Vol. 89, Issue 1, 3-14, July 2000
Effects of collagenase and elastase on the
mechanical properties of lung tissue strips
Huichin
Yuan1,
Stefanida
Kononov1,
Francisco S. A.
Cavalcante1,
Kenneth R.
Lutchen1,
Edward P.
Ingenito2, and
Béla
Suki1
1 Department of Biomedical Engineering, Boston University,
and 2 Brigham and Women's Hospital, Boston, Massachusetts 02215
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ABSTRACT |
The dynamic stiffness (H), damping
coefficient (G), and harmonic distortion (kd)
characterizing tissue nonlinearity of lung parenchymal strips from
guinea pigs were assessed before and after treatment with elastase or
collagenase between 0.1 and 3.74 Hz. After digestion, data were
obtained both at the same mean length and at the same mean force of the
strip as before digestion. At the same mean length, G and H decreased
by ~33% after elastase and by ~47% after collagenase treatment.
At the same mean force, G and H increased by ~7% after elastase and
by ~25% after collagenase treatment. The kd
increased more after collagenase (40%) than after elastase (20%)
treatment. These findings suggest that, after digestion, the fraction
of intact fibers decreases, which, at the same mean length, leads to a
decrease in moduli. At the same mean force, collagen fibers operate at
a higher portion of their stress-strain curve, which results in an
increase in moduli. Also, G and H were coupled so that hysteresivity
(G/H) did not change after treatments. However,
kd was decoupled from elasticity and was
sensitive to stretching of collagen, which may be of value in detecting
structural alterations in the connective tissue of the lung.
stiffness; damping; tissue resistance; nonlinearity; network
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INTRODUCTION |
THE RHEOLOGICAL
PROPERTIES of lung parenchymal tissue have been shown to exhibit
viscoelastic and nonlinear behavior (3, 8,
9, 12, 14, 18,
20, 24, 28, 29,
35, 41, 42), which appears to
play an important role in various aspects of the mechanics of
breathing. For example, lung tissue resistance is a major
component of total lung resistance around the breathing frequencies in
normal lungs (12, 18) and certain lung
diseases that alter parenchymal tissue constituents such as fibrosis
(38). Additionally, the stress-strain relationship of lung
tissue determines how lung volume changes with respect to
transpulmonary pressure. The dynamic stress-strain behavior of the
parenchyma also influences the distribution of ventilation and, hence,
can have a significant impact on gas exchange. This study addresses a
fundamental question: What structural elements in the parenchyma are
responsible for the linear viscoelastic and nonlinear behavior of lung tissue?
The lung tissue has a number of important structural components, such
as the connective tissue network, interstitial cells, and the surface
lining layer. For example, the surface lining layer is a significant
stress-bearing element in the lung tissue. Liquid filling of the lung
abolishes the gas-liquid interface and thus eliminates a significant
portion of the hysteresis of the isolated air-filled lung
(1, 5), which supports the notion that
surface lining is an important contributor to tissue resistance.
Schurch et al. (31) measured the surface tension-area curve of pulmonary surfactant extracts. They found that, after a few
consecutive cycles, the hysteresis of the surface film during small-amplitude cycling became negligible. This suggests that, during
tidal breathing, the contributions of surface film to lung hysteresis
are small. The surface film, however, may have an indirect influence on
lung hysteresis through the geometric alterations of the alveoli due to
reduced surface forces at low lung volumes (33).
Similarly, in a recent study (41), we found that the dynamic properties of parenchymal tissue strips from guinea pigs measured before and after loss of cell viability were statistically identical. Because of the absence of cross-bridge cycling, the average
energy dissipation in nonviable samples was only ~10% smaller than
in viable samples. Therefore, from these studies, one may conclude that
lung parenchymal mechanics are most likely dominated by the
extracellular matrix. The next question is then how alterations in the
extracellular matrix that occur in various interstitial lung diseases,
such as emphysema or fibrosis, affect the elastic and hysteretic
properties of lung parenchymal tissues.
The primary aim of this study was to gain more insight into the origin
of tissue elastic and hysterestic properties. To achieve this goal, we
investigated the linear and nonlinear mechanical contributions of the
constituents of the connective tissue, namely, the collagen-elastin
fiber network, to the overall mechanical properties of lung tissue
strips under the effects of various biochemical interventions mimicking
interstitial lung diseases.
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METHODS |
Sample Preparation
Lung parenchymal strips were obtained from healthy male guinea
pigs weighing 400-450 g and killed by intraperitoneal injection of
pentobarbital sodium. The fresh lungs were removed from the thoracic
cavity, placed in oxygenated Krebs-Ringer organ bath perfusate [(in
mM) 5 KCl, 137 NaCl, 2 CaCl2, 1 MgSO4, 1 NaH2PO4, and 24 NaHCO3] on ice,
and studied within 1 h. The pH was controlled with bubbling 5%
CO2-95% O2. Tissue strips of 4.5 × 4.5 × 10 mm in dimensions were prepared, and then each end of the
tissue strip was fixed by cyanoacrylate glue to small metal clips
attached to straight steel wires. The assembly was placed in a vertical glass tissue bath (Wilbur Scientific, Boston, MA), with the upper wire
attached to a force transducer and the lower wire to the lever arm of a
displacement generator.
Experimental Setup
The apparatus is described in detail in Ref. 41. Briefly, a
servo-controlled lever arm (model 300H, Cambridge Technologies) provided the desired elongations. The force developed by the tissue strip was measured by a force transducer (model 400A, Cambridge Technologies). Calibrations were performed between 0 and 2 g force by using standard weights. The transducer system was tested as in Ref.
41 and was shown to be linear and accurate to within 1% over the force
range (0-2 g) of interest with a hysteresis at least 10 times
smaller than that of the tissue strip. The servo-controlled lever arm
was driven by a displacement signal generated by a computer. The signal
was sent out from the digital/analog port of a data-acquisition board
(DT2812, Data Translation, Cambridge, MA) and then smoothed with a
low-pass filter (8-pole, R858L8EX, Frequency Devices, Haverhill, MA)
with a cutoff frequency of 15 Hz. Both displacement and force signals
were low-pass filtered at 15 Hz and then sampled at 50 Hz.
Protocol
Before the protocol was started, the system was aligned by
adjusting the horizontal position of the actuator so that the
hysteresis of the strip displayed on an oscilloscope during sinusoidal
oscillations was minimized. This is an important step because any
friction between the steel wire and the wall of the glass container can significantly contribute to the measured hysteresis of the tissue strip. The experiments were performed at room temperature. The strip
was preconditioned by first performing single slow stretch to 2 g
of mean force. The mean force was then reset to a desired value, and
the strip was oscillated sinusoidally at 1 Hz for ~5 min to avoid the
transients due to stretching the strip to 2 g of force.
Proteolytic enzymes were used to elucidate the effects of the
connective tissue components on the mechanical properties of lung
parenchyma. Collagen or elastin fibers were digested with collagenase
(1 mg, Sigma Chemical) or pancreatic elastase (5 µl, Sigma Chemical).
During digestion treatment, the strip was placed in a chamber filled
with PBS solution (37°C, pH 7.4) to which the appropriate enzyme
solution was added.
A total of 16 lung parenchymal strips was studied before and after
enzyme treatment: eight strips were treated with elastase for 60 min,
and eight strips were treated with collagenase for 30 min. The dynamic
properties of the strips were measured at a mean force of 1 g with
strain amplitudes of 5, 10, and 15%. After enzyme treatment, the
tissue strips lose part of their elastic recoil. As a consequence, when
the strips are stretched to the same distending force, the
corresponding length will be larger than it was before the treatment.
Thus the operating point on which the oscillations are superimposed can
be chosen as either the same static length or the same static force of
the strip as before treatment. To better characterize the alterations
in the mechanical properties, we repeated the oscillatory measurements both at the same mean length and at the same mean force as in control.
Additionally, in three strips from both the elastase- and the
collagenase-treated groups, the quasi-static stress-strain curve was
measured, and, in one strip from both groups, the time response of the
mechanical moduli was measured every 15 or 30 min for up to 3 h.
Measurement Approach
The quasi-static stress-strain curve was measured by using a
triangular wave in strain with a period of 200 s. For the dynamic measurements, instead of the traditional sinusoidal oscillation approach, we used a broad-band pseudorandom displacement input signal,
which allows a rapid assessment of the dynamic mechanical properties of
the tissue strips. The frequency composition of the displacement signal
was chosen so that the influence due to nonlinearities on the estimated
apparent complex moduli is minimized and so that higher order
nonlinearities can be identified for characterizing tissue
nonlinearities. The signal followed the composition proposed by Victor
and Shapley (39) and contained six input frequencies, a
flat power spectrum, and a set of random phases (see Table
1). The length of the sequence was 4,096 points, and the sampling rate was 60 Hz, which corresponds to a time
period of 68 s. For each dynamic force-displacement measurement,
three cycles were delivered, and only the last two cycles were
collected to avoid the effects of transients on the dynamic moduli.
This kind of sparse frequency composition of the input allows a rapid assessment of the impedance of modulus spectrum of the system simultaneously at many frequencies, and the estimated apparent spectrum
is very smooth as if it were measured with separate sinusoidals of some
equivalent amplitude (36).
Data Analysis
Characterization of strip mechanics.
The length input and force output signals were normalized to obtain
strain 
and stress T as
![&egr;(t)=[l(t)−l<SUB>o</SUB>]<IT>/l</IT><SUB>o</SUB><IT>; </IT>T(<IT>t</IT>)<IT>=</IT>F(<IT>t</IT>)<IT>/A</IT><SUB>o</SUB>](/content/vol89/issue1/fulltext/3/img001.gif)
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(1)
|
where l is length, lo is
reference length of the strip, F is force, Ao is
cross-sectional area of the strip corresponding to
lo, and t is time. The mechanical
properties of the strips are characterized by the complex modulus G*
defined in the frequency domain as
|
(2)
|
where j is the imaginary unit, 
is the circular
frequency, G' is the storage modulus or the component of the stress
that is in phase with strain, and G" is the loss modulus or the
component of the stress that is in phase with strain rate. The data
records of F(t) and l(t) were first
transformed to T(t) and (t), respectively, which were then divided into four blocks (4,096 points/cycle) with an
overlap percentage of 25%. The complex spectra for each cycle were
obtained by taking the fast Fourier transforms of the blocks. The G*
was then estimated in the frequency domain by taking the ratio of the
cross-power spectrum of T and and the autopower spectrum of .
The G* was also corrected for the frequency response of the measuring
apparatus, which was mainly due to asynchronous sampling of the
displacement and force channels. The hysteretic properties of the
tissue were characterized by the tissue hysteresivity, 
, introduced
by Fredberg and Stamenovic (9), which is defined as the
ratio of dissipated to stored energy over a force-length cycle and is
simply G"/G'. This allows the calculation of as a function of frequency.
Viscoelastic modeling.
The special design of the input signal allows a robust estimation of
the apparent linear transfer function of the system at the input
frequencies in the absence of very strong nonlinearities. Therefore, to
evaluate the dynamic properties of the tissue strip, we first fit a
linear viscoelastic model to the complex modulus spectra at the six
input frequencies. Many viscoelastic tissue models have been proposed
in the literature (3, 10,
12-14, 19, 22, 28,
29, 35). We chose the constant-phase model, which originated from the power law type of stress relaxation of a
rubber balloon (13)
|
(3)
|
where 
is the relaxation exponent. The Fourier transform of
Eq. 3 was later applied to lung impedance spectra in the
frequency domain by Hantos et al. (11, 12).
The tissue impedance Z() is described by
|
(4)
|
where the parameters G and H are the tissue damping and
elastance coefficients, respectively. Note that 
is not an
independent parameter in the model, and it governs the frequency
dependence of the real and imaginary parts of Z(). With only two
parameters (G and H), Hantos and co-workers showed that this model can
fit the tissue impedance in cat and dog lungs better than other
viscoelastic models (11, 12). Additionally, a
mathematical framework and a possible molecular basis of Eqs.
3 and 4 has also been offered (35). In our
previous study (41), we also observed that the lung tissue
behaved as if it had a purely viscous component R, which was
also added to the complex modulus G*() such that
|
(5)
|
Note that the first term is the G', which increases slowly and
quasi-logarithmically with where the exponent is a small number
between 0.04 and 0.1 (3, 11,
35). The second term is the G", which also increases
quasi-logarithmically and with the same exponent as the G' because
R is negligible at low frequencies (41). The
tissue in this model is the ratio of the imaginary and real parts
of G* and is a function of frequency. However, because the term
R is small compared with G
at low
frequencies and to remain consistent with previous analyses of whole
lung mechanics (11, 18, 35), we
define as the ratio G/H except when we examine the frequency
dependence of directly from G' and G". Using a global optimization
algorithm (6), we estimated the model parameters by
minimizing the following root-mean-square error (RMSE)
|
(6)
|
where i refers to the input
frequencies and N = 6.
Harmonic distortion.
When applying a broad-band input, the degree of system nonlinearity can
be characterized by how the moduli depend on the amplitude of the
strain input. Another way of characterizing nonlinearity is via the
so-called extended harmonic distortion index kd,
which quantifies the amount of both harmonic distortion and cross talk in the output signal (43). The coefficient
kd is defined as
|
(7)
|
where PTOT is the total power in the output and
PNI is the output power due to system nonlinearities only,
i.e., the power at noninput frequencies. The advantage of using
kd is that it can be calculated from a single
spectrum, whereas the traditional method of characterizing nonlinearity
requires the measurement of the moduli at several distinct amplitudes.
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RESULTS |
The quasi-static stress-strain curve of two tissue strips before
and after digestion with either elastase or collagenase is shown in
Fig. 1. There is a noticeable intersample
variability in the stress-strain curves of the control samples similar
to that found by Maksym and Bates (20). The effect of both
treatments is to shift the stress-strain curves to the right, resulting
in a softer tissue. Thus for any given strain before and after
treatment, the slope of the curve and hence the incremental elastic
modulus (Y) of the tissue must be smaller after digestion.
However, this may not be the case when the slopes are studied at the
same distending stress because of the nonlinear nature of the curves.
This phenomenon is further examined in terms of the dynamic moduli of
the tissue (see below). In general, collagenase always produced a
larger shift in the stress-strain curve than did elastase.
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Fig. 1.
Quasi-static stress-strain curves of 2 tissue strips
before and after enzymatic digestion. One of the strips was treated
with elastase and the other with collagenase. Continuous lines are
4th-order polynomial regressions.
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Figure 2 shows the data and model fits of
G' and G" and as a function of frequency in a typical strip, in
control and after treatment with elastase when the length of the tissue
was set to the value before digestion (same mean length). In control, both G' and G" increased steadily and approximately linearly with the
logarithm of frequency up to ~1 Hz, after which G" increased faster,
most likely due to the effect of the Newtonian resistance of the
tissue. Also, both G' and G" showed a slight negative strain amplitude
dependence. The ranges of G' and G" in control match those obtained in
our previous study (41). The observed dynamic behavior in
parenchymal strips from guinea pigs is consistent with data found in
other species with the use of a sinusoidal approach (24,
28) and in whole animal studies (11,
12, 18, 29). After elastase
treatment, the mean force in the tissue strip decreased by ~20%.
Correspondingly, both G' and G" shifted down by 40% in a parallel
fashion. The frequency dependence of G' and G" displayed a similar
behavior as in control, except that the small strain amplitude
dependence almost completely disappeared. Interestingly, ,
calculated as G"/G' as a function of frequency, showed virtually no
dependence on frequency (except a small increase above 2 Hz), strain
amplitude, and the conditions of the strip (Fig. 2C). The
mean value of was ~0.1, which is in good agreement with other
reported data (11, 26, 35,
41). The linear viscoelastic model provided good quality
fits to the data. However, the RMSE values obtained from fitting the
model to the data depended slightly on the condition. Compared with
control, they decreased by ~10% at the same mean length and
increased by 50-80% at the same mean force (data not shown).
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Fig. 2.
Storage modulus (G'; A), loss modulus (G";
B), and hysteresivity (; C) as a function of
frequency for a typical strip. Solid and open symbols, data before and
after elastase treatment, respectively. Circles and triangles, data at
strain amplitudes of 5 and 15%, respectively. Solid lines are model
fits.
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We evaluated the tissue properties before and after elastase and
collagenase treatment by examining the parameters G, H, R, , and kd. The population means of the
parameters obtained at strain amplitudes of 5, 10, and 15% before and
after elastase treatment are shown in Fig.
3 and before and after collagenase treatment in Fig. 4. In general, G and H
decreased and R and kd increased with
increasing strain amplitude and were statistically significant in many
cases. At the same mean length, G and H decreased after elastase
treatment by 30-35% (P < 0.02), and they
decreased even more significantly with collagenase treatment by
45-50% (P < 0.0004). Although R did
not change after elastase treatment, it decreased statistically
significantly in the collagenase-treated condition (P < 0.0001) independent of the strain amplitude. The effect of treatment
(collagenase or elastase) on both G and H was highly significant, but
there was no difference in the reduction in G due to elastase or
collagenase, whereas H was statistically significantly smaller after
collagenase treatment (P < 0.01). This resulted in a
slight (but not significant) increase in after collagenase
treatment so that the difference in after collagenase and elastase
became significant (P < 0.05). Nevertheless, did
not change compared with control after either treatment. The
kd increased after both treatments but reached a
statistically significant level (P < 0.001) only after
collagenase treatment. These changes in the parameters were accompanied
by significant decreases in the static operating stress in the strip
(~20 and ~30% decreases after elastase and collagenase treatment,
respectively, compared with control).
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Fig. 3.
Means ± SD of tissue damping (G;
A), tissue stiffness (H; B), Newtonian
resistance (R; C), (D), and
harmonic distortion (kd; E) measured
at 3 different strain amplitudes before (Ctr) and after elastase
treatment taken at the same mean length (ML) or same mean force (MF) as
in control. * Statistically significant difference (P < 0.05) between the value of a parameter (at a given strain amplitude and
condition ML or MF) and its corresponding value in control.
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Fig. 4.
Means ± SD of G (A), H (B),
R (C), (D), and
kd (E) measured at 3 different strain amplitudes before (Ctr) and after collagenase
treatment taken at the same ML or same MF as in control.
* Statistically significant difference (P < 0.05)
between the value of a parameter (at a given strain amplitude and
condition ML or MF) and its corresponding value in control.
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At the same mean force, both G and H increased statistically
significantly after collagenase treatment by 21% (P < 0.0002) and 29% (P < 0.0001), respectively, whereas G
and H increased only slightly after elastase treatment by 6 and 8%,
respectively. The value of showed a 10% increase after collagenase
treatment and a 17% reduction after elastase treatment, which was
statistically significant (P < 0.05). The values of
R increased statistically significantly after collagenase
treatment (P < 0.01) but not after elastase treatment.
The kd, and hence the degree of tissue
nonlinearity, was more sensitive to collagenase treatment. The
kd increased significantly by 40%
(P < 0.0001) after the strips were treated with
collagenase, whereas the corresponding percent increase in elastase-treated strips was only 20% (P < 0.008).
The time responses of the mechanical parameters normalized with
respect to their control values in two strips after elastase and
collagenase treatment are shown in Fig.
5. The digestion of collagen fibers had a
markedly stronger and faster effect on the parameters than did the
digestion of elastin fibers. Both G and H decreased by ~60% after
1 h of collagenase treatment. The elastase caused a similar but a
slower response in the strip. Both G and H decreased by 50% after
3 h of treatment. The values of R and fluctuated
and did not show systematic change after either enzyme treatment. The
kd increased by ~10% after 1 h following
elastase and collagenase treatment.
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Fig. 5.
Time dependence of the mechanical moduli G
(A), H (B), R (C), (D), and kd (E) normalized
by their value immediately before digestion was started
(Gc, Hc, Rc,
c, and kd,c, respectively).
 , Data obtained during elastase digestion;  ,
data obtained during collagenase digestion.
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DISCUSSION |
In the present study, we focused on the mechanical role of
the extracellular matrix, i.e., the elastin-collagen fiber network, by
measuring the mechanics of tissue strips in an organ bath, which
eliminates the influence of air-liquid interface. The mechanical roles
of elastin and collagen fibers were probed by examining the mechanical
properties of tissue strips obtained before and after treatments with
elastase and collagenase. Our main findings are as follows:
1) because the G' and G" were very sensitive to both
collagenase and elastase treatment, the elastin-collagen fiber network
dominates the macroscopic elastic and dissipative properties of the
tissue strip; 2) because was nearly insensitive to
either treatment, appears to be independent of the number of intact
fibers; and 3) because the operating stress and strain amplitudes we used in the study cover approximately the range of normal
breathing around functional residual capacity, collagen fibers also
contribute to tissue elasticity during normal breathing. Before
interpreting these results, we first discuss some important considerations regarding the manner in which the enzymatic digestion takes place.
The extracellular matrix can be altered biochemically by various enzyme
treatments. The extent of biochemical and structural change in the
fiber matrix depends largely on the specificity of these enzymes.
Modification of the physical characteristics of the tissue by the
enzymes depends on a number of factors, such as the molecular structure
of the target and its affinity for the enzyme, penetration of the
enzyme, and perhaps the total amount of tissue to be digested.
Pancreatic elastase is a highly active elastin-decomposing enzyme and
degrades amino acids at sites of the elastin molecule (23,
27). Collagenase attacks and cleaves amino acids at
specific binding sites of the collagen molecule (17,
32). From electron micrographs, Karlinsky et al.
(15) observed disruption of collagen fibers in parenchymal
tissue treated with collagenase and of elastic fibers treated with
elastase. They have also shown that the collagenase was not active
against elastin and that elastase had no detectable activity against
collagen. In the present study, no attempt was made to confirm the
specificity and extent of degradation of elastin and collagen produced
by elastase and collagenase treatment. Nevertheless, from our results it appears that the enzyme digestion is appropriate to study the mechanical contributions of the specific structural constituents, such
as elastin or collagen, in the peripheral part of the parenchyma.
Tissue Elastic Behavior
Our data suggest that both elastin and collagen contribute to
tissue elasticity in the strain range applied, which roughly corresponds to functional residual capacity during normal breathing. This somewhat contradicts the notion of independent functionality of
elastin and collagen fibers. Karlinsky et al. (15)
reported that the compliance of elastase-treated lungs decreased only
at low and medium lung volumes, whereas compliance of
collagenase-treated lungs decreased only at high lung volume. Their
data suggest that elastin provides great extensibility at low volumes,
whereas collagen limits lung extensibility at high volumes. However,
data obtained from experiments in tissue strips and lungs are not
directly comparable because of the differences in boundary conditions,
protocols, lack of gas-liquid interface, and so on. Also, the
parenchymal strip undergoes uniaxial deformation, whereas lungs undergo
a more uniform expansion during breathing. Although one can compare the
quasi-static stress-strain curves before and after treatment, we were
primarily interested in the dynamic contribution of the fibers to the
macroscopic behavior of the tissues. Thus we measured the dynamic
moduli and nonlinearity of the samples before and after digestion
around two operating points on the stress-strain curve: at the same
mean length and at the same mean stress as in control. These two
specific operating points were chosen to better understand the separate
roles of lung volume and transpulmonary pressure in lung mechanics.
At the same mean length or strain level, tissue elasticity as
characterized by H substantially decreased after either elastase or
collagenase treatment. This appears to be in agreement with the notion
that the extracellular elastin-collagen fiber network is the principal
contributor to tissue elasticity. The collagen fibers are nonlinear and
behave as a nearly perfect spring with large stiffness and can be
extended in length by only a few percent (34). The elastin
fibers are linear and viscoelastic with a stiffness of at least two
orders of magnitude lower than that of the collagen fibers
(10). It is worth noting that the H of the tissue strip is
far less than that of collagen or elastin fibers alone. This is most
likely a network effect: the total stiffness of a large network of
interconnected springs can be less than the spring constant of
individual springs. After digestion, the number of collagen or elastin
fibers is reduced in the fiber network. When this network is stretched
to the same mean length as before digestion, due to the reduction in
the number of springs, the static stress developed by the network will
be less than before digestion. Thus the incremental modulus or H of the
system will also decrease. The fact that digesting both elastin and
collagen results in a large decrease in H is also noteworthy. Mercer
and Crapo (23) found that the spatial distribution of
collagen is fairly uniform in the tissue. If we take a composite
network of soft and very stiff springs, such as that proposed by Wilson
and Bachofen (40) in which the stiff springs are spatially
uniformly distributed and stretch the network, it is conceivable that
most of the elastic response will primarily be due to the stiff
springs. Alternatively, if the soft springs are partially eliminated
(e.g., by digestion of elastin), the H of the system should not change appreciably. Yet Fig. 1 shows a large change in the quasi-static stress-strain curve, and Fig. 5 shows that there is a significant decrease in H as a function of time during elastin digestion. Given
that elastin has a Young's modulus (Y) at least two orders of magnitude smaller than collagen, it is surprising that, after elastin digestion, H decreases fairly rapidly by 40% in 1 h. This indicates that the actual topology of the network must play an important role in its macroscopic behavior.
To better understand tissue elasticity, we can study how various
network models that have been proposed in the literature would respond
to digestion. These models include fiber recruitment type of models,
such as those proposed by LaBan (16), Romero et al.
(30), or Maksym et al. (20, 21),
the line element model of the alveolar duct introduced by Wilson and
Bachofen (40), or other geometric models (7,
21). In the finite element model of the alveolar duct and
alveoli of Denny and Schroter (7), the elastin and
collagen fibers run parallel in the alveolar walls. In the alveolar
duct model of Wilson and Bachofen (40), the parenchyma is
conceptualized as a hexagonal mesh of line elements. The H of each line
element represents the resultant elasticity of both collagen and
elastin fibers. In both models, elastin and collagen would be stretched
simultaneously as the degree of deformation increases. However, the
contribution of the stiff collagen fibers becomes significant only at
high strains. This also means that the network should not be very
sensitive to collagen digestion at low strains. Our data are not
consistent with this interpretation. First, the tissue is extremely
sensitive to collagen digestion at all strains (see quasi-static
stress-strain curve in Fig. 1). Second, if collagen and elastin are
indeed mechanically in parallel, then the total elastic response would
be dominated by the much stiffer collagen. Thus disruption of elastin
fibers induced by enzymes could not result in a substantial decrease in
the elasticity of the tissue. Indeed, in the model of Denny and
Schroter (7), it was necessary to eliminate over 95% of
elastin to obtain an appreciable effect on the stress-strain curve. The
recruitment models of Maksym and Bates (20) and Romero et
al. (30) predict that the elastic behavior of lung tissue
is mostly determined by the stretched soft elastin fibers, but with
increasing strain the stiff collagen fibers are recruited. Also, as
they begin to contribute to the mechanics, the stress-strain curve
becomes more and more nonlinear. This idea is very attractive.
Depending on the model configuration and the initial prestress, these
kinds of models may be able to account for the fact that digesting
either elastin or collagen can result in a large change in the
stress-strain curve.
At the same prestress level, H estimated from the oscillatory data
remained approximately the same after treatment with elastase, whereas
it increased significantly after treatment with collagenase. Moretto et
al. (26) found that H in elastase-treated strips remained
unchanged at a fixed low prestress level, which is in agreement with
our results. However, they also found that, after elastase treatment, H
increased by up to severalfold in magnitude at a fixed high prestress
level. Because of disruption of elastin fibers, the tissue strips had
to be stretched to a larger length to reach the same prestress as in
control. As a result, recruitment of intact collagen fibers under a
larger degree of extension most likely dominated tissue elasticity at
the macroscopic level. From this analysis, one would expect a decrease
in tissue elasticity when the tissue strip was treated with
collagenase. Surprisingly, however, at the same prestress, H also
increased after collagenase treatment.
We can better understand the difference between incremental tissue
elasticity at the same mean length and at the same mean stress by
developing a simple continuum model of the fiber network. Let us
consider a system composed of a spatial distribution of elastic springs
in parallel with each characterized by its incremental spring constant
k = k(x, y; ). Here
x and y are the coordinates along the
cross-sectional area (A) of the strip, and is the strain
in the z direction. We also assume that the incremental modulus Y of the strip explicitly depends on , because
the tissue displays an exponential stress-strain curve
(34). If the density of springs, i.e., the number of
springs per unit A is 
(x, y), then
Y is given by
|
(8)
|
For simplicity, we assume that the system is homogeneous, i.e.,
k and are the same everywhere inside the tissue, so that Eq. 8 reduces to
|
(9)
|
where 0 denotes the equilibrium density of fibers.
Suppose now that the effect of digestion on the tissue is to uniformly reduce the density of fibers in the tissue. We express this
mathematically by explicitly making a function of time
|
(10)
|
where f is the fraction of remaining fibers after a
digestion period of t and depends on the fiber type (e.g.,
elastin or collagen), the actual enzyme and its specificity, the
concentration, and so on. After digestion, Eq. 9 can be
written as
|
(11)
|
Equation 11 is now in a form suitable to discuss our
results. If we compare the incremental moduli at the same mean length before and after digestion, then is the same in Eq. 11
for the control and the digested strip. However, because f(t)
< 1, Y after digestion must be smaller than in
control. If we compare Y at the same mean stress before and
after digestion, then the strain 1 before digestion is
smaller than the strain 2 after digestion. Due to the
exponential nonlinearity of the stress-strain curve, k(1) < k(2).
Thus, after digestion, the fibers are stretched more and their
k is higher. However, we also have a decreased fiber
density. Therefore, if the increase in k due to an increase in strain from 1 to 2 is larger than the
decrease in f(t), the macroscopic Y will increase
after digestion. This is the case for collagenase digestion (Fig. 4).
Alternatively, when the increase in k is balanced by a
decrease in fiber density, then the macroscopic incremental
Y can take similar values before and after digestion just
like in our data following elastase treatment (Fig. 3). Thus the
competing effects of decreasing fiber density and stretching the
remaining fibers will determine the incremental moduli in any given condition.
Tissue Hysteretic Behavior
The viscoelastic properties of lung tissue are reflected in the
particular stress relaxation behavior or the frequency dependence of
the complex modulus. When a step in strain is applied to the tissue,
the stress follows a slowly decaying power law over many time decades
(3, 29, 35). This type of
behavior is equivalent to a frequency dependence of the modulus that is
consistent with our constant-phase model in Eq. 4. Indeed,
the constant-phase model fits the data reasonably well under all of the
conditions we studied. More importantly, the exponent of the power
law in Eq. 4, which is related to the of the material,
changed very little following alterations of the extracellular matrix
constituents. In other words, parameter G behaves very similarly to
parameter H under all conditions: at the same mean length, the G
decreased significantly after elastase and collagenase treatment,
whereas, at the same prestress, it remained the same after treated with elastase and increased significantly after collagenase treatment. This
resulted in a small decrease in after elastin digestion. The
elastin digestion has an effect on the elastin fibers, which are
viscoelastic. On the other hand, collagen is almost purely elastic.
Thus, if the contribution of elastin fibers to the macroscopic viscoelasticity decreases, one would expect that the tissue would become more elastic. Nevertheless, changes in were small compared with changes in G and H. This can be visualized by plotting the relative change in G against the relative change in H for the various
conditions. Figure 6 shows that, indeed,
changes in the dissipative properties always follow changes in the
elastic properties of the fiber network. In Fig. 6, we also show data
from our previous study using methacholine challenge (41).
The data suggest that, irrespective of the manner in which we alter
tissue elasticity (e.g., challenge of interstitial cells, passive
length change, digestion of elastin or collagen), G always follows it.
This, in accord with Fredberg and Stamenovic (9), reflects
the very fundamental property of lung tissue as a composite matter.
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Fig. 6.
Relationship between relative change in G and H for
various interventions. Data for methacholine challenge were obtained
from Ref. 41.
|
|
The origin of this peculiar hysteretic behavior of lung tissue is still
speculative. Fredberg et al. (8) proposed that cross-bridge cycling within the contractile cells in the parenchyma plays an important role in tissue . Although it has been
demonstrated that cross-bridge cycling may affect tissue hysteresis
during active cell contraction induced by various types of agonists
(8), it does not seem to be important in baseline
conditions, because we found that cross-bridge cycling contributes at
most 10% to total tissue hysteresis (41). An alternative
explanation is the fiber-fiber interaction mechanism described by
Mijailovich et al. (25). In this model, the fibers are in
close contact, and the load between the fibers is transferred by a
stick-and-slip motion. The friction generated between the fibers is
considered as the primary source of tissue hysteresis. This model
provides predictions that are in reasonable agreement with the measured H and . Although it is still uncertain whether physical contacts exist between fibers in the lung parenchyma, Brown et al.
(4) provided some experimental evidence using electron
microscopy that, in certain connective tissue structures such as
ligamentum propatagiale, elastin and collagen fibers are in close
contact, and hence they may be mechanically connected in parallel. Suki et al. (35) suggested that a mechanistic basis for the
power law stress-relaxation behavior is a consequence of the so-called "reptation" motion of the collagen-elastin fibers, whereby the fibers rearrange through a series of highly constrained "wormlike" displacements or undulations under the influence of external stresses. In this picture, the distribution of fiber diameter and length is an
important factor in determining the power law type of stress relaxation. Our data suggest that tissue and hence the stress relaxation exponent were marginally affected by fiber digestion. Thus
the reptation model would contradict our data if the enzymes induced
fragmentation of the fibers and hence alterations in fiber concentration and distribution of fiber width and length. However, Morris and Stone (27) showed in electron microscopic
images that elastase induced small holes within the elastin fibers
without removing parts of the fibers. Whereas a collagen molecule is
cleaved by collagenase at a specific site leading to the production of two fragments, considering that a collagen fiber consists of a large
number of cross-linked tropocollagen molecules, fragmentation of parts
of these molecules may not lead to complete cleavage of an entire
collagen fiber. Thus, during digestion, the fibers would be damaged and
losing elasticity, but the actual mechanism of fiber motion may not be
significantly altered. Therefore, our data do not exclude, neither do
they support, fiber reptation as the mechanism for tissue . If fiber
fragmentation does occur after digestion, then it is likely that the
cross linking between fibers and the ground substance may play an
important role in lung tissue resistance. Stromberg and Wiederhielm
(34) argued that the stress relaxation could be considered
a consequence of delayed alignments of the fibers with macroscopic
stress. This delay would result from the resistance against the
movement of the fibers within the dense, viscous ground substance.
Tissue Nonlinearities
Lung tissue displays two distinct types of nonlinearities:
nonlinear elastic properties characterized by the quasi-static stress-strain curve (Refs. 20, 33; Fig. 1) and dynamic nonlinearities characterized by the dependence of the dynamic moduli on strain amplitude (Refs. 24, 41; Figs. 3 and 4). Of particular interest is the
fact that the nature of static and dynamic nonlinearities is opposite:
the incremental k along the quasi-static stress-strain curve
is an increasing function of stress and strain, whereas the dynamic
nonlinearity is a decreasing function of strain amplitude around a
fixed operating point. The quasi-static nonlinearity is likely related
to the recruitment-like behavior of collagen fibers (20,
21, 30) during stretching due to the highly nonlinear stress-strain behavior of collagen itself (34).
The origin of the dynamic nonlinearity is still not clear. It is likely that the nonlinearly elastic collagen, the linearly viscoelastic elastin, and the viscous ground substance all contribute to this phenomenon. Several models have been suggested to account for this type
of nonlinearities. For example, various cascade combinations of linear
viscoelastic and nonlinear elastic subsystems were applied to both
whole lung pressure-volume (19, 37) and
tissue strip stress-strain data (22, 42).
Although these models can fit the data well, they are phenomenological
in nature. Recently, Bates (2) derived a nonlinear model
of lung tissue rheology in which the fibers in the tissue are modeled
as rigid rods. When a step in strain is applied to the tissue, the
fibers rearrange with an instantaneous elastic response, and, with
time, the original random orientation of the fibers is restored via
diffusion, which gives rise to stress relaxation. The total stress
response of this model is nearly separable in instantaneous stress and
time-dependent relaxation, and hence the model provides a possible
mechanistic basis of Fung's (10) quasi-linear
viscoelastic theory. Although this model is able to account for the
nonlinearities in the instantaneous elastic response of the tissue
during a stress relaxation experiment, it fails to account for the
dynamic nonlinearities.
Our present findings suggest that dynamic nonlinearities increase after
a change in the structure of the extracellular matrix. At the same mean
stress, the kd increased considerably after
collagenase treatment and slightly after elastin digestion. In our
previous study, we postulated that increases in tissue dynamic
nonlinearities following methacholine challenge were a consequence of
stiffening of the fiber network induced by cell contraction
(41). If this were true, any increase or decrease in H
would be followed by an appropriate increase or decrease in
kd. In other words, one might expect a similar
coupling between elasticity and nonlinearity as the coupling between G
and H shown in Fig. 6. However, whereas at the same mean length H
decreased after either digestion, we never found a decrease in
kd that seemed to violate this coupling. Indeed,
plotting the relative change in kd as a function
of the relative change in H in Fig. 7
demonstrates that there is no single linear relationship between these
variables. Fig. 7 also shows our previous data of
kd and H after methacholine challenge of the
tissue strips. A striking feature of the data is that, when the H of
the tissue is changed via a passive change in mean stress or an active
cell contraction, the data follow a well-defined trajectory with a
positive slope. However, when the fiber network is biochemically and
hence structurally altered, the data follow an apparently orthogonal
trajectory. Recall that macroscopic elasticity is determined by the
number of fibers and their incremental H (see Eq. 11). It
may be that the elasticity at the same mean length is mostly determined
by the number of intact fibers and not by the nonlinear stress-strain
curve of the collagen. After digestion, the number of intact fibers
decreases. Thus the corresponding H decreases too, and the points on
the graph must move to the left. On the other hand, because the
remaining collagen fibers operate at a slightly higher mean length, the
system becomes more nonlinear and kd moves
north. This decoupling of elasticity and nonlinearity may prove very
useful in detecting biochemical and/or structural alterations in the
connective tissue matrix due to the presence of interstitial diseases.
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|
Fig. 7.
Relationship between relative change in
kd and H for various interventions. Data for
methacholine challenge were obtained from Ref. 41.
|
|
In summary, our findings suggest that, after digestion 1)
the fraction of intact fibers decreases; 2) at the same mean
length, a decrease in the number of intact fibers leads to a decrease in dynamic moduli; 3) at the same mean force, the collagen
fibers become more stretched than at the same mean length, and hence they operate at a higher portion of the nonlinear stress-strain curve,
which results in an increase in the dynamic moduli; and 4)
whereas damping and elasticity appeared to be always coupled, dynamic
nonlinearity was decoupled from elasticity after digestion and was
sensitive to the stretching of collagen. This latter fact may find
important implication in detecting structural alterations in the
connective tissue of the lung.
| |
ACKNOWLEDGEMENTS |
This study was supported by National Heart, Lung, and Blood
Institute Grants HL-59215-01A1 and HL-62269.
| |
FOOTNOTES |
Address for reprint requests and other correspondence:
B. Suki, Dept. Biomedical Engineering, Boston Univ., 44 Cummington St.,
Boston, MA 02215 (E-mail: bsuki{at}bu.edu).
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.
Received 9 November 1999; accepted in final form 3 February 2000.
| |
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ABSTRACT
INTRODUCTION
