Standardized Micro-Scale Mixing Evaluation

Transcription

1 Standardized Micro-Scale Mixing Evaluation Abstract Guillermo González-Fernández, Benjamin Yang Department of Electrical and Computer Engineering, University of Wisconsin-Madison 1415 Engineering Drive, Madison, WI The field of microfluidics has become increasingly important with the development of micro-fuel cells, DNA arrays, and various advancements towards the labon-a-chip concept. While researchers have proposed many methods of mixing, there has been no standardized comparison on the mixing efficiency of the proposed methods in literature. In this paper, the students implemented an image-based technique for evaluating the standardized mixing of results from a previous experiment. The results were then used as experimental validations of corresponding simulations. An additional program was developed to allow future researchers to evaluate mixing in any userdefined area of an image. 1. Introduction Mixing, while simple to perform on a macro-scale, can be very difficult to perform on a micro-scale. The difficulty arises from the low Reynolds number, which limits the fluid to the laminar regime. The lack of turbulence in this regime makes diffusion the only mixing mechanism. Mixing methods that enhance the diffusion process can be categorized into active and passive devices. Active devices utilize moving components to establish mixing, and often require outside power and complex fabrication processes. Passive channels encourage mixing only based on the geometry of the channel, and are easier to realize. By folding the liquid through in three-dimensions, the mixing can be greatly enhanced [1][2]. An example of a passive mixing device is the 3-dimensional serpentine channel shown in Figure 1 [3]: The goal of this project is to evaluate the mixing in images of passive devices through a previous investigation effort. The results are then used to validate the available simulation results. The experiment is ground breaking because it is the first to compare the different shapes with uniform parameters. Imageprocessing methods were used to enhance the image, detect the area of the channel, and, finally, evaluate the mixing based on a standard comparable to the simulation. Figure 1: An example of a serpentine mixing channel. Turning the fluid in all three dimensions enhances mixing. While it is more effective than its 2-D counterparts, this 3-D structure is much more difficult to fabricate.

2 2. Approach There are currently a total of five images based on two measuring methods. The first image is a picture of a channel with a fluorescent dye, Cy-5, flowing through both inlets. Such images are available for a Y-shaped channel and a square-wave channel, shown in Figure 2 (a) and : (a) Figure 2 (a) : Y-shaped channel with Cy-5 flowing through both inlets. Figure 2 : Square wave channel with Cy-5 flowing through both inlets. This image is compared with a second picture with Cy-5 flowing into one inlet, and water flowing into the other. Filters that pass only the florescent signal force the camera to only see the Cy-5, and the water is therefore invisible in the image. Such images for the Y-shaped and the square wave channel are given in Figure 3 (a) and : (a) Figure 3 (a) : Y-shaped channel with Cy-5 flowing through one inlet. Figure 3 : Square wave channel with Cy-5 flowing through one inlet. By comparing the measured intensity of the two images, one can evaluate the degree of mixing after a fixed distance. This method is similar to the optical methods performed in [4]. One of the main challenges is the lower signal-to-noise ratio in some of the images. This result is due to the limitations of the Cy-5 available to the experimenters during the acquisition of these images. There are three main tasks that must be performed to evaluate the mixing. The first is image enhancement to boost the signal-to-noise ratio. The criteria for success of this enhancement are to improve upon the result of the edge-detection. The second task

3 is the edge detection itself, which will determine the area inside the channel. The final task is to evaluate how well mixed the channels are by comparing the respective images in Figure (2) and Figure (3). The method of evaluation should correlate to that which was used in the simulation. The other set of images were taken after the students injected water and food coloring into both inlets at the same flow rate, and took a gray scale image under a microscope. These results will not correlate as well to the original simulations because food coloring is oilbased, and thus has very different properties than what was simulated. However, food coloring is visible enough to be viewed under a normal optical microscope, which allowed a much finer resolution to determine mixing. There is one image each of the standard Y-channel, square-wave, and a compartment-shaped channel using this method, shown to the right in Figure 4 (a),, and (c): Instead of creating a similar program to perform the same task as the previous set of images, a different program was created. The new software would determine the mixing in any user-defined area, allowing researchers to evaluate the extent of mixing in any given location of an image. Figure 4 (a): Figure 4 : Figure 4 (c): (a) (c) Y-shaped channel with food coloring Square wave channel with food coloring Compartment channel with food coloring 3. Work Performed The development of the mixing evaluation program can be separated into four categories, which are individually addressed in the following. 3.1 Image Enhancement From observing the images in Figure 2 and Figure 3, one can notice that most of the disturbance is in the form of salt noise. There are several different filtering methods that have been shown to be effective against salt noise in [5]. The first few attempts however, were an exploration to see if any of the built-in tools in MATLAB could get the job done. A myriad of filters and edge-detection schemes are available in MATLAB. Low pass filters include the Gaussian, Sobel, Prewitt, Laplacian, log, averaging and unsharpening filters. MATLAB also offers the Sobel, Prewitt, Roberts, log, zero-cross

4 and Canny edge detection methods. Every combination of these methods was used in broad survey to see whether the built-in MATLAB functions could perform the image enhancement and edge detection tasks. Due to the enormous number of possible combinations and parameters, a majority of the images are not included in this report. After extensive experimentation, the Gaussian and the averaging filter seemed to produce the most suitable images for the edge detection. Among those suitable images, the log and the Canny edge detection schemes seem to yield the best results. Samples of these results are shown below in Figure 5 and Figure 6: (a) Figure 5 (a): Result of the Gaussian filter. Figure 5 : Result of the averaging filter. We can observe that both of them do a decent job in removing the salt noise. As one can observe from Figure (6) (please refer to following page), none of the methods shown in Figure (5) eliminate the noise completely. Additionally, the methods used in Figure (6) are highly sensitive to the leftover noise, which is obvious in the result. Therefore, even though the edges are found in the channels, there is still too much unwanted signal for a computer to successfully evaluate which pixels belong inside the channel. Another key flaw with the low-pass filter is the lack of high-frequency components also blurs the edges of the channel. This drawback makes it more difficult for the edge detection portion of the program to accurately locate the sudden change in intensity that correlates to the edge of the channel.

5 (a) (c) (d) Figure (6): (a),, (c), (d) are respectively the result of the Guassian filter with log edge detection, Gaussian filter with Canny edge detection, averaging filter with log edge detection, and averaging filter with Canny edge detection. Observe that while most of these processes arrive at the outline of the channel, it is still highly sensitive the noise. The next step was to implement various methods in [5] that were shown to be effective against salt and pepper noise. The max, min and median filter were used to generate some preliminary results shown in Figure (7) below. As there is little pepper noise in the image compared to salt noise, the min filter naturally performed the best out of the three. However, further implementation of the edge detection showed that there is still too much noise left over for the images that had a lower signal to noise ratio, like the Y-channel images. Yet, it is worth noting that the results of these methods do not blur the edges like the low pass filter does. (a) (c) Figure (7): (a), and (c) are respectively the results of the min, max and median filter. We can see that the min filter seems to perform the best, but still not good enough.

6 Another image-processing method that is suitable for salt noise is the contraharmonic method, which is also described in [5]. This method extracts a portion of the image, and calculates a new value for the center pixel based on Equation (1) below: f ( x, y) = ( st, ) Sxy ( st, ) Sxy (, ) g s t (, ) g s t Q+ 1 Q (1) Here g(s,t) are the values of the original pixels while f(x,y) is the new value of the center pixel. The Q-factor in the equation is a user-defined variable, and approaches a max or min filter as Q approaches positive to negative infinity. When Q is negative, the filter is suitable for eliminating salt noise. Some sample results of the contra-harmonic filter are included in Figure (8) below: (a) (c) (d) Figure (8): (a) is the original image; is the result of the contra-harmonic filter for Q = -1; (c) is Q = -10, (d) is Q = -20. Until now, it seems like the contra-harmonic filter has the most promising results. As the Q-factor increases, there is a trade-off that is within the user s control between the strength of the signal, and the amount of noise in the image. Therefore, adjusting Q can lead to a potentially optimal image. In addition, the contra-harmonic does not blur the edges of the channel and therefore does not suffer the same flaw as the low-pass filters. However, a better method can be found after closer examination of the nature of the noise.

7 An even more effective method was devised after looking at the statistics of the noise. After reviewing the Fourier transform and the histogram (provided in Figure (9) below), one can conclude that the noise is Gaussian in nature. (a) Figure 9 (a): Fourier transform of the noise portion of the images. All of the images had roughly the same shape. Figure 9 : A histogram of the noise portion of the images shows the noise in all of the images have a Gaussian distribution that can be evaluated individually for each image. An inverse-gaussian filter was implemented based on this fact that was effective in removing a bulk of the noise. First, the program obtains a sample of the noise through a portion of the image that does not contain the channel. Next, the program runs through a series of iterations. Each iteration takes the Fourier transform of the image (F), and divides it by the Fourier transform of the noise sample (G), shown in Equation (2) below: ( ω) F = F ( ω) ( ω) n n+1 (2) Gn The next iteration samples the noise of the new image and performs the operation again if needed. Similar to the contra-harmonic filter, this method also lowers the signal given by the channel in a manner that can be controlled by the user. However, this method is much more effective than the contra-harmonic filter used previously. Ten iterations eliminate a majority of the salt noise, but still retain just enough signal of the channel for the edge detection program to be effective. The result of this method is the most satisfactory to date, and the results in Figure (10) shown in the following page is subject for edge detection and mixing evaluations in the subsequent sections.

8 (a) (c) (d) Figure (10): (a) is the original image; is the result of the inverse-gaussian method after the first iteration; (c) is the second iteration, (d) is after the 10 th iteration. 3.2 Edge Detection Extensive experimentation found a series of procedures based on morphological concepts that did an excellent job detecting the edges of the channels without the noise. The final method used the following structure elements in Figure (11): (a) (c) Figure (11): (a) is structure element 1; is structure element 2; (c) is structure element 3 The first step was to filter out some of the noise through a threshold method. It was found that much of the noise could be eliminated if the threshold was set at 40% of the maximum signal. The image was converted into a binary image with that 40% threshold being the cutoff. This result is shown in Figure (12-c).

9 (a) (c) (d) (e) (f) Figure (12): Edge detection methodology description (a) is the original square wave image; is the original y-channel image; (c) is the Y-channel after the threshold step; (d) is after eroding with structure element 3; (e) is the result of the dilate operation with structure element 2 and filling operation; (f) is the final edge detection result. The threshold method previously described eliminated much of the noise, but there is still some remaining, especially in the y-channel case where the available images had a lower signal-to-noise ratio. However, the remaining noise mostly consists of small, disconnected dots. Therefore an erosion operation with structure element 3 successfully eliminates the remainder of the noise. Figure (12-d) shows the result of this step.

10 After the noise has been eliminated the channel is reconstructed to the point where the border is one connected region. A dilation operation with structure element 2 accomplishes this task. Note that the previous two steps are similar to a closing operation, but with different structure elements for the erosion and dilation steps that produce more suitable results. (a) Figure (13): (a) is the final edge detection of the Y-channel after the straightening; is the final edge detection result of the square wave channel. After an outline of the channel is found, the next step is to find the actual thin edges. A filling operation is first performed on the image, which makes it one solid structure. The result of this step makes the image an ideal case, with clear and sharp borders. Finally, an edge detection scheme is used to output the final result, given in Figure (13). In the Y-channel case, which had a very low signal to noise ratio and a know channel shape, a straightening method was proposed by averaging the locations of the borders. Since the image is so ideal after the filling operation, most edge detection methods produce similar results. In the final version of the related program, the Canny method was used since it produced the best results in previous efforts. 3.3 Mixing Evaluation After the border has been detected, the final step to the end result is the evaluation of mixing itself. The mixing is determined by the following formula to correspond with simulations: M n xi x i= 1 = 1 (3) n M represents the result of the mixing evaluation; the summation represents the total differences between intensity values of the i'th pixel value and the overall average intensity value; n represents the number of pixels being evaluated. The logic behind this is that all the pixel values will be the average value in the perfectly well mixed case; therefore M will have a value of 1.

11 (a) Figure (14): The result of multiplication of the image with the binary mask from the edge detection step for: (a) the standard Y-channel case; the square wave case. Before evaluating the mixing, the program still needs to prep the image so that it only evaluates the channel portion of the image. The first step is to load the enhanced image of the user s choice as well as the binary image resulting from the edge detection. The binary image is then used as a mask and multiplied onto the enhanced image pixel by pixel. The resulting image is one with only the channel area as a non-zero value, such as that shown in Figure (14). The program then evaluates the mixing row-by-row using Equation (3), and produces a graph showing how the mixing improves while traveling down the length of the channel, similar to a representation used in [6]. 3.4 Custom-Area Mixing Evaluation Instead of repeating a similar process for the set of images shown in Figure (4), the students developed another image processing tool that would be helpful for the continuation of the mixing research project. The goal of the second program is to allow the users to evaluate mixing in any given location on a newly-acquire image by simply pointing and clicking with the mouse. The program first asks users for an input file, after which it displays the image. The user is then prompted to select an area on the graph to evaluate the mixing. The selected region is then displayed, extracted, and evaluated. The final output result is then displayed on the command window for the users reference. This new approach is similar to the old program in the evaluation methods, but it is a very speedy way to find single mixing evaluations of a given area in a newly acquired images. The new program is also more independent of the image type, as much of the edge detection methods are directed to the Cy-5 based setup, and is probably less universal in its capabilities.

12 4. Results 4.1 Image Enhancement Results Several enhancement methods were discussed in Section 3.1, and each did a decent job removing certain portions of the noise. The main objective of the image enhancement was to allow successful edge detection later on without false edges due to noise. After viewing the result of several filters applied on our images, the students acquired a feel for the functions of several filters, and began applying the operations one after another. This process has a great number of possible combinations, and the students found the best ones after extensive experimentation. They are: Combo 1: Average filter Gaussian filter Average filter Combo 2: Average filter Gaussian filter Gaussian filter Combo 3: Average filter Gaussian iterations Gaussian filter Combo 4: Average filter Gaussian iterations Average Filter (4) All of these four combinations yielded excellent results. The final image used to produce the best edge-detection outcome was a new image consisting of the average values of the result of the four combinations. The final output of this enhancement process had a high enough signal-to-noise ratio that even the noisiest of the Y-channel images produced good results, eliminating the need for the straightening step proposed in Section 3.1. The result of the enhancement process is given in Figure (15). (a) Figure (15): The final enhanced image used to detect the edges for: (a) the Y-channel; the square wave channel. 4.2 Edge Detection Results The procedure developed in Section 3.2 provided a majority of the concepts used to determine the edges of the channel. There were still several areas of refinement during the development of implementation. The first is the initial threshold step. In the case of a higher signal-to-noise ratio there was some success in finding the edge by simply setting a lower and upper limit to the threshold. This was not the case with the images available for the Y-channel, so the morphological method was still used.

13 (a) Figure (16): The final edge detection results for: (a) the Y-channel; the square wave channel. In the end, the canny method produced the best result for the final edge detection step. Also, when applied to the result of the image enhancement results, the final output is clean enough that it was not necessary to implement the straightening process proposed for the Y-channel image. The program was successful in detecting the edges of the channels for the images available without the need for human aid. The resulting binary image of the edge detection process is given in Figure (16). It is also noteworthy that the final edge detection method is independent of channel shape or optical method, as long as there is a sufficiently high signal-to-noise ratio in the image. Therefore, the method should be versatile enough to handle any general mixing evaluation application. 4.3 Mixing Evaluation Results The evaluation step found the extent of mixing versus channel length of the image, shown in Figure (17). A rough average of the output was then compared to the simulation results given in Figure (17-d). The simulations performed in the previous research effort predicted that the standard Y-channel would have a mixing efficiency of at the experimental flow rate of 0.1 m/s through the 100 µm by 100 µm cross section of the channel. The average value at the end of the channel gave a mixing efficiency of 0.233, which was 12% higher than the predicted value. Similarly, the simulations predicted a mixing efficiency of for the squarewave channel at the experimental flow rate. The image analysis yielded a mixing efficiency of 0.891, which was only 2% lower than the predicted value. The extent of mixing along the channel length followed the expected trends found in the simulation. The square wave channel became increasingly mixed along the length of the channel until it straightened out again. On the other hand, the Y-shaped channel remained at roughly the same mixing efficiency, as it is diffusion-limited making the improvement difficult to observe over the short channel distance. The relevant graphs that describe these results are on the next page in Figure (17).

14 (a) (c) Extent of Mixing standard zigzag Pressure Drop, Pa 0.2 serpentine square wave compartment Flow Rate, m/s (d) Figure (17): (a) is the evaluation of the mixing for both channels versus the channel length; and (c) both show images of the channel lengthwise for comparison purposes; (d) is the simulation prediction of the experimental results.

15 Figure (18): A screen shot showing the operation of the custom-area mixing program. A portion of interest in the image is selected by the user through the means of a mouse, and is displayed next to the original image for user verification. The program then evaluates the extent of mixing in the area and displays the result in the command window, shown in the lower portion of the screen shot. 4.4 Custom-Area Mixing Results As mentioned in Section 3.4, the food coloring images were used to develop a different tool: one that evaluates the mixing in a region of interest chosen by the user. This method is much more general; without the need for a test image used for edge detection, the program could directly estimate the extent of mixing for any custom image, so long as the concentration correlated to the intensity of the image. The operation of the program is described through the screen shot in Figure (18). The command window first prompts the user to select the desired image to evaluate, based on those available in the database. This input method can be altered so the user can load any file in the computer through an explorer window. The user is then asked to select an area to evaluate with his or her mouse. After the chosen area is displayed for verification, the estimated extent of mixing is displayed on the command window, and the user then has the option to select a different area for more evaluations.

16 5. Discussion There are several objectives to this project, as can be seen with the organization of Section 3 and Section 4. Each objective has a measure of success, which will be individually discussed in the following. The first portion of the project consisted of image enhancement. The goal of this step is to prepare the image such that the edge detection portion of the program can perform reliably, even for the available Y-channel image, where the signal-to-noise ratio is not as high. Not only does this imply the suppression of noise, but it also implies that blurring the image with a simple low-pass filter will be detrimental. The enhanced images have performed rather well in this respect, as the result of the Y-channel edges is straight enough that t no further adjustment was necessary. Visually, it also successfully removed much of the salt noise that plagued the image before enhancement. The edge detection portion also had a clear measure of success: to make a reasonable estimate of the region within the channel without being misled by whatever noise signal remains after the image enhancement. The output of the edge detection shown in Figure (16) looked more than reasonable, and led to good results in the image evaluation section. Furthermore, this was accomplished using only general means that were not specific to any characteristics of the image, other than the noise characteristics of the image acquisition process. This feature makes the program very useful for future mixing studies based on Cy-5 florescence detection. The simulation predictions are the measure of success for the mixing evaluations. The extent of mixing found in the outlet of the channel must correlate to that found in the simulation. In addition, the transient response with respect to channel length must correlate the trends shown in the simulation as well. For example, the standard Y- channel is expected to stay at roughly a constant mixing efficiency throughout the short length of the channel. The graphs in Figure (17-a) do indeed show these trends. In addition, the extent of mixing found at the outlet matched the simulations within 15%. While completely affirming and characterizing the reliability of the program require additional samples and measurements, the current set of programs are successful in meeting the above stated objectives based on the available images. There are several possible sources for inaccuracy in the results. The first is the inevitable effects of noise. The most straightforward way to improvement is to use a higher concentration of Cy-5 in the experiment. Unfortunately, this was not possible during the experiment that acquired the images. However, it can be seen that the higherconcentrated square wave image produced better edges with less enhancement than the Y-channel, which had a lower concentration. Also, there is the question as to the linearity between the measured intensity and the actual concentration. Several methods to characterize this relationship exist in the literature [7] [8], especially from researchers in DNA sensing, who have a strong interest in precise measurements of the concentration of Cy-5. Most of these methods cannot be implemented, however, due to lack of information concerning the light source used to produce these images. One can still argue that since the results correlate well with the simulations, that error caused by these assumptions and approximations are probably negligible.

17 6. Conclusion In summary, the students developed two general programs that analyzed and evaluated the extent of mixing in images of micro fluidic devices. The first was a program written to accurately evaluate mixing based on the intensity of Cy-5 fluorescence. The process involved image enhancement methods to remove the noise, which was prominent in images with a lower concentration of the dye. Various edge detection schemes then determined the region inside the channel. Finally, the extent of mixing at any location within the channel was evaluated based on an algorithm that correlated to that which was used in the simulations. Another program was developed for separate images where food coloring and water were injected into the inlets. The second program was much more general, with the purpose of immediate evaluation of mixing in any raw image, substituting additional images for edge detection with the help of the user. With this second program, the user can immediately estimate the extent of mixing for any custom area, without offering any more information than the image and the region of interest. The success was measured by how closely the results correlated with the simulations. The final measurements made by the program matched the simulated values within 15%, further affirming the validity of the methods and assumptions used. While more test images would be needed to further confirm the functionality of the programs, the final product performs well and produces reasonable results with all of the available data. 7. References [1] Bertsch, S. Heimgartner, P. Cousseau, and P. Renoud. Static micromixers based on large-scale industrial mixer geometry, Lab on a Chip, Vol 1, pp 56-60, [2] A.D. Strook et al., Chaotic Mixer for Microchannels, Science, vol 295, pp , 2002 [3] R. H. Liu, M. A. Stremler, K. V. Sharp, M. G. Olsen, J. G. Santiago, R. J. Adrian, H Aref, and D. J. Beebe. "Passive mixing in a three-dimensional serpentine microchannel", J. of MEMS, Vol 9, No. 2, pp , [4] V. Mengeaud, J. Josserand, and H. H. Girault. Mixing processes in a zigzag microchannel: finite element simulations and optical study, Analytical Chemistry, Vol 74, pp , [5] R. Gonzalez, R. Woods. Digital Image Processing, 2nd Edition. Prentice Hall, Upper Saddle River, N.J, [6] Kai Kang, R. Chevray. Visualization of fluid mixing in microchannels, IEEE Computer Graphics and Applications, Vol 25, Issue 6, pp 16-20, [7] Leming Shi, Weida Tong, Zhenqiang Su, et al. Microarry scanner calibration curves: characteristics and implications, BMC Bioinformatics, Vol 6, pp. 1-14, 2005 [8] Peter A. C. t Hoen, Rolf Turk, Judith M. Boer, et al. Intensity-based analysis of two color microarrays, Nucleic Acids Research, Vol 32, No 4, pp. e41-e47, 2004

18 8. Contribution Distribution Guillermo González-Fernández Benjamin Yang Literature Research 50% 50% Program Development 50% 50% Report Composition 40% 60% Presentation Preparation 60% 40% Total Contribution 50% 50% I hereby declare that the above table is an accurate approximation to the amount of contribution and effort we have put into the project. Guillermo González-Fernández Benjamin Yang