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J Appl Physiol 88: 1022-1028, 2000;
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Vol. 88, Issue 3, 1022-1028, March 2000

Mechanical properties of the tracheal mucosal membrane in the rabbit. II. Morphometric analysis

Lu Wang1,2, Kenneth L. Pinder1, Joel L. Bert1, Mitsushi Okazawa2, and Peter D. Paré2

1 Department of Chemical and Bio-Resource Engineering, University of British Columbia, Vancouver V6T 1Z4; and 2 Pulmonary Research Laboratory, St. Paul's Hospital, University of British Columbia, Vancouver, British Columbia, Canada V6Z 1Y6


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
REFERENCES

Folding of the airway mucosal membrane provides a mechanical load that impedes airway smooth muscle contraction. Mechanical testing of rabbit tracheal mucosal membrane showed that the membrane is stiffer in the longitudinal than in the circumferential direction of the airway. To explain this difference in the mechanical properties, we studied the morphological structure of the rabbit tracheal mucosal membrane in both longitudinal and circumferential directions. The collagen fibers were found to form a random meshwork, which would not account for differences in stiffness in the longitudinal and circumferential directions. The volume fraction of the elastic fibers was measured using a point-counting technique. The orientation of the elastic fibers in the tissue samples was measured using a new method based on simple geometry and probability. The results showed that the volume fraction of the elastic fibers in the rabbit tracheal mucosal membrane was ~5% and that the elastic fibers were mainly oriented in the longitudinal direction. Age had no statistically significant effect on either the volume fraction or the orientation of the elastic fibers. Linear correlations were found between the steady-state stiffness and the quantity of the elastic fibers oriented in the direction of testing.

elastin; collagen; imaging analysis


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
REFERENCES

EXAGGERATED AIRWAY NARROWING in some diseases such as asthma has been attributed to excessive airway smooth muscle (ASM) contraction (13). The ASM contraction deforms the airway mucosal membrane, i.e., the connective tissue inside the muscle ring. As a result, the epithelial cell layer, the basement membrane, and the submucosa tissue are folded during ASM contraction. Folding of the mucosal membrane is capable of sustaining pressure applied by the contracting ASM (11) and therefore impedes further ASM shortening. This is because the mucosal membrane, like all connective tissues, displays viscoelastic properties. These mechanical properties are dependent on the quantity and the organization of the elastic components (16), particularly the collagen and elastic fibers (8). Using well-defined antibodies (2) to a number of macromolecules, researchers have demonstrated that the mucosal membranes contain at least one type of collagen (type IV) and probably others, including types V and VI (9). A collagen fiber is composed of bundles of fibrils formed by the protein collagen. They impart a unique combination of flexibility (when coiled) and strength (when straightened) to the tissue. Elastic fibers are also found in the mucosal membranes (14). They are made of an amorphous core (elastin) surrounded by microfibrils that are partially embedded in thicker core fibers (12). Tissues containing a high proportion of elastic fibers are able to attain high strains, that is, to be stretched by a factor of 2-2.3 with respect to their unloaded length without rupture, and are able to return to their original shape when the forces are relaxed (3). In tissues that are rich in elastic fibers, the collagen fibers are not highly oriented and presumably do not become strained and do not stiffen the tissue until the applied stress is sufficient to orient them (7). It has been reported that the volume fractions of both collagen and elastic fibers in normal human dermis (10, 17) increase until 30-40 yr of age and then start to decrease.

We found that the tracheal mucosal membrane was stiffer in the longitudinal than in the circumferential direction of the airway (18). The hypotheses of this study are that the quantity of the elastic components is proportional to the stiffness of the mucosal membrane and that the quantity and/or orientation changes with age. The purpose of this study is to examine the orientation and the quantity of the collagen and the elastic fibers in the airway mucosal membrane and to correlate these morphometric measurements with the membrane's mechanical properties in tension.


    EXPERIMENTAL PROCEDURES
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ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
REFERENCES

Preparation

After being tested mechanically (18), the tissue samples were fixed and embedded (5) in paraffin. Multiple cross sections of 3- to 5-µm thickness were obtained. Because the samples were rectangular and the cross sections referred to the plane perpendicular to the long axis of the sample, the sections obtained from the circumferential samples were in the longitudinal direction of the airway and vice versa, as shown in Fig. 1. To reveal the morphology of the entire sample, the sections were obtained at roughly comparable spacing throughout the sample.


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Fig. 1.   Sections for morphometric measurements.

Six sections from each sample were randomly chosen for staining. With the use of previously described technique (15), two were stained with Verhoeff elastic staining, which caused the elastic fibers to appear dark purple or black; two were stained with Van Gieson's staining, which colored the collagen fibers pink; one was with combined Verhoeff and Van Gieson staining; and the last one was stained with standard hematoxalin and eosin (H&E) staining for use with confocal microscopy.

The H&E- and Van Gieson-stained specimens were used to examine the organization and the quantity of the collagen fibers under both light and confocal microscopy. The collagen fibers were seen to be densely packed in the mucosal membrane, were interwoven through the length of the trachea, and showed no specific orientation (Fig. 2). Because of its isotropic distribution in the tissue, the collagen mesh will likely contribute to the strength of the tissue equally in both longitudinal and circumferential directions. Therefore, the orientation and the relative volume fraction of the collagen fibers were not measured. On the other hand, the two-dimensional images of the elastic fibers (Fig. 3) suggested that the elastic fibers were oriented primarily in the longitudinal direction of the airway. Because we showed (18) that the longitudinal samples were stiffer than the circumferential ones, the morphological study was conducted to quantify the elastic fiber orientation.


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Fig. 2.   Three-dimensional image of collagen fibers obtained using confocal microscope; magnification, ×1,500. For comparison, inset a shows a two-dimensional (2D) image of elastic fibers (stained black) with vertical axis in longitudinal direction of an airway, and inset b shows a 2D image of cross section of same airway with elastic fibers stained black; magnification, ×2,000 for both insets. Epithelial cell layer is to right of image.



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Fig. 3.   a: 2D image of elastic fibers (stained black) with vertical axis in longitudinal direction of an airway. b: 2D image of cross section of same airway with elastic fibers stained black. Epithelial cell layer is to right of image. Photograph taken under a light microscope, oil lens ×2,000.

Methods

The elastic fiber orientation is a statistical estimation of the percentage of elastic fibers oriented in a specific direction with respect to the airway long axis and was studied using an image analysis system, Bioquant system IV (R&M Biometrics), linked with a light microscope. Because electron microscopy showed that the elastic fibers are 10-12 nm in diameter (7), single elastic fibers or microfibrils are not visible under the light microscope. It was assumed that the elastic fibers appear in bundles (fiber bundles). Each fiber bundle consists of hundreds of elastic fibers. The estimation of the fiber orientation was based on the shape and dimensions of bundles composed of single fibers (Fig. 4). For simplicity, the fiber bundles will be referred to as "fibers." One Verhoeff-stained section from each longitudinal and circumferential sample was randomly chosen for measurement, and the observer was blinded to its orientation in the airway. The selection of fibers for measurement on each section was systematically random, that is, the first fiber was randomly chosen, and then every fifth fiber, horizontally across the microscopic view, was selected. Fifty fibers from each section were studied. The epithelial cell layer was used as an orientation reference. An x-y coordinate system was constructed, with the x-axis parallel to the base of the epithelial cell layer, to measure the fiber orientation relative to the epithelial cell layer (Fig. 4). ax and bx are the maximal distances occupied by the fiber in the x and y coordinates. The length of a selected fiber was measured by tracing its entire length. The thickness was measured at an arbitrary point because it was found to be virtually constant throughout the length of the fiber.


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Fig. 4.   Classification of elastic fibers according to orientation in airway. ax and by, Maximal distances occupied by fiber in x and y coordinates.

The same sections used for estimating the elastic fiber orientation were also used to measure the volume fraction of the elastic fibers. The relative volume of the elastic fibers is defined as the percentage of the tissue sample volume occupied by elastic fibers and was measured on a grid that was generated by using the software Gridder (Pulmonary Research Laboratory, University of British Columbia, St. Paul's Hospital). The type, shape, and density of the grid were selected to minimize the coefficient of error (6, 19). A cross-shaped grid was chosen. The density of the grid was 775 points per field (6). The magnification was ×20 (limited by the size of the tissue sample). Each section was divided into five fields. Each field was of rectangular shape and included the complete thickness of the sample from the epithelial cells to the outermost layer of the submucosa. The long axis of a field was perpendicular to the long axis of the tissue sample on the section. According to conventional point-counting methodology (1, 19), the grid points falling on the elastic fibers are referred to as the target points, and the grid points falling on the tissue sample are called the total points. The target points and the total points were counted.

Analysis

Unlike methods of analyses based on point counting, there is no conventional protocol for estimating the orientation of fibers in light microscopic sections of biological tissue. We therefore developed a novel method based on simple geometric and probabilistic considerations.

Elastic fiber orientation. If a section was obtained as the cross section of a longitudinal sample, then the epithelial layer runs perpendicular to the long axis of the trachea. On the sections obtained as cross sections of the circumferential samples, the epithelium runs parallel to the long axis of the airway (Fig. 1).

As shown in Fig. 4, four types of fibers in each of the circumferential (types L, T, D, A) and longitudinal (types C, T, D, A) samples can be classified. Type D fibers appear to be dots, i.e., the ratio of length to thickness is <= 2. Type L or C fibers are straight fibers with (ax/by) > 2. Type L fibers run in the longitudinal direction, whereas type C fibers run in the circumferential direction of the airway. Type T fibers are wavy fibers that have a ratio (ax/by) between 0.5 and 2. This fiber type has components in both the longitudinal and circumferential directions of the airway. Type A fibers run across the thickness of the mucosal membrane, with (ax/by) < 0.5. The numbers of type L, C, T, and A fibers are expressed as Lf, Cf, Tf, and Af, respectively. The dots are, in fact, the cross sections of the L, C, or T types of fibers.

Type D fibers (dots) on the cross section of a circumferential sample are likely to be type C or type T fibers, which can be seen as straight or wavy fibers in the cross section of the longitudinal sample of the same airway. Similarly, the type D fibers on the cross section of a longitudinal sample correspond to type L or type T fibers, which can be seen as straight or wavy fibers on the cross section of the circumferential sample. Thus the number of D fibers in a cross section of the longitudinal samples was converted mathematically into the number of type L (Lconvt) and type T (Tconvt2) fibers
L<SUB>convt</SUB> = D<SUB>L</SUB> ⋅ <FR><NU>L<SUB>f</SUB></NU><DE>L<SUB>f</SUB> + T<SUB>f</SUB></DE></FR> (1a)

T<SUB>convt2</SUB> = D<SUB>L</SUB> ⋅ <FR><NU>T<SUB>f</SUB></NU><DE>L<SUB>f</SUB> + T<SUB>f</SUB></DE></FR> (1b)
where DL is the number of dots found in the cross section of a longitudinal sample and Lf and Tf are measured from the cross section of the circumferential sample of the same airway. Similarly, the number of type D fibers measured from the cross section of the circumferential samples was converted into the number of type C and type T fibers.

The numbers of the converted type L fibers and type C fibers were found to be similar to Lf, and Cf. The numbers of the converted type T fibers in the longitudinal and in the circumferential directions were found to be close to Tf in the longitudinal and circumferential direction, respectively. If one only considers fibers in a cross section of circumferential sample
Total fibers = L<SUB>f</SUB> + T<SUB>f</SUB> + A<SUB>f</SUB> + T<SUB>convt1</SUB> + C<SUB>convt</SUB> (2)
where Tconvt1 and Cconvt are converted from the dots in the cross sections of the circumferential samples. Adding Tf and Tconvt1 gives the number of type T fibers in the cross section of circumferential samples. Similarly, if one only considers fibers in the cross section of longitudinal samples
Total fibers = C<SUB>f</SUB> + T<SUB>f</SUB> + A<SUB>f</SUB> + T<SUB>convt2</SUB> + L<SUB>convt</SUB> (3)
where Tconvt2 and Lconvt are converted from the dots in the cross sections of the longitudinal samples.

The fiber orientation in a sample is given by the fraction of each type of fibers in the total. A computational program was written to calculate Lf, Cf, Tf, Af, Tconvt1, Tconvt2, Cconvt, Lconvt, and the total number of measured fibers. The fractions calculated from the cross sections of the longitudinal samples were compared with those from the cross sections of the circumferential samples. It was found that they were equal, and therefore they were combined to obtain an average, expressed as Lpercent, Cpercent, Tpercent, and Apercent for each airway.

Relative volume of the elastic fibers. Summing the target points and the total points throughout the five fields of each section gave the number of total target points and the number of overall total points. The ratio of the two gave the relative area fraction of the elastic fibers on the section. Because the thickness of the microscopic sections was greater than the diameters of the fibers, this could have caused a Holmes effect (19), which results from the elastic fibers from different depths being projected onto the imaged surface. To overcome this potential error, we calculated the volume fraction, a less biased parameter, to describe the abundance of the elastic fibers in the tissue sample.

It was assumed that the sections were of even thickness everywhere and, hence, that the area fraction was proportional to the value of the volume fraction of the elastic fibers (1, 19). Assuming that the systematic error due to section compression during histological processing is negligible, the volume fraction (Vv) of the elastic fibers was calculated (19) as
V<SUB>v</SUB> = A<SUB>v</SUB> ⋅ <IT>K</IT><SUB><IT>t</IT></SUB> (4)
where Av is the relative area fraction and Kt is a correction factor.

The elastic fibers were treated as long tubules of thickness delta  and length l. The microscopic sections were of thickness tt = 5 µm. The correction factor Kt was (19)
<IT>K</IT><SUB><IT>t</IT></SUB> = <FR><NU>&lgr;</NU><DE>&lgr; + <IT>gg</IT> (&lgr; + 0.5)</DE></FR> (5)
where the shape factors lambda  = l/delta and gg = tt/delta .

By substituting the average value of the measured l, delta , and tt, the correction factor Kt could be calculated. However, the true value of the average l was not found. This was because the entire length of the fibers could not be traced from one end of the sample to the other; instead, they appeared as shorter segments with various shapes depending on how they were oriented and how the section was cut. To obtain an estimate, we calculated the mean value of lambda  measured from type C, L, and A fibers and calculated the correction factor Kt to be 0.228.

Correlation of the mechanical properties and the morphometric results. To test the hypothesis that the measured steady-state stiffness correlates with the quantity of the elastic fibers in the particular direction of the airway, the quantity of the elastic fibers in the longitudinal direction of the airway (QL) was calculated as (Vv · Lpercent), i.e., the multiplication of the volume fraction of the elastic fibers in the tissue sample and the fraction of the total fibers that were oriented in the longitudinal direction of the airway. Similarly, the quantity of the elastic fibers in the circumferential direction (QC) was calculated as (Vv · Cpercent). QL and QC are volume fractions of straight fibers in the longitudinal and circumferential direction, respectively.


    RESULTS
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ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
REFERENCES

Sensitivity tests were carried out on the criteria set for each type of fiber orientation. Slight alteration of the values of the criteria had no significant effect on the result of the classification. The orientation of the elastic fibers expressed as the percentage of type L, C, T, and A is shown in Fig. 5. The results showed that ~57% of the elastic fibers were oriented in the longitudinal direction (type L) and ~8% were oriented in the circumferential direction of the airway (type C). The fibers that were oriented across the thickness of the mucosal membrane (type A) accounted for only 2%, whereas 33% of the total fibers were of wavy shape (type T), partly in the circumferential and partly in the longitudinal direction of the airway. No significant relationship between the fiber orientation and the age of the tested animals was found.


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Fig. 5.   Elastic fiber orientation in airway (expressed as means with SD as error bars).

The volume fraction of the elastic fibers (including all types of orientation) in the tracheal mucosal membrane was 5% on average. There was no difference in this estimation from samples taken from either the circumferential or longitudinal direction of the airways. There was also no significant relationship between the volume fraction of the elastic fibers and the age of the animals.

A significant linear relationship was found between the longitudinal steady-state stiffness (18) and QL (Fig. 6, r = 0.371, P = 0.019, steady-state stiffness = 8.2 + 210.2 QL, SE of the slope is 85.6, SE of the intercept is 2.6). In the circumferential direction, the linear relationship between steady-state stiffness and QC was also significant (Fig. 6, r = 0.378, P = 0.016, steady-state stiffness = 4.2 ± 515.3 QC, SE of the slope is 204.8, SE of the intercept is 1.0). The pooled steady-state stiffness, i.e., circumferential and longitudinal samples, correlated linearly with the pooled volume fraction of the elastic fibers in both the longitudinal and circumferential directions with r = 0.579 and P < 0.0001. 


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Fig. 6.   Correlation between steady-state stiffness and elastic fiber morphometry. Triangles with dotted center represent longitudinal samples, and circles with dotted center represent circumferential samples. QL and QC, volume fractions of straight fibers in longitudinal and circumferential direction, respectively.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
REFERENCES

The results of the study showed that the volume fraction of elastic fibers in the rabbit tracheal mucosal membrane was ~5% and that the elastic fibers were oriented mainly in the longitudinal direction. The quantity and the orientation of the elastic fibers could contribute to the difference in the stiffness of the membrane in the longitudinal and circumferential directions of the airway. Age had no statistically significant effect on either the volume fraction or the orientation of the elastic fibers.

We developed a novel method to quantify the orientation of the elastic fibers. There are several types of techniques that are presently used to observe the orientation of tissue components (7), for example, polarized light microscopy, transmission electron microscopy, scanning electron microscopy, and X-ray diffraction. However, these techniques require expensive and specialized equipment. The method of analyzing the fiber orientation developed in this study is quick and suitable for quantitative estimates of fiber orientation on light microscopic sections. The results of the morphological study led to a logical explanation of the physical properties of the tissue, which corroborates the approach taken.

Young's modulus for elastin is ~600 kPa (4). On average, the stiffness of the mucosal membrane was found to be between 8 and 18 kPa in the longitudinal direction. Because the volume of the elastic fibers was 5% of the mucosal membrane and because 57% of the fibers were oriented in the longitudinal direction, an apparent Young's modulus of the elastic fibers in the mucosal membrane could be estimated to be between 280 and 640 kPa, which agrees with the reported value for pure elastin. Despite the large variation in the data and the fact that the stiffness could be from many other structural components, it appears that the elastic fiber content may be the major contributor to the tissue stiffness.

There are many factors with respect to the elastic fibers that may influence the stiffness (8, 9, 14). On the basis of changes with age in the dermis (17), we have reasons to suspect age-related changes in the tracheal mucosal membrane. If the quantity of the elastic fibers decreased but the stiffness appeared unchanged with age, then there might be other factors, such as the cross-linking (8) of elastin, that increased with age. We found that the elastic fiber quantity was also not age related.

Fiber orientation is different in different organs and in different locations in the body, depending on the biological function of the tissue. For example, the collagen fibers in a tendon are roughly parallel to each other so that they can withstand uniaxial tension (7); the elastic fibers in an artery reorient circumferentially when the internal pressure rises so that they can reinforce the artery wall (8). The fact that the elastic fibers in the airway mucosal membrane are oriented mainly in the longitudinal direction and that the membrane is stiffer in the longitudinal direction suggests that the membrane resists elongation yet permits circumferential changes.

Our ultimate interest in this study was to assess the potential contribution of the airway mucosal membrane as a modulator of airway narrowing. It is likely that, in large airways like the trachea, cartilage is the most important structural element maintaining airway patency and providing an impediment to smooth muscle contraction. However, in peripheral airways, it has been suggested that folding of the mucosal membrane during contraction could provide a substantial elastic load to the muscle and contribute to airway stability (11, 20). To the extent that the morphometric characteristics and physiological parameters that we have defined for the trachea mucosal membrane can be extrapolated to the peripheral airways, the results of this study may help in quantifying the potential role of the mucosal membrane. However, the intraparenchymal bronchi might not have the same mucosal composition and elastic fiber orientation as the trachea. Our study provides a method for studying structure-function relationships in the soft connective tissues. Systematic investigation must be carried out to verify the structure of the elastic component in smaller airways before applying the knowledge of the tracheal mucosal membrane.

Folding of the mucosal membrane, which occurs during smooth muscle contraction, involves bending of the mucosal membrane, which entails both compression and extension of connective tissue components within it (20). For this reason, the data that we have compiled on the tensile stiffness and the morphometric determinants of tensile stiffness are not sufficient to quantify the physiological importance of the mucosal membrane. However, when the tissue stiffness in compression becomes available, the contribution of the mucosal membrane to airway hyperresponsiveness could be estimated.


    ACKNOWLEDGEMENTS

We thank Dr. Marek Labecki for contribution to the design of the computing algorithm, Julie Chow for histological assistance, and Stuart Greene for image production.


    FOOTNOTES

Financial support for this research was supplied by the Medical Research Council of Canada and the Natural Science and Engineering Research Council of Canada.

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

Address for reprint requests and other correspondence: P. D. Paré, Pulmonary Research Laboratory, Univ. of British Columbia, St. Paul's Hospital, McDonald Research Wing, 1081 Burrard St., Vancouver BC, Canada V6Z 1Y6 (E-mail: ppare{at}mrl.ubc.ca).

Received 4 November 1998; accepted in final form 14 October 1999.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
REFERENCES

1.   Aherne, W. A., and M. S. Dunnill. Morphometry. London: Arnold, 1982, p. 33-44.

2.   Cardoso, W. V., H. S. Sekhon, D. M. Hyde, and W. M. Thurlbeck. Collagen and elastin in human pulmonary emphysema. Am. Rev. Respir. Dis. 147: 975-981, 1993[Web of Science][Medline].

3.   Carton, R. W., J. Dainauskas, and J. W. Clark. Elastic properties of single elastic fiber. J. Appl. Physiol. 17: 547-551, 1962[Abstract/Free Full Text].

4.   Fung, Y. C. Biomechanics: Mechanical Properties of Living Tissues (2nd ed.). New York: Springer-Verlag, 1994, p. 251.

5.   Gordon, K., and P. Bradbury. Tissue processing, microtomy and paraffin sections. In: The Theory and Practice of Histological Techniques, edited by J. D. Bancroft, and A. Stevens. Edinburgh: Churchill Livingstone, 1977, p. 29-64.

6.   Gundersen, H. J. G., and E. B. Jensen. The efficiency of systematic sampling in stereology and its prediction. J. Microsc. 147: 229-263, 1987[Medline].

7.   Hukins, D. W. L. Collagen orientation. In: Connective Tissue Matrix, edited by D. W. L. Hukins. Basel: Verlag Chemie, 1984, p. 211-240.

8.   Hukins, D. W. L. Tissue components. In: Connective Tissue Matrix, edited by D. W. L. Hukins. Basel: Verlag Chemie, 1984, p. 1-16.

9.   Kleinman, H. K., and H. W. Schnaper. Basement membrane matrices in tissue development. Am. J. Respir. Cell Mol. Biol. 8: 238-239, 1993.

10.   Kohn, R. R., and S. L. Schnider. Collagen changes in aging skin. In: Aging and the Skin, edited by A. K. Balin, and A. M. Kligman. New York: Raven, 1989, p. 121-140.

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14.   Pasquali-Ronchetti, I., and C. Fornieri. The ultrastructural organization of the elastin fiber. In: Ultrastructure of the Connective Tissue Matrix, edited by A. Ruggeri, and P. M. Motta. Boston, MA: Nijhoff, 1984, p. 126-139.

15.   Reid, P. E. Histochemistry Laboratory Manual. Vancouver, BC: Department of Pathology, University of British Columbia, 1994, p. 59-62.

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17.   Vitellaro-Zuccarello, L., S. Cappelletti, V. Dal Pozzo Rossi, and M. Sari-Gorla. Stereological analysis of collagen and elastic fibers in the normal human dermis: variability with age, sex, and body region. Anat. Record. 238: 153-162, 1994[Medline].

18.   Wang, L., K. L. Pinder, J. L. Bert, P. D. Paré, and M. Okazawa. Mechanical properties of the tracheal mucosal membrane in the rabbit. I. Steady-state stiffness as a function of age. J. Appl. Physiol. 88: 1014-1021, 2000[Abstract/Free Full Text].

19.   Weibel, E. R. Practical methods for biological morphometry. In: Stereological Methods. London: Academic, 1979, vol. 1, p. 139-146.

20.   Wiggs, B. R., C. A. Hrousis, J. M. Drazen, and R. D. Kamm. On the mechanism of mucosal folding in normal and asthmatic airways. J. Appl. Physiol. 83: 1814-1821, 1997[Abstract/Free Full Text].


J APPL PHYSIOL 88(3):1022-1028
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