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Anal. Chem. 2007, 79, 2576-2582

Deconvolution Microscopy for Flow Visualization in Microchannels Zheng Xia,† Lou Cattafesta,† and Z. Hugh Fan*,†,‡

Department of Mechanical and Aerospace Engineering and Department of Biomedical Engineering, University of Florida, P.O. Box 116250, Gainesville, Florida 32611

Quantitative visualization of microflows is often needed to evaluate the efficiency of fluid mixing, study flow properties, investigate unusual flow behavior, and verify computational fluid dynamic simulations. In this work, we explore the technique of coupling a conventional optical microscope with a computational deconvolution algorithm to produce images of three-dimensional flows in plastic microfluidic channels. The approach, called deconvolution microscopy, is achieved by (1) optically sectioning the flow in the microchannel by collecting a series of fluorescence images at different focal planes along the optical axis and (2) removing the out-of-focus fluorescence signal by a deconvolution method to reconstruct the corrected three-dimensional concentration image. We compare three different classes of deconvolution algorithms for a uniform concentration test case and then demonstrate how deconvolution microscopy is useful for flow visualization and analysis of mixing in microfluidic channels. In particular, we employ the method to confirm the presence of twisting flows in a microchannel containing microfabricated ridges. Microfluidic systems are now widely used in chemical analysis and biological applications, as is evident from the rapid growth in the literature1 and their commercial utilization.2,3 Chemical reactions and biological assays in microfluidic devices often require mixing fluids such as in the homogenization of solutions of reagents used in an immunological assay. However, it is difficult to achieve convective mixing in laminar flows, which can be explained by the low Reynolds numbers resulting from the small microchannel dimensions. This limitation has long been recognized, and some efforts have been reported to address it. For instance, Whitesides’ group pioneered herringbone structures to achieve chaotic mixing4 while Johnson et al. used slanted wells * To whom correspondence should be addressed. E-mail: [email protected]. Fax: 352-392-7303. † Department of Mechanical and Aerospace Engineering. ‡ Department of Biomedical Engineering. (1) Dittrich, P. S.; Tachikawa, K.; Manz, A. Anal. Chem. 2006, 78, 38873908. (2) Raisi, F.; Blizard, B. A.; Raissi Shabari, A.; Ching, J.; Kintz, G. J.; Mitchell, J.; Lemoff, A.; Taylor, M. T.; Weir, F.; Western, L.; Wong, W.; Joshi, R.; Howland, P.; Chauhan, A.; Nguyen, P.; Petersen, K. E. J. Sep. Sci. 2004, 27, 275-283. (3) Tran, L.; Farinas, J.; Ruslim-Litrus, L.; Conley, P. B.; Muir, C.; Munnelly, K.; Sedlock, D. M.; Cherbavaz, D. B. Anal. Biochem. 2005, 341, 361-368.

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on the channel bottom to accomplish similar results.5 Enhanced mixing may also be obtained by pulsing the incoming flows,6,7 creating different surface properties,8,9 and other approaches.10-12 To evaluate the efficiency of fluid mixing, flow visualization is often used. Flow visualization is also important for studying microflow properties, investigating interesting flow behavior, and verifying computational fluid dynamics simulations.13 The primary methods used for microscale flow visualization are particle-based flow velocimetry such as particle image velocimetry (PIV)14 and optical imaging techniques enabled by fluorofores or dyes. PIV measures the velocity components in a two-dimensional plane due to the small depth of field of a high numerical aperture lens;15 thus, a more complicated stereo setup is required for visualization of a complex, three-dimensional flow. Optical imaging is a flow visualization method to study fluid motions inferred from color or fluorescence intensity.13 It has been used to study mixing in microflows,5-7,9-11,16-20 diffusion in a curved channel,21,22 and the shape of injected samples at an (4) Stroock, A. D.; Dertinger, S. K. W.; Ajdari, A.; Mezic, I.; Stone, H. A.; Whitesides, G. M. Science 2002, 295, 647-651. (5) Johnson, T. J.; Ross, D.; Locascio, L. E. Anal. Chem. 2002, 74, 45-51. (6) Glasgow, I.; Lieber, S.; Aubry, N. Anal. Chem. 2004, 76, 4825-4832. (7) Glasgow, I.; Aubry, N. Lab Chip 2003, 3, 114-120. (8) Kuksenok, O.; Yeomans, J. M.; Balazs, A. C. Phys. Rev. E 2002, 65, 031502031501. (9) Biddiss, E.; Erickson, D.; Li, D. Anal. Chem. 2004, 76, 3208-3213. (10) Chen, C. H.; Lin, H.; Lele, S. K.; Santiago, J. G. J. Fluid Mech. 2005, 524, 263-303. (11) Yaralioglu, G. G.; Wygant, I. O.; Marentis, T. C.; Khuri-Yakub, B. T. Anal. Chem. 2004, 76, 3694-3698. (12) Grumann, M.; Geipel, A.; Riegger, L.; Zengerle, R.; Ducree, J. Lab Chip 2005, 5, 560-565. (13) Sinton, D. Microfluidics Nanofluidics 2004, 1, 2-21. (14) Santiago, J. G.; Wereley, S. T.; Meinhart, C. D.; Beebe, D. J.; Adrian, R. J. Exp. Fluids 1998, 25, 316-319. (15) Devasenathipathy, S.; Santiago, J. G.; Wereley, S. T.; Meinhart, C. D.; Takehara, K. Exp. Fluids 2003, 34, 504-514. (16) Johnson, T. J.; Locascio, L. E. Lab Chip 2002, 2, 135-140. (17) He, B.; Burke, B. J.; Zhang, X.; Zhang, R.; Regnier, F. E. Anal. Chem. 2001, 73, 1942-1947. (18) Yoon, S. K.; Mitchell, M.; Choban, E. R.; Kenis, P. J. Lab Chip 2005, 5, 1259-1263. (19) Knight, J. B.; Vishwanath, A.; Brody, J. P.; Austin, R. H. Phys. Rev. Lett. 1998, 80, 3863-3866. (20) Ismagilov, R. F.; Stroock, A. D.; Kenis, P. J. A.; Whitesides, G.; Stone, H. A. Appl. Phys. Lett. 2000, 76, 2376-2378. (21) Molho, J. I.; Herr, A. E.; Mosier, B. P.; Santiago, J. G.; Kenny, T. W.; Brennen, R. A.; Gordon, G. B.; Mohammadi, B. Anal. Chem. 2001, 73, 1350-1360. (22) Wang, Y.; Lin, Q.; Mukherjee, T. Lab Chip 2004, 4, 453-463. 10.1021/ac062265n CCC: $37.00

© 2007 American Chemical Society Published on Web 02/06/2007

intersection.23,24 The majority of these optical imaging techniques acquire images by viewing from the top of a microchannel, visualizing a two-dimensional flow. Interpretation is thus straightforward when the vertical gradient components (from the top to the bottom of the channel) of flow variables are negligible. However, such top-view images can be easily misinterpreted if the flow is three-dimensional.25 For instance, two vertical layers of an unmixed stratified flow could be mistaken as a mixed flow because an image acquired from the top may show uniform fluorescent signals across the channel. Examples of a threedimensional flow include chaotic mixing due to transverse flows4,5 and advection in a three-dimensional serpentine channel with vertical through-holes.25-29 Characterization of these flows can be studied by confocal fluorescence microscopy.4,19,20 However, such a setup is expensive and complicated, preventing it from becoming a widely used method. In this work, we explore three-dimensional deconvolution microscopy, a simple and inexpensive technique that combines a conventional optical microscope with a deconvolution method. This technique collects a series of images at different focal planes and then uses a computational deconvolution process to remove the out-of-focus fluorescence signal and correct the images. Compared to confocal microscopy that physically removes the outof-focus light information via a pinhole, deconvolution microscopy employs a mathematical method to correct for optical blurring. Deconvolution microscopy has been used by medical and biological scientists for visualizing the cellular structures of tissue specimens; the details of the approach have recently been reviewed.30,31 Moreover, there is software that is commercially available for the application. Compared to confocal fluorescence microscopy, one advantage of deconvolution microscopy is its use of a widely available conventional optical microscope. In addition, it does not have the drawback of the confocal microscope that only allows a limited amount of light to pass through the pinhole (that is required due to confocal imaging). To our knowledge, this work is the first to apply deconvolution microscopy for visualizing flows in a microfabricated device. We briefly discuss the theoretical background before the description of the experimental results. THEORETICAL BACKGROUND Deconvolution microscopy is composed of two steps: optical sectioning and image reconstruction. Optical sectioning refers to the process of acquiring multiple images in a channel volume by displacing the focal plane of an objective lens along its optical axis, as illustrated in Figure 1. The objective lens of the microscope is traversed in discrete steps, and a stack of two-dimensional images of different sections are collected. Since the acquired images are blurred due to contributions outside the focal plane during the image formation, a digital postprocessscalled (23) Ermakov, S. V.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1998, 70, 4494-4504. (24) Shultz-Lockyear, L. L.; Colyer, C. L.; Fan, Z. H.; Roy, K. I.; Harrison, D. J. Electrophoresis 1999, 20, 529-538. (25) Munson, M. S.; Yager, P. Anal. Chim. Acta 2004, 507, 63-71. (26) Kim, D. S.; Lee, S. H.; Kwon, T. H.; Ahn, C. H. Lab Chip 2005, 5, 739747. (27) Liu, R. H.; Stremler, M. A.; Sharp, K. V.; Olsen, M. G.; Santiago, J. G.; Adrian, R. J.; Aref, H.; Beebe, D. J. J. Microelectromech. Syst. 2000, 9, 190-197. (28) Neils, C.; Tyree, Z.; Finlayson, B.; Folch, A. Lab Chip 2004, 4, 342-350.

Figure 1. Diagram of optical sectioning process for visualization of a microfluidic flow. (a) A device with a microchannel is placed on the microscope stage. The objective lens of an inverted microscope is moved in the axial direction to obtain the image corresponding to a focal plane at a desired depth of microchannel. The image is captured by a CCD camera. (b) A stack of images are acquired by adjusting the objective lens in a discrete step, ∆z, through the entire channel depth of the microchannel.

deconvolutionsis carried out to remove the blurring and to reconstruct a corrected three-dimensional image. Optical sectioning and the deconvolution algorithms used in this work are briefly discussed as follows; additional details can be found in the literature.31,32 Optical Sectioning. In essence, optical sectioning samples uniformly spaced, discrete planes from a continuous light signal in three-dimensional space. This sampling process must satisfy the Nyquist sampling theorem,33,34 which requires the sampling frequency to be greater than twice the input signal bandwidth in order to ensure perfect reconstruction of the original signal from the sampled version. In the spatial domain, this requires a sampling interval to be less than half of the characteristic dimension of the source signal. A CCD camera is used to sample the discrete planes along the optical axis. The sampling interval in the axial direction (∆z) is defined by the spacing between two adjacent image acquisitions. The axial resolution of a microscope is defined by rz ) (1.4λn)/ (NA2), where λ is the light wavelength, n is the refractive index of the media, and NA is the numerical aperture of the objective lens.31 To meet the requirement of the Nyquist sampling theorem, then ∆z e rz/2, or

∆z e 0.7λn/NA2

(1)

Convolution. The images acquired via optical sectioning are degraded for two reasons: optical blurring and image degradation due to electronic noise. Blurring is due to the optical aberration (29) Therriault, D.; White, S. R.; Lewis, J. A. Nat. Mater. 2003, 2, 265-271. (30) McNally, J. G.; Karpova, T.; Cooper, J.; Conchello, J. A. Methods: Companion Methods Enzymol 1999, 19, 373-385. (31) Sibarita, J. B. Microsc. Tech. 2005, 95, 201-243. (32) Gibson, S. F.; Lanni, F. J. Opt. Soc. Am., A 1991, 8, 1601-1613. (33) Oppenheim, A. V.; Schafer, R. W. Digital signal processing; Prentice Hall: Englewood Cliffs, NJ, 1975. (34) Figliola, R. S.; Beasley, D. E. Theory and Design for Mechanical Measurements, 3rd ed.; John Wiley & Sons: New York, 2000.

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Table 1. Comparison of Deconvolution Algorithms methods inverse filter constrained iteration Gold MLE blind deconvolution

description

pros

cons

transfers images from spatial domain to Fourier domain reconstructs images in a successive process under a variety of constraints reconstructs images with an estimated PSF in an iterative process under constraints

simple and fast, requires less computation

sensitive to noise, induces artificial defects, requires PSF requires more computation and PSF

less susceptible to noise less susceptible to noise, does not require PSF

is the most computationally intensive method

ref 36 37-40 41

of light during its passage through the microscope optical lenses. Among optical aberration,35 chromatic aberration is insignificant because band-pass filters are used in the optical system. Optic blurring occurs because each image taken at one focal plane is contaminated with the out-of-focus information from adjacent planes.31 However, this distortion is reproducible and inherent to the optical system and thus can be mathematically corrected. The imaging formation can be mathematically expressed as a convolution of the object (i.e., the fluorescein solution in the channel in this case) with a spatial function called the point spread function (PSF), which is the three-dimensional image recorded by the microscope when the input is a point source.31,32 PSF is the most fundamental characteristic of an imaging system and can be viewed as the impulse response function of a microscope in the spatial domain. The resultant three-dimensional image of a point source is thus defined by the PSF; hence, the intensity at any point in the image is a weighted sum of all the point sources in the channel. A mathematical description of this image formation process is given by a spatial convolution, i.e., a volume integration over space, of the spatial function of fluorescein concentration in the channel and the PSF of the microscope (see the Supporting Information).31 As a result, the images taken from the microscope deviate from the real fluorescence intensity. A deconvolution process must be undertaken to reconstruct the images by deblurring the image. As mentioned above, the other source of the image degradation is photonic and electronic noise during image acquisition. The electronic noise of the CCD camera can be rectified by a bias image, which is taken by the camera when light to the camera is completely blocked. Nonuniformity of the light source can be corrected by a flat-field image, which is taken when a fluorescein solution with uniform thickness is illuminated with the UV lamp of the microscope. The flat-field image also compensates for any variation in the sensitivity of different pixels in the CCD camera. These images will also be used in the deconvolution process to reduce both photonic and electronic noise. Deconvolution. A variety of deconvolution algorithms have been developed to remove the blurring and noise in images acquired via optical sectioning. These algorithms can be classified into three groups: inverse filter,36 constrained iteration,37-40 and

blind deconvolution.41 We investigated two implementations of the constrained iteration, namely, the Gold algorithm38 and the maximum likelihood estimation (MLE) by Richardson and by Lucy.39,40 Mathematical descriptions of each algorithm are summarized in the Supporting Information, and the advantages and disadvantages of each method, as well as essential references, are provided in the Table 1. We used and compared these methods for the microflow visualization test case, and then chose the best one for the mixing study as explained in Results and Discussion.

(35) Ingle, J. D.; Crouch, S. R. Spectrochemical analysis; Prentice Hall: Englewood Cliffs, NJ, 1988. (36) Chatwin, C. R.; Wang, R. K. Frequency Domain Filtering Strategies for Hybrid Optical Information Processing; John Wiley & Sons: New York, 1996. (37) Jansson, P. A.; Hunt, R. H.; Plyler, E. K. J. Opt. Soc. Am. 1970, 60, 596. (38) Gold, R. An Iterative Unfolding Method for Matrices; Argonne National Laboratory: Argonne, Ill, 1964. (39) Richardson, W. H. J. Opt. Soc. Am. 1972, 62, 55-59.

(40) Lucy, L. B. Astron. J. 1974, 79, 745-754. (41) Holmes, T. J. J. Opt. Soc. Am., A 1992, 9, 1052-1061. (42) Fredrickson, C. K.; Xia, Z.; Das, C.; Ferguson, R.; Tavares, F. T.; Fan, Z. H. J. Microelectromechan. Syst. 2006, 15, 1060-1068. (43) Fox, R. W.; McDonald, A. T. Introduction to fluid mechanics, 5th ed.; J. Wiley: New York, 1998. (44) Harrison, D. J.; Manz, A.; Fan, Z. H.; Ludi, H.; Widmer, H. M. Anal. Chem. 1992, 64, 1926-1932.

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EXPERIMENTAL METHODOLOGY Device Fabrication. Plastic microfluidic devices were fabricated using the procedure described previously.42 Briefly, a photomask was designed using AutoCAD. The pattern on the photomask was then reproduced in a glass plate via photolithography. Electroplating on the glass plate generated a nickel mold, which was employed to produce plastic parts from cyclic olefin copolymer resins (Ticona Topas 8007, Florence, KY) using a hydraulic press (Carver, Wabash, IN). Each plastic part was trimmed into a 1 in. × 3 in. substrate using a CNC milling machine, which was also used to drilled holes (2-mm diameter) at the ends of channels. The channels in the plastic substrate were sealed with 0.1-mm-thick film (Topas 8007) using a thermal laminator (Catena 35, GBC, Northbrook, IL), while the holes became wells. Figure 2 shows the plastic chip used in this work. The thickness of the device is 1.5 mm. Channels are 40 µm deep and 110 µm wide, except where specified otherwise. The dimensions of channels were measured using a Dektak II surface profiler (Sloan/Veeco, Woodbury, NY) before lamination. The hydraulic diameter43 of channels is 56 µm. Experimental Setup. A plastic device was connected to a syringe pump (KDS 100, KD Scientific, Holliston, MA) via the Nanoport kit (Upchurch, Oak Harbor, WA). Fluorescein solution (1 µM) was pumped into the device at a preset flow rate (5.2 µL/ min, or 2.3 cm/s based on the cross-sectional area). Using the hydraulic diameter of the channel and 3.3 × 10-6 cm2/s as the diffusion coefficient of fluorescein,44 the Peclet number4 of this flow is 3.9 × 103 (the Reynolds number is 1.3). The device was placed on the sample stage of an inverted microscope (IX51, Olympus America Inc., Melville, NY), which is equipped with a

Figure 2. (a) Picture of a plastic device with 6 channels; (b) layout of one channel indicated by the arrow. Three wells in the pattern (b) are numbered for references in the text. The channels are 110 µm wide and 40 µm deep except where specified otherwise. The lengths of the channels connecting wells 1, 2, and 3 to the intersection M are 4.6, 10.2, and 44.6 mm, respectively.

75-W xenon lamp (U-LH75X). A 20× objective lens (Olympus) with a numerical aperture of 0.5 was used. The light passed through an excitation filter (HQ480/40, Chroma Technology, Rockingham, VT), a beam splitter, and an emission filter (HQ535/ 50, Chroma Technology) and then was collected by a scientificgrade, cooled CCD camera (2184 × 1472 pixels, Apogee, Auburn, CA). The CCD pixel size is 6.8 µm × 6.8 µm. Optical Sectioning and Image Reconstruction. Prior to the acquisition of sample images, both bias and flat-field images were collected for optical calibration of the microscopy. The bias image was taken with the camera shutter closed; it was used for rectifying the noise level of the CCD camera. The flat-field image was taken when a fluorescein solution was contained between two flat glass slides and illuminated with the UV light; it was then used for calibrating the uneven UV illumination and the variation in the sensitivity of different regions of the camera. To collect images via optical sectioning, the microscope objective lens was moved in steps of 1 µm along the optical axis to acquire consecutive images. A total distance of 80 µm was displaced in the optical axial direction, ensuring a full sampling of the 40-µm-deep channel and enough information from the outof-focus neighboring region. The stack of 80 images, together with the bias and the flat-field images, were then imported into AutoDeblur and AutoVisualize (AutoQuant Imaging Inc, Troy, NY) for deconvolution analysis. A variety of deconvolution algorithms were studied, including the inverse filter, Gold, MLE, and blind MLE. A Dell computer with Intel Pentium 4 processor (OptiPlex GX270) was used for computation. RESULTS AND DISCUSSION Ridge Formation. As mentioned in the Experimental Section, plastic devices were fabricated from a metal mold, which was created from a glass plate. The channels in the glass plate were fabricated using photolithographic patterning and chemical etching.42 It is well-known that chemical etching in a glass plate results in isotropic etching. As illustrated in Figure 3a, isotropic etching removes materials laterally under the mask (called undercutting)

while it proceeds downward as indicated by the arrows. Therefore, the cross section of the channel is in the shape of a “D”, after the mask is removed and the bottom plate is sealed with another plate. A scanning electron micrograph (SEM) of such a channel is shown in Figure 3c. However, a ridge can be obtained when two features are designed close enough with an appropriate etching depth, as shown in Figure 3b. The ridges of different shapes and angles can be obtained in the channel by a judicious design, as illustrated in Figure 3d. The ridges in a channel are designed to mimic the herringbone structures4 or slanted wells5 described in the literature. The formation of herringbone structures requires anisotropic etching, which is possible in a silicon wafer, and then are transferred into a poly(dimethylsiloxane) device.4 However, this process is difficult to achieve in a glass plate. In addition, the creation of two channel depths (one for the channel and one for herringbone structures) requires a multiple photolithographic process with two photomasks and a more stringent optical alignment. Slanted wells were produced by using an additional stepslaser ablationsafter microfabrication of microchannels in a plastic device.5 The ridges are easier to produce than the herringbone structures or slanted wells due to the one-step operation. The ridges in Figure 3d were designed at a location immediately after the intersection (M) of two channels connecting to wells 1 and 2 in Figure 2. The height of ridge is 12 µm, the center-to-center distance between ridges is 76 µm, and the angle of the ridges with respect to the channel is 45°. Optical Sectioning. As discussed in Theoretical Background, the sampling interval in the optical axis must meet the Nyquist sampling theorem defined by eq 1. The sampling distance in the axial direction (∆z) was 1 µm, which was the adjustment step of the microscope objective lens. Using 520 nm for the emission wavelength of fluorescein, 0.5 for NA of the lens used, and 1 for the refractive index of air, the axial resolution of the microscope (rz) was calculated to be 2.9 µm. Therefore, our experiment condition met the requirement of Nyquist sampling theorem, ∆z e rz/2. Analytical Chemistry, Vol. 79, No. 6, March 15, 2007

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Figure 3. (a) Illustration of isotropic etching; (b) ridges obtained from judicious designs and isotropic etching; (c) picture of a D-shaped channel; (d) SEM picture of a ridged channel in a microfluidic device made from a cyclic olefin copolymer. The scaling bars in (c) and (d) are 100 and 200 µm, respectively.

Figure 4. Three-dimensional view of fluorescein in a channel by stacking raw images acquired by optical sectioning. The coordinate system is defined as follows: x in the flow direction, y in the horizontal direction, and z in the vertical direction. (a) Fluorescein flow in a smooth channel; (b) fluorescein flow in the ridged channel. The scaling bars in (a) and (b) are 80 and 150 µm, respectively.

We first pumped fluorescein solution into the microchannel from both inlets (wells 1 and 2 in Figure 2). As a result, uniform fluorescence signals should be observed in the mixing channel connected to well 3. This served as a test case to assess the accuracy of each algorithm. Using the optical sectioning described in the Experimental Section, we acquired images in the region with smooth surfaces and in the region with ridges. Figure 4 shows the three-dimensional view of the fluorescein flow in the channel by stacking all images together in sequence. Figure 4a is from the region with smooth surfaces, and Figure 4b is from the region with ridges. Although both images roughly indicate the image of the fluorescein flow (i.e., the shape of the channel), blurred edges and a hazy background are obvious. As explained in Theoretical Background, these optical distortions result from the aberration of the fluorescent emission and from photonic and electronic noise. Therefore, deconvolution is performed to rectify these effects, obtaining the correct fluorescent intensity values at the points in the channel, and reconstructing the actual image of the corresponding fluorescein flow. Deconvolution. As discussed in the Experimental Section, we first obtain the bias image and the flat-field image for optical calibration of the microscopy. These calibration images, as well 2580 Analytical Chemistry, Vol. 79, No. 6, March 15, 2007

as the image stack in Figure 4a, are entered into the deconvolution software, AutoDeblur. The raw images are offset by the bias image and then normalized by the flat-field images. A variety of deconvolution algorithms are then investigated for reconstructing the images, including the inverse filter, Gold, MLE, and blind MLE algorithms mentioned above. A theoretical PSF (see the Supporting Information) was used except for the blind MLE algorithm, which does not require an estimate of the PSF. Figure 5 shows the images after deconvolution using different algorithms. Each image is constructed as a yz plane, the crosssectional view of the smooth channel in Figure 4a. Due to isotropic etching, a D-shaped channel should be observed in the yz plane as indicated by the dashed line in each image. As explained in Table 1 and in the literature,31 the inverse filter deconvolution caused many artifacts as expected (Figure 5b). The strips in Figure 5c indicate that the Gold algorithm exhibited slow convergence and suffered from constructive artifacts.31 The results in Figure 5d-g suggest that the MLE and blind MLE delivered better results, even though they required longer computational time (∼30 min compared to a few seconds on the same computer for the non-MLE algorithms). When the number of iterations is increased from 30 to 60, the blind deconvolution algorithm

Figure 5. Cross-sectional image of a fluorescein flow in a D-shaped channel. The images are reconstructed to represent the yz plane of Figure 4a. The dashed lines indicate the expected shape. From left to right, pictures are the raw image (a) and corrected images using inverse filter (b), Gold algorithm with 30 iterations (c), MLE algorithm with 30 iterations (d), blind MLE with 30 iterations (e), MLE with 60 iterations (f), and blind MLE with 60 iterations (g).

Figure 6. (a) Layout of the channel in Figure 2 and the expanded view of ridges in the channel. Two channels connecting to wells 1 and 2 merge at the intersection, M. (b, c) Cross-sectional views (yz planes) of the fluorescein flow in ridged channel at different locations. Two streams of fluorescent solution and water were pumped into the channel simultaneously from wells 1 and 2, with equal flow velocity (2.3 cm/s). The location for each cross-sectional view is indicated at the bottom. Views from the raw image stack are presented in (b), and views from the deconvoluted image stack are in (c).

generates even better results than the MLE. The corrected image after 60 iterations of the blind MLE is the closest to the channel geometry. Therefore, the blind MLE deconvolution algorithm was chosen to study mixing as follows. Mixing. To study mixing, fluorescein solution is now introduced into the microchannel at well 1 of the device in Figure 6a, and pressurized water is introduced at well 2. The two paths merge at the intersection M, travel through the ridges in the channel, and finally exit at well 3. The top view (xy plane) of the first 36 ridges is in Figure 6a. Figure 6b shows the fluorescent images acquired at five locations downstream of the point M. The locations correspond

to the centers of the 1st, 12th, 24th, 36th, and 48th ridge in the channel as indicated in the figure. For each location, the raw image is the synthesized photograph by simply stacking together all pictures taken during optical sectioning. The reconstructed image after 60 iterations of the blind MLE for each location is shown in Figure 6c. The raw images from the 1st to the 48th ridge do not reveal any trend concerning the fluorescein distribution along the channel, whereas the reconstructed counterparts indicate the twisting flow as reported previously.4,5 The two flow streams, fluorescein and water, twist about the x-axis of the channel. The images indicate that the two streams started to mix at 12th ridges, and a portion of fluorescein transposed to the other side as Analytical Chemistry, Vol. 79, No. 6, March 15, 2007

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indicated by the fluorescence signal at 24th ridge. When two streams travel further along the ridged channel, mixing becomes more thorough, as indicated by the more uniform fluorescence intensity in the downstream portion of the channel (48th ridge). In addition, the reconstructed images possess much less haze and are in a better agreement with the channel geometry. The results clearly show that the reconstructed image is a better reflection of the mixture in the channel. Using the reconstructed image in Figure 6c, we are able to calculate the mixing efficiency. Following Johnson et al.,5 percentage of mixing is quantified using the formula mix% ) N 0 2 1/2 2 1/2 1 - [(1/N)∑N 1 (Ii - I∞) ] /[(1/N)∑1 (Ii - I∞) ] , where Ii is the intensity value at the ith pixel, I∞ is the intensity value when solution is perfectly mixed (at infinity), and I0i is the intensity value at the ith pixel at the beginning. The mixing percentages are 26, 38, 49, and 59% at 12th, 24th, 36th, and 48th ridge, respectively. These values are comparable to those reported in the literature4 and obtained using confocal microscopy for a flow with a similar Peclet number, which takes into account the difference in the flow rate and geometry.

comparison among a number of deconvolution algorithms, we found that the blind MLE deconvolution gave the best results for this microchannel application. Deconvolution microscopy was then used to study mixing in a ridged channel of a microfabricated device. The creation of ridges in the microchannel was accomplished by judicious device design and isotopic etching. We exploited deconvolution microscopy to confirm the presence of a twisting flow in a ridged channel. Although the ridges in the channel of this work are different from the microfabricated rectangular microwells in the channel reported in the literature,4,5 the resultant flow patterns are similar. Mixing is evident from the experimental results using streams of fluorescein and water.

SUMMARY We explored deconvolution microscopy for quantitative imaging of a three-dimensional flow in a microfluidic device. Compared to confocal fluorescence microscopy that is often used for visualizing three-dimensional flows, the deconvolution microscopic imaging employs a widely available conventional optical microscope. Optical sectioning is straightforward for acquiring a series of images at different focal planes, and the deconvolution can simply be carried out by commercially available software. A variety of deconvolution algorithms may be used to reconstruct the corrected three-dimensional image, depending on the optical setup, time allowed, and computational power available. After

NOTE ADDED AFTER ASAP PUBLICATION This paper was released ASAP on February 6, 2007, with production errors describing the mixing percentages of Figure 6c. The correct version was posted on February 16, 2007.

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ACKNOWLEDGMENT This work is supported in part by the startup fund from the University of Florida, Army Research Office (48461-LS), National Science Foundation (CHE-0515711), and Glenn Research Center of National Aeronautics and Space Administration (NASA) (NAG 3-2930). Useful discussions with Drs. Mark Sheplak and Renwei Mei of UF is greatly appreciated.

SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org Received for review November 29, 2006. Accepted December 7, 2006. AC062265N