research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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ISSN: 1600-5775

Usage of CO2 microbubbles as flow-tracing contrast media in X-ray dynamic imaging of blood flows

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aCenter for Biofluid and Biomimic Research, Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea, and bHyundai Heavy Industries, Ulsan 682-792, Republic of Korea
*Correspondence e-mail: sjlee@postech.ac.kr

(Received 21 March 2014; accepted 9 June 2014; online 31 July 2014)

X-ray imaging techniques have been employed to visualize various biofluid flow phenomena in a non-destructive manner. X-ray particle image velocimetry (PIV) was developed to measure velocity fields of blood flows to obtain hemodynamic information. A time-resolved X-ray PIV technique that is capable of measuring the velocity fields of blood flows under real physiological conditions was recently developed. However, technical limitations still remained in the measurement of blood flows with high image contrast and sufficient biocapability. In this study, CO2 microbubbles as flow-tracing contrast media for X-ray PIV measurements of biofluid flows was developed. Human serum albumin and CO2 gas were mechanically agitated to fabricate CO2 microbubbles. The optimal fabricating conditions of CO2 microbubbles were found by comparing the size and amount of microbubbles fabricated under various operating conditions. The average size and quantity of CO2 microbubbles were measured by using a synchrotron X-ray imaging technique with a high spatial resolution. The quantity and size of the fabricated microbubbles decrease with increasing speed and operation time of the mechanical agitation. The feasibility of CO2 microbubbles as a flow-tracing contrast media was checked for a 40% hematocrit blood flow. Particle images of the blood flow were consecutively captured by the time-resolved X-ray PIV system to obtain velocity field information of the flow. The experimental results were compared with a theoretically amassed velocity profile. Results show that the CO2 microbubbles can be used as effective flow-tracing contrast media in X-ray PIV experiments.

1. Introduction

Circulatory vascular diseases are one of the main causes of mortality. Abnormal blood flows with low wall shear stress were observed in regions affected by cardiovascular diseases (Hove et al., 2003[Hove, J. R., Köster, R. W., Forouhar, A. S., Acevedo-Bolton, G., Fraser, S. E. & Gharib, M. (2003). Nature (London), 421, 172-177.]). The quantitative velocity information of abnormal blood flows is important for the early diagnosis of cardiovascular diseases. Non-invasive imaging techniques are required to measure blood flows in vivo.

Among the various types of non-invasive imaging techniques, X-ray imaging techniques with high temporal and spatial resolutions are used to investigate hemodynamic characteristics. X-ray angiography provides only anatomical information on blood vessels and not quantitative flow information. The velocity fields of opaque biofluid flows were measured by adopting X-ray particle image velocimetry (PIV) (Lee & Kim, 2005a[Lee, S. J. & Kim, G. B. (2005a). J. Appl. Phys. 97, 064701.]; Lee et al., 2009[Lee, S. J., Kim, G. B., Yim, D. H. & Jung, S. Y. (2009). Rev. Sci. Instrum. 80, 033706.]). This technique combines the merits of both X-ray imaging and PIV techniques. The X-ray PIV technique has been applied to observe blood flows in an opaque tube (Kim & Lee, 2006[Kim, G. B. & Lee, S. J. (2006). Exp. Fluids, 41, 195-200.]). However, these studies were conducted at low Reynolds numbers. A time-resolved X-ray PIV technique was developed to measure flows at a high Reynolds number (Jung et al., 2013[Jung, S. Y., Park, H. W., Kim, B. H. & Lee, S. J. (2013). J. Synchrotron Rad. 20, 498-503.]). This technique was applied to observe blood flows under ex vivo conditions (Jamison et al., 2012[Jamison, R. A., Siu, K. K. W., Dubsky, S., Armitage, J. A. & Fouras, A. (2012). J. Synchrotron Rad. 19, 1050-1055.]).

Although the X-ray PIV technique has been gradually improved for a decade, some problems remain in its practical applications. One such problem is the deficiency of proper tracer particles suitable for X-ray PIV measurements. Although tracer particles such as silver-coated hollow glass beads (Im et al., 2007[Im, K. S., Fezzaa, K., Wang, Y. J., Liu, X., Wang, J. & Lai, M. C. (2007). Appl. Phys. Lett. 90, 091919.]), alumina particles (Lee & Kim, 2003[Lee, S. J. & Kim, G. B. (2003). J. Appl. Phys. 94, 3620.]) and tungsten oxide particles (Lee et al., 2009[Lee, S. J., Kim, G. B., Yim, D. H. & Jung, S. Y. (2009). Rev. Sci. Instrum. 80, 033706.]) have been employed in X-ray PIV experiments, such particles are not bio-compatible. The speckle patterns of red blood cells (RBCs) were also used to measure the velocity information of blood flows in an X-ray PIV experiment (Kim & Lee, 2006[Kim, G. B. & Lee, S. J. (2006). Exp. Fluids, 41, 195-200.]). However, considering the blurring and noise caused by the surrounding tissues of blood vessels, this approach was difficult to apply in in vivo experiments. Although microparticles made of iopamidol encapsulated by polyvinyl alcohol were suitable in terms of biocompatibility (Lee et al., 2010[Lee, S. J., Jung, S. Y. & Ahn, S. (2010). Biosens. Bioelectron. 25, 1571-1578.]), the X-ray absorption coefficient of such microparticles was not enough for in vivo measurements. Gold nanoparticles (Au NPs) incorporated into chitosan were found to provide a high X-ray absorption rate (Jung et al., 2012a[Jung, S. Y., Ahn, S., Nam, K. H., Lee, J. P. & Lee, S. J. (2012a). Int. J. Cardiovas. Imaging, 28, 1853-1858.]). However, most Au NPs agglomerated in blood flows. Given the technological limitations of tracer particles, the development of a new particle for X-ray PIV experiments is necessary.

CO2 gas has been widely used as an efficient X-ray contrast material in clinical angiographic imaging because of its high X-ray contrast (Durant et al., 1957[Durant, T. M., Stauffer, H. M., Oppenheimer, M. J. & Paul, R. E. (1957). Ann. Int. Med. 47, 191-201.]; Rautenberg, 1994[Rautenberg, E. (1994). Deutsch. Med. Wochenschr. 40, 1205.]). In the 1960s, CO2 gas was used to obtain angiographic images of the inferior vena cava and portal vein (Hipona & Park, 1967[Hipona, F. A. & Park, W. M. (1967). Am. J. Roentgenol. Radium Ther. Nucl. Med. 99, 606-611.]). Compared with iodine contrast media, CO2 gas did not exhibit hypersensitivity reactions (Song et al., 1999[Song, K., Cho, D., Shinn, K., Charlton, E. & Cho, K. (1999). Invest. Radiol. 34, 151-155.]). The intravascular supply of CO2 gas did not significantly change the pH, pCO2 and pO2 levels. No significant histological change and no difference in renal blood flows were also observed compared with iodinated contrast agents (Kerns & Hawkins, 1995[Kerns, S. R. & Hawkins, I. F. Jr (1995). Am. J. Roentgenol. 164, 735-741.]). Although the risks of CO2 angiography exist (Kerns & Hawkins, 1995[Kerns, S. R. & Hawkins, I. F. Jr (1995). Am. J. Roentgenol. 164, 735-741.]), the safe ranges of the injection rate and volume were already well known.

Hollow-type microparticles were reported to be suitable as flow tracers in X-ray PIV measurements (Lee et al., 2009[Lee, S. J., Kim, G. B., Yim, D. H. & Jung, S. Y. (2009). Rev. Sci. Instrum. 80, 033706.]). The visibility of hollow-type microparticles was greatly enhanced in phase-contrast X-ray images. In the present study, CO2 microbubbles were fabricated as flow-tracing contrast media to enhance the phase contrast further. Optimal fabricating conditions were found by comparing the size and number density of CO2 microbubbles. The duration time of the CO2 fabricated microbubbles were also compared. The developed CO2 microbubbles were used to measure the velocity fields of 40% hematocrit blood flowing in an opaque tube. The present CO2 microbubbles will be useful to investigate the hemodynamic characteristics of vascular diseases by the X-ray PIV system.

2. Materials and methods

2.1. Microbubble generation

Microbubbles were fabricated by mixing 5% human serum albumin (HSA) at 25 cc and CO2 gas at 20 cc. Approximately 20% HSA was purchased from ChungShibJa Pharmacy Co. Ltd (South Korea). The media of human serum albumin (HSA) is DI water which contains sodium chloride, sodium hydroxide and acetyl-tryptophane. The 5% HSA was produced by diluting 20% HSA in a phosphate buffered saline solution. Serum albumin is a common globular protein and has been widely adopted as the encapsulating shell material of many ultrasound contrast agents (Stride & Saffari, 2003[Stride, E. & Saffari, N. (2003). Proc. IME. H. 217, 429-447.]). Jeon et al. (2002[Jeon, D. S., Luo, H., Iwami, T., Miyamoto, T., Brasch, A. V., Mirocha, J., Naqvi, T. Z. & Siegel, R. J. (2002). J. Am. Collect. Cardiol. 39, 124-129.]) homogenized a gas-acqueous mixture by moving the plungers of two syringes connected by a threeway stopcock. However, the acquired quantity of microbubbles is too small to obtain velocity information using a PIV technique and the variation in microbubble size is large. Therefore, in this study, the technique is somewhat modified. Air bubbles have been known to produce arterial embolism. Significant embolic events, such as acute limb ischemia and cerebro­vascular accident, are caused by air bubbles (Holcomb et al., 2001[Holcomb, B. W., Loyd, J. E., Byrd, B. F., Wilsdorf, T. T., Casey-Cato, T., Mason, W. R. & Robbins, I. M. (2001). Chest, 119, 1602-1605.]). When venous air bubbles enter into the systemic arterial circulation, a paradoxical air embolism can be caused (Christin et al., 2007[Christin, F., Bouffard, Y., Rossi, R. & Delafosse, B. (2007). Echocardiography, 24, 867-869.]). Although material properties are clearly distinguishable in X-ray images, it is difficult to differentiate CO2 bubbles from air bubbles due to little difference in absorption and phase contrasts. The homogenizer is located in a CO2 chamber to make it directly contact with CO2 gas.

Fig. 1[link] shows a schematic of the microbubble generator used in the present study. Approximately 25 cc of 5% HSA and 20 cc of CO2 gas were supplied into syringe 1. Syringe 1 was sealed with rubber to prevent the intake of outside air and leakage of the inside CO2 gas. Syringe 2 was repeatedly pushed and pulled over ten times to mix the CO2 gas and HSA. The sealing rubber positioned inside the syringe 1 was shifted following the movement of the syringe 2. Microbubbles were generated by mechanical agitation with a homogenizer (IKA-T25 digital ULTRA-TURRAX, IKA, Germany). The mixed solution was homogenized under various rotation speeds and agitating times. The rotation speed and agitation time varied from 3 × 103 r.p.m. to 15 × 103 r.p.m. and 1 min to 7 min, respectively. The optimal fabricating conditions were determined by comparing the visibilities of the X-ray images. Selected microbubbles were left in the 40% hematocrit blood until the number of particles per interrogation window was less than 15. Information on the generated microbubbles was acquired every 3 min.

[Figure 1]
Figure 1
Schematic of the microbubble generator used in this study.

2.2. X-ray imaging and image processing

A high-speed imaging system is required to minimize the displacement of microbubbles during the exposure time of the X-ray beam to measure the information on the fabricated microbubbles accurately. The number and average size of the fabricated microbubbles were measured by employing a time-resolved X-ray imaging system equipped with a high-speed camera. Fig. 2(a)[link] shows a schematic of the X-ray imaging system. An image intensifier was attached in front of the camera. Experiments were conducted at the 6D beamline of the Pohang Light Source (PLS-II). The beam current was 202 mA and the storage energy of the synchrotron facility was 3 GeV. A polychromatic X-ray beam with beam flux of 2.2 × 1012 photon s−1 mm−2 was used in this experiment. The energy bandwidth and median energy of a 1 mm-thick silicon wafer are 18.6 and 23.54 keV, respectively. The beam size was 30 mm (H) × 5 mm (V). Several silicon wafers were installed in the pathway of the X-ray beam to minimize the damage by the strong X-ray beam flux on the biological samples. The test sample was placed approximately 30 m downstream from the source. Given that the biological samples provide a weak absorption contrast, the phase-contrast imaging technique was dominantly employed in this experiment. In phase-contrast X-ray imaging, the distance between the test sample and detector is important. Fig. 2(b)[link] shows X-ray images of a microbubble according to the sample–detector distance. When the distance is too large, the captured images become blurred. The visibility of the microbubbles decreases with decreasing the distance. The optimal distance was 50 cm, at which sharp boundaries of the microbubbles were observed. All X-ray images were acquired at this distance.

[Figure 2]
Figure 2
(a) Schematic of the time-resolved X-ray imaging system. (b) X-ray images of a microbubble at different distances between the sample and detectors.

As the X-ray beam passes through a CdWO4 scintillator (500 µm thickness), X-rays are converted to visible light. The conversion efficiency of the scintillators depends on the type of scintillator. Therefore, the selection of a proper scintillator in compliance with the given experimental condition is important. X-ray images were recorded by using a high-speed camera (1024 pixels × 1024 pixels; Ultima-APX, Photron, Japan). The frame rate for X-ray PIV measurements was 2000 frames s−1. It was reduced to 60 frames s−1 in the measurements of size and quantity of CO2 microbubbles. The field of view was 1600 µm × 1600 µm with a 10× objective lens. The effective pixel size was 1.6 µm × 1.6 µm. An image intensifier (HiCATT; Lambert Instrument, The Netherlands) was attached in front of the camera to amplify the light intensity. Raw X-ray images contained noise caused by the amplification procedure. Each image had low contrast because of the short exposure time employed for high-speed imaging. The noise effect of the image intensifier decreased and the image contrast increased by adapting a flat-field correction, which has been widely employed in X-ray imaging experiments to improve image quality (Jung et al., 2012b[Jung, S. Y., Lim, S. M. & Lee, S. J. (2012b). J. Hydrol. 452, 83-89.]). Median and spatial frequency filters were also adopted to remove the noise effects (Jung et al., 2013[Jung, S. Y., Park, H. W., Kim, B. H. & Lee, S. J. (2013). J. Synchrotron Rad. 20, 498-503.]).

3. Result and discussion.

3.1. Size and number density of microbubbles

A typical X-ray image of CO2 microbubbles is shown in Fig. 3(a)[link]. The scale bar indicates 50 µm. The image size is 200 µm (H) × 200 µm (V). In the X-ray image, the phase and absorption contrast effects simultaneously appear. The intensity difference caused by different absorption rates can be expressed by the Beer–Lambert law (Cullity & Stock, 2001[Cullity, B. D. & Stock, S. R. (2001). Elements of X-ray Diffraction. New Jersey: Prentice Hall.]),

[I=I_0\exp(-\mu{x}),\eqno(1)]

where I is the transmitted intensity and I0 is the intensity of the incident X-ray beam. I and I0 are obtained by averaging the intensities of the microbubbles and background, respectively. μ is the absorption coefficient of the test material. The transmitted intensity is influenced by penetration depth (x). Therefore, I has different values with the variation of bubble size. Fig. 3(b)[link] represents the intensity variation along the line marked in Fig. 3(a)[link]. The diameters of the microbubbles in the X-ray images were obtained by measuring the full width at half-maximum (FWHM) (Lee et al., 2010[Lee, S. J., Jung, S. Y. & Ahn, S. (2010). Biosens. Bioelectron. 25, 1571-1578.]). When the size of the microbubbles decreases and the amount of microbubbles increases, the ambiguity in the size measurement of the microbubbles in the X-ray images increases because of the overlapping microbubbles. Approximately 50 consecutive X-ray images were acquired at 60 frames s−1 to minimize such ambiguity. In the current study, the optimal amount of CO2 microbubbles suitable for X-ray PIV measurements was evaluated in terms of microbubble diameter.

[Figure 3]
Figure 3
(a) Typical phase-contrast X-ray image of microbubbles. The scale bar indicates 50 µm. (b) Intensity variation along the solid line marked in (a). db represents the diameter of the microbubble in the image.

Fig. 4[link] shows variations in the average size and number of microbubbles in the 1000 µm depth. The analyzed image size is equal to the interrogation window of 64 pixels × 64 pixels in the PIV measurement. In the PIV experiments, the number of particles in each interrogation window should be greater than 15 (Keane & Adrian, 1990[Keane, R. D. & Adrian, R. J. (1990). Meas. Sci. Technol. 1, 1202-1215.]). Therefore, the total number of microbubbles in each interrogation window is adjusted to be greater than 15. The number and size of microbubbles at a fixed agitation time of 3 min are represented as bar and line graphs, respectively (Fig. 4a[link]). The number of microbubbles rapidly increases with the increasing rotation speed of the homogenizer. The average value is 19.2, and the standard deviation is 1.30 at 15000 r.p.m. The size of the microbubbles gradually decreases with increasing rotation speed. The bubble size is 18.7 µm at 15000 r.p.m. Fig. 4(b)[link] represents the variations in the number and diameter of microbubbles with respect to the agitation time at a fixed rotation speed of 15000 r.p.m. The number of microbubbles continuously increases with increasing agitation time. The average number of microbubbles is 33.1 with a standard deviation of 4.05 at 7 min. The size of the microbubbles gradually decreases with increasing agitation times. The bubble size becomes 13.3 µm at 7 min. The spatial resolution of the time-resolved X-ray PIV system is approximately 5 µm at a frame rate of 2000 frames s−1. However, microbubbles with diameters of less than 12 µm are not clearly defined under the tested flow condition. The rotation speed of 15000 r.p.m. at 7 min agitation is determined as the optimal condition for generating CO2 microbubbles as tracer particles in X-ray PIV measurements. The total volume of generated microbubbles at the optimal condition in the chamber, 100 µm (H) × 100 µm (V) × 1000 µm (depth), is approximately 2.84 × 105 µm3. The volume of RBCs in the same volume is approximately 4.0 × 106 µm3. The volume fraction of microbubbles is 2.84% in the blood of 40% hematocrit. In the PIV experiment, the particle number density can affect the flow characteristics and accuracy. The number of microbubbles should be considered to minimize the interaction with RBCs. Therefore, the concentration of microbubbles needs to be adjusted with mixing plasma in each experimental condition.

[Figure 4]
Figure 4
Variations of the average size and number of microbubbles (a) with varying rotation speed of the homogenizer at a fixed agitation time of 3 min and (b) with varying agitation time at a rotation speed of 15000 r.p.m.

The number and size of the residual microbubbles fabricated at the optimal condition were measured until the number of particles in an interrogation window became less than 15. An X-ray image was recorded every 3 min. The variations in the size and number of microbubbles during 19 min are 1.8 µm and 20.3, respectively (Fig. 5[link]). The number of microbubbles is 14 at 16 min. Considering the measurement accuracy of PIV experiments, the consecutive recording of X-ray images was completed within 16 min. The number of microbubbles gradually decreases, but the size of the microbubbles slightly increases with time. Standard deviation in the measured bubble size also increases. CO2 gas mixed with blood for 19 min. The injection volume was suggested in a previous parameter study (Kerns & Hawkins, 1995[Kerns, S. R. & Hawkins, I. F. Jr (1995). Am. J. Roentgenol. 164, 735-741.]). CO2 gas was supplied within the recommended volume rate to minimize the risk of embolism because of the mixing of CO2 gas in the blood.

[Figure 5]
Figure 5
Variations in the size and number of residual microbubbles according to duration time. The rotation speed of the homogenizer and the agitation time are fixed at 15000 r.p.m. and 7 min, respectively.

Hollow CO2 microbubbles have better image contrast as flow tracers compared with other tracer particles that have been used in X-ray PIV experiments. The diameter of a particle image can be estimated from the width of the autocorrelation peak (Adrian & Westerweel, 2011[Adrian, R. J. & Westerweel, J. (2011). Particle Image Velocimetry. Cambridge University Press.]). In our pre­liminary experiments using the time-resolved X-ray PIV system with insufficient X-ray beam flux, the absorption contrast and phase-contrast effects of Sonazoid (GE Healthcare, USA) used as an ultrasound contrast agent (UCA) were weakly observed. Thus, the particle-image diameter estimated from the width of the autocorrelation peak is different from the real diameter of the bubble. The width of the autocorrelation peak was estimated using the FWHM technique.

This difference may somewhat affect the measurement accuracy of PIV experiments. Given that most particles are less than 10 µm, the UCA Sonazoid is difficult to use as flow-tracing contrast media in X-ray PIV experiments. Silver-coated hollow particles have high image contrast, but are limited to non-clinical applications. It is difficult to observe individual Au NPs separately, due to the technological limitation in spatial resolution of the X-ray imaging system. Therefore, clusters of Au NPs have been used as flow-tracing contrast media. Considering that wall shear stress is estimated from the velocity gradient of the flow in the region near the vessel wall, Au NPs do not fit well for in vivo measurements of hemodynamic parameters.

Iopamidol was encapsulated by PVA as an absorption-based tracer particle. Therefore, the contrast of the X-ray image of the encapsulated particle was decreased under in vivo conditions because of the surrounding tissues and organs. This indicates that the signal-to-noise ratio (SNR) is not sufficient to conduct the X-ray PIV velocity field measurements with the PVA–iopamidol particles. In a previous study, Kariya et al. (2013[Kariya, S., Komemushi, A., Nakatani, M., Yoshida, R., Sawada, S. & Tanigawa, N. (2013). Clin. Radiol. 68, 346-351.]) obtained images of abdominal aorta of a swine by using CO2 microbubble as an absorption-based contrast agent. Therefore, its SNR was relatively low compared with other contrast agents. In this study, CO2 microbubbles were used as phase-contrast-based tracer particles. In a biological sample, the phase-shift effect of an X-ray beam propagating through tissues is 1000 times larger than the loss of intensity caused by absorption contrast (Fitzgerald, 2001[Fitzgerald, R. (2001). Phys. Today, 54(4), 21.]; Lewis, 2004[Lewis, R. A. (2004). Phys. Med. Biol. 49, 3573-3583.]). Therefore, CO2 microbubbles which are employed as phase-contrast-based tracer particles are useful for investigating velocity information of opaque blood flows.

Although CO2 microbubbles have several merits such as good biocompatibility, high image contrast and superior flow trackability, some problems still remain. The size and quantity of microbubbles are influenced by the surface tension of the mixture and the local pressure around the homogenizer. Therefore, generating microbubbles by following the guidelines suggested in this study is recommended.

3.2. Feasibility of microbubbles as flow-tracing contrast media

The velocity fields of 40% HCT blood flowing in a 1.5 mm-diameter opaque silicon tube were measured by using the time-resolved X-ray PIV system. Blood was supplied by a syringe pump at a flow rate of 1.9 ml min−1. Microbubbles were seeded into the tube by using a syringe pump at a flow rate of 0.1 ml min−1. The average flow rate in the tube was about 18.8 mm s−1. The mixture of the microbubbles and blood was injected after fully stirring.

X-ray images were consecutively acquired at a frame rate of 2000 frames s−1 with an exposure time of 160 µs. Velocity information was obtained by applying a cross-correlation PIV algorithm to the X-ray images. The interrogation window was 64 pixels × 64 pixels with 50% overlapping. The mean velocity field was obtained by an ensemble averaging 500 instantaneous velocity fields statistically. The velocity vectors contain buoyancy effects caused by the density difference between the test blood and CO2 gas. The terminal velocity of the microbubbles was determined by using a modified Stokes law (Lee & Kim, 2005b[Lee, S. J. & Kim, S. (2005b). Exp. Fluids, 39, 490-495.]),

[U_{\rm{T}}={{gd_{\rm{b}}^{\,2}}\over{18\mu}}\Delta\rho,\eqno(2)]

where g is the gravitational acceleration and db is the diameter of the microbubbles. μ is the fluid viscosity and Δρ is the density difference. The terminal velocity of the microbubbles was calculated as 0.043 mm s−1. The value of the terminal velocity was subtracted from PIV raw data. The maximum velocity measured at the centerline is approximately 22.08 mm s−1 at a Reynolds number of 11.75.

The X-ray images contain all velocity information obtained along the X-ray pathway. A mathematical formulation was adopted to compensate for the amassed volumetric flow information. The amassed velocity profile in a circular pipe can be represented as two-thirds of the velocity profile of the Poiseuille flow (Lee & Kim, 2003[Lee, S. J. & Kim, G. B. (2003). J. Appl. Phys. 94, 3620.]). Given that the blood flow has shear-thinning characteristics, the velocity profile of the blood flows in a circular pipe can be also be expressed as follows (Yeom et al., 2014[Yeom, E., Nam, K. H., Paeng, D. G. & Lee, S. J. (2014). Ultrasonics, 54, 205-216.]),

[V(r)=V_{\max}\left(1-\left|r/R\right|^K\right),\eqno(3)]

where K and R are the bluntness index and the radius of the circular tube, respectively. V(r) represents the velocity at the radial position r, and Vmax is the local maximum velocity at the center of the vessel. The K index was changed according to the flow and blood conditions.

Fig. 6(a)[link] shows a schematic of the amassed flow velocity in a circular pipe. The whole velocity profiles along the X-ray propagation direction were integrated to obtain the amassed velocity profile with the relationship of r2 = x2 + y2,

[\eqalignno{U_{\rm{Amassed}}\left(x\right)&= {{2\int\limits_{0}^{\left({R}^{2}-{x}^{2}\right)^{1/2}} {V}_{\max}\left(1-{\left|{{x}/{R}}\right|}^{K}\right)\,{\rm{d}}y }\over{ 2\left({R}^{2}-{x}^{2}\right)^{1/2} }} \cr& =\alpha(x){V_{\max}}\left({1-{{\left|{{{{x}}/{{R}}}}\right|}^{{K}}}}\right),&(4)}]

where α(x) represents the ratio of amassed velocity to the original velocity at radial position X/R. The α value was obtained by Romberg integration at each radial position. The radial position was uniformly divided into 6232 regions, and the circular pipe was divided into 3.049 × 107 segments. The theoretically amassed velocity profile and experimental results were curve-fitted iteratively with a varying K index. The ideal K index is 3.85. The maximum coefficient of determination in the fitted curves is 0.9945, and the difference in velocity data is 3.34%. Fig. 6(b)[link] shows variations of the α value for K = 2 (Poiseuille flow) and K = 3.85 (shear-thinning flow). The α value for the Poiseuille flows is fixed at 2/3, whereas the α value at K = 3.85 appears as a function of radial position. The α values for K = 3.85 is curve-fitted into a sixth-order polynominal with R2 = 0.9999. Fig. 6(c)[link] represents the time-averaged velocity field of a blood flow without compensating for the buoyancy effects. Fig. 6(d)[link] shows the streamwise mean velocity profiles of the blood flow. Solid dots denote the measured velocity data, including the buoyancy effect of microbubbles. The black dashed line represents the theoretical velocity profile, and the red dashed line indicates the amassed velocity profile at K = 3.85. The error bars represent the standard deviation of each velocity data. The standard deviation of each velocity component was about 0.3794. The error level increases with the increase of radial distance from the tube center. Tangelder et al. (1986[Tangelder, G. J., Slaaf, D. W., Muijtjens, A. M. M., Arts, T., oude Egbrink, M. G. A. O. & Reneman, R. S. (1986). Circ. Res. 59, 505-514.]) measured velocity profiles using a fluorescence microscopy. The bluntness index (K index) for the measured velocity profiles was varied from 2.4 to 4, depending on experimental conditions. Bishop et al. (2001[Bishop, J. J., Nance, P. R., Popel, A. S., Intraglietta, M. & Johnson, P. C. (2001). Am. J. Physiol. Heart Circ. Physiol. 208, H222-H236.]) also revealed that the K index for a low Reynolds number blood flow measured with an intravital microscope was about 3.8. Therefore, the K index of 3.85 for the present study at a low Reynolds number blood flow seems to be reasonable. The reproducibility of the measured flow velocities was checked by statistical analysis of 18 velocity data sets. The mean velocity field of each data set was obtained by ensemble averaging of 100 instantaneous velocity fields. Fig. 7[link] shows variation of the centerline velocity for each data set at different flow rate. Error bars represent standard deviation of the centerline velocity. The measurement accuracy of PIV experiments is usually larger than 0.1 pixel for each displacement (Westerweel, 2000[Westerweel, J. (2000). Exp. Fluids, 29, S3-S12.]) and the theoretical corresponding error is ±0.32 mm s−1 for the present experimental conditions. In these experiments, the standard deviation of the centerline maximum velocity was 0.396. The average flow rate was 1.978 ml min−1 and the standard deviation was 0.048. A red line indicates the injection flow rate of 2.0 ml min−1. The difference between the measured and injected flow rates is approximately 1.1%. The microsphere method is reported to have around 5% in statistical flow estimation (Prinzen & Bassingthwaighte, 2000[Prinzen, F. W. & Bassingthwaighte, J. B. (2000). Cardiovasc. Res. 45, 13-21.]; Nose et al., 1985[Nose, Y., Nakamura, T. & Nakamura, M. (1985). Basic Res. Cardiol. 80, 417-429.]). PET has about 10% error (Su et al., 2013[Su, Y., Arbelaez, A. M., Benzinger, T. L. S., Snyder, A. Z., Vlassenko, A. G., Mintun, M. A. & Raichle, M. E. (2013). J. Cereb. Blood Flow Metab. 33, 115-121.]) and MRI velocimetry has at least 3% error (Kadbi et al., 2014[Kadbi, M., Negahdar, M. J., Cha, J. W., Traughber, M., Martin, P., Stoddard, M. F. & Amini, A. A. (2014). Magn. Reson. Med. doi:10.1002/mrm.25188.]). These results show that the measurement accuracy of the synchrotron X-ray PIV method is sufficient to measure blood flows.

[Figure 6]
Figure 6
(a) Schematic of the amassed velocity profile. (b) Variations of the α value along the radial position for K = 3.85 and K = 2. (c) Mean velocity field of microbubbles seeded in blood flow of 40% hematocrit in a circular tube. (d) Comparison of streamwise mean velocity profiles: theoretical center-sectional velocity profile (black dots), theoretically amassed velocity profile (red dots) and measured amassed velocity profile (solid dots).
[Figure 7]
Figure 7
Variation of the ensemble-averaged centerline velocity according to flow rate.

In the present study, CO2 microbubbles are demonstrated to be suitable as flow-tracing contrast media for X-ray PIV measurements of blood flows. The measured flow rate and velocity are well matched with those of theoretical prediction. X-ray images of CO2 microbubbles were acquired using the phase-contrast X-ray imaging technique. The phase-contrast X-ray imaging technique has been widely used in biomedical applications (Zhou & Brahme, 2008[Zhou, S. A. & Brahme, A. (2008). Phys. Med. 24, 129-148.]; Takeda et al., 2002[Takeda, T., Momose, A., Wu, J., Yu, Q., Zeniya, T., Thet-Thet-Lwin, Yoneyama, A. & Itai, Y. (2002). Circulation, 105, 1708-1712.]). Although the velocity field information of blood flows was obtained, the synchrotron facility availability and dose limitations still remained for clinical applications. These limitations will be overcome in the near future with technological advances in X-ray sources by which phase-contrast X-ray images can be acquired (Hemberg et al., 2003[Hemberg, O., Otendal, M. & Hertz, H. M. (2003). Appl. Phys. Lett. 83, 1483.]; Tuohimaa et al., 2007[Tuohimaa, T., Otendal, M. & Hertz, H. M. (2007). Appl. Phys. Lett. 91, 074104.]; Lundström et al., 2012[Lundström, U., Larsson, D. H., Burvall, A., Takman, P. A. C., Scott, L., Brismar, H. & Hertz, H. M. (2012). Phys. Med. Biol. 57, 2603-2617.]). Therefore, the CO2 microbubbles method proposed in this study can be used to investigate blood flows of animal models in the present stage. However, the ultimate goal of this experimental technique is to investigate hemodynamic characteristics of cardiovascular diseases under in vivo clinical applications in the future.

4. Conclusion

Several tracer particles developed for X-ray PIV experiments have been tested to measure flows in an opaque conduit. However, tracer particles have technological limitations in practical applications to measure blood flows, due to toxicity and low image contrast. Hollow CO2 microbubbles were fabricated in this study by mechanical agitation to overcome these technological limitations. They were fabricated at various operating conditions in terms of the rotation speed of the homogenizer and agitation time to determine the optimal fabrication condition. The optimal microbubbles were generated at a rotation speed of 15000 r.p.m. of the homogenizer at an agitation time of 7 min. The size of the microbubbles at the optimal condition is 13.3 µm, and the number of microbubbles is approximately 33.1. The feasibility and usefulness of the developed CO2 microbubbles as flow-tracing contrast media were verified, and the velocity field of a blood flow in a circular tube was successfully measured within a 3.34% error level. Compared with other tracer particles, CO2 microbubbles are convenient to use and easy to fabricate. They also have high image contrast and superior biocapability. These hollow CO2 microbubbles will have strong potential in the X-ray PIV measurements of blood flows for investigating hemodynamic characteristics.

Acknowledgements

This work was supported by a National Research Foundation of Korea grant funded by the Korea government (MSIP) (No. 20080061991).

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