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Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement
Flow Measurement and Instrumentation ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement D. Nguyen Huu a, D. Kikuchi a, O. Maruyama b, A. Sapkota c,n, M. Takei a a
Graduate School of Mechanical Engineering, Division of Artificial System Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan National Institutes of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba, Ibaraki 305-8564, Japan c Department of Information and Computer Engineering, National Institute of Technology, Kisarazu College, 2-11-1 Kiyomidai-Higashi, Kisarazu, Chiba 2920041, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 25 November 2015 Received in revised form 19 May 2016 Accepted 28 June 2016
A Cole-Cole analysis of electrical impedance of blood was performed to explore the possibility of monitoring thrombus formation in extracorporeal blood circulation. Thrombus formation experiments were conducted in both static and flowing conditions by changing the coagulability of the bovine and swine blood. Among the four Cole-Cole parameters which are the relaxation frequency fc, the resistance at zero frequency R0 , the resistance at infinite frequency R∞, shape factor α , the relaxation frequency fc first increased, reached to the characteristic peak and then decreased during thrombus formation. Other ColeCole parameters were either monotonically increasing or decreasing throughout the time without any characteristic point. Additionally, change of pattern followed the same increasing/decreasing pattern for all red blood cells (RBCs) concentrations. Simulations were made on the basis of Hanai's mixture formula to evaluate the results. On the basis of evaluation, the peak time is considered as the time to form the RBCs aggregation. Hence, the monitoring of the relaxation frequency fc is the appropriate strategy form thrombus detection. It provides the possibility of visualizing thrombus formation based on the single tomographic image of relaxation frequency distribution instead of multiple tomographic images of impedance at various frequencies in multifrequency electrical tomography. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Cole-Cole analysis Thrombus detection Extracorporeal circulation Multifrequency tomography
1. Introduction Extracorporeal blood flow circulation such as percutaneous cardio-pulmonary support (PCPS), extracorporeal membrane oxygenation (ECMO), ventricular assistance devices (VAD) and dialyzer have serious complexity related to thrombus formation [1,2]. that is because absence or low administration of anticoagulation drugs increases the risk of thrombus formation, and large amount of anticoagulation drugs results to bleeding problems. even though anticoagulant therapy in the extracorporeal circulation is highly required, controlling the amount and the timing of anticoagulant is very difficult. the controlling of the anticoagulant is generally performed by evaluating the thrombus formation on the basis of clinical tests like activated clotting time (ACT). however, the blood should be withdrawn regularly from blood flow circulation and the single clinical test requires several minutes. therefore, in order to optimize the amount and the timing of anticoagulant, a real time visualization of thrombus formation is necessary. n
Corresponding author. E-mail address: [email protected] (A. Sapkota).
Currently, there are a few studies based on optical, ultrasonic and electrical measurement principles for the real-time thrombus detection in the extracorporeal blood flow circulation. Oshima et al. developed a system using a laser beam that can measure the red blood cells (RBCs) concentration by investigating different optical propagations in prethrombus blood for various levels of RBCs density and RBCs aggregation [3]. However, in the case of various biocompatible coating in the channel wall, the optical measurement for thrombus formation is impossible. Huang et al. reported a thrombus detection using ultrasonic method [4]. However, the ultrasonic method has some inherent limitation such as the inability to differentiate air emboli from thrombus. The electrical method [5–12] seems better alternative to the both methods. However, there is a lack of detailed study regarding the measurement of the electrical properties of blood in the condition of thrombus formation and some of them are contradictory. In one of the initial study, it was reported that impedance measurement could be useful to determine the RBC aggregation [6,7]. Similar conclusion was made in one of the recent study [8]. However, impedance measurement results in another study failed to measure RBC aggregation [9]. Instead, it was reported that the capacitance measurement could facilitate the accurate detection of RBC aggregation. Consistent with this report, Hayashi et al. [10] too
http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025 0955-5986/& 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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infinite frequency R1, and shape factor α of well-known Cole-Cole analysis [14]. The possibility of expressing thrombus formation in terms of any of these parameters reduces the frequency sensitivity, and the number of image reconstructions required for multifrequency tomography can also be reduced. There are other ways too for reducing the multifrequency data in terms of basic circuit parameters. In one of the study, we used a complex nonlinear least squares approach for the data analysis of impedance spectroscopy [13]. However, in through analysis, the critical parameters failed to show strict correlation to the activated clotting time parameters. In this paper, thrombus formation results of the experiments for both static and flowing blood conditions are reported with the possibility of thrombus detection in blood in terms of Cole-Cole parameters.
observed a relation between the relative permittivity (which itself is the measure of blood capacitance) and the RBC aggregation. The present authors have also conducted various experiments measuring the resistivity and relative permittivity of thrombogenic and non-thrombogenic blood. In one of the study, we developed an electrical measurement system for the monitoring of thrombus formation by using electrical resistance tomography (ERT) [11]. The tomography imaging of thrombus was possible due to the difference in the resistivities of thrombus and blood. However, this method has some limitations that resistivity tomography can only provide the information of the presence of thrombus because thrombus resistivity may be higher or lower depending upon the concentration of red blood cells (RBCs) in the thrombus. In another study, we found that the permittivity measurement, not the resistivity measurement, has direct relationship with the size of thrombus [12,13]. Additionally, it is found that the permittivity based detection has frequency sensitivity, and the relationship between permittivity and thrombus size is insignificant outside a certain narrow frequency range. Additionally, to determine a suitable frequency range for each application is a difficult task as it depends upon the samples and the nature of the progress of the thrombus formation process. In terms of electrical tomography, it demands the multiple tomographic images at multiple frequencies. However, it is possible to reduce the multifrequency measurement data into four basic parameters of the relaxation frequency fc, the resistance at zero frequency R0, the resistance at
2.1. Experimental setup Fig. 1a shows the experimental setup for the static condition which was made up of an equilateral cubic container, an impedance analyzer (Agilent Technologies, USA; 4294A) and a controlling PC. The container was made of polymethyl methacrylate (PMMA) with inner dimension din ¼20 mm and wall thickness tw ¼2.0 mm. Two SUS304 electrodes (width length thickness:
20mm
Controlling PC
2. Materials and methods
Impedance Analyzer Electrode (A=200mm2)
din=20mm
Static condition Roller pump
Impedance Analyzer
PC
Thermostat
Reservoir
Sensor Flow direction Port for adding CaCl2
Port for withdrawing ACT blood
Thermostatic bath
d2=12mm
Flowing condition Sensor tube (Polyvinyl chloride) l2=60mm
Y
O
Electrode Stainless Steel
Y
X
O
Tube Electrode Blood
Z d1=11.4mm
l1=31mm
Sensor Fig. 1. Experimental setup for static and flowing conditions. a) Static condition. b) Flowing condition. c) Sensor.
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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Table 1 Added amount of CaCl2 throughout the flowing experiment. t [min]
0
20
40
55
70
85
Added amount [mL] Total amount [mL]
73 73
10 83
10 93
10 103
10 113
10 123
20 mm 20 mm 0.15 mm) for impedance measurement were affixed to the two symmetric inner surfaces of the container. These electrodes were connected to the impedance analyzer by a coaxial cable (Four-terminal probe L2000: Hioki E.E. Corporation, Japan). Fig. 1b shows the experimental setup for the flowing circulation condition which consisted of a roller pump (RP-PLB; Furue Science K.K., Japan), a thermostatic bath, a circulation tube, a reservoir, an impedance analyzer, a sensor, and a controlling PC. As shown in the figure, two ports for purposes of adding CaCl2 and withdrawing the ACT blood were connected to the circulation tube. Fig. 1c shows the schematic of the sensor with two stainless rings. Each ring had internal diameter d1 ¼11.4 mm, external diameter d2 ¼12 mm, and the length l1 ¼31 mm. The two rings were connected by the sensor tube with the length l3 ¼60 mm along the flow direction and were connected to the impedance analyzer by the coaxial cable. The electrodes have contact with the blood as shown in the Fig. 1c. The blood was circulated in the tube by the roller pump. The length of the blood circulation tube was 4 m. The thermostatic bath was used to maintain the flowing blood at constant temperature by the thermostat. 2.2. Blood samples Swine blood is similar to human blood from hematological and biochemical perspective [15]. The aggregation process of RBC is also close to human blood [16]. Hence, swine blood (Shibaura Zouki K.K., Japan) is appropriate for the thrombus formation experiment to avoid ethical matter of human blood. However, in the static condition, it is difficult to differentiate rouleaux formation from the thrombus formation because the swine blood immediately undergoes rouleaux formation. That is why bovine blood (Shibaura Zouki K.K., Japan) was used in the static condition instead of swine blood. The blood samples were prevented from natural thrombus formation by the addition of tri-sodium citrate solution (0.011 M; Shibaura Zouki K.K., Japan) after the blood withdrawal from swine and bovine subjects. The blood samples transferred to the experimental room by refrigerating transport were kept at room temperature about one hour before starting experiments. The hematocrit H (i.e. the concentration of RBCs) of whole blood was measured by centrifuge (Micro Hematocrit Centrifuge Model 3220, Kubota Corporation, Japan) at 12,000 rpm for 5 min. 2.3. Experimental conditions and method 2.3.1. Static condition Thrombus formation experiment was carried out in three hematocrit value (H ¼0.2, 0.3 and 0.4). These blood samples were prepared by adding to or withdrawing the plasma from the whole blood. Thrombus formation was triggered by the addition of 25 vol% (1.0 mL) calcium chloride solution (0.02 M CaCl2, Sysmex Corporation, USA) into the 3.0 mL blood in the equilateral cubic container. The measurement is started just after CaCl2 addition as the time t¼ 0.0 min. Regarding measuring electrical properties, impedance Z and phase shift θ were measured by sweeping the frequency f from f ¼1 kHz to 5 MHz at 201 points in the linear scale. We fixed the excitation current in our case. The excitation current amplitude was set at 0.1 mA. Regarding the choice of the
Fig. 2. Cole-Cole Plot. R: Resistance [Ω]. X: Reactance [Ω]. R0: Resistance in the case of f¼ 0 [Hz]. R1: Resistance in the case of f ¼1 [Hz]. ω: Angular frequency [rad/s] ( ω ¼ 2πf). fc: Relaxation frequency [Hz]. α: Shape factor (0 r α r1).
ln
U V Relaxation frequency fc
O
ln(f)
Fig. 3. Relation between the data points y ¼ln|U/V| and x¼ ln(f).
linear scale, we expected to collect more data in the medium frequency range between 500 Hz and 2.5 MHz so that we can have accurate peak of Cole-Cole plot while also taking the measurement at lower frequency range of few 1 kHz and higher frequency range of 5 MHz. Resistance R and reactance X are calculated as follows from measured Z and θ.
R = Z cos θ
(1)
X = Z sin θ
(2)
The experiments were conducted at room temperature within 60 min. Furthermore, an experiment in the absence of thrombus formation was performed as a control experiment for comparison. 2.3.2. Flowing condition In the flowing condition, the blood circulation tube was filled with 900 mL swine whole blood (H ¼0.41). The reservoir was put in the thermostatic bath that always maintained the circulating swine blood's temperature at 37 °C. Before starting the experiment to measure electrical properties, the blood was circulated by using the roller pump at a constant flow rate Q¼2.16 L/min for about 5 min to prevent sedimentation of RBCs throughout the flowing condition experiment. Table 1 shows the added amount of CaCl2 added into the circulation tube every 15∼20 min to change coagulability of flowing blood. Furthermore, during this experiment, the blood samples were withdrawn from a port on the circulation tube to measure Activated Clotting Time (ACT) in clinical aspect every 20 min by Sonoclot Analyzer (Model SC1, Sienco, Inc., America) to evaluate the coagulability of flowing blood. ACT measures the time until the beginning of fibrin formation by placing the blood in the cuvette which contains a high concentration of activator (glass beard). According to the handling of this model, ACT of the normal blood is from 100 to 150 s. The blood with ACT less than 100 seconds is in a very high coagulation state. The measuring condition of the electrical measurement was the same as in the static condition. The experiments were conducted for 120 min.
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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Fig. 4. Change of Cole-Cole plot and Cole-Cole parameters undergoing thrombus formation in the static condition: a) Cole-Cole plot, b)R0, c)R1, d) α, e)fc at all thrombus formation process, f) the first 5 min change of fc from starting. a) Cole-Cole Plot of thrombus formation process. b) Resistance in the case of f¼ 0: R0. c) resistance in the case of f¼ 1: R1. d) shape factor α. e) Relaxation frequency fc (all process). f) relaxation frequency fc (the first 5 min from starting).
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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Z * = R + jX = R∞ +
5
( R 0 − R ∞) α
1 + ( jωτ )
(3)
where Z * is complex impedance as a function of angular frequency (ω ¼2πf) and relaxation time τ. R0 and R1 are resistances at zero and infinite frequencies respectively, and α is shape factor (0 r α r1) that shows the deviation from the pure capacitance (i.e. α ¼1) [13]. Eq. (3) is not only used to represent the impedance data of the blood as showed in Fig. 2; also it is used to analyze blood's properties by using R0, R1, α and fc. The fc is the relaxation frequency that is the frequency where X has the maximum value. R0, R1, and α can be calculated using the circle's center O(x0,y0) and its radius r by
R0 = x0 +
r 2 − y02
(4)
R∞ = x 0 −
r 2 − y02
(5)
Fig. 5. Relationship between H and tp.
α=
⎛ y ⎞ 2φ 2 0 ⎟ = arcsin⎜⎜ ⎟ π π r ⎠ ⎝
(6)
However, calculating the parameter fc directly from the circle's center O and radius r is impossible. U and V as presented in Fig. 2 are calculated on the basis of
Fig. 6. Change in Cole-Cole Plot of thrombus formation in flowing condition.
R 0 − R∞ U = Z * − R∞ = α 1 + ( jωτ )
V = Z * − R0 =
(7)
( −R0 + R∞)( jωτ )α α 1 + ( jωτ )
(8)
then,
⎛ U ⎞ U = ( ωτ )−α → ln⎜ ⎟ = − α ln( f ) − ln fc ⎝ V ⎠ V
{
( )}
(9)
The Eq. (9) implies that the relationship between the data points y¼ln(|U/V|) and x ¼ln(f) is linear (Fig. 3). Because, fc is the frequency where the reactance X has the maximum value and is the frequency where U is equal to V. Thus, the intersection of this straight line with the ln(f) axis provides the relaxation frequency fc. Fig. 7. Change of relaxation frequency fc and ACT value undergoing thrombus formation in the flowing condition.
3. Results and discussions Table 2 Electric parameters of plasma, RBCs membrane, and cytoplasm. Static permittivity of plasma [dimensionless] Conductivity of plasma [S m 1] Static permittivity of RBCs membrane [dimensionless] Conductivity of RBCs membrane [S m 1] Static permittivity of cytoplasm [dimensionless] Conductivity of cytoplasm [S m 1]
3.1. Results of static and flowing conditions εp ¼74 sp ¼ 1.7 εm ¼ 3.4 sm ¼ 0 εcp ¼60 scp ¼ 1.0
2.4. Cole-Cole analysis and the calculation of Cole-Cole parameters Fig. 2 shows Cole-Cole plot fitted from the resistance R and the reactance X by performing circle fitting [17]. This Cole-Cole plot is close to semi-circle with the centre depressed below the axis of resistance X, which is described by
Fig. 4a shows the Cole-Cole plot at various times t during thrombus formation process of the blood sample (H¼0.4) in the static condition. As shown in the figure, R0 and R1 in Cole-Cole plot move rightward to the higher R as the time elapses. This movement was observed irrespective of H. Fig. 4b–d shows the temporal change of three parameters R0, R1 and α during thrombus formation process. These three parameters i.e. R0, R1 and α are either monotonically increasing or decreasing throughout the time. Furthermore, the temporal change patterns of R0, R1 and α in the absence of thrombus formation were similar to their change patterns during thrombus formation process. Fig. 4e shows the temporal change of the last parameter fc during thrombus formation process. Fig. 4f is an enlarged figure of Fig. 4e. The fc at first increased to reach to the peak point at the
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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Fig. 8. Simulation models A and B.
Fig. 9. Simulation results of model A. a) Cole-Cole plot. b) Relaxation frequency fc and shape factor α.
Fig. 10. Simulation results of model B. a) Cole-Cole plot. b) Relaxation frequency fc and shape factor α.
peak time tp; and then, fc decreased for all hematocrit values H during thrombus formation process as shown in Fig. 4f. The dot lines in Fig. 4e and Fig. 4f represents the change in fc of the blood
without thrombus formation. The fc was found to be monotonically decreasing in the absence of thrombus formation without characteristic peak point. Additionally, the relationship between H
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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and tp is shown in Fig. 5. The peak time tp was increased with the increase of H. This phenomenon is due to the decrease in the plasma concentration for higher H, and subsequent decrease in the concentration of coagulation factors that triggers the thrombus in blood. This relation between plasma concentration and thrombus formation is also pointed out by a previous study [4]. Therefore, we consider fc as a characteristic parameter to indicate the thrombus formation process. Change of Cole-Cole plot and fc during thrombus formation in the flowing condition were shown in Fig. 6 and Fig. 7. The change in characteristic parameter for thrombus formation i.e. relaxation frequency fc in the flowing condition is qualitatively similar to the change in static condition. In Fig. 7, the characteristic peak time tp was about tp ¼85 min. ACT of the blood at that time was below 100 s. On the basis of our previous studies, the blood at this moment is in a very high coagulability state, and thrombus is easily formed. Therefore, the ACT result also supports the assumption that the appearance of the tp is a special moment that remarks the change in coagulability of the blood during the thrombus formation process. Hence, the discussions and evaluations are made on the basis of fc and tp. 3.2. Discussions and evaluation of results In this section, we have made discussions and evaluations on why the relaxation frequency fc showed the characteristic changes as mentioned at the Section 3.1. Hanai mixture formula represents a complex permittivity of a suspension of homogeneously dispersed cells [10]. In the case of the blood, the Hanai mixture formula is expressed by 1
ε* − εc* ⎛ εp* ⎞ 3 ⎜⎜ ⎟⎟ = 1 − H εp* − εc* ⎝ ε* ⎠
(10)
where ε is the complex blood permittivity, H is hematocrit which is the volume fraction of the RBCs, εp* is the complex permittivity of the plasma, εc* is the complex RBCs permittivity. The εc* is described by *
εc* = εm*
* 2( 1 − v)εm* + ( 1 + 2v)εcp * * ( 2 + v)εm + ( 1 − v)εcp
(11)
* is the where εm* is the complex permittivity of RBCs membrane, εcp complex permittivity of cytoplasm, and v¼ {r/(r þd)3}. r is the RBCs radius and d is the thickness of RBCs membrane which are r ¼6.0 μm and d¼ 5.0 mm in case of swine and bovine blood [10]. The complex permittivity of plasma εp*, RBCs membrane εm* and * are described by cytoplasm εcp
εx* = εx − jσx/ε0ω
( x = p, m,cp)
(12)
εx is static permittivity, and sx is conductivity. εx, sx of plasma, RBCs membrane, and cytoplasm are shown in Table 2. j is an imaginary unit, ω is an angular frequency, ε0 is the permittivity of vacuum (ε0 ¼8.9 10 12 F m 1). The conversion from the blood complex permittivity ε* to the complex impedance Z* is Z* =
1 din jωε0ε* A
(13)
where din ¼ 20 mm is the inner dimension of the equilateral cubic container a distance between electrodes in Fig. 1(a), and A¼ 200 mm2 is a contact area of the electrode and the blood. Thrombus formation process is a cascade of several biochemical and biophysical processes. First of all, coagulation factors such as fibrinogen, thrombin in blood plasma undergoes the biochemical reactions, and fibrin gel is formed from fibrinogen. RBC
7
aggregation takes place after RBCs are trapped by the fibrin gel [18]. In order to evaluate the response of these processes in the experimental results, two simulation models were considered on the basis of the complex permittivity of the models in the Eq. (10). Model A as shown in Fig. 8 represents a change in the complex plasma permittivity εp* in blood due to the changes in coagulation factors concentration and in its nature during thrombus formation. Therefore, plasma permittivity was increased up to 30% from its original permittivity in the simulation model under the fixed RBCs concentration H¼ 0.4. Fig. 9 shows the simulation results of Model A, which indicates the relaxation frequency fc is increased with the increase of the complex plasma permittivity εp*. Model B represents the RBCs aggregation as shown in Fig. 8. The concept of the aggregation in Model B is that the region of the distribution of RBCs shrinks from their original distribution throughout container in the absence of aggregation. In another word, the aggregation level Lagg( Lagg ¼ 1 ϕa) increases with the decrease in the effective volume fraction of an aggregated region ϕa. The simulation of Model B was carried out in two steps. In the first step, complex permittivity of an aggregated region εa* was calculated from the Eq. (10) by replacing ε* and H by εa*, ϕca. ϕca ¼ H/ϕa is a volume fraction of RBCs in an aggregated region. In the second step, the complex permittivity of model B ε* is described by 1
ε* − εa* ⎛ εp* ⎞ 3 ⎜⎜ ⎟⎟ = Lagg εp* − εa* ⎝ ε* ⎠
(14)
As shown in Fig. 10, the relaxation frequency fc is decreased as the aggregation level Lagg is increased. From these simulation results it can be considered that the increase in frequency fc at the beginning is due to the change in coagulation factors as represented by simulation model A. The peak point of the relaxation frequency fc is considered as a point at which RBC aggregation starts as the relaxation frequency starts to decrease, after this point the decrease of fc is consistent with simulation model B. Finally, from experimental and simulation results, it is clear that the single parameter fc derived from multifrequency measurement data can give the idea of thrombus formation. It is shown that how permittivity change results to the change in relaxation frequency. The percentage changes were taken to see only the pattern of change of relaxation frequency. However, quantifying the aggregation level and change in plasma concentration on the basis of obtained relaxation frequency needs further investigation. In addition to these results, there are still various technical aspects that need to be studied. One of them is the material used for the electrode. It is necessary to use the robust material like gold or platinum in actual application that demands longer use. Another aspect is reasons why the other three parameters don’t differentiate the thrombotic condition from non-thrombotic condition. And, finally the reproducibility in the case of human blood should be tested.
4. Conclusions In this study, thrombus formation experiments were conducted in a static condition and a flowing condition to analyze the electrical impedance data of blood by Cole-Cole analysis. Four parameters of the Cole-Cole model were evaluated on the basis of multifrequency measurement data of impedance of the blood undergoing thrombus formation. The following are revealed:
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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1) Three parameters R0, R1 and α were either monotonically increasing or decreasing throughout the time. The patterns of the changes in three parameters were not significant enough to give the information of thrombus formation. 2) The fc increased at first to reach to the peak point; and then decreased. The peak time tp which is the time when the peak point appears was higher for the higher value of H. Furthermore, simulation based on the two different stages (change in coagulation factors and aggregation) of thrombus formation using Hanai mixture formula was performed, and the following are revealed:
[2] [3]
[4]
[5]
[6]
3) The relaxation frequency fc increased with the increased of coagulation factors permittivity. The relaxation frequency fc decreased with the growth of RBC aggregation. 4) The peak time tp of the relaxation frequency fc is considered as a special timing at which RBC aggregation starts Cole-Cole simulation results provided the reasonable logic behind the change in fc of the experiment. That is the increase of fc is caused by the increase of coagulation factors permittivity, and the decrease of fc is caused by the growth of RBC aggregation. The results are important because it provides a single significant parameter derived from the measurements taken at multiple frequencies. It shows the possibility of reconstructing a single tomographic image to visualize the thrombus in the blood instead of multiple images reconstructed for resistance or capacitance at multiple frequencies.
Acknowledgements The work was supported by the Grant in Aid-For Scientific Research for Young researchers (26750143), Challenging Exploratory Research (26630046). A research grant from Asahi Glass Foundation, Grant-in-Aid for innovative ideas (Hyper-BioAssembler Grant number: 26106708).
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Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement D. Nguyen Huu a, D. Kikuchi a, O. Maruyama b, A. Sapkota c,n, M. Takei a a
Graduate School of Mechanical Engineering, Division of Artificial System Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan National Institutes of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba, Ibaraki 305-8564, Japan c Department of Information and Computer Engineering, National Institute of Technology, Kisarazu College, 2-11-1 Kiyomidai-Higashi, Kisarazu, Chiba 2920041, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 25 November 2015 Received in revised form 19 May 2016 Accepted 28 June 2016
A Cole-Cole analysis of electrical impedance of blood was performed to explore the possibility of monitoring thrombus formation in extracorporeal blood circulation. Thrombus formation experiments were conducted in both static and flowing conditions by changing the coagulability of the bovine and swine blood. Among the four Cole-Cole parameters which are the relaxation frequency fc, the resistance at zero frequency R0 , the resistance at infinite frequency R∞, shape factor α , the relaxation frequency fc first increased, reached to the characteristic peak and then decreased during thrombus formation. Other ColeCole parameters were either monotonically increasing or decreasing throughout the time without any characteristic point. Additionally, change of pattern followed the same increasing/decreasing pattern for all red blood cells (RBCs) concentrations. Simulations were made on the basis of Hanai's mixture formula to evaluate the results. On the basis of evaluation, the peak time is considered as the time to form the RBCs aggregation. Hence, the monitoring of the relaxation frequency fc is the appropriate strategy form thrombus detection. It provides the possibility of visualizing thrombus formation based on the single tomographic image of relaxation frequency distribution instead of multiple tomographic images of impedance at various frequencies in multifrequency electrical tomography. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Cole-Cole analysis Thrombus detection Extracorporeal circulation Multifrequency tomography
1. Introduction Extracorporeal blood flow circulation such as percutaneous cardio-pulmonary support (PCPS), extracorporeal membrane oxygenation (ECMO), ventricular assistance devices (VAD) and dialyzer have serious complexity related to thrombus formation [1,2]. that is because absence or low administration of anticoagulation drugs increases the risk of thrombus formation, and large amount of anticoagulation drugs results to bleeding problems. even though anticoagulant therapy in the extracorporeal circulation is highly required, controlling the amount and the timing of anticoagulant is very difficult. the controlling of the anticoagulant is generally performed by evaluating the thrombus formation on the basis of clinical tests like activated clotting time (ACT). however, the blood should be withdrawn regularly from blood flow circulation and the single clinical test requires several minutes. therefore, in order to optimize the amount and the timing of anticoagulant, a real time visualization of thrombus formation is necessary. n
Corresponding author. E-mail address: [email protected] (A. Sapkota).
Currently, there are a few studies based on optical, ultrasonic and electrical measurement principles for the real-time thrombus detection in the extracorporeal blood flow circulation. Oshima et al. developed a system using a laser beam that can measure the red blood cells (RBCs) concentration by investigating different optical propagations in prethrombus blood for various levels of RBCs density and RBCs aggregation [3]. However, in the case of various biocompatible coating in the channel wall, the optical measurement for thrombus formation is impossible. Huang et al. reported a thrombus detection using ultrasonic method [4]. However, the ultrasonic method has some inherent limitation such as the inability to differentiate air emboli from thrombus. The electrical method [5–12] seems better alternative to the both methods. However, there is a lack of detailed study regarding the measurement of the electrical properties of blood in the condition of thrombus formation and some of them are contradictory. In one of the initial study, it was reported that impedance measurement could be useful to determine the RBC aggregation [6,7]. Similar conclusion was made in one of the recent study [8]. However, impedance measurement results in another study failed to measure RBC aggregation [9]. Instead, it was reported that the capacitance measurement could facilitate the accurate detection of RBC aggregation. Consistent with this report, Hayashi et al. [10] too
http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025 0955-5986/& 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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infinite frequency R1, and shape factor α of well-known Cole-Cole analysis [14]. The possibility of expressing thrombus formation in terms of any of these parameters reduces the frequency sensitivity, and the number of image reconstructions required for multifrequency tomography can also be reduced. There are other ways too for reducing the multifrequency data in terms of basic circuit parameters. In one of the study, we used a complex nonlinear least squares approach for the data analysis of impedance spectroscopy [13]. However, in through analysis, the critical parameters failed to show strict correlation to the activated clotting time parameters. In this paper, thrombus formation results of the experiments for both static and flowing blood conditions are reported with the possibility of thrombus detection in blood in terms of Cole-Cole parameters.
observed a relation between the relative permittivity (which itself is the measure of blood capacitance) and the RBC aggregation. The present authors have also conducted various experiments measuring the resistivity and relative permittivity of thrombogenic and non-thrombogenic blood. In one of the study, we developed an electrical measurement system for the monitoring of thrombus formation by using electrical resistance tomography (ERT) [11]. The tomography imaging of thrombus was possible due to the difference in the resistivities of thrombus and blood. However, this method has some limitations that resistivity tomography can only provide the information of the presence of thrombus because thrombus resistivity may be higher or lower depending upon the concentration of red blood cells (RBCs) in the thrombus. In another study, we found that the permittivity measurement, not the resistivity measurement, has direct relationship with the size of thrombus [12,13]. Additionally, it is found that the permittivity based detection has frequency sensitivity, and the relationship between permittivity and thrombus size is insignificant outside a certain narrow frequency range. Additionally, to determine a suitable frequency range for each application is a difficult task as it depends upon the samples and the nature of the progress of the thrombus formation process. In terms of electrical tomography, it demands the multiple tomographic images at multiple frequencies. However, it is possible to reduce the multifrequency measurement data into four basic parameters of the relaxation frequency fc, the resistance at zero frequency R0, the resistance at
2.1. Experimental setup Fig. 1a shows the experimental setup for the static condition which was made up of an equilateral cubic container, an impedance analyzer (Agilent Technologies, USA; 4294A) and a controlling PC. The container was made of polymethyl methacrylate (PMMA) with inner dimension din ¼20 mm and wall thickness tw ¼2.0 mm. Two SUS304 electrodes (width length thickness:
20mm
Controlling PC
2. Materials and methods
Impedance Analyzer Electrode (A=200mm2)
din=20mm
Static condition Roller pump
Impedance Analyzer
PC
Thermostat
Reservoir
Sensor Flow direction Port for adding CaCl2
Port for withdrawing ACT blood
Thermostatic bath
d2=12mm
Flowing condition Sensor tube (Polyvinyl chloride) l2=60mm
Y
O
Electrode Stainless Steel
Y
X
O
Tube Electrode Blood
Z d1=11.4mm
l1=31mm
Sensor Fig. 1. Experimental setup for static and flowing conditions. a) Static condition. b) Flowing condition. c) Sensor.
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Table 1 Added amount of CaCl2 throughout the flowing experiment. t [min]
0
20
40
55
70
85
Added amount [mL] Total amount [mL]
73 73
10 83
10 93
10 103
10 113
10 123
20 mm 20 mm 0.15 mm) for impedance measurement were affixed to the two symmetric inner surfaces of the container. These electrodes were connected to the impedance analyzer by a coaxial cable (Four-terminal probe L2000: Hioki E.E. Corporation, Japan). Fig. 1b shows the experimental setup for the flowing circulation condition which consisted of a roller pump (RP-PLB; Furue Science K.K., Japan), a thermostatic bath, a circulation tube, a reservoir, an impedance analyzer, a sensor, and a controlling PC. As shown in the figure, two ports for purposes of adding CaCl2 and withdrawing the ACT blood were connected to the circulation tube. Fig. 1c shows the schematic of the sensor with two stainless rings. Each ring had internal diameter d1 ¼11.4 mm, external diameter d2 ¼12 mm, and the length l1 ¼31 mm. The two rings were connected by the sensor tube with the length l3 ¼60 mm along the flow direction and were connected to the impedance analyzer by the coaxial cable. The electrodes have contact with the blood as shown in the Fig. 1c. The blood was circulated in the tube by the roller pump. The length of the blood circulation tube was 4 m. The thermostatic bath was used to maintain the flowing blood at constant temperature by the thermostat. 2.2. Blood samples Swine blood is similar to human blood from hematological and biochemical perspective [15]. The aggregation process of RBC is also close to human blood [16]. Hence, swine blood (Shibaura Zouki K.K., Japan) is appropriate for the thrombus formation experiment to avoid ethical matter of human blood. However, in the static condition, it is difficult to differentiate rouleaux formation from the thrombus formation because the swine blood immediately undergoes rouleaux formation. That is why bovine blood (Shibaura Zouki K.K., Japan) was used in the static condition instead of swine blood. The blood samples were prevented from natural thrombus formation by the addition of tri-sodium citrate solution (0.011 M; Shibaura Zouki K.K., Japan) after the blood withdrawal from swine and bovine subjects. The blood samples transferred to the experimental room by refrigerating transport were kept at room temperature about one hour before starting experiments. The hematocrit H (i.e. the concentration of RBCs) of whole blood was measured by centrifuge (Micro Hematocrit Centrifuge Model 3220, Kubota Corporation, Japan) at 12,000 rpm for 5 min. 2.3. Experimental conditions and method 2.3.1. Static condition Thrombus formation experiment was carried out in three hematocrit value (H ¼0.2, 0.3 and 0.4). These blood samples were prepared by adding to or withdrawing the plasma from the whole blood. Thrombus formation was triggered by the addition of 25 vol% (1.0 mL) calcium chloride solution (0.02 M CaCl2, Sysmex Corporation, USA) into the 3.0 mL blood in the equilateral cubic container. The measurement is started just after CaCl2 addition as the time t¼ 0.0 min. Regarding measuring electrical properties, impedance Z and phase shift θ were measured by sweeping the frequency f from f ¼1 kHz to 5 MHz at 201 points in the linear scale. We fixed the excitation current in our case. The excitation current amplitude was set at 0.1 mA. Regarding the choice of the
Fig. 2. Cole-Cole Plot. R: Resistance [Ω]. X: Reactance [Ω]. R0: Resistance in the case of f¼ 0 [Hz]. R1: Resistance in the case of f ¼1 [Hz]. ω: Angular frequency [rad/s] ( ω ¼ 2πf). fc: Relaxation frequency [Hz]. α: Shape factor (0 r α r1).
ln
U V Relaxation frequency fc
O
ln(f)
Fig. 3. Relation between the data points y ¼ln|U/V| and x¼ ln(f).
linear scale, we expected to collect more data in the medium frequency range between 500 Hz and 2.5 MHz so that we can have accurate peak of Cole-Cole plot while also taking the measurement at lower frequency range of few 1 kHz and higher frequency range of 5 MHz. Resistance R and reactance X are calculated as follows from measured Z and θ.
R = Z cos θ
(1)
X = Z sin θ
(2)
The experiments were conducted at room temperature within 60 min. Furthermore, an experiment in the absence of thrombus formation was performed as a control experiment for comparison. 2.3.2. Flowing condition In the flowing condition, the blood circulation tube was filled with 900 mL swine whole blood (H ¼0.41). The reservoir was put in the thermostatic bath that always maintained the circulating swine blood's temperature at 37 °C. Before starting the experiment to measure electrical properties, the blood was circulated by using the roller pump at a constant flow rate Q¼2.16 L/min for about 5 min to prevent sedimentation of RBCs throughout the flowing condition experiment. Table 1 shows the added amount of CaCl2 added into the circulation tube every 15∼20 min to change coagulability of flowing blood. Furthermore, during this experiment, the blood samples were withdrawn from a port on the circulation tube to measure Activated Clotting Time (ACT) in clinical aspect every 20 min by Sonoclot Analyzer (Model SC1, Sienco, Inc., America) to evaluate the coagulability of flowing blood. ACT measures the time until the beginning of fibrin formation by placing the blood in the cuvette which contains a high concentration of activator (glass beard). According to the handling of this model, ACT of the normal blood is from 100 to 150 s. The blood with ACT less than 100 seconds is in a very high coagulation state. The measuring condition of the electrical measurement was the same as in the static condition. The experiments were conducted for 120 min.
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Fig. 4. Change of Cole-Cole plot and Cole-Cole parameters undergoing thrombus formation in the static condition: a) Cole-Cole plot, b)R0, c)R1, d) α, e)fc at all thrombus formation process, f) the first 5 min change of fc from starting. a) Cole-Cole Plot of thrombus formation process. b) Resistance in the case of f¼ 0: R0. c) resistance in the case of f¼ 1: R1. d) shape factor α. e) Relaxation frequency fc (all process). f) relaxation frequency fc (the first 5 min from starting).
Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i
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Z * = R + jX = R∞ +
5
( R 0 − R ∞) α
1 + ( jωτ )
(3)
where Z * is complex impedance as a function of angular frequency (ω ¼2πf) and relaxation time τ. R0 and R1 are resistances at zero and infinite frequencies respectively, and α is shape factor (0 r α r1) that shows the deviation from the pure capacitance (i.e. α ¼1) [13]. Eq. (3) is not only used to represent the impedance data of the blood as showed in Fig. 2; also it is used to analyze blood's properties by using R0, R1, α and fc. The fc is the relaxation frequency that is the frequency where X has the maximum value. R0, R1, and α can be calculated using the circle's center O(x0,y0) and its radius r by
R0 = x0 +
r 2 − y02
(4)
R∞ = x 0 −
r 2 − y02
(5)
Fig. 5. Relationship between H and tp.
α=
⎛ y ⎞ 2φ 2 0 ⎟ = arcsin⎜⎜ ⎟ π π r ⎠ ⎝
(6)
However, calculating the parameter fc directly from the circle's center O and radius r is impossible. U and V as presented in Fig. 2 are calculated on the basis of
Fig. 6. Change in Cole-Cole Plot of thrombus formation in flowing condition.
R 0 − R∞ U = Z * − R∞ = α 1 + ( jωτ )
V = Z * − R0 =
(7)
( −R0 + R∞)( jωτ )α α 1 + ( jωτ )
(8)
then,
⎛ U ⎞ U = ( ωτ )−α → ln⎜ ⎟ = − α ln( f ) − ln fc ⎝ V ⎠ V
{
( )}
(9)
The Eq. (9) implies that the relationship between the data points y¼ln(|U/V|) and x ¼ln(f) is linear (Fig. 3). Because, fc is the frequency where the reactance X has the maximum value and is the frequency where U is equal to V. Thus, the intersection of this straight line with the ln(f) axis provides the relaxation frequency fc. Fig. 7. Change of relaxation frequency fc and ACT value undergoing thrombus formation in the flowing condition.
3. Results and discussions Table 2 Electric parameters of plasma, RBCs membrane, and cytoplasm. Static permittivity of plasma [dimensionless] Conductivity of plasma [S m 1] Static permittivity of RBCs membrane [dimensionless] Conductivity of RBCs membrane [S m 1] Static permittivity of cytoplasm [dimensionless] Conductivity of cytoplasm [S m 1]
3.1. Results of static and flowing conditions εp ¼74 sp ¼ 1.7 εm ¼ 3.4 sm ¼ 0 εcp ¼60 scp ¼ 1.0
2.4. Cole-Cole analysis and the calculation of Cole-Cole parameters Fig. 2 shows Cole-Cole plot fitted from the resistance R and the reactance X by performing circle fitting [17]. This Cole-Cole plot is close to semi-circle with the centre depressed below the axis of resistance X, which is described by
Fig. 4a shows the Cole-Cole plot at various times t during thrombus formation process of the blood sample (H¼0.4) in the static condition. As shown in the figure, R0 and R1 in Cole-Cole plot move rightward to the higher R as the time elapses. This movement was observed irrespective of H. Fig. 4b–d shows the temporal change of three parameters R0, R1 and α during thrombus formation process. These three parameters i.e. R0, R1 and α are either monotonically increasing or decreasing throughout the time. Furthermore, the temporal change patterns of R0, R1 and α in the absence of thrombus formation were similar to their change patterns during thrombus formation process. Fig. 4e shows the temporal change of the last parameter fc during thrombus formation process. Fig. 4f is an enlarged figure of Fig. 4e. The fc at first increased to reach to the peak point at the
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Fig. 8. Simulation models A and B.
Fig. 9. Simulation results of model A. a) Cole-Cole plot. b) Relaxation frequency fc and shape factor α.
Fig. 10. Simulation results of model B. a) Cole-Cole plot. b) Relaxation frequency fc and shape factor α.
peak time tp; and then, fc decreased for all hematocrit values H during thrombus formation process as shown in Fig. 4f. The dot lines in Fig. 4e and Fig. 4f represents the change in fc of the blood
without thrombus formation. The fc was found to be monotonically decreasing in the absence of thrombus formation without characteristic peak point. Additionally, the relationship between H
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and tp is shown in Fig. 5. The peak time tp was increased with the increase of H. This phenomenon is due to the decrease in the plasma concentration for higher H, and subsequent decrease in the concentration of coagulation factors that triggers the thrombus in blood. This relation between plasma concentration and thrombus formation is also pointed out by a previous study [4]. Therefore, we consider fc as a characteristic parameter to indicate the thrombus formation process. Change of Cole-Cole plot and fc during thrombus formation in the flowing condition were shown in Fig. 6 and Fig. 7. The change in characteristic parameter for thrombus formation i.e. relaxation frequency fc in the flowing condition is qualitatively similar to the change in static condition. In Fig. 7, the characteristic peak time tp was about tp ¼85 min. ACT of the blood at that time was below 100 s. On the basis of our previous studies, the blood at this moment is in a very high coagulability state, and thrombus is easily formed. Therefore, the ACT result also supports the assumption that the appearance of the tp is a special moment that remarks the change in coagulability of the blood during the thrombus formation process. Hence, the discussions and evaluations are made on the basis of fc and tp. 3.2. Discussions and evaluation of results In this section, we have made discussions and evaluations on why the relaxation frequency fc showed the characteristic changes as mentioned at the Section 3.1. Hanai mixture formula represents a complex permittivity of a suspension of homogeneously dispersed cells [10]. In the case of the blood, the Hanai mixture formula is expressed by 1
ε* − εc* ⎛ εp* ⎞ 3 ⎜⎜ ⎟⎟ = 1 − H εp* − εc* ⎝ ε* ⎠
(10)
where ε is the complex blood permittivity, H is hematocrit which is the volume fraction of the RBCs, εp* is the complex permittivity of the plasma, εc* is the complex RBCs permittivity. The εc* is described by *
εc* = εm*
* 2( 1 − v)εm* + ( 1 + 2v)εcp * * ( 2 + v)εm + ( 1 − v)εcp
(11)
* is the where εm* is the complex permittivity of RBCs membrane, εcp complex permittivity of cytoplasm, and v¼ {r/(r þd)3}. r is the RBCs radius and d is the thickness of RBCs membrane which are r ¼6.0 μm and d¼ 5.0 mm in case of swine and bovine blood [10]. The complex permittivity of plasma εp*, RBCs membrane εm* and * are described by cytoplasm εcp
εx* = εx − jσx/ε0ω
( x = p, m,cp)
(12)
εx is static permittivity, and sx is conductivity. εx, sx of plasma, RBCs membrane, and cytoplasm are shown in Table 2. j is an imaginary unit, ω is an angular frequency, ε0 is the permittivity of vacuum (ε0 ¼8.9 10 12 F m 1). The conversion from the blood complex permittivity ε* to the complex impedance Z* is Z* =
1 din jωε0ε* A
(13)
where din ¼ 20 mm is the inner dimension of the equilateral cubic container a distance between electrodes in Fig. 1(a), and A¼ 200 mm2 is a contact area of the electrode and the blood. Thrombus formation process is a cascade of several biochemical and biophysical processes. First of all, coagulation factors such as fibrinogen, thrombin in blood plasma undergoes the biochemical reactions, and fibrin gel is formed from fibrinogen. RBC
7
aggregation takes place after RBCs are trapped by the fibrin gel [18]. In order to evaluate the response of these processes in the experimental results, two simulation models were considered on the basis of the complex permittivity of the models in the Eq. (10). Model A as shown in Fig. 8 represents a change in the complex plasma permittivity εp* in blood due to the changes in coagulation factors concentration and in its nature during thrombus formation. Therefore, plasma permittivity was increased up to 30% from its original permittivity in the simulation model under the fixed RBCs concentration H¼ 0.4. Fig. 9 shows the simulation results of Model A, which indicates the relaxation frequency fc is increased with the increase of the complex plasma permittivity εp*. Model B represents the RBCs aggregation as shown in Fig. 8. The concept of the aggregation in Model B is that the region of the distribution of RBCs shrinks from their original distribution throughout container in the absence of aggregation. In another word, the aggregation level Lagg( Lagg ¼ 1 ϕa) increases with the decrease in the effective volume fraction of an aggregated region ϕa. The simulation of Model B was carried out in two steps. In the first step, complex permittivity of an aggregated region εa* was calculated from the Eq. (10) by replacing ε* and H by εa*, ϕca. ϕca ¼ H/ϕa is a volume fraction of RBCs in an aggregated region. In the second step, the complex permittivity of model B ε* is described by 1
ε* − εa* ⎛ εp* ⎞ 3 ⎜⎜ ⎟⎟ = Lagg εp* − εa* ⎝ ε* ⎠
(14)
As shown in Fig. 10, the relaxation frequency fc is decreased as the aggregation level Lagg is increased. From these simulation results it can be considered that the increase in frequency fc at the beginning is due to the change in coagulation factors as represented by simulation model A. The peak point of the relaxation frequency fc is considered as a point at which RBC aggregation starts as the relaxation frequency starts to decrease, after this point the decrease of fc is consistent with simulation model B. Finally, from experimental and simulation results, it is clear that the single parameter fc derived from multifrequency measurement data can give the idea of thrombus formation. It is shown that how permittivity change results to the change in relaxation frequency. The percentage changes were taken to see only the pattern of change of relaxation frequency. However, quantifying the aggregation level and change in plasma concentration on the basis of obtained relaxation frequency needs further investigation. In addition to these results, there are still various technical aspects that need to be studied. One of them is the material used for the electrode. It is necessary to use the robust material like gold or platinum in actual application that demands longer use. Another aspect is reasons why the other three parameters don’t differentiate the thrombotic condition from non-thrombotic condition. And, finally the reproducibility in the case of human blood should be tested.
4. Conclusions In this study, thrombus formation experiments were conducted in a static condition and a flowing condition to analyze the electrical impedance data of blood by Cole-Cole analysis. Four parameters of the Cole-Cole model were evaluated on the basis of multifrequency measurement data of impedance of the blood undergoing thrombus formation. The following are revealed:
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1) Three parameters R0, R1 and α were either monotonically increasing or decreasing throughout the time. The patterns of the changes in three parameters were not significant enough to give the information of thrombus formation. 2) The fc increased at first to reach to the peak point; and then decreased. The peak time tp which is the time when the peak point appears was higher for the higher value of H. Furthermore, simulation based on the two different stages (change in coagulation factors and aggregation) of thrombus formation using Hanai mixture formula was performed, and the following are revealed:
[2] [3]
[4]
[5]
[6]
3) The relaxation frequency fc increased with the increased of coagulation factors permittivity. The relaxation frequency fc decreased with the growth of RBC aggregation. 4) The peak time tp of the relaxation frequency fc is considered as a special timing at which RBC aggregation starts Cole-Cole simulation results provided the reasonable logic behind the change in fc of the experiment. That is the increase of fc is caused by the increase of coagulation factors permittivity, and the decrease of fc is caused by the growth of RBC aggregation. The results are important because it provides a single significant parameter derived from the measurements taken at multiple frequencies. It shows the possibility of reconstructing a single tomographic image to visualize the thrombus in the blood instead of multiple images reconstructed for resistance or capacitance at multiple frequencies.
Acknowledgements The work was supported by the Grant in Aid-For Scientific Research for Young researchers (26750143), Challenging Exploratory Research (26630046). A research grant from Asahi Glass Foundation, Grant-in-Aid for innovative ideas (Hyper-BioAssembler Grant number: 26106708).
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Please cite this article as: D. Nguyen Huu, et al., Cole-Cole analysis of thrombus formation in an extracorporeal blood flow circulation using electrical measurement, Flow Measurement and Instrumentation (2016), http://dx.doi.org/10.1016/j.flowmeasinst.2016.06.025i