Abstract

We have developed a novel technique to quantify submicron scale mass density fluctuations in weakly disordered heterogeneous optical media using confocal fluorescence microscopy. Our method is based on the numerical evaluation of the light localization properties of an ‘optical lattice’ constructed from the pixel intensity distributions of images obtained with confocal fluorescence microscopy. Here we demonstrate that the technique reveals differences in the mass density fluctuations of the fluorescently labeled molecules between normal and cancer cells, and that it has the potential to quantify the degree of malignancy of cancer cells. Potential applications of the technique to other disease situations or characterizing disordered samples are also discussed.

© 2017 Optical Society of America

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2016 (1)

S. Koho, E. Fazeli, J. E. Eriksson, and P. E. Hänninen, “Image Quality Ranking Method for Microscopy,” Sci. Rep. 6, 28962 (2016).
[Crossref] [PubMed]

2015 (2)

T. Vujasinovic, J. Pribic, K. Kanjer, N. T. Milosevic, Z. Tomasevic, Z. Milovanovic, D. Nikolic-Vukosavljevic, and M. Radulovic, “Gray-level co-occurrence matrix texture analysis of breast tumor images in prognosis of distant metastasis risk,” Microsc. Microanal. 21(3), 646–654 (2015).
[Crossref] [PubMed]

V. Roukos, G. Pegoraro, T. C. Voss, and T. Misteli, “Cell cycle staging of individual cells by fluorescence microscopy,” Nat. Protoc. 10(2), 334–348 (2015).
[Crossref] [PubMed]

2013 (1)

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

2012 (1)

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

2011 (4)

R. Lopes, A. Ayache, N. Makni, P. Puech, A. Villers, S. Mordon, and N. Betrouni, “Prostate cancer characterization on MR images using fractal features,” Med. Phys. 38(1), 83–95 (2011).
[Crossref] [PubMed]

A. B. Tosun and C. Gunduz-Demir, “Graph run-length matrices for histopathological image segmentation,” IEEE Trans. Med. Imag. 30(3), 721–732 (2011).
[Crossref]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

J. S. Kim, P. Pradhan, V. Backman, and I. Szleifer, “The influence of chromosome density variations on the increase in nuclear disorder strength in carcinogenesis,” Phys. Biol. 8(1), 015004 (2011).
[Crossref] [PubMed]

2010 (3)

Z. Darzynkiewicz, “Critical Aspects in Analysis of Cellular DNA Content,” Curr. Protoc. Cytom. 52, 721 (2010).

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

K. Metze, R. L. Adam, and G. Kayser, “Pathophysiology of cancer and the entropy concept. Model-based reasoning in science and technology,” Stud. Comput. Intell. 314, 199–206 (2010).

2009 (3)

J. C. Waters, “Accuracy and precision in quantitative fluorescence microscopy,” J. Cell Biol. 185(7), 1135–1148 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

2008 (2)

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

L. Fass, “Imaging and cancer: a review,” Mol. Oncol. 2(2), 115–152 (2008).
[Crossref] [PubMed]

2007 (1)

2002 (1)

P. Pradhan and S. Sridhar, “From chaos to disorder: statistics of the eigenfunctions of microwave cavities,” Pramana 58(2), 333–341 (2002).
[Crossref]

2000 (1)

P. Pradhan and S. Sridhar, “Correlations due to localization in quantum eigenfunctions of disordered microwave cavities,” Phys. Rev. Lett. 85(11), 2360–2363 (2000).
[Crossref] [PubMed]

1996 (2)

J. M. Schmitt and G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. 21(16), 1310–1312 (1996).
[Crossref] [PubMed]

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

1993 (1)

B. Kramer and A. Mackinnon, “Localization—theory and experiment,” Rep. Prog. Phys. 56(12), 1469–1564 (1993).
[Crossref]

1991 (1)

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
[Crossref]

1985 (1)

P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys. 57(2), 287–337 (1985).
[Crossref]

1979 (1)

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization—absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

1953 (1)

R. Barer, K. F. A. Ross, and S. Tkaczyk, “Refractometry of living cells,” Nature 171(4356), 720–724 (1953).
[Crossref] [PubMed]

1952 (1)

H. G. Davies and M. H. F. Wilkins, “Interference microscopy and mass determination,” Nature 169(4300), 541 (1952).
[Crossref] [PubMed]

Abrahams, E.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization—absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

Adam, R. L.

K. Metze, R. L. Adam, and G. Kayser, “Pathophysiology of cancer and the entropy concept. Model-based reasoning in science and technology,” Stud. Comput. Intell. 314, 199–206 (2010).

Anderson, P. W.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization—absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

Ayache, A.

R. Lopes, A. Ayache, N. Makni, P. Puech, A. Villers, S. Mordon, and N. Betrouni, “Prostate cancer characterization on MR images using fractal features,” Med. Phys. 38(1), 83–95 (2011).
[Crossref] [PubMed]

Backman, V.

J. S. Kim, P. Pradhan, V. Backman, and I. Szleifer, “The influence of chromosome density variations on the increase in nuclear disorder strength in carcinogenesis,” Phys. Biol. 8(1), 015004 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Barer, R.

R. Barer, K. F. A. Ross, and S. Tkaczyk, “Refractometry of living cells,” Nature 171(4356), 720–724 (1953).
[Crossref] [PubMed]

Betrouni, N.

R. Lopes, A. Ayache, N. Makni, P. Puech, A. Villers, S. Mordon, and N. Betrouni, “Prostate cancer characterization on MR images using fractal features,” Med. Phys. 38(1), 83–95 (2011).
[Crossref] [PubMed]

Beuthan, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Bogojevic, A.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

Brand, R. E.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

Capoglu, I. R.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Chang, J.-S.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

Cook, G. J.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

Damania, D.

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

Darzynkiewicz, Z.

Z. Darzynkiewicz, “Critical Aspects in Analysis of Cellular DNA Content,” Curr. Protoc. Cytom. 52, 721 (2010).

Davies, H. G.

H. G. Davies and M. H. F. Wilkins, “Interference microscopy and mass determination,” Nature 169(4300), 541 (1952).
[Crossref] [PubMed]

Davnall, F.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

de Arruda, J. G. F.

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

de Arruda, L. F.

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

de Arruda, P. F. F.

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

de Godoy, M. F.

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

Dravid, V. P.

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

Eriksson, J. E.

S. Koho, E. Fazeli, J. E. Eriksson, and P. E. Hänninen, “Image Quality Ranking Method for Microscopy,” Sci. Rep. 6, 28962 (2016).
[Crossref] [PubMed]

Fass, L.

L. Fass, “Imaging and cancer: a review,” Mol. Oncol. 2(2), 115–152 (2008).
[Crossref] [PubMed]

Fazeli, E.

S. Koho, E. Fazeli, J. E. Eriksson, and P. E. Hänninen, “Image Quality Ranking Method for Microscopy,” Sci. Rep. 6, 28962 (2016).
[Crossref] [PubMed]

Ganeshan, B.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

Gatti, M.

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

Goh, V.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

Goldberg, M. J.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

Gunduz-Demir, C.

A. B. Tosun and C. Gunduz-Demir, “Graph run-length matrices for histopathological image segmentation,” IEEE Trans. Med. Imag. 30(3), 721–732 (2011).
[Crossref]

Hänninen, P. E.

S. Koho, E. Fazeli, J. E. Eriksson, and P. E. Hänninen, “Image Quality Ranking Method for Microscopy,” Sci. Rep. 6, 28962 (2016).
[Crossref] [PubMed]

Heifetz, A.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Helfmann, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Hensing, T.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

Herrig, M.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

John, S.

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
[Crossref]

Joshi, H. M.

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

Junior, F. N. F.

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

Kanjer, K.

T. Vujasinovic, J. Pribic, K. Kanjer, N. T. Milosevic, Z. Tomasevic, Z. Milovanovic, D. Nikolic-Vukosavljevic, and M. Radulovic, “Gray-level co-occurrence matrix texture analysis of breast tumor images in prognosis of distant metastasis risk,” Microsc. Microanal. 21(3), 646–654 (2015).
[Crossref] [PubMed]

Kayser, G.

K. Metze, R. L. Adam, and G. Kayser, “Pathophysiology of cancer and the entropy concept. Model-based reasoning in science and technology,” Stud. Comput. Intell. 314, 199–206 (2010).

Kim, J. S.

J. S. Kim, P. Pradhan, V. Backman, and I. Szleifer, “The influence of chromosome density variations on the increase in nuclear disorder strength in carcinogenesis,” Phys. Biol. 8(1), 015004 (2011).
[Crossref] [PubMed]

Koho, S.

S. Koho, E. Fazeli, J. E. Eriksson, and P. E. Hänninen, “Image Quality Ranking Method for Microscopy,” Sci. Rep. 6, 28962 (2016).
[Crossref] [PubMed]

Kramer, B.

B. Kramer and A. Mackinnon, “Localization—theory and experiment,” Rep. Prog. Phys. 56(12), 1469–1564 (1993).
[Crossref]

Kumar, G.

Kunte, D.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Lee, P. A.

P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys. 57(2), 287–337 (1985).
[Crossref]

Li, X.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Licciardello, D. C.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization—absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

Liu, Y.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Ljungqvist, G.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

Lopes, R.

R. Lopes, A. Ayache, N. Makni, P. Puech, A. Villers, S. Mordon, and N. Betrouni, “Prostate cancer characterization on MR images using fractal features,” Med. Phys. 38(1), 83–95 (2011).
[Crossref] [PubMed]

Mackinnon, A.

B. Kramer and A. Mackinnon, “Localization—theory and experiment,” Rep. Prog. Phys. 56(12), 1469–1564 (1993).
[Crossref]

Makni, N.

R. Lopes, A. Ayache, N. Makni, P. Puech, A. Villers, S. Mordon, and N. Betrouni, “Prostate cancer characterization on MR images using fractal features,” Med. Phys. 38(1), 83–95 (2011).
[Crossref] [PubMed]

Metze, K.

K. Metze, R. L. Adam, and G. Kayser, “Pathophysiology of cancer and the entropy concept. Model-based reasoning in science and technology,” Stud. Comput. Intell. 314, 199–206 (2010).

Miles, K. A.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

Milosevic, N. T.

T. Vujasinovic, J. Pribic, K. Kanjer, N. T. Milosevic, Z. Tomasevic, Z. Milovanovic, D. Nikolic-Vukosavljevic, and M. Radulovic, “Gray-level co-occurrence matrix texture analysis of breast tumor images in prognosis of distant metastasis risk,” Microsc. Microanal. 21(3), 646–654 (2015).
[Crossref] [PubMed]

Milovanovic, Z.

T. Vujasinovic, J. Pribic, K. Kanjer, N. T. Milosevic, Z. Tomasevic, Z. Milovanovic, D. Nikolic-Vukosavljevic, and M. Radulovic, “Gray-level co-occurrence matrix texture analysis of breast tumor images in prognosis of distant metastasis risk,” Microsc. Microanal. 21(3), 646–654 (2015).
[Crossref] [PubMed]

Minet, O.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Misteli, T.

V. Roukos, G. Pegoraro, T. C. Voss, and T. Misteli, “Cell cycle staging of individual cells by fluorescence microscopy,” Nat. Protoc. 10(2), 334–348 (2015).
[Crossref] [PubMed]

Mohammed, J.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

Mordon, S.

R. Lopes, A. Ayache, N. Makni, P. Puech, A. Villers, S. Mordon, and N. Betrouni, “Prostate cancer characterization on MR images using fractal features,” Med. Phys. 38(1), 83–95 (2011).
[Crossref] [PubMed]

Moreira, R. D.

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

Muldoon, J.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

Müller, G.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Murta, L. O.

P. F. F. de Arruda, M. Gatti, F. N. F. Junior, J. G. F. de Arruda, R. D. Moreira, L. O. Murta, L. F. de Arruda, and M. F. de Godoy, “Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer,” BMC Clin. Pathol. 13(1), 6 (2013).
[Crossref] [PubMed]

Ng, F.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

Nikolic-Vukosavljevic, D.

T. Vujasinovic, J. Pribic, K. Kanjer, N. T. Milosevic, Z. Tomasevic, Z. Milovanovic, D. Nikolic-Vukosavljevic, and M. Radulovic, “Gray-level co-occurrence matrix texture analysis of breast tumor images in prognosis of distant metastasis risk,” Microsc. Microanal. 21(3), 646–654 (2015).
[Crossref] [PubMed]

Pegoraro, G.

V. Roukos, G. Pegoraro, T. C. Voss, and T. Misteli, “Cell cycle staging of individual cells by fluorescence microscopy,” Nat. Protoc. 10(2), 334–348 (2015).
[Crossref] [PubMed]

Pradhan, P.

J. S. Kim, P. Pradhan, V. Backman, and I. Szleifer, “The influence of chromosome density variations on the increase in nuclear disorder strength in carcinogenesis,” Phys. Biol. 8(1), 015004 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

P. Pradhan and S. Sridhar, “From chaos to disorder: statistics of the eigenfunctions of microwave cavities,” Pramana 58(2), 333–341 (2002).
[Crossref]

P. Pradhan and S. Sridhar, “Correlations due to localization in quantum eigenfunctions of disordered microwave cavities,” Phys. Rev. Lett. 85(11), 2360–2363 (2000).
[Crossref] [PubMed]

Pribic, J.

T. Vujasinovic, J. Pribic, K. Kanjer, N. T. Milosevic, Z. Tomasevic, Z. Milovanovic, D. Nikolic-Vukosavljevic, and M. Radulovic, “Gray-level co-occurrence matrix texture analysis of breast tumor images in prognosis of distant metastasis risk,” Microsc. Microanal. 21(3), 646–654 (2015).
[Crossref] [PubMed]

Puech, P.

R. Lopes, A. Ayache, N. Makni, P. Puech, A. Villers, S. Mordon, and N. Betrouni, “Prostate cancer characterization on MR images using fractal features,” Med. Phys. 38(1), 83–95 (2011).
[Crossref] [PubMed]

Radulovic, M.

T. Vujasinovic, J. Pribic, K. Kanjer, N. T. Milosevic, Z. Tomasevic, Z. Milovanovic, D. Nikolic-Vukosavljevic, and M. Radulovic, “Gray-level co-occurrence matrix texture analysis of breast tumor images in prognosis of distant metastasis risk,” Microsc. Microanal. 21(3), 646–654 (2015).
[Crossref] [PubMed]

Ramakrishnan, T. V.

P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys. 57(2), 287–337 (1985).
[Crossref]

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization—absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

Ray, D.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

Rogers, J. D.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Ross, K. F. A.

R. Barer, K. F. A. Ross, and S. Tkaczyk, “Refractometry of living cells,” Nature 171(4356), 720–724 (1953).
[Crossref] [PubMed]

Roukos, V.

V. Roukos, G. Pegoraro, T. C. Voss, and T. Misteli, “Cell cycle staging of individual cells by fluorescence microscopy,” Nat. Protoc. 10(2), 334–348 (2015).
[Crossref] [PubMed]

Roy, H. K.

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Sanghera, B.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

Schmitt, J. M.

Selmi, M.

F. Davnall, C. S. Yip, G. Ljungqvist, M. Selmi, F. Ng, B. Sanghera, B. Ganeshan, K. A. Miles, G. J. Cook, and V. Goh, “Assessment of tumor heterogeneity: an emerging imaging tool for clinical practice?” Insights Imaging 3(6), 573–589 (2012).
[Crossref] [PubMed]

Sheppard, C. J. R.

Sridhar, S.

P. Pradhan and S. Sridhar, “From chaos to disorder: statistics of the eigenfunctions of microwave cavities,” Pramana 58(2), 333–341 (2002).
[Crossref]

P. Pradhan and S. Sridhar, “Correlations due to localization in quantum eigenfunctions of disordered microwave cavities,” Phys. Rev. Lett. 85(11), 2360–2363 (2000).
[Crossref] [PubMed]

Sturgis, C.

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

Subramanian, H.

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman, “Partial-wave microscopic spectroscopy detects subwavelength refractive index fluctuations: an application to cancer diagnosis,” Opt. Lett. 34(4), 518–520 (2009).
[Crossref] [PubMed]

H. Subramanian, H. K. Roy, P. Pradhan, M. J. Goldberg, J. Muldoon, R. E. Brand, C. Sturgis, T. Hensing, D. Ray, A. Bogojevic, J. Mohammed, J.-S. Chang, and V. Backman, “Partial wave spectroscopic microscopy for detection of nanoscale alterations of field carcinogenesis,” Cancer Res. 69, 5357–5363 (2009).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Szleifer, I.

J. S. Kim, P. Pradhan, V. Backman, and I. Szleifer, “The influence of chromosome density variations on the increase in nuclear disorder strength in carcinogenesis,” Phys. Biol. 8(1), 015004 (2011).
[Crossref] [PubMed]

Taflove, A.

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008).
[Crossref] [PubMed]

Tkaczyk, S.

R. Barer, K. F. A. Ross, and S. Tkaczyk, “Refractometry of living cells,” Nature 171(4356), 720–724 (1953).
[Crossref] [PubMed]

Tomasevic, Z.

T. Vujasinovic, J. Pribic, K. Kanjer, N. T. Milosevic, Z. Tomasevic, Z. Milovanovic, D. Nikolic-Vukosavljevic, and M. Radulovic, “Gray-level co-occurrence matrix texture analysis of breast tumor images in prognosis of distant metastasis risk,” Microsc. Microanal. 21(3), 646–654 (2015).
[Crossref] [PubMed]

Tosun, A. B.

A. B. Tosun and C. Gunduz-Demir, “Graph run-length matrices for histopathological image segmentation,” IEEE Trans. Med. Imag. 30(3), 721–732 (2011).
[Crossref]

Turzhitsky, V.

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis,” Phys. Biol. 8(2), 026012 (2011).
[Crossref] [PubMed]

P. Pradhan, D. Damania, H. M. Joshi, V. Turzhitsky, H. Subramanian, H. K. Roy, A. Taflove, V. P. Dravid, and V. Backman, “Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells,” Appl. Phys. Lett. 97(24), 243704 (2010).
[Crossref] [PubMed]

Villers, A.

R. Lopes, A. Ayache, N. Makni, P. Puech, A. Villers, S. Mordon, and N. Betrouni, “Prostate cancer characterization on MR images using fractal features,” Med. Phys. 38(1), 83–95 (2011).
[Crossref] [PubMed]

Voss, T. C.

V. Roukos, G. Pegoraro, T. C. Voss, and T. Misteli, “Cell cycle staging of individual cells by fluorescence microscopy,” Nat. Protoc. 10(2), 334–348 (2015).
[Crossref] [PubMed]

Vujasinovic, T.

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Figures (6)

Fig. 1
Fig. 1

Construction of a disordered optical lattice from confocal imaging (schematic pictures): (a’) Imaging of a sample with a laser beam. (a) Voxel-wise scanning on the xy- plane (z = constant) to construct a confocal 2D plane image of a DAPI stained cell nucleus targeting DNA molecules. (b) A typical confocal image- 2D micrograph. (c) A sample disordered optical lattice of the size of confocal image: each dot in the optical lattice is determined from the pixel intensity values in confocal fluorescence image, as shown in (b).

Fig. 2
Fig. 2

Schematic flowchart for comparing the structural disorder using confocal micrographs. (i) The confocal images of the nuclei of two samples were obtained. (ii) Optical lattices are constructed and eigenvalues are obtained by solving the Anderson tight binding model Hamiltonian. (iii) The structural disorder of the samples are then obtained by calculating the inverse participation ratio (IPR) of the systems from the eigenfunctions in a Gaussian color noise model and compared.

Fig. 3
Fig. 3

(a), (b), and (c): Representative confocal images of a normal astrocyte, an astrocyte progenitor, and a U87 astrocytoma cell nuclei, respectively. (a’), (b’) and (c’): Their corresponding Lsd(<IPR>) images (2D IPR plot) at sample length L = 0.4 µm (we have taken Lsd(<IPR>) = <IPR>). The scale bar in the confocal image corresponds to 5 µm.

Fig. 4
Fig. 4

Bar plots for mean Lsd(<IPR>) values (n = 12-15 cells, 3-5 micrographs per cell, 3 sets) for the normal astrocyte, astrocyte progenitor, and U87 astrocytoma cells nuclei at sample length L = 1.6 µm. Student’s t-test obtained p-value < 0.05 for each pair.

Fig. 5
Fig. 5

Structural disorder at different sample length scales (L) (sample size L × L). n = 12-15 cells for each type of normal astrocyte, astrocyte progenitor, and U87 astrocytoma cells, where 3-5 confocal micrographs for each cell around mid-nucleus were considered for the analysis.

Fig. 6
Fig. 6

Schematic flowchart for IPR calculation and 2D IPR image construction from confocal fluorescence image.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

I CFM (r)dV(ρ).
ε(x,y)= dn(x,y) n 0 d I CFM (x,y) < I CFM > .
H= i ε i |ii| +t <ij> (|ij|+|ji|) ,
IPR(L) L×L = 1 N i=1 N 0 L 0 L E i 4 (x,y)dxdy .
IPR(L) L sd = d n 2 1/2 × l c .

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