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Isotropy and homogeneity of lung tissue deformation
ISOTROPY
AND HOMOGENEITY OF LUNG TISSUE DEFORMATION* RONALD C. TAI and GEORGE C. LEE
Faculty
of Engineering
and Applied Sciences, State Umverslty Amherst, NY 14260, U.S A
of New York at Buffalo,
force-extension tests on lung tissue cubes taken from excised dog lungs were performed to examine relative directional-dependent deformation behavior (isotropy) and locational-dependent deformation behavior (homogeneity). Four types of specimens were used: parenchyma tissue cubes from relatively young dogs (group A), parenchyma cubes from older aging dogs (group B), tissue cubes with intact pleural membranes on the cube surfaces (group C), and tissue cubes with one relatively large airway oriented along one of the principal axes (group D). The effects ofaging and the presence of a pleural membrane and an airway on the deformation of lung tissue were also examined. Results indicate that mild anisotropic parenchymal deformation (less than 10% of the mean deformation) exists in relatively young lungs and to a lesser degree in older dogs. No significant locational dependence of deformation was found between upper and lower lobes. The pleural membrane slightly affected the directional deformation behavior pattern of the parenchyma tissue. The presence of an airway caused considerable data scatter with possible deformation characteristic change. It is concluded that the assumption of an intially isotropic and homogeneous parenchyma in gross modeling of lung deformation is reasonable. Abstract-Triaxial
mation lead to conclusions of either isotropic (Ardila et al.. 1974) or anisotropic (Hill, 1971) lung expansion. Anisbtropic strains have also been found in intact dog lungs using biplane videoroentgenographic analysis (Chevalier ef al., 1976). Hoppin ef al. (1975) performed triaxial tests on cubical lung tissue specimens and observed some irregular directional extension behavior, but the focus of attention was not on material isotropy. There seem to be few reported studies concerning the homogeneity of the lung tissue properties. For dogs (Frank, 1963) and for monkeys (Pare et al.. 1978) it has been shown that the upper lobe contains more volume per unit weight of tissue (specific volume) than the lower lobe at the same transpulmonary pressure. Interlobar and intralobar nonuniform deformation based on uneven distribution of bolus gas was also observed in isolated lungs of dogs and monkeys (Glaister rr al., 1973). The present investigation is intended to examine possible anisotropic or non-uniform properties of dog lung tissues using the technique of Hoppin et al. ( 1975). No attempt is made to obtain the stress-strain (or force-deformation) properties of the parenchyma.
INTRODUCTION of the interdependence concept of lung tissue by Mead et al. (1970), there have been a number of studies concerned with the application of elasticity theory to the analysis of lung tissue deformation (Fung, 1974,1975 ; Lee and Frankus, 1975a, b ; Lee et al., 1976). More recently, numerical models have been developed to predict the gross lung deformation behavior (Fung et al.. 1978 ; Liu and Lee, 1978 ; Vawter el al.. 1975; West and Matthews, 1972). In all the analytical efforts, an isotropic, homogeneous parenchyma has been assumed. In order to refine the analytical approaches, it is desirable that the assumption of material isotropy and homogeneity be substantiated. Major analytical efforts will be required if the lung parenchyma behaves as an anisotropic inhomogeneous continuum. Morphometrical observations at the alveolar level on lung parenchyma of various animals have led some authors to conclude that parenchyma deforms isotropically (D’Angelo, 1972; Forrest, 1970; Glazier et al., 1967) while others conclude differently (Forrest, 1976; Klingele and Staub, 1970;Tsunoda et al.. 1974). In most studies, the criterion for determining isotropy is whether the parenchyma deformation actually observed can be described by the length-volume or area-volume relationship of an ideal isotropic material. Macroscopically, lung tissue strips taken in different orientations behave similarly and fail to show systematic variations in properties (Fukaya et al.. 1972; Redford, 1957). Observations on pleural surface deforSince the introduction
SPECIMENS
Prepararions Healthy mongrel dogs (17-30 kg body weight) were anesthetized and sacrificed by exsanguination. The lungs were excised and a tracheal cannula was installed. After leak tests with air inflation to 30 mm H,O, each left lung was degassed in a vacuum chamber and readied for pressure-volume measurements. Two air ventilated inflationAeflation cycles between 0 and 30 cm H,O were carried out. This was followed by one
* Receit:ed 22 July 19X0. c United
AND METHODS
States Government 243
244
RONALDC. TATand GEORGEC. LEE
I
+
Croniocoudol direction
Fig. 1. Definition sketch of coordinate system and orientation for homogeneous cubes. saline ventilated cycle. The absolute volume of the lungs was measured between cycles by water displacement. The deflation limb of the second cycle in air and the first cycle in saline were used for comparison with the measurements on tissue cubes. All measurements were done at room temperature. After the saline pressure-volume measurements, the lungs were separated into lobes, suspended in saline, and kept deep frozen at - 20°C for 24 hr. Using a band saw each lobe was cut into thick slices with sections lying perpendicular to the body craniocaudal direction. Two types of tissue cubes were cut from these slices. The first type was intended to be homogeneous and free of major airways and was taken from immediate subpleural areas near the middle portion of the upper and lower lobes. The second type of specimen was intended to provide inhomogeneous cubes. They contained either the visceral pleural membrane or a straight airway in one of the three principal directions of the cubes. The intact orientation of homogeneous specimens were carefully followed and recorded, using a universal coordinate system consisting of x-, y- and z-axes. These cubes were taken in a way such that the x-axis was perpendicular to the pleural surface, the z-axis along the body craniocaudal direction, and the y-axis in the third direction as shown in Fig. 1. Two groups of dogs (thus specimens) were used for homogeneous cubes : young dogs (group A, nos. 1, 2, 3) and older dogs (group B, nos. 4, 5) both free of respiratory disease symptoms. Comparable numbers of specimens were taken from the upper and lower lobes for each group. For inhomogeneous cubes two groups of specimens were studied. In Group C the cubes contain an intact visceral pleural membrane on each of the two approximately parallel opposite surfaces along the x-axis. The only location suitable for obtaining this type of specimen is the apex of the upper lobe. The other group (group D) consisted of cubes having a straight airway with a size ranging from 1.8-4.0 mm i-d. and lying along one of the axes. The exact intact orientations of the tissue cubes of group D were not traced but their locations were noted.
The volumes of the cubical specimens of groups A and B were approx. (1.3 cm)‘. The size of the specimens in groups C and D may have deviated from (1.3 cm)3 in order to include pleural surfaces or airways, The number of tissue specimens tested are summarized in Table 1. The cubical tissue specimens were deformed by applying forces to each surface through four string-plate units, each consisting of a thin circular plastic plate of approx. 3 mm attached to the end of a 20cm-long silk thread. The plastic plates were attached to the cube surface by Eastman 910 adhesive. The four plates were placed symmetrically near the corners on each surface of the cube. Stretching
apparatus
The tissue cubes were tested on a stretching apparatus shown schematically in Fig. 2. One equalizing unit was used for the four strings from the same cube surface to minimize unequal deformations of the surface. Each unit consisted of three thin flat aluminium bars with strings attached through the equally spaced holes shown in Fig. 2. The force was applied by adding calibrated weights onto the strings in each direction. The force-transmitting strings were aligned in such a way that the suspended tissue cube could be submerged in saline solution in a square lucite tank. By
Table 1. Number of cubes tested by categories Category
Number of Cubes
Group A : Dog No. 1 Dog No. 2 Dog No. 3
5 (upper lobe 2; lower lobe 3) 4 (upper lobe 2; lower lobe 2) 4 (upper lobe 2; lower lobe 2)
B: No. 4 No. 5 C:
7 (upper lobe 3; lower lobe 4) 4 (upper lobe 2; lower lobe 2) 4
Group Dog Dog Group
Group D:
9
Displacement marker and scale
Fig. 2. Schematic drawing of the triaxial test apparatus.
Lung tissue deformation lowering or raising the liquid level in the tank, tissues could be tested in air or in saline solution. The weight hook at the free end, which also served as a counterweight, exerted a dead load of 1.7 g along each axis at all times. The linear deformation of the cube in each direction was indicated by the position of a marker (on the string) on a fixed scale. Deformation
measurements
A correlation between the absolute deformation and the scale reading was established through a calibration cycle of an inflation-deflation maneuver where at every loading level the actual linear dimensions of the specimen were measured with a vernier caliber (0.05 mm accuracy) and recorded along with the corresponding scale reading. Obviously the way the loadings were applied to the specimens surfaces caused uneven deformation on the surface with peaks and troughs. The peak-to-peak and trough-to-trough distance measured between two opposite surfaces along each axis were plotted against the scale readings (Fig. 3). A linear correlation for each axis in air or in saline solution were drawn for the specimen and each was used to determine the average dimensions for a specific scale reading. Reference
dimensions
The reference state used in the investigation incorporated two quantities : (1) the net tissue volume of the cubical specimen and (2) the resting cube configuration in saline (saline equilibrium state). Specifically, the reference state of a lung tissue cube is defined as one which has the same volume as the collapsed lung tissue but the same configuration as in the saline equilibrium state. Reference dimensions are thus the
Specimen
03 sab5
x- axIs
01 0
1
/
I 1
1
I
2
245
dimensions of this fictitious reference state. All cube deformations were expressed as extension ratios based on the reference dimensions. By including the net tissue volume of the cube in reference dimensions, the absolute deformation of each specific cube may be normalized with its own size. This facilitates comparisons among cubes of different sizes. Furthermore, by using the net tissue volume rather than the saline equilibrium volume, the inter-specimen differences in saline equilibrium volume can be avoided. Specific volume (volume per unit wet tissue weight) was used as a compatible “lung volume” for direct comparisons between cubes and lobes. The average linear dimensions of the cubes and the surface loadings are the basis for calculating the deformed cube volumes and the apparent stresses. The average stress for the three directions was obtained and was used for the pressure-volume relationships. In order to establish reference dimensions as well as forcedeformation behavior, several physical quantities of the cubical specimens had to be obtained. Saline equilibrium dimensions were measured twice, using a vernier caliber, once before and once after stretching in saline, with no applied forces on the cube. Only the latter measurement was used to calculate reference dimensions. The volume and weight of each specimen were measured after the completion of an entire cube test with the force applying attachments removed. Tissue volume was measured by the water displacement method in a small buret and the wet and dry tissue weight were measured with a balance (0.005 g accuracy). Test procedure
For triaxial measurements the loading ranges were 0-70g (air) and O-30 g (saline). These correspond approximately to, from less than 1 cm H,O to 30cm H,O in air and to 1Ocm H,O in saline. Three types of loading cycles were used. For equal triaxial loading all three directions were stretched simultaneously by the same amount of force during the inflationdeflation maneuver. For uniaxial loading, the loading ranges for the main loading axis were lo-70 g in air and 5-30 g in saline while the loadings along the other two (lateral) axes were held constant at 40g in air and 20g in saline. The third type of measurement was the calibration cycle ofequal triaxial loading. The entire experiment for each specimen consists of two equal triaxial loading cycles, followed by three uniaxial loading cycles, one along each axis, and one calibration cycle at the end.
I
3 RESULTS AND DISCUSSIONS
Measured Length km) Fig. 3. Calibration of displacement reading against actually measured cube dimension. Open symbols for loading and solid symbols for unloading. Each point pair having the same
reading value gives the peak-to-peak and trough-to-trough measurements, respectively.
Reference
dimensions and saline equilibrium
dimensions
In deformation analysis a reliable reference state is essential for establishing consistent and meaningful evaluations. For the study ofintact lungs the total lung
RONALD C. TAI and GEORGE C. LEE
246
capacity (TLC) is usually chosen as the reference state and lung volumes are expressed in terms of the percentage of parenchymal tissue as an elastic material. The commonly used reference state for elastic deformation is the undeformed state of the material. Since the resting volume of an air-filled lung is dictated by the amount of trapped air, it is extremely difficult, if not impossible, to recognize and measure its undeformed volume. For this reason, in the present study the reference dimensions (at a fictitious reference state) were chosen as the combination of cube saline equilibrium configurations and wet tissue volume. The confidence in using these two physical quantities is gained from the previous study by Vawter (1977) and the consistent measurements obtained in the present study. The ratios established from the measured wet tissue volume, net tissue weight, and saline equilibrium volume of the cubes and the lungs used in groups A and B are summarized in Table 2. The three ratios shown are saline equilibrium to tissue volume ratio (V&V,), saline equilibrium volume to wet tissue weight ratio (VJW,), and wet density (WJV,). There is no statistically significant difference in the mean ratios of the tissue specimens between the upper and lower lobes. This implies homogeneity of the lung parenchyma. The values in Table 2 also show that the ratios ofgroup B are greater than those of group A. These differences suggest a significantly larger Vs, for group B than for group A. Comparisons of the actual measurements between the two groups A and B show a higher mean value of Vs,/V, and V,JW, and lower values of density for group B. There is no statistically significant difference in V&V, between the two groups. Another observation can be made from Table 2. A consistently higher ratio was obtained for cubes than for the whole left lung. This may imply a restraining effect of the pleural membrane on the resting volume of parenchyma tissue. For all tissue specimens, including those not used for tests, the mean wet-to-dry tissue weight Table 2. Ratios
of specimen
ratio is 6.43 f 0.75 (mean &S.E.). The mean saline equilibrium volumes for group A (V&J, = 5.22 + 0.70 for cubes and 3.53 f 0.34 for left lungs) are comparable to the results obtained by Vawter (1977) for dog lobes (V,,/V, = 2.74 f 0.20) where 1.0 has been added to the originally reported value. Two factors may contribute to these differences. The first is a possible freezing effect which may alter the tissue structure, thus the resting volume. Secondly, there is the increasing contribution of recoil pressure from the pleural membrane as the lung volume decreases observed by Nagao (1973). The visceral pleural membrane thus may limit the resting volume ofthe parenchyma in the absence of surface forces. Consequently, the lobe will exhibit a smaller saline equilibrium volume than thedissected parenchyma. More experimental data are necessary to further assess the saline equilibrium state. Since the reference dimensions defined in the present study involve a saline equilibrium configuration (the ratios of the dimensions) rather than the absolute saline equilibrium volume, the resulting extension ratios are suitable for comparison among individual tissue specimens. Homogeneity
General tissue deformation behavior is determined in the present study by observing the characteristics of the ).-a, relationships; the maximum .(at highest loading) and minimum (at 1.7-g loading) extension ratio (i,,,, and &,,in)were averaged for individual axes and are compared among different axes, between upper and lower lobes, and among different categories of cubes. The statistical means and the standard errors of &ll,Xand &, for the three axes for all groups and categories are shown in Figs. 4 and 5. Differences in extensions for the three axes generally exist. In groups A and B, nearly identical anisotropic patterns are found for the upper and lower lobes (Fig. 4). The physical
measurements
V SE
VSE
V,
W,
W, V,
W/g)
(g/cc)
n
CUBES Group A: Upper Lobes Lower Lobes All (upper & lower)
546~0.81 5.04+0.59 5.22 f 0.70
6.26+0.70 5.63 kO.56 5.90 + 0.68
0.87f0.05 0.89 f 0.04 0.84 + 0.04
6 8 14
Group B : Upper Lobes Lower Lobes All (upper & lower)
8.25 kO.45 7.7OkO.80 7.95 f 0.70
8.53 + 0.73 8.65 +0.56 8.59 f 0.61
0.97 io.10 0.89 f 0.06 0.93 * 0.09
5 6 11
3.53 +0.35 4.19kO.59
4.56kO.17 6.18kO.87
0.77 * 0.05 0.68 +0.001
3 2
LEFT LUNG Group A Group B Note:
For definitions
of ratios
see text; all ratios
in mean
+ SE. n = number
of specimens.
Lung
Symbols
Cube Am, 1.
Y
*
a
0
0
I” s(1111e A
.
.
In
Ol,
may contribute to these findings (Pare et al., 1978). The difference in functional demand of the upper and lower regions of the lung may also require the direct examination of the existence of the regional differences in tissue property. In the present study the only upper-lower regional difference that was found was the slightly higher scatter in the data for the lower lobes in group A shown in Fig. 4. All differences in the mean extension between cubes from the upper and lower lobes are statistically insignificant (Tables 3 and 4). The extrapolation of dog lung tissue data to human may be at least partially justified by the fact that the upper-to-lower lobe difference tends to be greater in dog lungs because of the predominant diaphragmatic breathing. Therefore, we may conclude that it is proper to consider lung parenchymal tissue as a homogeneous material in gross lung elastic deformation studies. In other words, the tissue elasticity property per se is not a contributing factor leading to lung regional inhomogeneous behavior.
-bar --Am,”
Group A 3o
Lower Lobe
Upper Lobe
247
tissue deformation
25
‘-t--r
Group B
Isotropy
Isotropy of the lung tissue deformation behavior was determined by examining the line patterns formed by the mean maximum extension points as shown in Fig. 5. For an isotropic material all the line patterns should be straight horizontal lines. Since mean maximum extension points as observed do not form horizontal lines and the scattering of individual data varies, the differences in maximum extensions between the axes have to be quantified further. The relative degrees of anisotropy at maximum extension are given in Table 5 for groups A and B. The statistical significance of the anisotropic deformation observed is given in Tables 6 and 7 for the same two groups. From these tables it is obvious that parenchyma tissue shows more anisotropic deformation in air than in saline and more for group A (younger dogs) than for group B (aging dogs). In fact, the only statistically significant anisotropy at maximum extension is presented in group A for tests in air. Therefore, anisotropic deformation seems to exist. However, for the practical purpose of gross lung deformation analysis, the anisotropy found in this study may not be significant enough to justify the added complications of an anisotropic analysis.
Fig. 4. Line patterns of cube mean maximum and minimum extension ratios between upper and lower lobes for group A and group B specimens. Symbols represent mean values and vertical bars denote SE. For group A upper lobes n = 6; lower lobes n = 7. For group B upper lobes n = 5; lower lobes n = 6. statistical significance of the homogeneity implied are shown in detail in Tables 3 and 4. These are relatively insignificant differences in extension behavior for the upper and lower lobe tissue and thus a11 mean results seen in the following sections include both upper and lower lobe specimens. Among the published reports, ditTerence in pressure-volume relationships (Frank, 1963 ; Pare et al., 1978) and ventilation behavior (Faridy et al.. 1967; Glaister et al.. 1973) between the upper and lower lobes of animal lungs has been observed. These results suggested the possibility that elasticity of lung tissue is not uniform throughout the whole lung, although the preferentially pooling of blood or edema in the lower lobes during the preparation of the lungs
3OyA
rc
0
@J f”T
fPP f lo---
i XYIXYZ
XYZXYZ
ryzxyr
xyzxyr
1
Cube Axis Fig. 5. Line patterns
of cube mean maximum and minimum extension ratios. (a) group group C. (d) group D. Symbols are the same as in Fig. 6.
A. lb) group
B ICI
RONALD C. TAI and GEORGEC. LEE
248 Table 3. Comparison
(paired
t-test) of mean i.,,,
and &,
between
6 upper and 7 lower lobe specimens
in group
A
Cube Axis
Extension
X
Ratio
Y
z
.
In air
P>O.40 P>O.40
P>O.40 pro.40
P > 0.80 P > 0.80
In saline
PzO.80 PzO.80
P>O.20 PIO.20
P>O.O5 P>O.40
Table 4. Comparison
(paired
r-test) of mean I.,,,,, and R,,, between
5 upper
and 6 lower lobe specimens
in group
Cube Axis Extension
X
Ratio
z
Y
In air
i *inax * mi”
P>O.20 P>O.40
P > 0.20 P>O.80
P>O.40 P>O.80
In saline
i ‘rn.X Alli”
P>O.lO P>O.40
P>O.80 P>O.80
P>O.40 P>O.lO
Table 5. Relative
degree of anisotropy
at maximum
extension (&n,X), - (~.ln,X)Z
(&n,X), - (L3, (L)*y.
(Lx)lyr
(%)
(%)
Group A 8.81 5.42
In air In saline
Group A 6.82 2.53
Group B 2.71 1.86
Group B 3.10 0.74
-Note:
1 (&,,),
2. (L)xyl
(&,&,
= *c(L),
and (%,,,), are the mean of A,,,,, in x. y, and z direction, + (L)y
Table 6. Comparison
+
respectively,
for all cubes in a group.
v.mA1.
and Lmin of 13 specimens
(paired r-test) of mean i.,,,
between
axes for group
A
Axis Pair Extension
Ratio
i ‘IllaX i.d”
In air
In saline
Table 7. Comparison
(paired
X-Y
Y-2
Z-X
P
P
P>O.20 P
P>O.l P > 0.05
P > 0.20 P>O.80
P>O.l P <0.05
r-test) of mean I.,,,
and &,
of 11 specimens
between
axes for group
B
Axis Pair Extension
Ratio
X-Y
Y-2
z-.x
In air
I*rnali L”
P10.05 P < 0.02
P>O.lO P>O.O5
P > 0.80 P
In saline
i‘iVIa% Li”
P>O.20 P > 0.20
P>O.40 pro.40
P > 0.40 P>O.lO
B
249
Lung tissue deformation Lung tissue isotropy is generally investigated through two approaches : microscopic and macroscop ic. At the microscopic level, previous investigations reported either isotropic (D’Angelo, 1972; Forrest 1970; Glazier et al.. 1967) or anisotropic (Forrest, 1976 ; Klingele and Staub, 1972 ; Tsunoda et al., 1974) deformations. At the macroscopic level, except for the report of Chevalier et al. (1976) where anisotropic expansion within intact lungs has been observed using implanted markers, most in vitro studies seem to agree on isotropic behavior (Ardila et al., 1974; Fukaya et al., 1972; Hills, 1971; Redford, 1957). Any observed in uiuo anisotropic deformations may be caused by either the material property or the constraining effect of the chestwall. The in uiuo approach thus may reveal more parenchymal tissue property without the influence of the chestwall. Aging eflect Some major findings in the present study concerning the aging tissue compared to the relatively young groups are : higher saline equilibrium volumes, higher overall extension ratios (paired t-test, all P < 0.001) for similar extension ranges, and less apparent anisotropic deformation. Considering the possible visceral pleural limiting effect and the higher resting volume in saline for group B, the pleural membrane contribution to lung recoil in older lungs seem to be greater than in younger lungs. This may imply that at a comparable deformed volume, aging tissue would be more compliant than young tissue. The smaller difference in i.,,, between the saline and air cases for aging tissue also could mean a less effective alveolar surface force system in the aging tissue than in the younger tissue. A number of studies on the aging lung may be found in the literature, mostly for intact human lungs. It is generally recognized that in aging humans the reduced elasticity of lung pressure-volume (curve shifting to the left) and the increased resting volume of the rib cage results in an increase of functional residual capacity and residual volume while there is no significant change in total lung capacity. Sugihara et al. (1971) have studied human lung tissue strips and have attributed the smaller maximum extension ratio for aging lungs to the increased resting length. Hieronymi (1961) reported that dry lung weight remains equal or decreases slightly with age while the gross dimensions and the size of alveoli decreases. The results from the present study in dogs tend to support these findings. Very limited information is available for the mechanical properties of aging dog lungs. To the authors’ knowledge, the only study by Robinson and Gillespie (1973) shows similar characteristic aging effects in dogs and humans. The pressure-volume curves of the excised aging dog lungs in the present study compare well with the in uivo measurements (Fig. 6). However, the increase in maximum specific volume which was observed has not been reported for in uivo cases. Again, the in uivo approach suffers some
0
40 Transpulmanary
Fig. 6. Static
30
20
Pressure
(cmH20)
pressure-volume deflation curves lungs for group B dogs.
of excised
drawbacks. First, the monitored pleural pressure (or esophageal pressures) are subject to measurement errors, especially at low lung volumes. Secondly, the definition of lung volumes such as TLC which is usually used as a universal base for the detection of lung volume change, especially when cross-species differences are concerned, does not have a common basis for comparison. Third, the aging effect of the rib cage is always present simultaneously and cannot be isolated. The in vitro experiment is therefore a better approach for seeking fundamental understanding and quantification of aging effects on lung tissue per se since the predominant boundary conditions around the lungs are not present. EJects of pleura and large airways on parenchymai deformation Tissue cubes with pleura seem to deform at a higher extension level with about the same extension range as homogeneous cubes but the standard errors are slightly higher (Fig. 5). Tissue cubes with airways carry fairly large standard errors (Fig. 5). However, the mean extension ranges are about the same as for homogeneous cubes. The absolute extension ratio values are lower. The obvious line pattern differences between groups A and C are only in the y-axis where the extension values in group C are higher. Because of the larger spread in the data for group D. the line patterns observed should not be emphasized at the present time although they carry characteristics similar to the other groups. The results of cube physical measurements seem to support a previous finding that the visceral membrane may play an important role in determining the recoil pressure of lung lobes at low lung volumes (Nagao, 1973). If this is the case, one would expect a slightly smaller resting volume for a cube in group C than for a
250
RONALD
C.
TAI
comparable cube in group A. The consequence is thus a possible higher overall extension for group C than for group A cubes which is the case as is shown in Figs. 7(a) and (c). On the other hand, because of its unique location it is also possible that the tissue taken from the apex of the lung (where group C specimens were taken) may behave slightly differently from tissue taken from other parts of the lungs. The synchronization of the deformational characteristics of the whole lung including the airways is one of the main concerns in airway mechanical properties. Several studies have addressed this issue but conclusions differ (Hahn, 1976; Hughes et al., 1972; Prakash and Hyatt, 1978; Sittipong and Hyatt, 1974; Wilson et al., 1974). The original thought in this part of the study was to assess this issue using the results from group D. The results show smaller mean extensions for the group D cubes (Figs. 7a and 7d). However, the scatter in the data is considerable. Since the size of the airway cannot be precisely controlled, it is believed that the airway size variation contributes to the relatively poor results for group D. A contributing factor may be that the reference dimensions seem to be much less defined because of the existence of airways in place of tissue. However, the group D data are the first of this kind to be reported. Experimental effects Since the present experimental investigation involves the processes of preparing cubical specimens from excised lungs and setting them up for mechanical deformation testing, the introduction of artifacts is inevitable. Several important factors relating to these problems will be discussed briefly in this section. The introduction of saline into alveolar regions during specimen preparation ieads to partial loss of alveolar surface active material. Several studies on air pressure-volume characteristics specifically addressed this effect. Findings include a reduction in maximum lung volume and overall compliance for excised dog lungs (Johnson et al.. 1964) and a shift to the right for the pressure-volume curve for excised cat lungs (Bachofen et al.. 1970) and intact dog lungs (Huber et al., 1971). The typical air pressure-volume deflation curves in Fig. 7 for lungs (before saline introduction) and cubes (after saline introduction) confirm the earlier findings. Creep occurred (for a few seconds) after each load increment. Pressure-volume hysteresis was observed for all specimens during the air-filling cycles but was much milder during the saline-filling cycles. An interesting finding was that tissue cubes consistently reached higher maximum extension ratios in saline than in air; this is indicated in Fig. 5. Possible reasons are the loss of alveolar surface material during saline washing and changes in the tissue elasticity due to freezing. It has been observed that the freezing process reduces the extensional capacity of aortic and mitral valve leaflets when compared with fresh specimens (Clark, 1973). The observed changes in the
and
GEORGE
C. LET
I IO Pressure
Dog No I 20
4 I 30
IcmH20)
Fig. 7. Comparison of pressure volume deflation curves of lungs and cubes. Solid lines for in-air and solid line with circles for in-saline. Cross-hatched areas show ranges of spread of curves for cubes from the same dog. stress-strain relationship, however, seem to depend on the orientation of the force-bearing components and the collagen and elastin fibers in the specimens. Since the overall arrangements of collagen and elastin fibers in alveolar walls are random, freezing effects should not significantly bias the results for the detection of isotropy and homogeneity of lung deformation. The previous report by Hoppin et al. (1975) on triaxial cube tests using a similar approach also indicated no observable change in tissue elasticity. Freeze-drying of the cube surface is an essential step in the preparation of specimens for the attachment of the force-applying device. The dehydration of tissue involved only the most outer layer of the cubical specimens. There was no difficulty in hydrating the surface part during the thawing of the cube. Faridy (1973) reported minimal changes in the lobar pressure-volume relationship but some enlargement of the alveolar space after a thorough dehydration-hydration process. Any effect of freezedrying in the present study is believed to have been insignificant. The mechanical attachments for the application of force on the cube surfaces is essential to the present study. The effects of employing these discrete attachments on cube deformation has been assessed using one homogeneous cube. After fully stretching at maximum loading in air, the cube was quick-frozen with liquid nitrogen, freeze-dried and fixed in formalin. Observations on the sectional internal surface revealed a very uniform overall expansion of the alveoli except near the immediate regions of the attachments offorce application where a thin layer of flattened alveoli was identified. But this layer amounted to a very small portion of the total tissue volume and is expected to have had little effect on tissue recoil. There was even less effect for the stretching in saline. This boundary effect is expected to have contributed to the dilference in the P-V curves between the lung and the cubes as well as to the difference in the maximum volume between the air and saline curves of the same cube. In testing a highly compliant lung tissue, a gravitational distortion effect almost always is present.
251
Lung tissue deformation
especially at low extension levels. Since gravitational effects are due to the mounting of the cube on the apparatus as well as to the dead load imposed by the set-up, the total effect is considered an apparatus effect. A special sequence of tests which involved the repeated testing of the same specimen mounted in different orientations with respect to the apparatus were performed. Results showed that the directional characteristics such as the line patterns of I.,,, in Fig. 5 were not affected
by the mounting
SUMMARY
orientation
of the specimen.
AND CONSLUSIONS
Triaxial stretching tests using specially prepared dog lung tissue cubes from different locations in left lungs were performed to detect any possible directionalor locational-dependent deformation behavior for relatively young dogs and aging dogs, as well as to detect the effects of pleural membrane and airway on cube deformation. No obvious locationaldependent deformation behavior was observed, indicating a uniformity of dog lung parenchyma over the lungs. Patterns of directional-dependent deformation were noticed indicating mild anisotropic behavior in general, especially for younger dogs. Aging tissue showed fewer anisotropic patterns. The existence of either a pleural membrane or a single airway in the specimens affected the deformation pattern to different degrees and caused large scatter in the results which do not permit more quantitative conclusions. Considering the results of the present study, the assumption of a homogeneous, isotropic parenchymal tissue seems to be practical for the purpose of lung regional volume analysis using elastic deformation theories.
elastic behavior
of excised dogs’ lungs, J. appl. Pb.ysiol. 34,
597-605. Faridy, E. E., Kidd, R. and Milic-Emili, J. (1967)Topographical distribution of inspired gas in excised lobes of dogs. J. appl. Physiol. 22, 760-766.
Forrest, J. B. (1970) The effect of changes in lung volume on the size and shape of alveoli. J. Physiol. 210, 533-547.
Forrest, J. B. (1976) Lung tissue plasticity: morphometric analysis of anisotropic strain in liquid filled lungs. Respir. Physiol. 27, 223-239. Frank, N. R. (1963) A comparison of static volume-pressure relations of excised pulmonary lobes of dogs. J. appl. Physiol. 18, 274-278. Fukaya, H., Martin, C. J., Young, A. C. and Katsura, S. (1972) Mechanical properties of alveolar walls. J. appl. Phpsiol. 15, 190-213. Fung, Y. C. (1974) A theory of elasticity of the lung. J. appl. Mech. 41, S-14. Fung, Y. C. (1975) Stress, deformation and atlectasis of the lung. Circ. Res. 37, 481-496. Fung, Y. C.,Tong, P. and Patitucci, P. (1978) Stress and strain in the lung, AXE J. Engng Mech. Dia. 104, 201-223. Glaister, D. H., Schroter. R. C., Sudlow. M. F. and MihcEmili, J. (1973) Transpulmonary pressure gradient and ventilation distribution in excised lungs. Respu. Physiol. 17, 365-385. Glazier, J. B., Hughes, J. M. B., Maloney, J. E. and West, J. B. (1967) Vertical gradient of alveolar size in lungs of dogs frozen intact. J. appl. Physiol. 23, 694-705. Hahn, H. L., Graf, P. D. and Nadel, J. A. (1976) Effect of vagal tone on airway diameter and on lung volume in anesthetized dogs. J. appl. Physiol. 41, 58 I --589. Hieronymi, G. (1961) On the change in the morphology of the human lung due to aging. Erg&. Path. Anar. 41, l-62. Hills, B. A. (1971) Geometric irreversibility and compliance hysteresis in the lung. Respir. Physiol. 13, 50 -61. Hoppin, F. G. Jr., Lee, G. C. and Dawson, S. V. (1975) Properties of lung parenchyma in distortion J appl. Physiol. 39, 742-75 1. Huber, G. L., Edmunds, L. H. Jr. and Fmley. T. 1\1. (1971) ENect of experimental saline lavage on pulmonary mechanics and morphology. Anr. Rev. Re~pir. Di\ 104, 337-347.
Hughes, J. M. B., Hoppin, F. C. Jr. and Mead, J. (1972) Effect of lung inflatil on on bronchial length and diameter in
Acknowledgemetlrs~The authors wish to express +I.-:LLlCll----a a&J&Xc;excised lungs. J. appl..Physiol. 32, 25.-35. ciation to Drs. Joseph and Thomas Gregor y for their Johnson, J. W. C., Permutt, S., Sipple, J. H. and Salem, E. S. assistance in this study by providing laboratory space in the (1964) Effect of intra-alveolar fluid on pulmonary surface Department of Anatomical Sciences. They also a cknowledge tension properties. J. appl. Physiol 19, 769 777 the Department of Oral Pathology for providing the use ofss Klingele, T. G. and Staub, N. C. (1970) Alveolar shape freeze-drying equipment. This study was supported by Grant changes with volume in isolated air-filled lobes of cat lung. HL-14495 from the National Heart, Lung, and Blood .I.‘,,.. 1.1 J.. appr.In,mysrok ~8, ‘II l-414. Institute. Lee. G. C. and Frankus. A. (1975a) Aonlicatlon of slnrle . alveolus model to Lung elasticity problem. ASCE National Structural Engineering Convention. New Orleans. Lee, G. C. and Frankus. A. (1975b) Elasticity properties of REFERENCES lung parenchyma derived from experimental distortion data. Biophys: J. 15, 481-493. Ardila, R., Horie, T. and Hilderbrandt, J. (1974) Macroscopic isotropy of lung expansion. Respir. Physiol. 20, 105-115. Lee, G. C., Frankus. A. and Chen. P D (1976) Small Bachofen, H., Hildebrandt, J. and Bachofen, M. (1970) distortion properties of lung parenchyma as a compressible Pressure-volume curves of air- and saline-filled excised continuum. J. Biomech. 9, 641.-648. lungs surface tension in situ. J. apul. Phrsiol. 29.422-431. Liu, J. T. and Lee, G. C. (1978) Static limte deformation Chevalier, P. A., Greenleaf, J. F.. Rot%, R. A. and Wood, E. H. analysis of the lung. ASCE J. E~J~J Mech 0~. 104, 225-238. (1976) Biplane videoroentgenographic analysis of dynamic Mead, J., Takashima, T. and Lelth. D. (1970) Stress disrrlregional lung strains in dogs. J. app/. Physiol. 40, 118-122. bution in lungs: a model of pulmonary elasticity J. uppl Clark, R. E. (1973) Stress-strain characteristics of fresh and Ph!,siol. 28, 596-608. frozen human aortic and mitral leaflets and chordae tenineae. Implications for clinical use. J. Thoroc. CarNagao. K. (1973) Experimental studies on mechanical prodiouasc. Surg. 66, 202-208. perties of the visceral pleura. Nihon C’,lir .1. .Med 15, D-Angelo, E. (1972) Local alveolar size and transpulmonary 307- 327. pressure in siru and in isolated lungs. Respir. Physiol. 14, Pare, P. D., Boncher, R., Mlchoud. M. C’ and Hogg. J. C‘ 251-266. (1978) Static lung mechanics of intact and excised rhesus Faridy. E. E. (1973) Effect of hydration and dehydration on monkey lungs and lobes .I. uppl PII\ W/ RL,.$I)II. E~III, 1
252 Exercise
RONALDC. TAI and Physiol. 44, 547-552.
Prakash, U. B. and Hyatt, R. E. (1978) Static mechanical properties of bronchi in normal excised human lungs. J. appl. Physiol. Respir. Enuir. Exercise Physiol. 45, 45-50. Redford, E. P. (1957) Recent studies of mechanical properties of mammalian lungs. In : Tissue Elasticity, pp.- 177-190. American Physiology Society, Washington. Robinson, N. E. and Gillspie, J. R. (1973) Lung volumes in aging beagle dogs. .J. appl. Physiol. 35, 317-321. Sittinona. R. and Hvatt. R. E. (1974) Static mechanical behav& of bronchj in excised dog lungs. J. appl. Physiol. 37, 201-206.
Sugihara, T., Martin, C. J. and Hilderbrandt, J. (1971) Length-tension properties of alveolar wall in man. J. appl. Physiol. 30, 874-878.
GOERGE
C. LEE
Tsunoda, S., Fukaya, H., Sugihara, T., Martin, C. J. and Hilderbrandt, J. (1974) Lung volume, thickness of aiveolar wall and microscopic anisotropy of expansion. Respir. Physiol. 22, 285-296.
Vawter, D. L. (1977) Stress-free equilibrium volume of the lung. Physiol. Respir. Envir. Exercise Physiol. 43, 3-7. Vawter, D. L., Matthews, F. L. and West, J. B. (1975) Effect of shape and size of lung and chestwall on stresses in the lung. J. appl. Physiol. 39, 9-17. West. J. B. and Matthews, F. M. (1972) Stresses. strains and surface pressures in the.lung caused by its weight. J. appl. Physioi. 32, 332-345.
Wilson, A. G., Massarella, G. R. and Pride, N. B. (1974) Elastic properties of airways in human lungs post morten. Am. Rev. Respir. Dis. 110, 716-729.
AND HOMOGENEITY OF LUNG TISSUE DEFORMATION* RONALD C. TAI and GEORGE C. LEE
Faculty
of Engineering
and Applied Sciences, State Umverslty Amherst, NY 14260, U.S A
of New York at Buffalo,
force-extension tests on lung tissue cubes taken from excised dog lungs were performed to examine relative directional-dependent deformation behavior (isotropy) and locational-dependent deformation behavior (homogeneity). Four types of specimens were used: parenchyma tissue cubes from relatively young dogs (group A), parenchyma cubes from older aging dogs (group B), tissue cubes with intact pleural membranes on the cube surfaces (group C), and tissue cubes with one relatively large airway oriented along one of the principal axes (group D). The effects ofaging and the presence of a pleural membrane and an airway on the deformation of lung tissue were also examined. Results indicate that mild anisotropic parenchymal deformation (less than 10% of the mean deformation) exists in relatively young lungs and to a lesser degree in older dogs. No significant locational dependence of deformation was found between upper and lower lobes. The pleural membrane slightly affected the directional deformation behavior pattern of the parenchyma tissue. The presence of an airway caused considerable data scatter with possible deformation characteristic change. It is concluded that the assumption of an intially isotropic and homogeneous parenchyma in gross modeling of lung deformation is reasonable. Abstract-Triaxial
mation lead to conclusions of either isotropic (Ardila et al.. 1974) or anisotropic (Hill, 1971) lung expansion. Anisbtropic strains have also been found in intact dog lungs using biplane videoroentgenographic analysis (Chevalier ef al., 1976). Hoppin ef al. (1975) performed triaxial tests on cubical lung tissue specimens and observed some irregular directional extension behavior, but the focus of attention was not on material isotropy. There seem to be few reported studies concerning the homogeneity of the lung tissue properties. For dogs (Frank, 1963) and for monkeys (Pare et al.. 1978) it has been shown that the upper lobe contains more volume per unit weight of tissue (specific volume) than the lower lobe at the same transpulmonary pressure. Interlobar and intralobar nonuniform deformation based on uneven distribution of bolus gas was also observed in isolated lungs of dogs and monkeys (Glaister rr al., 1973). The present investigation is intended to examine possible anisotropic or non-uniform properties of dog lung tissues using the technique of Hoppin et al. ( 1975). No attempt is made to obtain the stress-strain (or force-deformation) properties of the parenchyma.
INTRODUCTION of the interdependence concept of lung tissue by Mead et al. (1970), there have been a number of studies concerned with the application of elasticity theory to the analysis of lung tissue deformation (Fung, 1974,1975 ; Lee and Frankus, 1975a, b ; Lee et al., 1976). More recently, numerical models have been developed to predict the gross lung deformation behavior (Fung et al.. 1978 ; Liu and Lee, 1978 ; Vawter el al.. 1975; West and Matthews, 1972). In all the analytical efforts, an isotropic, homogeneous parenchyma has been assumed. In order to refine the analytical approaches, it is desirable that the assumption of material isotropy and homogeneity be substantiated. Major analytical efforts will be required if the lung parenchyma behaves as an anisotropic inhomogeneous continuum. Morphometrical observations at the alveolar level on lung parenchyma of various animals have led some authors to conclude that parenchyma deforms isotropically (D’Angelo, 1972; Forrest, 1970; Glazier et al., 1967) while others conclude differently (Forrest, 1976; Klingele and Staub, 1970;Tsunoda et al.. 1974). In most studies, the criterion for determining isotropy is whether the parenchyma deformation actually observed can be described by the length-volume or area-volume relationship of an ideal isotropic material. Macroscopically, lung tissue strips taken in different orientations behave similarly and fail to show systematic variations in properties (Fukaya et al.. 1972; Redford, 1957). Observations on pleural surface deforSince the introduction
SPECIMENS
Prepararions Healthy mongrel dogs (17-30 kg body weight) were anesthetized and sacrificed by exsanguination. The lungs were excised and a tracheal cannula was installed. After leak tests with air inflation to 30 mm H,O, each left lung was degassed in a vacuum chamber and readied for pressure-volume measurements. Two air ventilated inflationAeflation cycles between 0 and 30 cm H,O were carried out. This was followed by one
* Receit:ed 22 July 19X0. c United
AND METHODS
States Government 243
244
RONALDC. TATand GEORGEC. LEE
I
+
Croniocoudol direction
Fig. 1. Definition sketch of coordinate system and orientation for homogeneous cubes. saline ventilated cycle. The absolute volume of the lungs was measured between cycles by water displacement. The deflation limb of the second cycle in air and the first cycle in saline were used for comparison with the measurements on tissue cubes. All measurements were done at room temperature. After the saline pressure-volume measurements, the lungs were separated into lobes, suspended in saline, and kept deep frozen at - 20°C for 24 hr. Using a band saw each lobe was cut into thick slices with sections lying perpendicular to the body craniocaudal direction. Two types of tissue cubes were cut from these slices. The first type was intended to be homogeneous and free of major airways and was taken from immediate subpleural areas near the middle portion of the upper and lower lobes. The second type of specimen was intended to provide inhomogeneous cubes. They contained either the visceral pleural membrane or a straight airway in one of the three principal directions of the cubes. The intact orientation of homogeneous specimens were carefully followed and recorded, using a universal coordinate system consisting of x-, y- and z-axes. These cubes were taken in a way such that the x-axis was perpendicular to the pleural surface, the z-axis along the body craniocaudal direction, and the y-axis in the third direction as shown in Fig. 1. Two groups of dogs (thus specimens) were used for homogeneous cubes : young dogs (group A, nos. 1, 2, 3) and older dogs (group B, nos. 4, 5) both free of respiratory disease symptoms. Comparable numbers of specimens were taken from the upper and lower lobes for each group. For inhomogeneous cubes two groups of specimens were studied. In Group C the cubes contain an intact visceral pleural membrane on each of the two approximately parallel opposite surfaces along the x-axis. The only location suitable for obtaining this type of specimen is the apex of the upper lobe. The other group (group D) consisted of cubes having a straight airway with a size ranging from 1.8-4.0 mm i-d. and lying along one of the axes. The exact intact orientations of the tissue cubes of group D were not traced but their locations were noted.
The volumes of the cubical specimens of groups A and B were approx. (1.3 cm)‘. The size of the specimens in groups C and D may have deviated from (1.3 cm)3 in order to include pleural surfaces or airways, The number of tissue specimens tested are summarized in Table 1. The cubical tissue specimens were deformed by applying forces to each surface through four string-plate units, each consisting of a thin circular plastic plate of approx. 3 mm attached to the end of a 20cm-long silk thread. The plastic plates were attached to the cube surface by Eastman 910 adhesive. The four plates were placed symmetrically near the corners on each surface of the cube. Stretching
apparatus
The tissue cubes were tested on a stretching apparatus shown schematically in Fig. 2. One equalizing unit was used for the four strings from the same cube surface to minimize unequal deformations of the surface. Each unit consisted of three thin flat aluminium bars with strings attached through the equally spaced holes shown in Fig. 2. The force was applied by adding calibrated weights onto the strings in each direction. The force-transmitting strings were aligned in such a way that the suspended tissue cube could be submerged in saline solution in a square lucite tank. By
Table 1. Number of cubes tested by categories Category
Number of Cubes
Group A : Dog No. 1 Dog No. 2 Dog No. 3
5 (upper lobe 2; lower lobe 3) 4 (upper lobe 2; lower lobe 2) 4 (upper lobe 2; lower lobe 2)
B: No. 4 No. 5 C:
7 (upper lobe 3; lower lobe 4) 4 (upper lobe 2; lower lobe 2) 4
Group Dog Dog Group
Group D:
9
Displacement marker and scale
Fig. 2. Schematic drawing of the triaxial test apparatus.
Lung tissue deformation lowering or raising the liquid level in the tank, tissues could be tested in air or in saline solution. The weight hook at the free end, which also served as a counterweight, exerted a dead load of 1.7 g along each axis at all times. The linear deformation of the cube in each direction was indicated by the position of a marker (on the string) on a fixed scale. Deformation
measurements
A correlation between the absolute deformation and the scale reading was established through a calibration cycle of an inflation-deflation maneuver where at every loading level the actual linear dimensions of the specimen were measured with a vernier caliber (0.05 mm accuracy) and recorded along with the corresponding scale reading. Obviously the way the loadings were applied to the specimens surfaces caused uneven deformation on the surface with peaks and troughs. The peak-to-peak and trough-to-trough distance measured between two opposite surfaces along each axis were plotted against the scale readings (Fig. 3). A linear correlation for each axis in air or in saline solution were drawn for the specimen and each was used to determine the average dimensions for a specific scale reading. Reference
dimensions
The reference state used in the investigation incorporated two quantities : (1) the net tissue volume of the cubical specimen and (2) the resting cube configuration in saline (saline equilibrium state). Specifically, the reference state of a lung tissue cube is defined as one which has the same volume as the collapsed lung tissue but the same configuration as in the saline equilibrium state. Reference dimensions are thus the
Specimen
03 sab5
x- axIs
01 0
1
/
I 1
1
I
2
245
dimensions of this fictitious reference state. All cube deformations were expressed as extension ratios based on the reference dimensions. By including the net tissue volume of the cube in reference dimensions, the absolute deformation of each specific cube may be normalized with its own size. This facilitates comparisons among cubes of different sizes. Furthermore, by using the net tissue volume rather than the saline equilibrium volume, the inter-specimen differences in saline equilibrium volume can be avoided. Specific volume (volume per unit wet tissue weight) was used as a compatible “lung volume” for direct comparisons between cubes and lobes. The average linear dimensions of the cubes and the surface loadings are the basis for calculating the deformed cube volumes and the apparent stresses. The average stress for the three directions was obtained and was used for the pressure-volume relationships. In order to establish reference dimensions as well as forcedeformation behavior, several physical quantities of the cubical specimens had to be obtained. Saline equilibrium dimensions were measured twice, using a vernier caliber, once before and once after stretching in saline, with no applied forces on the cube. Only the latter measurement was used to calculate reference dimensions. The volume and weight of each specimen were measured after the completion of an entire cube test with the force applying attachments removed. Tissue volume was measured by the water displacement method in a small buret and the wet and dry tissue weight were measured with a balance (0.005 g accuracy). Test procedure
For triaxial measurements the loading ranges were 0-70g (air) and O-30 g (saline). These correspond approximately to, from less than 1 cm H,O to 30cm H,O in air and to 1Ocm H,O in saline. Three types of loading cycles were used. For equal triaxial loading all three directions were stretched simultaneously by the same amount of force during the inflationdeflation maneuver. For uniaxial loading, the loading ranges for the main loading axis were lo-70 g in air and 5-30 g in saline while the loadings along the other two (lateral) axes were held constant at 40g in air and 20g in saline. The third type of measurement was the calibration cycle ofequal triaxial loading. The entire experiment for each specimen consists of two equal triaxial loading cycles, followed by three uniaxial loading cycles, one along each axis, and one calibration cycle at the end.
I
3 RESULTS AND DISCUSSIONS
Measured Length km) Fig. 3. Calibration of displacement reading against actually measured cube dimension. Open symbols for loading and solid symbols for unloading. Each point pair having the same
reading value gives the peak-to-peak and trough-to-trough measurements, respectively.
Reference
dimensions and saline equilibrium
dimensions
In deformation analysis a reliable reference state is essential for establishing consistent and meaningful evaluations. For the study ofintact lungs the total lung
RONALD C. TAI and GEORGE C. LEE
246
capacity (TLC) is usually chosen as the reference state and lung volumes are expressed in terms of the percentage of parenchymal tissue as an elastic material. The commonly used reference state for elastic deformation is the undeformed state of the material. Since the resting volume of an air-filled lung is dictated by the amount of trapped air, it is extremely difficult, if not impossible, to recognize and measure its undeformed volume. For this reason, in the present study the reference dimensions (at a fictitious reference state) were chosen as the combination of cube saline equilibrium configurations and wet tissue volume. The confidence in using these two physical quantities is gained from the previous study by Vawter (1977) and the consistent measurements obtained in the present study. The ratios established from the measured wet tissue volume, net tissue weight, and saline equilibrium volume of the cubes and the lungs used in groups A and B are summarized in Table 2. The three ratios shown are saline equilibrium to tissue volume ratio (V&V,), saline equilibrium volume to wet tissue weight ratio (VJW,), and wet density (WJV,). There is no statistically significant difference in the mean ratios of the tissue specimens between the upper and lower lobes. This implies homogeneity of the lung parenchyma. The values in Table 2 also show that the ratios ofgroup B are greater than those of group A. These differences suggest a significantly larger Vs, for group B than for group A. Comparisons of the actual measurements between the two groups A and B show a higher mean value of Vs,/V, and V,JW, and lower values of density for group B. There is no statistically significant difference in V&V, between the two groups. Another observation can be made from Table 2. A consistently higher ratio was obtained for cubes than for the whole left lung. This may imply a restraining effect of the pleural membrane on the resting volume of parenchyma tissue. For all tissue specimens, including those not used for tests, the mean wet-to-dry tissue weight Table 2. Ratios
of specimen
ratio is 6.43 f 0.75 (mean &S.E.). The mean saline equilibrium volumes for group A (V&J, = 5.22 + 0.70 for cubes and 3.53 f 0.34 for left lungs) are comparable to the results obtained by Vawter (1977) for dog lobes (V,,/V, = 2.74 f 0.20) where 1.0 has been added to the originally reported value. Two factors may contribute to these differences. The first is a possible freezing effect which may alter the tissue structure, thus the resting volume. Secondly, there is the increasing contribution of recoil pressure from the pleural membrane as the lung volume decreases observed by Nagao (1973). The visceral pleural membrane thus may limit the resting volume ofthe parenchyma in the absence of surface forces. Consequently, the lobe will exhibit a smaller saline equilibrium volume than thedissected parenchyma. More experimental data are necessary to further assess the saline equilibrium state. Since the reference dimensions defined in the present study involve a saline equilibrium configuration (the ratios of the dimensions) rather than the absolute saline equilibrium volume, the resulting extension ratios are suitable for comparison among individual tissue specimens. Homogeneity
General tissue deformation behavior is determined in the present study by observing the characteristics of the ).-a, relationships; the maximum .(at highest loading) and minimum (at 1.7-g loading) extension ratio (i,,,, and &,,in)were averaged for individual axes and are compared among different axes, between upper and lower lobes, and among different categories of cubes. The statistical means and the standard errors of &ll,Xand &, for the three axes for all groups and categories are shown in Figs. 4 and 5. Differences in extensions for the three axes generally exist. In groups A and B, nearly identical anisotropic patterns are found for the upper and lower lobes (Fig. 4). The physical
measurements
V SE
VSE
V,
W,
W, V,
W/g)
(g/cc)
n
CUBES Group A: Upper Lobes Lower Lobes All (upper & lower)
546~0.81 5.04+0.59 5.22 f 0.70
6.26+0.70 5.63 kO.56 5.90 + 0.68
0.87f0.05 0.89 f 0.04 0.84 + 0.04
6 8 14
Group B : Upper Lobes Lower Lobes All (upper & lower)
8.25 kO.45 7.7OkO.80 7.95 f 0.70
8.53 + 0.73 8.65 +0.56 8.59 f 0.61
0.97 io.10 0.89 f 0.06 0.93 * 0.09
5 6 11
3.53 +0.35 4.19kO.59
4.56kO.17 6.18kO.87
0.77 * 0.05 0.68 +0.001
3 2
LEFT LUNG Group A Group B Note:
For definitions
of ratios
see text; all ratios
in mean
+ SE. n = number
of specimens.
Lung
Symbols
Cube Am, 1.
Y
*
a
0
0
I” s(1111e A
.
.
In
Ol,
may contribute to these findings (Pare et al., 1978). The difference in functional demand of the upper and lower regions of the lung may also require the direct examination of the existence of the regional differences in tissue property. In the present study the only upper-lower regional difference that was found was the slightly higher scatter in the data for the lower lobes in group A shown in Fig. 4. All differences in the mean extension between cubes from the upper and lower lobes are statistically insignificant (Tables 3 and 4). The extrapolation of dog lung tissue data to human may be at least partially justified by the fact that the upper-to-lower lobe difference tends to be greater in dog lungs because of the predominant diaphragmatic breathing. Therefore, we may conclude that it is proper to consider lung parenchymal tissue as a homogeneous material in gross lung elastic deformation studies. In other words, the tissue elasticity property per se is not a contributing factor leading to lung regional inhomogeneous behavior.
-bar --Am,”
Group A 3o
Lower Lobe
Upper Lobe
247
tissue deformation
25
‘-t--r
Group B
Isotropy
Isotropy of the lung tissue deformation behavior was determined by examining the line patterns formed by the mean maximum extension points as shown in Fig. 5. For an isotropic material all the line patterns should be straight horizontal lines. Since mean maximum extension points as observed do not form horizontal lines and the scattering of individual data varies, the differences in maximum extensions between the axes have to be quantified further. The relative degrees of anisotropy at maximum extension are given in Table 5 for groups A and B. The statistical significance of the anisotropic deformation observed is given in Tables 6 and 7 for the same two groups. From these tables it is obvious that parenchyma tissue shows more anisotropic deformation in air than in saline and more for group A (younger dogs) than for group B (aging dogs). In fact, the only statistically significant anisotropy at maximum extension is presented in group A for tests in air. Therefore, anisotropic deformation seems to exist. However, for the practical purpose of gross lung deformation analysis, the anisotropy found in this study may not be significant enough to justify the added complications of an anisotropic analysis.
Fig. 4. Line patterns of cube mean maximum and minimum extension ratios between upper and lower lobes for group A and group B specimens. Symbols represent mean values and vertical bars denote SE. For group A upper lobes n = 6; lower lobes n = 7. For group B upper lobes n = 5; lower lobes n = 6. statistical significance of the homogeneity implied are shown in detail in Tables 3 and 4. These are relatively insignificant differences in extension behavior for the upper and lower lobe tissue and thus a11 mean results seen in the following sections include both upper and lower lobe specimens. Among the published reports, ditTerence in pressure-volume relationships (Frank, 1963 ; Pare et al., 1978) and ventilation behavior (Faridy et al.. 1967; Glaister et al.. 1973) between the upper and lower lobes of animal lungs has been observed. These results suggested the possibility that elasticity of lung tissue is not uniform throughout the whole lung, although the preferentially pooling of blood or edema in the lower lobes during the preparation of the lungs
3OyA
rc
0
@J f”T
fPP f lo---
i XYIXYZ
XYZXYZ
ryzxyr
xyzxyr
1
Cube Axis Fig. 5. Line patterns
of cube mean maximum and minimum extension ratios. (a) group group C. (d) group D. Symbols are the same as in Fig. 6.
A. lb) group
B ICI
RONALD C. TAI and GEORGEC. LEE
248 Table 3. Comparison
(paired
t-test) of mean i.,,,
and &,
between
6 upper and 7 lower lobe specimens
in group
A
Cube Axis
Extension
X
Ratio
Y
z
.
In air
P>O.40 P>O.40
P>O.40 pro.40
P > 0.80 P > 0.80
In saline
PzO.80 PzO.80
P>O.20 PIO.20
P>O.O5 P>O.40
Table 4. Comparison
(paired
r-test) of mean I.,,,,, and R,,, between
5 upper
and 6 lower lobe specimens
in group
Cube Axis Extension
X
Ratio
z
Y
In air
i *inax * mi”
P>O.20 P>O.40
P > 0.20 P>O.80
P>O.40 P>O.80
In saline
i ‘rn.X Alli”
P>O.lO P>O.40
P>O.80 P>O.80
P>O.40 P>O.lO
Table 5. Relative
degree of anisotropy
at maximum
extension (&n,X), - (~.ln,X)Z
(&n,X), - (L3, (L)*y.
(Lx)lyr
(%)
(%)
Group A 8.81 5.42
In air In saline
Group A 6.82 2.53
Group B 2.71 1.86
Group B 3.10 0.74
-Note:
1 (&,,),
2. (L)xyl
(&,&,
= *c(L),
and (%,,,), are the mean of A,,,,, in x. y, and z direction, + (L)y
Table 6. Comparison
+
respectively,
for all cubes in a group.
v.mA1.
and Lmin of 13 specimens
(paired r-test) of mean i.,,,
between
axes for group
A
Axis Pair Extension
Ratio
i ‘IllaX i.d”
In air
In saline
Table 7. Comparison
(paired
X-Y
Y-2
Z-X
P
P
P>O.20 P
P>O.l P > 0.05
P > 0.20 P>O.80
P>O.l P <0.05
r-test) of mean I.,,,
and &,
of 11 specimens
between
axes for group
B
Axis Pair Extension
Ratio
X-Y
Y-2
z-.x
In air
I*rnali L”
P10.05 P < 0.02
P>O.lO P>O.O5
P > 0.80 P
In saline
i‘iVIa% Li”
P>O.20 P > 0.20
P>O.40 pro.40
P > 0.40 P>O.lO
B
249
Lung tissue deformation Lung tissue isotropy is generally investigated through two approaches : microscopic and macroscop ic. At the microscopic level, previous investigations reported either isotropic (D’Angelo, 1972; Forrest 1970; Glazier et al.. 1967) or anisotropic (Forrest, 1976 ; Klingele and Staub, 1972 ; Tsunoda et al., 1974) deformations. At the macroscopic level, except for the report of Chevalier et al. (1976) where anisotropic expansion within intact lungs has been observed using implanted markers, most in vitro studies seem to agree on isotropic behavior (Ardila et al., 1974; Fukaya et al., 1972; Hills, 1971; Redford, 1957). Any observed in uiuo anisotropic deformations may be caused by either the material property or the constraining effect of the chestwall. The in uiuo approach thus may reveal more parenchymal tissue property without the influence of the chestwall. Aging eflect Some major findings in the present study concerning the aging tissue compared to the relatively young groups are : higher saline equilibrium volumes, higher overall extension ratios (paired t-test, all P < 0.001) for similar extension ranges, and less apparent anisotropic deformation. Considering the possible visceral pleural limiting effect and the higher resting volume in saline for group B, the pleural membrane contribution to lung recoil in older lungs seem to be greater than in younger lungs. This may imply that at a comparable deformed volume, aging tissue would be more compliant than young tissue. The smaller difference in i.,,, between the saline and air cases for aging tissue also could mean a less effective alveolar surface force system in the aging tissue than in the younger tissue. A number of studies on the aging lung may be found in the literature, mostly for intact human lungs. It is generally recognized that in aging humans the reduced elasticity of lung pressure-volume (curve shifting to the left) and the increased resting volume of the rib cage results in an increase of functional residual capacity and residual volume while there is no significant change in total lung capacity. Sugihara et al. (1971) have studied human lung tissue strips and have attributed the smaller maximum extension ratio for aging lungs to the increased resting length. Hieronymi (1961) reported that dry lung weight remains equal or decreases slightly with age while the gross dimensions and the size of alveoli decreases. The results from the present study in dogs tend to support these findings. Very limited information is available for the mechanical properties of aging dog lungs. To the authors’ knowledge, the only study by Robinson and Gillespie (1973) shows similar characteristic aging effects in dogs and humans. The pressure-volume curves of the excised aging dog lungs in the present study compare well with the in uivo measurements (Fig. 6). However, the increase in maximum specific volume which was observed has not been reported for in uivo cases. Again, the in uivo approach suffers some
0
40 Transpulmanary
Fig. 6. Static
30
20
Pressure
(cmH20)
pressure-volume deflation curves lungs for group B dogs.
of excised
drawbacks. First, the monitored pleural pressure (or esophageal pressures) are subject to measurement errors, especially at low lung volumes. Secondly, the definition of lung volumes such as TLC which is usually used as a universal base for the detection of lung volume change, especially when cross-species differences are concerned, does not have a common basis for comparison. Third, the aging effect of the rib cage is always present simultaneously and cannot be isolated. The in vitro experiment is therefore a better approach for seeking fundamental understanding and quantification of aging effects on lung tissue per se since the predominant boundary conditions around the lungs are not present. EJects of pleura and large airways on parenchymai deformation Tissue cubes with pleura seem to deform at a higher extension level with about the same extension range as homogeneous cubes but the standard errors are slightly higher (Fig. 5). Tissue cubes with airways carry fairly large standard errors (Fig. 5). However, the mean extension ranges are about the same as for homogeneous cubes. The absolute extension ratio values are lower. The obvious line pattern differences between groups A and C are only in the y-axis where the extension values in group C are higher. Because of the larger spread in the data for group D. the line patterns observed should not be emphasized at the present time although they carry characteristics similar to the other groups. The results of cube physical measurements seem to support a previous finding that the visceral membrane may play an important role in determining the recoil pressure of lung lobes at low lung volumes (Nagao, 1973). If this is the case, one would expect a slightly smaller resting volume for a cube in group C than for a
250
RONALD
C.
TAI
comparable cube in group A. The consequence is thus a possible higher overall extension for group C than for group A cubes which is the case as is shown in Figs. 7(a) and (c). On the other hand, because of its unique location it is also possible that the tissue taken from the apex of the lung (where group C specimens were taken) may behave slightly differently from tissue taken from other parts of the lungs. The synchronization of the deformational characteristics of the whole lung including the airways is one of the main concerns in airway mechanical properties. Several studies have addressed this issue but conclusions differ (Hahn, 1976; Hughes et al., 1972; Prakash and Hyatt, 1978; Sittipong and Hyatt, 1974; Wilson et al., 1974). The original thought in this part of the study was to assess this issue using the results from group D. The results show smaller mean extensions for the group D cubes (Figs. 7a and 7d). However, the scatter in the data is considerable. Since the size of the airway cannot be precisely controlled, it is believed that the airway size variation contributes to the relatively poor results for group D. A contributing factor may be that the reference dimensions seem to be much less defined because of the existence of airways in place of tissue. However, the group D data are the first of this kind to be reported. Experimental effects Since the present experimental investigation involves the processes of preparing cubical specimens from excised lungs and setting them up for mechanical deformation testing, the introduction of artifacts is inevitable. Several important factors relating to these problems will be discussed briefly in this section. The introduction of saline into alveolar regions during specimen preparation ieads to partial loss of alveolar surface active material. Several studies on air pressure-volume characteristics specifically addressed this effect. Findings include a reduction in maximum lung volume and overall compliance for excised dog lungs (Johnson et al.. 1964) and a shift to the right for the pressure-volume curve for excised cat lungs (Bachofen et al.. 1970) and intact dog lungs (Huber et al., 1971). The typical air pressure-volume deflation curves in Fig. 7 for lungs (before saline introduction) and cubes (after saline introduction) confirm the earlier findings. Creep occurred (for a few seconds) after each load increment. Pressure-volume hysteresis was observed for all specimens during the air-filling cycles but was much milder during the saline-filling cycles. An interesting finding was that tissue cubes consistently reached higher maximum extension ratios in saline than in air; this is indicated in Fig. 5. Possible reasons are the loss of alveolar surface material during saline washing and changes in the tissue elasticity due to freezing. It has been observed that the freezing process reduces the extensional capacity of aortic and mitral valve leaflets when compared with fresh specimens (Clark, 1973). The observed changes in the
and
GEORGE
C. LET
I IO Pressure
Dog No I 20
4 I 30
IcmH20)
Fig. 7. Comparison of pressure volume deflation curves of lungs and cubes. Solid lines for in-air and solid line with circles for in-saline. Cross-hatched areas show ranges of spread of curves for cubes from the same dog. stress-strain relationship, however, seem to depend on the orientation of the force-bearing components and the collagen and elastin fibers in the specimens. Since the overall arrangements of collagen and elastin fibers in alveolar walls are random, freezing effects should not significantly bias the results for the detection of isotropy and homogeneity of lung deformation. The previous report by Hoppin et al. (1975) on triaxial cube tests using a similar approach also indicated no observable change in tissue elasticity. Freeze-drying of the cube surface is an essential step in the preparation of specimens for the attachment of the force-applying device. The dehydration of tissue involved only the most outer layer of the cubical specimens. There was no difficulty in hydrating the surface part during the thawing of the cube. Faridy (1973) reported minimal changes in the lobar pressure-volume relationship but some enlargement of the alveolar space after a thorough dehydration-hydration process. Any effect of freezedrying in the present study is believed to have been insignificant. The mechanical attachments for the application of force on the cube surfaces is essential to the present study. The effects of employing these discrete attachments on cube deformation has been assessed using one homogeneous cube. After fully stretching at maximum loading in air, the cube was quick-frozen with liquid nitrogen, freeze-dried and fixed in formalin. Observations on the sectional internal surface revealed a very uniform overall expansion of the alveoli except near the immediate regions of the attachments offorce application where a thin layer of flattened alveoli was identified. But this layer amounted to a very small portion of the total tissue volume and is expected to have had little effect on tissue recoil. There was even less effect for the stretching in saline. This boundary effect is expected to have contributed to the dilference in the P-V curves between the lung and the cubes as well as to the difference in the maximum volume between the air and saline curves of the same cube. In testing a highly compliant lung tissue, a gravitational distortion effect almost always is present.
251
Lung tissue deformation
especially at low extension levels. Since gravitational effects are due to the mounting of the cube on the apparatus as well as to the dead load imposed by the set-up, the total effect is considered an apparatus effect. A special sequence of tests which involved the repeated testing of the same specimen mounted in different orientations with respect to the apparatus were performed. Results showed that the directional characteristics such as the line patterns of I.,,, in Fig. 5 were not affected
by the mounting
SUMMARY
orientation
of the specimen.
AND CONSLUSIONS
Triaxial stretching tests using specially prepared dog lung tissue cubes from different locations in left lungs were performed to detect any possible directionalor locational-dependent deformation behavior for relatively young dogs and aging dogs, as well as to detect the effects of pleural membrane and airway on cube deformation. No obvious locationaldependent deformation behavior was observed, indicating a uniformity of dog lung parenchyma over the lungs. Patterns of directional-dependent deformation were noticed indicating mild anisotropic behavior in general, especially for younger dogs. Aging tissue showed fewer anisotropic patterns. The existence of either a pleural membrane or a single airway in the specimens affected the deformation pattern to different degrees and caused large scatter in the results which do not permit more quantitative conclusions. Considering the results of the present study, the assumption of a homogeneous, isotropic parenchymal tissue seems to be practical for the purpose of lung regional volume analysis using elastic deformation theories.
elastic behavior
of excised dogs’ lungs, J. appl. Pb.ysiol. 34,
597-605. Faridy, E. E., Kidd, R. and Milic-Emili, J. (1967)Topographical distribution of inspired gas in excised lobes of dogs. J. appl. Physiol. 22, 760-766.
Forrest, J. B. (1970) The effect of changes in lung volume on the size and shape of alveoli. J. Physiol. 210, 533-547.
Forrest, J. B. (1976) Lung tissue plasticity: morphometric analysis of anisotropic strain in liquid filled lungs. Respir. Physiol. 27, 223-239. Frank, N. R. (1963) A comparison of static volume-pressure relations of excised pulmonary lobes of dogs. J. appl. Physiol. 18, 274-278. Fukaya, H., Martin, C. J., Young, A. C. and Katsura, S. (1972) Mechanical properties of alveolar walls. J. appl. Phpsiol. 15, 190-213. Fung, Y. C. (1974) A theory of elasticity of the lung. J. appl. Mech. 41, S-14. Fung, Y. C. (1975) Stress, deformation and atlectasis of the lung. Circ. Res. 37, 481-496. Fung, Y. C.,Tong, P. and Patitucci, P. (1978) Stress and strain in the lung, AXE J. Engng Mech. Dia. 104, 201-223. Glaister, D. H., Schroter. R. C., Sudlow. M. F. and MihcEmili, J. (1973) Transpulmonary pressure gradient and ventilation distribution in excised lungs. Respu. Physiol. 17, 365-385. Glazier, J. B., Hughes, J. M. B., Maloney, J. E. and West, J. B. (1967) Vertical gradient of alveolar size in lungs of dogs frozen intact. J. appl. Physiol. 23, 694-705. Hahn, H. L., Graf, P. D. and Nadel, J. A. (1976) Effect of vagal tone on airway diameter and on lung volume in anesthetized dogs. J. appl. Physiol. 41, 58 I --589. Hieronymi, G. (1961) On the change in the morphology of the human lung due to aging. Erg&. Path. Anar. 41, l-62. Hills, B. A. (1971) Geometric irreversibility and compliance hysteresis in the lung. Respir. Physiol. 13, 50 -61. Hoppin, F. G. Jr., Lee, G. C. and Dawson, S. V. (1975) Properties of lung parenchyma in distortion J appl. Physiol. 39, 742-75 1. Huber, G. L., Edmunds, L. H. Jr. and Fmley. T. 1\1. (1971) ENect of experimental saline lavage on pulmonary mechanics and morphology. Anr. Rev. Re~pir. Di\ 104, 337-347.
Hughes, J. M. B., Hoppin, F. C. Jr. and Mead, J. (1972) Effect of lung inflatil on on bronchial length and diameter in
Acknowledgemetlrs~The authors wish to express +I.-:LLlCll----a a&J&Xc;excised lungs. J. appl..Physiol. 32, 25.-35. ciation to Drs. Joseph and Thomas Gregor y for their Johnson, J. W. C., Permutt, S., Sipple, J. H. and Salem, E. S. assistance in this study by providing laboratory space in the (1964) Effect of intra-alveolar fluid on pulmonary surface Department of Anatomical Sciences. They also a cknowledge tension properties. J. appl. Physiol 19, 769 777 the Department of Oral Pathology for providing the use ofss Klingele, T. G. and Staub, N. C. (1970) Alveolar shape freeze-drying equipment. This study was supported by Grant changes with volume in isolated air-filled lobes of cat lung. HL-14495 from the National Heart, Lung, and Blood .I.‘,,.. 1.1 J.. appr.In,mysrok ~8, ‘II l-414. Institute. Lee. G. C. and Frankus. A. (1975a) Aonlicatlon of slnrle . alveolus model to Lung elasticity problem. ASCE National Structural Engineering Convention. New Orleans. Lee, G. C. and Frankus. A. (1975b) Elasticity properties of REFERENCES lung parenchyma derived from experimental distortion data. Biophys: J. 15, 481-493. Ardila, R., Horie, T. and Hilderbrandt, J. (1974) Macroscopic isotropy of lung expansion. Respir. Physiol. 20, 105-115. Lee, G. C., Frankus. A. and Chen. P D (1976) Small Bachofen, H., Hildebrandt, J. and Bachofen, M. (1970) distortion properties of lung parenchyma as a compressible Pressure-volume curves of air- and saline-filled excised continuum. J. Biomech. 9, 641.-648. lungs surface tension in situ. J. apul. Phrsiol. 29.422-431. Liu, J. T. and Lee, G. C. (1978) Static limte deformation Chevalier, P. A., Greenleaf, J. F.. Rot%, R. A. and Wood, E. H. analysis of the lung. ASCE J. E~J~J Mech 0~. 104, 225-238. (1976) Biplane videoroentgenographic analysis of dynamic Mead, J., Takashima, T. and Lelth. D. (1970) Stress disrrlregional lung strains in dogs. J. app/. Physiol. 40, 118-122. bution in lungs: a model of pulmonary elasticity J. uppl Clark, R. E. (1973) Stress-strain characteristics of fresh and Ph!,siol. 28, 596-608. frozen human aortic and mitral leaflets and chordae tenineae. Implications for clinical use. J. Thoroc. CarNagao. K. (1973) Experimental studies on mechanical prodiouasc. Surg. 66, 202-208. perties of the visceral pleura. Nihon C’,lir .1. .Med 15, D-Angelo, E. (1972) Local alveolar size and transpulmonary 307- 327. pressure in siru and in isolated lungs. Respir. Physiol. 14, Pare, P. D., Boncher, R., Mlchoud. M. C’ and Hogg. J. C‘ 251-266. (1978) Static lung mechanics of intact and excised rhesus Faridy. E. E. (1973) Effect of hydration and dehydration on monkey lungs and lobes .I. uppl PII\ W/ RL,.$I)II. E~III, 1
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Prakash, U. B. and Hyatt, R. E. (1978) Static mechanical properties of bronchi in normal excised human lungs. J. appl. Physiol. Respir. Enuir. Exercise Physiol. 45, 45-50. Redford, E. P. (1957) Recent studies of mechanical properties of mammalian lungs. In : Tissue Elasticity, pp.- 177-190. American Physiology Society, Washington. Robinson, N. E. and Gillspie, J. R. (1973) Lung volumes in aging beagle dogs. .J. appl. Physiol. 35, 317-321. Sittinona. R. and Hvatt. R. E. (1974) Static mechanical behav& of bronchj in excised dog lungs. J. appl. Physiol. 37, 201-206.
Sugihara, T., Martin, C. J. and Hilderbrandt, J. (1971) Length-tension properties of alveolar wall in man. J. appl. Physiol. 30, 874-878.
GOERGE
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Tsunoda, S., Fukaya, H., Sugihara, T., Martin, C. J. and Hilderbrandt, J. (1974) Lung volume, thickness of aiveolar wall and microscopic anisotropy of expansion. Respir. Physiol. 22, 285-296.
Vawter, D. L. (1977) Stress-free equilibrium volume of the lung. Physiol. Respir. Envir. Exercise Physiol. 43, 3-7. Vawter, D. L., Matthews, F. L. and West, J. B. (1975) Effect of shape and size of lung and chestwall on stresses in the lung. J. appl. Physiol. 39, 9-17. West. J. B. and Matthews, F. M. (1972) Stresses. strains and surface pressures in the.lung caused by its weight. J. appl. Physioi. 32, 332-345.
Wilson, A. G., Massarella, G. R. and Pride, N. B. (1974) Elastic properties of airways in human lungs post morten. Am. Rev. Respir. Dis. 110, 716-729.