Abstract

Biological tissue has a complex structure and exhibits rich spectroscopic behavior. There has been no tissue model until now that has been able to account for the observed spectroscopy of tissue light scattering and its anisotropy. Here we present, for the first time, a plum pudding random medium (PPRM) model for biological tissue which succinctly describes tissue as a superposition of distinctive scattering structures (plum) embedded inside a fractal continuous medium of background refractive index fluctuation (pudding). PPRM faithfully reproduces the wavelength dependence of tissue light scattering and attributes the “anomalous” trend in the anisotropy to the plum and the powerlaw dependence of the reduced scattering coefficient to the fractal scattering pudding. Most importantly, PPRM opens up a novel venue of quantifying the tissue architecture and microscopic structures on average from macroscopic probing of the bulk with scattered light alone without tissue excision. We demonstrate this potential by visualizing the fine microscopic structural alterations in breast tissue (adipose, glandular, fibrocystic, fibroadenoma, and ductal carcinoma) deduced from noncontact spectroscopic measurement.

© 2017 Optical Society of America

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References

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2015 (2)

B. C. Wilson, “Detection and treatment of dysplasia in Barrett’s esophagus: a pivotal challenge in translating biophotonics from bench to bedside,” J. Biomed. Opt. 12, 051401 (2015).
[Crossref]

M. Schlather, A. Malinowski, M. Peter Strokorb, M. Oesting, and K. Strokorb, “Analysis, simulation and prediction of multivariate random field with package RandomFields,” J. Stat. Software 63, 1–25 (2015).

2014 (1)

J. D. Rogers, A. J. Radosevich, and V. Backman, “Modeling light scattering in tissue as continuous random media using a versatile refractive index correlation function,” IEEE J. Sel. Top. Quant. Electron. 20, 173–186 (2014).
[Crossref]

2013 (3)

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58, R37–R61 (2013).
[Crossref] [PubMed]

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
[Crossref] [PubMed]

2012 (4)

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
[Crossref] [PubMed]

H. A. Foster, D. K. Griffin, and J. M. Bridger, “Interphase chromosome positioning in in vitro porcine cells and ex vivo porcine tissues,” BMC Cell Biol. 13, 30 (2012).
[Crossref] [PubMed]

M. R. Hajihashemi, S. R. Grobmyer, S. Z. Al-Quran, and H. Jiang, “Noninvasive evaluation of nuclear morphometry in breast lesions using multispectral diffuse optical tomography,” PLOS One 7, e45714 (2012).
[Crossref] [PubMed]

Y. Pu, W. Wang, M. Al-Rubaiee, S. K. Gayen, and M. Xu, “Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues,” Appl. Spectr. 66, 828–834 (2012).
[Crossref]

2011 (1)

A. N. Bashkatov, E. A. Genina, and V. V. Tuchin, “Optical properties of skin, subcutaneous, and muscle tissues: a review,” J. Innov. Opt. Health Sci. 04, 9–38 (2011).
[Crossref]

2010 (1)

Y. Zhu, T. Fearn, G. Mackenzie, B. Clark, J. M. Dunn, I. J. Bigio, S. G. Bown, and L. B. Lovat, “Elastic scattering spectroscopy for detection of cancer risk in Barrett’s esophagus: experimental and clinical validation of error removal by orthogonal subtraction for increasing accuracy,” J. Biomed. Opt. 14, 044022 (2010).
[Crossref]

2009 (1)

2008 (2)

R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16, 2304–2314 (2008).
[Crossref]

M. Xu, T. T. Wu, and J. Y. Qu, “Unified Mie and fractal scattering by cells and experimental study on application in optical characterization of cellular and subcellular structures,” J. Biomed. Opt. 13, 038802 (2008).

2007 (2)

2006 (4)

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

R. S. Brock, X.-H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectr. Rad. Transfer 102, 25–36 (2006).
[Crossref]

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “The importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. B 82, 194–198 (2006).
[Crossref] [PubMed]

M. Xu, “Superposition rule for light scattering by a composite particle,” Opt. Lett. 31, 3223–3225 (2006).
[Crossref] [PubMed]

2005 (2)

2004 (2)

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

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
[Crossref] [PubMed]

2000 (2)

1998 (3)

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, 397–400 (1998).
[Crossref]

J. M. Schmitt and G. Kumar, “Optical scattering properties of soft tissue: A discrete particle model,” Appl. Opt. 37, 2788–2797 (1998).
[Crossref]

L. F. Barbisan, J. Russo, and M. L. Mello, “Nuclear and nucleolar image analysis of human breast epithelial cells transformed by benzo[a]pyrene and transfected with the c-Ha-ras oncogene,” Anal. Cellular Path. 16, 193–199 (1998).
[Crossref]

1997 (2)

D. Wales and J. Doye, “Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms,” J. Phys. Chem. A 5639, 5111–5116 (1997).
[Crossref]

A. G. Yodh, B. Tromberg, E. Sevick-Muraca, and D. Pine, “Diffusing photons in turbid media,” JOSA A 14, 136–342 (1997).

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, 2428–2431 (1995).
[Crossref] [PubMed]

1991 (1)

B. Chance, “Optical methods,” Ann. Rev. Biophys. Biophys. Chem. 20, 1–28 (1991).
[Crossref]

1990 (3)

W. F. Cheong, S. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quant. Elecron. 26, 2166–2185 (1990).
[Crossref]

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissue in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

1984 (1)

V. S. Remizovich, “Theoretical description of elastic reflection of particles (photons) incident at grazing angles without the use of the diffusion approximation,” Sov. Phys. JETP 60, 290–297 (1984).

1981 (1)

B. J. Uscinski, H. G. Booker, and M. Marians, “Intensity fluctuation due to a deep phase screen with a power law spectrum,” Proc. Royal Soc. A 374, 503–530 (1981).
[Crossref]

1980 (1)

Alfano, R. R.

M. Xu and R. R. Alfano, “Fractal mechanisms of light scattering in biological tissue and cells,” Opt. Lett. 30, 3051–3053 (2005).
[Crossref] [PubMed]

M. Xu, M. Alrubaiee, and R. R. Alfano, “Fractal mechanism of light scattering for tissue optical biopsy,” in “Optical Biopsy VI,”, vol. 6091 of Proc. SPIE, R. R. Alfano and A. Katz, eds. p. 60910E, (SPIE2006).
[Crossref]

Algaba, F.

B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
[Crossref] [PubMed]

Al-Quran, S. Z.

M. R. Hajihashemi, S. R. Grobmyer, S. Z. Al-Quran, and H. Jiang, “Noninvasive evaluation of nuclear morphometry in breast lesions using multispectral diffuse optical tomography,” PLOS One 7, e45714 (2012).
[Crossref] [PubMed]

Alrubaiee, M.

M. Xu, M. Alrubaiee, and R. R. Alfano, “Fractal mechanism of light scattering for tissue optical biopsy,” in “Optical Biopsy VI,”, vol. 6091 of Proc. SPIE, R. R. Alfano and A. Katz, eds. p. 60910E, (SPIE2006).
[Crossref]

Al-Rubaiee, M.

Y. Pu, W. Wang, M. Al-Rubaiee, S. K. Gayen, and M. Xu, “Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues,” Appl. Spectr. 66, 828–834 (2012).
[Crossref]

Backman, V.

J. D. Rogers, A. J. Radosevich, and V. Backman, “Modeling light scattering in tissue as continuous random media using a versatile refractive index correlation function,” IEEE J. Sel. Top. Quant. Electron. 20, 173–186 (2014).
[Crossref]

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
[Crossref] [PubMed]

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

Badizadegan, K.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
[Crossref] [PubMed]

Barbisan, L. F.

L. F. Barbisan, J. Russo, and M. L. Mello, “Nuclear and nucleolar image analysis of human breast epithelial cells transformed by benzo[a]pyrene and transfected with the c-Ha-ras oncogene,” Anal. Cellular Path. 16, 193–199 (1998).
[Crossref]

Barth, R. J.

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

Bashkatov, A. N.

A. N. Bashkatov, E. A. Genina, and V. V. Tuchin, “Optical properties of skin, subcutaneous, and muscle tissues: a review,” J. Innov. Opt. Health Sci. 04, 9–38 (2011).
[Crossref]

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, 2428–2431 (1995).
[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, 2428–2431 (1995).
[Crossref] [PubMed]

Bigio, I. J.

Y. Zhu, T. Fearn, G. Mackenzie, B. Clark, J. M. Dunn, I. J. Bigio, S. G. Bown, and L. B. Lovat, “Elastic scattering spectroscopy for detection of cancer risk in Barrett’s esophagus: experimental and clinical validation of error removal by orthogonal subtraction for increasing accuracy,” J. Biomed. Opt. 14, 044022 (2010).
[Crossref]

Booker, H. G.

B. J. Uscinski, H. G. Booker, and M. Marians, “Intensity fluctuation due to a deep phase screen with a power law spectrum,” Proc. Royal Soc. A 374, 503–530 (1981).
[Crossref]

Boone, C. W.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
[Crossref] [PubMed]

Bown, S. G.

Y. Zhu, T. Fearn, G. Mackenzie, B. Clark, J. M. Dunn, I. J. Bigio, S. G. Bown, and L. B. Lovat, “Elastic scattering spectroscopy for detection of cancer risk in Barrett’s esophagus: experimental and clinical validation of error removal by orthogonal subtraction for increasing accuracy,” J. Biomed. Opt. 14, 044022 (2010).
[Crossref]

Bridger, J. M.

H. A. Foster, D. K. Griffin, and J. M. Bridger, “Interphase chromosome positioning in in vitro porcine cells and ex vivo porcine tissues,” BMC Cell Biol. 13, 30 (2012).
[Crossref] [PubMed]

Brock, R. S.

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X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
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V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
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Y. Zhu, T. Fearn, G. Mackenzie, B. Clark, J. M. Dunn, I. J. Bigio, S. G. Bown, and L. B. Lovat, “Elastic scattering spectroscopy for detection of cancer risk in Barrett’s esophagus: experimental and clinical validation of error removal by orthogonal subtraction for increasing accuracy,” J. Biomed. Opt. 14, 044022 (2010).
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K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
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K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
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V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
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Dunn, A. K.

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B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
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K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
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R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16, 2304–2314 (2008).
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H. A. Foster, D. K. Griffin, and J. M. Bridger, “Interphase chromosome positioning in in vitro porcine cells and ex vivo porcine tissues,” BMC Cell Biol. 13, 30 (2012).
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V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
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V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissue in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
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Y. Pu, W. Wang, M. Al-Rubaiee, S. K. Gayen, and M. Xu, “Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues,” Appl. Spectr. 66, 828–834 (2012).
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A. N. Bashkatov, E. A. Genina, and V. V. Tuchin, “Optical properties of skin, subcutaneous, and muscle tissues: a review,” J. Innov. Opt. Health Sci. 04, 9–38 (2011).
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K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
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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, 397–400 (1998).
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H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
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H. A. Foster, D. K. Griffin, and J. M. Bridger, “Interphase chromosome positioning in in vitro porcine cells and ex vivo porcine tissues,” BMC Cell Biol. 13, 30 (2012).
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B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
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M. R. Hajihashemi, S. R. Grobmyer, S. Z. Al-Quran, and H. Jiang, “Noninvasive evaluation of nuclear morphometry in breast lesions using multispectral diffuse optical tomography,” PLOS One 7, e45714 (2012).
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V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
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R. S. Brock, X.-H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectr. Rad. Transfer 102, 25–36 (2006).
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X. Ma, J. Q. Lu, H. Ding, and X.-H. Hu, “Bulk optical parameters of porcine skin dermis at eight wavelengths from 325 to 1557 nm,” Opt. Lett. 30, 412 (2005).
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B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
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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, 2428–2431 (1995).
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Jiang, H.

M. R. Hajihashemi, S. R. Grobmyer, S. Z. Al-Quran, and H. Jiang, “Noninvasive evaluation of nuclear morphometry in breast lesions using multispectral diffuse optical tomography,” PLOS One 7, e45714 (2012).
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Jiang, S.

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
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V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
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K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
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V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
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R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16, 2304–2314 (2008).
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H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
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Kogel, C.

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
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A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
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Kromine, A. K.

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

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

Laughney, A. M.

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
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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, 2428–2431 (1995).
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V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
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H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, and V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[Crossref] [PubMed]

Lovat, L. B.

Y. Zhu, T. Fearn, G. Mackenzie, B. Clark, J. M. Dunn, I. J. Bigio, S. G. Bown, and L. B. Lovat, “Elastic scattering spectroscopy for detection of cancer risk in Barrett’s esophagus: experimental and clinical validation of error removal by orthogonal subtraction for increasing accuracy,” J. Biomed. Opt. 14, 044022 (2010).
[Crossref]

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R. S. Brock, X.-H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectr. Rad. Transfer 102, 25–36 (2006).
[Crossref]

X. Ma, J. Q. Lu, H. Ding, and X.-H. Hu, “Bulk optical parameters of porcine skin dermis at eight wavelengths from 325 to 1557 nm,” Opt. Lett. 30, 412 (2005).
[Crossref] [PubMed]

Ma, X.

Mackenzie, G.

Y. Zhu, T. Fearn, G. Mackenzie, B. Clark, J. M. Dunn, I. J. Bigio, S. G. Bown, and L. B. Lovat, “Elastic scattering spectroscopy for detection of cancer risk in Barrett’s esophagus: experimental and clinical validation of error removal by orthogonal subtraction for increasing accuracy,” J. Biomed. Opt. 14, 044022 (2010).
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B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
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M. Schlather, A. Malinowski, M. Peter Strokorb, M. Oesting, and K. Strokorb, “Analysis, simulation and prediction of multivariate random field with package RandomFields,” J. Stat. Software 63, 1–25 (2015).

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B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
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McKenney, J.

B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
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Meldrum, D. R.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
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Michels, R.

R. Michels, F. Foschum, and A. Kienle, “Optical properties of fat emulsions,” Opt. Express 16, 2304–2314 (2008).
[Crossref]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

Moan, J.

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “The importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. B 82, 194–198 (2006).
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Moch, H.

B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
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Montironi, R.

B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
[Crossref] [PubMed]

Mourant, J. R.

R. S. Brock, X.-H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectr. Rad. Transfer 102, 25–36 (2006).
[Crossref]

Munger, K.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
[Crossref] [PubMed]

Nandakumar, V.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
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Nielsen, K. P.

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “The importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. B 82, 194–198 (2006).
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Oesting, M.

M. Schlather, A. Malinowski, M. Peter Strokorb, M. Oesting, and K. Strokorb, “Analysis, simulation and prediction of multivariate random field with package RandomFields,” J. Stat. Software 63, 1–25 (2015).

Patterson, M. S.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissue in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

Paulsen, K. D.

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

Peter Strokorb, M.

M. Schlather, A. Malinowski, M. Peter Strokorb, M. Oesting, and K. Strokorb, “Analysis, simulation and prediction of multivariate random field with package RandomFields,” J. Stat. Software 63, 1–25 (2015).

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissue in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

Pine, D.

A. G. Yodh, B. Tromberg, E. Sevick-Muraca, and D. Pine, “Diffusing photons in turbid media,” JOSA A 14, 136–342 (1997).

Pogue, B. W.

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

Poplack, S. P.

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

Prahl, S.

W. F. Cheong, S. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quant. Elecron. 26, 2166–2185 (1990).
[Crossref]

Pu, Y.

Y. Pu, W. Wang, M. Al-Rubaiee, S. K. Gayen, and M. Xu, “Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues,” Appl. Spectr. 66, 828–834 (2012).
[Crossref]

Qu, J. Y.

M. Xu, T. T. Wu, and J. Y. Qu, “Unified Mie and fractal scattering by cells and experimental study on application in optical characterization of cellular and subcellular structures,” J. Biomed. Opt. 13, 038802 (2008).

T. T. Wu, J. Y. Qu, and M. Xu, “Unified Mie and fractal scattering by biological cells and subcellular structures,” Opt. Lett. 32, 2324–2326 (2007).
[Crossref] [PubMed]

Radosevich, A. J.

J. D. Rogers, A. J. Radosevich, and V. Backman, “Modeling light scattering in tissue as continuous random media using a versatile refractive index correlation function,” IEEE J. Sel. Top. Quant. Electron. 20, 173–186 (2014).
[Crossref]

Remizovich, V. S.

V. S. Remizovich, “Theoretical description of elastic reflection of particles (photons) incident at grazing angles without the use of the diffusion approximation,” Sov. Phys. JETP 60, 290–297 (1984).

Richards-Kortum, R.

Rizzo, E. J.

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

Rogers, J. D.

J. D. Rogers, A. J. Radosevich, and V. Backman, “Modeling light scattering in tissue as continuous random media using a versatile refractive index correlation function,” IEEE J. Sel. Top. Quant. Electron. 20, 173–186 (2014).
[Crossref]

Roy, H. K.

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

Russo, J.

L. F. Barbisan, J. Russo, and M. L. Mello, “Nuclear and nucleolar image analysis of human breast epithelial cells transformed by benzo[a]pyrene and transfected with the c-Ha-ras oncogene,” Anal. Cellular Path. 16, 193–199 (1998).
[Crossref]

Schlather, M.

M. Schlather, A. Malinowski, M. Peter Strokorb, M. Oesting, and K. Strokorb, “Analysis, simulation and prediction of multivariate random field with package RandomFields,” J. Stat. Software 63, 1–25 (2015).

Schmitt, J. M.

Schwab, M. C.

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

Senechal, P.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
[Crossref] [PubMed]

Sevick-Muraca, E.

A. G. Yodh, B. Tromberg, E. Sevick-Muraca, and D. Pine, “Diffusing photons in turbid media,” JOSA A 14, 136–342 (1997).

Shapshay, S. M.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
[Crossref] [PubMed]

Shaw, P. J.

P. J. Shaw, “Nucleolus,” in Encyclopedia of Life Sciences (John Wiley & Sons, Ltd., 2005).
[Crossref]

Sheetse, E. E.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
[Crossref] [PubMed]

Sheppard, C. J. R.

Song, X.

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

Srigley, J. R.

B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
[Crossref] [PubMed]

Srinivasan, S.

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

Stamnes, J. J.

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “The importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. B 82, 194–198 (2006).
[Crossref] [PubMed]

Stamnes, K.

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “The importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. B 82, 194–198 (2006).
[Crossref] [PubMed]

Starosta, M. S.

Strokorb, K.

M. Schlather, A. Malinowski, M. Peter Strokorb, M. Oesting, and K. Strokorb, “Analysis, simulation and prediction of multivariate random field with package RandomFields,” J. Stat. Software 63, 1–25 (2015).

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

Tromberg, B.

A. G. Yodh, B. Tromberg, E. Sevick-Muraca, and D. Pine, “Diffusing photons in turbid media,” JOSA A 14, 136–342 (1997).

Tromberg, B. J.

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

Tuchin, V. V.

A. N. Bashkatov, E. A. Genina, and V. V. Tuchin, “Optical properties of skin, subcutaneous, and muscle tissues: a review,” J. Innov. Opt. Health Sci. 04, 9–38 (2011).
[Crossref]

Uscinski, B. J.

B. J. Uscinski, H. G. Booker, and M. Marians, “Intensity fluctuation due to a deep phase screen with a power law spectrum,” Proc. Royal Soc. A 374, 503–530 (1981).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Vicsek, T.

T. Vicsek, Fluctuation and Scaling in Biology (Oxford University Press, New York, 2001).

Wales, D.

D. Wales and J. Doye, “Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms,” J. Phys. Chem. A 5639, 5111–5116 (1997).
[Crossref]

Wali, R. K.

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

Wang, R. K.

R. K. Wang, “Modeling optical properties of soft tissue by fractal distribution of scatterers,” J. Mod. Opt. 47, 103–120 (2000).
[Crossref]

Wang, W.

Y. Pu, W. Wang, M. Al-Rubaiee, S. K. Gayen, and M. Xu, “Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues,” Appl. Spectr. 66, 828–834 (2012).
[Crossref]

Wang, X.

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

X. Wang, “Estimation of scatterer size and number density in near-infrared tomography,” Ph.D. thesis, Dartmouth College (2007).

Weidner, D. A.

R. S. Brock, X.-H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectr. Rad. Transfer 102, 25–36 (2006).
[Crossref]

Welch, A. J.

W. F. Cheong, S. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quant. Elecron. 26, 2166–2185 (1990).
[Crossref]

Wells, W. A.

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

Wilson, B. C.

B. C. Wilson, “Detection and treatment of dysplasia in Barrett’s esophagus: a pivotal challenge in translating biophotonics from bench to bedside,” J. Biomed. Opt. 12, 051401 (2015).
[Crossref]

Wiscombe, W. J.

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, 397–400 (1998).
[Crossref]

Wu, T. T.

M. Xu, T. T. Wu, and J. Y. Qu, “Unified Mie and fractal scattering by cells and experimental study on application in optical characterization of cellular and subcellular structures,” J. Biomed. Opt. 13, 038802 (2008).

T. T. Wu, J. Y. Qu, and M. Xu, “Unified Mie and fractal scattering by biological cells and subcellular structures,” Opt. Lett. 32, 2324–2326 (2007).
[Crossref] [PubMed]

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissue in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

Xu, M.

Y. Pu, W. Wang, M. Al-Rubaiee, S. K. Gayen, and M. Xu, “Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues,” Appl. Spectr. 66, 828–834 (2012).
[Crossref]

M. Xu, T. T. Wu, and J. Y. Qu, “Unified Mie and fractal scattering by cells and experimental study on application in optical characterization of cellular and subcellular structures,” J. Biomed. Opt. 13, 038802 (2008).

T. T. Wu, J. Y. Qu, and M. Xu, “Unified Mie and fractal scattering by biological cells and subcellular structures,” Opt. Lett. 32, 2324–2326 (2007).
[Crossref] [PubMed]

M. Xu, “Superposition rule for light scattering by a composite particle,” Opt. Lett. 31, 3223–3225 (2006).
[Crossref] [PubMed]

M. Xu and R. R. Alfano, “Fractal mechanisms of light scattering in biological tissue and cells,” Opt. Lett. 30, 3051–3053 (2005).
[Crossref] [PubMed]

M. Xu, M. Alrubaiee, and R. R. Alfano, “Fractal mechanism of light scattering for tissue optical biopsy,” in “Optical Biopsy VI,”, vol. 6091 of Proc. SPIE, R. R. Alfano and A. Katz, eds. p. 60910E, (SPIE2006).
[Crossref]

Yodh, A. G.

A. G. Yodh, B. Tromberg, E. Sevick-Muraca, and D. Pine, “Diffusing photons in turbid media,” JOSA A 14, 136–342 (1997).

Zhao, L.

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “The importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. B 82, 194–198 (2006).
[Crossref] [PubMed]

Zhu, Y.

Y. Zhu, T. Fearn, G. Mackenzie, B. Clark, J. M. Dunn, I. J. Bigio, S. G. Bown, and L. B. Lovat, “Elastic scattering spectroscopy for detection of cancer risk in Barrett’s esophagus: experimental and clinical validation of error removal by orthogonal subtraction for increasing accuracy,” J. Biomed. Opt. 14, 044022 (2010).
[Crossref]

Am. J. Surg. Path. (1)

B. Delahunt, J. C. Cheville, G. Martignoni, P. A. Humphrey, C. Magi-Galluzzi, J. McKenney, L. Egevad, F. Algaba, H. Moch, D. J. Grignon, R. Montironi, and J. R. Srigley, “The International Society of Urological Pathology (ISUP) grading system for renal cell carcinoma and other prognostic parameters,” Am. J. Surg. Path. 37, 1490–1504 (2013).
[Crossref] [PubMed]

Anal. Cellular Path. (1)

L. F. Barbisan, J. Russo, and M. L. Mello, “Nuclear and nucleolar image analysis of human breast epithelial cells transformed by benzo[a]pyrene and transfected with the c-Ha-ras oncogene,” Anal. Cellular Path. 16, 193–199 (1998).
[Crossref]

Ann. Rev. Biophys. Biophys. Chem. (1)

B. Chance, “Optical methods,” Ann. Rev. Biophys. Biophys. Chem. 20, 1–28 (1991).
[Crossref]

Appl. Opt. (2)

Appl. Spectr. (1)

Y. Pu, W. Wang, M. Al-Rubaiee, S. K. Gayen, and M. Xu, “Determination of optical coefficients and fractal dimensional parameters of cancerous and normal prostate tissues,” Appl. Spectr. 66, 828–834 (2012).
[Crossref]

BMC Cell Biol. (1)

H. A. Foster, D. K. Griffin, and J. M. Bridger, “Interphase chromosome positioning in in vitro porcine cells and ex vivo porcine tissues,” BMC Cell Biol. 13, 30 (2012).
[Crossref] [PubMed]

Breast Cancer Res. (1)

A. M. Laughney, V. Krishnaswamy, E. J. Rizzo, M. C. Schwab, R. J. Barth, D. J. Cuccia, B. J. Tromberg, K. D. Paulsen, B. W. Pogue, and W. A. Wells, “Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging,” Breast Cancer Res. 15, R61 (2013).
[Crossref] [PubMed]

Faraday Discuss. (1)

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheetse, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279 (2004).
[Crossref] [PubMed]

Gastroenterology (1)

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

IEEE J. Quant. Elecron. (1)

W. F. Cheong, S. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quant. Elecron. 26, 2166–2185 (1990).
[Crossref]

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

J. D. Rogers, A. J. Radosevich, and V. Backman, “Modeling light scattering in tissue as continuous random media using a versatile refractive index correlation function,” IEEE J. Sel. Top. Quant. Electron. 20, 173–186 (2014).
[Crossref]

J. Biomed. Opt. (4)

X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A. Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Image reconstruction of effective mie scattering parameters of breast tissue in vevo with near-infrared tomography,” J. Biomed. Opt. 11, 041106 (2006).
[Crossref] [PubMed]

M. Xu, T. T. Wu, and J. Y. Qu, “Unified Mie and fractal scattering by cells and experimental study on application in optical characterization of cellular and subcellular structures,” J. Biomed. Opt. 13, 038802 (2008).

B. C. Wilson, “Detection and treatment of dysplasia in Barrett’s esophagus: a pivotal challenge in translating biophotonics from bench to bedside,” J. Biomed. Opt. 12, 051401 (2015).
[Crossref]

Y. Zhu, T. Fearn, G. Mackenzie, B. Clark, J. M. Dunn, I. J. Bigio, S. G. Bown, and L. B. Lovat, “Elastic scattering spectroscopy for detection of cancer risk in Barrett’s esophagus: experimental and clinical validation of error removal by orthogonal subtraction for increasing accuracy,” J. Biomed. Opt. 14, 044022 (2010).
[Crossref]

J. Innov. Opt. Health Sci. (1)

A. N. Bashkatov, E. A. Genina, and V. V. Tuchin, “Optical properties of skin, subcutaneous, and muscle tissues: a review,” J. Innov. Opt. Health Sci. 04, 9–38 (2011).
[Crossref]

J. Mod. Opt. (1)

R. K. Wang, “Modeling optical properties of soft tissue by fractal distribution of scatterers,” J. Mod. Opt. 47, 103–120 (2000).
[Crossref]

J. Photochem. Photobiol. B (1)

K. P. Nielsen, L. Zhao, J. J. Stamnes, K. Stamnes, and J. Moan, “The importance of the depth distribution of melanin in skin for DNA protection and other photobiological processes,” J. Photochem. Photobiol. B 82, 194–198 (2006).
[Crossref] [PubMed]

J. Phys. Chem. A (1)

D. Wales and J. Doye, “Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms,” J. Phys. Chem. A 5639, 5111–5116 (1997).
[Crossref]

J. Quant. Spectr. Rad. Transfer (1)

R. S. Brock, X.-H. Hu, D. A. Weidner, J. R. Mourant, and J. Q. Lu, “Effect of detailed cell structure on light scattering distribution: FDTD study of a B-cell with 3D structure constructed from confocal images,” J. Quant. Spectr. Rad. Transfer 102, 25–36 (2006).
[Crossref]

J. Stat. Software (1)

M. Schlather, A. Malinowski, M. Peter Strokorb, M. Oesting, and K. Strokorb, “Analysis, simulation and prediction of multivariate random field with package RandomFields,” J. Stat. Software 63, 1–25 (2015).

JOSA A (1)

A. G. Yodh, B. Tromberg, E. Sevick-Muraca, and D. Pine, “Diffusing photons in turbid media,” JOSA A 14, 136–342 (1997).

Opt. Express (3)

Opt. Lett. (6)

Phys. Med. Biol. (3)

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissue in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58, R37–R61 (2013).
[Crossref] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

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, 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, 397–400 (1998).
[Crossref]

PLOS One (2)

M. R. Hajihashemi, S. R. Grobmyer, S. Z. Al-Quran, and H. Jiang, “Noninvasive evaluation of nuclear morphometry in breast lesions using multispectral diffuse optical tomography,” PLOS One 7, e45714 (2012).
[Crossref] [PubMed]

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. W. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLOS One 7, e29230 (2012).
[Crossref] [PubMed]

Proc. Royal Soc. A (1)

B. J. Uscinski, H. G. Booker, and M. Marians, “Intensity fluctuation due to a deep phase screen with a power law spectrum,” Proc. Royal Soc. A 374, 503–530 (1981).
[Crossref]

Sov. Phys. JETP (1)

V. S. Remizovich, “Theoretical description of elastic reflection of particles (photons) incident at grazing angles without the use of the diffusion approximation,” Sov. Phys. JETP 60, 290–297 (1984).

Other (7)

T. Vicsek, Fluctuation and Scaling in Biology (Oxford University Press, New York, 2001).

M. Xu, M. Alrubaiee, and R. R. Alfano, “Fractal mechanism of light scattering for tissue optical biopsy,” in “Optical Biopsy VI,”, vol. 6091 of Proc. SPIE, R. R. Alfano and A. Katz, eds. p. 60910E, (SPIE2006).
[Crossref]

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

X. Wang, “Estimation of scatterer size and number density in near-infrared tomography,” Ph.D. thesis, Dartmouth College (2007).

P. J. Shaw, “Nucleolus,” in Encyclopedia of Life Sciences (John Wiley & Sons, Ltd., 2005).
[Crossref]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

The codes for the PPRM model, fitting procedures and the data can be found at http://www.faculty.fairfield.edu/mxu .

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Figures (9)

Fig. 1
Fig. 1 The normalized scattering coefficient β−2 μslmax (〈δm(0)2−1 μsl), reduced scattering coefficient β−2 μ′s lmax (〈δm(0)2−1 μ′sl), the anisotropy factor g, and the scattering power b in the fractal (top row) and Whittle-Matern (bottom row) continuous medium model. The size parameter is klmax and kl, respectively, in the two models. The scattering power b is fitted from μ′s (λ) over the spectral window 500nm < λ < 700nm centered at 600nm.
Fig. 2
Fig. 2 The scattering efficiencies collapse approximately to one universal curve for |m − 1| ≤ 0.15 and 0 < x < 200 after proper scaling. The variations in the anisotropy factor increases with the refractive index m. The shaded region in g within 2 ≤ |m − 1|−1 x ≤ 3.8 corresponds to the “anomalous” increasing anisotropy factor with the wavelength within the visible and near-infrared spectral range observed in most biological tissues.
Fig. 3
Fig. 3 The Plum Pudding Random Medium model treats tissue as a composite medium with some prominent distinctive structures (plum) embedded inside a continuum (pudding). The former includes, for example, the nuclear structure in soft tissue. The latter incorporates smaller scattering structures such as organelles and refractive index variations throughout the tissue continuum. PPRM faithfully reproduces the wavelength dependence of tissue light scattering and attributes the “anomalous” trend in the anisotropy (g increases with the wavelength) to the plum and the powerlaw dependence of the reduced scattering coefficient on the wavelength to the fractal scattering pudding.
Fig. 4
Fig. 4 Plum pudding random medium tissue model fitting of the fresh porcine dermis tissue. The columns from left to right show μs, μ′s and g. The background refractive index fluctuation and the core are shown together with the PPRM tissue model. Experimental data is adapted from Ma et al [10].
Fig. 5
Fig. 5 The plum (core) and pudding (background refractive index fluctuation) in fresh porcine dermis. The whole window size is 30μm × 30μm. The blue square delineates a unit cell which contains exactly one core. A core of most probable radius āc exp(−δ2) is shown, surrounded by a shaded area of radius a ¯ c exp ( δ 2 + 2 log 2 δ ) at which the number density of the core drops to half maximum. The core has a relative refractive index mc = 1.172 (“red” color).
Fig. 6
Fig. 6 Plum pudding random medium tissue model fitting to from top row to bottom row (a) normal breast adipose tissue, (b) normal glandular breast tissue, (c) fibrocystic tissue, (d) fibroadenoma, and (e) ductal carcinoma. The columns from left to right show μs, μ′s and g. The background refractive index fluctuation and the core are shown together with the PPRM tissue model. Experimental data is adapted from Peters et al [35].
Fig. 7
Fig. 7 The plum (core) and pudding (background refractive index fluctuation) in (a) normal breast adipose tissue, (b) normal glandular breast tissue, (c) fibrocystic tissue, (d) fibroadenoma, and (e) ductal carcinoma. The whole window size is 30μm ×30μm. The blue square delineates a unit cell which contains exactly one core. A core of most probable radius āc exp(−δ2) is shown, surrounded by a shaded area of radius a ¯ c exp ( δ 2 + 2 log 2 δ ) at which the number density of the core drops to half maximum.
Fig. 8
Fig. 8 The scattering efficiency Qsca, the reduced scattering efficiency Q′sca, the anisotropy factor g, and the γ factor for optically soft particle of size parameter 10 < x < 200. The empirical expressions (in solid lines) and the exact values from Mie theory (in symbols) are shown for m = 1.01, m = 1.02, ..., m = 1.05.
Fig. 9
Fig. 9 The anisotropy factor g and γ for polydispersed soft particles (νeff = 1.0%). The symbols are from Mie calculations and the solid lines are from the empirical expressions for g = 1 − Q̄′sca/sca and γ = Q̄″sca/Q̄′sca over the range 1 ≤ |m − 1| x ≤ 17.5.

Tables (5)

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Table 1 Fitted parameters for fresh porcine dermis tissue. The fluctuation amplitude δ m ( 0 ) 2 is computed from β by assuming the inner cutoff for the background refractive index fluctuations to be lmin = 20nm.

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Table 2 Fitted parameters for (a) normal breast adipose tissue, (b) normal glandular breast tissue, (c) fibrocystic tissue, (d) fibroadenoma, and (e) ductal carcinoma. The fluctuation amplitude δ m ( 0 ) 2 is computed from β by assuming the inner cutoff for the background refractive index fluctuations to be lmin = 20nm.

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Table 3 Relative importance of the background refractive index fluctuation (pudding) vs the core (plum) to the scattering coefficient μs and the reduced scattering coefficient μ′s at the probing wavelengths of 500nm and 1100nm.

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Table 4 The light scattering expressions of the fractal and Whittle-Matern continuous medium model in the limit of X = klmax, kl ≫ 1 where α δ m ( 0 ) 2 π 1 / 2 Γ ( ν + 3 / 2 ) | Γ ( ν ) |, and X = 2πn0lmax/λ and 2πn0l/λ, respectively, in the fractal and Whittle-Matern model. Both models behave alike in this limit and their scattering properties dependence on wavelength reduces to a power law with an identical power if interchanging Df and (4 − 2ν).

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Table 5 Parameters for empirical expressions of sca, Q̄′sca and Q̄″sca.

Equations (23)

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| S bg ( q ) | 2 { μ 2 1 = 2 π k 6 V R ^ ( q ) { μ 2 ( parallel polarized ) 1 ( perpendicular polarized )
σ ( θ , ϕ ) = 2 π k 4 V R ^ ( q ) ( sin 2 ϕ + μ 2 cos 2 ϕ ) .
μ s , bg = σ ( θ , ϕ ) d Ω = π k 2 1 1 | S bg ( q ) | 2 ( 1 + μ 2 ) d μ ,
μ s , bg = σ ( θ , ϕ ) ( 1 μ ) d Ω = π k 2 1 1 | S bg ( q ) | 2 ( 1 + μ 2 ) ( 1 μ ) d μ
R ( r ) = β 2 ( r l max ) 4 D f Γ [ ( 4 D f ) , r l max ] .
| S bg ( q ) | 2 = 2 π β 2 V k 3 X 3 7 D f F 2 1 ( 2 , 7 D f 2 , 9 D f 2 , 2 ( 1 μ ) X 2 )
R ( r ) = δ m ( 0 ) 2 2 1 ν | Γ ( ν ) | 1 ( r l ) ν K ν ( r l )
| S bg ( q ) | 2 = 2 δ m ( 0 ) 2 Γ ( ν + 3 2 ) V k 3 X 3 π 1 / 2 | Γ ( ν ) | [ 1 + 2 ( 1 μ ) X 2 ] ν 3 2
| S ( q ) | 2 ¯ = | S core ( q ) | 2 + | S bg ( q ) | 2
Q ¯ sca ( x ¯ , m , δ ) = a ¯ 2 a 2 Q sca ( k a , m ) f ( a ) d a ,
Q ¯ sca ( x ¯ , m , δ ) = a ¯ 2 a 2 Q sca ( k a , m ) f ( a ) d a
μ s = μ s , core + μ s , bg = N c π a ¯ c 2 Q ¯ sca ( x ¯ c , m c , δ ) + μ s , bg ,
μ s = μ s , core + μ s , bg = N c π a ¯ c 2 Q ¯ sca ( x ¯ c , m c , δ ) + μ s , bg
f ( a ) = 1 2 π δ a 1 exp [ ln 2 ( a a ¯ ) / 2 δ 2 ] .
a eff = 0 a 3 f ( a ) d a 0 a 2 f ( a ) d a = a exp ( 5 δ 2 / 2 )
ν eff = 0 ( a a eff ) 2 a 2 f ( a ) d a ( a eff ) 2 0 a 2 f ( a ) d a = exp ( δ 2 ) 1 .
C sca ( x , m ) = π a 2 Q sca ( x , m )
C sca ( x , m ) = π a 2 Q sca ( x , m )
Q sca ( x , m ) = 2 4 η sin η + 4 η 2 ( 1 cos η ) ,
Q sca ( x , m ) = 2 π | m 1 | 2 ( 0.578 3.256 | m 1 | ) x 2.690 | m 1 | + 0.217 ,
Q sca ( x , m ) = γ ( x , m ) Q sca ( x , m )
γ ( x , m ) = 32.2 | m 1 | 2 5.22 | m 1 | + 1.929 ( 0.1528 | m 1 | 0.00076 ) × ( η 12 . 07 + 424.72 | m 1 | 4465.1 | m 1 | 2 ) η .
[ μ ¯ s , meas 2 λ ( μ s , mod μ s , meas ) 2 μ ¯ s , meas 2 λ ( μ s , mod μ s , meas ) 2 + g ¯ meas 2 λ ( g mod g meas ) 2 ] 1 / 2

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