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Time domain reflectometry: measurement of free water in normal lung and pulmonary edema

Nobuhiro Miura1,2, Sumie Shioya1, Daisaku Kurita1, Teruyoshi Shigematsu1, and Satoru Mashimodagger ,2

1 Department of Internal Medicine, Tokai University School of Medicine, Isehara, Kanagawa 259-1193; and 2 Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan

    ABSTRACT
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Abstract
Introduction
Materials & Methods
Results
Discussion
References

The free water content of lung tissue was investigated by dielectric spectroscopy in normal lungs and in pulmonary edema induced by oleic acid in rats. The dielectric relaxation in a frequency range of 107 to 1010 Hz was measured with the time domain reflectometry method at 25°C. Three dielectric relaxation processes were analyzed for the lung tissue. A high-frequency process around 10 GHz was attributed to the orientation of free water molecules based on the relaxation time [log tau h (in s) = -11.03]. The dielectric strength (Delta epsilon ) of this high-frequency peak (Delta epsilon h) should reflect the amount of free water in the tissue. Because the measured Delta epsilon h depended on the air content of the lung samples, the value of Delta epsilon h was corrected for the air content of each sample as determined by the point-counting method in the area where the time domain reflectometry data were obtained. The lungs of rats that received an injection of oleic acid had a significantly increased free water content [(Delta epsilon h of lung/Delta epsilon of pure water) × density of pure water] compared with that in the normal lung (0.76 vs. 0.59 g/cm3). These results indicate that free water occupies ~60% of the total volume of normal lung tissue and that there is an increase in free water in pulmonary edema.

lung tissue water; oleic acid-induced lung injury

    INTRODUCTION
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Abstract
Introduction
Materials & Methods
Results
Discussion
References

THE CHANGE IN LUNG TISSUE WATER in pulmonary edema, which is defined as an accumulation of water in the extravascular space, has been evaluated by gravimetric water content, distribution of tracers (e.g., radionucleides), and morphometry. These methods have been useful in evaluating the static state of lung tissue water. On the other hand, changes in the physical properties of water molecules, i.e., alterations in the mobility of water molecules, in pulmonary edema have rarely been investigated. Previously, Shioya and colleagues (19-22) found changes in the nuclear magnetic resonance (NMR) relaxation times T1 and T2 for various experimental lung injuries, indicating changes in the physical state of water in lung tissue. Increases in the NMR T2 relaxation time without accompanying increases in gravimetric water content suggested an alteration in the free and bound water fractions of lung tissue water. There should, therefore, be changes in the content of free water in diseased lungs, especially in pulmonary edema.

The microwave dielectric method has been one of the most reliable techniques for investigating the dynamic structure of water in macromolecules such as deoxyribonucleic acids (26), globular proteins (15, 16), and polysaccharides (24). Dielectric relaxation measurements have been applied to various biological tissues (6). In the past, Surowiec et al. (23) and Schwan and Kay (17) measured the dielectric properties of lung tissue; however, they did not apply a high enough frequency to observe the dielectric dispersion and absorption of free water. Recent developments in the time domain reflectometry (TDR) method have now made the measurement easy and fast, giving the absorption and dispersion data continuously in a frequency range of 100 kHz to 10 GHz (2, 4, 14). In this study, we used the TDR method to measure the free water content in normal lungs and in pulmonary edema in rats, investigating the changes in lung tissue water. Our results may provide new insights concerning water in the lung based on its dynamic behavior.

    MATERIALS AND METHODS
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Abstract
Introduction
Materials & Methods
Results
Discussion
References

Preparation of animals. Nine 250-g Wistar-strain male rats were used. All the experiments were performed in adherence with the guidelines for animal experiments in the School of Medicine, Tokai University (Kanagawa, Japan). Rats were anesthetized with 60 mg/kg of pentobarbital sodium intraperitoneally. Pulmonary edema was induced in four rats by injection of oleic acid (0.12 mg/kg) into the tail vein, and the rats were used 4-5 h after injection. Five rats served as normal controls. The left lung was removed for experiments immediately after exsanguination via the abdominal aorta.

Dielectric relaxation measurements. TDR (2, 4, 14) dielectric measurements in the frequency range of 107 to 1010 Hz were performed at 25°C. An incident pulse with a rise time of 35 ps was generated by a pulse generator and passed through a semirigid coaxial cable, the top of which was cut flat and plated with gold to prevent oxidation. The top of the cable was in direct contact with the surface of the lung in a sample bottle that was tightly sealed and placed in a water bath (25°C) with a temperature control system. TDR measurement of the lung samples was started within 5 min after exsanguination and completed in 20 min. The reflected pulse from the sample was recorded in the time domain at the sampling head (HP54121A, Hewlett-Packard) and digitized by a digitizing oscilloscope mainframe (HP54121B, Hewlett-Packard).

The reflected pulses from the unknown and reference samples were measured, and the complex permittivity for each sample was obtained after Fourier transformation of those pulse forms with a personal computer (PC9800FA, NEC). If a sample with known permittivity (&egr;*<SUB>s</SUB>) is used as a reference sample, the permittivity of an unknown sample (&egr;*<SUB><IT>x</IT></SUB>) is given as
&egr;<SUB><IT>x</IT></SUB>*(ω) = &egr;<SUB>s</SUB>*(ω) <FR><NU>1 + {(<IT>cf</IT><SUB>s</SUB>)/[<IT>j</IT>ω(&ggr;<IT>d</IT>) &egr;<SUB>s</SUB>*(ω)]}&rgr;<IT>f</IT><SUB><IT>x</IT></SUB></NU><DE>1 + {[<IT>j</IT>ω(&ggr;<IT>d</IT>)&egr;<SUB>s</SUB>*(ω)]/(c<IT>f</IT><SUB>s</SUB>)}&rgr;<IT>f</IT><SUB>s</SUB></DE></FR> (1)
where
&rgr; = <FR><NU><IT>r</IT><SUB>s</SUB>(ω) − <IT>r</IT><SUB><IT>x</IT></SUB>(ω)</NU><DE><IT>r</IT><SUB>s</SUB>(ω) + <IT>r</IT><SUB><IT>x</IT></SUB>(ω)</DE></FR> (2)
and
<IT>f<SUB>x</SUB></IT> = Z<SUB><IT>x</IT></SUB>cot Z<SUB><IT>x</IT></SUB>, Z<SUB><IT>x</IT></SUB> = (ω<IT>d</IT>/<IT>c</IT>) <RAD><RCD>&egr;<SUB><IT>x</IT></SUB>*(ω)</RCD></RAD> (3)
<IT>f</IT><SUB>s</SUB> = Z<SUB>s</SUB>cot Z<SUB>s</SUB>, Z<SUB>s</SUB> = (ω<IT>d</IT>/<IT>c</IT>) <RAD><RCD>&egr;<SUB>s</SUB>*(ω)</RCD></RAD> (4)
where d is the geometric length; gamma d is the effective electric length (0.18-0.22 mm); rs(omega ) and rx(omega ) are the Fourier transforms of the reflected pulse from the reference [Rs(t)] and unknown [Rx(t)] samples, respectively; j is the imaginary unit; omega  is the angular frequency; and c is the speed of propagation in vacuo. The gamma d was determined by measuring two known samples, water and acetone. The measured values for water and acetone were adjusted to the known values by selecting an appropriate value of gamma d.

To attain better precision in the gigahertz region, a bilinear analysis was employed (1, 14). This analysis provides the unknown permittivity as
&egr;<SUB><IT>x</IT></SUB>* = <FR><NU><IT>A</IT>&egr;*<SUB><IT>x</IT>ap</SUB></NU><DE>1 + <IT>B</IT>&egr;*<SUB><IT>x</IT>ap</SUB></DE></FR> (5)
where A and B are the complex constants depending on omega , and a value for apparent epsilon *x (epsilon *xap) is obtained from Eqs. 1-4. In this study, air was chosen as a standard sample, for which the permittivity = 1. To determine the values for A and B, two samples with known permittivities, water and acetone, were used.

Histological examination. After the TDR measurements, lung tissue samples were fixed with 10% Formalin-saline and prepared for light microscopy examination with hematoxylin and eosin staining.

Normalization of the dielectric strength for the actual tissue volume. The complex permittivity (epsilon *) for biological tissues is represented as the sum of several relaxation processes of the Havriliak-Negami (8) equation
&egr;*(ω) = &egr;<SUB>∞</SUB> + <LIM><OP>∑</OP><LL><IT>n</IT>=1</LL><UL><IT>m</IT></UL></LIM> <FR><NU>&Dgr;&egr;<SUB>n</SUB></NU><DE>[1 + (<IT>j</IT>ω&tgr;<SUB><IT>n</IT></SUB>)<SUP>&bgr;<SUB><IT>n</IT></SUB></SUP>]<SUP>&agr;<SUB><IT>n</IT></SUB></SUP></DE></FR> (6)
where epsilon infinity is the dielectric constant at (omega  right-arrow infinity ), m is the number of relaxation processes, Delta epsilon is the relaxation strength, tau  is the relaxation time, and alpha  and beta  are parameters describing distribution of the relaxation time. The parameters in the equation were determined by least squares fitting (15).

In the TDR measurement of lung tissue, the measured Delta epsilon is a value for a unit volume of lung tissue including the air, and the air, for which the permittivity is almost equal to 1, decreases the apparent dielectric constant of the lung. To compare the values of Delta epsilon obtained from lung samples of various air content, we normalized the measured Delta epsilon with the actual lung tissue volume without alveolar air. To make the TDR data and the measured actual tissue volume consistent, several microscopy sections were prepared in the area where the TDR electrode was attached (Fig. 1A). The actual tissue volume for each sample was determined by the point-counting method with light microscopy as [points on tissue/total points (sum of points on tissue and air)] (27). With a micrometer (U-OCM SQ 10/10, Olympus), a total of 242 points (500 µm in width and 250 µm in depth) were counted under high power (×400) in the area where the TDR measurement was performed. For each sample, measurements were made at least three times, and the averaged values are used as the actual tissue volumes.


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Fig. 1.   Microscopic views of lung samples (hematoxylin and eosin staining). A: a passively collapsed normal lung contains air. Normalized dielectric strength value (Delta epsilon n) of 44.2 for this sample was calculated from measured dielectric strength (Delta epsilon h) of 28.5 and estimated actual tissue volume of 0.64. On surface of lung, traces of time domain reflectometry (TDR) electrode can be identified as an indentation (arrowheads). Actual tissue volume was determined by point-counting method for an area 500 µm in width and 250 µm in depth that most effectively contributed to TDR signal. Magnification, ×100; bar, 100 µm. B: a degassed lung sample that contains almost no air has an actual tissue volume of 0.97. Delta epsilon n of 45.7 is close to that of a passively collapsed normal lung. Magnification, ×100. C: a lung receiving an injection of oleic acid shows massive pulmonary edema. Alveolar walls are necrotic, and alveoli are filled with edema fluid. Delta epsilon n was 55.8, and actual tissue volume was 0.92. Magnification, ×400.

To verify this normalization, we compared the normalized Delta epsilon for passively collapsed lungs with some air and a degassed lung without air. When the chest is opened under ambient pressure, the lung passively collapses because the chest cavity is normally maintained under negative pressure. In the degassed lung, the Delta epsilon should be affected less by air than by the passively collapsed lung. The degassed lung was prepared by inserting a tracheal tube into an anesthetized rat and allowing it to breath 100% O2 for 20 min. The tracheal tube was clamped shut for 5 min to allow the complete absorption of intra-alveolar O2. In contrast to air, which consists of 21% O2 and 79% inactive nitrogen, 100% O2 is completely removed from the alveoli by the circulating blood. The heart continues to beat actively for ~5 min even after ventilation ceases. After exsanguination from the abdominal aorta, the degassed lung was excised for TDR measurement.

Gravimetric measurement of water content. A lung tissue sample for the measurement of gravimetric water content was excised from the same lung used for the TDR measurement, placed in a glass tube, and sealed tightly until measured. The samples were placed in a vacuum desiccator to dehydrate for 24 h. Water content (in percent) was calculated from the difference in sample weight before and after desiccation as [(wet weight - dry weight)/wet weight] × 100.

Statistical analysis. Data are expressed as means ± SD. Comparisons for the data between groups were performed with a Mann-Whitney U-test. A correlation between the water content and dielectric strength was analyzed by linear regression. A value of P < 0.05 was considered significant.

    RESULTS
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Abstract
Introduction
Materials & Methods
Results
Discussion
References

Figure 1 shows microscopic views of a sample of normal passively collapsed lung with a tissue volume of 0.64 (A), a sample of degassed lung with a tissue volume of 0.97 (B), and a lung 4 h after injection of oleic acid with a tissue volume of 0.92 (C). The degassed lung shows almost complete absorption of alveolar air by the inhalation of 100% O2. The oleic acid-treated lung shows massive pulmonary edema with alveoli filled with edema fluid. The alveolar walls are necrotic.

Dielectric dispersion (epsilon ', real part) and absorption (epsilon '', imaginary part) curves observed for a normal rat lung at 25°C are shown in Fig. 2A. Three relaxation processes, low (l), intermediate (m), and high (h) frequency, were analyzed for the lung tissue in a frequency range from 1 MHz to 10 GHz. The permittivity is thus described by
&egr;*(ω) − &egr;<SUB>∞</SUB> = <FR><NU>&Dgr;&egr;<SUB>l</SUB></NU><DE>1 + <IT>j</IT>ω&tgr;<SUB>l</SUB></DE></FR> + <FR><NU>&Dgr;&egr;<SUB>m</SUB></NU><DE>(1 + <IT>j</IT>ω&tgr;<SUB>m</SUB>)<SUP>&agr;<SUB>m</SUB></SUP></DE></FR> + <FR><NU>&Dgr;&egr;<SUB>h</SUB></NU><DE>1 + (<IT>j</IT>ω&tgr;<SUB>h</SUB>)<SUP>&bgr;<SUB>h</SUB></SUP></DE></FR> (7)
The parameters in the equation were determined by least squares fitting.


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Fig. 2.   A: frequency dependence of dielectric dispersion (epsilon ', real part; top) and absorption (epsilon '', imaginary part; bottom) for a normal lung. Three peaks of low (l)-, intermediate (m)-, and high (h)-frequency ( f ) processes were obtained for lung tissue. High-frequency relaxation process at 10-GHz peak can be attributed to reorientation of free (bulk) water molecules based on its relaxation time of log tau h (in s) = -11.03 at 25°C. B: magnified view of high-frequency area. Shown are best fits where theoretical curves (solid lines) agree well with measured data (bullet ).

Figure 2B shows a magnified view of the high-frequency region. The high-frequency process around 10 GHz, which is well separated from the other two lower-frequency processes, can be attributed to the orientation of free water based on its relaxation time of log tau h (in s) = -11.03. Although our measurements did not cover the frequency at this peak, tau h and Delta epsilon h were determined with a high level of accuracy by assuming a Cole-Cole-type relaxation process, with the value epsilon infinity determined by least squares fitting. The value epsilon infinity did not vary in normal lungs and pulmonary edema, and the theoretical curves agreed well with the measured data as shown in Fig. 2. The parameters analyzed for this relaxation process are shown in Table 1. The values for a degassed lung were close to the mean values for the normal lung, except for the value of Delta epsilon h and the actual tissue volume. The similar normalized Delta epsilon h (Delta epsilon n) values (means ± SD) for the passively collapsed lung and a degassed lung indicate that normalization of Delta epsilon h with the actual tissue volume is effective.

                              
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Table 1.   Water content of lung tissue and dielectric relaxation parameters for free water peak

In oleic acid-induced injury, the Delta epsilon n was significantly greater compared with that in the normal lung. The gravimetric water content was markedly increased for the oleic acid-treated lung. The increase in Delta epsilon n (Y) was significantly correlated with the increase in water content (X): Y = -82.53 + 1.61X (r = 0.925; P < 0.001; n = 8 lungs).

    DISCUSSION
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References

In the dielectric relaxation measurement of lung tissue, three relaxation processes were analyzed in a frequency range from 1 MHz to 10 GHz, the low, intermediate, and high processes. The low-frequency process around 1 MHz could be an electrode polarization (6). The intermediate-frequency relaxation process, with a peak between 10 and 100 MHz, may be explained by the reorientation of water molecules restricted by the macromolecules in the tissue (15, 16, 26). The Maxwell-Wagner effect occurring on the cell interface and the micro-Brownian motion of the other biomolecules might also contribute to this peak (12). These two processes would overlap with each other in these measurements, and their origins have not yet been determined for biological tissues. The high-frequency relaxation process around 10 GHz was well separated from the other two lower-frequency processes and was attributed to the orientation of free water. A recent microwave dielectric study (13) has revealed that the elementary structure of water is cyclic, consisting of six molecules linked together by hydrogen bonding. In view of the dielectric properties, the structure of free water in the tissues was not different from that of pure water, judging from the relaxation time.

In the dielectric relaxation measurements for lung tissue containing air in the alveoli, as shown in Fig. 1A, the measured Delta epsilon should be underestimated. Although a significantly greater Delta epsilon was measured in pulmonary edema compared with the normal lung, the increase could be affected by the increase in tissue volume due to the obliteration of air spaces by the accumulation of edema fluid in the alveoli. To normalize the effects of varied tissue volume on Delta epsilon h, we corrected the measured Delta epsilon with the actual tissue volume for each sample. The actual tissue volume was determined in the area where the TDR measurements were performed so that these data are consistent. The Delta epsilon n for the oleic acid-treated lung was significantly greater than that for the normal lung. These results indicate an actual increase in free water in the edematous lung.

An important parameter in dielectric spectroscopy is Delta epsilon . For the relaxation process due to the orientation of free water, the value of Delta epsilon depends on the number of water molecules measured by the TDR method, if it is assumed that the local structure of free water is the same as that of pure water. This behavior was observed in the polymer solution. In this case, the content of the free water per unit volume [Cf (in g/cm3)] can be estimated from the Delta epsilon h as
C<SUB>f</SUB> = <FENCE><FR><NU>&Dgr;&egr;<SUB>h</SUB></NU><DE>&Dgr;&egr;<SUB>w</SUB></DE></FR></FENCE>C<SUB>w</SUB> (8)
where Delta epsilon w is the relaxation strength of pure water and Cw is the density of pure water at 25°C (=0.997 g/cm3).

With the use of Delta epsilon n, the Cf can be calculated using Delta epsilon w = 73.16 at 25°C (9) and Cw = 0.997 g/cm3. The calculated values are shown in Table 1. The Cf value of 0.59 g/cm3 for normal lung tissue is close to the reported value of 0.54 g/cm3 for the gray matter of brain tissue (10). These results suggest that water with the same physical properties as pure water occupies ~60% of the tissue volume in the normal lung. With theoretical approaches other than Eq. 8, the calculated results may differ from our data. However, the trends in water content for edematous tissue would be the same regardless of the approach. It has been supposed that the water in biological tissues has a characteristic structure and physicochemical properties different from those of pure water (11, 25). However, recent dielectric studies (5, 6, 11) with the TDR method have also suggested the existence of water with the features of pure water in biological materials.

Oleic acid-induced lung injury is one of the most popular animal models of acute permeability pulmonary edema and fatty embolism (3). The early stage of oleic acid-induced lung injury is characterized by massive pulmonary edema with cellular necrosis and alveolar flooding. The histology observed in this study was consistent with that reported by other investigators (3). In measurements of the oleic acid-treated lung, the Delta epsilon of the free water process as well as the Delta epsilon n was significantly greater than those of the normal lung. The calculated value of Cf was markedly increased. These results quantitatively indicate that an increase in free water is an essential feature of pulmonary edema.

Although TDR measurements are not destructive and not invasive, it may be difficult to apply this method to lungs in vivo unless the air content for a sample is known. In addition, TDR data can be obtained only for a limited area just under the electrode. The advantage of this method is that fractional changes in free water can be evaluated for the tissue. In contrast, gravimetry only measures net changes in the weight of water, and this method cannot be used to measure water content in vivo. With NMR measurements, dynamic changes in tissue water caused by macromolecular derangement can be detected as changes in relaxation times, and this method can also be used for measurements of living tissues by magnetic resonance imaging (18). However, the data obtained by NMR do not differentiate free water fractions from other more restricted water fractions in the tissue. NMR and TDR gave different results that can be explained by differences in the experimental time scale (7). TDR has a time resolution on the order of a few picoseconds, in contrast to NMR with its time resolution of a few milliseconds, making it possible to observe the relaxation process due to the orientation of free water in aqueous solutions with a high solute concentration.

In conclusion, we have, for the first time, quantified the amount of free water in lung tissue with the TDR method, showing that normal lung tissue has a free water content of 0.59 g/cm3. In the pulmonary edema induced by injection of oleic acid, there was a significant increase in the free water content of the lung.

    ACKNOWLEDGEMENTS

We are grateful to Dr. Chizuko Tsuji for technical assistance.

    FOOTNOTES

dagger Deceased 29 March 1996.

This study was supported by a Research Promotion Grant from the Tokai University (Kanagawa, Japan) General Research.

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

Address for reprint requests: S. Shioya, Dept. of Internal Medicine, Tokai Univ. School of Medicine, Isehara, Kanagawa 259-1193, Japan.

Received 2 February 1998; accepted in final form 11 September 1998.

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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References

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Am J Physiol Lung Cell Mol Physiol 276(1):L207-L212
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