ELSEVIER Biochimica et Biophysica Acta 1201 (1994) 179-185

BB. Biochi~ic~a et Biophysica A~ta

Contributions of suspending medium to electrical impedance of blood

Tian -Xian Z h a o *

Karolinska Institute, Department of Medical Engineering, F60, Novum, Huddinge Hospital, S-141 86 Huddinge, Sweden

Received 20 April 1994

Abstract

Blood cells from ten normal subjects, anticoagulated with dried sodium heparin, were washed twice with phosphate-buffered saline (PBS) and resuspended with autologous plasma, serum, serum plus sodium heparin, and PBS. The resistance Rp and capacitance C m of these suspensions were determined by measuring the impedances at three frequencies 100 kHz, 800 kHz and 1.2 MHz, and found to be dependent on the proteins and electrolytes of the suspending medium. Two suspensions with the same medium resistivity might have different resistances if the contents of the two mediums are different. The fibrinogen, serum proteins, sodium heparin and membrane contributed to C m by 20%, 14%, 2% and 64%, respectively. For the samples with buffered sodium citrate as anticoagulant and in the haematocrit range 30-60%, the group washed and resuspended with PBS had a consistently decreased Rp and C m compared to the original group. Sodium heparin seemed to be the best anticoagulant when studying the electrical impedance of blood. The influence of suspending medium might result in part from the altered interfacial polarisation. The results might be useful for understanding the origin of the impedance of blood, and imply that impedance measurement may be an alternative method for screening purposes for diseases that involve abnormal compositions of certain plasma proteins.

Keywords: Electrical impedance; Electrolyte; Erythrocyte; Inteffacial polarisation; Membrane; Plasma protein; (Blood)

I. Introduction

The electrical impedance of blood is determined primar- ily by plasma resistance Rp, cell interior fluid resistance R i and cell membrane capacitance C m [1,2]. The measure- ment of Rp has been used in the impedance plethysmogra- phy and the impedance cardiography, and for estimating the haematocrit (Hct), etc. [3]. The three parameters might be also useful for detecting certain pathological changes of blood. For example, Rp was found greater for house painters than for normal subjects [4]. Ballario et al. [5] reported a significantly lower capacitance for homozygous fl-thalassemia samples as about 0 . 5 / zF / cm 2, compared to 1.1 /xF/cm 2 for normal samples.

Under certain circumstances, such as during haemodial- ysis and autologous blood transfusion, and while investi- gating the electrical characteristics of pure cell membranes, the blood needs to be washed or mixed with some physio- logical solutions. The impedance is then likely altered by the added solutions. Mohapatra et al. [6], for example,

* Corresponding author. Fax: + 46 8 7795550.

0304-4165/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD! 0 3 0 4 - 4 1 6 5 ( 9 4 ) 0 0 0 6 9 - A

reported a lower resistivity of blood from haemodialysis patients. The reason might be that during haemodialysis, certain plasma contents were replaced by dialysate, the resistivity of which might be lower than that of plasma. McMahon and Carpenter [7] reported a lower haematocrit value for autologous transfusion blood samples obtained by the electrical conductivity method as compared to the conventional method. In their experiments, the blood lost from patient during surgery was processed in an autolo- gous transfusion system, in which the collected blood was washed with physiological saline, and the packed blood cells were transferred to a reservoir bag for subsequent reinfusion. The resistivity of the suspending medium was lower than that of plasma, resulting in a lower value of the measured resistance and haematocrit.

Also, the electrical capacitance of blood has been found to be influenced by the electrolytes in the suspending medium. Bordi et al. [8] reported that the capacitances of the erythrocytes washed twice with isotonic saline solution and resuspended into LiC1, NaC1, KC1 and CsC1 solutions were 0.355, 0.317, 0.179 and 0 .175/xF/cm 2, respectively. The authors explained the difference as caused by a vary- ing effect of different cations on the structure of the erythrocyte membranes, such as the roughness of the mem-

180 T.X. Zhao / Biochimica et Biophysica Acta 1201 (1994) 179-185

brane surface. Cametti et al. [9] showed that the permittiv- ity of the lymphocytes was increased after incubation with two gangliosides (GM1 and GM3). The increased values, however, were different for the samples treated with GM1 and GM3. The changed polarisability of the hydrophilic region of the membranes was proposed as the reason for the differences. Zhao et al. [10] found that the specific membrane capacities were 1 .3/xF/cm 2, 1.3/ . tF/cm 2, and 1.6 /xF/cm 2 for the samples with acid citrate dextrose (ACD), ethylenediaminetetraacetic acid (EDTA), and buffered sodium citrate as anticoagulants, respectively, which were all greater than the commonly used figure 1.0 /zF/cm 2.

In summary, the components of the suspending medium affect both the resistance and the capacitance of blood cell suspensions. The extent of these effects and their mecha- nisms, however, have not been satisfactorily investigated. Hence, the aim of the present study was to explore the contributions of plasma proteins, electrolytes, and blood cells to the impedance of blood.

I IBM PC

Measuring cell

Signal sources

Rref Detectors

Temperalure~ ~ Ajuminium block controllers Test tube

Blood Fig. 2. Block diagram of the measur ing system.

2. Materials and methods

2.1. Theory and measuring system

The theory and the measuring system have been de- scribed in detail in a previous paper [10]. In brief, the electrical impedance of blood can be approximately simu- lated by a three element circuit in which Rp is in parallel with R i and C m in series, as shown in Fig. 1. For such a circuit, if the amplitudes of three impedances Z(wo), Z(Wl), Z(to 2) are measured at different frequencies oo o, w 1, 0~2, the values of the three elements can be determined a s :

R p = Z ( w o ) K~o (1)

Rp R i = (2)

K 1 - K 0 - F ] ( 1 - K 0)

K° K 1 - K o - F1Ka(1- Ko) - 1

1 ~ 1 - K o

Crn=---~o K ° R 2 - ( R p + R i ) 2 (3)

Rp Cm

- 7 - Fig. 1. Three-element model of blood impedance. Rp represents plasma resistance, R i cell interior resistance and C m cell membrane capacitance.

where,

F1-- ,KI= ==--=,, (-00 ] 0")0

t z(,Oo) ] '

FIK2(1 - K1)(] - - F 2 ) - F2KI(1 - K2)(1 - F1) K o =

F1(1 - K1)(1 - K2F2) - F2(1 - K2)(1 - K1F1)

The diagram of the measuring system is shown in Fig. 2. Blood is drawn by a roller pump from a test tube into a specially designed flow-through measuring cell which was calibrated using saline solutions with various concentra- tions of NaC1 in the range 30-100 mmol/1. The tetrapolar technique is used to reduce the errors caused by the polarisation of the electrodes. Three constant currents with frequencies 100 kHz, 800 kHz and 1.2 MHz are consecu- tively applied to the blood sample and the reference resis- tor, Rr~ f. The ratio of the voltages detected from blood and Rre f is then a measure of the impedance of the blood. The temperatures of the test tube and measuring cell are ad- justed to 37 + 0.1°C by two temperature controllers. The maximum measuring errors are estimated to 0.5% f o r Rp, 5% for Cm, and 10% for R i.

2.2. Samples

The washing of blood cells was accomplished by centri- fuging the sample at 1000 × g for 10 min and mixing the packed cells with about twice as much phosphate-buffered saline (PBS, pH 7.4) and centrifuging the suspension again. The packed cells were washed once more and then

T2(. Zhao / Biochiraica et Biophysica Acta 1201 (1994) 179-185 181

Table 1 Impedance parameters at 37°C of washed blood cells resuspended in various solutions, expressed as mean + S.D., n = 10

Medium RploO Riloo Cml00 pp (12cm) (12cm) (pF/cm) (Ocm)

Plasma 389.3 + 12.9 148.5 + 2.2 928.2 + 62.2 69.4 + 1.6 SSH 374.3+ 6.9 150.4+10.9 741.1+35.0 69.1+1.5 Serum 374.1+ 9.6 148.0+13.9 724.9+36.1 69.1+1.6 PBS 289.0+ 4.8 137.2+16.6 592.0+33.1 56.1+0.2

SSH, serum plus dried sodium heparin; PBS, phosphate-buffered saline

on each 2 ml blood sample. For each measurement, 0.5 ml blood was drawn into the measuring cell by a roller pump and the measurement started after a delay of 45 s to allow the blood to reach thermal equilibrium and the blood cells to settle. The sample tube was removed and agitated between each of the four measurements. The first two measurements were ignored, however, since they were merely used for checking that the sample had reached a constant temperature and that the rinsing water had been sufficiently removed from the cell. The means of the last two measurements were used as the results for the sample.

mixed with certain solutions to obtain a sample with any desired haematocrit.

To study the contributions of fibrinogen, serum pro- teins, anticoagulant, and erythrocytes to the impedance, 50 ml blood was drawn into five glass tubes (Becton Dickin- son Vacutainer, 10 ml each) from each of ten normal subjects. Two tubes were plain (no anticoagulant) and three with dried sodium heparin as anticoagulant. The serum, obtained from the two plain tubes after centrifuging the coagulated blood, was divided into two parts, one of which was put into an unused tube with dried sodium heparin to get the serum-sodium-heparin (SSH) solution. The cells and the original plasma were separated by centri- fuging the three tubes of anticoagulated blood. After being washed twice with PBS, the packed cells were divided into four parts, each of which was then mixed with one of the four mediums: plasma, serum, SSH, or PBS. In this way, four samples with various suspending mediums were ob- tained from each subject. The haematocrits of all the samples were controlled within 46-52%. The resistivity of each suspending medium was also measured for all sam- ples.

For comparison between original and washed samples in a wide haematocrit range and with another type of anticoagulant instead of sodium heparin, twenty normal subjects were used for the original group and another twenty for the washed group. From each subject, about 10 ml blood was drawn into two vacuum tubes, each contain- ing 1.25 ml buffered sodium citrate as anticoagulant. By reconstituting the proportions of original plasma and blood cells (for the original group) or PBS and washed cells (for the washed group), two or three samples with haematocrits between 30% and 60% were obtained for each subject for later measurement.

2.3. Procedures of measurement

Before measurement, the samples, contained in 5 ml plastic tubes, were placed inside an incubator with the temperature controlled to 37 + 1.5°C, and agitated for at least 20 min by a roller mixer. The haematocrit of each sample was determined by centrifuging two capillary tubes with the blood at 12000 rev/min for 5 min in a micro- centrifuge. Four impedance measurements were then made

2.4. Statistics

Paired t-tests were used to verify the significance of the differences of impedance values for the samples with various suspending solutions. To study whether there is a significant difference in a wide haematocrit range caused by washing, t-tests were performed on the slopes of the linear regression formulas for both Rp and C m between the original and washed samples. Analyses of covariance were performed on the intercepts to illustrate if the two regression lines are parallel but differ in position.

2.5. Normalisation for haematocrit

For comparison between different samples, it is neces- sary to eliminate the influence of hct with which rp, c m and r i are almost linearly related in a narrow haematocrit range. When h was introduced to represent haematocrit in decimal, i.e., h = Hct/lO0, rp, c m and r i could be nor- malised to 100% haematocrit by calculating the ratios rploo = rp/h, Cml00 = Cm/h and the product riloo = r i )< h, respectively.

3. Results

The impedance parameters for washed blood cells re- suspended with various mediums are shown in Table 1. The significance levels of the differences by paired t-tests are shown in Table 2. Fig. 3 shows the original data for the capacitance.

Table 2 Comparison by paired t-tests for the impedance parameters among the samples with various suspending solutions

Rpl00 Riloo Cml0O Pp

PLA-SER 0.001 0.9 0.001 0.01 PLA-SSH 0.001 0.7 0.001 0.2 PLA-PBS 0.001 0.1 0.001 0.001 SER-SSII 0.9 0.4 0.01 0.8 SER-PBS 0.001 0.1 0.001 0.001 SSH-PBS 0.001 0.05 0.001 0.001

The figures indicate P < . SSH, serum plus dried sodium heparin; PBS, phosphate-buffered saline.

182 T.X. Zhao / Biochimica et Biophysica Acta 1201 (1994) 179-185

12 O0

•EulO00 ID

Q.

400

II o r . l , . , I . . . . . ... ""., .U, ..../" " l . . ..,"'

" i . . . . . . U'*'" "',,. .,." " ' " / " i ,

O . •

,.'.A'-, .'::~'" R . '" 2:::" ",~'o-..::,i . . . . . "::::e:::: . . . . ::::~.:::,.-e'""

V ' . . . . . . • ' " " . . . . V" . . . . . . . " ' V - . _ . . ~ . . . . . . , ~ . . . . . . ~ • ' ' ' ' ' ' IV

. y - ' NP"

I I I t I I I [ I I

1 2 3 4 5 6 7 8 9 10 Sample number

Fig. 3. Haematocrit normalised capacitance (C m / h ) of erythrocytes washed with PBS and resuspended with various solutions: plasma (•) , serum plus dried sodium heparin (O), serum ( • ) and PBS (•) .

220

~ ' 1 8 0

• ~ 140

100 30 60

mlb

% - .," d i l l • O Q

i i II oo°o ° .,. ...~r

,If, 't'=" " o t ~ " . t . ' . . ;

o .° J J

4O 5O Haematocrit (%)

Fig. 4. Scatter plot of plasma resistance Rp at 37°C versus haematocrit (Hct) for normal blood samples anticoagulated with buffered sodium citrate. Linear equations were obtained: original group (•) : Rp = 110.6/(1 - h)-50.3; washed group (O): Rp = 86.4/(1 - h)-25.5, both with r = 0.994, P < 0.001.

The resistivities of PBS (pp) and its corresponding suspension (Rpl00) were significantly lower than those of all other three mediums and of their suspensions. Both pp and Rpl00 of the serum group were not significantly different from those of the SSH group, but lower than those of the plasma group. Between the SSH group and plasma group, Rpl00 was significantly different (about 4%), while pp was not. Rit00 did not show any significant difference, except for that between the SSH and PBS groups.

The values for Cmloo were different for the samples with various mediums, successively decreasing in the order plasma, SSH, serum and PBS. The difference in Cml00 between the plasma and SSH groups, that is 928 p F / c m - 741 p F / c m = 187 p F / c m , should be due to the contribu- tion of fibrinogen. Similarly, the difference between the SSH and serum groups, 741 p F / c m - 725 p F / c m = 16 p F / c m , should be due to sodium heparin, and that be- tween the serum and PBS groups, 725 p F / c m - 592 p F / c m = 133 p F / c m , mainly due to the serum proteins. Assuming the capacitance of the PBS group arises mainly from the membranes (neglecting the effect of PBS), the percentage contributions of fibrinogen, serum proteins, sodium heparin, and membrane to the total capacitance of whole blood, i.e., that of the plasma group (928 pF /cm) , were estimated to 20%, 14%, 2%, and 64%, respectively.

For the samples anticoagulated with sodium citrate, both Rp and C m for the group washed and resuspended with PBS were significantly lower than those for the original group in the haematocrit range 30-60%, as shown in Figs. 4 and 5. The relationships between Rp and h were determined by performing least-squares regression, yield- ing: Rp = 110.6/(1 - h) - 50.3 ( r = 0.994, P < 0.001) and Rp = 86.4/(1 - h) - 25.5 (r = 0.994, P < 0.001) for the original and PBS groups, respectively. Both the slopes and intercepts were significantly different, P < 0.001. The relationships between C m and h were also determined as:

C m = 587 × h + 81 ( r = 0.96, P < 0.001) and C m = 587 × h - 1.6 ( r = 0.97, P < 0.001) for the original and PBS groups, respectively. The intercepts of the two regression lines were significantly different ( P < 0.001), while the slopes were not.

4. D i s c u s s i o n

No big difference was found for the cell interior resis- tance R i among the samples with various suspending mediums. The reason might be that the influence of the medium on R i was small and could not be detected by the present measuring system. Hence the following discussions will be focused on the plasma resistance Rp and mem- brane capacitance C m.

450

~ 350

~250

• =~= ==

• ; %

• • eQ o • ,I • ,,=- % . , . . - . , . ¢ • ==q= ;Ooo "o

= . . . . : .% o ° 0 % qP

• e o o

o:

150 t I 30 40 50 60

Haematocrit (%)

Fig. 5. Scatter plot of capacitance C m at 37°C versus haematocrit (Hct) for normal blood samples anticoagulated with buffered sodium citrate. Linear equations were obtained: original group ( • ): C~ = 587 × h + 81 (r = 0.96, P < 0.001); washed group (O): C m = 587× h - 1.6 (r = 0.97, P < o.ool).

T.X. Zhao / Biochimica et Biophysica Acta 1201 (1994) 179-185 183

Bound = Diffuse -!- "t- i lay er i ayer

+ ~ i i ÷

+ + ,, +

+ - - 4 - - I H P | C~ur~ter -4- -I- ~ O H P ions

Fig. 6. Schematic drawing for the interface between the membrane surface of a red cell and the suspending medium.

4.1. Interfacial polarisation

It is well-known that there exists an interface around the blood cells because of the different electrical properties of the cells and suspending medium. Such an interface con- sists of two ionic layers: a bound layer and a diffuse layer as shown in Fig. 6 [11]. The bound layer consists of the inner and outer Helmholtz planes. The inner plane is the locus of negative ions which are adsorbed from the solu- tion by covalent binding, dispersion forces, etc. The outer plane is the locus of solvated and positively charged counter-ions, attracted to the negatively charged surface by Coulombic forces. Beyond the bound layer is the diffuse region, containing loosely bound and highly solvated counter-ions.

When an external electric field is applied, three types of modifications of the interface will probably take place. First, the separation of the centres of positive and negative charges in the radial direction causes an apparent dipole moment. Second, the bound and the diffuse counter-ions will move tangentially along the surfaces of the cells. Third, certain macromolecules will orient so as to reduce their potential energy [11-13]. Such an interfacial polarisa- tion may affect the effective resistance and capacitance of the suspension. In the frequency range of the present study, however, the tangential movement of the counter- ions is not the case.

4.2. Resistance

The measured effective resistance for a spheroid sus- pension is given by the Maxwell-Fricke equation:

Rp = pp(1 + h / x ) / ( 1 - h) ,

where pp is the resistivity of the suspending medium, h the volume concentration of the spheroids, and x the form factor depending on the shape of the spheroids [14]. For spherical particles, x equals 2; while for red cells with biconcave shape, x approximately equals 1.1. After nor- malisation for h, Rpl00 should be directly proportional to pp, and inversely proportional to x.

The lower value for Rp100 for the PBS group compared to the other three groups (Table 1) is caused mainly by the decreased pp since the resistivity of PBS, 5 6 . 1 0 c m , is

lower than those of plasma, serum and SSH, which are all about 69 Ocm. The consistently lower Rp for the washed group in a wide Hct range compared to the original one (Fig. 4) is also caused mainly by the decreased pp since that for samples with sodium citrate was found to be 62.6 Ocm [10].

Also, the altered pp seems to be the main cause for the influence of the type of anticoagulant on blood resistance since the resistivities and amounts of added solutions are different for various anticoagulants [15]. Among the four types of commonly used anticoagulants, ACD, EDTA, sodium citrate and sodium heparin, the samples with sodium heparin have the largest resistance value, while those with sodium citrate have the smallest. A comparison between Fig. 4 and Table 1 of the present study reveals that Rpl00 for sodium heparin samples, 389 g2cm, is about 13% larger than that for sodium citrate samples, 342 Ocm. No significant difference, however, was found for both Rpl00 and pp between the serum and SSH samples (Table 1), indicating that the influence of dried sodium heparin on the resistance of blood is negligible. Hence, the use of dried sodium heparin as an anticoagulant might be better than the other types when studying the resistance of blood.

The difference in pp between the plasma and SSH samples is 0.3 g-2cm ( 6 9 . 4 0 c m - 69.1 I2cm), which, according to the Maxwell-Fricke formula mentioned above, should result in an increase in Rpl00 by about 1 .70cm, if x = 1.1 and h = 0.5. The measured ARpl0O, however, was 15 g2cm (389 O c m - 374 12cm). The extra increase in Rpl00 by the fibrinogen for the plasma samples might be caused mainly through interracial polarisation.

The conductance of the interracial layer contributes to the measured effective resistance [12], and is proportional to the ion mobility [16]. It is well-known that the mobility of an ion is determined by its molecular mass, size and shape. Fibrinogen, as an elongated or needle-shaped molecule with a length of 60 nm and a molecular weight of 400 000 [17], should have a smaller mobility than that of most of the other substances in the plasma. For pure plasma solution without blood cells, the difference in resistance caused by fibrinogen is too small to be detected by the present measuring system because of low concentra- tion of fibrinogen (normally 0.3% by weight). When blood cells are present, however, fibrinogen, as charged, is easily adsorbed to the interface around the cell surfaces, decreas- ing the conductance or increasing the resistance of the region. Hence, even though the resistivities of two sus- pending mediums are the same, the measured effective resistances of their suspensions might be different if the contents of the two mediums, such as plasma proteins, are different.

4.3. Capacitance

The capacitance of a red cell suspension comprises two parts: the cell membranes and the interface between the

184 T3f. Zhao / Biochimica et Biophysica Acta 1201 (1994) 179-185

membranes and suspending medium. The membrane of a cell, consisting of lipids and proteins, electrically acts as a capacitor which is the major origin of the measured capaci- tance. The interface will also make a large contribution to the measured capacitance probably in two ways: the for- mation of the apparent dipole and the rotation of macro- molecules [12,13].

The fibrinogen and serum proteins are normally charged and can be attracted to the interface region, enhancing the interracial polarisation and increasing the effective capaci- tance of the suspension. The results of the present study show that the total plasma proteins can contribute to the capacitance by some 34%. The concentration of the fib- rinogen in plasma is only 0.3% by weight, much lower than that of albumin, 4%, and that of globulin, 2.7% [17]. The contribution of fibrinogen to the capacitance, how- ever, is even larger than that of the latter two (20% over 14%). The reason might be that the fibrinogen molecule is three to six times as large in weight, and three to five times as long, as the other two [17], indicating that the amount of the capacitance contribution of a substance in the suspend- ing medium might be dependent on its molecular size and shape.

The electrolytes can also influence the capacitance of a cell suspension, as demonstrated by the results of Bordi et al. [8] and of Cametti et al. [9]. The reason, similar to that for proteins, might be that the electrolytes can be adsorbed to the interface, altering the interfacial polarisation.

The influence of the type of anticoagulant on the capac- itance has been reported in a previous paper [15]. It had been shown that the samples with sodium heparin had around 20% higher capacitance than those with sodium citrate, which is in agreement with the results from a comparison between Table 1 and Fig. 5 of the present study (928 pF/cm and 785 pF/cm). The reason does not seem to be due to the different capability of the anticoagu- lants to alter the polarisation, since sodium heparin ele- vated the capacitance by only 2%. A more likely reason is that the plasma proteins were diluted by the sodium citrate since its volume fraction in the whole blood was up to 20%. Hence, as was the case when measuring the resis- tance, dried sodium heparin might be the most advanta- geous when studying the capacitance of blood.

The specific capacity of the red cell membrane was first reported by Fricke [18] as 0.80 IzF/cm 2. Such a figure of about 1.0 /xF/cm 2 has been confirmed by many re- searchers and become almost a biophysical constant [2]. From the present study, however, a value of 1.6 /zF/cm 2 was obtained using Cole's formula [2] for blood anticoagu- lated with sodium heparin (928 pF/cm). This higher value seems reasonable since the blood in Fricke's study was defibrinated, hence with no fibrinogen. Using the capaci- tance value for the PBS suspensions in the present study, that is 592 pF/cm, C O is calculated as 1.0 /xF/cm z, which is comparable to Fricke's result.

4.4. Conclusions

(1) For two suspending mediums with the same resistiv- ity, the resistances of their blood cell suspensions might be different if the contents of the two mediums, especially the high molecular substances like plasma proteins, are not the same.

(2) The plasma proteins can make a large contribution to the measured capacitance of blood through interfacial polarisation. The quantity of the contribution seems highly dependent on the size and shape of the molecules.

(3) Various anticoagulants can affect the resistance of blood by the different resistivities and volumes of the added solutions, which alter the plasma resistivity differ- ently. The type of anticoagulant can also influence the capacitance, mainly by the different volumes of the added solutions, which dilute the plasma proteins to different extents. Dried sodium heparin seems to be better than ACD, EDTA and sodium citrate if the primary aim is to study the electrical impedance parameters.

(4) The dependence of resistance and capacitance on the contents of suspending medium indicates that the measure- ment of blood impedance might be useful for screening purposes for diseases that involve abnormal concentration of certain plasma proteins.

Acknowledgments

I appreciate the support of professor H~kan Elmqvist, head of the Department of Medical Engineering, Karolin- ska Institute. The project was supported in part by a grant from the Swedish National Board for Industrial and Tech- nical Development (No. 623-90-1169).

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