels, and rc indicates the rib cage.

Figure I oB shows corresponding volume-motion relationships of the abdomen with the rib cage at 40 % and 60 % of its total excursion. The maximum variation between estimated volumes of two points for a given motion is about 4 % of vital capacity, which corresponds to that seen in the rib cage. The dotted line has the equation

Vab = 0.28 Mab

where ab indicates the abdomen.

( > 2


total motion. Closed circles in B indicate fixation of the rib cage at 407~ and open circles that at 607~ of its total motion.

The redundance of the two volume-motion relationships was mentioned in the THEORY section: once the volume change of one of two parts is defined that of the total system being known the other can be obtained by subtraction. From equation I we estimate that the rib cage accounts for 70 % of the volume change during a vital capacity maneuver in the standing posture. By subtraction, the abdomen accounts for 30 % of the volume change. The corresponding values from equation 2 are 72 % and 28 %. The close correspondence of these two estimates is to be expected.

Figure I IA and B, shows volume-motion relationships of the rib cage and abdomen in the supine posture.

The relationships in the supine posture show somewhat greater disparity than in the standing posture and they are slightly curvilinear. Again, linear approximations yield similar estimates of the relative contributions to the vital capacity. That for the rib cage is

Vrc = 0.66 Mrc (3)

and for the abdomen

Vab = 0.3 Mab (4)

From equation 3 we estimate that the rib cage accounts for 66 % of VC in the supine posture. By subtraction, the abdomen accounts for 34 70. The corresponding values from equation 4 are 70 % and 30 %. Again, the close correspondence is to be expected. Also, it appears that the relative contributions of the rib cage and abdomen to the vital capacity are nearly the same in the two postures.

Comparison of Direct and Indirect Estimates of Lung Volume Change

We were interested to see if points on the relative motion diagram reached during actual breathing were at

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JM

SUPINE

ti 80 % vc

2 RELAXATION

I G lr

L 0

Z 0 F:

!2


FIG. 12. Relative motion diagrams during relaxation after inspiring various volumes while voluntarily emphasizing either rib-cage or abdominal contributions. The broken line indicates the relaxation and dotted lines the relative motion isovolume diagram in the supine posture for the same subject. Closed circles indicate the points at which the subject stops his effort to inspire. Open circles indicate the end of voluntary relaxation, against a closed airway.

lung volumes corresponding to ones predicted by inter- polation from the isovolume lines. To this end we had subjects inspire various volumes from the resting end- expiratory level, emphasizing voluntarily the contribution of either the rib cage or abdomen. After inspiring, the subjects held volume constant momentarily, while the pen of the X-Y recorder was activated, and then relaxed against a closed airway. The airway was then opened and the subjects breathed out maximally into a spirometer. The volumes expired were compared with ones estimated relative to RV on the relative motion isovolume diagram. These comparisons were made in three subjects in the supine posture.

Figure 12 shows tracings for one subject (JM), superimposed on the isopleths shown in Fig. 7B. Figure 13 shows the relationships between lung volumes measured by a spirometer directly and those estimated graphically in three subjects. Closed circles indicate breaths in which the contributior of the rib cage was emphasized, and open circles ones in which the contribution of the abdomen was emphasized. These correspond to tracings to the left of the relaxation curve in Fig. I 2 in the first instance and to the right in the second. All points are close to the line of identity; however, there is a tendency for over- estimation of the volumes measured indirectly when subjects emphasized the contribution of the rib cage. This may possibly reflect a small degree of elevation of the spinal arch during this maneuver.

Volume Changes of the Rib Cage and Abdomen During Breathing

Figure 14, A and B, presents average relative volume diagrams derived from the relative motion isovolume diagrams in Fig. g, A and B.

SUPINE

I * 1 1

0 20 40 60 80 IOd

DIRECT VOLUME ; oh OF VC

FIG. 13. Comparison of direct and indirect estimates of lung volume change.

The outermost dashed line has been drawn through points corresponding to the extremes of the isopleths. The solid line corresponds to the relaxed state. All deviations from the relaxation line require muscular activity. All points to the left of the relaxation line require inspiratory activity operating on the rib cage, or expiratory activity operating on the abdomen, or some combination of these. All points to the right require expiratory activity operating on the rib cage, or inspiratory activity operating on the abdomen, or some combination of these. Points on the relaxation line imply no muscular activity only in the instance of relaxation against an obstructed airway. When the airway is not obstructed, a particular pattern of muscle activity will be required to maintain the relative volumes of the rib cage and abdomen the same as during relaxation (except at one vo1u1nc, namely, that reached during relaxation without airway obstruction).

It is appropriate at this point to state that virtually all previous analyses of the mechanical behavior of the chest wall have been based on the assumption that in actual breathing the muscles of respiration deform the chest wall in the same way that pressures applied to the respiratory system externally would deform it; or, in other words, that the active and passive configurations of the chest wall are the same. In terms of the relative motion diagrams this assumption implies that breathing takes place in the near neighborhood of the relaxation lines. We are in a position to examine this assumption. We have already demonstrated that the departures from this configuration are at least potentially great, but this point, in itself, is trivial. Of more importance are the relationships occurring during actual breathing.

The vital capacity. We have not examined the pathway of relative volume change during the vital capacity maneuver but merely the points at its extremes. Observation of the pen motion of the X-Y recorder during the maneuver suggests that it is not confined to the near neighborhood of the relaxation line. Certainly it departs from this

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SEPARATE VOLUME CHANGES OF RIB CAGE AND ABDOMEN 4’9

ABDOMINAL

RELAXATION

FIG. 14. Volume changes of the rib cage and abdomen during breathing. Volume changes are expressed as a percent of vital capacity. Volume changes of the rib cage are plotted on the Y axis and those of the abdomen on the X axis and diagonal lines indicate the volume change of the lungs. Large closed circles indicate the maximum inspiratory and expiratory level with airway open. The continuous line with open circles indicates the volume changes during relaxation and the short dotted line those during quiet breathing including the end-expiratory level (FRC). The outermost dashed line indicates the range of possible configurations of the chest wall that can be produced voluntarily while maintaining mouth pressure within Ca & 20 cm H20. The 45’ lines correspond to equal volume contribution.

STANDING


lNSP>

FIG. 15. Relative motion diagram for a subject (DL) in the standing posture during quiet breathing before and after a voluntary effort in which he increased rib-cage volume while decreasing that of the abdomen.

line at IOO % VC and RV in both postures. At IOO 70

VC the deviation is inspiratory for the rib cage and expiratory for the abdomen. At RV the same holds in the standing posture and to a smaller and probably insig- nificant extent in the supine. The relative contributions to the vital capacity of the rib cage and abdomen have already been described. In the case of the abdomen the volume change between the extremes of the vital capacity is substantially less than the maximum of which it is capable, as represented graphically by the maximum width of the outermost loop.

Quiet breathing. The short dotted lines in Fig. 14, A and B, are drawn between the average end-inspiratory and end-expiratory points during quiet breathing. (Individ- ual tracings of relative motions during quiet breathing are shown in Fig. 7, A and B.) It is apparent, and this was true in all individual instances, that quiet breathing does not take place along the relaxation line. In the supine posture (Fig. 14l3) the end-expiratory point was near the relaxation line but the end-inspiratory point, in all instances, fell to the right. The abdomen accounted for 68 70 of the volume change; whereas in the same range along the relaxation line it would account for only 28 % of a similar volume change.

In the standing subjects (Fig. 14A) the departure from the relaxation line was of a different sort. Here the end- expiratory point fell to the right of the relaxation line. We think that this may reflect hysteresis of the relaxation line. All relaxation points were obtained immediately after a maximally deep inspiration. The tracings during quiet breathing were obtained without any previous deep breaths. It may be that relatively long-term effects of the force of gravity account for the increase in abdominal volume at end expiration relative to the relaxation line. Figure 15 presents a relative motion diagram for a subject (DL) in the standing posture during quiet breathing before and after a voluntary effort in which he increased rib-cage volume while decreasing that of the abdomen.

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S TANDIN

P .’

, - . .

p RELAXATIOtd GURL/E ++==-

Q: .‘- *’

*/- ..O”

w’--& MOTION OF ABDOMEN

0 ‘0° % VG .a

_.-- 0’.

.’ 60% ..=-

.Q . .

fALKlh16 :

. ..%O% F-k FRC :

*.*- /

...*&/&. :

SUST

SINGING &

. - . - o’.-

. -

FIG. 16. Pathways of relative motions during voluntary hyperventilation, talking, singing, and sustained soft tones in the standing and supine posture, superimposed on the relaxation curve at different fixed lung volumes.

Subsequent spontaneous breathing fell close to the relaxation line.

In general, in the standing posture the relative contribution of abdomen and rib cage more nearly corresponded to the slope of the relaxation line but i n all instances the abdominal contribution was greater than would be expec ted. We have concluded that during quiet breath ing the configuration of the chest wall at end expiration probably does correspond to the relaxed configuration, but that inspiration distorts the chest wall from this configuration and in a direction consistent with dominance of inspiratory forces operating on the abdomen.

Voluntary Hyperventilation

Relative motion diagrams during voluntary hyperventilation in both postures are shown in the upper tracings of Fig. 16, which are representative of all subjects. Pathways during this maneuver are nearly along the relaxation curve in both postures.

Talking

Pathways during talking in both postures are shown in the middle tracing of Fig. 16. In the standing posture deviation to the left from the relaxation curve is dominant and the configuration of the rib cage is sustained at

the end-inspiratory level (about 50-60 % VC) while abdominal motion is dominant. In the supine posture slight deviation to the right from the relaxation curve is seen. The configuration of the rib cage is also nearly sustained at 20-40 % of VC while abdominal motion is dominant.

Singing and Sustained Soft Tones

Pathways during singing and during the production of sustained soft tones in both postures are shown in the lower tracings of Fig. 16. In the standing posture the abdomen shifts remarkably in the expiratory direction and the configuration of the abdomen is nearly fixed at 20 ‘% VC. This suggests that the contraction of the abdominal expiratory muscles is sustained during singing, compared to that during talking, while the rib cage maintains a comparably high inspiratory level (40-60 % VC). The pathway during the production of sustained soft tones is essentially an extrapolation of that during singing. In the supine posture the pathway during sustained soft tones shows a particular pattern; above 50-60 % VC the abdominal motion is pronounced, while the configuration of the rib cage is sustained at a high inspiratory level. In contrast, below this lung volume virtually all motion is carried out by the rib cage. Path- ways during singing are nearly along the relaxation curve in the supine posture.

Bouhuys et al. (4) have recently described respiratory mechanics in trained and untrained singers. They concluded that the singing of soft tones at high lung volumes would require the rib cage to be held in a more inspiratory position than during related breathing. Our results, which are only prelirninary in this connection, support this prediction.

DISCUSSION

All previous estimates of the work of breathing which have included the work done on the chest wall have been based on the assumption that the configuration of the chest wall during breathing is the same as that during voluntary relaxation against an obstructed airway at the same lung volume. We have demonstrated that this assumption is incorrect. The significance of the observed departures to the work of breathing awaits further measurements together with simultaneous measurements of the appropriate .driving pressures.

Our method for partitioning the volume displacements of the chest wall is based on the assumption that the chest wall has two moving “parts.” We have shown that the relative motions of the rib cage and abdomen are confined very nearly to single lines as long as total respiratory volume is held constant (Fig. 7, A and B). This supports our assumption since either additional moving parts or additional degrees of freedom within the parts would tend to produce departures from single lines. But the isovolume maneuver used to produce these lines was highly artificial. Do these relationships apply to breath-

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SEPARATE VOLUME CHANGES OF RIB CAGE AND ABDOMEN A.21 A

ing? Our comparisons of volumes derived from these relationships with ones directly measured (Fig. 13) offer only a partial answer since they also were based on artificial breathing maneuvers. A better answer awaits further comparisons during natural breathing.

With the exception of the estimates made by Wade (6), which will be considered separately, previous attempts to partition volume displacements of the chest wall have been either geometrical or’ plethysmographic. In the first instance linear displacements, e.g., movements of the X-ray shadow of the diaphragm or changes in circumference of the chest wall are converted to volume displacements by applying them to some geometrical model. In the second instance the part to be studied is isolated by means of a physical partition and the volume displacements on one side of this partition are recorded plethys- mographically. The estimates of Agostoni et al. (I) are a recent example of the first approach, and those of Bergofsky (3) of the second.

Those using either the geometrical or the plethysmographic method must face the problem of defining the physical extent of the part in question-either to specify the dimensions of the model or to position the partition. In our method we must make certain that our measurements are made at some point within the margins of the part, but we have no need to define the location of the margins of these parts. The geometrical and plethysmographic methods must also take into account any motions of the margins. This presents a particular difficulty in the case of partitional plethysmography : if the margin moves the partition itself must move, and one then has the added necessity to take into account volume displacements of the physical partition itself. Bergofsky (3) reported that the abdomen contributed one-third or less of the tidal volume during quiet breathing. We have found that the abdomen contributes more than one-half of such tidal volumes. Any cephalad displacement of the partition would subtract volume from the chamber sur- rounding the abdomen. We suggest that this sort of artifact may explain the discrepancies between our results and Bergofsky’s.

Agostoni et al. ( I) used the geometrical approach to estimate the volume changes of the rib cage, and obtained that of the “diaphragm-abdomen” by subtraction. We feel that the difficulty of assigning an appropriate geometry to these measurements renders the estimates of doubtful accuracy.

Wade (6) made extensive measurements of the linear movements of the diaphragm and of changes in circumference of the rib cage during breathing. He also made estimates of the volume displacements based on these measurements along lines similar in concept to our own measurements. He assumed that all volume displacements could be accounted for by movements of the diaphragm or changes in chest circumference. In essence, then, he postulated a system with two moving parts-the diaphragm and the rib cage. Furthermore, he assumed the volume-motion relationships of the two parts to be

linear and uninfluenced by posture. From average values of motions and volume change in the upright and supine postures he developed simultaneous equations expressing total volume change as the sum of the two motions measured. He then solved these for the separate volume- motion relationships, and estimated that “. . . in a full vital capacity about one-quarter of the ventilation is due to chest expansion and three-quarters to diaphragmatic movement.”

Wade measured diaphragmatic movement relative to the rib cage, and his estimates of the volumes displaced by the diaphragm would correspond to our estimates of abdominal displacement (and his estimates of chest expansion to our estimates of rib cage displacement) only in one highly restricted and unrealistic case: namely, if the points of attachment at the margins of the diaphragm were fixed relative to the rest of the body. The diaphragm and abdominal wall would in this case be opposite surfaces of the same part, and would move equally in terms of displacements of their surfaces. But the attachments of the diaphragm are not fixed, and it is an oversimplifica- tion to assign movements of the diaphragm to abdominal displacements. Depending on the action of the other muscles of respiration, inspiratory displacements of the diaphragm, i.e., movement in the caudad direction relative to its points of attachments, may be associated with outward movement of the abdominal wall, no movement, or even inward movement. In the second instance, cephalad motion of the points of attachment due to elevation of the rib cage would be just sufficient to nullify displacement of the abdomen by the diaphragm. In the third instance, elevation of the rib cage would be so great that the net effect of rib-cage elevation and diaphragmatic contraction would be to displace the abdominal wall inward.

In terms of our analysis, then, displacement of the diaphragm as measured by Wade contributes both to abdominal and rib-cage expansion. Since the rib cage is elevated from RV to TLC, i.e., over the range of the inspiratory vital capacity, it follows that part of the diaphragmatic displacement must have contributed to rib- cage expansion. If both Wade’s and our estimates of the partitioning of VC are correct, the combination of a 30 % contribution of the abdomen found by us together with a 70 % contribution of diaphragmatic movement found by him suggests that more than half of the diaphragmatic excursion is associated with chest expansion. The 25 % value for the contribution of chest expansion, given by Wade, would then represent the additional expansion of the rib cage not directly related to movement of the diaphragm.

To these considerations we add the anatomic findings of Keith (5) that the area of the diaphragm in contact with the lung constitutes approximately 28 % of the lung’s external pleural surface, i.e., of the surface in contact with either the diaphragm or the rib cage. We have found a closely similar value, 25 %, for inflated and dried dog lungs. It is of interest that the surfaces of the rib cage and abdomen presented to the lung surface are

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422

in nearly the same proportion as are their relative displacements during maximal volume change.

Wade (6) has stressed that the relative contribution of diaphragmatic contraction to movements of the rib cage and abdomen depends on the state of contraction of the other respiratory muscles. For example, tensing of the abdominal muscles favors rib-cage expansion, and vice versa. Agostoni et al. (I) have pointed out that, in addition, the contribution of the diaphragm to the relative movements of the rib cage and abdomen depends on the action of gravity, and in particular upon the action of gravity on the abdominal contents. Due to the hydrau- lic action of the abdominal contents the compliance of the abdomen is greater in the supine than in the upright posture (2). On the other hand, the compliance of the rib cage decreases as lung volume decreases and is, therefore, less during quiet breathing in the supine than in the upright posture. As a result, movement of the central portion of the diaphragm in the caudad direction should be favored in the supine posture, and hence the relative contribution of the diaphragm to abdominal displacement should be increased. The greater contribution of the abdomen to the tidal volume in the supine posture, which Agostoni and colleagues found and which we have confirmed, (Fig. 14B) presumably has such a basis.

REFERENCES

AGOSTONI, E., P. MOGNONI, G. TORRI, AND F. SARACINO. Rela- tion between changes of rib cage circumference and lung volume. J. APPZ. Physiol. 20 : I I 79- 1 I 86, I 965. AGOSTONI, E., AND H. RAHN. Abdominal and thoracic pressures at different lung volumes. J. APPZ. Physiol. 15 : 1087-1092, I 960. BERGOFSKY, E. H. Relative contributions of the rib cage and the

diaphragm to ventilation in man. J. ApPZ. Physiol. 19: 698-306,

1964.


We have stressed the high degree of volume dependence between the rib cage and abdomen under isovolume conditions. Indeed, we have based our analysis on this dependence. We need, in closing, to emphasize the re- markable degree of volume independence of these parts when total volume change is unconstrained. This independence is illustrated graphically by the size of the area closed by the dashed lines encompassing the extremes of the isopleths in Fig. 14, A, B. The maximum width of this enclosed area indicates the maximum volume change that can take place in the abdomen with the rib cage fixed. It is seen to exceed substantially the volume change of the abdomen in the vital capacity maneuver-indeed, in the supine posture it is nearly twice that volume. Similarly, the maximum height of this enclosed area indicates that with the abdomen fixed the rib cage is capable of producing a volume change equal to or even slightly greater than its contribution to the over-all vital capacity. The sum of these individual vital capacities, i.e., the sum of the individual maximal excursions, equals 124 70 VC in the standing posture and I 27 7% VC in the supine posture. Clearly, when the possible influence of restraints to the chest wall on volume capability is considered, the volume reserve of the respiratory system is seen to be greater than has hitherto been aDnreciated.

BOUHUYS, A., D. F. PROCTOR, AND J. MEAD. Kinetic aspects o singing. J. AppZ. Physiol. 2 I : 483-496, I 966. KEITH, SIR ARTHUR. Respiration in man. In: Further Advance in Physiology. London : Edward Arnold, I gog. WADE, 0. L. Movements of the thoracic cage and diaphragm in respiration. J. Physiol., London I 24: I 93.2 I 2, I 954.

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measurement of the separate volume changes of rib cage and ......degrees of freedom of a closed...

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