Abstract

Optical scattering strength of fractal optical disordered media with varying fractal dimension is reported. The diffusion limited aggregation (DLA) technique is used to generate fractal samples in 2D and 3D, and fractal dimensions are calculated using the box-counting method. The degree of structural disorder of these samples is calculated using their light localization strength, via the inverse participation ratio (IPR) analyses of the optical eigenfunctions. Results show non-monotonous behavior of the disorder-induced scattering strength with the fractal dimension, attributed to competition between the increasing structural disorder due to the decrease in fractal dimension versus the decrease in scattering centers due to decreasing fractality.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
    [Crossref]

2018 (2)

S. Bhandari, S. Choudannavar, E. R. Avery, P. Sahay, and P. Pradhan, “Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA),” Biomed. Phys. Eng. Express 4(6), 065020 (2018).
[Crossref]

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

2017 (1)

2007 (1)

2005 (1)

2004 (2)

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

2003 (1)

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

2001 (1)

C. M. Sorensen, “Light Scattering by Fractal Aggregates: A Review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
[Crossref]

2000 (2)

J. W. Baish and R. K. Jain, “Fractals and cancer,” Cancer Res. 60(14), 3683–3688 (2000).

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]

1999 (1)

J. P. Gollub and J. S. Langer, “Pattern formation in nonequilibrium physics,” Rev. Mod. Phys. 71(2), S396–S403 (1999).
[Crossref]

1998 (2)

V. N. Prigodin and B. L. Altshuler, “Long-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems,” Phys. Rev. Lett. 80(9), 1944–1947 (1998).
[Crossref]

D. S. Coffey, “Self-organization, complexity and chaos: The new biology for medicine,” Nat. Med. 4(8), 882–885 (1998).
[Crossref]

1997 (1)

S. S. Cross, “Fractals in Pathology,” J. Pathol. 182(1), 1–8 (1997).
[Crossref]

1996 (1)

1994 (1)

P. Pradhan and N. Kumar, “Localization of light in coherently amplifying random media,” Phys. Rev. B 50(13), 9644–9647 (1994).
[Crossref]

1990 (1)

E. Ben-Jacob and P. Garik, “The formation of patterns in non-equilibrium growth,” Nature 343(6258), 523–530 (1990).
[Crossref]

1989 (2)

B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimension of profiles,” Phys. Rev. A 39(3), 1500–1512 (1989).
[Crossref]

B. B. Mandelbrot, A. Blumen, M. Fleischmann, D. J. Tildesley, and R. C. Ball, “Fractal geometry: what is it, and what does it do?” Proc. R. Soc. Lond. A 423(1864), 3–16 (1989).
[Crossref]

1985 (1)

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

1983 (1)

T. A. Witten and L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27(9), 5686–5697 (1983).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Alfano, R. R.

Almabadi, H. M.

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

P. Sahay, H. M. Almabadi, H. M. Ghimire, O. Skalli, and P. Pradhan, “Light localization properties of weakly disordered optical media using confocal microscopy: application to cancer detection,” Opt. Express 25(13), 15428–15440 (2017).
[Crossref]

Altshuler, B. L.

V. N. Prigodin and B. L. Altshuler, “Long-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems,” Phys. Rev. Lett. 80(9), 1944–1947 (1998).
[Crossref]

Anderson, P. W.

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Avery, E. R.

S. Bhandari, S. Choudannavar, E. R. Avery, P. Sahay, and P. Pradhan, “Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA),” Biomed. Phys. Eng. Express 4(6), 065020 (2018).
[Crossref]

Backman, V.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

Baish, J. W.

J. W. Baish and R. K. Jain, “Fractals and cancer,” Cancer Res. 60(14), 3683–3688 (2000).

Ball, R. C.

B. B. Mandelbrot, A. Blumen, M. Fleischmann, D. J. Tildesley, and R. C. Ball, “Fractal geometry: what is it, and what does it do?” Proc. R. Soc. Lond. A 423(1864), 3–16 (1989).
[Crossref]

Ben-Jacob, E.

E. Ben-Jacob and P. Garik, “The formation of patterns in non-equilibrium growth,” Nature 343(6258), 523–530 (1990).
[Crossref]

Bhandari, S.

S. Bhandari, S. Choudannavar, E. R. Avery, P. Sahay, and P. Pradhan, “Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA),” Biomed. Phys. Eng. Express 4(6), 065020 (2018).
[Crossref]

Blumen, A.

B. B. Mandelbrot, A. Blumen, M. Fleischmann, D. J. Tildesley, and R. C. Ball, “Fractal geometry: what is it, and what does it do?” Proc. R. Soc. Lond. A 423(1864), 3–16 (1989).
[Crossref]

Chauhan, S. C.

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

Chen, K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

Choudannavar, S.

S. Bhandari, S. Choudannavar, E. R. Avery, P. Sahay, and P. Pradhan, “Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA),” Biomed. Phys. Eng. Express 4(6), 065020 (2018).
[Crossref]

Coffey, D. S.

D. S. Coffey, “Self-organization, complexity and chaos: The new biology for medicine,” Nat. Med. 4(8), 882–885 (1998).
[Crossref]

Cross, S. S.

S. S. Cross, “Fractals in Pathology,” J. Pathol. 182(1), 1–8 (1997).
[Crossref]

Dubuc, B.

B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimension of profiles,” Phys. Rev. A 39(3), 1500–1512 (1989).
[Crossref]

Fleischmann, M.

B. B. Mandelbrot, A. Blumen, M. Fleischmann, D. J. Tildesley, and R. C. Ball, “Fractal geometry: what is it, and what does it do?” Proc. R. Soc. Lond. A 423(1864), 3–16 (1989).
[Crossref]

Ganju, A.

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

Garik, P.

E. Ben-Jacob and P. Garik, “The formation of patterns in non-equilibrium growth,” Nature 343(6258), 523–530 (1990).
[Crossref]

Ghimire, H. M.

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

P. Sahay, H. M. Almabadi, H. M. Ghimire, O. Skalli, and P. Pradhan, “Light localization properties of weakly disordered optical media using confocal microscopy: application to cancer detection,” Opt. Express 25(13), 15428–15440 (2017).
[Crossref]

Goldberg, M. J.

H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

Gollub, J. P.

J. P. Gollub and J. S. Langer, “Pattern formation in nonequilibrium physics,” Rev. Mod. Phys. 71(2), S396–S403 (1999).
[Crossref]

Hart, J.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

Iversen, P.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

Jaggi, M.

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

Jain, R. K.

J. W. Baish and R. K. Jain, “Fractals and cancer,” Cancer Res. 60(14), 3683–3688 (2000).

Kim, Y.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

Kim, Y. L.

H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

Kiminezhadmalaie, M.

H. Namazi and M. Kiminezhadmalaie, “Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA,” https://www.hindawi.com/journals/cmmm/2015/242695/ .

Koetsier, J. L.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

Kromin, A. K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

Kromine, A. K.

H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

Kumar, G.

Kumar, N.

P. Pradhan and N. Kumar, “Localization of light in coherently amplifying random media,” Phys. Rev. B 50(13), 9644–9647 (1994).
[Crossref]

Kunte, D. P.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

Langer, J. S.

J. P. Gollub and J. S. Langer, “Pattern formation in nonequilibrium physics,” Rev. Mod. Phys. 71(2), S396–S403 (1999).
[Crossref]

Lee, P. A.

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

Liu, Y.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

Madugula, M.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

Mandelbrot, B. B.

B. B. Mandelbrot, A. Blumen, M. Fleischmann, D. J. Tildesley, and R. C. Ball, “Fractal geometry: what is it, and what does it do?” Proc. R. Soc. Lond. A 423(1864), 3–16 (1989).
[Crossref]

Namazi, H.

H. Namazi and M. Kiminezhadmalaie, “Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA,” https://www.hindawi.com/journals/cmmm/2015/242695/ .

Pradhan, P.

S. Bhandari, S. Choudannavar, E. R. Avery, P. Sahay, and P. Pradhan, “Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA),” Biomed. Phys. Eng. Express 4(6), 065020 (2018).
[Crossref]

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

P. Sahay, H. M. Almabadi, H. M. Ghimire, O. Skalli, and P. Pradhan, “Light localization properties of weakly disordered optical media using confocal microscopy: application to cancer detection,” Opt. Express 25(13), 15428–15440 (2017).
[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]

P. Pradhan and N. Kumar, “Localization of light in coherently amplifying random media,” Phys. Rev. B 50(13), 9644–9647 (1994).
[Crossref]

Prigodin, V. N.

V. N. Prigodin and B. L. Altshuler, “Long-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems,” Phys. Rev. Lett. 80(9), 1944–1947 (1998).
[Crossref]

Quiniou, J. F.

B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimension of profiles,” Phys. Rev. A 39(3), 1500–1512 (1989).
[Crossref]

Ramakrishnan, T. V.

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

Roques-Carmes, C.

B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimension of profiles,” Phys. Rev. A 39(3), 1500–1512 (1989).
[Crossref]

Roy, H. K.

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

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P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
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S. Bhandari, S. Choudannavar, E. R. Avery, P. Sahay, and P. Pradhan, “Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA),” Biomed. Phys. Eng. Express 4(6), 065020 (2018).
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P. Sahay, H. M. Almabadi, H. M. Ghimire, O. Skalli, and P. Pradhan, “Light localization properties of weakly disordered optical media using confocal microscopy: application to cancer detection,” Opt. Express 25(13), 15428–15440 (2017).
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T. A. Witten and L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27(9), 5686–5697 (1983).
[Crossref]

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Skalli, O.

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

P. Sahay, H. M. Almabadi, H. M. Ghimire, O. Skalli, and P. Pradhan, “Light localization properties of weakly disordered optical media using confocal microscopy: application to cancer detection,” Opt. Express 25(13), 15428–15440 (2017).
[Crossref]

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C. M. Sorensen, “Light Scattering by Fractal Aggregates: A Review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
[Crossref]

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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]

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B. B. Mandelbrot, A. Blumen, M. Fleischmann, D. J. Tildesley, and R. C. Ball, “Fractal geometry: what is it, and what does it do?” Proc. R. Soc. Lond. A 423(1864), 3–16 (1989).
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B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimension of profiles,” Phys. Rev. A 39(3), 1500–1512 (1989).
[Crossref]

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H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

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T. A. Witten and L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27(9), 5686–5697 (1983).
[Crossref]

Xu, M.

Yallapu, M. M.

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
[Crossref]

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B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimension of profiles,” Phys. Rev. A 39(3), 1500–1512 (1989).
[Crossref]

Aerosol Sci. Technol. (1)

C. M. Sorensen, “Light Scattering by Fractal Aggregates: A Review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
[Crossref]

Biomed. Phys. Eng. Express (1)

S. Bhandari, S. Choudannavar, E. R. Avery, P. Sahay, and P. Pradhan, “Detection of colon cancer stages via fractal dimension analysis of optical transmission imaging of tissue microarrays (TMA),” Biomed. Phys. Eng. Express 4(6), 065020 (2018).
[Crossref]

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J. W. Baish and R. K. Jain, “Fractals and cancer,” Cancer Res. 60(14), 3683–3688 (2000).

Gastroenterology (1)

H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126(4), 1071–1081 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9(2), 243–256 (2003).
[Crossref]

J. Biophotonics (1)

P. Sahay, A. Ganju, H. M. Almabadi, H. M. Ghimire, M. M. Yallapu, O. Skalli, M. Jaggi, S. C. Chauhan, and P. Pradhan, “Quantification of photonic localization properties of targeted nuclear mass density variations: Application in cancer-stage detection,” J. Biophotonics 11(5), e201700257 (2018).
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S. S. Cross, “Fractals in Pathology,” J. Pathol. 182(1), 1–8 (1997).
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Mol. Cancer Ther. (1)

H. K. Roy, P. Iversen, J. Hart, Y. Liu, J. L. Koetsier, Y. Kim, D. P. Kunte, M. Madugula, V. Backman, and R. K. Wali, “Down-regulation of SNAIL suppresses MIN mouse tumorigenesis: modulation of apoptosis, proliferation, and fractal dimension,” Mol. Cancer Ther. 3(9), 1159–1165 (2004).

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E. Ben-Jacob and P. Garik, “The formation of patterns in non-equilibrium growth,” Nature 343(6258), 523–530 (1990).
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Opt. Express (1)

Opt. Lett. (3)

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P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Phys. Rev. A (1)

B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimension of profiles,” Phys. Rev. A 39(3), 1500–1512 (1989).
[Crossref]

Phys. Rev. B (2)

T. A. Witten and L. M. Sander, “Diffusion-limited aggregation,” Phys. Rev. B 27(9), 5686–5697 (1983).
[Crossref]

P. Pradhan and N. Kumar, “Localization of light in coherently amplifying random media,” Phys. Rev. B 50(13), 9644–9647 (1994).
[Crossref]

Phys. Rev. Lett. (2)

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]

V. N. Prigodin and B. L. Altshuler, “Long-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems,” Phys. Rev. Lett. 80(9), 1944–1947 (1998).
[Crossref]

Proc. R. Soc. Lond. A (1)

B. B. Mandelbrot, A. Blumen, M. Fleischmann, D. J. Tildesley, and R. C. Ball, “Fractal geometry: what is it, and what does it do?” Proc. R. Soc. Lond. A 423(1864), 3–16 (1989).
[Crossref]

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J. P. Gollub and J. S. Langer, “Pattern formation in nonequilibrium physics,” Rev. Mod. Phys. 71(2), S396–S403 (1999).
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Other (1)

H. Namazi and M. Kiminezhadmalaie, “Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA,” https://www.hindawi.com/journals/cmmm/2015/242695/ .

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Figures (4)

Fig. 1.
Fig. 1. Fractal structures generated by diffusion limited aggregation (DLA) simulation method in 2D with increasing stickiness parameter from left (a) for Df = 1.68 to right (b) for Df = 1.89. Numerically generated disorder matrix by random cut (RC) method simulation in 2D with randomly cutting lattice points or randomly decreasing lattice points from left (c) for Df = 1.87 to right (d) for Df = 1.33.
Fig. 2.
Fig. 2. 2D and lower fractal dimensions < IPR(Df)> vs Df plots. Averaged < IPR(Df)> against Df plots for: (a) DLA and (b) RC systems simulations shown with L=64, for different ɛ/t values. Energy ratio ɛ/t vary between 0.625 and 10 with intervals of 0.625, and the large ratios a correspond to larger maximum < IPR > values.
Fig. 3.
Fig. 3. 3D and lower fractal dimension < IPR(Df)> plots. Averaged < IPR(Df)> against Df plots for (a) DLA and (b) RC systems simulation shown for L=16 and different ɛ/t values. Energy ratio ɛ/t varies between 0.625 and 10 with interval of 0.625; large ratios correspond to larger maximum < IPR > values.
Fig. 4.
Fig. 4. Turning points Dft against energy ratio ɛ/t in 2D and 3D. (a) 2D system with size L2=(64)2. (b) 3D system with size L3=163. Blue squares ($\color{blue}{\square}$) represent RC method while red Xs ($\color{red}{\textrm{X}}$) represent DLA.

Equations (4)

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

H = i ε i | i i | + t i j { | i j | + | j i | .
< I P R > N = 1 N i = 1 N 0 L 0 L Ψ i 4 ( x , y ) d x d y ,
< I P R >= << I P R > N > e n s e m b l e d n × l c .
D f = l i m r 0 [ l n ( N r ( r ) ) / l n ( 1 / r ) ] .

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