Home Search Collections Journals About Contact us My IOPscience Dielectric properties of blood: an investigation of haematocrit dependence This content has been downloaded from IOPscience. Please scroll down to see the full text. 2003 Physiol. Meas. 24 137 (http://iopscience.iop.org/0967-3334/24/1/310) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 193.50.135.4 This content was downloaded on 26/08/2014 at 15:16 Please note that terms and conditions apply. INSTITUTE OF PHYSICS PUBLISHING PHYSIOLOGICAL MEASUREMENT Physiol. Meas. 24 (2003) 137–147 PII: S0967-3334(03)53485-2 Dielectric properties of blood: an investigation of haematocrit dependence F Jaspard, M Nadi and A Rouane Laboratoire d’Instrumentation Electronique de Nancy, Faculté des Sciences, BP 239, 54506 Vandoeuvre les Nancy Cedex, France Received 12 September 2002, in final form 5 November 2002 Published 17 January 2003 Online at stacks.iop.org/PM/24/137 Abstract We have investigated the haematocrit dependence of the electrical parameters (relative permittivity and conductivity) of blood. The measuring set-up, composed of an impedancemeter (HP 4291A), an open-ended coaxial line and a temperature controlling set, was designed for dielectric measurements in the 1 MHz to 1 GHz frequency range. Measurements were performed on ex vivo animal (cow and sheep) blood at 37 ◦ C. The two dielectric parameters appeared to be strongly dependent on the haematocrit. The permittivity versus frequency decreases then increases when the haematocrit decreases. The conductivity increases in the whole frequency range when the haematocrit decreases. Due to the lack of comparative data on the frequency range explored, we compare the dielectric profiles with those deduced from the Maxwell–Fricke theoretical model. Keywords: bio-impedance, electrical properties, bioelectromagnetism, dielectric spectroscopy, blood properties 1. Introduction The evaluation of the interaction between electromagnetic waves and biological tissues is a challenge of utmost importance for different applications, such as medical diagnostics and therapy, or in the general problem of electromagnetic dosimetry. To quantify these interactions, one approach is to use a numerical model performed on a computer. This method requires precise knowledge of parameters that characterize the electrical behaviour of the biological tissue: the relative complex permittivity (ε∗ = ε − jε ) or the complex conductivity (σ ∗ = σ  − jσ  ). These parameters are directly related by the following equation (Inan and Inan 1998) σ ∗ = jε0 2πf ε∗ 0967-3334/03/010137+11$30.00 © 2003 IOP Publishing Ltd Printed in the UK (1) 137 138 F Jaspard et al HP 4291A Material analyzer Thermostat Thermostated bath (37°C) Computer Extension coaxial cable Open ended coaxial probe Blood sample in the Plexiglas container Figure 1. Experimental set-up. where ε0 is the vacuum permittivity and f is the frequency. The two values usually used to completely describe the electrical comportment are the real parts of the relative permittivity (ε ) and conductivity (σ  ). Blood is a complex biological tissue present all over the body. Knowledge of its electrical behaviour is thus very important for the modelling of biological tissues with respect to the in vivo characteristics. Recently, we have presented an experimental set-up for the measurement of the relative permittivity and the conductivity of blood in the frequency range of 1 MHz to 1 GHz (Jaspard and Nadi 2002). This device permits us to investigate the electrical behaviour of blood and its dependence on the two main influencing factors: temperature and haematocrit. In this previous publication, we have presented results concerning the dielectric evolution as a function of temperature. In this paper, we complete this study with the investigation of the haematocrit dependence. The haematocrit level refers to the blood volume concentration of red blood cells. Several authors have studied the electrical dependence of blood on this parameter in low frequencies below 100 kHz. The influence on the electrical comportment has been studied directly through the permittivity and the conductivity (Pfützner 1984), through the resistivity (Geddes and Sadler 1973, Hill and Thomson 1975) or by using the electrical lumped elements of the Fricke model (Zhao 1993). At higher frequencies, to our knowledge, only one study of the influence of haematocrit has been performed on human blood (Bianco et al 1979a, b) over a frequency range of 100–2000 MHz. In the following investigation, we propose a study of the influence of haematocrit on the dielectric properties (ε and σ  ) of animal blood (cow and sheep) at body temperature (37 ◦ C) in the frequency range between 1 MHz to 1 GHz. These results are complementary to those obtained by the previously cited authors. In order to validate our experimental data, we have used the classical theoretical analysis developed by Maxwell (1873) and Fricke (1924, 1925). 2. Method and measurement 2.1. Experimental set-up The determination of the electrical characteristics of blood requires a specific device and an adapted experimental approach. The instrumentation used consists of an impedancemeter (HP 4291A), using a volt–amperemetric method, associated with an open-ended coaxial probe. The measuring cell is presented in more detail in Jaspard and Nadi (2001). The electrodes, which have diameters of 3 mm and 10 mm, are in copper covered by a thin deposit of nickel, so as to avoid all oxidation phenomena, and are filled with Teflon. The blood sample is placed in a Plexiglas tube partially submerged in a thermostated bath, which allows us to obtain blood at 37 ◦ C. Figure 1 shows the experimental set-up used. Dielectric properties of blood 139 Relative permittivity 10000 1000 100 Hct=20% Hct=31.5% Hct=41% Hct=55% Hct=71% 10 1 10 100 1000 Frequency (MHz) Figure 2. Relative permittivity of cow blood versus frequency for different haematocrit levels (Hct). The modelling of the electric behaviour of the probe is a fundamental step, which relates the complex permittivity (or conductivity) of the biological tissue to the measured electrical impedance. We have opted for the lumped electrical equivalent circuit (Stuchly et al 1974, Kraszeski and Stuchly 1983, Stuchly and Stuchly 1984), which has been presented in more detail in Jaspard and Nadi (2002). The validation of this experimental set-up, in the frequency range from 1 MHz to 1 GHz, was performed on standard products (water, saline solutions, methanol, ethanol and glycerol) and has shown close agreement with the reference data (Jaspard and Nadi 2001, 2002). In particular, at these frequencies, it appears that the lumped model constitutes a suitable model and the polarization impedance is insignificant with respect to the measured blood impedance. 2.2. Blood samples Five litres of cow blood and three litres of sheep blood were sampled (each sample from the same individual). Heparin was used as an anticoagulant in dosages of 55 000 UI (11 ml) and 30 000 UI (6 ml), respectively, for cow and sheep blood. The samples were taken 15 min post-mortem, and immediately set in an isothermal tank (about +10 ◦ C). Then, after 1 h, they were set in a cold room (+5 ◦ C) for less than two days. The levels of haematocrit were adjusted variously between 20–70%. The level of erythrocytes was lowered by diluting each blood sample with its own plasma. The increase of haematocrit was realized after a low-speed centrifugation to separate plasma and red cells without damage. 2.3. Experimental measurements Figures 2–5 present dielectric results obtained for the cow and sheep blood at 37 ◦ C for different levels of haematocrit. The dielectric parameters are deduced from the mean of a set of ten measurements. For an easy reading, only the values obtained with haematocrit close to 40% were associated with dispersion lines representing twice the standard deviation of the mean. 140 F Jaspard et al Relative permittivity 10000 1000 100 Hct=21.5% Hct=30% Hct=42% Hct=55% Hct=71% 10 1 10 100 1000 Frequency (MHz) Figure 3. Relative permittivity of sheep blood versus frequency for different haematocrit levels (Hct). 1,8 1,6 Conductivity (S/m) 1,4 1,2 1 0,8 0,6 Hct=20% Hct=31.5% Hct=41% Hct=55% Hct=71% 0,4 0,2 0 1 10 100 1000 Frequency (MHz) Figure 4. Conductivity of cow blood versus frequency for different haematocrit levels (Hct). Measurements were made after having slowly mixed the blood samples in order to homogenize the medium. Compared to the other evolution measured, permittivity measurements performed on cow blood with a haematocrit of 31.5% show significant divergences attributed to errors which need to be defined more precisely. Dielectric properties of blood 141 1,8 1,6 Conductivity (S/m) 1,4 1,2 1 0,8 0,6 Hct=21.5% Hct=30% Hct=42% Hct=50% Hct=70% 0,4 0,2 0 1 10 100 1000 Frequency (MHz) Figure 5. Conductivity of sheep blood versus frequency for different haematocrit levels (Hct). 2.4. Results and discussion The different dielectric evolutions observed may be explained by considering blood as a heterogeneous medium essentially constituting erythrocytes in plasma. The other elements are less numerous and can be neglected in a first approximation (Trautman and Newbower 1983). Plasma can be considered as a homogeneous medium with an electrical behaviour close to a physiological solution (Trautman and Newbower 1983). Erythrocytes are composed of a thin membrane electrically similar to a perfect capacitance (Schwan 1957). This membrane delimits the internal medium of the cell, which is principally constituted of haemoglobin. The following analysis does not take into account the permittivity divergence observed at 31.5%. This singularity is attributed to errors that need to be defined more precisely At low frequencies, the cell membrane is a perfect capacitance. Then, it involves a high relative permittivity (1000–2000) and a conductivity process essentially due to the ionic activity of the suspending medium (plasma). The increase of the haematocrit induces an increase in the number of membranes with a decrease in the volume of plasma. Then, we observe an increase of the relative permittivity with a drop of the conductivity when the haematocrit increases. At high frequencies, the erythrocyte membrane appears to be entirely short-circuited and the cell interior participates in the electrical mechanism. The relative permittivity decreases significantly (50–70) whereas the conductivity presents a marked increase induced by the relaxation of the water molecules, which is stacked to the ionic conductivity still present. For the permittivity, the variations observed as a function of the haematocrit are opposite to those at low frequencies. When the haematocrit increases, the permittivity decreases. This phenomenon is due to the cell membranes, which, at these frequencies, no longer influence the electrical comportment of blood. The inner medium of the erythrocytes has a relative permittivity of 45 (Pauly and Schwan 1966) at high frequencies, slightly lower than that of plasma, of the order of 70 (Cook 1951). Thus, the relative permittivity reaches 45 with an increase of the haematocrit and 70 with a decrease of the haematocrit. 142 F Jaspard et al We note the lack of sensitivity around 40 and 80 MHz for cow and sheep blood, respectively. In fact, around 50 MHz, the cell membrane can be considered partially shortcircuited. Then, at this frequency, the relative permittivity of the erythrocytes is of the same order as that of the plasma around 70 (Cook 1951). Blood can be considered as an electrical homogeneous medium and the haematocrit presents some influence on the total relative permittivity. Contrary to the permittivity evolution, the conductivity presents no singularity. In the whole frequency range explored, we observed a decrease with the increase of the haematocrit. For high haematocrit, the cell interior liquid provides the conductivity of blood whereas, when the haematocrit is weak, the plasma ensures the conduction process. 3. Comparison with the Maxwell–Fricke model Due to the lack of comparative data, the validation of the results obtained remains difficult. In the frequency range explored, only one previous study concerned the dielectric evolution as a function of haematocrit (Bianco et al 1979a, b). The results obtained by Bianco et al on human blood, at 24 ◦ C, were carried out at the following frequencies: 100, 500, 1000, 1500 and 2000 MHz. They have presented dielectric evolutions similar to our own measurements. Nevertheless, because of the lack of data at frequencies over 100 MHz, we cannot observe significantly the change of the relative permittivity variation. Thus, to conclude definitively on the validity of our results, we propose to compare our data with the Maxwell–Fricke theoretical analysis. 3.1. Maxwell–Fricke model of suspended cells Frequently used in the study of the blood dielectric comportment (Schwan 1983, Pauly and Schwan 1966, Bianco et al 1979a, b), the Maxwell–Fricke model allows us to approach the electrical behaviour of whole blood or its constituents. This model was first proposed by Maxwell (1873) who calculated the conductivity of a dilute suspension (plasma) of spherical particles (erythrocytes). Maxwell’s theory was applied for a static field and Wagner (1914) extended this analysis to the case of an alternating field. The results obtained relate the complex conductivity of the continuous (plasma) and suspended phases (red cell) to that of the mixture (blood) using the following equation (Foster and Schwan 1996) ∗ σRC − σP∗ σB∗ − σP∗ = Hct ∗ σB∗ + ησP∗ σRC + ησP∗ (2) ∗ are the complex conductivity of blood, plasma and red cells respectively, where σB∗ , σP∗ and σRC and Hct is the haematocrit. The factor η is a ‘form factor’ introduced by Fricke (1924, 1925) ∗ /σP∗ ratio. η is not a factor that is critical for the to take into account the shape cell and σRC ∗ evaluation of σB , hence we assume η = 2 in the entire frequency range from 1 MHz to 1 GHz. This value supposes that erythrocytes are spherical particles. The erythrocyte dielectric comportment can be described supposing that these cells are like homogeneous spherical particles of radius R surrounded by a thin membrane of thickness d. Equation (3) gives an extension of the Maxwell–Fricke equation (Foster and Schwan 1996)
 ∗ ∗ ∗ σRC − σMB R 3 σI∗ − σMB = ∗ ∗ ∗ σRC + 2σMB R + d σI∗ + 2σMB (3) ∗ represent the complex conductivity of the interior medium and of the where σI∗ and σMB membrane, respectively. If the membrane thickness is small compared to the cell radii, Dielectric properties of blood 143 Table 1. Frequency dependence of the dielectric values of plasma and interior erythrocyte liquid used in the Maxwell–Fricke model. Plasma Freq. (MHz) εP σP 1 2 4 8 20 40 80 200 400 800 1000 70 – – – – – – – – – – 1.4 – – – – – – 1.45 1.53 1.67 1.75 (S Interior red cell liquid m−1)  εint  (S m−1) σint 65.5 65 64.5 63 59 55 51 48 46 45 45 0.5 – – – – – – 0.55 0.63 0.77 0.85 equation (3) reduces to (Foster and Schwan 1996) ∗ = σRC σI∗ + 1+ 2d ∗ σ R MB ∗ ∗ d σI −σMB ∗ R σMB . (4) 3.2. Method for comparison with the Maxwell–Fricke model We propose to validate our results by comparing them with the Maxwell–Fricke theoretical analysis. For this, dielectric values of the elementary constituents of blood have been adjusted until we obtain close agreement between the dielectric model and our measured values (with haematocrit around 40%). Following this, we varied the haematocrit and observed the evolution of the dielectric parameters. 3.3. Electrical definition of the blood constituents Theoretical dielectric profiles were obtained by considering plasma as a homogeneous medium with an electrical behaviour close to a physiological solution (Trautman and Newbower 1983). Then, the relative permittivity of plasma (εP ) is considered to be constant and equal to 70 at 37 ◦ C (Cook 1951). The corresponding ionic conductivity (σP ) used in the Maxwell– Fricke model is 1.4 S m−1 at 37 ◦ C, which is smaller than the value found by Geddes and Sadler (1973), about 1.7 S m−1 at 37 ◦ C for human blood. Nevertheless, values found by Cook (1951) and Ulgen and Sezdi (1997) for human blood at 35 ◦ C (1.55 S m−1) and 37 ◦ C (1.54 S m−1), respectively, agree with our results. At frequencies below 80 MHz, the relaxation of the water molecules increases the total conductivity (σP ). The plasma complex conductivity (σP∗ ) used in the Maxwell–Fricke model is given in table 1. In a first approximation, the biconcave shape of the erythrocytes is approached by a spherical particle of radius R = 2.4 µm (Schwan 1957). The cell membrane thickness is d = 7.5 nm (Aimé-Genty 1999) and the membrane capacitance is CMB = 0.8 µF cm−2 (Schwan ∗ ) is given by the following 1957). The complex conductivity of the erythrocyte membrane (σMB expression (Foster and Schwan 1996): ∗ σMB = jωCMB d. (5) 144 F Jaspard et al Table 2. Frequency dependence of the dielectric values of sheep blood (Hct = 42%) and cow blood (Hct = 41%) compared with the results obtained from the Maxwell–Fricke model (Hct = 40%). Sheep blood (Hct 42%) Cow blood (Hct 41%) Maxwell–Fricke (Hct 40%) Freq. (MHz) ε σ  (S m−1) ε σ  (S m−1) ε σ  (S m−1) 1 2 4 8 20 40 80 200 400 800 1000 1387 787 486 308 154 93 71.3 59.5 57.2 54.6 52.8 0.69 0.71 0.76 0.86 0.97 1.01 1.04 1.10 1.18 1.32 1.38 1370 755 446 268 133 83.3 66.7 57.1 54.7 52.1 50.5 0.71 0.72 0.75 0.82 0.88 0.90 0.92 0.96 1.03 1.19 1.29 1301 1092 682 303 111 76 65 61 60 59 59 0.72 0.76 0.85 0.93 0.96 0.97 0.98 1.03 1.12 1.26 1.34 Pauly and Schwan (1966) listed the internal low-frequency conductance at 25 ◦ C of seven different species and, in particular, for cow blood (0.43 S m−1) and sheep blood (0.44 S m−1). Ulgen and Sezdi (1997) and Bianco et al (1979a, b) found values of around 0.4 and 0.6 S m−1, respectively, for human erythrocytes at 37 ◦ C. The static conductivity of 0.5 S m−1, which agrees with the preceding values, is used in the Maxwell–Fricke model. At higher frequencies, the conductivity increases due to the relaxation of the water molecules. Table 2 gives the conductivity (σI ) used in the Maxwell–Fricke model. The frequency behaviour of the relative permittivity of the red cell interior liquid (εI ) was determined by Pauly and Schwan (1966) and Bianco et al (1979a, b) above 100 MHz using a Maxwell–Fricke analysis. They found similar results for εI between 60–50 in a frequency range of 100–300 MHz. Pauly and Schwan (1966) have also directly measured the relative permittivity of a packed bovine erythrocyte lysed with saponin in the frequency range of 1–300 MHz. The values used in the Maxwell–Fricke model are summarized in table 1. They are taken from the work of Mouneime (1986), who measured the relative permittivity of a 30% suspension of haemoglobin at 25 ◦ C prepared by lysis and filtration. These values are in agreement with the above-mentioned research. 3.4. Results and discussion Table 2 lists dielectric values measured on cow blood at 41% and on sheep blood at 42%. To estimate the suitability between the model and the measurements, we give in parallel, in table 2, values obtained from the Maxwell–Fricke model, using the above electric definition of the elementary blood constituents, for a haematocrit of 40%. More significant divergences appear at low frequencies between 1–10 MHz on the permittivity values. These may be due essentially to the erythrocyte capacitive influence. In order to ‘smooth’ the dielectric curve, we must adjust the capacitive effect of the cell membrane with the parameters Cm, d, R and η. Another parasitic effect could be due to the limits of the Maxwell–Fricke theory. In fact, this model takes into account only one relaxation process with a single relaxation frequency in accordance with Debye theory. This supposes that all erythrocytes have the same morphological characteristics (form, radius and thickness). Naturally, this is not exactly the case and the relaxation process is better described using the notion of relaxation frequency distribution. Nevertheless, despite this divergence, Dielectric properties of blood 145 Relative permittivity 10000 1000 100 Hct=20% Hct=30% Hct=40% Hct=50% Hct=70% 10 1 10 100 1000 Frequency (MHz) Figure 6. Frequency dependence of dielectric values obtained from the Maxwell–Fricke model: relative permittivity versus haematocrit (Hct). 1,8 1,6 Conductivity (S/m) 1,4 1,2 1 0,8 0,6 Hct=20% Hct=30% Hct=40% Hct=50% Hct=70% 0,4 0,2 0 1 10 100 1000 Frequency (MHz) Figure 7. Frequency dependence of dielectric values obtained from the Maxwell–Fricke model: conductivity versus haematocrit (Hct). the precision of this model appears to be sufficient to estimate the dielectric evolution as a function of the haematocrit. The permittivity and conductivity profiles obtained from the Maxwell–Fricke model for different haematocrit levels are presented in figures 6and 7. The dielectric evolutions appearing from this model are close to the variations measured. In particular, we see the inversion of the sign of the permittivity evolution around 50 MHz in accordance with our measurements. 146 F Jaspard et al 4. Conclusion In this paper, we show the attraction of using the volt–amperemetric method for dielectric spectroscopic systematic measurements. The measurements were performed on whole blood versus haematocrit in the frequency range of 1 MHz to 1 GHz. Thus, our results appear to complement previous results, principally realized at low frequency (Pfützner 1984, Geddes and Sadler 1973, Hill and Thomson 1975). The validation of the results was performed using the Maxwell–Fricke analysis, which constitutes a classical theoretical tool for confirming the dielectric comportment of blood. The results obtained agree with the experimental spectroscopic profile. The two dielectric parameters have different evolutions as a function of haematocrit. The data obtained for conductivity indicate a marked increase of this parameter when haematocrit decreases. The variations measured for the relative permittivity present a marked sensitivity and a specific change of sign around 50 MHz. At this frequency, for permittivity, blood appears to be an electrical homogeneous medium. It appears that the frequency range around 50 MHz is a critical point for the relative permittivity for which haematocrit and temperature (Jaspard and Nadi 2002) induce no significant variation. These measurements and observations may help in electromagnetic dosimetry or in the development of biomedical instrumentation: blood analysers, extra-body blood regulation systems, applications with respect to blood disorders, bio-impedancemetry. Acknowledgments The authors would like to thank Patrice Roth, University of Nancy, for the realization of the measuring probe. They would also like to thank Laure Joly MD of the hospital of Nice for her help. 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