Abstract

A Monte Carlo method was derived from the optical scattering properties of spheroidal particles and used for modeling diffuse photon migration in biological tissue. The spheroidal scattering solution used a separation of variables approach and numerical calculation of the light intensity as a function of the scattering angle. A Monte Carlo algorithm was then developed which utilized the scattering solution to determine successive photon trajectories in a three-dimensional simulation of optical diffusion and resultant scattering intensities in virtual tissue. Monte Carlo simulations using isotropic randomization, Henyey–Greenstein phase functions, and spherical Mie scattering were additionally developed and used for comparison to the spheroidal method. Intensity profiles extracted from diffusion simulations showed that the four models differed significantly. The depth of scattering extinction varied widely among the four models, with the isotropic, spherical, spheroidal, and phase function models displaying total extinction at depths of 3.62, 2.83, 3.28, and 1.95 cm, respectively. The results suggest that advanced scattering simulations could be used as a diagnostic tool by distinguishing specific cellular structures in the diffused signal. For example, simulations could be used to detect large concentrations of deformed cell nuclei indicative of early stage cancer. The presented technique is proposed to be a more physical description of photon migration than existing phase function methods. This is attributed to the spheroidal structure of highly scattering mitochondria and elongation of the cell nucleus, which occurs in the initial phases of certain cancers. The potential applications of the model and its importance to diffusive imaging techniques are discussed.

© 2013 Optical Society of America

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2010 (3)

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

F. E. Robles, S. Chowdhury, and A. Wax, “Assessing hemoglobin concentration using spectroscopic optical coherence tomography for feasibility of tissue diagnostics,” Biomed. Opt. Express 1, 310–317 (2010).
[CrossRef]

2009 (4)

M. Friebel, J. Helfmann, U. Netz, and M. Meinke, “Influence of oxygen saturation on the optical scattering properties of human red blood cells in the spectral range 250 to 2000 nm,” J. Biomed. Opt. 14, 034001 (2009).
[CrossRef]

H. J. Böhringer, E. Lankenau, F. Stellmacher, E. Reusche, G. Hüttmann, and A. Giese, “Imaging of human brain tumor tissue by near-infrared laser coherence tomography,” Acta Neurochirugica 151, 507–517 (2009).
[CrossRef]

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

X. Su, K. Singh, W. Rozmus, C. Backhouse, and C. Capjack, “Light scattering characterization of mitochondrial aggregation in single cells,” Opt. Express 17, 13381–13388 (2009).
[CrossRef]

2007 (1)

2006 (1)

P. Kirby, “Calculation of spheroidal wave functions,” Comp. Phys. Commun. 175, 465–472 (2006).

2005 (2)

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

L. Liu, A. Vo, G. Liu, and W. L. McKeehan, “Distinct structural domains within C19ORF5 support association with stabilized microtubules and mitochondrial aggregation and genome destruction,” Cancer Res. 65, 4191–4201 (2005).
[CrossRef]

2002 (1)

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

2001 (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

2000 (2)

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

1998 (1)

T. Rother, “Generalization of the separation of variables method for non-spherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

1996 (2)

N. V. Voshchinnikov, “Electromagnetic scattering by homogenous and coated spheroids: calculations using the separation of variables method,” J. Quant. Spectrosc. Radiat. Transfer 55, 627–636 (1996).
[CrossRef]

A. Dunn and R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Top. Quantum Electron. 2, 898–905 (1996).
[CrossRef]

1995 (2)

B. Beauvoit, S. M. Evans, T. W. Jenkins, E. E. Miller, and B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef]

Y. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34, 4573–4588 (1995).
[CrossRef]

1982 (1)

E. Carlsen, “Transillumination light scanning,” Diagn. Imaging 4, 28–34 (1982).

1975 (1)

1972 (1)

C. M. Gros, Y. Quenneville, and Y. J. Hummel, “Diaphanologie mammaire,” Radiol. Electrol. Med. Nucl. 53, 297–306 (1972).

1969 (1)

T. H. Ji and D. W. Urry, “Correlation of light scattering and absorption flattening effects with distortions in the circular dichroism patterns of mitochondrial membrane fragments,” Biochem. Biophys. Res. Commun. 34, 404–411 (1969).
[CrossRef]

1967 (1)

C. E. Wenner, E. J. Harris, and B. C. Pressman, “Relationship of the light scattering properties of mitochondria to the metabolic state in intact ascites cells,” J. Biol. Chem. 242, 3454–3459 (1967).

1966 (1)

L. Zamboni, D. R. Mishell, J. H. Bell, and M. Baca, “Fine structure of the human ovum in the pronuclear stage,” J. Cell Biol. 30, 579–600 (1966).
[CrossRef]

1945 (1)

A. Claude and E. F. Fullam, “An electron microscope study of isolated mitochondria: method and preliminary results,” J. Exp. Med. 81, 51–62 (1945).
[CrossRef]

1941 (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

1929 (1)

M. Cutler, “Transillumination as an aid in the diagnosis of breast lesions,” Surg. Gynecol. Obstet. 48, 721–727 (1929).

Amoh, Y.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Asano, S.

Baca, M.

L. Zamboni, D. R. Mishell, J. H. Bell, and M. Baca, “Fine structure of the human ovum in the pronuclear stage,” J. Cell Biol. 30, 579–600 (1966).
[CrossRef]

Backhouse, C.

Barth, R. J.

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Beauvoit, B.

B. Beauvoit, S. M. Evans, T. W. Jenkins, E. E. Miller, and B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef]

Bell, J. H.

L. Zamboni, D. R. Mishell, J. H. Bell, and M. Baca, “Fine structure of the human ovum in the pronuclear stage,” J. Cell Biol. 30, 579–600 (1966).
[CrossRef]

Boas, D. A.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Böhringer, H. J.

H. J. Böhringer, E. Lankenau, F. Stellmacher, E. Reusche, G. Hüttmann, and A. Giese, “Imaging of human brain tumor tissue by near-infrared laser coherence tomography,” Acta Neurochirugica 151, 507–517 (2009).
[CrossRef]

Boutet, J.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

Bouvet, M.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Brocker, C.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Butler, J.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

Canpolat, M.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

Capjack, C.

Carlsen, E.

E. Carlsen, “Transillumination light scanning,” Diagn. Imaging 4, 28–34 (1982).

Cerussi, A.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

Chance, B.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

B. Beauvoit, S. M. Evans, T. W. Jenkins, E. E. Miller, and B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef]

Choe, R.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

Chowdhury, S.

Claude, A.

A. Claude and E. F. Fullam, “An electron microscope study of isolated mitochondria: method and preliminary results,” J. Exp. Med. 81, 51–62 (1945).
[CrossRef]

Culver, J. P.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

Custo, A.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Cutler, M.

M. Cutler, “Transillumination as an aid in the diagnosis of breast lesions,” Surg. Gynecol. Obstet. 48, 721–727 (1929).

Dan, I.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Debourdeau, M.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

diFlorio-Alexander, R. M.

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Dimarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Dinten, J.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

Duboeuf, F.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

Dunn, A.

A. Dunn and R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Top. Quantum Electron. 2, 898–905 (1996).
[CrossRef]

Durduran, T.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

Espinoza, J.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

Esponda-Ramos, O.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

Evans, S. M.

B. Beauvoit, S. M. Evans, T. W. Jenkins, E. E. Miller, and B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef]

Fischl, B.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford University, 1957).

Freyer, J. P.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

Friebel, M.

M. Friebel, J. Helfmann, U. Netz, and M. Meinke, “Influence of oxygen saturation on the optical scattering properties of human red blood cells in the spectral range 250 to 2000 nm,” J. Biomed. Opt. 14, 034001 (2009).
[CrossRef]

Fullam, E. F.

A. Claude and E. F. Fullam, “An electron microscope study of isolated mitochondria: method and preliminary results,” J. Exp. Med. 81, 51–62 (1945).
[CrossRef]

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Giammarco, J.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

Giese, A.

H. J. Böhringer, E. Lankenau, F. Stellmacher, E. Reusche, G. Hüttmann, and A. Giese, “Imaging of human brain tumor tissue by near-infrared laser coherence tomography,” Acta Neurochirugica 151, 507–517 (2009).
[CrossRef]

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Grimson, W. E. L.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Gros, C. M.

C. M. Gros, Y. Quenneville, and Y. J. Hummel, “Diaphanologie mammaire,” Radiol. Electrol. Med. Nucl. 53, 297–306 (1972).

Guyon, L.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

Harris, E. J.

C. E. Wenner, E. J. Harris, and B. C. Pressman, “Relationship of the light scattering properties of mitochondria to the metabolic state in intact ascites cells,” J. Biol. Chem. 242, 3454–3459 (1967).

Helfmann, J.

M. Friebel, J. Helfmann, U. Netz, and M. Meinke, “Influence of oxygen saturation on the optical scattering properties of human red blood cells in the spectral range 250 to 2000 nm,” J. Biomed. Opt. 14, 034001 (2009).
[CrossRef]

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Herve, L.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

Hoffman, R. M.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Holboke, M. J.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

Hummel, Y. J.

C. M. Gros, Y. Quenneville, and Y. J. Hummel, “Diaphanologie mammaire,” Radiol. Electrol. Med. Nucl. 53, 297–306 (1972).

Hüttmann, G.

H. J. Böhringer, E. Lankenau, F. Stellmacher, E. Reusche, G. Hüttmann, and A. Giese, “Imaging of human brain tumor tissue by near-infrared laser coherence tomography,” Acta Neurochirugica 151, 507–517 (2009).
[CrossRef]

Jenkins, T. W.

B. Beauvoit, S. M. Evans, T. W. Jenkins, E. E. Miller, and B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef]

Ji, T. H.

T. H. Ji and D. W. Urry, “Correlation of light scattering and absorption flattening effects with distortions in the circular dichroism patterns of mitochondrial membrane fragments,” Biochem. Biophys. Res. Commun. 34, 404–411 (1969).
[CrossRef]

Jiang, P.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Jiang, S.

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Johnson, T. M.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

Kaufman, P. A.

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Kirby, P.

P. Kirby, “Calculation of spheroidal wave functions,” Comp. Phys. Commun. 175, 465–472 (2006).

Lankenau, E.

H. J. Böhringer, E. Lankenau, F. Stellmacher, E. Reusche, G. Hüttmann, and A. Giese, “Imaging of human brain tumor tissue by near-infrared laser coherence tomography,” Acta Neurochirugica 151, 507–517 (2009).
[CrossRef]

Lanning, R.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

Li, Z.

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Liu, G.

L. Liu, A. Vo, G. Liu, and W. L. McKeehan, “Distinct structural domains within C19ORF5 support association with stabilized microtubules and mitochondrial aggregation and genome destruction,” Cancer Res. 65, 4191–4201 (2005).
[CrossRef]

Liu, L.

L. Liu, A. Vo, G. Liu, and W. L. McKeehan, “Distinct structural domains within C19ORF5 support association with stabilized microtubules and mitochondrial aggregation and genome destruction,” Cancer Res. 65, 4191–4201 (2005).
[CrossRef]

Matanock, A.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

McKeehan, W. L.

L. Liu, A. Vo, G. Liu, and W. L. McKeehan, “Distinct structural domains within C19ORF5 support association with stabilized microtubules and mitochondrial aggregation and genome destruction,” Cancer Res. 65, 4191–4201 (2005).
[CrossRef]

Meinke, M.

M. Friebel, J. Helfmann, U. Netz, and M. Meinke, “Influence of oxygen saturation on the optical scattering properties of human red blood cells in the spectral range 250 to 2000 nm,” J. Biomed. Opt. 14, 034001 (2009).
[CrossRef]

Mesquita, R.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Miller, E. E.

B. Beauvoit, S. M. Evans, T. W. Jenkins, E. E. Miller, and B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef]

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Mishell, D. R.

L. Zamboni, D. R. Mishell, J. H. Bell, and M. Baca, “Fine structure of the human ovum in the pronuclear stage,” J. Cell Biol. 30, 579–600 (1966).
[CrossRef]

Moossa, A. R.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Mourant, J. R.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

Netz, U.

M. Friebel, J. Helfmann, U. Netz, and M. Meinke, “Influence of oxygen saturation on the optical scattering properties of human red blood cells in the spectral range 250 to 2000 nm,” J. Biomed. Opt. 14, 034001 (2009).
[CrossRef]

Paulsen, K. D.

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Peltie, P.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

Pham, T.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

Pogue, B. W.

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Pressman, B. C.

C. E. Wenner, E. J. Harris, and B. C. Pressman, “Relationship of the light scattering properties of mitochondria to the metabolic state in intact ascites cells,” J. Biol. Chem. 242, 3454–3459 (1967).

Quenneville, Y.

C. M. Gros, Y. Quenneville, and Y. J. Hummel, “Diaphanologie mammaire,” Radiol. Electrol. Med. Nucl. 53, 297–306 (1972).

Reusche, E.

H. J. Böhringer, E. Lankenau, F. Stellmacher, E. Reusche, G. Hüttmann, and A. Giese, “Imaging of human brain tumor tissue by near-infrared laser coherence tomography,” Acta Neurochirugica 151, 507–517 (2009).
[CrossRef]

Richards-Kortum, R.

A. Dunn and R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Top. Quantum Electron. 2, 898–905 (1996).
[CrossRef]

Robles, F. E.

Rother, T.

T. Rother, “Generalization of the separation of variables method for non-spherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

Rozmus, W.

Saroul, L.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

Shah, N.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

Singh, K.

Stellmacher, F.

H. J. Böhringer, E. Lankenau, F. Stellmacher, E. Reusche, G. Hüttmann, and A. Giese, “Imaging of human brain tumor tissue by near-infrared laser coherence tomography,” Acta Neurochirugica 151, 507–517 (2009).
[CrossRef]

Stetter, K.

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Su, X.

Svaasand, L.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

Tomita, K.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Tromberg, B. J.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

Tsuchiya, H.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Tsuji, K.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Tsuzuki, D.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Urry, D. W.

T. H. Ji and D. W. Urry, “Correlation of light scattering and absorption flattening effects with distortions in the circular dichroism patterns of mitochondrial membrane fragments,” Biochem. Biophys. Res. Commun. 34, 404–411 (1969).
[CrossRef]

Vo, A.

L. Liu, A. Vo, G. Liu, and W. L. McKeehan, “Distinct structural domains within C19ORF5 support association with stabilized microtubules and mitochondrial aggregation and genome destruction,” Cancer Res. 65, 4191–4201 (2005).
[CrossRef]

Voshchinnikov, N. V.

N. V. Voshchinnikov, “Electromagnetic scattering by homogenous and coated spheroids: calculations using the separation of variables method,” J. Quant. Spectrosc. Radiat. Transfer 55, 627–636 (1996).
[CrossRef]

Vray, D.

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

Wang, J.

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Wang, L. V.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007), pp. 37–60.

Wax, A.

Wells, W.

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Wenner, C. E.

C. E. Wenner, E. J. Harris, and B. C. Pressman, “Relationship of the light scattering properties of mitochondria to the metabolic state in intact ascites cells,” J. Biol. Chem. 242, 3454–3459 (1967).

Wu, H.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007), pp. 37–60.

Xu, M.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Xu, Y.

Yamamoto, G.

Yamamoto, N.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Yamauchi, K.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Yang, M.

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

Yodh, A. G.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

Zamboni, L.

L. Zamboni, D. R. Mishell, J. H. Bell, and M. Baca, “Fine structure of the human ovum in the pronuclear stage,” J. Cell Biol. 30, 579–600 (1966).
[CrossRef]

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Zubkov, L.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

Acta Neurochirugica (1)

H. J. Böhringer, E. Lankenau, F. Stellmacher, E. Reusche, G. Hüttmann, and A. Giese, “Imaging of human brain tumor tissue by near-infrared laser coherence tomography,” Acta Neurochirugica 151, 507–517 (2009).
[CrossRef]

Anal. Biochem. (1)

B. Beauvoit, S. M. Evans, T. W. Jenkins, E. E. Miller, and B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef]

Appl. Opt. (2)

Astrophys. J. (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Biochem. Biophys. Res. Commun. (1)

T. H. Ji and D. W. Urry, “Correlation of light scattering and absorption flattening effects with distortions in the circular dichroism patterns of mitochondrial membrane fragments,” Biochem. Biophys. Res. Commun. 34, 404–411 (1969).
[CrossRef]

Biomed. Opt. Express (1)

Cancer Res. (2)

K. Yamauchi, M. Yang, P. Jiang, N. Yamamoto, M. Xu, Y. Amoh, K. Tsuji, M. Bouvet, H. Tsuchiya, K. Tomita, A. R. Moossa, and R. M. Hoffman, “Real-time in vivo dual-color imaging of intracapillary cancer cell and nucleus deformation and migration,” Cancer Res. 65, 4246–4252 (2005).
[CrossRef]

L. Liu, A. Vo, G. Liu, and W. L. McKeehan, “Distinct structural domains within C19ORF5 support association with stabilized microtubules and mitochondrial aggregation and genome destruction,” Cancer Res. 65, 4191–4201 (2005).
[CrossRef]

Comp. Phys. Commun. (1)

P. Kirby, “Calculation of spheroidal wave functions,” Comp. Phys. Commun. 175, 465–472 (2006).

Diagn. Imaging (1)

E. Carlsen, “Transillumination light scanning,” Diagn. Imaging 4, 28–34 (1982).

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

A. Dunn and R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Top. Quantum Electron. 2, 898–905 (1996).
[CrossRef]

IEEE Signal Process. Mag. (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

J. Biol. Chem. (1)

C. E. Wenner, E. J. Harris, and B. C. Pressman, “Relationship of the light scattering properties of mitochondria to the metabolic state in intact ascites cells,” J. Biol. Chem. 242, 3454–3459 (1967).

J. Biomed Opt. (1)

J. Boutet, L. Herve, M. Debourdeau, L. Guyon, P. Peltie, J. Dinten, L. Saroul, F. Duboeuf, and D. Vray, “Bimodal ultrasound and fluorescence approach for prostate cancer diagnosis,” J. Biomed Opt. 14, 064001 (2009).
[CrossRef]

J. Biomed. Opt. (2)

M. Friebel, J. Helfmann, U. Netz, and M. Meinke, “Influence of oxygen saturation on the optical scattering properties of human red blood cells in the spectral range 250 to 2000 nm,” J. Biomed. Opt. 14, 034001 (2009).
[CrossRef]

J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A. Matanock, K. Stetter, and J. P. Freyer, “Light scattering from cells: the contribution of the nucleus and the effects of proliferative status,” J. Biomed. Opt. 5, 131–137 (2000).
[CrossRef]

J. Cell Biol. (1)

L. Zamboni, D. R. Mishell, J. H. Bell, and M. Baca, “Fine structure of the human ovum in the pronuclear stage,” J. Cell Biol. 30, 579–600 (1966).
[CrossRef]

J. Exp. Med. (1)

A. Claude and E. F. Fullam, “An electron microscope study of isolated mitochondria: method and preliminary results,” J. Exp. Med. 81, 51–62 (1945).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

N. V. Voshchinnikov, “Electromagnetic scattering by homogenous and coated spheroids: calculations using the separation of variables method,” J. Quant. Spectrosc. Radiat. Transfer 55, 627–636 (1996).
[CrossRef]

T. Rother, “Generalization of the separation of variables method for non-spherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

Med. Phys. (1)

J. Wang, S. Jiang, Z. Li, R. M. diFlorio-Alexander, R. J. Barth, P. A. Kaufman, B. W. Pogue, and K. D. Paulsen, “In vivo quantitative imaging of normal and cancerous breast tissue using broadband diffuse optical tomography,” Med. Phys. 37, 3715–3724 (2010).
[CrossRef]

Neoplasia (1)

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, and J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef]

NeuroImage (1)

A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. L. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49, 561–567 (2010).
[CrossRef]

Opt. Express (2)

Phys. Med. Biol. (1)

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47, 2847–2861 (2002).
[CrossRef]

Radiol. Electrol. Med. Nucl. (1)

C. M. Gros, Y. Quenneville, and Y. J. Hummel, “Diaphanologie mammaire,” Radiol. Electrol. Med. Nucl. 53, 297–306 (1972).

Surg. Gynecol. Obstet. (1)

M. Cutler, “Transillumination as an aid in the diagnosis of breast lesions,” Surg. Gynecol. Obstet. 48, 721–727 (1929).

Other (3)

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007), pp. 37–60.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

C. Flammer, Spheroidal Wave Functions (Stanford University, 1957).

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Figures (9)

Fig. 1.
Fig. 1.

Scattered intensity measured on the surface of a spheroid for the case of ζ=0.3. The image was generated using the presented spheroidal scattering solution and corresponds to light incident on the spheroid at an angle of 17.76° from the z axis. The spheroid’s azimuthal (ϕ) and polar angles (η) are shown on the vertical and horizontal axes, respectively.

Fig. 2.
Fig. 2.

Scattered intensity measured on the surface of a sphere. The image was generated by modifying the eccentricity of spheroids until they were approximately spherical. The symmetry and lack of dependence on an incident angle suggest the scattering solution is accurate. The sphere’s azimuthal (ϕ) and polar angles (θ) are shown on the vertical and horizontal axes, respectively.

Fig. 3.
Fig. 3.

Diagram of scattering events in the spheroidal coordinate system. The incident direction lies in the xz plane, and the incident angle ζ is measured from the z axis. Once a scattering direction is determined, it becomes the incident angle in a subsequent rotated coordinate system. At each scattering site, local coordinates must be transformed into the global coordinate system.

Fig. 4.
Fig. 4.

Simulated diffusion profile using an isotropic scattering technique. The diffused intensity generated by the Monte Carlo algorithm is shown (a) on the plane y=0, (b) along the x axis, and (c) along the z axis. Surface plots of (d) the surface intensity and (e) the depth intensity are also shown.

Fig. 5.
Fig. 5.

Alternate views of the isotropic diffusion profile shown in Fig. 4. The intensity is shown measured (a) along the surface of the tissue. (b) 3D model, which was rendered using a series of 2D profiles measured along consecutive planes in the image grid. (c) Cross section of the 3D model. Surface simulations are of particular interest in diagnostic applications.

Fig. 6.
Fig. 6.

Comparison of diffusion profiles. The images were generated by Monte Carlo algorithms that used different scattering methods. These included (a) isotropic scattering, (b) Mie scattering (spheres), (c) spheroidal scattering, and (d) the Henyey–Greenstein phase function. The differences between profiles indicate that scattering mechanisms have a significant effect on diffusion.

Fig. 7.
Fig. 7.

Plots of depth intensities measured along the z axis (top) and surface intensities measured along the x axis (bottom) of the diffusion profiles shown in Fig. 6. Profiles of this type allow for a quantitative description of the differences between diffusion profiles.

Fig. 8.
Fig. 8.

Plots of depth intensities measured along the z axis (top) for varying concentrations of spheroids among spherical constituents. Detailed analysis of the intensity variation is shown in the bar graph (bottom). Measurable differences (2%14%) exist between the profiles, which supports the hypothesis that diffusion simulations could be used as a diagnostic tool by detecting the presence of cancerous cells (spheroids) among healthy cells (spheres).

Fig. 9.
Fig. 9.

Anisotropy of the spheroidal scattering distributions plotted as a function of the incident angle.

Equations (22)

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2E+k2E=0,2H+k2H=0.
2ψ+k2ψ=0.
P(ϕ)=eimϕ,
ddη[(1η2)dSmn(η)dη]+(λmnc2η2m21η2)Smn(η)=0,
Smn(η)=r=0,1drmnPm+rm(η).
ddξ[(ξ21)dRmn(ξ)dξ][λmnc2ξ2+m2(ξ21)]Rmn(ξ)=0.
Rmn(1)(ξ)=1[r=0,1(r+2m)!r!drmn][ξ21ξ2]m2r=0,1ir+nmdrmn(r+2m)!r!jm+r(cξ).
Rmn(2)(ξ)=1[r=0,1(r+2m)!r!drmn][ξ21ξ2]m2r=0,1ir+nmdrmn(r+2m)!r!ym+r(cξ)
M(k)mn(j)=×(rψ(k)mn(j)),N(k)mn(j)=1k(×M(k)mn(j)).
E(i)=m=0n=min[gmn(ζ)Memn(1)+ifmn(ζ)Nomn(1)],
H(i)=H(I)m=0n=min[fmn(ζ)Momn(1)igmn(ζ)Nemn(1)].
E(s)=m=0n=min[βmnMemn(3)+iαmnNomn(3)],
H(s)=H(I)m=0n=min[αmnMomn(3)iβmnNemn(3)].
E(t)=m=0n=min[δmnMemn(1)+iγmnNomn(1)],
H(t)=H(II)m=0n=min[γmnMomn(1)iδmnNemn(1)].
Eη(i)+Eη(s)=Eη(t),Eϕ(i)+Eϕ(s)=Eϕ(t),Hη(i)+Hη(s)=Hη(t),Hϕ(i)+Hϕ(s)=Hϕ(t).
s=lnξμtrlnξμs.
p(cosθ)=1g22(1+g22gcosθ)32.
cosη=12g[1+g2(1g21g+2gϵ)2]
cosη=2ϵ1
ϕ=2πϵ.
cosθ=2π0πp(θ)sinθcosθdθ=g.

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