Abstract

A novel Fourier-based image analysis method for measuring fractal features is presented which can significantly reduce artifacts due to non-fractal edge effects. The technique is broadly applicable to the quantitative characterization of internal morphology (texture) of image features with well-defined borders. In this study, we explore the capacity of this method for quantitative assessment of intracellular fractal morphology of mitochondrial networks in images of normal and diseased (precancerous) epithelial tissues. Using a combination of simulated fractal images and endogenous two-photon excited fluorescence (TPEF) microscopy, our method is shown to more accurately characterize the exponent of the high-frequency power spectral density (PSD) of these images in the presence of artifacts that arise due to cellular and nuclear borders.

© 2012 OSA

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2012 (1)

K. P. Quinn, E. Bellas, N. Fourligas, K. Lee, D. L. Kaplan, and I. Georgakoudi, “Characterization of metabolic changes associated with the functional development of 3D engineered tissues by non-invasive, dynamic measurement of individual cell redox ratios,” Biomaterials 33(21), 5341–5348 (2012).
[CrossRef] [PubMed]

2011 (3)

J. M. Levitt, M. E. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Automated biochemical, morphological, and organizational assessment of precancerous changes from endogenous two-photon fluorescence images,” PLoS ONE 6(9), e24765 (2011).
[CrossRef] [PubMed]

H. Gothwal, S. Kedawat, and R. Kumar, “Cardiac arrhythmias detection in an ECG beat signal using fast Fourier transform and artificial neural network,” J. Biomed. Sci. Eng. 4(04), 289–296 (2011).
[CrossRef]

A. C. Sullivan, J. P. Hunt, and A. L. Oldenburg, “Fractal analysis for classification of breast carcinoma in optical coherence tomography,” J. Biomed. Opt. 16(6), 066010 (2011).
[CrossRef] [PubMed]

2010 (2)

2009 (3)

R. Lopes and N. Betrouni, “Fractal and multifractal analysis: A review,” Med. Image Anal. 13(4), 634–649 (2009).
[CrossRef] [PubMed]

J. D. Rogers, I. R. Capo?lu, and V. Backman, “Nonscalar elastic light scattering from continuous random media in the Born approximation,” Opt. Lett. 34(12), 1891–1893 (2009).
[CrossRef] [PubMed]

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res. 69(3), 1199–1204 (2009).
[CrossRef] [PubMed]

2008 (1)

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

2007 (2)

J. M. Levitt, M. Hunter, C. Mujat, M. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Diagnostic cellular organization features extracted from autofluorescence images,” Opt. Lett. 32(22), 3305–3307 (2007).
[CrossRef] [PubMed]

K. Doi, “Computer-aided diagnosis in medical imaging: historical review, current status and future potential,” Comput. Med. Imaging Graph. 31(4-5), 198–211 (2007).
[CrossRef] [PubMed]

2006 (2)

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and B. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt. 11(6), 064007 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

R. Rossignol, R. Gilkerson, R. Aggeler, K. Yamagata, S. J. Remington, and R. A. Capaldi, “Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells,” Cancer Res. 64(3), 985–993 (2004).
[CrossRef] [PubMed]

2003 (1)

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

2002 (1)

D. L. Turcotte, “Fractals in petrology,” Lithos 65(3-4), 261–271 (2002).
[CrossRef]

2001 (2)

G. Dougherty and G. M. Henebry, “Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images,” Med. Eng. Phys. 23(6), 369–380 (2001).
[CrossRef] [PubMed]

M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18(4), 948–960 (2001).
[CrossRef] [PubMed]

1998 (1)

A. J. Einstein, H. S. Wu, and J. Gil, “Self-Affinity and lacunarity of chromatin texture in benign and malignant breast epithelial cell nuclei,” Phys. Rev. Lett. 80(2), 397–400 (1998).
[CrossRef]

1997 (2)

T. H. Wilson, “Fractal strain distribution and its implications for cross section balancing: further discussion,” J. Struct. Geol. 19(1), 129–132 (1997).
[CrossRef]

C. Meyers, T. J. Mayer, and M. A. Ozbun, “Synthesis of infectious human papillomavirus type 18 in differentiating epithelium transfected with viral DNA,” J. Virol. 71(10), 7381–7386 (1997).
[PubMed]

1996 (1)

1995 (1)

Y. Gazit, D. A. Berk, M. Leunig, L. T. Baxter, and R. K. Jain, “Scale-invariant behavior and vascular network formation in normal and tumor tissue,” Phys. Rev. Lett. 75(12), 2428–2431 (1995).
[CrossRef] [PubMed]

1993 (1)

H. S. Wu, “Fractal strain distribution and its implications for cross section balancing,” J. Struct. Geol. 15(12), 1497–1507 (1993).
[CrossRef]

1991 (1)

F. Normant and C. Tricot, “Method for evaluating the fractal dimension of curves using convex hulls,” Phys. Rev. A 43(12), 6518–6525 (1991).
[CrossRef] [PubMed]

1978 (1)

F. I. Harris, “On the use of windows for harmonic analysis with discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[CrossRef]

1971 (1)

C. R. Hackenbrock, “Ultrastructural bases for metabolically linked mechanical activity in mitochondria. I. Reversible ultrastructural changes with change in metabolic steady state in isolated liver mitochondria,” J. Cell Biol. 51, 123–137 (1971).

1968 (1)

C. R. Hackenbrock, “Ultrastructural bases for metabolically linked mechanical activity in mitochondria. II. Electron transport-linked ultrastructural transformations in mitochondria,” J. Cell Biol. 37(2), 345–369 (1968).
[CrossRef] [PubMed]

1966 (1)

C. R. Hackenbrock, T. G. Rehn, E. C. Weinbach, and J. J. Lemasters, “Oxidative phosphorylation and ultrastructural transformation in mitochondria in the intact ascites tumor cell,” J. Cell Biol. 30, 269–297 (1966).
[CrossRef] [PubMed]

1962 (1)

B. Chance, P. Cohen, F. Jobsis, and B. Schoener, “Intracellular oxidation-reduction states in vivo,” Science 137(3529), 499–508 (1962).
[CrossRef] [PubMed]

1927 (1)

O. Warburg, F. Wind, and E. Negelein, “The metabolism of tumor in the body,” J. Gen. Physiol. 8(6), 519–530 (1927).
[CrossRef] [PubMed]

Abou-Sleiman, P.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Aggeler, R.

R. Rossignol, R. Gilkerson, R. Aggeler, K. Yamagata, S. J. Remington, and R. A. Capaldi, “Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells,” Cancer Res. 64(3), 985–993 (2004).
[CrossRef] [PubMed]

Alfano, R. R.

Alt-Holland, A.

Backman, V.

J. D. Rogers, I. R. Capo?lu, and V. Backman, “Nonscalar elastic light scattering from continuous random media in the Born approximation,” Opt. Lett. 34(12), 1891–1893 (2009).
[CrossRef] [PubMed]

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Badizadegan, K.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Bandmann, O.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Bartek, M.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and B. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt. 11(6), 064007 (2006).
[CrossRef] [PubMed]

Baxter, L. T.

Y. Gazit, D. A. Berk, M. Leunig, L. T. Baxter, and R. K. Jain, “Scale-invariant behavior and vascular network formation in normal and tumor tissue,” Phys. Rev. Lett. 75(12), 2428–2431 (1995).
[CrossRef] [PubMed]

Bellas, E.

K. P. Quinn, E. Bellas, N. Fourligas, K. Lee, D. L. Kaplan, and I. Georgakoudi, “Characterization of metabolic changes associated with the functional development of 3D engineered tissues by non-invasive, dynamic measurement of individual cell redox ratios,” Biomaterials 33(21), 5341–5348 (2012).
[CrossRef] [PubMed]

Berk, D. A.

Y. Gazit, D. A. Berk, M. Leunig, L. T. Baxter, and R. K. Jain, “Scale-invariant behavior and vascular network formation in normal and tumor tissue,” Phys. Rev. Lett. 75(12), 2428–2431 (1995).
[CrossRef] [PubMed]

Betrouni, N.

R. Lopes and N. Betrouni, “Fractal and multifractal analysis: A review,” Med. Image Anal. 13(4), 634–649 (2009).
[CrossRef] [PubMed]

Boone, C. W.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Capaldi, R. A.

R. Rossignol, R. Gilkerson, R. Aggeler, K. Yamagata, S. J. Remington, and R. A. Capaldi, “Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells,” Cancer Res. 64(3), 985–993 (2004).
[CrossRef] [PubMed]

Capoglu, I. R.

Chalut, K. J.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res. 69(3), 1199–1204 (2009).
[CrossRef] [PubMed]

Chance, B.

B. Chance, P. Cohen, F. Jobsis, and B. Schoener, “Intracellular oxidation-reduction states in vivo,” Science 137(3529), 499–508 (1962).
[CrossRef] [PubMed]

Christie, R.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Cohen, P.

B. Chance, P. Cohen, F. Jobsis, and B. Schoener, “Intracellular oxidation-reduction states in vivo,” Science 137(3529), 499–508 (1962).
[CrossRef] [PubMed]

Cookson, M. R.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Doi, K.

K. Doi, “Computer-aided diagnosis in medical imaging: historical review, current status and future potential,” Comput. Med. Imaging Graph. 31(4-5), 198–211 (2007).
[CrossRef] [PubMed]

Dougherty, G.

G. Dougherty and G. M. Henebry, “Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images,” Med. Eng. Phys. 23(6), 369–380 (2001).
[CrossRef] [PubMed]

Einstein, A. J.

A. J. Einstein, H. S. Wu, and J. Gil, “Self-Affinity and lacunarity of chromatin texture in benign and malignant breast epithelial cell nuclei,” Phys. Rev. Lett. 80(2), 397–400 (1998).
[CrossRef]

Feld, M. S.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Fourligas, N.

K. P. Quinn, E. Bellas, N. Fourligas, K. Lee, D. L. Kaplan, and I. Georgakoudi, “Characterization of metabolic changes associated with the functional development of 3D engineered tissues by non-invasive, dynamic measurement of individual cell redox ratios,” Biomaterials 33(21), 5341–5348 (2012).
[CrossRef] [PubMed]

Garlick, J.

Gazit, Y.

Y. Gazit, D. A. Berk, M. Leunig, L. T. Baxter, and R. K. Jain, “Scale-invariant behavior and vascular network formation in normal and tumor tissue,” Phys. Rev. Lett. 75(12), 2428–2431 (1995).
[CrossRef] [PubMed]

Georgakoudi, I.

K. P. Quinn, E. Bellas, N. Fourligas, K. Lee, D. L. Kaplan, and I. Georgakoudi, “Characterization of metabolic changes associated with the functional development of 3D engineered tissues by non-invasive, dynamic measurement of individual cell redox ratios,” Biomaterials 33(21), 5341–5348 (2012).
[CrossRef] [PubMed]

J. M. Levitt, M. E. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Automated biochemical, morphological, and organizational assessment of precancerous changes from endogenous two-photon fluorescence images,” PLoS ONE 6(9), e24765 (2011).
[CrossRef] [PubMed]

J. Xylas, A. Alt-Holland, J. Garlick, M. Hunter, and I. Georgakoudi, “Intrinsic optical biomarkers associated with the invasive potential of tumor cells in engineered tissue models,” Biomed. Opt. Express 1(5), 1387–1400 (2010).
[CrossRef] [PubMed]

W. L. Rice, D. L. Kaplan, and I. Georgakoudi, “Two-photon microscopy for non-invasive, quantitative monitoring of stem cell differentiation,” PLoS ONE 5(4), e10075 (2010).
[CrossRef] [PubMed]

J. M. Levitt, M. Hunter, C. Mujat, M. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Diagnostic cellular organization features extracted from autofluorescence images,” Opt. Lett. 32(22), 3305–3307 (2007).
[CrossRef] [PubMed]

Giacomelli, M. G.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res. 69(3), 1199–1204 (2009).
[CrossRef] [PubMed]

Gil, J.

A. J. Einstein, H. S. Wu, and J. Gil, “Self-Affinity and lacunarity of chromatin texture in benign and malignant breast epithelial cell nuclei,” Phys. Rev. Lett. 80(2), 397–400 (1998).
[CrossRef]

Gilkerson, R.

R. Rossignol, R. Gilkerson, R. Aggeler, K. Yamagata, S. J. Remington, and R. A. Capaldi, “Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells,” Cancer Res. 64(3), 985–993 (2004).
[CrossRef] [PubMed]

Gopal, V.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Gothwal, H.

H. Gothwal, S. Kedawat, and R. Kumar, “Cardiac arrhythmias detection in an ECG beat signal using fast Fourier transform and artificial neural network,” J. Biomed. Sci. Eng. 4(04), 289–296 (2011).
[CrossRef]

Hackenbrock, C. R.

C. R. Hackenbrock, “Ultrastructural bases for metabolically linked mechanical activity in mitochondria. I. Reversible ultrastructural changes with change in metabolic steady state in isolated liver mitochondria,” J. Cell Biol. 51, 123–137 (1971).

C. R. Hackenbrock, “Ultrastructural bases for metabolically linked mechanical activity in mitochondria. II. Electron transport-linked ultrastructural transformations in mitochondria,” J. Cell Biol. 37(2), 345–369 (1968).
[CrossRef] [PubMed]

C. R. Hackenbrock, T. G. Rehn, E. C. Weinbach, and J. J. Lemasters, “Oxidative phosphorylation and ultrastructural transformation in mitochondria in the intact ascites tumor cell,” J. Cell Biol. 30, 269–297 (1966).
[CrossRef] [PubMed]

Harris, F. I.

F. I. Harris, “On the use of windows for harmonic analysis with discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[CrossRef]

Henebry, G. M.

G. Dougherty and G. M. Henebry, “Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images,” Med. Eng. Phys. 23(6), 369–380 (2001).
[CrossRef] [PubMed]

Hunt, J. P.

A. C. Sullivan, J. P. Hunt, and A. L. Oldenburg, “Fractal analysis for classification of breast carcinoma in optical coherence tomography,” J. Biomed. Opt. 16(6), 066010 (2011).
[CrossRef] [PubMed]

Hunter, M.

Hyman, B. T.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Jain, R. K.

Y. Gazit, D. A. Berk, M. Leunig, L. T. Baxter, and R. K. Jain, “Scale-invariant behavior and vascular network formation in normal and tumor tissue,” Phys. Rev. Lett. 75(12), 2428–2431 (1995).
[CrossRef] [PubMed]

Jobsis, F.

B. Chance, P. Cohen, F. Jobsis, and B. Schoener, “Intracellular oxidation-reduction states in vivo,” Science 137(3529), 499–508 (1962).
[CrossRef] [PubMed]

Kalashnikov, M.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Kaplan, D. L.

K. P. Quinn, E. Bellas, N. Fourligas, K. Lee, D. L. Kaplan, and I. Georgakoudi, “Characterization of metabolic changes associated with the functional development of 3D engineered tissues by non-invasive, dynamic measurement of individual cell redox ratios,” Biomaterials 33(21), 5341–5348 (2012).
[CrossRef] [PubMed]

W. L. Rice, D. L. Kaplan, and I. Georgakoudi, “Two-photon microscopy for non-invasive, quantitative monitoring of stem cell differentiation,” PLoS ONE 5(4), e10075 (2010).
[CrossRef] [PubMed]

Kartazayeva, S. A.

Kedawat, S.

H. Gothwal, S. Kedawat, and R. Kumar, “Cardiac arrhythmias detection in an ECG beat signal using fast Fourier transform and artificial neural network,” J. Biomed. Sci. Eng. 4(04), 289–296 (2011).
[CrossRef]

Keller, J. B.

Klaffke, S.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Koopman, W. J.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Kumar, G.

Kumar, R.

H. Gothwal, S. Kedawat, and R. Kumar, “Cardiac arrhythmias detection in an ECG beat signal using fast Fourier transform and artificial neural network,” J. Biomed. Sci. Eng. 4(04), 289–296 (2011).
[CrossRef]

Lee, K.

K. P. Quinn, E. Bellas, N. Fourligas, K. Lee, D. L. Kaplan, and I. Georgakoudi, “Characterization of metabolic changes associated with the functional development of 3D engineered tissues by non-invasive, dynamic measurement of individual cell redox ratios,” Biomaterials 33(21), 5341–5348 (2012).
[CrossRef] [PubMed]

Lemasters, J. J.

C. R. Hackenbrock, T. G. Rehn, E. C. Weinbach, and J. J. Lemasters, “Oxidative phosphorylation and ultrastructural transformation in mitochondria in the intact ascites tumor cell,” J. Cell Biol. 30, 269–297 (1966).
[CrossRef] [PubMed]

Leunig, M.

Y. Gazit, D. A. Berk, M. Leunig, L. T. Baxter, and R. K. Jain, “Scale-invariant behavior and vascular network formation in normal and tumor tissue,” Phys. Rev. Lett. 75(12), 2428–2431 (1995).
[CrossRef] [PubMed]

Levitt, J. M.

J. M. Levitt, M. E. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Automated biochemical, morphological, and organizational assessment of precancerous changes from endogenous two-photon fluorescence images,” PLoS ONE 6(9), e24765 (2011).
[CrossRef] [PubMed]

J. M. Levitt, M. Hunter, C. Mujat, M. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Diagnostic cellular organization features extracted from autofluorescence images,” Opt. Lett. 32(22), 3305–3307 (2007).
[CrossRef] [PubMed]

Lopes, R.

R. Lopes and N. Betrouni, “Fractal and multifractal analysis: A review,” Med. Image Anal. 13(4), 634–649 (2009).
[CrossRef] [PubMed]

Mayer, T. J.

C. Meyers, T. J. Mayer, and M. A. Ozbun, “Synthesis of infectious human papillomavirus type 18 in differentiating epithelium transfected with viral DNA,” J. Virol. 71(10), 7381–7386 (1997).
[PubMed]

McLaughlin-Drubin, M.

McLaughlin-Drubin, M. E.

J. M. Levitt, M. E. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Automated biochemical, morphological, and organizational assessment of precancerous changes from endogenous two-photon fluorescence images,” PLoS ONE 6(9), e24765 (2011).
[CrossRef] [PubMed]

Meyers, C.

C. Meyers, T. J. Mayer, and M. A. Ozbun, “Synthesis of infectious human papillomavirus type 18 in differentiating epithelium transfected with viral DNA,” J. Virol. 71(10), 7381–7386 (1997).
[PubMed]

Mortiboys, H.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Moscoso, M.

Mujat, C.

Münger, K.

J. M. Levitt, M. E. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Automated biochemical, morphological, and organizational assessment of precancerous changes from endogenous two-photon fluorescence images,” PLoS ONE 6(9), e24765 (2011).
[CrossRef] [PubMed]

J. M. Levitt, M. Hunter, C. Mujat, M. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Diagnostic cellular organization features extracted from autofluorescence images,” Opt. Lett. 32(22), 3305–3307 (2007).
[CrossRef] [PubMed]

Negelein, E.

O. Warburg, F. Wind, and E. Negelein, “The metabolism of tumor in the body,” J. Gen. Physiol. 8(6), 519–530 (1927).
[CrossRef] [PubMed]

Ni, X.

Nikitin, A. Y.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Normant, F.

F. Normant and C. Tricot, “Method for evaluating the fractal dimension of curves using convex hulls,” Phys. Rev. A 43(12), 6518–6525 (1991).
[CrossRef] [PubMed]

Oldenburg, A. L.

A. C. Sullivan, J. P. Hunt, and A. L. Oldenburg, “Fractal analysis for classification of breast carcinoma in optical coherence tomography,” J. Biomed. Opt. 16(6), 066010 (2011).
[CrossRef] [PubMed]

Olpin, S.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Ostrander, J. H.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res. 69(3), 1199–1204 (2009).
[CrossRef] [PubMed]

Ozbun, M. A.

C. Meyers, T. J. Mayer, and M. A. Ozbun, “Synthesis of infectious human papillomavirus type 18 in differentiating epithelium transfected with viral DNA,” J. Virol. 71(10), 7381–7386 (1997).
[PubMed]

Papanicolaou, G.

Paulsen, K. D.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and B. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt. 11(6), 064007 (2006).
[CrossRef] [PubMed]

Pogue, B. W.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and B. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt. 11(6), 064007 (2006).
[CrossRef] [PubMed]

Popescu, G.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Quinn, K. P.

K. P. Quinn, E. Bellas, N. Fourligas, K. Lee, D. L. Kaplan, and I. Georgakoudi, “Characterization of metabolic changes associated with the functional development of 3D engineered tissues by non-invasive, dynamic measurement of individual cell redox ratios,” Biomaterials 33(21), 5341–5348 (2012).
[CrossRef] [PubMed]

Rehn, T. G.

C. R. Hackenbrock, T. G. Rehn, E. C. Weinbach, and J. J. Lemasters, “Oxidative phosphorylation and ultrastructural transformation in mitochondria in the intact ascites tumor cell,” J. Cell Biol. 30, 269–297 (1966).
[CrossRef] [PubMed]

Remington, S. J.

R. Rossignol, R. Gilkerson, R. Aggeler, K. Yamagata, S. J. Remington, and R. A. Capaldi, “Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells,” Cancer Res. 64(3), 985–993 (2004).
[CrossRef] [PubMed]

Rice, W. L.

W. L. Rice, D. L. Kaplan, and I. Georgakoudi, “Two-photon microscopy for non-invasive, quantitative monitoring of stem cell differentiation,” PLoS ONE 5(4), e10075 (2010).
[CrossRef] [PubMed]

Rogers, J. D.

Rossignol, R.

R. Rossignol, R. Gilkerson, R. Aggeler, K. Yamagata, S. J. Remington, and R. A. Capaldi, “Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells,” Cancer Res. 64(3), 985–993 (2004).
[CrossRef] [PubMed]

Schmitt, J. M.

Schoener, B.

B. Chance, P. Cohen, F. Jobsis, and B. Schoener, “Intracellular oxidation-reduction states in vivo,” Science 137(3529), 499–508 (1962).
[CrossRef] [PubMed]

Smeitink, J. A.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Stoner, G. D.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Sullivan, A. C.

A. C. Sullivan, J. P. Hunt, and A. L. Oldenburg, “Fractal analysis for classification of breast carcinoma in optical coherence tomography,” J. Biomed. Opt. 16(6), 066010 (2011).
[CrossRef] [PubMed]

Thomas, K. J.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Tricot, C.

F. Normant and C. Tricot, “Method for evaluating the fractal dimension of curves using convex hulls,” Phys. Rev. A 43(12), 6518–6525 (1991).
[CrossRef] [PubMed]

Turcotte, D. L.

D. L. Turcotte, “Fractals in petrology,” Lithos 65(3-4), 261–271 (2002).
[CrossRef]

Wang, X.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and B. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt. 11(6), 064007 (2006).
[CrossRef] [PubMed]

Warburg, O.

O. Warburg, F. Wind, and E. Negelein, “The metabolism of tumor in the body,” J. Gen. Physiol. 8(6), 519–530 (1927).
[CrossRef] [PubMed]

Wax, A.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res. 69(3), 1199–1204 (2009).
[CrossRef] [PubMed]

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Webb, W. W.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Weinbach, E. C.

C. R. Hackenbrock, T. G. Rehn, E. C. Weinbach, and J. J. Lemasters, “Oxidative phosphorylation and ultrastructural transformation in mitochondria in the intact ascites tumor cell,” J. Cell Biol. 30, 269–297 (1966).
[CrossRef] [PubMed]

Wells, W.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and B. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt. 11(6), 064007 (2006).
[CrossRef] [PubMed]

Willems, P. H.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Williams, R. M.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Wilson, T. H.

T. H. Wilson, “Fractal strain distribution and its implications for cross section balancing: further discussion,” J. Struct. Geol. 19(1), 129–132 (1997).
[CrossRef]

Wind, F.

O. Warburg, F. Wind, and E. Negelein, “The metabolism of tumor in the body,” J. Gen. Physiol. 8(6), 519–530 (1927).
[CrossRef] [PubMed]

Wood, N. W.

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Wu, H. S.

A. J. Einstein, H. S. Wu, and J. Gil, “Self-Affinity and lacunarity of chromatin texture in benign and malignant breast epithelial cell nuclei,” Phys. Rev. Lett. 80(2), 397–400 (1998).
[CrossRef]

H. S. Wu, “Fractal strain distribution and its implications for cross section balancing,” J. Struct. Geol. 15(12), 1497–1507 (1993).
[CrossRef]

Xylas, J.

Yamagata, K.

R. Rossignol, R. Gilkerson, R. Aggeler, K. Yamagata, S. J. Remington, and R. A. Capaldi, “Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells,” Cancer Res. 64(3), 985–993 (2004).
[CrossRef] [PubMed]

Zipfel, W. R.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Ann. Neurol. (1)

H. Mortiboys, K. J. Thomas, W. J. Koopman, S. Klaffke, P. Abou-Sleiman, S. Olpin, N. W. Wood, P. H. Willems, J. A. Smeitink, M. R. Cookson, and O. Bandmann, “Mitochondrial function and morphology are impaired in parkin-mutant fibroblasts,” Ann. Neurol. 64(5), 555–565 (2008).
[CrossRef] [PubMed]

Biomaterials (1)

K. P. Quinn, E. Bellas, N. Fourligas, K. Lee, D. L. Kaplan, and I. Georgakoudi, “Characterization of metabolic changes associated with the functional development of 3D engineered tissues by non-invasive, dynamic measurement of individual cell redox ratios,” Biomaterials 33(21), 5341–5348 (2012).
[CrossRef] [PubMed]

Biomed. Opt. Express (1)

Cancer Res. (2)

R. Rossignol, R. Gilkerson, R. Aggeler, K. Yamagata, S. J. Remington, and R. A. Capaldi, “Energy substrate modulates mitochondrial structure and oxidative capacity in cancer cells,” Cancer Res. 64(3), 985–993 (2004).
[CrossRef] [PubMed]

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res. 69(3), 1199–1204 (2009).
[CrossRef] [PubMed]

Comput. Med. Imaging Graph. (1)

K. Doi, “Computer-aided diagnosis in medical imaging: historical review, current status and future potential,” Comput. Med. Imaging Graph. 31(4-5), 198–211 (2007).
[CrossRef] [PubMed]

J. Biomed. Opt. (2)

A. C. Sullivan, J. P. Hunt, and A. L. Oldenburg, “Fractal analysis for classification of breast carcinoma in optical coherence tomography,” J. Biomed. Opt. 16(6), 066010 (2011).
[CrossRef] [PubMed]

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and B. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt. 11(6), 064007 (2006).
[CrossRef] [PubMed]

J. Biomed. Sci. Eng. (1)

H. Gothwal, S. Kedawat, and R. Kumar, “Cardiac arrhythmias detection in an ECG beat signal using fast Fourier transform and artificial neural network,” J. Biomed. Sci. Eng. 4(04), 289–296 (2011).
[CrossRef]

J. Cell Biol. (3)

C. R. Hackenbrock, “Ultrastructural bases for metabolically linked mechanical activity in mitochondria. II. Electron transport-linked ultrastructural transformations in mitochondria,” J. Cell Biol. 37(2), 345–369 (1968).
[CrossRef] [PubMed]

C. R. Hackenbrock, T. G. Rehn, E. C. Weinbach, and J. J. Lemasters, “Oxidative phosphorylation and ultrastructural transformation in mitochondria in the intact ascites tumor cell,” J. Cell Biol. 30, 269–297 (1966).
[CrossRef] [PubMed]

C. R. Hackenbrock, “Ultrastructural bases for metabolically linked mechanical activity in mitochondria. I. Reversible ultrastructural changes with change in metabolic steady state in isolated liver mitochondria,” J. Cell Biol. 51, 123–137 (1971).

J. Gen. Physiol. (1)

O. Warburg, F. Wind, and E. Negelein, “The metabolism of tumor in the body,” J. Gen. Physiol. 8(6), 519–530 (1927).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. Struct. Geol. (2)

H. S. Wu, “Fractal strain distribution and its implications for cross section balancing,” J. Struct. Geol. 15(12), 1497–1507 (1993).
[CrossRef]

T. H. Wilson, “Fractal strain distribution and its implications for cross section balancing: further discussion,” J. Struct. Geol. 19(1), 129–132 (1997).
[CrossRef]

J. Virol. (1)

C. Meyers, T. J. Mayer, and M. A. Ozbun, “Synthesis of infectious human papillomavirus type 18 in differentiating epithelium transfected with viral DNA,” J. Virol. 71(10), 7381–7386 (1997).
[PubMed]

Lithos (1)

D. L. Turcotte, “Fractals in petrology,” Lithos 65(3-4), 261–271 (2002).
[CrossRef]

Med. Eng. Phys. (1)

G. Dougherty and G. M. Henebry, “Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images,” Med. Eng. Phys. 23(6), 369–380 (2001).
[CrossRef] [PubMed]

Med. Image Anal. (1)

R. Lopes and N. Betrouni, “Fractal and multifractal analysis: A review,” Med. Image Anal. 13(4), 634–649 (2009).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. A (1)

F. Normant and C. Tricot, “Method for evaluating the fractal dimension of curves using convex hulls,” Phys. Rev. A 43(12), 6518–6525 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97(13), 138102 (2006).
[CrossRef] [PubMed]

Y. Gazit, D. A. Berk, M. Leunig, L. T. Baxter, and R. K. Jain, “Scale-invariant behavior and vascular network formation in normal and tumor tissue,” Phys. Rev. Lett. 75(12), 2428–2431 (1995).
[CrossRef] [PubMed]

A. J. Einstein, H. S. Wu, and J. Gil, “Self-Affinity and lacunarity of chromatin texture in benign and malignant breast epithelial cell nuclei,” Phys. Rev. Lett. 80(2), 397–400 (1998).
[CrossRef]

PLoS ONE (2)

J. M. Levitt, M. E. McLaughlin-Drubin, K. Münger, and I. Georgakoudi, “Automated biochemical, morphological, and organizational assessment of precancerous changes from endogenous two-photon fluorescence images,” PLoS ONE 6(9), e24765 (2011).
[CrossRef] [PubMed]

W. L. Rice, D. L. Kaplan, and I. Georgakoudi, “Two-photon microscopy for non-invasive, quantitative monitoring of stem cell differentiation,” PLoS ONE 5(4), e10075 (2010).
[CrossRef] [PubMed]

Proc. IEEE (1)

F. I. Harris, “On the use of windows for harmonic analysis with discrete Fourier transform,” Proc. IEEE 66(1), 51–83 (1978).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A. 100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Science (1)

B. Chance, P. Cohen, F. Jobsis, and B. Schoener, “Intracellular oxidation-reduction states in vivo,” Science 137(3529), 499–508 (1962).
[CrossRef] [PubMed]

Other (6)

B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, “Energy conversion: Mitochondria and Chloroplasts,” in Molecular Biology of the Cell (Garland Science, 2002) http://www.ncbi.nlm.nih.gov/books/NBK21063/ .

R. F. Voss, in Fundamental Algorithms for Computer Graphics, edited by R. A. Earnshaw (Springer-Verlag, Berlin, 1985).

R. E. Blahut, Theory of Remote Image Formation (Cambridge University Press, 2004).

D. L. Turcotte, Fractals and Chaos in Geology and Geophysics (Cambridge Univ. Press, 1997).

P. Meakin, Fractals, Scaling, and Growth Far from Equilibrium (Cambridge University Press, 1998).

B. Mandelbrot, The Fractal Geometry of Nature (W.H. Freeman and Company, 2000).

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Figures (5)

Fig. 1
Fig. 1

(a) Power spectral density of generated scale invariant images of varying fractal character with fits (shown in panels b-f) for β = 0, 1, 2, 3, 4.

Fig. 2
Fig. 2

(a) Split panel of two representative simulated cell object (SCO) images without (left) and with a nuclear structure (right) (b) PSD spectra from SCO images with digitally applied fractals and a black background showing there is no sensitivity to β values greater than 3. (c) PSD spectra from SCO images without (black) and with nuclear structures (gray) containing SCOs that have 35 μm and 12μm for cell and nuclear diameters, respectively, the average value of the foreground in the background, and a β = 2.8. A shoulder that can be attributed to the nuclear border can be seen in the spectrum of the model images with nuclear structures. The spectrum is smoother than in (b) as a result of the change in background value.

Fig. 3
Fig. 3

(a-c) Representative original TPEF images from superficial, para-basal, and basal layers, respectively and (d) measured β exponents from corresponding PSD spectra and fits. Binary masks of cell borders (e-f) and corresponding PSD spectra and fits (h) demonstrating that a clear association of β exponents to morphology persists in the absence of high frequency spatial information. All images are 238 x 238 μm2.

Fig. 4
Fig. 4

Nomograms of measured β parameters for superficial (a), parabasal (b), and basal (c) epithelial layers of normal tissue. Plotted are input versus measured power-law exponents from linear fits of the radially-sampled PSDs for simulated images of varying input β parameters and background. Representative images with black background (green, solid lines), with the average value of the foreground in the background (blue, dashed lines) and images that have been clone stamped (red, dotted lines).

Fig. 5
Fig. 5

(a) Representative original and DOC-corrected TPEF images of superficial, para-basal, and basal layers of epithelial tissues made with healthy human foreskin keratinocytes (HFK) and HPV-transfected keratinocytes with the average β values for 5 different fields for each group displayed under each image with standard deviations. (b) β values from each HFK (green) and HPV (red) tissue sorted by tissue layer, before and after DOC.

Tables (2)

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Table 1 β values and corresponding statistical processes

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Table 2 Impact of nuclear structure on βM values from representative SCO images

Equations (6)

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F( k )= 1 N 2 x=0 N1 y=0 N1 W( r ) e 2πi( k · r ) N .
Φ( k )= F( k ) | F( k ) | .
Φ'( k )=T( k )Φ( k ),
W( r )= 1 N 2 k x =0 N1 k y =0 N1 Φ'( k ) e 2πi( k · r ) N .
T( k )= k β/2 ,
R( k )=A k β ,

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