Dielectric Coagulometry: A New Approach To Estimate Venous

Oct 29, 2010 - We present dielectric coagulometry as a new technique to estimate the risk of venous thrombosis by measuring the permittivity change ...
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Anal. Chem. 2010, 82, 9769–9774

Dielectric Coagulometry: A New Approach To Estimate Venous Thrombosis Risk Yoshihito Hayashi,*,† Yoichi Katsumoto,† Shinji Omori,† Akio Yasuda,† Koji Asami,‡ Makoto Kaibara,§ and Isao Uchimura| Life Science Laboratory, Advanced Materials Laboratories, Sony Corporation, 113-8510 Tokyo, Japan, Laboratory of Molecular Aggregation Analysis, Division of Multidisciplinary Chemistry, Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan, Institute of Physical and Chemical Research (RIKEN), Wako, 351-0198 Saitama, Japan, and Department of Endocrinology and Metabolism, Tokyo Medical and Dental University, 113-8510 Tokyo, Japan We present dielectric coagulometry as a new technique to estimate the risk of venous thrombosis by measuring the permittivity change associated with the blood coagulation process. The method was first tested for a simple system of animal erythrocytes suspended in fibrinogen solution, where the coagulation rate was controlled by changing the amount of thrombin added to the suspension. Second, the method was applied to a more realistic system of human whole blood, and the inherent coagulation process was monitored without artificial acceleration by a coagulation initiator. The time dependence of the permittivity at a frequency around 1 MHz showed a distinct peak at a time that corresponds to the clotting time. Our theoretical modeling revealed that the evolution of heterogeneity and the sedimentation in the system cause the peak of the permittivity. Blood clots formed in a deep vein often detach into the bloodstream, pass through the veins and the heart, and finally occlude the lung arteries. This pulmonary thromboembolism (PTE) is lethal and the third cause of excess mortality in U.S. hospitals.1 Therefore, preventative care of deep vein thrombosis (DVT) is important especially for those who have high-risk factors. The risk increases with increase of blood coagulation activity or coagulability that is enhanced by various factors such as diabetes, cancer, pregnancy, obesity, and aging, although the effects on individuals are quite diverse.1,2 Although the origin of hypercoagulability is not completely understood, it is suggested that blood-borne tissue factor activates extrinsic coagulation,3,4 while factor IX-activating enzyme on the * To whom correspondence should be addressed. Fax: +81 3 5803 4790. E-mail: [email protected]. † Sony Corp. ‡ Kyoto University. § RIKEN. | Tokyo Medical and Dental University. (1) Geerts, W. H.; Bergqvist, D.; Pineo, G. F.; Heit, J. A.; Samama, C. M.; Lassen, M. R.; Colwell, C. W. Chest 2008, 133, 381S–453S. (2) Petrauskiene, V.; Falk, M.; Waernbaum, I.; Norberg, M.; Eriksson, J. W. Diabetologia 2005, 48, 1017–1021. (3) Mackman, N. Arterioscler., Thromb., Vasc. Biol. 2004, 24, 1015–1022. (4) Giesen, P. L. A.; Rauch, U.; Bohrmann, B.; Kling, D.; Roque´, M.; Fallon, J. T.; Badimon, J. J.; Himber, J.; Riederer, M. A.; Nemerson, Y. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 2311–2315. 10.1021/ac101927n  2010 American Chemical Society Published on Web 10/29/2010

erythrocyte membrane (erythroelastase-IX) activates intrinsic coagulation.5-7 This implies that hypercoagulability involves both plasma components and blood cells. It should also be noted that the rate of thrombus formation in a deep vein is much lower than that of activated hemostasis, for example, after an injury. In other words, the difference of coagulability in the hypercoagulable and normal statuses is very small. Thus, early detection of DVT risk requires high sensitivity to this small difference. In this sense, standard blood coagulation tests such as prothrombin time (PT) and activated partial thromboplastin time (APTT) are not suitable for the purpose; they do not allow measuring the subtle change of inherent coagulability because of artificial activation by addition of excess coagulation initiator (tissue factor and contact factor activator for PT and APTT, respectively). Other methods including 8 D-dimer quantification have certain limitations in either sensitivity, disease-specificity, measurement time, ease of use, or cost. In addition, the role of enzymatic reactions on the erythrocyte surfaces in coagulability is not taken into account in those testing methods, which examine a plasma sample separated from the whole blood. The damped oscillation rheometer, on the other hand, is a unique apparatus that allows quantitatively measuring a clotting time without artificial activation of blood coagulation for estimation of hypercoagulability.7,9 However, because measurement needs to be continued for at least 30 min to exclude the possibility of hypercoagulability for a specimen, the throughput of analysis is problematic for clinical application. For introduction of a routine DVT risk test into diagnosis, therefore, we must devise an analytical method that provides a clotting time well correlated with that from the rheometer and can potentially be implemented in an instrument capable of processing multiple specimens in parallel. For this purpose, dielectric spectroscopy (DS) is worthy of attention because multiple specimens can be measured by a single impedance analyzer with a multiplexer, and the sample cartridge can be miniaturized. On the other hand, it is not easy to (5) Iwata, H.; Kaibara, M. Blood Coagulation Fibrinolysis 2002, 13, 489–496. (6) Iwata, H.; Kaibara, M.; Dohmae, N.; Takio, K.; Himeno, R.; Kawakami, S. Biochem. Biophys. Res. Commun. 2004, 316, 65–70. (7) Kaibara, M. J. Biorheol. 2009, 23, 2–10. (8) Stein, P. D.; Hull, R. D.; Patel, K. C.; Olson, R. E.; Ghali, W. A.; Brant, R.; Biel, R. K.; Bharadia, V.; Kalra, N. K. Ann. Intern. Med. 2004, 140, 589– 602. (9) Kaibara, M. Biorheology 1985, 22, 197–208.

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miniaturize the rheometer that inherently requires a precise mechanical setup for each specimen. Therefore, the sensitivity of DS to blood coagulation is discussed here. DS is a method to measure a frequency dependence of complex permittivity of a sample, ε* ) ε′ - jε′′ ) ε′ - jκ/ωε0, where ε′ and ε′′ are the real and imaginary parts of the complex permittivity, respectively, j is the imaginary unit, κ is the conductivity, ω is the angular frequency, and ε0 is the permittivity of vacuum. The main dielectric response of blood in a frequency range from hundreds kHz to tens MHz is interfacial polarization that is attributed to accumulation of charge carriers at the interface between the cytoplasm and the erythrocyte membrane.10-12 The previous DS study for erythrocyte suspensions showed clear distinction of dielectric spectra for erythrocytes of different shapes obtained by controlling the medium pH,13 and these experimental results agreed well with the theoretical simulations.14 It is also reported that rouleaux formation of erythrocytes causes remarkable increase of the dielectric relaxation strength.15,16 From these studies, the complex permittivity is expected to change through blood coagulation process, where nonhomogeneity of the system dynamically changes in both mesoscopic and macroscopic scales. Such changes include aggregation of blood cells, sedimentation of them, formation of fibrin networks, inclusion of the aggregated cells in the networks resulting in clots, and retraction of the clots by the effect of platelets. The previous DS studies suggest the permittivity changes according to those changes, but no study has been performed to correlate the permittivity changes and the biochemical phenomena in blood coagulation process. In this work, therefore, we report the first feasibility study of the blood coagulation test based on DS. At first, a simple system of erythrocytes washed by phosphate-buffered saline (PBS) and suspended in fibrinogen solution was used. This model system enables controlling the coagulation rate by changing the amount of thrombin added to the suspension and showing the sensitivity of DS to the most essential part of the blood coagulation process such as forming of fibrinous network under the presence of blood cells. Next, we applied the method to human whole blood. DS and rheological measurements were always conducted for the same specimens for critical comparison. Theoretical consideration was also done to understand the origin of the observed dielectric response. EXPERIMENTAL SECTION Sample Preparation. Blood specimens of rabbit, bovine, and horse, which were collected and immediately mixed with the equal volume of Alsever’s solution, were supplied from Kohjin Bio Co., Ltd., stored at 277 K, and used for experiment within two weeks after blood collection. Both fibrinogen and thrombin were obtained (10) Takashima, S. Electrical Properties of Biopolymers and Membranes; Adam Hilger: Bristol, 1989. (11) Foster, K. R.; Schwan, H. P. Crit. Rev. Biomed. Eng. 1989, 17, 25–104. (12) Livshits, L.; Caduff, A.; Talary, M. S.; Lutz, H. U.; Hayashi, Y.; Puzenko, A.; Shendric, A.; Feldman, Y. J. Phys. Chem. B 2009, 113, 2212–2220. (13) Hayashi, Y.; Oshige, I.; Katsumoto, Y.; Omori, S.; Yasuda, A.; Asami, K. Phys. Med. Biol. 2008, 53, 2553–2564. (14) Katsumoto, Y.; Hayashi, Y.; Oshige, I.; Omori, S.; Kishii, N.; Yasuda, A.; Asami, K. Biophys. J. 2008, 95, 3043–3047. (15) Irimajiri, A.; Ando, M.; Matsuoka, R.; Ichinowatari, T.; Takeuchi, S. Biochim. Biophys. Acta 1996, 1290, 207–209. (16) Asami, K.; Sekine, K. J. Phys. D: Appl. Phys. 2007, 40, 2197–2204.

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from Sigma Ltd. Stock solution of thrombin (10 NIH units/mL in double deionized water) was prepared, dispensed in aliquots, and kept frozen at 243 K until it was used. Before DS and rheological measurements, the Alsever’s solution and the plasma were removed from the blood specimens by centrifugation at 500g for 5 min. The sediment was washed in PBS by centrifugation at 500g for 5 min and resuspended in PBS, and then the equal volume of 4.4 mg/mL fibrinogen solution in PBS was added to the suspension. The volume fraction of erythrocytes in the final suspension was approximately 20%. Optical microscope observation showed that rabbit erythrocytes transformed to echinocytes,13 while bovine and horse erythrocytes retained the native biconcave shape. The prepared suspensions were incubated at 310 K for 10 min, and then the thrombin solution was added to start the coagulation reaction just before the DS or rheological measurement. Human whole blood mixed with 1/10 volume of 3.8% trisodium citrate as an anticoagulant was obtained from healthy volunteers who gave informed consents, and all the experiments were completed within 5 h after blood collection. The blood was dispensed in tubes made of polypropylene that is known to be inactive for blood coagulation, incubated at 310 K for 10 min, and then 250 mM CaCl2 aqueous solution was so added that the final concentration became 85 µL/mL just before the DS or rheological measurement. We note that accumulation of Ca2+ in cytoplasm could induce shape transform of erythrocytes from the native biconcave shape to echinus-like spinous shape (i.e., echinocytes).17 In the present study, fortunately, we confirmed there are no shape changes of erythrocytes by the presence of Ca2+ during the experiments. DS Measurement. Coagulation process of a sample was monitored by DS for the period of less than or equal to 60 min with the interval of 1 or 2 min at 310 K in a frequency range from 40 Hz to 110 MHz using an impedance analyzer (Agilent 4294A) with a probe kit (Agilent 42941A). A sample holder of plate capacitor type used consists of a polypropylene cylinder tube (the inner diameter and length are 9.0 mm and 12 mm, respectively) and two electrode plates (the diameter and thickness of the insertion site are 9.0 mm and 5.0 mm, respectively) squeezed into the top and bottom parts of the tube. Thus, the distance between the two electrodes is 2 mm. Two types of the electrodes were prepared: gold plated ones for the model system of animal erythrocytes and titanium ones for human whole blood to minimize the artificial activation of coagulation on electrode surfaces. (Note that there are no essential differences between gold plated electrodes and titanium electrodes in the case of the model system.) The tube has two holes with the diameter of approximately 0.7 mm through the cylindrical surface, which are occluded by one of the electrodes when it is completely squeezed into the tube. Before injection of the sample, the electrodes were not completely squeezed in the tube so as to leave the two holes open though the side wall. The sample holder was warmed at 310 K in a thermostatic air chamber. Either thrombin or CaCl2 solution was added into the incubated sample. Just after that, the sample was injected into the sample holder through one of the holes with the other one working as an air vent, and the electrodes were completely squeezed to occlude the holes. A portion of (17) Allan, D.; Michell, R. H. Nature 1975, 258, 348–349.

Figure 1. Frequency dependences of ε′ (solid curves) and κ (broken curves) for a cell suspension of rabbit erythrocytes in PBS with fibrinogen where the volume fraction of the cells was approximately 0.2 (red curves) and for the buffer without cells (black curves) at 310 K.

the sample spilled from the holes was wiped, the sample holder was set on a fixture connected to the impedance analyzer, and DS measurements were started. The delay time from the addition of the thrombin or CaCl2 solution to the start of measurement was approximately 2 min. In this work, we defined the clotting time with respect to the start of DS measurement. Although the delay was unavoidable in manually performed experiments of this work, it can be precisely controlled and corrected for by the automated dielectric coagulometer we have been developing. Effects of Electrode Polarization and Data Analysis. The main artifact of DS measurements for biological materials comes from electrode polarization due to the formation of ionic double layers near the electrode surfaces.18,19 The amplitude of this effect increases with decrease of frequency and often exceeds the true dielectric response of a sample in the low frequency region. In the present work, fortunately, the dielectric response of cells was large enough to be observed and evaluated even without any correction of the electrode polarization because of the high volume fraction of the cells in the sample. Figure 1 shows the typical dielectric response of a cell suspension and that of the supernatant without cells. The effects of the electrode polarization are visible as increase of ε′ and decrease of κ with decrease of frequency in the low frequency region for both the suspension and the supernatant. In the frequency region from 500 kHz to 50 MHz, the dielectric relaxation of the interfacial polarization of erythrocytes was observed for the suspension (Figure 1). In the present work, we focused on ε′ to monitor the coagulation process using the normalized value ε′/ε′t)0, where ε′t)0 is equal to ε′ at time t ) 0. Rheological Measurements. The damped oscillation rheometer was used to monitor the coagulation process of a sample at 310 K in a polypropylene tube. The details of the method are described in previous papers.7,9 The clotting time of the sample (Ti) was obtained from analysis of the logarithmic damping factor (LDF). The LDF value accurately reflects the fluidity of the sample, and the initial change of LDF corresponds to the initiation of clot formation. The delay time between injection of the thrombin or CaCl2 solution and the start of measurement was approximately 30 s. (18) Bordi, F.; Cametti, C.; Gili, T. Bioelectrochemistry 2001, 54, 53–61. (19) Feldman, Y.; Ermolina, I.; Hayashi, Y. IEEE Trans. Dielectr. Electr. Insul. 2003, 10, 728–753.

RESULTS AND DISCUSSION Rabbit Echinocytes. First, we present and discuss changes of the dielectric response during the coagulation process of the simple model system using animal blood. In the suspension of rabbit erythrocytes, echinocytes were dominant as shown in Figure 2A,13 and these cells did not form the rouleaux. The value of ε′/ε′t)0 in the frequency range from a few kHz to hundreds kHz increased as the coagulation proceeded (Figure 2B). Because the electrode polarization is dominant in these frequencies, this result indicates that the electrode polarization was affected during the measurement, although the detailed mechanism has not been understood. In frequencies around 1 MHz, where the interfacial polarization of erythrocytes is dominant,13 ε′/ε′t)0 showed a peak at a certain time. This behavior is clearly demonstrated in Figure 2C, which is the cross-sectional view of the three-dimensional data of Figure 2B at 730 kHz, for example. The time corresponding to this peak was reduced by one-half with the twice increase of thrombin concentration (100 munits/ mL) added to the suspension, and no peak appeared for the control experiment without addition of thrombin. Furthermore, the times of the peaks in Figure 2C were equal to the clotting times determined by rheological measurements as shown in Figure 2D. These results indicate that monitoring of the dielectric response at around 1 MHz (in particular, between 300 kHz and 4 MHz) makes it possible to obtain the clotting time. As shown in the next section, this finding holds true also for suspensions of native biconcave-shaped erythrocytes. Bovine and Horse Erythrocytes with Biconcave Shapes. Next, we show the results of DS measurements for the coagulation model systems with bovine and horse erythrocytes, where the cells retained the native biconcave shapes. It is known that the bovine erythrocytes do not form the rouleaux;20 in contrast, the horse erythrocytes tend to form it as shown in Figure 3A. Figure 3B shows the change of the dielectric response for the horse erythrocyte suspension during the coagulation. Similar to the rabbit erythrocytes, the time dependence of ε′/ε′t)0 at 760 kHz showed a peak at a certain time as shown in Figure 3C and D. Interestingly, ε′/ε′t)0 for the horse erythrocyte suspension without addition of thrombin (i.e., the control sample) increased at the beginning of the measurement (Figure 3D). This increase is most probably due to rouleaux formation of horse erythrocytes. In the case of the horse erythrocyte suspension with thrombin, the effect of the rouleaux formation seems to overlap with the change of ε′/ε′t)0 by the coagulation. Human Whole Blood. The time dependence of ε′/ε′t)0 with the coagulation process of human whole blood triggered by addition of Ca2+ showed a peak at the time denoted as Ti(DS) (Figure 4A). In the initial stage, ε′/ε′t)0 increased both with and without addition of Ca2+. This increase is attributable to the rouleaux formation of erythrocytes.15,16 The rouleaux formation accelerates the sedimentation process.15 The effect of the sedimentation upon the control sample without addition of Ca2+ appeared as the decrease of ε′/ε′t)0 following the initial increase. In the presence of Ca2+, on the other hand, the increase of ε′/ε′t)0 originating from the early reaction of blood coagulation exceeded the decrease by the sedimentation. (20) Ba¨umler, H.; Neu, B.; Mitlo ¨hner, R.; Georgieva, R.; Meiselman, H. J.; Kiesewetter, H. Biorheology 2001, 38, 39–51.

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Figure 2. (A) SEM image: Rabbit echinocytes as a constituent part of the model coagulation system. (B) Time dependence of the normalized dielectric spectra of the model coagulation system (thrombin concentration of 50 munits/mL). (C) Cross-sectional views of the normalized dielectric spectra sliced at 730 kHz. Red, blue, and black symbols correspond to thrombin concentrations of 100, 50, and 0 munit/mL, respectively. (D) LDF curves obtained by the damped oscillation rheometer for the model coagulation system with thrombin concentration of 100 and 50 munit/ mL, as shown by red and blue symbols, respectively.

Figure 3. (A) Optical microscopy image of horse erythrocytes with rouleau formation. (B) Time dependence of the normalized dielectric spectra of the model coagulation system with horse erythrocytes. (C) Cross-sectional views of the normalized dielectric spectra sliced at 760 kHz for model coagulation system with bovine erythrocytes. Red and black plots correspond to thrombin concentrations of 30 and 0 munit/mL, respectively. (D) The same as (C), but for horse erythrocytes with thrombin concentration of 50 munit/mL for red plots.

Through the progress of coagulation, a fibrinous network develops capturing an increasing number of erythrocytes, resulting in large-scale aggregation. Because the sedimentation rate of large aggregates is high, ε′/ε′t)0 rapidly decreased after Ti(DS) (Figure 4A). Figure 4B shows the LDF curve for the human whole blood observed by the damped oscillation rheometer. The clotting time Ti(LDF) was determined from a cross point of the initial LDF level and the tangent line at the maximum decreasing rate (Figure 4B).7 It is reported that Ti(LDF) is small for hypercoagulable blood of pregnant women and patients with diabetes or lower leg deep vein thrombosis.7 This means that Ti(LDF) is a good parameter for the quantitative evaluation of DVT risk. Figure 4C shows good correlation between Ti(DS) and Ti(LDF). Therefore, DS is an alternative for the DVT risk evaluation. Theoretical Explanation of the DS Response during Blood Coagulation. Our experimental results for both the simple model system and the human whole blood showed that the permittivity of a sample first increased, reached a peak, and then decreased. The time at the peak agreed well with the clotting time determined from the rheological measurement. To understand the mechanism 9772

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of this dielectric response, we demonstrate numerical simulation for simplified models using Hanai’s theory for a dense colloid suspension.21 We assume a suspension of homogeneously dispersed spherical cells before the coagulation starts as shown in Figure 5A. As the coagulation proceeds, aggregation of cells occurs and causes heterogeneous distribution of cells. We consider two regions: one with high cell concentration and the other without cells (voids). We tested four different systems: (a) spherical voids surrounded by high cell concentration region, (b) spherical aggregates surrounded by void space, (c) two separated phases with the boundary parallel to the electric field, and (d) two separated phases with the boundary perpendicular to the electric field. The geometric and electric parameters used in the calculations of permittivity are listed in Table 1. In general, the permittivity of a diluted suspension of spherical cells is described by the Maxwell-Wagner mixture formula, where effects of intercellular interactions are not considered.10 For a dense suspension like human whole blood, however, the (21) Hanai, T. Kolloidn. Zh. 1960, 171, 23–31.

Figure 4. (A) Time dependences of the normalized dielectric spectra at 760 kHz for the human whole blood through a coagulation process (red plots) and a control experiment (black plots). The dotted line shows the peak time of the normalized dielectric spectrum defined as the dielectric coagulation time Ti(DS). (B) The LDF curve for the human whole blood that was taken from the same blood collection tube for (A). The dotted line shows the clotting time Ti(LDF). (C) Correlation between Ti(DS) and Ti(LDF) for four healthy donors.

intercellular interactions are not negligible. The Hanai mixture formula that takes into account the interactions should give better representation of our experimental results.10,22 According to the Hanai mixture formula, the complex permittivity of a suspension of homogeneously dispersed cells is described by

( )

ε* - ε*c ε*s ε*s - ε*c ε*

1/3

) 1 - φc

(1)

where ε*c is the complex permittivity of a cell and described by ε*c ) ε*m

2(1 - v)ε*m + (1 + 2v)ε*cp (2 + v)ε*m + (1 - v)ε*cp

(2)

where v ) {r/(r + d)}3. (See also Table 1 for the definitions of other parameters.) To calculate the permittivities corresponding to the models (a)-(d) in Figure 5A, the complex permittivity of the void ε*v and that of the aggregated region ε*a are required. We assumed (22) Kaneko, H.; Asami, K.; Hanai, T. Colloid Polym. Sci. 1991, 269, 1039– 1044.

Figure 5. (A) A schematic model of a spherical cell and that of a homogeneously distributed suspension. Aggregation and sedimentation of cells cause the spatial distribution of cell volume fraction. Four simplified models from (a) to (d) presented consist of aggregated region with high volume fraction (pink) and void without cells (light blue). (B) Dielectric spectra for the models from (a) to (d) in (A) calculated by Hanai’s equation. The broken curve shows the spectrum for the homogeneous suspension. (C) Changes of normalized dielectric constants at 100 kHz with aggregation level expressed by the volume fraction of voids for the models from (a) to (d). Table 1. Geometric and Electric Parameters in the Modeled Coagulation System Geometric Parameters cell radius thickness of cell membrane volume fraction of cell volume fraction of aggregated region volume fraction of void region volume fraction of cell in aggregated region Electric Parameters complex permittivities static permittivity of surrounding medium conductivity of surrounding medium static permittivity of cell membrane specific cell membrane capacitance conductivity of cell membrane static permittivity of cytoplasm conductivity of cytoplasm

r ) 6.0 µm d ) 5.0 nm φc ) 0.4 φa φv ) 1 - φa φca ) φc/φa ε*x ) εx - jκx/ωε0, x ) s, m, cp εs ) 74 κs ) 1.7 S m-1 εm ) Cmd/ε0 ) 3.4 Cm ) 0.6 µF cm-2 κm ) 0 εcp ) 60 κcp ) 1.0 S m-1

ε*v ) ε*s (i.e., the voids contain no cells) and obtained ε*a from eq 1 by replacing ε* and φc by ε*a and φca, respectively. Finally, the complex permittivity of the whole system ε* was also obtained from eq 1 by, respectively, replacing ε*, c ε*, s and φc by ε*, v ε*, a and φv for model (a) and ε*, c ε*, s and φc by ε*, a ε*, v and φa for model (b). In models (c) and (d), ε* is calculated for a parallel and series connection of the two phases as ε* ) φvε*v -1 -1 + φaε*a and (ε*)-1 ) (ε*/φ + (ε*/φ v v) a a) , respectively. Figure Analytical Chemistry, Vol. 82, No. 23, December 1, 2010

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5B shows the results for the models (a)-(d) with φv ) 0.2. Furthermore, Figure 5C shows the φv dependences of the normalized dielectric constants at 100 kHz for the same models. Only in model (c) are the dielectric constants smaller than those for the intact suspension. The effects of the sedimentation reproduced for the models (c) and (d) agreed well with the previously reported experimental results.23 Because our experimental setup coincides with model (c), the observed decrease of the dielectric constant is explained by the sedimentation. A more realistic model can be the hybrid of models (a), (b), and (c). In the initial stage of the coagulation, the effect of the sedimentation is weaker than that of the local aggregation of cells. Thus, the dielectric constant increases as shown for models (a) and (b). However, as the coagulation progresses, the size of aggregates increases and approaches the macroscopic level; the gelation also proceeded in parallel. The effects appeared as the increase of the macroscopic viscosity and the decrease of the dielectric constant following the increase of the sedimentation rate. Therefore, the peak of the dielectric constant is found at the time close to the clotting time observed by the rheological method.

CONCLUSIONS The permittivity of both the model system of animal erythrocytes and the human whole blood at a frequency around 1 MHz was found to be sensitive to the coagulation process. Its temporal dependence exhibited a peak at the time, which agreed well with the rheologically determined clotting time. These findings were explained by our theoretical consideration. The increase of the permittivity during the initial stage is due to the increase of the heterogeneity of the system as the local aggregates of erythrocytes grew. As the coagulation further progressed, the sedimentation of large aggregates became dominant and caused the decrease of the permittivity. Therefore, dielectric coagulometry as proposed by this study allows quantitative monitoring of the blood coagulation activity and thus is a promising technique for DVT risk evaluation.

(23) Asami, K.; Hanai, T. Colloid Polym. Sci. 1992, 270, 78–84.

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ACKNOWLEDGMENT We thank Y. Shiga for his assistance in experiments.

Received for review July 21, 2010. Accepted October 4, 2010.