Abstract

We combine the finite-difference time-domain method with pulse response techniques in order to calculate the light scattering properties of biological cells over a range of wavelengths simultaneously. The method we describe can be used to compute the scattering patterns of cells containing multiple heterogeneous organelles, providing greater geometric flexibility than Mie theory solutions. Using a desktop computer, we calculate the scattering patterns for common homogeneous models of biological cells and also for more complex representations of cellular morphology. We find that the geometry chosen significantly impacts scattering properties, emphasizing the need for careful consideration of appropriate theoretical models of cellular scattering and for accurate microscopic determination of optical properties.

© Optical Society of America

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  1. R. Marchesini, M. Brambilla, C. Clemente, M. Maniezzo, A. Sichirollo, A. Testori, D. Venturoli, and N. Cascinelli, "In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions. I, Reflectance measurements," Photochem. Photobiol. 53, 77-84 (1991).
    [CrossRef] [PubMed]
  2. J. Mourant, I. Bigio, J. Boyer, T. Johnson, R. Conn, T. Johnson, and T. Shimada, "Spectroscopic diagnosis of bladder cancer with elastic light scattering," Lasers Surg. Med. 17, 350-357 (1995).
    [CrossRef] [PubMed]
  3. J. Mourant, I. Bigio, J. Boyer, T. Johnson, and J. Lacey, "Elastic scattering spectroscopy as a diagnostic for differentiating pathologies in the gastrointestinal tract: preliminary testing," J. Biomed. Opt. 1, 192-199 (1996).
    [CrossRef] [PubMed]
  4. Z. Ge, K. Schomacker, and N. Nishioka, "Identification of colonic dysplasia and neoplasia by diffuse reflectance spectroscopy and pattern recognition techniques," Appl. Spectrosc. 52, 833-839 (1998).
    [CrossRef]
  5. G. Zonios, L. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. Feld, "Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo," Appl. Opt. 38, 6628-6637 (1999).
    [CrossRef]
  6. J. Mourant, T. Fuselier, J. Boyer, T. Johnson, and I. Bigio, "Predictions and measurements of scattering and absorption over broad wavelength ranges in tissue phantoms," Appl. Opt. 36, 949-957 (1997).
    [CrossRef] [PubMed]
  7. L. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. Crawford, and M. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Opt. Lett. 80, 627-630.
  8. V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, "Polarized light scattering spectroscopy for quantitative measurement of epithelial structures in situ," IEEE J. Sel. Topics Quantum Electron. 5, (1999).
    [CrossRef]
  9. K. Sokolov, R. Drezek, K. Gossage, and R. Richards-Kortum, "Reflectance spectroscopy with polarized light: is it sensitive to cellular and nuclear morphology," Opt. Lett. 5, 302-317 (1999).
  10. J. Mourant, J. Freyer, A. Hielscher, A. Eick, D. Shen, and T. Johnson, "Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics," Appl. Opt. 37, 3586-3593 (1998).
    [CrossRef]
  11. L. McGann, M. Walterson, L. Hogg, "Light scattering and cell volumes in osmotically stressed and frozen thawed cells," Cytometry. 9, 33-38 (1988).
    [CrossRef] [PubMed]
  12. A. Brunsting and P. Mullaney, "Light scattering from coated spheres: model for biological cells," Appl. Opt. 3, 675-680 (1972).
    [CrossRef]
  13. P. Sloot, and C. Figdor, "Elastic light scattering from nucleated blood cells: rapid numerical analysis," Appl. Opt. 25, 3559-3565 (1986).
    [CrossRef] [PubMed]
  14. A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech, Boston, 1995).
  15. Z. Liao, H. Wong, B. Yang, and Y. Yuan, "A transmitting boundary for transient wave analysis," Sci. Sin. Ser. A. 27, 1063-1076 (1984).
  16. J Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]
  17. A. Dunn, C. Smithpeter, A. Welch, and R. Richards-Kortum, "Finite-Difference Time-Domain Simulation of Light Scattering from Single Cells," J. Biomed. Opt. 2, 262-266 (1997).
    [CrossRef] [PubMed]
  18. A. Dunn, and R. Richards-Kortum, "Three-dimensional computation of light scattering from cells," IEEE J. Sel. Topics Quantum Electron. 2, 898-894 (1996).
    [CrossRef]
  19. R. Drezek, A. Dunn, and R. Richards-Kortum," Light scattering from cells: finite-difference time-domain simulations and goniometric measurements," Appl. Opt. 38, 3651-3661 (1999).
    [CrossRef]
  20. C. Furse, S. Mathur, and O. Gandi, "Improvements to the finite-difference time-domain method for calculating the radar cross section of a perfectly conducting target," IEEE Trans. Microwave Theory Tech. 38, 919-927 (1990).
    [CrossRef]
  21. C. Britt, "Solution of electromagnetic scattering problems using time domain techniques," IEEE Trans. Antennas Propagat. 37, 1181-1192 (1989).
    [CrossRef]
  22. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  23. R. Meyer, "Light scattering from biological cells: dependence of backscatter radiation on membrane thickness and refractive index," Appl. Opt. 18, 585-590 (1979).
    [CrossRef] [PubMed]
  24. M. Anderson, J. Jordon, A. Morse, and F. Sharp, A Text and Atlas of Integrated Colposcopy. (Mosby, St. Louis, 1993).
  25. C. MacAulay, and B. Palcic, "Fractal texture features based on optical density surface area: use in image analysis of cervical cells," Analyt. Quant. Cytol. Histo. 12, 394-398 (1990).
  26. B. Palcic, D. Garner, and C. MacAulay, "Image cytometry and chemoprevention in cervical cancer," J Cell Biochem (Suppl). 23, 43-54 (1995).
    [CrossRef]
  27. A. Taflove, Advances in Computational Electrodynamics: The Finite Difference Time Domain Method (Artech, Boston, 1998).
  28. A. Dunn, Light Scattering Properties of Cells. PhD Dissertation, (University of Texas at Austin, Austin, TX, 1997).

Other

R. Marchesini, M. Brambilla, C. Clemente, M. Maniezzo, A. Sichirollo, A. Testori, D. Venturoli, and N. Cascinelli, "In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions. I, Reflectance measurements," Photochem. Photobiol. 53, 77-84 (1991).
[CrossRef] [PubMed]

J. Mourant, I. Bigio, J. Boyer, T. Johnson, R. Conn, T. Johnson, and T. Shimada, "Spectroscopic diagnosis of bladder cancer with elastic light scattering," Lasers Surg. Med. 17, 350-357 (1995).
[CrossRef] [PubMed]

J. Mourant, I. Bigio, J. Boyer, T. Johnson, and J. Lacey, "Elastic scattering spectroscopy as a diagnostic for differentiating pathologies in the gastrointestinal tract: preliminary testing," J. Biomed. Opt. 1, 192-199 (1996).
[CrossRef] [PubMed]

Z. Ge, K. Schomacker, and N. Nishioka, "Identification of colonic dysplasia and neoplasia by diffuse reflectance spectroscopy and pattern recognition techniques," Appl. Spectrosc. 52, 833-839 (1998).
[CrossRef]

G. Zonios, L. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. Feld, "Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo," Appl. Opt. 38, 6628-6637 (1999).
[CrossRef]

J. Mourant, T. Fuselier, J. Boyer, T. Johnson, and I. Bigio, "Predictions and measurements of scattering and absorption over broad wavelength ranges in tissue phantoms," Appl. Opt. 36, 949-957 (1997).
[CrossRef] [PubMed]

L. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. Crawford, and M. Feld, "Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution," Opt. Lett. 80, 627-630.

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, "Polarized light scattering spectroscopy for quantitative measurement of epithelial structures in situ," IEEE J. Sel. Topics Quantum Electron. 5, (1999).
[CrossRef]

K. Sokolov, R. Drezek, K. Gossage, and R. Richards-Kortum, "Reflectance spectroscopy with polarized light: is it sensitive to cellular and nuclear morphology," Opt. Lett. 5, 302-317 (1999).

J. Mourant, J. Freyer, A. Hielscher, A. Eick, D. Shen, and T. Johnson, "Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics," Appl. Opt. 37, 3586-3593 (1998).
[CrossRef]

L. McGann, M. Walterson, L. Hogg, "Light scattering and cell volumes in osmotically stressed and frozen thawed cells," Cytometry. 9, 33-38 (1988).
[CrossRef] [PubMed]

A. Brunsting and P. Mullaney, "Light scattering from coated spheres: model for biological cells," Appl. Opt. 3, 675-680 (1972).
[CrossRef]

P. Sloot, and C. Figdor, "Elastic light scattering from nucleated blood cells: rapid numerical analysis," Appl. Opt. 25, 3559-3565 (1986).
[CrossRef] [PubMed]

A. Taflove, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech, Boston, 1995).

Z. Liao, H. Wong, B. Yang, and Y. Yuan, "A transmitting boundary for transient wave analysis," Sci. Sin. Ser. A. 27, 1063-1076 (1984).

J Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

A. Dunn, C. Smithpeter, A. Welch, and R. Richards-Kortum, "Finite-Difference Time-Domain Simulation of Light Scattering from Single Cells," J. Biomed. Opt. 2, 262-266 (1997).
[CrossRef] [PubMed]

A. Dunn, and R. Richards-Kortum, "Three-dimensional computation of light scattering from cells," IEEE J. Sel. Topics Quantum Electron. 2, 898-894 (1996).
[CrossRef]

R. Drezek, A. Dunn, and R. Richards-Kortum," Light scattering from cells: finite-difference time-domain simulations and goniometric measurements," Appl. Opt. 38, 3651-3661 (1999).
[CrossRef]

C. Furse, S. Mathur, and O. Gandi, "Improvements to the finite-difference time-domain method for calculating the radar cross section of a perfectly conducting target," IEEE Trans. Microwave Theory Tech. 38, 919-927 (1990).
[CrossRef]

C. Britt, "Solution of electromagnetic scattering problems using time domain techniques," IEEE Trans. Antennas Propagat. 37, 1181-1192 (1989).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).

R. Meyer, "Light scattering from biological cells: dependence of backscatter radiation on membrane thickness and refractive index," Appl. Opt. 18, 585-590 (1979).
[CrossRef] [PubMed]

M. Anderson, J. Jordon, A. Morse, and F. Sharp, A Text and Atlas of Integrated Colposcopy. (Mosby, St. Louis, 1993).

C. MacAulay, and B. Palcic, "Fractal texture features based on optical density surface area: use in image analysis of cervical cells," Analyt. Quant. Cytol. Histo. 12, 394-398 (1990).

B. Palcic, D. Garner, and C. MacAulay, "Image cytometry and chemoprevention in cervical cancer," J Cell Biochem (Suppl). 23, 43-54 (1995).
[CrossRef]

A. Taflove, Advances in Computational Electrodynamics: The Finite Difference Time Domain Method (Artech, Boston, 1998).

A. Dunn, Light Scattering Properties of Cells. PhD Dissertation, (University of Texas at Austin, Austin, TX, 1997).

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Figures (4)

Fig. 1.
Fig. 1.

Validation of the pulse response FDTD code. Comparison of FDTD pulse response results with Mie theory predictions for a 4 µm circular object (m=1.02, λ=1 µm and λ=2 µm). Curves are normalized to scattered intensity at 0°.

Fig 2.
Fig 2.

Validation of the pulse response FDTD code. Calculated scattering diagrams for a series of infinite cylinders (m=1.50, x=1.2 to 2.4). The left graph shows curves obtained by plotting the intensity data corresponding to particular size parameters. The right image displays the calculated scattering over a range of size parameters. The color scale corresponds to the log of the scattered intensity. Each curve in the graph on the left corresponds to a horizontal line through the image on the right.

Fig 3.
Fig 3.

Four models of cellular scattering: (1) nucleus only, (2) cytoplasm only, (3) nucleus and cytoplasm, and (4) nucleus and cytoplasm containing organelles. The color scale corresponds to the log of the scattered intensity.

Fig 4.
Fig 4.

Top: Scattering from normal (left) and dysplastic (right) cervical cell. Note elevated scattering in dysplastic cell. The increased scattering at small angles is due to a larger nucleus to cytoplasm ratio. The increased scattering at high angles is due to alterations in chromatin structure, resulting in increased heterogeneity in nuclear refractive index. The color scale corresponds to the log of the scattered intensity. Bottom: Integrated scattered intensities over three angular ranges (0–20°, 80–100°, and 160–180°) for normal (left) and dysplastic (right) cervical cells

Equations (1)

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G ( k Δ f ) = Δ t n = 0 N 1 g ( n Δ t ) exp ( j 2 π kn N ) , k = 0 , 1 , 2 , , NF

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