Abstract

Embryonic stem (ES) cells are an important factor in the development of cell-based therapeutic strategies. In this work, the use of digital holographic interferometric microscopy and statistical identification for automatic discrimination of ES cells and fibroblast (FB) cells is discussed in detail. The proposed algorithm first reduces the complex data structure to lower dimensions. Then, based on asymptotic normality, model-based clustering and linear discriminant analysis are applied to the transformed data to obtain the classification between ES and FB cells. The proposed algorithm is robust because it does not depend on parametric assumptions and can be extended to the classification of other cell image data. Experimental results are presented to demonstrate the performance of the system.

© 2014 Optical Society of America

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2013 (1)

2011 (2)

A. Anand, V. K. Chhaniwal, and B. Javidi, “Imaging embryonic stem cell dynamics using quantitative 3D digital holographic microscopy,” IEEE Photon. J. 3, 546–554 (2011).
[CrossRef]

M. Pudlasa, D. A. C. Berrio, M. Votteler, S. Koch, S. Thude, H. Walles, and K. Schenke-Laylanda, “Non-contact discrimination of human bone marrow-derived mesenchymal stem cells and fibroblasts using Raman spectroscopy,” Med. Laser Appl. 26, 119–125 (2011).
[CrossRef]

2010 (4)

2009 (1)

I. K. Moon, M. Daneshpanah, A. Stern, and B. Javidi, “Automated three-dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

2008 (2)

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

U. Gopinathan, G. Pedrini, and W. Osten, “Coherence effects in digital in-line holographic microscopy,” J. Opt. Soc. Am. A 25, 2459–2466 (2008).
[CrossRef]

2007 (1)

I. Moon and B. Javidi, “Three dimensional identification of stem cells computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007).
[CrossRef]

2006 (1)

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

2005 (3)

2002 (3)

C. Fraley and A. E. Raftery, “Model-based clustering, discriminant analysis and density estimation,” J. Am. Stat. Assoc. 97, 611–631 (2002).
[CrossRef]

G. Pedrini and H. J. Tiziani, “Short-coherence digital microscopy by use of a lensless holographic imaging system,” Appl. Opt. 41, 4489–4496 (2002).
[CrossRef]

U. Schnars and W. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

2001 (1)

D. C. Colter, I. Sekiya, and D. J. Prockop, “Identification of a subpopulation of rapidly self renewing and multi potential adult stem cells in colonies of human marrow stromal cells,” Proc. Natl. Acad. Sci. USA 98, 7841–7845 (2001).
[CrossRef]

2000 (1)

1999 (2)

1998 (1)

1997 (1)

A. K. Gangopadhyay, R. Disario, and D. K. Dey, “A nonparametric approach to k-sample inference based on entropy,” J. Nonparametr. Stat. 8, 237–252 (1997).
[CrossRef]

1995 (1)

R. E. Kass and A. E. Raftery, “Bayes factors,” J. Am. Stat. Assoc. 90, 773–795 (1995).
[CrossRef]

1993 (2)

J. D. Banfield and A. E. Raftery, “Model-based Gaussian and non-Gaussian clustering,” Biometrics 49, 803–821 (1993).
[CrossRef]

P. Hall and S. C. Morton, “On the estimation of entropy,” Ann. Inst. Stat. Math. 45, 69–88 (1993).
[CrossRef]

1989 (1)

H. Joe, “Estimation of entropy and other functionals of a multivariate density,” Ann. Inst. Stat. Math. 41, 683–697 (1989).
[CrossRef]

1978 (1)

G. Schwarz, “Estimating the dimension of a model,” Ann. Stat. 6, 461–464 (1978).
[CrossRef]

1977 (1)

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1–38 (1977).

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

1962 (1)

E. Parzen, “On estimation of a probability density function and mode,” Ann. Math. Stat. 33, 1065–1076 (1962).
[CrossRef]

1936 (1)

R. A. Fisher, “The use of multiple measurements in taxonomic problems,” Ann. Eugen. 7, 179–188 (1936).
[CrossRef]

Alfieri, D.

Anand, A.

Banfield, J. D.

J. D. Banfield and A. E. Raftery, “Model-based Gaussian and non-Gaussian clustering,” Biometrics 49, 803–821 (1993).
[CrossRef]

Berrio, D. A. C.

M. Pudlasa, D. A. C. Berrio, M. Votteler, S. Koch, S. Thude, H. Walles, and K. Schenke-Laylanda, “Non-contact discrimination of human bone marrow-derived mesenchymal stem cells and fibroblasts using Raman spectroscopy,” Med. Laser Appl. 26, 119–125 (2011).
[CrossRef]

Bevilacqua, F.

Carapezza, E.

Chen, S.

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

Chhaniwal, V.

Chhaniwal, V. K.

A. Anand, V. K. Chhaniwal, and B. Javidi, “Imaging embryonic stem cell dynamics using quantitative 3D digital holographic microscopy,” IEEE Photon. J. 3, 546–554 (2011).
[CrossRef]

Colomb, T.

Colter, D. C.

D. C. Colter, I. Sekiya, and D. J. Prockop, “Identification of a subpopulation of rapidly self renewing and multi potential adult stem cells in colonies of human marrow stromal cells,” Proc. Natl. Acad. Sci. USA 98, 7841–7845 (2001).
[CrossRef]

Coppola, G.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).

Cuche, E.

Daneshpanah, M.

D. Shin, M. Daneshpanah, A. Anand, and B. Javidi, “Optofluidic system for three dimensional sensing and identification of micro-organisms with digital holographic microscopy,” Opt. Lett. 35, 4066–4068 (2010).
[CrossRef]

I. K. Moon, M. Daneshpanah, A. Stern, and B. Javidi, “Automated three-dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

De Nicola, S.

Dempster, A. P.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1–38 (1977).

Depeursinge, C.

Dey, D. K.

A. K. Gangopadhyay, R. Disario, and D. K. Dey, “A nonparametric approach to k-sample inference based on entropy,” J. Nonparametr. Stat. 8, 237–252 (1997).
[CrossRef]

Disario, R.

A. K. Gangopadhyay, R. Disario, and D. K. Dey, “A nonparametric approach to k-sample inference based on entropy,” J. Nonparametr. Stat. 8, 237–252 (1997).
[CrossRef]

Dubois, F.

Eijkelenboom, A.

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

El Mallahi, A.

Emery, Y.

Faridian, A.

Ferraro, P.

Finizio, A.

Fisher, R. A.

R. A. Fisher, “The use of multiple measurements in taxonomic problems,” Ann. Eugen. 7, 179–188 (1936).
[CrossRef]

Fraley, C.

C. Fraley and A. E. Raftery, “Model-based clustering, discriminant analysis and density estimation,” J. Am. Stat. Assoc. 97, 611–631 (2002).
[CrossRef]

C. Fraley and A. E. Raftery, “MCLUST version 3 for R: normal mixture modeling and model-based clustering,” (Department of Statistics, University of Washington, 2006, revised 2009).

Frauel, Y.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

Gangopadhyay, A. K.

A. K. Gangopadhyay, R. Disario, and D. K. Dey, “A nonparametric approach to k-sample inference based on entropy,” J. Nonparametr. Stat. 8, 237–252 (1997).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gopinathan, U.

Grilli, S.

Guo, W.

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

Hall, P.

P. Hall and S. C. Morton, “On the estimation of entropy,” Ann. Inst. Stat. Math. 45, 69–88 (1993).
[CrossRef]

Hopp, D.

Huangfu, D.

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

Javidi, B.

A. Anand, V. K. Chhaniwal, and B. Javidi, “Imaging embryonic stem cell dynamics using quantitative 3D digital holographic microscopy,” IEEE Photon. J. 3, 546–554 (2011).
[CrossRef]

D. Shin, M. Daneshpanah, A. Anand, and B. Javidi, “Optofluidic system for three dimensional sensing and identification of micro-organisms with digital holographic microscopy,” Opt. Lett. 35, 4066–4068 (2010).
[CrossRef]

A. Anand and B. Javidi, “Three dimensional microscopy with single beam wavefront sensing and reconstruction from volume speckle fields,” Opt. Lett. 35, 766–768 (2010).
[CrossRef]

A. Anand, V. Chhaniwal, and B. Javidi, “Real-time digital holographic microscopy for phase contrast 3D imaging of dynamic phenomena,” J. Display Technol. 6, 500–505 (2010).
[CrossRef]

I. K. Moon, M. Daneshpanah, A. Stern, and B. Javidi, “Automated three-dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

I. Moon and B. Javidi, “Three dimensional identification of stem cells computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007).
[CrossRef]

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4492–4506 (2005).
[CrossRef]

P. Ferraro, S. Grilli, D. Alfieri, S. De Nicola, A. Finizio, G. Pierattini, B. Javidi, G. Coppola, and V. Striano, “Extended focused image in microscopy by digital holography,” Opt. Express 13, 6738–6749 (2005).
[CrossRef]

B. Javidi and E. Tajahuerce, “Three dimensional object recognition using digital holography,” Opt. Lett. 25, 610–612 (2000).
[CrossRef]

Joannes, L.

Joe, H.

H. Joe, “Estimation of entropy and other functionals of a multivariate density,” Ann. Inst. Stat. Math. 41, 683–697 (1989).
[CrossRef]

Jueptner, W.

U. Schnars and W. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2005).

Kass, R. E.

R. E. Kass and A. E. Raftery, “Bayes factors,” J. Am. Stat. Assoc. 90, 773–795 (1995).
[CrossRef]

Koch, S.

M. Pudlasa, D. A. C. Berrio, M. Votteler, S. Koch, S. Thude, H. Walles, and K. Schenke-Laylanda, “Non-contact discrimination of human bone marrow-derived mesenchymal stem cells and fibroblasts using Raman spectroscopy,” Med. Laser Appl. 26, 119–125 (2011).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry (Wiley, 2005).

Laird, N. M.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1–38 (1977).

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Legros, J.-C.

Maehr, R.

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

Magistretti, P. J.

Marquet, P.

Matoba, O.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

Melton, D. A.

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

Minetti, C.

Moon, I.

I. Moon and B. Javidi, “Three dimensional identification of stem cells computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007).
[CrossRef]

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4492–4506 (2005).
[CrossRef]

Moon, I. K.

I. K. Moon, M. Daneshpanah, A. Stern, and B. Javidi, “Automated three-dimensional identification and tracking of micro/nano biological organisms by computational holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

Morton, S. C.

P. Hall and S. C. Morton, “On the estimation of entropy,” Ann. Inst. Stat. Math. 45, 69–88 (1993).
[CrossRef]

Muhlestein, W.

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

Murphy, D. B.

D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging (Wiley-Liss, 2001).

Naughton, T.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636–653 (2006).
[CrossRef]

Osafune, K.

D. Huangfu, K. Osafune, R. Maehr, W. Guo, A. Eijkelenboom, S. Chen, W. Muhlestein, and D. A. Melton, “Induction of pluripotent stem cells from primary human fibroblasts with only Oct4 and Sox2,” Nat. Biotechnol. 26, 1269–1275 (2008).
[CrossRef]

Osten, W.

Parzen, E.

E. Parzen, “On estimation of a probability density function and mode,” Ann. Math. Stat. 33, 1065–1076 (1962).
[CrossRef]

Pedrini, G.

Pierattini, G.

Prockop, D. J.

D. C. Colter, I. Sekiya, and D. J. Prockop, “Identification of a subpopulation of rapidly self renewing and multi potential adult stem cells in colonies of human marrow stromal cells,” Proc. Natl. Acad. Sci. USA 98, 7841–7845 (2001).
[CrossRef]

Pudlasa, M.

M. Pudlasa, D. A. C. Berrio, M. Votteler, S. Koch, S. Thude, H. Walles, and K. Schenke-Laylanda, “Non-contact discrimination of human bone marrow-derived mesenchymal stem cells and fibroblasts using Raman spectroscopy,” Med. Laser Appl. 26, 119–125 (2011).
[CrossRef]

Raftery, A. E.

C. Fraley and A. E. Raftery, “Model-based clustering, discriminant analysis and density estimation,” J. Am. Stat. Assoc. 97, 611–631 (2002).
[CrossRef]

R. E. Kass and A. E. Raftery, “Bayes factors,” J. Am. Stat. Assoc. 90, 773–795 (1995).
[CrossRef]

J. D. Banfield and A. E. Raftery, “Model-based Gaussian and non-Gaussian clustering,” Biometrics 49, 803–821 (1993).
[CrossRef]

C. Fraley and A. E. Raftery, “MCLUST version 3 for R: normal mixture modeling and model-based clustering,” (Department of Statistics, University of Washington, 2006, revised 2009).

Rappaz, B.

Ripley, B. D.

W. N. Venables and B. D. Ripley, Modern Applied Statistics with S (Springer, 2002).

Rubin, D. B.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1–38 (1977).

Schenke-Laylanda, K.

M. Pudlasa, D. A. C. Berrio, M. Votteler, S. Koch, S. Thude, H. Walles, and K. Schenke-Laylanda, “Non-contact discrimination of human bone marrow-derived mesenchymal stem cells and fibroblasts using Raman spectroscopy,” Med. Laser Appl. 26, 119–125 (2011).
[CrossRef]

Schnars, U.

U. Schnars and W. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Inverted digital holographic interferometric microscope for automatic identification of ES cells and FB cells.

Fig. 2.
Fig. 2.

Phase contrast images obtained after subtracting the obtained phase without the cells (ϕR) from the phase obtained with cells (ϕO). (a) Phase contrast image for ES cells; (b) phase contrast image for FB cells.

Fig. 3.
Fig. 3.

OPL distributions of (a) ES cells and (b) FB cells.

Fig. 4.
Fig. 4.

(a) Phase contrast image of a group of stem cells. (b) Thresholded image used to determine the location of cells.

Fig. 5.
Fig. 5.

Reconstructed image planes of a cell and the process of data extraction.

Fig. 6.
Fig. 6.

Box plots of the negative entropy values estimates I^ij values [see Eq. (19)] of six ES cells and six FB cells.

Fig. 7.
Fig. 7.

Fitted parameters (μi,σi) of the negative entropy estimates of 12 cells: the six FB cells are denoted by triangles, and the six ES cells are denoted by squares.

Tables (1)

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Table 1. Posterior Probabilities of Linear Discriminant Analysis

Equations (19)

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U(x,y,d)=U¯(fX,fY;0)eik1λ2fX2λ2fY2dei2π(fXx+fYy)dfXdfY,
ϕ(x,y)=arctanIm[U(x,y)]Re[U(x,y)].
Δϕ(x,y)=2πλΔ(x,y),
H(f)=f(x)logf(x)dx.
I(f)=f(x)logf(x)dx.
I^=n1i=1nlogf^(xi).
I^=n1i=1nlogf^(i)(xi),
I^=n1i=1nlog(1(n1)j=1,jin|H|1/2K(H1/2(xjxi))),
I^=I¯+op(n1/2).
l(μk,Σk,τk,zik|x)=logi=1n{[k=1Gϕk(xi|μk,Σk)zik]τ1zi1τGziG}=i=1nk=1Gziklog[τkϕk(xi|μk,Σk)].
z^ik=τ^kϕk(xi|μ^k,Σ^k)k=1Gτ^kϕk(xi|μ^k,Σ^k).
τ^k=nkn,μ^k=i=1nz^ikxink,nk=i=1nz^ik.
B12(D)=posterior oddspior odds=P(M1|D)/P(M2|D)P(M1)/P(M2)=P(D|M1)P(D|M2).
2logp(D|Mk)2logp(D|θ^k,Mk)νklog(n)=BICk,
P(classk|x)=πkfk(x)k=1Gπkfk(x)πkfk(x).
(xμk)Σk1(xμk)+log|Σk|2logπk,
Lk=xΣ1μkμkΣ1μk/2+logπk,
yijk=logf^ij(k)(xijk)=log(11001l=1,lk100|H|1/2K(H1/2(xijlxijk))),
y¯ij.=1100k=1100logf^ij(k)(xijk)=I^ij.

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