Abstract

An improved technique for fractal characterization called the modified blanket method is introduced that can quantify surrounding fractal structures on a pixel by pixel basis without artifacts associated with scale-dependent image features such as object size. The method interprets images as topographical maps, obtaining information regarding the local surface area as a function of image resolution. Local fractal dimension (FD) can be quantified from the power law exponent derived from the surface area and image resolution relationship. We apply this technique on simulated cell images of known FD and compared the obtained values to power spectral density (PSD) analysis. Our method is sensitive to a wider FD range (2.0–4.5), having a mean error of 1.4% compared to 6% for PSD analysis. This increased sensitivity and an ability to compute regional FD properties enabled the discrimination of the differences in radiation resistant cancer cell responses that could not be detected using PSD analysis.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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  6. K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
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  20. M. P. Paskaš, I. S. Reljin, and B. D. Reljin, “Multifractal Framework Based on Blanket Method,” The Scientific World Journal 2015, 894546 (2015)
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  24. D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
    [Crossref] [PubMed]
  25. O. I. Kolenc and K. P. Quinn, “Evaluating Cell Metabolism Through Autofluorescence Imaging of NAD(P)H and FAD,” Antioxid. Redox Signal. 2018, 20177451 (2018).
    [Crossref] [PubMed]
  26. W. Y. Hsu, C. C. Lin, M. S. Ju, and Y. N. Sun, “Wavelet-based fractal features with active segment selection: application to single-trial EEG data,” J. Neurosci. Methods 163(1), 145–160 (2007).
    [Crossref] [PubMed]
  27. J. M. Zook and K. M. Iftekharuddin, “Statistical analysis of fractal-based brain tumor detection algorithms,” Magn. Reson. Imaging 23(5), 671–678 (2005).
    [Crossref] [PubMed]
  28. R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2018 (3)

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

O. I. Kolenc and K. P. Quinn, “Evaluating Cell Metabolism Through Autofluorescence Imaging of NAD(P)H and FAD,” Antioxid. Redox Signal. 2018, 20177451 (2018).
[Crossref] [PubMed]

2017 (2)

D. Pendin, R. Filadi, and P. Pizzo, “The Concerted Action of Mitochondrial Dynamics and Positioning: New Characters in Cancer Onset and Progression,” Front. Oncol. 7(102), 102 (2017).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

2016 (1)

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

2015 (2)

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

M. P. Paskaš, I. S. Reljin, and B. D. Reljin, “Multifractal Framework Based on Blanket Method,” The Scientific World Journal 2015, 894546 (2015)

2013 (2)

K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
[Crossref] [PubMed]

D. H. MacDonald, M. Hunter, K. P. Quinn, and I. Georgakoudi, “Autocorrelation method for fractal analysis in nonrectangular image domains,” Opt. Lett. 38(21), 4477–4479 (2013).
[Crossref] [PubMed]

2012 (2)

J. Xylas, K. P. Quinn, M. Hunter, and I. Georgakoudi, “Improved Fourier-based characterization of intracellular fractal features,” Opt. Express 20(21), 23442–23455 (2012).
[Crossref] [PubMed]

I. Georgakoudi and K. P. Quinn, “Optical Imaging Using Endogenous Contrast to Assess Metabolic State,” Annu. Rev. Biomed. Eng. 14(1), 351–367 (2012).
[Crossref] [PubMed]

2009 (1)

J. Li, Q. Du, and C. Sun, “An improved box-counting method for image fractal dimension estimation,” Pattern Recognit. 42(11), 2460–2469 (2009).
[Crossref]

2008 (1)

A. A. Dukes, V. S. Van Laar, M. Cascio, and T. G. Hastings, “Changes in endoplasmic reticulum stress proteins and aldolase A in cells exposed to dopamine,” J. Neurochem. 106(1), 333–346 (2008).
[Crossref] [PubMed]

2007 (3)

R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
[Crossref] [PubMed]

W. Y. Hsu, C. C. Lin, M. S. Ju, and Y. N. Sun, “Wavelet-based fractal features with active segment selection: application to single-trial EEG data,” J. Neurosci. Methods 163(1), 145–160 (2007).
[Crossref] [PubMed]

R. M. Rangayyan and T. M. Nguyen, “Fractal Analysis of Contours of Breast Masses in Mammograms,” J. Digit. Imaging 20(3), 223–237 (2007).
[Crossref] [PubMed]

2005 (1)

J. M. Zook and K. M. Iftekharuddin, “Statistical analysis of fractal-based brain tumor detection algorithms,” Magn. Reson. Imaging 23(5), 671–678 (2005).
[Crossref] [PubMed]

2002 (1)

J. H. Brown, V. K. Gupta, B. L. Li, B. T. Milne, C. Restrepo, and G. B. West, “The fractal nature of nature: power laws, ecological complexity and biodiversity,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 357(1421), 619–626 (2002).
[Crossref] [PubMed]

2001 (1)

D. Chappard, A. Chennebault, M. Moreau, E. Legrand, M. Audran, and M. F. Basle, “Texture analysis of X-ray radiographs is a more reliable descriptor of bone loss than mineral content in a rat model of localized disuse induced by the Clostridium botulinum toxin,” Bone 28(1), 72–79 (2001).
[Crossref] [PubMed]

1999 (2)

S. B. Berman and T. G. Hastings, “Dopamine oxidation alters mitochondrial respiration and induces permeability transition in brain mitochondria: implications for Parkinson’s disease,” J. Neurochem. 73(3), 1127–1137 (1999).
[Crossref] [PubMed]

K. Foroutan-pour, P. Dutilleul, and D. L. Smith, “Advances in the implementation of the box-counting method of fractal dimension estimation,” Appl. Math. Comput. 105(2), 195–210 (1999).
[Crossref]

1996 (1)

J. W. Byng, N. F. Boyd, E. Fishell, R. A. Jong, and M. J. Yaffe, “Automated analysis of mammographic densities,” Phys. Med. Biol. 41(5), 909–923 (1996).
[Crossref] [PubMed]

1994 (1)

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

1990 (1)

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

1989 (1)

J. B. Bassingthwaighte, R. B. King, and S. A. Roger, “Fractal Nature of Regional Myocardial Blood Flow Heterogeneity,” Circ. Res. 65(3), 578–590 (1989).
[Crossref] [PubMed]

1984 (1)

S. Peleg, J. Naor, R. Hartley, and D. Avnir, “Multiple Resolution Texture Analysis and Classification,” IEEE Trans. Pattern Anal. Mach. Intell. 6(4), 518–523 (1984).
[Crossref] [PubMed]

Alhallak, K.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

Alonzo, C. A.

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

Audran, M.

D. Chappard, A. Chennebault, M. Moreau, E. Legrand, M. Audran, and M. F. Basle, “Texture analysis of X-ray radiographs is a more reliable descriptor of bone loss than mineral content in a rat model of localized disuse induced by the Clostridium botulinum toxin,” Bone 28(1), 72–79 (2001).
[Crossref] [PubMed]

Avnir, D.

S. Peleg, J. Naor, R. Hartley, and D. Avnir, “Multiple Resolution Texture Analysis and Classification,” IEEE Trans. Pattern Anal. Mach. Intell. 6(4), 518–523 (1984).
[Crossref] [PubMed]

Balu, M.

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

Basle, M. F.

D. Chappard, A. Chennebault, M. Moreau, E. Legrand, M. Audran, and M. F. Basle, “Texture analysis of X-ray radiographs is a more reliable descriptor of bone loss than mineral content in a rat model of localized disuse induced by the Clostridium botulinum toxin,” Bone 28(1), 72–79 (2001).
[Crossref] [PubMed]

Bassingthwaighte, J. B.

J. B. Bassingthwaighte, R. B. King, and S. A. Roger, “Fractal Nature of Regional Myocardial Blood Flow Heterogeneity,” Circ. Res. 65(3), 578–590 (1989).
[Crossref] [PubMed]

Benhamou, C. L.

R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
[Crossref] [PubMed]

Berman, S. B.

S. B. Berman and T. G. Hastings, “Dopamine oxidation alters mitochondrial respiration and induces permeability transition in brain mitochondria: implications for Parkinson’s disease,” J. Neurochem. 73(3), 1127–1137 (1999).
[Crossref] [PubMed]

Boyd, N. F.

J. W. Byng, N. F. Boyd, E. Fishell, R. A. Jong, and M. J. Yaffe, “Automated analysis of mammographic densities,” Phys. Med. Biol. 41(5), 909–923 (1996).
[Crossref] [PubMed]

Bretteil, S.

R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
[Crossref] [PubMed]

Brown, J. H.

J. H. Brown, V. K. Gupta, B. L. Li, B. T. Milne, C. Restrepo, and G. B. West, “The fractal nature of nature: power laws, ecological complexity and biodiversity,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 357(1421), 619–626 (2002).
[Crossref] [PubMed]

Byng, J. W.

J. W. Byng, N. F. Boyd, E. Fishell, R. A. Jong, and M. J. Yaffe, “Automated analysis of mammographic densities,” Phys. Med. Biol. 41(5), 909–923 (1996).
[Crossref] [PubMed]

Caldwell, C. B.

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

Cascio, M.

A. A. Dukes, V. S. Van Laar, M. Cascio, and T. G. Hastings, “Changes in endoplasmic reticulum stress proteins and aldolase A in cells exposed to dopamine,” J. Neurochem. 106(1), 333–346 (2008).
[Crossref] [PubMed]

Chappard, D.

D. Chappard, A. Chennebault, M. Moreau, E. Legrand, M. Audran, and M. F. Basle, “Texture analysis of X-ray radiographs is a more reliable descriptor of bone loss than mineral content in a rat model of localized disuse induced by the Clostridium botulinum toxin,” Bone 28(1), 72–79 (2001).
[Crossref] [PubMed]

Chennebault, A.

D. Chappard, A. Chennebault, M. Moreau, E. Legrand, M. Audran, and M. F. Basle, “Texture analysis of X-ray radiographs is a more reliable descriptor of bone loss than mineral content in a rat model of localized disuse induced by the Clostridium botulinum toxin,” Bone 28(1), 72–79 (2001).
[Crossref] [PubMed]

Clark, R. A.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Clarke, L. P.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Cooke, G.

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

Dings, R. P. M.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

Du, Q.

J. Li, Q. Du, and C. Sun, “An improved box-counting method for image fractal dimension estimation,” Pattern Recognit. 42(11), 2460–2469 (2009).
[Crossref]

Dukes, A. A.

A. A. Dukes, V. S. Van Laar, M. Cascio, and T. G. Hastings, “Changes in endoplasmic reticulum stress proteins and aldolase A in cells exposed to dopamine,” J. Neurochem. 106(1), 333–346 (2008).
[Crossref] [PubMed]

Dutilleul, P.

K. Foroutan-pour, P. Dutilleul, and D. L. Smith, “Advances in the implementation of the box-counting method of fractal dimension estimation,” Appl. Math. Comput. 105(2), 195–210 (1999).
[Crossref]

Estrade, A.

R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
[Crossref] [PubMed]

Filadi, R.

D. Pendin, R. Filadi, and P. Pizzo, “The Concerted Action of Mitochondrial Dynamics and Positioning: New Characters in Cancer Onset and Progression,” Front. Oncol. 7(102), 102 (2017).
[Crossref] [PubMed]

Fishell, E.

J. W. Byng, N. F. Boyd, E. Fishell, R. A. Jong, and M. J. Yaffe, “Automated analysis of mammographic densities,” Phys. Med. Biol. 41(5), 909–923 (1996).
[Crossref] [PubMed]

Foroutan-pour, K.

K. Foroutan-pour, P. Dutilleul, and D. L. Smith, “Advances in the implementation of the box-counting method of fractal dimension estimation,” Appl. Math. Comput. 105(2), 195–210 (1999).
[Crossref]

Garcia-Moliner, M. L.

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

Georgakoudi, I.

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
[Crossref] [PubMed]

D. H. MacDonald, M. Hunter, K. P. Quinn, and I. Georgakoudi, “Autocorrelation method for fractal analysis in nonrectangular image domains,” Opt. Lett. 38(21), 4477–4479 (2013).
[Crossref] [PubMed]

J. Xylas, K. P. Quinn, M. Hunter, and I. Georgakoudi, “Improved Fourier-based characterization of intracellular fractal features,” Opt. Express 20(21), 23442–23455 (2012).
[Crossref] [PubMed]

I. Georgakoudi and K. P. Quinn, “Optical Imaging Using Endogenous Contrast to Assess Metabolic State,” Annu. Rev. Biomed. Eng. 14(1), 351–367 (2012).
[Crossref] [PubMed]

Greene, N. P.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

Griffin, R. J.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

Gupta, V. K.

J. H. Brown, V. K. Gupta, B. L. Li, B. T. Milne, C. Restrepo, and G. B. West, “The fractal nature of nature: power laws, ecological complexity and biodiversity,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 357(1421), 619–626 (2002).
[Crossref] [PubMed]

Harba, R.

R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
[Crossref] [PubMed]

Harris, R. M.

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

Hartley, R.

S. Peleg, J. Naor, R. Hartley, and D. Avnir, “Multiple Resolution Texture Analysis and Classification,” IEEE Trans. Pattern Anal. Mach. Intell. 6(4), 518–523 (1984).
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A. A. Dukes, V. S. Van Laar, M. Cascio, and T. G. Hastings, “Changes in endoplasmic reticulum stress proteins and aldolase A in cells exposed to dopamine,” J. Neurochem. 106(1), 333–346 (2008).
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S. B. Berman and T. G. Hastings, “Dopamine oxidation alters mitochondrial respiration and induces permeability transition in brain mitochondria: implications for Parkinson’s disease,” J. Neurochem. 73(3), 1127–1137 (1999).
[Crossref] [PubMed]

Hayden, R. S.

K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
[Crossref] [PubMed]

Holdsworth, D. W.

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

House, M.

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

Hsu, W. Y.

W. Y. Hsu, C. C. Lin, M. S. Ju, and Y. N. Sun, “Wavelet-based fractal features with active segment selection: application to single-trial EEG data,” J. Neurosci. Methods 163(1), 145–160 (2007).
[Crossref] [PubMed]

Hunter, M.

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

D. H. MacDonald, M. Hunter, K. P. Quinn, and I. Georgakoudi, “Autocorrelation method for fractal analysis in nonrectangular image domains,” Opt. Lett. 38(21), 4477–4479 (2013).
[Crossref] [PubMed]

J. Xylas, K. P. Quinn, M. Hunter, and I. Georgakoudi, “Improved Fourier-based characterization of intracellular fractal features,” Opt. Express 20(21), 23442–23455 (2012).
[Crossref] [PubMed]

Iftekharuddin, K. M.

J. M. Zook and K. M. Iftekharuddin, “Statistical analysis of fractal-based brain tumor detection algorithms,” Magn. Reson. Imaging 23(5), 671–678 (2005).
[Crossref] [PubMed]

Jenkins, S. V.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

Jennane, R.

R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
[Crossref] [PubMed]

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J. W. Byng, N. F. Boyd, E. Fishell, R. A. Jong, and M. J. Yaffe, “Automated analysis of mammographic densities,” Phys. Med. Biol. 41(5), 909–923 (1996).
[Crossref] [PubMed]

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

Ju, M. S.

W. Y. Hsu, C. C. Lin, M. S. Ju, and Y. N. Sun, “Wavelet-based fractal features with active segment selection: application to single-trial EEG data,” J. Neurosci. Methods 163(1), 145–160 (2007).
[Crossref] [PubMed]

Kallergi, M.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Kaplan, D. L.

K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
[Crossref] [PubMed]

Karaliota, S.

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

Karalis, K. P.

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

Kelly, K. M.

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

King, R. B.

J. B. Bassingthwaighte, R. B. King, and S. A. Roger, “Fractal Nature of Regional Myocardial Blood Flow Heterogeneity,” Circ. Res. 65(3), 578–590 (1989).
[Crossref] [PubMed]

Kolenc, O. I.

O. I. Kolenc and K. P. Quinn, “Evaluating Cell Metabolism Through Autofluorescence Imaging of NAD(P)H and FAD,” Antioxid. Redox Signal. 2018, 20177451 (2018).
[Crossref] [PubMed]

Lee, D. E.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

Lee, K.

K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
[Crossref] [PubMed]

Legrand, E.

D. Chappard, A. Chennebault, M. Moreau, E. Legrand, M. Audran, and M. F. Basle, “Texture analysis of X-ray radiographs is a more reliable descriptor of bone loss than mineral content in a rat model of localized disuse induced by the Clostridium botulinum toxin,” Bone 28(1), 72–79 (2001).
[Crossref] [PubMed]

Lemineur, G.

R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
[Crossref] [PubMed]

Li, B. L.

J. H. Brown, V. K. Gupta, B. L. Li, B. T. Milne, C. Restrepo, and G. B. West, “The fractal nature of nature: power laws, ecological complexity and biodiversity,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 357(1421), 619–626 (2002).
[Crossref] [PubMed]

Li, J.

J. Li, Q. Du, and C. Sun, “An improved box-counting method for image fractal dimension estimation,” Pattern Recognit. 42(11), 2460–2469 (2009).
[Crossref]

Lin, C. C.

W. Y. Hsu, C. C. Lin, M. S. Ju, and Y. N. Sun, “Wavelet-based fractal features with active segment selection: application to single-trial EEG data,” J. Neurosci. Methods 163(1), 145–160 (2007).
[Crossref] [PubMed]

Liu, Z.

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

Lorey, R. A.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

MacDonald, D. H.

McLaughlin-Drubin, M. E.

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

Milne, B. T.

J. H. Brown, V. K. Gupta, B. L. Li, B. T. Milne, C. Restrepo, and G. B. West, “The fractal nature of nature: power laws, ecological complexity and biodiversity,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 357(1421), 619–626 (2002).
[Crossref] [PubMed]

Moreau, M.

D. Chappard, A. Chennebault, M. Moreau, E. Legrand, M. Audran, and M. F. Basle, “Texture analysis of X-ray radiographs is a more reliable descriptor of bone loss than mineral content in a rat model of localized disuse induced by the Clostridium botulinum toxin,” Bone 28(1), 72–79 (2001).
[Crossref] [PubMed]

Munger, K.

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

Münger, K.

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

Naor, J.

S. Peleg, J. Naor, R. Hartley, and D. Avnir, “Multiple Resolution Texture Analysis and Classification,” IEEE Trans. Pattern Anal. Mach. Intell. 6(4), 518–523 (1984).
[Crossref] [PubMed]

Nguyen, T. M.

R. M. Rangayyan and T. M. Nguyen, “Fractal Analysis of Contours of Breast Masses in Mammograms,” J. Digit. Imaging 20(3), 223–237 (2007).
[Crossref] [PubMed]

Paskaš, M. P.

M. P. Paskaš, I. S. Reljin, and B. D. Reljin, “Multifractal Framework Based on Blanket Method,” The Scientific World Journal 2015, 894546 (2015)

Peleg, S.

S. Peleg, J. Naor, R. Hartley, and D. Avnir, “Multiple Resolution Texture Analysis and Classification,” IEEE Trans. Pattern Anal. Mach. Intell. 6(4), 518–523 (1984).
[Crossref] [PubMed]

Pendin, D.

D. Pendin, R. Filadi, and P. Pizzo, “The Concerted Action of Mitochondrial Dynamics and Positioning: New Characters in Cancer Onset and Progression,” Front. Oncol. 7(102), 102 (2017).
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Pizzo, P.

D. Pendin, R. Filadi, and P. Pizzo, “The Concerted Action of Mitochondrial Dynamics and Positioning: New Characters in Cancer Onset and Progression,” Front. Oncol. 7(102), 102 (2017).
[Crossref] [PubMed]

Poston, W. L.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Pouli, D.

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

Priebe, C. E.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Qian, W.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Quinn, K. P.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

O. I. Kolenc and K. P. Quinn, “Evaluating Cell Metabolism Through Autofluorescence Imaging of NAD(P)H and FAD,” Antioxid. Redox Signal. 2018, 20177451 (2018).
[Crossref] [PubMed]

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
[Crossref] [PubMed]

D. H. MacDonald, M. Hunter, K. P. Quinn, and I. Georgakoudi, “Autocorrelation method for fractal analysis in nonrectangular image domains,” Opt. Lett. 38(21), 4477–4479 (2013).
[Crossref] [PubMed]

J. Xylas, K. P. Quinn, M. Hunter, and I. Georgakoudi, “Improved Fourier-based characterization of intracellular fractal features,” Opt. Express 20(21), 23442–23455 (2012).
[Crossref] [PubMed]

I. Georgakoudi and K. P. Quinn, “Optical Imaging Using Endogenous Contrast to Assess Metabolic State,” Annu. Rev. Biomed. Eng. 14(1), 351–367 (2012).
[Crossref] [PubMed]

Rajaram, N.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

Rangayyan, R. M.

R. M. Rangayyan and T. M. Nguyen, “Fractal Analysis of Contours of Breast Masses in Mammograms,” J. Digit. Imaging 20(3), 223–237 (2007).
[Crossref] [PubMed]

Reljin, B. D.

M. P. Paskaš, I. S. Reljin, and B. D. Reljin, “Multifractal Framework Based on Blanket Method,” The Scientific World Journal 2015, 894546 (2015)

Reljin, I. S.

M. P. Paskaš, I. S. Reljin, and B. D. Reljin, “Multifractal Framework Based on Blanket Method,” The Scientific World Journal 2015, 894546 (2015)

Restrepo, C.

J. H. Brown, V. K. Gupta, B. L. Li, B. T. Milne, C. Restrepo, and G. B. West, “The fractal nature of nature: power laws, ecological complexity and biodiversity,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 357(1421), 619–626 (2002).
[Crossref] [PubMed]

Rius-Diaz, F.

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

Roger, S. A.

J. B. Bassingthwaighte, R. B. King, and S. A. Roger, “Fractal Nature of Regional Myocardial Blood Flow Heterogeneity,” Circ. Res. 65(3), 578–590 (1989).
[Crossref] [PubMed]

Rogers, G. W.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Smith, D. L.

K. Foroutan-pour, P. Dutilleul, and D. L. Smith, “Advances in the implementation of the box-counting method of fractal dimension estimation,” Appl. Math. Comput. 105(2), 195–210 (1999).
[Crossref]

Solka, J. L.

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Sridharan, G. V.

K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
[Crossref] [PubMed]

Stapleton, S. J.

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

Sun, C.

J. Li, Q. Du, and C. Sun, “An improved box-counting method for image fractal dimension estimation,” Pattern Recognit. 42(11), 2460–2469 (2009).
[Crossref]

Sun, Y. N.

W. Y. Hsu, C. C. Lin, M. S. Ju, and Y. N. Sun, “Wavelet-based fractal features with active segment selection: application to single-trial EEG data,” J. Neurosci. Methods 163(1), 145–160 (2007).
[Crossref] [PubMed]

Thieu, H. T.

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

Tromberg, B. J.

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

Van Laar, V. S.

A. A. Dukes, V. S. Van Laar, M. Cascio, and T. G. Hastings, “Changes in endoplasmic reticulum stress proteins and aldolase A in cells exposed to dopamine,” J. Neurochem. 106(1), 333–346 (2008).
[Crossref] [PubMed]

Vargas, I.

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

Varone, A.

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

Weiser, W. J.

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

West, G. B.

J. H. Brown, V. K. Gupta, B. L. Li, B. T. Milne, C. Restrepo, and G. B. West, “The fractal nature of nature: power laws, ecological complexity and biodiversity,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 357(1421), 619–626 (2002).
[Crossref] [PubMed]

Xylas, J.

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

J. Xylas, K. P. Quinn, M. Hunter, and I. Georgakoudi, “Improved Fourier-based characterization of intracellular fractal features,” Opt. Express 20(21), 23442–23455 (2012).
[Crossref] [PubMed]

Yaffe, M. J.

J. W. Byng, N. F. Boyd, E. Fishell, R. A. Jong, and M. J. Yaffe, “Automated analysis of mammographic densities,” Phys. Med. Biol. 41(5), 909–923 (1996).
[Crossref] [PubMed]

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

Zook, J. M.

J. M. Zook and K. M. Iftekharuddin, “Statistical analysis of fractal-based brain tumor detection algorithms,” Magn. Reson. Imaging 23(5), 671–678 (2005).
[Crossref] [PubMed]

Annu. Rev. Biomed. Eng. (1)

I. Georgakoudi and K. P. Quinn, “Optical Imaging Using Endogenous Contrast to Assess Metabolic State,” Annu. Rev. Biomed. Eng. 14(1), 351–367 (2012).
[Crossref] [PubMed]

Antioxid. Redox Signal. (1)

O. I. Kolenc and K. P. Quinn, “Evaluating Cell Metabolism Through Autofluorescence Imaging of NAD(P)H and FAD,” Antioxid. Redox Signal. 2018, 20177451 (2018).
[Crossref] [PubMed]

Appl. Math. Comput. (1)

K. Foroutan-pour, P. Dutilleul, and D. L. Smith, “Advances in the implementation of the box-counting method of fractal dimension estimation,” Appl. Math. Comput. 105(2), 195–210 (1999).
[Crossref]

Bone (1)

D. Chappard, A. Chennebault, M. Moreau, E. Legrand, M. Audran, and M. F. Basle, “Texture analysis of X-ray radiographs is a more reliable descriptor of bone loss than mineral content in a rat model of localized disuse induced by the Clostridium botulinum toxin,” Bone 28(1), 72–79 (2001).
[Crossref] [PubMed]

Cancer Lett. (1)

C. E. Priebe, J. L. Solka, R. A. Lorey, G. W. Rogers, W. L. Poston, M. Kallergi, W. Qian, L. P. Clarke, and R. A. Clark, “The application of fractal analysis to mammographic tissue classification,” Cancer Lett. 77(2-3), 183–189 (1994).
[Crossref] [PubMed]

Circ. Res. (1)

J. B. Bassingthwaighte, R. B. King, and S. A. Roger, “Fractal Nature of Regional Myocardial Blood Flow Heterogeneity,” Circ. Res. 65(3), 578–590 (1989).
[Crossref] [PubMed]

Front. Oncol. (1)

D. Pendin, R. Filadi, and P. Pizzo, “The Concerted Action of Mitochondrial Dynamics and Positioning: New Characters in Cancer Onset and Progression,” Front. Oncol. 7(102), 102 (2017).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Peleg, J. Naor, R. Hartley, and D. Avnir, “Multiple Resolution Texture Analysis and Classification,” IEEE Trans. Pattern Anal. Mach. Intell. 6(4), 518–523 (1984).
[Crossref] [PubMed]

Int. J. Cancer (1)

J. Xylas, A. Varone, K. P. Quinn, D. Pouli, M. E. McLaughlin-Drubin, H. T. Thieu, M. L. Garcia-Moliner, M. House, M. Hunter, K. Munger, and I. Georgakoudi, “Noninvasive assessment of mitochondrial organization in three-dimensional tissues reveals changes associated with cancer development,” Int. J. Cancer 136(2), 322–332 (2015).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

K. Alhallak, S. V. Jenkins, D. E. Lee, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “Optical imaging of radiation-induced metabolic changes in radiation-sensitive and resistant cancer cells,” J. Biomed. Opt. 22(6), 060502 (2017).
[Crossref] [PubMed]

J. Digit. Imaging (1)

R. M. Rangayyan and T. M. Nguyen, “Fractal Analysis of Contours of Breast Masses in Mammograms,” J. Digit. Imaging 20(3), 223–237 (2007).
[Crossref] [PubMed]

J. Neurochem. (2)

A. A. Dukes, V. S. Van Laar, M. Cascio, and T. G. Hastings, “Changes in endoplasmic reticulum stress proteins and aldolase A in cells exposed to dopamine,” J. Neurochem. 106(1), 333–346 (2008).
[Crossref] [PubMed]

S. B. Berman and T. G. Hastings, “Dopamine oxidation alters mitochondrial respiration and induces permeability transition in brain mitochondria: implications for Parkinson’s disease,” J. Neurochem. 73(3), 1127–1137 (1999).
[Crossref] [PubMed]

J. Neurosci. Methods (1)

W. Y. Hsu, C. C. Lin, M. S. Ju, and Y. N. Sun, “Wavelet-based fractal features with active segment selection: application to single-trial EEG data,” J. Neurosci. Methods 163(1), 145–160 (2007).
[Crossref] [PubMed]

Magn. Reson. Imaging (1)

J. M. Zook and K. M. Iftekharuddin, “Statistical analysis of fractal-based brain tumor detection algorithms,” Magn. Reson. Imaging 23(5), 671–678 (2005).
[Crossref] [PubMed]

Med. Image Anal. (1)

R. Jennane, R. Harba, G. Lemineur, S. Bretteil, A. Estrade, and C. L. Benhamou, “Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection,” Med. Image Anal. 11(1), 91–98 (2007).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Pattern Recognit. (1)

J. Li, Q. Du, and C. Sun, “An improved box-counting method for image fractal dimension estimation,” Pattern Recognit. 42(11), 2460–2469 (2009).
[Crossref]

Philos. Trans. R. Soc. Lond. B Biol. Sci. (1)

J. H. Brown, V. K. Gupta, B. L. Li, B. T. Milne, C. Restrepo, and G. B. West, “The fractal nature of nature: power laws, ecological complexity and biodiversity,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 357(1421), 619–626 (2002).
[Crossref] [PubMed]

Phys. Med. Biol. (2)

C. B. Caldwell, S. J. Stapleton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35(2), 235–247 (1990).
[Crossref] [PubMed]

J. W. Byng, N. F. Boyd, E. Fishell, R. A. Jong, and M. J. Yaffe, “Automated analysis of mammographic densities,” Phys. Med. Biol. 41(5), 909–923 (1996).
[Crossref] [PubMed]

Sci. Adv. (1)

Z. Liu, D. Pouli, C. A. Alonzo, A. Varone, S. Karaliota, K. P. Quinn, K. Münger, K. P. Karalis, and I. Georgakoudi, “Mapping metabolic changes by noninvasive, multiparametric, high-resolution imaging using endogenous contrast,” Sci. Adv. 4(3), eap9302 (2018).
[Crossref] [PubMed]

Sci. Rep. (2)

K. P. Quinn, G. V. Sridharan, R. S. Hayden, D. L. Kaplan, K. Lee, and I. Georgakoudi, “Quantitative metabolic imaging using endogenous fluorescence to detect stem cell differentiation,” Sci. Rep. 3(3432), 3432 (2013).
[Crossref] [PubMed]

D. E. Lee, K. Alhallak, S. V. Jenkins, I. Vargas, N. P. Greene, K. P. Quinn, R. J. Griffin, R. P. M. Dings, and N. Rajaram, “A Radiosensitizing Inhibitor of HIF-1 alters the Optical Redox State of Human Lung Cancer Cells In Vitro,” Sci. Rep. 8(1), 8815 (2018).
[Crossref] [PubMed]

Sci. Transl. Med. (1)

D. Pouli, M. Balu, C. A. Alonzo, Z. Liu, K. P. Quinn, F. Rius-Diaz, R. M. Harris, K. M. Kelly, B. J. Tromberg, and I. Georgakoudi, “Imaging mitochondrial dynamics in human skin reveals depth-dependent hypoxia and malignant potential for diagnosis,” Sci. Transl. Med. 8(367), 367ra169 (2016).
[Crossref] [PubMed]

The Scientific World Journal (1)

M. P. Paskaš, I. S. Reljin, and B. D. Reljin, “Multifractal Framework Based on Blanket Method,” The Scientific World Journal 2015, 894546 (2015)

Other (2)

T. M. Cabral and R. M. Rangayyan, Fractal Analysis of Breast Masses in Mammograms (Morgan & Claypool Publishers, 2012).

F. Bartolomé and A. Y. Abramov, “Measurement of mitochondrial NADH and FAD Autofluorescence in Live Cells,” in Mitochondrial Medicine Methods in Molecular Biology, V. Weissig and M. Edeas, eds. (Humana Press, 2015).

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Figures (5)

Fig. 1
Fig. 1 Steps of the Modified Blanket Method. (a) Resize the image of interest and a disk kernel. (b) Compute the horizontal (x) and vertical (y) gradients of the image. (c) Convolve the absolute value of each gradient image with a disk kernel to sum up local changes in intensity. (d) Compute the sum of the convolved x- and y- gradient images to create a surface area (SA) map. (e) Resize the SA map to the original image size, and record SA at each pixel. (f) Repeat steps (a)-(e) at different image resolutions (i.e. pixel sizes) to produce a set of SA maps. (g) Compute the FD from the power law exponent of the local surface area vs. pixel size curve at each pixel. (h) Assign the corresponding FD value to each pixel to produce a FD map.
Fig. 2
Fig. 2 Modified Blanket Method Simulation. (A) Effect of utilizing convolution and erosion radii (CR & ER) of equal size in the measured fractal dimension of cells with a diameter of 120 pixels. The black line represents the true FD. (B) Effect of utilizing convolution and erosion radii of varied size in the measured fractal dimension. Red lines represent CR = 5, Blue lines represent CR = 10. Erosion radius is set to ER = 0, 5, or 10. (C) Percentage error of the analysis with equal convolution and erosion radii size. (D) Percentage error of the analysis with varied convolution and erosion radii size. (E) Representative FD maps with a true FD value of 3.5 show the edge effects produced by cell boundaries when cell mask erosion is not applied prior to computing the average FD value.
Fig. 3
Fig. 3 Comparison of the accuracy of the MBM and PSD analysis of simulated images (120 pixel diameter cells). (A) The MBM (red) is accurate over a larger range of FD values than PSD analysis (blue). (B) Mean error in PSD analysis is significantly higher when FD < 2.75. (C) Representative FD maps of cells with FD of 2.5 and 3.5 demonstrate the accuracy of the MBM. (D) Representative clone-stamped images and PSD curves indicate the PSD is less accurate for smaller FD values.
Fig. 4
Fig. 4 Average time required to compute FD through the MBM and PSD analysis on simulated circular cells images for increasing image resolutions of 128 x 128, 256 x 256, 512 x 512, 1024 x 1024, 2048 x 2048, and 4096 x 4096 pixels. An increase in CR from 5 to 25 results in a modest increase in computational time.
Fig. 5
Fig. 5 Lung Cancer Cells Study (A) Representative FD maps corresponding to lung cancer cells of both the control (left) and radiation-resistant (right) group. Top row shows FD maps without erosion and bottom row shows FD maps with erosion. The images were obtained at time periods of 1 and 24 hours post radiation. (B) Clone stamped images obtained during the PSD analysis at time periods of 1 and 24 hours as shown in panel (A). (C) Summary data demonstrate that the differences of eroding and not eroding the cell objects with the MBM approach are minimal. The MBM method detects significant temporal changes in the mitochondrial organization of radiation resistant cell line at 24 hours, which matches independent measurements of the optical redox ratio of FAD/(NADH + FAD) autofluorescence intensities detailed in [23,24]. Interestingly, the PSD approach does not reveal the temporal changes detected using the optical redox ratio and MBM.

Equations (3)

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R( k )=A ( k ) β
FD=2 Δlog(SA) Δlog(pixelsize) =2β
FD= (8β) 2