## Analysis of cellular objects through diffraction images acquired by flow cytometry |

Optics Express, Vol. 21, Issue 21, pp. 24819-24828 (2013)

http://dx.doi.org/10.1364/OE.21.024819

Acrobat PDF (1783 KB)

### Abstract

It was found that the diffraction images acquired along the side scattering directions with objects in a cell sample contain pattern variations at both the global and local scales. We show here that the global pattern variation is associated with the categorical size and morphological heterogeneity of the imaged objects. An automated image processing method has been developed to separate the acquired diffraction images into three types of global patterns. Combined with previously developed method for quantifying local texture pattern variations, the new method allows fully automated analysis of diffraction images for rapid and label-free classification of cells according to their 3D morphology.

© 2013 Optical Society of America

## 1. Introduction

1. A. K. Dunn, C. L. Smithpeter, A. J. Welch, and R. R. Richards-Kortum, “Finite-difference time-domain simulation of light scattering from single cells,” J. Biomed. Opt. **2**(3), 262–266 (1997). [CrossRef] [PubMed]

5. H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, “Angle-resolved Mueller matrix study of light scattering by B-cells at three wavelengths of 442, 633, and 850 nm,” J. Biomed. Opt. **12**(3), 034032 (2007). [CrossRef] [PubMed]

7. A. N. Shvalov, I. V. Surovtsev, A. V. Chernyshev, J. T. Soini, and V. P. Maltsev, “Particle classification from light scattering with the scanning flow cytometer,” Cytometry **37**(3), 215–220 (1999). [CrossRef] [PubMed]

8. D. I. Strokotov, A. E. Moskalensky, V. M. Nekrasov, and V. P. Maltsev, “Polarized light-scattering profile-advanced characterization of nonspherical particles with scanning flow cytometry,” Cytometry A **79**(7), 570–579 (2011). [CrossRef] [PubMed]

9. S. Holler, Y. Pan, R. K. Chang, J. R. Bottiger, S. C. Hill, and D. B. Hillis, “Two-dimensional angular optical scattering for the characterization of airborne microparticles,” Opt. Lett. **23**(18), 1489–1491 (1998). [CrossRef] [PubMed]

14. X. Su, Y. Qiu, L. Marquez-Curtis, M. Gupta, C. E. Capjack, W. Rozmus, A. Janowska-Wieczorek, and Y. Y. Tsui, “Label-free and noninvasive optical detection of the distribution of nanometer-size mitochondria in single cells,” J. Biomed. Opt. **16**(6), 067003 (2011). [CrossRef] [PubMed]

13. X. Su, S. E. Kirkwood, M. Gupta, L. Marquez-Curtis, Y. Qiu, A. Janowska-Wieczorek, W. Rozmus, and Y. Y. Tsui, “Microscope-based label-free microfluidic cytometry,” Opt. Express **19**(1), 387–398 (2011). [CrossRef] [PubMed]

14. X. Su, Y. Qiu, L. Marquez-Curtis, M. Gupta, C. E. Capjack, W. Rozmus, A. Janowska-Wieczorek, and Y. Y. Tsui, “Label-free and noninvasive optical detection of the distribution of nanometer-size mitochondria in single cells,” J. Biomed. Opt. **16**(6), 067003 (2011). [CrossRef] [PubMed]

15. K. M. Jacobs, J. Q. Lu, and X. H. Hu, “Development of a diffraction imaging flow cytometer,” Opt. Lett. **34**(19), 2985–2987 (2009). [CrossRef] [PubMed]

19. Y. Sa, Y. Feng, K. M. Jacobs, J. Yang, R. Pan, I. Gkigkitzis, J. Q. Lu, and X. H. Hu, “Study of low speed flow cytometry for diffraction imaging with different chamber and nozzle designs,” Cytometry A (to be published). [PubMed]

17. K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express **2**(6), 1717–1726 (2011). [CrossRef] [PubMed]

18. S. Yu, J. Zhang, M. S. Moran, J. Q. Lu, Y. Feng, and X. H. Hu, “A novel method of diffraction imaging flow cytometry for sizing microspheres,” Opt. Express **20**(20), 22245–22251 (2012). [CrossRef] [PubMed]

21. R. D. Castellone, N. R. Leffler, L. Dong, and L. V. Yang, “Inhibition of tumor cell migration and metastasis by the proton-sensing GPR4 receptor,” Cancer Lett. **312**(2), 197–208 (2011). [CrossRef] [PubMed]

17. K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express **2**(6), 1717–1726 (2011). [CrossRef] [PubMed]

23. C. Cortes and V. Vapnik, “Support-vector networks,” Mach. Learn. **20**(3), 273–297 (1995). [CrossRef]

24. C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” (2001), http://www.csie.ntu.edu.tw/~cjlin/libsvm.

## 2. Methods

16. K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J Biophotonics **2**(8-9), 521–527 (2009). [CrossRef] [PubMed]

17. K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express **2**(6), 1717–1726 (2011). [CrossRef] [PubMed]

15. K. M. Jacobs, J. Q. Lu, and X. H. Hu, “Development of a diffraction imaging flow cytometer,” Opt. Lett. **34**(19), 2985–2987 (2009). [CrossRef] [PubMed]

18. S. Yu, J. Zhang, M. S. Moran, J. Q. Lu, Y. Feng, and X. H. Hu, “A novel method of diffraction imaging flow cytometry for sizing microspheres,” Opt. Express **20**(20), 22245–22251 (2012). [CrossRef] [PubMed]

25. A. G. Hoekstra, M. D. Grimminck, and P. M. A. Sloot, “Large Scale Simulations of Elastic Light Scattering by a Fast Discrete Dipole Approximation,” Int. J. Mod. Phys. C **9**(01), 87–102 (1998). [CrossRef]

27. M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express **15**(26), 17902–17911 (2007). [CrossRef] [PubMed]

4. R. S. Brock, X. H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectrosc. Radiat. Transf. **102**(1), 25–36 (2006). [CrossRef]

28. Y. Zhang, Y. Feng, C. R. Justus, W. Jiang, Z. Li, J. Q. Lu, R. S. Brock, M. K. McPeek, D. A. Weidner, L. V. Yang, and X. H. Hu, “Comparative study of 3D morphology and functions on genetically engineered mouse melanoma cells,” Integr Biol (Camb) **4**(11), 1428–1436 (2012). [CrossRef] [PubMed]

_{ij}) with i or j = 1, 2, 3, 4 was first obtained and normalized by equating the full-sphere angular integral of the M

_{11}element to 1 [3

3. J. Q. Lu, P. Yang, and X. H. Hu, “SSimulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. **10**, 024022 (2005). [CrossRef] [PubMed]

_{0}as

_{ij}onto an area in the Z-Y place corresponding to the CCD sensor centered on the x-axis. We have selected an angular range of Δθ

_{s}= ± 18° and Δϕ

_{s}= ± 14° for obtaining the simulated diffraction images according to the experimental setup. In these calculations, we do not consider the imaging optics used in the experimental system shown in Fig. 1(a). Therefore, the simulated diffraction images should only be used as a guide to understand the correlation between object’s morphology and cross-polarized diffraction image pairs instead of a tool for inverse solutions.

## 3. Results and discussion

_{h}= 1.3340. Through our numerical studies, we found that the heterogeneity of the nucleus and large number of mitochondria have to be considered to obtain diffraction images of normal speckle patterns similar to those in Figs. 1 and 3. For this purpose the refractive index inside the nucleus, n

_{n}, was set to take the values of [1.3797, 1.3897, 1.3997, 1.4097, 1.4197] according to the fluorescence intensity of the nuclear dye (Syto-61, Life Technologies) while the index of mitochondria was set as n

_{m}= 1.4200. The refractive indices of other cellular organelles are given by n

_{nu}= 1.4397 for nucleoli, n

_{nm}= 1.4097 for nuclear membrane and n

_{c}= 1.3675 for cytoplasm of full cell structures.

24. C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” (2001), http://www.csie.ntu.edu.tw/~cjlin/libsvm.

30. N. Kanopoulos, N. Vasanthavada, and R. L. Baker, “Design of an image edge detection filter using the Sobel operator,” IEEE J. Solid-State Circuits **23**(2), 358–367 (1988). [CrossRef]

_{a}(z, y), where a = h, v, l, r, and a complete edge image E

_{T}(z, y) by summing the 4 directional images. These images were made binary again by setting those pixels of maximum intensity for speckle borderlines to 1 against the background by all other pixels set to 0. Examples of the binary edge images are presented in Fig. 3(a). From the binary edge images the number of the pixels of 1 in each image can be quickly summed for a set of 5 borderline length parameters as [C

_{v}, C

_{h}, C

_{l}, C

_{r}] and C

_{T}. Once these parameters were obtained we can separate those images of the stripe patterns from the other two types of speckle patterns. This is accomplished by comparing two C parameters in a pair of edge images, [C

_{v}, C

_{h}] or [C

_{l}, C

_{r}], consisting of mutually perpendicular directions. If the following conditions are satisfied in one pair of the C parameterswhere

*C*is the lesser of the two C parameters in the pair and

_{1}*C*= 2500 is a threshold, then the diffraction image is declared as the stripe type with the stripe directions along or approximately along the direction of the edge image with C

_{th}_{2}.

*f*we can derive a histogram

_{th}*N(f)*of high frequency pixels in

*P*(

*u, v*) with

*f*= (

*u*

^{2}+

*v*

^{2})

^{1/2}and N as the number of pixels with

*f*>

*f*and

_{th}*P*(

*u, v*) > 0.02⋅

*P*(0, 0). The later ensures that the selected high frequency pixels have intensities above the noise background. The sum of

*N(f)*yields the number of pixels having high power and frequency, N

_{P}, in the power spectrum image

*P*(

*u, v*). Examples of edge images and

*N(f)*for each of the three pattern types of the diffraction images are demonstrated in Fig. 3.

_{T}and N

_{P}values larger than those of the images with large speckle patterns. Still we found the presence of noise due to spurious light and the large morphological variations of the imaged objects can lead to significant fluctuations in the absolute values of C

_{T}and N

_{P}and their relative differences among samples of different cells. To achieve automated classification, one has to develop a calibration procedure to minimize the effect of these fluctuations. As the third step of image processing to be described below we have employed a k-means clustering technique [31

31. T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: analysis and implementation,” IEEE Trans. Pattern Anal. Mach. Intell. **24**(7), 881–892 (2002). [CrossRef]

_{Pai}, C

_{Tai}) with a = s or p for each of the two plots. The initial centers were then updated by the averaged values of the N

_{P}and C

_{T}parameters in each plot and the process iterated until the two centers converged to the final values of (N

_{Paf}, C

_{Taf}). To reduce the effect of fluctuation in C

_{T}and N

_{P}, we modified the standard k-means clustering technique for the above iteration with two changes. First only those dots within a circle of radius R from a current center location were counted, with R determined empirically, to obtain the updated location. Secondly, the updating of the centers for the image type of large speckle patterns was limited to the region of small N

_{P}and C

_{T}based on the fact that these images cannot have large values. If the updating led to a new center for this group of dots outside the limited region, the initial center was used instead.

23. C. Cortes and V. Vapnik, “Support-vector networks,” Mach. Learn. **20**(3), 273–297 (1995). [CrossRef]

24. C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” (2001), http://www.csie.ntu.edu.tw/~cjlin/libsvm.

_{P1}, C

_{T1}) yield better results of SVM classification [20]. For the data set shown in Fig. 4(a) or 4(b), the group of s-polarized images received the higher rank with 1 = s followed by 2 = p. After correct ranking, the SVM analysis can be performed using a classification vector of four parameters (N

_{P1}, C

_{T1}, N

_{P2}, C

_{T2}), for each imaged object. To further eliminate the need for training the SVM algorithm repeatedly for different data sets, we developed a method to scale a new data set according to the reference set shown in Fig. 4(b). Specifically, the four parameters extracted from a cross-polarized diffraction image pair in the new data set are scaled as followswhere i = 1 or 2, N

_{Pif}and C

_{Tif}are the averaged parameter values obtained by the k-means clustering analysis on the new data set,

## 4. Summary

**2**(6), 1717–1726 (2011). [CrossRef] [PubMed]

## Acknowledgment

## References and links

1. | A. K. Dunn, C. L. Smithpeter, A. J. Welch, and R. R. Richards-Kortum, “Finite-difference time-domain simulation of light scattering from single cells,” J. Biomed. Opt. |

2. | J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. |

3. | J. Q. Lu, P. Yang, and X. H. Hu, “SSimulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt. |

4. | R. S. Brock, X. H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectrosc. Radiat. Transf. |

5. | H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, “Angle-resolved Mueller matrix study of light scattering by B-cells at three wavelengths of 442, 633, and 850 nm,” J. Biomed. Opt. |

6. | M. R. Melamed, T. Lindmo, and M. L. Mendelsohn, |

7. | A. N. Shvalov, I. V. Surovtsev, A. V. Chernyshev, J. T. Soini, and V. P. Maltsev, “Particle classification from light scattering with the scanning flow cytometer,” Cytometry |

8. | D. I. Strokotov, A. E. Moskalensky, V. M. Nekrasov, and V. P. Maltsev, “Polarized light-scattering profile-advanced characterization of nonspherical particles with scanning flow cytometry,” Cytometry A |

9. | S. Holler, Y. Pan, R. K. Chang, J. R. Bottiger, S. C. Hill, and D. B. Hillis, “Two-dimensional angular optical scattering for the characterization of airborne microparticles,” Opt. Lett. |

10. | J. Neukammer, C. Gohlke, A. Höpe, T. Wessel, and H. Rinneberg, “Angular distribution of light scattered by single biological cells and oriented particle agglomerates,” Appl. Opt. |

11. | K. Singh, C. Liu, C. Capjack, W. Rozmus, and C. J. Backhouse, “Analysis of cellular structure by light scattering measurements in a new cytometer design based on a liquid-core waveguide,” IEE proceedings |

12. | X. T. Su, K. Singh, C. Capjack, J. Petrácek, C. Backhouse, and W. Rozmus, “Measurements of light scattering in an integrated microfluidic waveguide cytometer,” J. Biomed. Opt. |

13. | X. Su, S. E. Kirkwood, M. Gupta, L. Marquez-Curtis, Y. Qiu, A. Janowska-Wieczorek, W. Rozmus, and Y. Y. Tsui, “Microscope-based label-free microfluidic cytometry,” Opt. Express |

14. | X. Su, Y. Qiu, L. Marquez-Curtis, M. Gupta, C. E. Capjack, W. Rozmus, A. Janowska-Wieczorek, and Y. Y. Tsui, “Label-free and noninvasive optical detection of the distribution of nanometer-size mitochondria in single cells,” J. Biomed. Opt. |

15. | K. M. Jacobs, J. Q. Lu, and X. H. Hu, “Development of a diffraction imaging flow cytometer,” Opt. Lett. |

16. | K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J Biophotonics |

17. | K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express |

18. | S. Yu, J. Zhang, M. S. Moran, J. Q. Lu, Y. Feng, and X. H. Hu, “A novel method of diffraction imaging flow cytometry for sizing microspheres,” Opt. Express |

19. | Y. Sa, Y. Feng, K. M. Jacobs, J. Yang, R. Pan, I. Gkigkitzis, J. Q. Lu, and X. H. Hu, “Study of low speed flow cytometry for diffraction imaging with different chamber and nozzle designs,” Cytometry A (to be published). [PubMed] |

20. | Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Classification of Jurkat T and Ramos B cells,” Opt. Lett. submitted. |

21. | R. D. Castellone, N. R. Leffler, L. Dong, and L. V. Yang, “Inhibition of tumor cell migration and metastasis by the proton-sensing GPR4 receptor,” Cancer Lett. |

22. | M. Born and E. Wolf, |

23. | C. Cortes and V. Vapnik, “Support-vector networks,” Mach. Learn. |

24. | C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” (2001), http://www.csie.ntu.edu.tw/~cjlin/libsvm. |

25. | A. G. Hoekstra, M. D. Grimminck, and P. M. A. Sloot, “Large Scale Simulations of Elastic Light Scattering by a Fast Discrete Dipole Approximation,” Int. J. Mod. Phys. C |

26. | M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transf. |

27. | M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express |

28. | Y. Zhang, Y. Feng, C. R. Justus, W. Jiang, Z. Li, J. Q. Lu, R. S. Brock, M. K. McPeek, D. A. Weidner, L. V. Yang, and X. H. Hu, “Comparative study of 3D morphology and functions on genetically engineered mouse melanoma cells,” Integr Biol (Camb) |

29. | M. Moran, |

30. | N. Kanopoulos, N. Vasanthavada, and R. L. Baker, “Design of an image edge detection filter using the Sobel operator,” IEEE J. Solid-State Circuits |

31. | T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: analysis and implementation,” IEEE Trans. Pattern Anal. Mach. Intell. |

**OCIS Codes**

(110.1650) Imaging systems : Coherence imaging

(170.1530) Medical optics and biotechnology : Cell analysis

(290.5850) Scattering : Scattering, particles

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: August 29, 2013

Revised Manuscript: September 26, 2013

Manuscript Accepted: September 26, 2013

Published: October 9, 2013

**Citation**

Jun Zhang, Yuanming Feng, Marina S. Moran, Jun Q. Lu, Li V. Yang, Yu Sa, Ning Zhang, Lixue Dong, and Xin-Hua Hu, "Analysis of cellular objects through diffraction images acquired by flow cytometry," Opt. Express **21**, 24819-24828 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-24819

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### References

- A. K. Dunn, C. L. Smithpeter, A. J. Welch, and R. R. Richards-Kortum, “Finite-difference time-domain simulation of light scattering from single cells,” J. Biomed. Opt.2(3), 262–266 (1997). [CrossRef] [PubMed]
- J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt.5(2), 131–137 (2000). [CrossRef] [PubMed]
- J. Q. Lu, P. Yang, and X. H. Hu, “SSimulations of light scattering from a biconcave red blood cell using the finite-difference time-domain method,” J. Biomed. Opt.10, 024022 (2005). [CrossRef] [PubMed]
- R. S. Brock, X. H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectrosc. Radiat. Transf.102(1), 25–36 (2006). [CrossRef]
- H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, “Angle-resolved Mueller matrix study of light scattering by B-cells at three wavelengths of 442, 633, and 850 nm,” J. Biomed. Opt.12(3), 034032 (2007). [CrossRef] [PubMed]
- M. R. Melamed, T. Lindmo, and M. L. Mendelsohn, Flow Cytometry and Sorting (Wiley-Liss, 1990).
- A. N. Shvalov, I. V. Surovtsev, A. V. Chernyshev, J. T. Soini, and V. P. Maltsev, “Particle classification from light scattering with the scanning flow cytometer,” Cytometry37(3), 215–220 (1999). [CrossRef] [PubMed]
- D. I. Strokotov, A. E. Moskalensky, V. M. Nekrasov, and V. P. Maltsev, “Polarized light-scattering profile-advanced characterization of nonspherical particles with scanning flow cytometry,” Cytometry A79(7), 570–579 (2011). [CrossRef] [PubMed]
- S. Holler, Y. Pan, R. K. Chang, J. R. Bottiger, S. C. Hill, and D. B. Hillis, “Two-dimensional angular optical scattering for the characterization of airborne microparticles,” Opt. Lett.23(18), 1489–1491 (1998). [CrossRef] [PubMed]
- J. Neukammer, C. Gohlke, A. Höpe, T. Wessel, and H. Rinneberg, “Angular distribution of light scattered by single biological cells and oriented particle agglomerates,” Appl. Opt.42(31), 6388–6397 (2003). [CrossRef] [PubMed]
- K. Singh, C. Liu, C. Capjack, W. Rozmus, and C. J. Backhouse, “Analysis of cellular structure by light scattering measurements in a new cytometer design based on a liquid-core waveguide,” IEE proceedings 151, 10–16 (2004).
- X. T. Su, K. Singh, C. Capjack, J. Petrácek, C. Backhouse, and W. Rozmus, “Measurements of light scattering in an integrated microfluidic waveguide cytometer,” J. Biomed. Opt.13(2), 024024 (2008). [CrossRef] [PubMed]
- X. Su, S. E. Kirkwood, M. Gupta, L. Marquez-Curtis, Y. Qiu, A. Janowska-Wieczorek, W. Rozmus, and Y. Y. Tsui, “Microscope-based label-free microfluidic cytometry,” Opt. Express19(1), 387–398 (2011). [CrossRef] [PubMed]
- X. Su, Y. Qiu, L. Marquez-Curtis, M. Gupta, C. E. Capjack, W. Rozmus, A. Janowska-Wieczorek, and Y. Y. Tsui, “Label-free and noninvasive optical detection of the distribution of nanometer-size mitochondria in single cells,” J. Biomed. Opt.16(6), 067003 (2011). [CrossRef] [PubMed]
- K. M. Jacobs, J. Q. Lu, and X. H. Hu, “Development of a diffraction imaging flow cytometer,” Opt. Lett.34(19), 2985–2987 (2009). [CrossRef] [PubMed]
- K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J Biophotonics2(8-9), 521–527 (2009). [CrossRef] [PubMed]
- K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express2(6), 1717–1726 (2011). [CrossRef] [PubMed]
- S. Yu, J. Zhang, M. S. Moran, J. Q. Lu, Y. Feng, and X. H. Hu, “A novel method of diffraction imaging flow cytometry for sizing microspheres,” Opt. Express20(20), 22245–22251 (2012). [CrossRef] [PubMed]
- Y. Sa, Y. Feng, K. M. Jacobs, J. Yang, R. Pan, I. Gkigkitzis, J. Q. Lu, and X. H. Hu, “Study of low speed flow cytometry for diffraction imaging with different chamber and nozzle designs,” Cytometry A (to be published). [PubMed]
- Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Classification of Jurkat T and Ramos B cells,” Opt. Lett.submitted.
- R. D. Castellone, N. R. Leffler, L. Dong, and L. V. Yang, “Inhibition of tumor cell migration and metastasis by the proton-sensing GPR4 receptor,” Cancer Lett.312(2), 197–208 (2011). [CrossRef] [PubMed]
- M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
- C. Cortes and V. Vapnik, “Support-vector networks,” Mach. Learn.20(3), 273–297 (1995). [CrossRef]
- C. C. Chang and C. J. Lin, “LIBSVM: a library for support vector machines,” (2001), http://www.csie.ntu.edu.tw/~cjlin/libsvm .
- A. G. Hoekstra, M. D. Grimminck, and P. M. A. Sloot, “Large Scale Simulations of Elastic Light Scattering by a Fast Discrete Dipole Approximation,” Int. J. Mod. Phys. C9(01), 87–102 (1998). [CrossRef]
- M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transf.106(1-3), 558–589 (2007). [CrossRef]
- M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express15(26), 17902–17911 (2007). [CrossRef] [PubMed]
- Y. Zhang, Y. Feng, C. R. Justus, W. Jiang, Z. Li, J. Q. Lu, R. S. Brock, M. K. McPeek, D. A. Weidner, L. V. Yang, and X. H. Hu, “Comparative study of 3D morphology and functions on genetically engineered mouse melanoma cells,” Integr Biol (Camb)4(11), 1428–1436 (2012). [CrossRef] [PubMed]
- M. Moran, Correlating the Morphological and Light Scattering Properties of Biological Cells, Ph.D. Dissertation (East Carolina University, 2013).
- N. Kanopoulos, N. Vasanthavada, and R. L. Baker, “Design of an image edge detection filter using the Sobel operator,” IEEE J. Solid-State Circuits23(2), 358–367 (1988). [CrossRef]
- T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, “An efficient k-means clustering algorithm: analysis and implementation,” IEEE Trans. Pattern Anal. Mach. Intell.24(7), 881–892 (2002). [CrossRef]

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