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Vol. 83, Issue 5, 1420-1431, 1997
1 Department of Biomedical
Engineering, ABSTRACT Yuan, Huichin, Edward P. Ingenito, and Béla Suki.
Dynamic properties of lung parenchyma: mechanical contributions of
fiber network and interstitial cells. J. Appl.
Physiol. 83(5): 1420-1431, 1997.
elastic modulus; hysteresivity; nonlinearity; collagen-elastin
matrix; cross bridge
INTRODUCTION THE MECHANICAL PROPERTIES of the lung parenchyma are
critical determinants of the physiological functions of the lung. For example, the stress-strain relationship of the parenchyma determines how lung volume changes with respect to transpulmonary pressure. It
also influences the distribution of ventilation and thus impacts significantly on gas exchange. The hysteretic properties of parenchymal tissues together with alveolar surface film are the two most important components accounting for lung tissue resistance, which appears to be a
major component of total lung resistance around the breathing frequencies (17, 18, 25, 26, 38). Although various models have been
proposed (9, 28, 36), the basic mechanisms at the structural level that
determine tissue resistance and elastance of the lung remain largely
speculative.
From a structural point of view, lung parenchyma can be considered as a
mesh of connective tissue elements (40). The extracellular matrix is
composed of protein fibers and amorphous matrix or ground substance.
The protein fibers, thought to be the main load-bearing elements within
the tissue, include elastin and collagen fibers (33, 40). The cells
that synthesize and secrete individual extracellular matrix components
are embedded in or lie on the connective tissue matrix (40). However,
little is known about the mechanical interaction of these components
(4) and how they affect lung mechanics, particularly the hysteretic
properties of lung tissues. Several models have been proposed to
account for how the fiber elements interact to determine the
macroscopic mechanics of the lung, such as the fiber-fiber interaction
model (27), the reptation theory describing fiber motion (36), or the
gradual straightening of wavy fibers (23). Interstitial cells also
influence the overall mechanics because lung tissues respond to various
agonist challenge such as methacholine (MCh) or histamine (9, 18, 24,
26, 31, 32). Indeed, Fredberg et al. (9) found that the hysteretic
properties of parenchymal tissue strips correlated with the contractile
state of tissues responding to different agonists. However, Fukaya et
al. (12) observed that the length-tension relationship of the lung
parenchyma did not change appreciably within 36 h, over which period
viability of the tissue is not maintained. To our knowledge, no direct
measurement has been made to compare the contributions of cellular
elements and fiber network to the macroscopic mechanical properties of parenchymal tissues. This is the primary purpose of the present study.
We measured the dynamic properties of lung parenchymal tissue strips in
their viable and nonviable states. We also assessed the influence of
metabolically active cells on tissue mechanics during contraction
induced by MCh challenge. To simultaneously follow all parameters
characterizing the mechanical status of the strip, we applied
specially designed pseudorandom length oscillations that
contained energy at selected discrete frequencies between 0.07 and 2.4 Hz. By minimizing the bias on the apparent complex modulus due to
nonlinearities, this approach allows for mapping the frequency
response as well as characterizing the nonlinearities from a
single force-length recording. Our results indicate that connective
tissues play an important role in determining the mechanical status of
the parenchymal strip even during contraction of interstitial cells.
METHODS Sample Preparation
Experimental Setup
We investigated
the contributions of the connective tissue fiber network and
interstitial cells to parenchymal mechanics in a surfactant-free
system. In eight strips of uniform dimension from guinea pig lung, we
assessed the storage (G
) and loss (G") moduli by using
pseudorandom length oscillations containing a specially designed set of
seven frequencies from 0.07 to 2.4 Hz at baseline, during methacholine
(MCh) challenge, and after death of the interstitial cells.
Measurements were made at mean forces of 0.5 and 1 g and strain
amplitudes of 5, 10, and 15% and were repeated 12 h later in the same,
but nonviable samples. The results were interpreted using a linear
viscoelastic model incorporating both tissue damping (G) and stiffness
(H). The G and G" increased linearly with the logarithm
of frequency, and both G and H showed negative strain amplitude and
positive mean force dependence. After MCh challenge, the G and
G" spectra were elevated uniformly, and G and H increased by
<15%. Tissue stiffness, strain amplitude, and mean force dependence
were virtually identical in the viable and nonviable samples. The G and
hence energy dissipation were ~10% smaller in the nonviable samples
due to absence of actin-myosin cross-bridge cycling. We conclude that
the connective tissue network may also dominate parenchymal mechanics
in the intact lung, which can be influenced by the tone or contraction
of interstitial cells.
Linearity and hysteresis of the measurement system itself were tested with a steel spring of known stiffness (0.2 N/cm2) similar to that of the tissue strip. The spring was attached to the apparatus in the same way as the lung tissue strip, and the same experimental protocol was carried out. The measured spring stiffness showed neither frequency nor amplitude dependence and thereby appeared to be ideally Hookean. The hysteresis area showed very weak frequency and amplitude dependence, and it was very small, more than an order of magnitude smaller than that of the tissue strip. In other words, the apparatus was able to measure tissue elastic and dissipative properties with very small hysteresis area, an order of magnitude smaller than that expected for the parenchymal strip.
Protocol
The experiments were performed at room temperature. Before the protocol was started, the system had to be aligned. Proper alignment was crucial and was ensured as follows. The force-length relationship of the strip was displayed on an oscilloscope during sinusoidal oscillations, and the hysteresis area between force and displacement was minimized by adjusting the horizontal position of the actuator. The strip was then preconditioned by performing single slow stretch to 2 g of mean force. The mean force was reset to 0.5 g, and the strip was oscillated sinusoidally at 2 Hz for ~5 min until steady state was reached. The dynamic properties of the strip (see below) were measured at 5, 10, and 15% peak-to-peak strain amplitudes of the length oscillations. A similar preconditioning procedure was applied again, and the measurements were repeated at a mean force of ~1 g. After control measurements, MCh (10
5 M)
was added to the tissue bath, and the dynamic response was measured
continuously for 20-25 min. In one strip, the MCh response was
obtained at 0.5 g of mean force and 5% strain amplitude, whereas for
the other seven strips, the mechanical properties were measured at a
mean force of 1 g and 10% strain amplitude. After completion of the
MCh challenge, the MCh was washed out, and the strip was left at room
temperature in the tissue bath for at least 12 h, a period over which
cellular components become nonviable. Another strip was also prepared
from a nearby region of the same lung and stored at 4°C during this
period. The control protocol was then repeated for both strips. The
loss of viability of these two strips was confirmed by observing no
response to MCh. To identify the various conditions, the control tissue
strips will be denoted by V to indicate a viable strip. The same
samples after 12 h of storage in the tissue bath will be denoted by N
(nonviable strip), and the strips prepared from the same lung and kept
at 4°C for 12 h will be called preserved, denoted by P.
Measurement Approach
Instead of the traditional sinusoidal oscillation approach, we used a broad-band pseudorandom displacement input signal. The signal was a sum of seven sinusoids chosen according to the nonsum-nondifference (NSND) frequency composition introduced by Suki and Lutchen (37). The NSND signal includes frequency components that are not integer multiples of each other, and the input frequencies cannot be obtained as a linear combination of two, three, or four different input frequencies corresponding to NSND orders of two, three, or four, respectively. The essence of the NSND signal is to avoid harmonic distortion and minimize the influence of cross talk in the output at the input frequencies. For not strongly nonlinear systems, the interactions among the components are reduced to a level that the response can be considered as if it were measured with independent sine waves of an equivalent amplitude (37). In this study, we chose a fourth-order NSND signal with flat power spectrum and random phases as the displacement input signal. The length of the NSND sequence was 2,048 points, so that using a sampling rate of 50 Hz corresponded to a time period of 41 s. The frequency components and their corresponding phase angles are given in Table 1. For each condition, a total of three NSND cycles was delivered, and only the last two cycles were collected to avoid transients.
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Data Analysis
Characterization of strip mechanics. The displacement input and force output were normalized to obtain strain
and stress T as
![&egr;(<IT>t</IT>) = [<IT>l</IT>(<IT>t</IT>) − <IT>l</IT><SUB>o</SUB>]/<IT>l</IT><SUB>o</SUB>; T(<IT>t</IT>) = F(<IT>t</IT>)/<IT>A</IT><SUB>o</SUB>](/content/vol83/issue5/fulltext/1420/img001.gif)
|
(1) |
|
(2) |
is
the circular frequency. In Eq. 2,
G is the storage modulus or elastance defining the component of
the stress that is in phase with the displacement. G" is the
loss modulus or component of the stress that is in phase with strain
rate. The calculation of G* was carried out as follows. 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 (2,048 points/cycle) with an overlap
percentage of 25%. The complex spectra for each cycle was obtained by
taking the fast Fourier transforms of the blocks. The complex modulus
G* was then estimated in the frequency domain by taking the ratio of
the average T and spectra, which had been corrected for the
frequency response of the measuring apparatus. The hysteretic
properties of the tissue were characterized by the tissue
hysteresivity, 
, introduced by Fredberg and Stamenovic (11) and
defined as the ratio of dissipated to stored energy over a force-length
cycle, which is simply G"/G. This allows the calculation
of as a function of frequency.
Viscoelastic modeling.
The special design of the NSND input signal allows a robust estimation
of the apparent linear transfer function of the system at the NSND
frequencies in the absence of very strong nonlinearities. Therefore, to
evaluate the dynamic properties of the tissue strip, we fitted a linear
viscoelastic model to the complex modulus spectra at the seven input
frequencies at both mean force levels and at all input amplitudes.
Several viscoelastic tissue models have been proposed and examined in
the literature (3, 13, 17-21, 29, 30, 36). We chose the
constant-phase model that originated from the power law type of stress
relaxation of a rubber balloon (20)
|
(3) |
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. (18). The
tissue impedance Z() is described by
|
(4) |
|
is not an independent parameter and governs the frequency dependence of the real and imaginary parts of Z(). With only
two parameters, G and H, Hantos et al. (17, 18) showed that this model
can fit the tissue impedance in cat and dog lungs better than other
viscoelastic models. Additionally, a mathematical framework and a
possible molecular basis of Eqs. 3 and 4 have also been offered (36). According to our preliminary modeling, we observed that the tissues behaved as if they had a purely viscous component
R, which was also added to the complex
modulus G*() such that
|
(5) |
, since is between 0.04 and 0.1 (3,
17, 36). The second term is the loss modulus, which also increases
quasilogarithmically and with the same exponent as the storage modulus,
since R is negligible at low frequencies. The tissue
hysteresivity, , in this model is the ratio of the imaginary and
real parts of G*. However, because the term R is small
compared with G
and to
remain consistent with previous analyses of whole lung mechanics (17,
25, 26, 36, 38), we define as the ratio G/H except when we examine
the frequency dependence of directly from G and G".
By use of a global optimization algorithm (7), the model parameters
were estimated by minimizing the following root-mean-square error
(RMSE)
|
(6) |
i refers to the NSND
frequencies and N = 7 is the number of
NSND frequencies.
Harmonic distortion.
When a NSND broad-band input is applied, the degree of system
nonlinearity can be characterized by the so-called extended harmonic
distortion index,
kd, which
quantifies the influence of both harmonic distortion and cross talk
(42). The coefficient kd is defined as
|
(7) |
Statistical Analysis
By use of paired t-test and analysis of variance, statistical analysis was carried out to compare the mechanical properties of the parenchymal strips corresponding to the different mean forces, input levels, and conditions (V, N, P).RESULTS
Basic Tissue Mechanics
Examples of G and G" as a function of frequency in one of
the tissue strips are shown in Fig. 1,
A and
B, respectively, corresponding to the
two mean forces and the three strain amplitudes. As evident from Fig.
1, the most important feature of the mechanical behavior of the
parenchymal strip is that both G and G" increased
steadily and approximately linearly with the logarithm of frequency
regardless of the mean force and strain amplitude. G increased
by ~20 and 30% with increases in frequency from 0.07 to 2 Hz for
mean forces of 0.5 and 1 g, respectively. The magnitudes of both
G and G" were mean force dependent, i.e., the tissue was
stiffer and more dissipative at 1 than at 0.5 g. In addition, at both
mean forces, G and G" showed a negative strain amplitude
dependence. These findings are consistent with data found in other
species (27, 29) and in whole lungs measured in situ (17, 18, 25, 26, 30, 38).
(A), loss
modulus G" (B), and
hysteresivity (C) as a function
of frequency for a typical viable strip. Open and filled symbols denote
data at 0.5 and 1 g of mean force, respectively. 
and 
, 
and
, and 
and 
denote data at strain amplitudes of 5, 10, and
15%, respectively.
The values of G are close to those obtained in guinea pigs by
Ingenito et al. (21) using sinusoidal oscillations corresponding to a
similar prestress level. The magnitude of G obtained by others
are somewhat higher (9, 24, 27, 32), but their data are not directly
comparable to ours due to differences in species or protocol (mean
force was much higher and/or stretch history was different).
Because G" shows only slight frequency dependence, the
corresponding tissue resistance
(G"/
)
decreases nearly hyperbolically with frequency, which is consistent with whole animal studies (2, 17, 18, 25, 26, 36, 38). The
hysteresivity , calculated as G"/G, showed virtually no dependence on frequency, mean force, or strain amplitude except for
the slight amplitude dependence at 0.5 g (Fig.
1C). All measured strips showed a
qualitatively and quantitatively similar behavior, which is consistent
with data reported in the literature (3, 9, 11, 27, 29, 32).
Mechanics of Viable and Nonviable Tissues
Comparison of the mean force and frequency dependence of G and
G" in a strip in the V and N conditions is shown in Fig.
2. The tissue strip in both conditions
demonstrated a very similar mechanical behavior. Also, the model
provided good quality fits to all data. The RMSE values obtained from
fitting the model to all strip data under all conditions are summarized
in Table 2. Paired
t-test indicated that the RMSE values
corresponding to different conditions were not significantly different
from each other. We therefore concluded that the constant-phase model
provided equal quality fits to the data under all conditions. The good correspondence between model and data suggests that our oscillatory data are consistent with the slow power law type of stress relaxation (Eq. 3 with exponent = 0.075 ± 0.012) observed by Bates et al. (3) in tissue strips and by others in
isolated lungs (19, 30).
(A)
and G" (B) for a strip
oscillated with 10% strain amplitude at mean forces of 0.5 (, )
and 1 g (, ) before (open symbols) and after (filled symbols )
death of interstitial cells. Solid and dashed lines are corresponding model fits.
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We evaluated and compared tissue mechanical properties under different
conditions (V, N, P) by examining the parameters tissue damping G,
tissue elastance H, pure viscous resistance
R, and harmonic distortion index
kd. The
population mean of G for the three strain amplitudes is shown in Fig.
3, A and
B, at the two mean forces. The G
showed a mild negative strain amplitude and a stronger and positive
mean force dependence. For example, when the mean force was 0.5 g for
condition V, the mean G at 5% strain amplitude decreased by 5.2 and
10.8% when strain amplitude increased to 10 and 15%, respectively. As
the mean force increased to 1 g, G increased by 40, 35, and 34% for
strain amplitudes of 5, 10, and 15%, respectively. Analysis of
variance indicated that, although the strain amplitude and mean force
dependence of G were statistically significant
(P < 0.002 and
P < 0.004, respectively), G did not
depend on the conditions V, N, or P. The H displayed a very similar
behavior (Fig. 4). The values of H showed
statistically significant strain amplitude and mean force dependence
(P < 0.002 and
P < 0.02, respectively) but no
dependence on the condition V, N, or P regardless of strain amplitude
or mean force. Nevertheless, across all strain amplitudes and mean
forces, the population means of G and H in the V condition tended to be
higher than in the N condition by 10.9 ± 2.1 and 4.4 ± 3.7%,
respectively.
In contrast to G and H, R displayed a
positive strain amplitude dependence (Fig.
5) that was also statistically significant (P < 0.0003). Interestingly,
R depends on neither the mean force nor the condition (V, N, or P). R is
negligible at low frequencies, but it can amount to up to 20-25%
of G" at the highest frequency (~2.5 Hz). Notably, in the
viable tissue at 0.5 g and with 5% strain amplitude [which is in
the range of normal breathing near functional residual capacity
(FRC)], purely viscous behavior was not observed, since the
population mean of R was not
statistically different from zero. Although the
R is thought to be related to the
viscosity of ground substance (36), its physiological significance is
not clear. Lutchen et al. (26) found a small, purely viscous component
of lung tissue resistance in open-chest dogs but concluded that it had
no physiological relevance to breathing.
Hysteresivity calculated as G/H decreased by ~10% (Fig.
6) when mean force increased to 1 g. This
change was statistically significant
(P < 0.04). The also showed a
slight strain amplitude dependence, i.e., it dropped by ~5% when
amplitude increased from 5 to 15% (P < 0.02), but only at 0.5 g of mean force. Nevertheless, similarly to
all other mechanical indexes, the values of did not depend on the
conditions (V, N, P) of the strips. The negative amplitude and mean
force dependence of are in good agreement with the findings of
Navajas et al. (29). The negative mean force dependence of is also
consistent with the results of Mijailovich et al. (27); however, they
observed a positive amplitude dependence of . At around a fixed lung
volume, Suki et al. (38) found a small negative volume-amplitude
dependence of in intact dog lungs. Again, across all strain
amplitudes and mean forces, the means of in the V condition tended
to be higher than in the N condition by 6.3 ± 3.1%.
. A: 0.5 g mean force;
B: 1 g mean force. For definitions see Fig. 3.
The values of kd
calculated for different mean forces, strain amplitudes and conditions
are shown in Fig. 7. Statistical analysis showed that kd
did not depend on the conditions V, N, or P of the tissue. However,
kd showed strong
positive strain amplitude as well as mean force dependence
(P < 0.0005 and
P < 0.002, respectively). For
example, for condition V and at 0.5 g of mean force,
kd increased by
58 and 120% for strain amplitudes of 10 and 15%, respectively, from
its value at 5% strain amplitude. As mean force increased to 1 g,
kd increased by
25, 21, and 19% for strain amplitudes of 5, 10, and 15%,
respectively. This indicated the presence of nonlinearities in the
tissue strip. The strain amplitude-dependent characteristics of
kd in the lung
tissue strip are very similar to the volume-dependent behavior of
kd in intact
lungs (42), implying that nonlinearities of the lung are mostly
contributed by lung tissues.
MCh Response
Figure 8 shows an example of the model parameters G, H,, and
kd normalized by
their control values (denoted by subscript c) as a function of time
measured at 1 g of mean force with 10% strain amplitude during MCh
challenge. G, H, , and
kd displayed a
peak response with increases of 9, 5, 4, and 5%, respectively, ~5
min after MCh was added. In six of the eight strips, G and H showed a
peak response, whereas in the other two strips they displayed a plateau
response. The time- to-peak response also varied from 5 to 10 min among
the strips. The variability of time course response to MCh challenge
among strips could be partly attributed to different elapsed times
between excision and the start of the experiments. More importantly
perhaps, the differences in the response to MCh challenge may possibly
be due to the fact that the strips were excised from different
locations. Ludwig and Dallaire (24) have shown that the volume
proportions of alveolar, blood vessel, and bronchial walls do not
correlate with the tissue elastance in subpleural parenchymal strips
under baseline conditions. However, in a subsequent study, they
found that, after acetylcholine-induced constriction, the increases in
elastance and resistance and time-to-peak response were greater
in strips from more proximal locations containing greater amounts of
bronchial and blood vessel walls than in subpleural strips (32).
(C), and
kd
(D), normalized by their control values (denoted by
subscript c) evaluated at every 40 s after methacholine (MCh) challenge
in a typical tissue strip. Arrows indicate time at which MCh was added
to organ bath.
Next we applied statistical analysis to examine the influence of MCh on
the mechanical properties of the parenchyma. The data portions during
control and peak response (or plateau in strips without a distinct peak
response) were evaluated for all strips and the mean values of G, H,
R, and
kd are compared
in Fig. 9. During MCh challenge, G
increased by a small amount (6%) from 0.058 ± 0.011 N/cm2 in control to 0.062 ± 0.009 N/cm2, which, however, was
statistically significant (P < 0.02). Similarly, H also increased significantly by 7% from 0.57 ± 0.13 to 0.62 ± 0.13 N/cm2
(P < 0.004), and
kd increased
slightly and nonsignificantly by 6% from 11.6 ± 3.7 to 12.3 ± 3.1. R showed a tendency to increase (from 0.61 ± 0.21 × 103 to 0.68 ± 0.17 × 103
N · s · cm2),
but it did not reach a statistically significant level. These changes
are comparable to those found by others in strips (9, 24, 31, 32) but
smaller than the values obtained in intact animals (18, 25, 26).
3
N · s · cm2.
DISCUSSION
The major stress-bearing elements of the lung parenchyma are the extracellular fiber matrix, the surface lining layer, and the contractile apparatus. The micromechanical basis of parenchymal elasticity is relatively well understood (34, 41). However, the fundamental mechanisms responsible for the dissipative and nonlinear properties of lung tissues are still speculative. In this study, we address one important aspect of this question: what are the separate contributions of the collagen-elastin fiber network and interstitial cells to the mechanical properties of the parenchyma as an integrated tissue system? We achieve this by eliminating the confounding influence of the air-liquid interface in the tissue bath and comparing the mechanics in samples under viable and nonviable conditions. Our findings suggest that tissue mechanics at the macroscopic level are dominated by the connective tissue fiber network, whereas interstitial cells play a less significant role. Before discussing the underlying mechanisms and physiological implications, we first address some issues related to the new methodology that we introduced to assess the dynamic properties of the tissue strip.
Measurement Approach
All previous studies have used sinusoidal length oscillations as input to the tissue strip (9, 21, 24, 27, 29, 31, 32). The advantage of the sinusoidal oscillation approach is that it is simple and easy to analyze the data. However, it has several drawbacks with regard to both linear and nonlinear system analysis. First, to assess the frequency and amplitude-dependent characteristics of tissue mechanical properties at a fixed mean force, measurements need to be repeated at each frequency and amplitude of interest. Because stress relaxation in lung tissue is a long-lasting process (3, 19, 30, 36) and strip viability may vary with time, the mean force may change from one measurement to the other, and hence the data at different frequencies and amplitudes may not correspond to the same condition. Second, a single sinusoid is the least suitable input signal to detect, analyze, and characterize possible nonlinearities in a system (37). Because the main purpose of this study was to carefully compare all aspects including nonlinearities of the mechanical characteristics of the tissue strip, we introduced a new method to investigate these properties. Our NSND pseudorandom input waveform overcomes most of the above difficulties because it allows for an efficient and simultaneous assessment of the frequency-dependent properties as well as a characterization of tissue nonlinearities. Because the response to the NSND input can be considered as if it were obtained by applying individual sinusoids of some equivalent amplitude, the detailed mechanical properties of the strip can be evaluated from a single measurement record, so that the frequency-dependent and nonlinear features correspond to the same mean force. This is indeed very important because, as Fig. 1 demonstrates, mean force has a significant influence on the mechanics. Furthermore, the NSND signal is especially useful in following the dynamic response of the mechanical parameters of the tissue during MCh challenge. By use of single sinusoids, mapping the frequency- and amplitude-dependent characteristics of the tissues is prohibited during the transient response of the system if the period of the sinusoids is comparable to the transients.Comparison of Viable and Nonviable States
The primary result of this study is that the mechanical status of the parenchymal strip is nearly identical in the viable (V) and the two nonviable (N and P) states of the samples. This paradigm gives rise to the following two hypotheses: 1) the interstitial cells do not contribute to the mechanical properties of the parenchyma at all, or 2) the contribution of the cells to the macroscopic mechanics is independent of whether or not the cells are metabolically active.With regard to the first possibility, the interstitial cells embedded in and anchored to the fiber network may remain relaxed or the degree of stretch may not be high enough to bring alteration in the sample's overall mechanical properties. Another possibility is that, because the stiffness of the interstitial cells is much smaller than that of the elastin-collagen fiber network, the mechanical contribution of the cells would be completely negligible. However, during stimulation of the contractile cells both mean force and stiffness increase. Due to the strong coupling between mean force and elasticity for a wide spectrum of agents (9), it appears that the increase in stiffness is a direct consequence of the increase in mean force caused by the contraction of interstitial cells. One may speculate that, during contraction, the activation of contractile cells results in increased local tensions throughout the extracellular fiber network, which in turn produce a corresponding change in the mechanical properties of parenchyma. Furthermore, Fredberg et al. (9) also found that, when the strip was exposed to isoproterenol, an agent that reduces the smooth muscle tone, both mean force and tissue stiffness decreased in a correlated manner. Thus it then seems unlikely that in control the cells do not contribute to the macroscopic mechanics.
To resolve the apparent contradiction that the mechanics are very
similar in the V, N, and P conditions, we first note that the
elasticity of the contractile cells is provided by the number of myosin
heads of the attached cross bridges (9). After death of interstitial
cells, a state of rigor develops (39) in which the cross bridges freeze
and the contribution of the cells to the sample's elasticity would
become passive depending on the number of attached cross bridges. If
the average number of frozen cross bridges within the contractile cell
population is similar to the mean number of attached cross bridges over
a force-length cycle in the viable cells under control conditions, then
we would observe a macroscopically similar stiffness or H in the viable and nonviable samples. The average relative difference between the mean
H values in the V and N conditions was 4.4 ± 3.7%, with H being
larger in viable samples. With regard to energy dissipation, Fredberg
et al. (10) recently showed that mechanical friction in smooth muscle
cells is associated with the rate of cross-bridge cycling. They also
argued that, in the steady state, rapidly cycling cross bridges convert
to slowly cycling latch bridges, a state characterized by low
mechanical energy dissipation. Accordingly, in the nonviable samples,
in which cross-bridge cycling rate is zero due to the lack of metabolic
activity, one may expect less energy dissipation and hence smaller G. This is in good agreement with our data, since the mean G and values corresponding to different strain rates and mean forces were on
average 10.9 ± 2.1 and 6.3 ± 3.1% larger in the viable
samples, respectively, but these differences did not reach a
significant level due to interindividual variability. Although our data
do not allow us to estimate the contribution of cells to parenchymal
elasticity, the above arguments suggest that metabolic activity of
cells may provide ~10% of lung tissue resistance during
physiological tidal stretching near FRC. We therefore favor the second
hypothesis that the mechanical contribution of the cells to the
macroscopic mechanics are about the same in viable and nonviable
tissues, but their contribution remains small both during control and
MCh challenge for the range of strain amplitudes, mean forces, and agonist concentration studied here.
Finally, it may also be possible that the mechanics of parenchyma are contributed to by different mechanisms in the viable and nonviable samples. In this case, however, the apparent mechanical behavior due to the separate mechanisms must be well matched. The existence of a "plastic matching" at low frequencies as a general biomechanical principle has indeed been proposed both at a much larger scale for the components of the respiratory system (2) and at the level of parenchyma between the various constituents of lung tissue (11). Below, we expand on several possible mechanisms that apparently have matched hysteretic properties and can influence the mechanical behavior of the parenchymal tissue strip.
Tissue Mechanics: Possible Mechanisms
The basic characteristics of the viscoelastic properties of lung tissues are that both the storage and loss moduli increase almost linearly with the logarithm of frequency at all strain amplitudes and at both mean forces (Fig. 1). This frequency dependence is consistent with the constant-phase model of Eq. 4, which also implies that the stress relaxation of the tissue would follow a slowly decaying power law (Eq. 3) over many time decades (3, 36). The negative amplitude and positive mean force dependence of the tissue parameters G and H are phenomenologically consistent with either plasticity (19, 35) or nonlinear viscoelasticity (13, 21, 29, 37). Although the fundamental mechanism that gives rise to these particular viscoelastic properties of lung tissue has not been unequivocally identified, several potential mechanisms have been offered.Recently, Suki et al. (36) argued that a mechanistic basis for the constant-phase-type tissue viscoelasticity or 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 particular, the reptation of branching fibers as originally described by de Gennes (14, 15) and the distribution of fiber width and length (6) have been identified as candidate mechanisms at the level of the fiber network responsible for the macroscopic viscoelasticity. It was concluded (36) that, based on the architecture of the microstructure of the lung, slow reptation of branching fibers can contribute to the viscoelastic properties of lung tissue, whereby G and H would depend on the concentration of fibers and their average distance. Our data are indeed consistent with this behavior. Additionally, as argued by Suki et al. (36), on the basis of polymer viscoelasticity, the parameter R may reflect the viscous properties of the ground substance. The fact that R depends on strain amplitude (Fig. 5) suggests that the ground substance behaves as a non-Newtonian viscous fluid. However, the reptation model has several deficiencies. First, when the fibers are in close proximity, they could attach to each other through some charged groups, which would then give rise to static friction. Indeed, dry friction seems to provide a contribution to reptation in gel electrophoresis (5). Second, the reptation does not yet explain the mean force dependence of tissue elasticity.
Another possibility is the fiber-fiber interaction described by Mijailovich et al. (27). This model also identifies the connective tissue network as the primary source of the macroscopic behavior. In this picture, the fibers are in close contact, and a stick-and-slip motion transfers the load between the fibers. In the linear regime, this model provides predictions that are similar to measured stiffness and hysteresivity. Although the predictions of the model were in reasonable agreement with measured data, this model does not take into account the statistical nature of the orientation, length, width, and branching of the fibers within the tissue, and it predicts at higher frequencies a convergence of the elastic moduli corresponding to different amplitudes, which our data do not support.
Fredberg et al. (9) have demonstrated the existence of distinct
mechanical states due to contractile cells in the parenchyma, i.e, the
changes in hysteresivity differed according to the concentration and
type of agonist by which parenchymal tissue was stimulated. More
recently, studying airway smooth muscle mechanics, Fredberg et al. (10)
provided experimental evidence that is directly associated with the
cross-bridge cycling rate and hence the metabolic state of the cells.
Because has been shown to be invariant of frequency, such a
mechanical behavior is also consistent with a slow, power law-like
stress relaxation. Indeed, the hysteresivity calculated from our data
in Fig. 1 is fairly constant with frequency. Thus cell mechanical
properties could, in principle, account for our data. However, we found
that the tissue samples in their viable and nonviable states had nearly
identical mechanical parameters, implying that the extracellular matrix
may also play an important role in the mechanical properties of normal
intact lung tissues. Nevertheless, this does not mean that the cellular
components do not influence the mechanics. The increase of tissue
stiffness during MCh challenge (though small, i.e., <15%) can only
be due to contraction of cells. Additionally, for higher concentrations and different contractile agents, cells may play a much more important role. Indeed, Fredberg et al. (9) found increases in tissue stiffness
as high as 50% when the tissue was challenged with histamine.
It is possible that all of the above mechanisms contribute to some extent to the observed tissue mechanics. If the contributions of the different mechanisms occur at overlapping time scales, then the macroscopic relaxation could be a result of many interacting mechanisms. The lung tissues, being composed of innumerable protein molecules, cells, and fibers interacting in a complicated manner, have been postulated by Bates et al. (3) to exhibit a rheological behavior that is a reflection of the complexity of the system per se. Accordingly, a "nonmechanistic mechanism" could be the so-called self-organized criticality that has been proposed as the common underlying basis for the ubiquitous occurrence of fractals and 1/f noise in nature (1). In this picture, strong nonlinearities exist in the system at the stress-bearing level. During stretching, strain energy would accumulate, and when a threshold is reached, part of the energy is spilled onto its neighbors. When the neighbors take up the energy, they may themselves reach their own thresholds and transfer the extra energy to further neighbors. This can lead to cascades of energy spillover with their energy magnitudes and spatial extension covering orders of magnitudes. This mechanism would then manifest itself at the macroscopic level as a very long power law-like stress relaxation. The strong elementary nonlinearities could then be static friction (5) or the type of fiber-fiber interaction described by Mijailovich et al. (27). Although this idea is attractive, no direct experimental evidence supports it. Nevertheless, it seems quite plausible that the mechanisms (reptation, fiber-fiber interaction, contractility of cells) discussed above are not mutually exclusive.
Regarding the nonlinear behavior of the tissue, we first note that both the strain amplitude dependence of G and H and the values of kd were identical in the V, N, or P conditions. Thus similar mechanical nonlinearities must be present in the viable and nonviable tissue. The above three mechanisms (reptation, fiber-fiber interactions, and cell mechanical properties) display apparently similar negative amplitude dependence of the mechanical moduli. In the reptation model, the stress-relaxation modulus is reduced when strain amplitude is increased (8). The fiber-fiber interaction model (27) appears at the macroscopic level as plastoelasticity with negative amplitude dependence of the stiffness and damping (or G and H). Also, trachealis smooth muscle shows a very strong nonlinear behavior, which would again predict a negative amplitude dependence of H (16). This has been attributed to the number of cross bridges attached (9, 10). Taken together, because amplitude dependence of G and H is the same in V, N, and P conditions, we suspect that the mechanism for the nonlinear behavior in the intact lung is most likely related to the characteristics of the collagen-elastin fiber network. We need to point out that this type of nonlinearity is quite different from the nonlinear quasistatic pressure-volume curve of the lung. The quasistatic pressure-volume curve predicts a positive dependence of the incremental moduli on the applied input amplitude. Therefore the mechanism behind the negative amplitude dependence during dynamic stretching is not likely to be related to the exponential stress-strain curve of the strip. Instead, it is related to the mechanism responsible for the hysteretic or viscoelastic nature of the tissue. During MCh challenge, kd also increased slightly but systematically by 4-10% from control. This may indicate that the contraction of cells results in an increased mean force and, hence, slight increases in tissue nonlinearities via a stiffening of the fiber network. We thus conclude that the basic tissue mechanics are mainly due to extracellular fiber network, which can be modified by the tone or contraction of interstitial cells.
Mechanics of Parenchymal Strips During MCh Challenge
After MCh challenge, the time course response of the mechanical parameters is consistent with the findings in the literature (9). The slight increase in at the peak response is in agreement with the
simple molecular interpretation of in contractile cells associated
with the increase in cross-bridge cycling rate (9, 10). We also
observed that the mean force developed by the tissue strip at a fixed
length increased by 4-10% from control, which is less than the
28% reported by Fredberg et al. (9). However, the MCh concentration
they used was 10 times higher
(104 vs.
105 M). Because the mean
force appears to be a key factor in determining the mechanics, we
tested if the G and G" spectra would be the same at
identical mean forces independent of whether the increase in mean force
was achieved by passive stretching or active contraction of cells. We
thus compared the G and G" spectra when the mean force
increased from 0.5 to 0.53 g due to cell contraction and when the mean
force was adjusted with passive stretching to 0.53 g. As Fig.
10 demonstrates, the increase in tissue
stiffness from its value in control at 0.5 g of mean force is the same
regardless of whether the increased force was produced by passive
stretch or active cell contraction. This is in accord with the data of Fredberg et al. (9), who found that increases in tissue stiffness are
always closely associated with increases in active force over a wide
spectrum of contractile agonists. Additionally, because after both
constriction and passive stretching the G spectrum is shifted in
a parallel fashion, this behavior is invariant of frequency.
(A) and G" (B) spectra
corresponding to same increases in mean force by active cell
contraction and passive stretching.
This appears to be a consequence of the anatomical arrangement of the interstitial cells in the neighborhood of the collagen-elastin fiber network within the alveolar septa. Recently, Salerno et al. (31) argued that there are contractile cells in the alveolar walls responding separately from smooth muscles in the small airways. Thus, besides the smooth muscle cells in the alveolar entrance rings, the myofibroblast cells or Kapanci cells (22), for example, which produce and maintain collagen fibers, are also contractile cells and run close and almost parallel to these fibers (40). Therefore, by their contraction, they may induce local tension or shear in the neighborhood of the fibers and hence influence the macroscopic mechanics indirectly, through the fiber network. An interesting implication of this is that, conceptually, the interstitial cells are mechanically in parallel with the fiber system rather than in series. Accordingly, the parenchyma can be conceptualized as a hexagonal mesh of line elements (41). Each line element would be an in-parallel connection of two springs, one with a low elastic constant to represent the cells and the other with a high elastic constant for the elastin-collagen fibers. An increase in the stiffness of the soft springs due to active cell contraction would simply lead to an equivalent increase in elastic modulus of the whole system, importantly, however, independent of the frequency.
In contrast to G, the G" spectra do not fall exactly on
the same curve after MCh response and after passive stretching. This suggests that contraction and passive stretching correspond to different hysteretic states of the tissue as suggested by Fredberg et
al. (9). One possibility is that passive stretching involves more
connective tissue response than active contraction.
In summary, this study indicates that interstitial cells within the normal parenchyma do not directly influence tissue stiffness at the macroscopic level and may contribute to tissue resistance by <12%. During contraction of interstitial cells, the response is almost equivalent to a shift in passive mean force, which implies that cells and fibers are mechanically coupled in parallel. These findings suggest that the connective tissue network is the dominant factor in determining the mechanical properties of the parenchyma, but the basic tone of the fiber network and hence the corresponding macroscopic mechanical parameters of the tissue can be modulated by the contraction of interstitial cells. As a consequence, the extracellular fiber network plays an important role in the lung at the level of parenchymal mechanics after agonist-induced contraction. Finally, our results also support the notion that the dramatic increases in pulmonary resistance and elastance during MCh challenge are probably not due to alterations at the parenchymal tissue level (26).
ACKNOWLEDGEMENTS
This work was partly supported by National Science Foundation Grant BES-9503008.
FOOTNOTES
Address for reprint requests: B. Suki, Dept. of Biomedical Engineering, Boston University, 44 Cummington St., Boston, MA 02215.
Received 21 January 1997; accepted in final form 25 June 1997.
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ABSTRACT
3.02 