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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 24025–24038
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Assessment of the flow velocity of blood cells in a microfluidic device using joint spectral and time domain optical coherence tomography

Danuta M. Bukowska, Ladislav Derzsi, Szymon Tamborski, Maciej Szkulmowski, Piotr Garstecki, and Maciej Wojtkowski  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 24025-24038 (2013)
http://dx.doi.org/10.1364/OE.21.024025


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Abstract

Although Doppler optical coherence tomography techniques have enabled the imaging of blood flow in mid-sized vessels in biological tissues, the generation of velocity maps of capillary networks remains a challenge. To better understand the origin and information content of the Doppler signal from small vessels and limitations of such measurements, we used joint spectral and time domain optical coherence tomography to monitor the flow in a model, semitransparent microchannel device. The results obtained for Intralipid, whole blood, as well as separated red blood cells indicate that the technique is suitable to record velocity profiles in vitro, in a range of microchannel configurations.

© 2013 OSA

1. Introduction

Microcirculation in arterioles, capillaries and venules is essential component in supporting the physiological conditions necessary for the health of tissues and organs [1

1. Y. Sugii, S. Nishio, and K. Okamoto, “In vivo PIV measurement of red blood cell velocity field in microvessels considering mesentery motion,” Physiol. Meas. 23(2), 403–416 (2002). [CrossRef] [PubMed]

]. The measurement of circulation velocity is important for scientific and clinical purposes because it may be indicative of many pathological conditions, including arterial hypertension, ischemia, inflammation, and diabetes [2

2. G. Mchedlishvili and N. Maeda, “Blood flow structure related to red cell flow: A determinant of blood fluidity in narrow microvessels,” Jpn. J. Physiol. 51(1), 19–30 (2001). [CrossRef] [PubMed]

]. It has been previously suggested that non-continuum behavior of blood flow through such microvessels, with outer diameters between 5 and 80 µm, may lead to complex flow mechanisms that are not yet clearly understood [1

1. Y. Sugii, S. Nishio, and K. Okamoto, “In vivo PIV measurement of red blood cell velocity field in microvessels considering mesentery motion,” Physiol. Meas. 23(2), 403–416 (2002). [CrossRef] [PubMed]

]. Such concerns have prompted the adaptation of various optical techniques to measurement of the velocity profiles of blood flow both in vivo [3

3. S. Einav, H. J. Berman, R. L. Fuhro, P. R. DiGiovanni, J. D. Fridman, and S. Fine, “Measurement of blood flow in vivo by Laser Doppler Anemometry through a microscope,” Biorheology 12(3-4), 203–205 (1975). [PubMed]

5

5. A. Nakano, Y. Sugii, M. Minamiyama, and H. Niimi, “Measurement of red cell velocity in microvessels using particle image velocimetry (PIV),” Clin. Hemorheol. Microcirc. 29(3-4), 445–455 (2003). [PubMed]

] and in vitro [6

6. M. Baker and H. Wayland, “On-line volume flow rate and velocity profile measurement for blood in microvessels,” Microvasc. Res. 7(1), 131–143 (1974). [CrossRef] [PubMed]

9

9. R. Lima, S. Wada, M. Takeda, K.-i. Tsubota, and T. Yamaguchi, “In vitro confocal micro-PIV measurements of blood flow in a square microchannel: The effect of the haematocrit on instantaneous velocity profiles,” J. Biomech. 40(12), 2752–2757 (2007). [CrossRef] [PubMed]

], often providing scattered and contradictory results.

The most commonly used methods for mapping blood flow velocity distribution have been double-slit photometry [6

6. M. Baker and H. Wayland, “On-line volume flow rate and velocity profile measurement for blood in microvessels,” Microvasc. Res. 7(1), 131–143 (1974). [CrossRef] [PubMed]

], video microscopy [10

10. H. L. Goldsmith and V. T. Turitto, “Rheological aspects of thrombosis and hemostasis - basic principles and applications,” Thromb. Haemost. 55, 415–435 (1986). [PubMed]

], laser-Doppler velocimetry (LDV) and anemometry (LDA) [3

3. S. Einav, H. J. Berman, R. L. Fuhro, P. R. DiGiovanni, J. D. Fridman, and S. Fine, “Measurement of blood flow in vivo by Laser Doppler Anemometry through a microscope,” Biorheology 12(3-4), 203–205 (1975). [PubMed]

]. Studies of blood flow behavior at a microscopic level based on these techniques have been limited by several factors, including poor spatial resolution, limited accuracy, optical errors introduced by scattering and refraction at the walls of the microvessels, the high concentration of blood cells, and lack of sufficient computing power for reliable image and signal processing [11

11. R. Lima, “Flow behavior of labeled red blood cells in microchannels: A confocal micro-PTV assessment,” IFMBE Proc. 31, 1047–1050 (2010). [CrossRef]

]. Recent advances in optics, computation and image processing, have enabled the use of a number of newer optical methods for the analysis of microcirculation, often offering superior measurement accuracy and spatial resolution.

It is not clear whether the range of reported differences observed are caused by the complex and not yet fully understood character of blood flow, or by limitations of the technique. Although micro-PIV has many advantages and is widely used by the bio-microfluidics community, the resolution of the system is influenced by many factors, such as the out-of-focus particle images, density and size of the tracer particles (very often in blood studies additional fluorescent particles are required), size and optical characteristics of the microchannel and image quality [9

9. R. Lima, S. Wada, M. Takeda, K.-i. Tsubota, and T. Yamaguchi, “In vitro confocal micro-PIV measurements of blood flow in a square microchannel: The effect of the haematocrit on instantaneous velocity profiles,” J. Biomech. 40(12), 2752–2757 (2007). [CrossRef] [PubMed]

].

Therefore, in this study, we investigated the flow of Intralipid and blood in rectangular polydimethylsiloxane (PDMS) microchannels, 40 µm in depth and varied widths, as a first step towards the detailed understanding of blood flow behavior in microcapillaries. Imaging was performed with a Fourier-domain OCT setup. Data analysis was performed by using a joint spectral and time domain OCT method (STdOCT) [36

36. M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint spectral and time domain optical coherence tomography,” Opt. Express 16(9), 6008–6025 (2008). [CrossRef] [PubMed]

, 37

37. M. Szkulmowski, I. Grulkowski, D. Szlag, A. Szkulmowska, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation by complex ambiguity free joint spectral and time domain optical coherence tomography,” Opt. Express 17(16), 14281–14297 (2009). [CrossRef] [PubMed]

]. The results of measurements were in good agreement with a theoretical model presented in Section 2.1.

2. Extraction of velocity in rectangular channels

2.1. Analytical solution

Yun et al. demonstrated via numerical simulations how the velocity profile changes for γ ranging between 0.2 and 5 [43

43. J. H. Yun, M.-S. Chun, and H. W. Jung, “The geometry effect on steady electrokinetic flows in curved rectangular microchannels,” Phys. Fluids 22(5), 052004–1 −10 (2010). [CrossRef]

]. They compared the velocity profiles at the vertical and horizontal sections and showed that as γis reduced, the velocity profile becomes horizontal by spreading to both sides of the wall and the portion of the maximum axial velocity is clearly forced to the wall and the viscous shear is dominated by the shorter cross-dimension. In the shorter direction, the flow is, to a very good approximation, parabolic, while profiles in the longer direction exhibit extended plateaus in the center of the channel, and changes in the velocity only close to the walls. An intuitive picture is given by the extreme case of a narrow slit (with an infinite aspect ratio of width to height) where in direction perpendicular to the walls one observes a parabolic profile of speed of flow, while in the direction along the slit the profile is flat.

Figure 1(c) presents numerical simulation showing how the velocity profiles is changing depending on γ. The channel geometry corresponds to cross-sections of the microchannels used in our experiments.

2.2. Extraction of flow velocity using Doppler OCT

The Doppler frequency shift of waves scattered from a moving object is proportional to the velocity of the scattering medium:
fD=2vzcf0=2vmaxcosαcf0=2vmaxcosαλ0,
(2)
wherefD is the Doppler shift,vzis the object velocity in the direction of propagation, and vmaxis the blood flow velocity in the center of the capillary. The incident beam having speed of c (cvmax), optical frequency off0and the corresponding wavelength λ0, αangle between the light propagation path and the direction of flow. Figure 2
Fig. 2 Scheme of Doppler OCT flow measurement and data visualization: (a) Coordinate system for flow through optical beam: Q- volumetric flow rate, vmax – blood flow velocity in the centre of capillary, vz – axial velocity component, vx – transverse velocity component, α – angle between the light propagation path and the direction of flow. (b) One-dimensional data presents spatial distribution of vz and is called Doppler velocity profile (i.). Afterword Doppler velocity profile is color-coded. Red and blue indicate flow in opposite directions. The value of the axial velocity is displayed as color saturation (ii.). When three-dimensional data are collected then velocity map is created (iii). (Also see subsection 3.2.)
presents scheme of Doppler OCT flow measurement and data visualization.

However, there are upper and lower velocity measurement ranges. The range of the axial velocities that can be measured unambiguously with a given sampling intervalΔt is limited by [21

21. I. Grulkowski, I. Gorczynska, M. Szkulmowski, D. Szlag, A. Szkulmowska, R. A. Leitgeb, A. Kowalczyk, and M. Wojtkowski, “Scanning protocols dedicated to smart velocity ranging in Spectral OCT,” Opt. Express 17(26), 23736–23754 (2009). [CrossRef] [PubMed]

]:

v=z,maxrange±λ04Δt.
(3)

3. Materials and methods

3.1. Experimental setup

In the experiments, we used a standard Fourier-domain OCT system, comprising a spectrally broadband light source (Ti:S laser, λ0 = 795 nm, Δλ = 155 nm, FemtoLaser, Austria) which provides the measured axial resolution (FWHM) of 2 µm in tissue. After entering the fiber coupler, the light is split into a reference arm (50% of light power) and an object arm (50% of light power), and after that is collimated with 19-mm focal length achromatic lenses (Thorlabs, USA) (Fig. 3
Fig. 3 (a) The experimental set-up. CMOS - CMOS camera, DG – diffraction grating, PC - polarization controller, NDF - neutral density filter, DC - dispersion compensation, RM –reference mirror, c, L1, L2 - lenses, MO – microscope objective. (b) Scanning protocol used in experiments; Trep – repetition time.
). In the reference arm, we implemented polarization control of light propagating in the fiber, light attenuation, and dispersion compensation. In the object arm, the light emerging from the collimator is directed to the galvanometer scanners. The achromatic lenses L1 and L2 (f1 = f2 = 50 mm, Thorlabs, USA) relay the beam to the microscope objective (10 × Thorlabs,USA). This optical setup enables for imaging with 8µm transverse resolution, which is measured experimentally. The OCT signal detected by a custom-designed spectrometer containing a collimating lens (Schneider Kreuznach Tele-Xenar, 2.2/70mm, Germany), a volume holographic diffraction grating (1200 LP/mm, Wasatch Photonics, USA), a telecentric f-theta lens (effective focal length 79.6 mm, Sill Optics), and a 12-bit CMOS line-scan camera (spl4096-140 km, Basler Sprint, Germany).

The experimentally determined sensitivity of the system is 98 dB, measured with 800 µW power incident of light at the object and a camera exposure time of 8.6µs. The measured signal roll-off is 19 dB over the entire imaging depth (1.8 mm). The imaging speed depends on two camera settings: the number of active pixels, and the exposure time. We used 2048 of the 4096 available camera pixels.

Experiments were performed using a microfluidic device (see Subsection 3.4). The following fluids has been used: a water solution of Intralipid (0.5% v/v), human blood and blood cells suspensions diluted in physiological saline. The flow was initialized and maintained with a syringe pump (AP24, Ascor, Poland). The power of the light incident on the sample was set to 800µW.

3.2. Method of data analysis and data visualization

We retrieve axial velocity using a joint spectral and time domain OCT (STdOCT) method detailed elsewhere [36

36. M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint spectral and time domain optical coherence tomography,” Opt. Express 16(9), 6008–6025 (2008). [CrossRef] [PubMed]

, 37

37. M. Szkulmowski, I. Grulkowski, D. Szlag, A. Szkulmowska, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation by complex ambiguity free joint spectral and time domain optical coherence tomography,” Opt. Express 17(16), 14281–14297 (2009). [CrossRef] [PubMed]

]. In this technique, the OCT signal is acquired while the object is scanned laterally with sufficient oversampling for Doppler signal analysis. In this way, the spectral fringe signals (A-scans) are registered both in wave number k and in time space, creating a two-dimensional data set. We applied 2-D Fourier transformation to the signal to obtain simultaneously both structural images [Fig. 4(b)
Fig. 4 Schematic drawing of rectangular microchannel for two different types of branching in the middle of the channel (indicated as 1. and 2.): (a) Top view of the channel. (b) Structural en face OCT projections of Intralipid 0.5% flow in microfluidics system. Marked areas #1 and #2 indicate the region taken for detailed analysis in the section 4. (c) Velocity map corresponding to structural en face image. The reversal of flow is observed in channel’ trifurcation.
] and Doppler frequency maps corresponding to the axial velocity [Fig. 4(c)]. The structural cross-sectional images are displayed in gray scale. The flow information is displayed in color-coded velocity maps. Red and blue indicate flow in opposite directions. The value of the axial velocity is displayed as color saturation.

3.3. Blood sample preparation

Venous blood was drawn from a healthy adult volunteer in the laboratory of a diagnostic center of blood analysis. Blood samples were procured in K2 EDTA coated tubes to prevent coagulation and to not affect the shape of red blood cells (RBCs). Concentrates of cell components were also prepared in the diagnostic center, according to its own standard techniques. The information regarding the number and properties of blood components was provided by flow cytometry. Additionally, a commercial Nikon microscope (Inverted Microscope, Eclipse, Ti-E/B) system was used to obtain the optical images of the measured OCT samples. All the blood samples were stored hermetically at 4°C until the experiment was performed at room temperature. Studies were approved by Ethic Committee on Clinical Investigation of Nicolaus Copernicus University, in accordance to the tenets of the Helsinki Declaration.

3.4. PDMS microchannel

We decided to use PDMS microchannels for several reasons. First of all glass microchannels are not ideal for the study of blood flow properties at a microscopic level, primarily because of fabrication and physicochemical factors, e.g. microvessels are elastic, while glass capillaries are rigid [46

46. N. Maeda, “Erythrocyte rheology in microcirculation,” Jpn. J. Physiol. 46(1), 1–14 (1996). [CrossRef] [PubMed]

]. Second, the fabrication of microchannels in glass is limited in depth and width because glass is isotropically etched by hydrofluoric acid using a metal mask, which has a limited durability against the etchant [13

13. R. Lima, S. Wada, S. Tanaka, M. Takeda, T. Ishikawa, K. I. Tsubota, Y. Imai, and T. Yamaguchi, “In vitro blood flow in a rectangular PDMS microchannel: experimental observations using a confocal micro-PIV system,” Biomed. Microdevices 10(2), 153–167 (2008). [CrossRef] [PubMed]

]. In the case of transparent and elastic material such as PDMS it is possible to fabricate channels with tight precision using the soft lithography technique [47

47. F. S. Ligler, “Perspective on optical biosensors and integrated sensor systems,” Anal. Chem. 81(2), 519–526 (2009). [CrossRef] [PubMed]

]. As a consequence they can easily be transferred onto the microscope to be combined with suitable read-out techniques [48

48. A. Alrifaiy and K. Ramser, “How to integrate a micropipette into a closed microfluidic system: absorption spectra of an optically trapped erythrocyte,” Biomed. Opt. Express 2(8), 2299–2306 (2011). [CrossRef] [PubMed]

]. Moreover PDMS is porous, which may mimic microvascular systems and to perform in vitro experiments.

The network of channels used in this study was fabricated based on rapid prototyping of masters using high-resolution printing and contact lithography, molding PDMS, and contact sealing of oxidized PDMS surfaces. A detailed description of the fabrication process is given by Duffy et al. [49

49. D. C. Duffy, J. C. McDonald, O. J. A. Schueller, and G. M. Whitesides, “Rapid prototyping of microfluidic systems in poly(dimethylsiloxane),” Anal. Chem. 70(23), 4974–4984 (1998). [CrossRef] [PubMed]

]. We designed the photomask in AutoCAD 2010 and printed on thin flexible foil at high resolution (40,640 dpi). A layer of SU8 3005 negative photoresist (MicroChem, USA) was deposited on a 3” silicon wafer using a spincoater (G3P-8 Spincoat, Cookson Electronics, USA). The photomask was placed on the top of the photoresist prior to exposure to UV light (through an i-line filter, λ = 365 nm). The uncured photoresist was removed with a developer, thus, obtaining the required pattern (master) for replica molding. A PDMS elastomer (Dow Corning, USA) was mixed with a curing agent (1:10 (w/w)) and with 0.5% w/w titanium dioxide pigment (TiO2) and then degassed in a vacuum. The Si-wafer with the cured photoresist master was placed into a plastic petridish, immersed in the degassed PDMS and cured in an oven at 70°C for 3 hours. The PDMS was than peeled off and holes were punched for inlets and outlets. Then a PDMS microchannel device along with a thin glass plate (d = 0.2mm) were treated with oxygen plasma for 50 seconds. The pieces were brought into contact, which resulted in a permanent bond. The ready device was then left to rest for 24 hours in order for the hydrophobic character to recover. PE tubes (BD, Intramedic, USA; OD = 1.22mm/ID = 0.76mm) were connected to the inlets and outlets.

We used microchannels of two different geometries, with semitransparent properties, obtained by mixing the PDMS with titanium dioxide (TiO2).The geometry of the channels is presented in Fig. 4.

4. Results and discussion

We measured the three-dimensional velocity distribution of various fluids at several locations across the microfluidic network. In Fig. 4, fifteen en face images of Intralipid circulation are fused, covering an area of 18 mm × 1.3 mm. Figure 4(b) presents structural en face projection, when 4(c) presents Doppler en face projection. The images were scanned with exposure time equal to 5 µs, and repetition time equal to 8 µs, which corresponds to the velocity range of ± 24.7 mm/s. The Intralipid was introduced into the microchannels at a flow rate of 6 ml/h. The result confirms that we are able to obtain a velocity map in a narrow rectangular microchannel. Moreover, the figure presents also how sensitive is the measurement, since in the region of the channel’s trifurcation, a color change appeared on the en face projection of the Doppler signal [Fig. 4(b)], what indicates reversal of the flow in the region of changing widths.

4.1. Flow of Intralipid solution through rectangular microchannels: evaluation of the technique

In order to evaluate the measurement technique, we first conducted a set of experiments on the microfluidic device with a solution of Intralipid, which is a fat emulsion that is used clinically. However, it is also widely used in optical experiments, as a biological tissue phantom, because it's highly scattering properties with low absorption. In order to tune phantom to values resembling those of blood we diluted Intralipid in water (0.5% v/v).

Figures 5
Fig. 5 Three-dimensional imaging of Intralipid flow in the microfluidic device in the region with a cross-section of 300µm × 40µm (#1, γ = 0.13). (a) An example of structural OCT image from 3D data set. (b) Axial velocity map corresponding to the structural image. (c) Three-dimensional representation of axial velocity profiles obtained from OCT data. (d) Comparison of ensemble-averaged total velocity of Intralipid with the theoretical model.
and 6
Fig. 6 Three-dimensional imaging of Intralipid flow in microfluidics device localized in the multiple channels region with 6 parallel channels, cross-section of 50µm × 40µm each (#2, γ = 0.8). (a) An example of structural OCT image from 3D data set. The Intralipid is observed only in 4 channels from 6. (b) Axial velocity map corresponding to the structural image. The flow is observed in 3 channels from 6, because of flow resistances and clogging of the channels; (c) Three-dimensional representation of axial velocity profiles obtained from OCT data; (d) Comparison of ensemble-averaged total velocity of Intralipid from the central channel and the theoretical model in the central plane.
present the velocity fields of Intralipid flowing in a microfluidic system. We recorded the velocity maps at two different locations within the device to test the measurement technique against two different aspect ratios γ. In both cases, we scanned an area of 1.2mm × 1.2mm at repetition time of 8 µs, corresponding to an axial velocity range of ± 24.7 mm/s. In the first case (Fig. 5) the microchannel was placed at an angle of α = (78.7 ± 0.4) degrees relative to the imaging beam. We used a wider part of the microchannel with a cross-section of 300µm × 40µm (γ = 0.13). The flow rate was 2 ml/h.

Figure 6 shows the results obtained in the central region of the microfluidic network consisting of 6 parallel channels, each with a cross-sections of 50µm × 40µm. These corresponds to γ = 0.8 for a single channel, so a parabolic profile should be observed. Here the volumetric flow rate was 2 ml/h and the angle of the incident beam α = (71 ± 0.5) degrees.

Figures 5 and 6 show the steady properties of the flow and confirm that the proposed theoretical model is in good agreement with the experimental data. The small fluctuations in the experimental profiles of velocity are observable, but they do not introduce any systematic deviations from the model. In both cases the error bars indicate one standard deviation, which is determined by the standard deviation of the Doppler angle estimation. Figure 6 shows that the Intralipid solution did not flow through all channels in the parallel section. This was caused by the flow’s resistances in some parts of the device that appeared and channels clogging.

Figure 7
Fig. 7 Three-dimensional imaging of Intralipid flow in microfluidics device. Flow behavior at the beginning, in the central region and at the end of the channel is presented, respectively. (a) An example of structural OCT image from 3D data set. (b) Axial velocity map corresponding to the structural image. Please note, that there is no flow visible in one of the channel in the central region. (c) Three-dimensional representation of axial velocity profiles obtained from OCT data. (d) Axial velocity profile in the central plane.
presents that using the OCT technique, the velocity in each portion of a branched network can be mapped precisely. Here, the measurements at the beginning and at the end of the channel were made in different distances (closer at the beginning and more far at the end) from the trifurcation. Since the Intralipid didn’t flow through all channels increased resistances were observed, which influenced the profile at the beginning of the trifurcated channel (see Fig. 7(d), top panel). We also imaged the channel in location more distant from the trifurcation where flow was stabilized.

For this study we chose the microchannel with trifurcation in the middle and having a cross-sections equal to S1 = 300µm × 40µm, at the beginning and at the end of the trifurcation, and S2 = 100µm × 40µm in each parallel channel. In this case, we investigated the flow behavior at the beginning, in the central region and at the end of the microfluidics device. If the fluid flows through all channels after the trifurcation, according to the continuity flow equation, we received the following formula: S1v1=3S2v2=3(13S1)v2v1=v2, where v1 - maximum velocity in the area where the cross-section equals S1, v2 – maximum velocity in the area where the cross-section equals S2. In our case we assumed that the channel aspect ratio is large, and hence the profiles of the smaller channels are very similar to that of the larger channel. Therefore, the value of maximal velocities are inserted into the formula. Since on the structural image we are able to see the scattering signal in all channels [Fig. 7(a)] and we observed, that one of the branched channel is clogged (no Doppler signal was received) the above formula should be rewritten as follows: S1v1=S2(v21+v22), where v21 and v22 are velocity values in the two permeable channels. Hence, S1v1=(13S1)(v21+v22)3v1=(v21+v22).The averaged maximum peak axial velocity values present in [Fig. 7(d)], inserted into the above formula give us values (21 mm/s) = (11mm/s + 10.6mm/s). The differences in mean value are below 5%.

4.2. In vitro imaging of blood

Figures 8(b) and 8(c) show OCT structural image and Doppler map obtained from 3-D data set at the beginning of the microfluidics device, while Figs. 8(d)-6(f) show a three-dimensional representation of axial velocity profiles obtained from OCT data and a comparison of averaged velocity profiles in vertical and horizontal sections with theory. Also to ascertain whether the law of mass conservation holds true in the case of blood flow we measured flow in different parts of the channel (Fig. 8, second and third panel).

Upon examination of the velocity profile, higher deviations between Intralipid and blood were observed. These deviations become much clearer on the axial profiles. However, the averaged profiles obtained bear out the theory, and obey the law of mass conservation.

Figure 9 shows that we are able to receive structural information about blood flow, even if single cells are moving in the channel (Fig. 9, third row). Furthermore, Doppler OCT M-scan can be reconstructed. However, together with a reduction of the concentration of RBCs, a higher dispersion in axial velocity values is observed. For the sample where the concentration of RBCs was reduced to 40 000 RBCs per µl we could observe signals coming from individual cells (indicated as numbers 1, 2, and 3 in Fig. 9). In this case dispersion of the velocity values is higher, probably as a result of increasing the free passage of the traveling RBCs. The channel’s cross-section is much higher than the size of cells, so they can easily change direction during the flow, which influences the axial velocity read-out. Therefore, for detailed analysis of a single cell flow the microchannel cross-section should be reduced to the dimensions of single cell.

5. Conclusions

We demonstrated the capability of joint spectral and time domain optical coherence tomography to assess human blood velocity in vitro, in three dimensions, in rectangular PDMS microchannels and with high sensitivity. The measurements presented in this study show that the Doppler OCT method can be effectively integrated with a PDMS microchannel, in a range of configuration, to monitor the flow of various concentration of blood. The results obtained for both Intralipid and for blood agreed well with the theoretical model even if they are tested for different values of microchannel aspect ratio. It means that the velocity profiles are parabolic, in both cases, in microchannel with aspect ratio larger than γ = 0.8 and starts to be flat for γ less than 0.4. However, in the case of blood flow small fluctuations are observed which become higher with a reduction of the concentration of RBCs, probably as a result of increasing the free passage of the traveling RBCs. The channel’s cross-section is much higher than the size of cells, so they can easily change transversal direction during the flow, which influences the axial velocity read-out. Therefore, for detailed analysis of a single cell flow the microchannel cross-section should be reduced to the dimensions of the single blood cell.

Microfluidics is a technologically emerging area that has attracted significant research in the fields of biology, medicine and chemistry. It has been applied to optical techniques, such as Raman Spectroscopy, fluorescence microscopy, phase contrast microscopy and others, to acquire information not only about blood flow, but also about blood structure and properties. Hence applying microfluidics device to other OCT studies should also be taken into consideration. It may play an important role in the development of a more accurate biochip devices for various chemical and biomedical application.

Acknowledgments

The authors would like to kindly acknowledge Teresa Behrendt and Malgorzata Kesy from the Diagnosis Laboratory for giving their support in blood sample preparation; Prof. Aleksander Balter and Agnieszka Gorska for access to the Nikon microscope. This project was financed by National Science Center proj.“Maestro” (decision No DEC-2011/02/A/ST2/00302)” (M. Wojtkowski). This project was also co-financed by the EuroHORCs-European Science Foundation EURYI Award EURYI-01/2008-PL (M. Wojtkowski), National Laboratory of Quantum Technology (M. Wojtkowski), the National Centre for Research and Development Grant No. PBS1/A9/20/2013 (M. Szkulmowski, D. Bukowska) and by the Polish Ministry of Science and Higher Education (years 2011–2015) (M. Szkulmowski). D. Bukowska acknowledges the grants of the Nicolaus Copernicus University (398-F). D. Bukowska and S. Tamborski acknowledge grants from the European Social Fund and the Polish Government within the integrated Regional Development Operational Programme, Action 2.6, by project Step in the future III and IV-years 2010, 2011,2012. P. Garstecki and L. Derzsi acknowledge project co-operated within the Foundation for Polish Science Team Programme TEAM/2008-1/1 co-financed by the EU European Regional Development Fund and within the European Research Council Starting Grant 279647.

References and links

1.

Y. Sugii, S. Nishio, and K. Okamoto, “In vivo PIV measurement of red blood cell velocity field in microvessels considering mesentery motion,” Physiol. Meas. 23(2), 403–416 (2002). [CrossRef] [PubMed]

2.

G. Mchedlishvili and N. Maeda, “Blood flow structure related to red cell flow: A determinant of blood fluidity in narrow microvessels,” Jpn. J. Physiol. 51(1), 19–30 (2001). [CrossRef] [PubMed]

3.

S. Einav, H. J. Berman, R. L. Fuhro, P. R. DiGiovanni, J. D. Fridman, and S. Fine, “Measurement of blood flow in vivo by Laser Doppler Anemometry through a microscope,” Biorheology 12(3-4), 203–205 (1975). [PubMed]

4.

H. Golster, M. Lindén, S. Bertuglia, A. Colantuoni, G. Nilsson, and F. Sjöberg, “Red blood cell velocity and volumetric flow assessment by enhanced high-resolution laser Doppler imaging in separate vessels of the hamster cheek pouch microcirculation,” Microvasc. Res. 58(1), 62–73 (1999). [CrossRef] [PubMed]

5.

A. Nakano, Y. Sugii, M. Minamiyama, and H. Niimi, “Measurement of red cell velocity in microvessels using particle image velocimetry (PIV),” Clin. Hemorheol. Microcirc. 29(3-4), 445–455 (2003). [PubMed]

6.

M. Baker and H. Wayland, “On-line volume flow rate and velocity profile measurement for blood in microvessels,” Microvasc. Res. 7(1), 131–143 (1974). [CrossRef] [PubMed]

7.

T. Cochrane, J. C. Earnshaw, and A. H. G. Love, “Laser Doppler measurement of blood velocity in microvessels,” Med. Biol. Eng. Comput. 19(5), 589–596 (1981). [CrossRef] [PubMed]

8.

C. Alonso, A. R. Pries, O. Kiesslich, D. Lerche, and P. Gaehtgens, “Transient rheological behaviour of blood in low-shear tube flow - velocity profiles and effective viscosity,” Am, J. Physiol. 268, H25–H32 (1995).

9.

R. Lima, S. Wada, M. Takeda, K.-i. Tsubota, and T. Yamaguchi, “In vitro confocal micro-PIV measurements of blood flow in a square microchannel: The effect of the haematocrit on instantaneous velocity profiles,” J. Biomech. 40(12), 2752–2757 (2007). [CrossRef] [PubMed]

10.

H. L. Goldsmith and V. T. Turitto, “Rheological aspects of thrombosis and hemostasis - basic principles and applications,” Thromb. Haemost. 55, 415–435 (1986). [PubMed]

11.

R. Lima, “Flow behavior of labeled red blood cells in microchannels: A confocal micro-PTV assessment,” IFMBE Proc. 31, 1047–1050 (2010). [CrossRef]

12.

R. D. Keane and R. J. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49(3), 191–215 (1992). [CrossRef]

13.

R. Lima, S. Wada, S. Tanaka, M. Takeda, T. Ishikawa, K. I. Tsubota, Y. Imai, and T. Yamaguchi, “In vitro blood flow in a rectangular PDMS microchannel: experimental observations using a confocal micro-PIV system,” Biomed. Microdevices 10(2), 153–167 (2008). [CrossRef] [PubMed]

14.

Y. Sugii, R. Okuda, K. Okamoto, and H. Madarame, “Velocity measurement of both red blood cells and plasma of in vitro blood flow using high-speed micro PIV technique,” Meas. Sci. Technol. 16(5), 1126–1130 (2005). [CrossRef]

15.

L. Bitsch, L. H. Olesen, C. H. Westergaard, H. Bruus, H. Klank, and J. P. Kutter, “Micro particle-image velocimetry of bead suspensions and blood flows,” Exp. Fluids 39(3), 507–511 (2005). [CrossRef]

16.

M. Wojtkowski, “High-speed optical coherence tomography: basics and applications,” Appl. Opt. 49(16), D30–D61 (2010). [CrossRef] [PubMed]

17.

Y. Wang and R. Wang, “Autocorrelation optical coherence tomography for mapping transverse particle-flow velocity,” Opt. Lett. 35(21), 3538–3540 (2010). [CrossRef] [PubMed]

18.

V. J. Srinivasan, H. Radhakrishnan, E. H. Lo, E. T. Mandeville, J. Y. Jiang, S. Barry, and A. E. Cable, “OCT methods for capillary velocimetry,” Biomed. Opt. Express 3(3), 612–629 (2012). [CrossRef] [PubMed]

19.

A. Szkulmowska, M. Szkulmowski, D. Szlag, A. Kowalczyk, and M. Wojtkowski, “Three-dimensional quantitative imaging of retinal and choroidal blood flow velocity using joint spectral and time domain optical coherence tomography,” Opt. Express 17(13), 10584–10598 (2009). [CrossRef] [PubMed]

20.

V. J. Srinivasan, S. Sakadzić, I. Gorczynska, S. Ruvinskaya, W. Wu, J. G. Fujimoto, and D. A. Boas, “Quantitative cerebral blood flow with optical coherence tomography,” Opt. Express 18(3), 2477–2494 (2010). [CrossRef] [PubMed]

21.

I. Grulkowski, I. Gorczynska, M. Szkulmowski, D. Szlag, A. Szkulmowska, R. A. Leitgeb, A. Kowalczyk, and M. Wojtkowski, “Scanning protocols dedicated to smart velocity ranging in Spectral OCT,” Opt. Express 17(26), 23736–23754 (2009). [CrossRef] [PubMed]

22.

X. Xu, L. Yu, and Z. Chen, “Effect of erythrocyte aggregation on hematocrit measurement using spectral-domain optical coherence tomography,” IEEE Trans. Biomed. Eng. 55(12), 2753–2758 (2008). [CrossRef] [PubMed]

23.

X. Q. Xu, Y. C. Ahn, and Z. P. Chen, “Feasibility of Doppler variance imaging for red blood cell aggregation characterization,” J. Biomed. Opt. 14(6), 060507 (2009). [CrossRef] [PubMed]

24.

Z. P. Chen, T. E. Milner, D. Dave, and J. S. Nelson, “Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media,” Opt. Lett. 22(1), 64–66 (1997). [CrossRef] [PubMed]

25.

X. J. Wang, T. E. Milner, Z. P. Chen, and J. S. Nelson, “Measurement of fluid-flow-velocity profile in turbid media by the use of optical Doppler tomography,” Appl. Opt. 36(1), 144–149 (1997). [CrossRef] [PubMed]

26.

X. J. Wang, T. E. Milner, and J. S. Nelson, “Characterization of fluid flow velocity by Optical Doppler Tomography,” Opt. Lett. 20(11), 1337–1339 (1995). [CrossRef] [PubMed]

27.

V. X. D. Yang, M. L. Gordon, B. Qi, J. Pekar, S. Lo, E. Seng-Yue, A. Mok, B. C. Wilson, and I. A. Vitkin, “High speed, wide velocity dynamic range Doppler optical coherence tomography (Part I): System design, signal processing, and performance,” Opt. Express 11(7), 794–809 (2003). [CrossRef] [PubMed]

28.

R. A. Leitgeb, L. Schmetterer, W. Drexler, A. F. Fercher, R. J. Zawadzki, and T. Bajraszewski, “Real-time assessment of retinal blood flow with ultrafast acquisition by color Doppler Fourier domain optical coherence tomography,” Opt. Express 11(23), 3116–3121 (2003). [CrossRef] [PubMed]

29.

Z. P. Chen, T. E. Milner, X. J. Wang, S. Srinivas, and J. S. Nelson, “Optical Doppler tomography: Imaging in vivo blood flow dynamics following pharmacological intervention and photodynamic therapy,” Photochem. Photobiol. 67(1), 56–60 (1998). [CrossRef] [PubMed]

30.

J. Moger, S. J. Matcher, C. P. Winlove, and A. Shore, “Measuring red blood cell flow dynamics in a glass capillary using Doppler optical coherence tomography and Doppler amplitude optical coherence tomography,” J. Biomed. Opt. 9(5), 982–994 (2004). [CrossRef] [PubMed]

31.

J. Moger, S. J. Matcher, C. P. Winlove, and A. Shore, “The effect of multiple scattering on velocity profiles measured using Doppler OCT,” J. Phys. D 38(15), 2597–2605 (2005). [CrossRef]

32.

S. G. Proskurin, I. A. Sokolova, and R. K. Wang, “Imaging of non-parabolic velocity profiles in converging flow with optical coherence tomography,” Phys. Med. Biol. 48(17), 2907–2918 (2003). [CrossRef] [PubMed]

33.

L. Wang, W. Xu, M. Bachman, G. P. Li, and Z. P. Chen, “Imaging and quantifying of microflow by phase-resolved optical Doppler tomography,” Opt. Commun. 232(1-6), 25–29 (2004). [CrossRef]

34.

L. An and R. K. Wang, “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express 16(15), 11438–11452 (2008). [CrossRef] [PubMed]

35.

R. K. Wang and L. An, “Doppler optical micro-angiography for volumetric imaging of vascular perfusion in vivo,” Opt. Express 17(11), 8926–8940 (2009). [CrossRef] [PubMed]

36.

M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint spectral and time domain optical coherence tomography,” Opt. Express 16(9), 6008–6025 (2008). [CrossRef] [PubMed]

37.

M. Szkulmowski, I. Grulkowski, D. Szlag, A. Szkulmowska, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation by complex ambiguity free joint spectral and time domain optical coherence tomography,” Opt. Express 17(16), 14281–14297 (2009). [CrossRef] [PubMed]

38.

J. Lauri, M. Wang, M. Kinnunen, and R. Myllyla, “Measurement of microfluidic flow velocity profile with two Doppler optical coherence tomography systems,” Proc. SPIE 6863, 68630F (2008). [CrossRef]

39.

S. G. Li, Z. G. Xu, S. F. Yoon, and Z. P. Fang, “Feasibility study on bonding quality inspection of microfluidic devices by optical coherence tomography,” J. Biomed. Opt. 16(6), 066011 (2011). [CrossRef] [PubMed]

40.

C. W. Xi, D. L. Marks, D. S. Parikh, L. Raskin, and S. A. Boppart, “Structural and functional imaging of 3D microfluidic mixers using optical coherence tomography,” Proc. Natl. Acad. Sci. U.S.A. 101(20), 7516–7521 (2004). [CrossRef] [PubMed]

41.

Y. C. Ahn, W. Y. Jung, J. Zhang, and Z. P. Chen, “Investigation of laminar dispersion with optical coherence tomography and optical Doppler tomography,” Opt. Express 13(20), 8164–8171 (2005). [CrossRef] [PubMed]

42.

H. Bruus, “Theoretical microfluidics,”(Oxford University Press, 2008).

43.

J. H. Yun, M.-S. Chun, and H. W. Jung, “The geometry effect on steady electrokinetic flows in curved rectangular microchannels,” Phys. Fluids 22(5), 052004–1 −10 (2010). [CrossRef]

44.

Y. C. Ahn, W. Jung, and Z. P. Chen, “Quantification of a three-dimensional velocity vector using spectral-domain Doppler optical coherence tomography,” Opt. Lett. 32(11), 1587–1589 (2007). [CrossRef] [PubMed]

45.

R. M. Werkmeister, N. Dragostinoff, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. A. Leitgeb, and L. Schmetterer, “Bidirectional Doppler Fourier-domain optical coherence tomography for measurement of absolute flow velocities in human retinal vessels,” Opt. Lett. 33(24), 2967–2969 (2008). [CrossRef] [PubMed]

46.

N. Maeda, “Erythrocyte rheology in microcirculation,” Jpn. J. Physiol. 46(1), 1–14 (1996). [CrossRef] [PubMed]

47.

F. S. Ligler, “Perspective on optical biosensors and integrated sensor systems,” Anal. Chem. 81(2), 519–526 (2009). [CrossRef] [PubMed]

48.

A. Alrifaiy and K. Ramser, “How to integrate a micropipette into a closed microfluidic system: absorption spectra of an optically trapped erythrocyte,” Biomed. Opt. Express 2(8), 2299–2306 (2011). [CrossRef] [PubMed]

49.

D. C. Duffy, J. C. McDonald, O. J. A. Schueller, and G. M. Whitesides, “Rapid prototyping of microfluidic systems in poly(dimethylsiloxane),” Anal. Chem. 70(23), 4974–4984 (1998). [CrossRef] [PubMed]

OCIS Codes
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.4500) Medical optics and biotechnology : Optical coherence tomography
(280.2490) Remote sensing and sensors : Flow diagnostics

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: July 10, 2013
Revised Manuscript: September 4, 2013
Manuscript Accepted: September 9, 2013
Published: October 1, 2013

Citation
Danuta M. Bukowska, Ladislav Derzsi, Szymon Tamborski, Maciej Szkulmowski, Piotr Garstecki, and Maciej Wojtkowski, "Assessment of the flow velocity of blood cells in a microfluidic device using joint spectral and time domain optical coherence tomography," Opt. Express 21, 24025-24038 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-24025


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References

  1. Y. Sugii, S. Nishio, and K. Okamoto, “In vivo PIV measurement of red blood cell velocity field in microvessels considering mesentery motion,” Physiol. Meas.23(2), 403–416 (2002). [CrossRef] [PubMed]
  2. G. Mchedlishvili and N. Maeda, “Blood flow structure related to red cell flow: A determinant of blood fluidity in narrow microvessels,” Jpn. J. Physiol.51(1), 19–30 (2001). [CrossRef] [PubMed]
  3. S. Einav, H. J. Berman, R. L. Fuhro, P. R. DiGiovanni, J. D. Fridman, and S. Fine, “Measurement of blood flow in vivo by Laser Doppler Anemometry through a microscope,” Biorheology12(3-4), 203–205 (1975). [PubMed]
  4. H. Golster, M. Lindén, S. Bertuglia, A. Colantuoni, G. Nilsson, and F. Sjöberg, “Red blood cell velocity and volumetric flow assessment by enhanced high-resolution laser Doppler imaging in separate vessels of the hamster cheek pouch microcirculation,” Microvasc. Res.58(1), 62–73 (1999). [CrossRef] [PubMed]
  5. A. Nakano, Y. Sugii, M. Minamiyama, and H. Niimi, “Measurement of red cell velocity in microvessels using particle image velocimetry (PIV),” Clin. Hemorheol. Microcirc.29(3-4), 445–455 (2003). [PubMed]
  6. M. Baker and H. Wayland, “On-line volume flow rate and velocity profile measurement for blood in microvessels,” Microvasc. Res.7(1), 131–143 (1974). [CrossRef] [PubMed]
  7. T. Cochrane, J. C. Earnshaw, and A. H. G. Love, “Laser Doppler measurement of blood velocity in microvessels,” Med. Biol. Eng. Comput.19(5), 589–596 (1981). [CrossRef] [PubMed]
  8. C. Alonso, A. R. Pries, O. Kiesslich, D. Lerche, and P. Gaehtgens, “Transient rheological behaviour of blood in low-shear tube flow - velocity profiles and effective viscosity,” Am, J. Physiol.268, H25–H32 (1995).
  9. R. Lima, S. Wada, M. Takeda, K.-i. Tsubota, and T. Yamaguchi, “In vitro confocal micro-PIV measurements of blood flow in a square microchannel: The effect of the haematocrit on instantaneous velocity profiles,” J. Biomech.40(12), 2752–2757 (2007). [CrossRef] [PubMed]
  10. H. L. Goldsmith and V. T. Turitto, “Rheological aspects of thrombosis and hemostasis - basic principles and applications,” Thromb. Haemost.55, 415–435 (1986). [PubMed]
  11. R. Lima, “Flow behavior of labeled red blood cells in microchannels: A confocal micro-PTV assessment,” IFMBE Proc.31, 1047–1050 (2010). [CrossRef]
  12. R. D. Keane and R. J. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res.49(3), 191–215 (1992). [CrossRef]
  13. R. Lima, S. Wada, S. Tanaka, M. Takeda, T. Ishikawa, K. I. Tsubota, Y. Imai, and T. Yamaguchi, “In vitro blood flow in a rectangular PDMS microchannel: experimental observations using a confocal micro-PIV system,” Biomed. Microdevices10(2), 153–167 (2008). [CrossRef] [PubMed]
  14. Y. Sugii, R. Okuda, K. Okamoto, and H. Madarame, “Velocity measurement of both red blood cells and plasma of in vitro blood flow using high-speed micro PIV technique,” Meas. Sci. Technol.16(5), 1126–1130 (2005). [CrossRef]
  15. L. Bitsch, L. H. Olesen, C. H. Westergaard, H. Bruus, H. Klank, and J. P. Kutter, “Micro particle-image velocimetry of bead suspensions and blood flows,” Exp. Fluids39(3), 507–511 (2005). [CrossRef]
  16. M. Wojtkowski, “High-speed optical coherence tomography: basics and applications,” Appl. Opt.49(16), D30–D61 (2010). [CrossRef] [PubMed]
  17. Y. Wang and R. Wang, “Autocorrelation optical coherence tomography for mapping transverse particle-flow velocity,” Opt. Lett.35(21), 3538–3540 (2010). [CrossRef] [PubMed]
  18. V. J. Srinivasan, H. Radhakrishnan, E. H. Lo, E. T. Mandeville, J. Y. Jiang, S. Barry, and A. E. Cable, “OCT methods for capillary velocimetry,” Biomed. Opt. Express3(3), 612–629 (2012). [CrossRef] [PubMed]
  19. A. Szkulmowska, M. Szkulmowski, D. Szlag, A. Kowalczyk, and M. Wojtkowski, “Three-dimensional quantitative imaging of retinal and choroidal blood flow velocity using joint spectral and time domain optical coherence tomography,” Opt. Express17(13), 10584–10598 (2009). [CrossRef] [PubMed]
  20. V. J. Srinivasan, S. Sakadzić, I. Gorczynska, S. Ruvinskaya, W. Wu, J. G. Fujimoto, and D. A. Boas, “Quantitative cerebral blood flow with optical coherence tomography,” Opt. Express18(3), 2477–2494 (2010). [CrossRef] [PubMed]
  21. I. Grulkowski, I. Gorczynska, M. Szkulmowski, D. Szlag, A. Szkulmowska, R. A. Leitgeb, A. Kowalczyk, and M. Wojtkowski, “Scanning protocols dedicated to smart velocity ranging in Spectral OCT,” Opt. Express17(26), 23736–23754 (2009). [CrossRef] [PubMed]
  22. X. Xu, L. Yu, and Z. Chen, “Effect of erythrocyte aggregation on hematocrit measurement using spectral-domain optical coherence tomography,” IEEE Trans. Biomed. Eng.55(12), 2753–2758 (2008). [CrossRef] [PubMed]
  23. X. Q. Xu, Y. C. Ahn, and Z. P. Chen, “Feasibility of Doppler variance imaging for red blood cell aggregation characterization,” J. Biomed. Opt.14(6), 060507 (2009). [CrossRef] [PubMed]
  24. Z. P. Chen, T. E. Milner, D. Dave, and J. S. Nelson, “Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media,” Opt. Lett.22(1), 64–66 (1997). [CrossRef] [PubMed]
  25. X. J. Wang, T. E. Milner, Z. P. Chen, and J. S. Nelson, “Measurement of fluid-flow-velocity profile in turbid media by the use of optical Doppler tomography,” Appl. Opt.36(1), 144–149 (1997). [CrossRef] [PubMed]
  26. X. J. Wang, T. E. Milner, and J. S. Nelson, “Characterization of fluid flow velocity by Optical Doppler Tomography,” Opt. Lett.20(11), 1337–1339 (1995). [CrossRef] [PubMed]
  27. V. X. D. Yang, M. L. Gordon, B. Qi, J. Pekar, S. Lo, E. Seng-Yue, A. Mok, B. C. Wilson, and I. A. Vitkin, “High speed, wide velocity dynamic range Doppler optical coherence tomography (Part I): System design, signal processing, and performance,” Opt. Express11(7), 794–809 (2003). [CrossRef] [PubMed]
  28. R. A. Leitgeb, L. Schmetterer, W. Drexler, A. F. Fercher, R. J. Zawadzki, and T. Bajraszewski, “Real-time assessment of retinal blood flow with ultrafast acquisition by color Doppler Fourier domain optical coherence tomography,” Opt. Express11(23), 3116–3121 (2003). [CrossRef] [PubMed]
  29. Z. P. Chen, T. E. Milner, X. J. Wang, S. Srinivas, and J. S. Nelson, “Optical Doppler tomography: Imaging in vivo blood flow dynamics following pharmacological intervention and photodynamic therapy,” Photochem. Photobiol.67(1), 56–60 (1998). [CrossRef] [PubMed]
  30. J. Moger, S. J. Matcher, C. P. Winlove, and A. Shore, “Measuring red blood cell flow dynamics in a glass capillary using Doppler optical coherence tomography and Doppler amplitude optical coherence tomography,” J. Biomed. Opt.9(5), 982–994 (2004). [CrossRef] [PubMed]
  31. J. Moger, S. J. Matcher, C. P. Winlove, and A. Shore, “The effect of multiple scattering on velocity profiles measured using Doppler OCT,” J. Phys. D38(15), 2597–2605 (2005). [CrossRef]
  32. S. G. Proskurin, I. A. Sokolova, and R. K. Wang, “Imaging of non-parabolic velocity profiles in converging flow with optical coherence tomography,” Phys. Med. Biol.48(17), 2907–2918 (2003). [CrossRef] [PubMed]
  33. L. Wang, W. Xu, M. Bachman, G. P. Li, and Z. P. Chen, “Imaging and quantifying of microflow by phase-resolved optical Doppler tomography,” Opt. Commun.232(1-6), 25–29 (2004). [CrossRef]
  34. L. An and R. K. Wang, “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express16(15), 11438–11452 (2008). [CrossRef] [PubMed]
  35. R. K. Wang and L. An, “Doppler optical micro-angiography for volumetric imaging of vascular perfusion in vivo,” Opt. Express17(11), 8926–8940 (2009). [CrossRef] [PubMed]
  36. M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint spectral and time domain optical coherence tomography,” Opt. Express16(9), 6008–6025 (2008). [CrossRef] [PubMed]
  37. M. Szkulmowski, I. Grulkowski, D. Szlag, A. Szkulmowska, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation by complex ambiguity free joint spectral and time domain optical coherence tomography,” Opt. Express17(16), 14281–14297 (2009). [CrossRef] [PubMed]
  38. J. Lauri, M. Wang, M. Kinnunen, and R. Myllyla, “Measurement of microfluidic flow velocity profile with two Doppler optical coherence tomography systems,” Proc. SPIE6863, 68630F (2008). [CrossRef]
  39. S. G. Li, Z. G. Xu, S. F. Yoon, and Z. P. Fang, “Feasibility study on bonding quality inspection of microfluidic devices by optical coherence tomography,” J. Biomed. Opt.16(6), 066011 (2011). [CrossRef] [PubMed]
  40. C. W. Xi, D. L. Marks, D. S. Parikh, L. Raskin, and S. A. Boppart, “Structural and functional imaging of 3D microfluidic mixers using optical coherence tomography,” Proc. Natl. Acad. Sci. U.S.A.101(20), 7516–7521 (2004). [CrossRef] [PubMed]
  41. Y. C. Ahn, W. Y. Jung, J. Zhang, and Z. P. Chen, “Investigation of laminar dispersion with optical coherence tomography and optical Doppler tomography,” Opt. Express13(20), 8164–8171 (2005). [CrossRef] [PubMed]
  42. H. Bruus, “Theoretical microfluidics,”(Oxford University Press, 2008).
  43. J. H. Yun, M.-S. Chun, and H. W. Jung, “The geometry effect on steady electrokinetic flows in curved rectangular microchannels,” Phys. Fluids 22(5), 052004–1 −10 (2010). [CrossRef]
  44. Y. C. Ahn, W. Jung, and Z. P. Chen, “Quantification of a three-dimensional velocity vector using spectral-domain Doppler optical coherence tomography,” Opt. Lett.32(11), 1587–1589 (2007). [CrossRef] [PubMed]
  45. R. M. Werkmeister, N. Dragostinoff, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. A. Leitgeb, and L. Schmetterer, “Bidirectional Doppler Fourier-domain optical coherence tomography for measurement of absolute flow velocities in human retinal vessels,” Opt. Lett.33(24), 2967–2969 (2008). [CrossRef] [PubMed]
  46. N. Maeda, “Erythrocyte rheology in microcirculation,” Jpn. J. Physiol.46(1), 1–14 (1996). [CrossRef] [PubMed]
  47. F. S. Ligler, “Perspective on optical biosensors and integrated sensor systems,” Anal. Chem.81(2), 519–526 (2009). [CrossRef] [PubMed]
  48. A. Alrifaiy and K. Ramser, “How to integrate a micropipette into a closed microfluidic system: absorption spectra of an optically trapped erythrocyte,” Biomed. Opt. Express2(8), 2299–2306 (2011). [CrossRef] [PubMed]
  49. D. C. Duffy, J. C. McDonald, O. J. A. Schueller, and G. M. Whitesides, “Rapid prototyping of microfluidic systems in poly(dimethylsiloxane),” Anal. Chem.70(23), 4974–4984 (1998). [CrossRef] [PubMed]

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