Abstract

The FDTD method was used to simulate focused Gaussian beam propagation through multiple inhomogeneous biological cells. To our knowledge this is the first three dimensional computational investigation of a focused beam interacting with multiple biological cells using FDTD. A parametric study was performed whereby three simulated cells were varied by organelle density, nuclear type and arrangement of internal cellular structure and the beam focus depth was varied within the cluster of cells. Of the organelle types investigated, it appears that the cell nuclei are responsible for the greatest scattering of the focused beam in the configurations studied. Additional simulations to determine the optical scattering from 27 cells were also run and compared to the three cell case. No significant degradation of two-photon lateral imaging resolution was predicted to occur within the first 40 µm of imaging depth.

© 2009 Optical Society of America

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2008 (2)

I. R. Capoglu, A. Taflove, and V. Backman, "Generation of an incident focused light pulse in FDTD," Opt. Express 16(23), 19,208-19,220 (2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-19208.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

2006 (4)

M. Oheim, D. J. Michael, M. Geisbauer, D. Madsen, and R. H. Chow, "Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches," Adv. Drug Del. Rev. 58(7), 788-808 (2006).
[CrossRef]

P. Theer and W. Denk, "On the fundamental imaging-depth limit in two-photon microscopy," J. Opt. Soc. Am. A 23(12), 3139-3149 (2006).
[CrossRef]

C. Liu and C. E. Capjack, "Effects of cellular fine structure on scattered light pattern," IEEE Trans. Nanobiosci. 5(2), 76-82 (2006).
[CrossRef]

W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53(18), 2691-2700 (2006).
[CrossRef]

2005 (3)

2003 (3)

2001 (2)

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, "Two-photon microscopy in brain tissue: parameters influencing the imaging depth," J. Neurosci. Methods 112(2), 205 (2001).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, "Numerical Modelling of Optical Trapping," Comp. Phys. Comm. 142, 468-471 (2001).
[CrossRef]

2000 (1)

1999 (1)

1998 (1)

1997 (1)

W. Denk and K. Svoboda, "Photon upmanship: Why multiphoton imaging is more than a gimmick," Neuron 18(3), 351-357 (1997).
[CrossRef]

1996 (3)

A. Dunn and R. Richards-Kortum, "Three-dimensional computation of light scattering from cells," IEEE J. Sel. Top. Quantum Electron. 2(4), 898-905 (1996).

J.-P. Berenger, "Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J. Comput. Phys. 127(2), 363-379 (1996).
[CrossRef]

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1(2), 200-211 (1996).
[CrossRef]

1990 (1)

W. Denk, J. Strickler, and W. Webb, "2-Photon Laser Scanning Fluorescence Microscopy," Science 248(4951), 73-76 (1990).
[CrossRef]

1989 (1)

J. P. Barton and D. R. Alexander, "Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

1981 (1)

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. 23(4), 377-382 (1981).
[CrossRef]

1975 (1)

A. Taflove and M. Brodwin, "Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell’s Equations," IEEE Trans. Microwave Theory Tech. 23(8), 623-630 (1975).
[CrossRef]

1974 (1)

A. Brunsting and P. F. Mullaney, "Differential Light Scattering from Spherical Mammalian Cells," Biophys. J. 14(6), 439 (1974).
[CrossRef]

1966 (1)

K. Yee, "Numerical solution of inital boundary value problems involving maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14(3), 302-307 (1966).

Alexander, D. R.

J. P. Barton and D. R. Alexander, "Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

Backman, V.

I. R. Capoglu, A. Taflove, and V. Backman, "Generation of an incident focused light pulse in FDTD," Opt. Express 16(23), 19,208-19,220 (2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-19208.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

X. Li, A. Taflove, and V. Backman, "Recent progress in exact and reduced-order modeling of light-scattering properties of complex structures," IEEE J. Sel. Top. Quantum Electron. 11(4), 759-765 (2005).

Barton, J. P.

J. P. Barton and D. R. Alexander, "Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

Beaurepaire, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, "Two-photon microscopy in brain tissue: parameters influencing the imaging depth," J. Neurosci. Methods 112(2), 205 (2001).
[CrossRef]

Beauvoit, B.

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1(2), 200-211 (1996).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, "Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J. Comput. Phys. 127(2), 363-379 (1996).
[CrossRef]

Berns, M. W.

Bishop, A. I.

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, "Numerical Modelling of Optical Trapping," Comp. Phys. Comm. 142, 468-471 (2001).
[CrossRef]

Brodwin, M.

A. Taflove and M. Brodwin, "Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell’s Equations," IEEE Trans. Microwave Theory Tech. 23(8), 623-630 (1975).
[CrossRef]

Brunsting, A.

A. Brunsting and P. F. Mullaney, "Differential Light Scattering from Spherical Mammalian Cells," Biophys. J. 14(6), 439 (1974).
[CrossRef]

Capjack, C. E.

C. Liu and C. E. Capjack, "Effects of cellular fine structure on scattered light pattern," IEEE Trans. Nanobiosci. 5(2), 76-82 (2006).
[CrossRef]

Capoglu, I. R.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

I. R. Capoglu, A. Taflove, and V. Backman, "Generation of an incident focused light pulse in FDTD," Opt. Express 16(23), 19,208-19,220 (2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-19208.

Chaigneau, E.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, "Two-photon microscopy in brain tissue: parameters influencing the imaging depth," J. Neurosci. Methods 112(2), 205 (2001).
[CrossRef]

Challener, W.

Chance, B.

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1(2), 200-211 (1996).
[CrossRef]

Charpak, S.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, "Two-photon microscopy in brain tissue: parameters influencing the imaging depth," J. Neurosci. Methods 112(2), 205 (2001).
[CrossRef]

Choi, K.

Chow, R. H.

M. Oheim, D. J. Michael, M. Geisbauer, D. Madsen, and R. H. Chow, "Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches," Adv. Drug Del. Rev. 58(7), 788-808 (2006).
[CrossRef]

Coleno, M.

Deng, X.

Denk, W.

P. Theer and W. Denk, "On the fundamental imaging-depth limit in two-photon microscopy," J. Opt. Soc. Am. A 23(12), 3139-3149 (2006).
[CrossRef]

W. Denk and K. Svoboda, "Photon upmanship: Why multiphoton imaging is more than a gimmick," Neuron 18(3), 351-357 (1997).
[CrossRef]

W. Denk, J. Strickler, and W. Webb, "2-Photon Laser Scanning Fluorescence Microscopy," Science 248(4951), 73-76 (1990).
[CrossRef]

Dong, C.-Y.

C.-Y. Dong, K. Koenig, and P. So, "Characterizing point spread functions of two-photon fluorescence microscopy in turbid medium," J. Biomed. Opt. 8(3), 450-459 (2003).
[CrossRef]

Drezek, R.

Dunn, A.

R. Drezek, A. Dunn, and R. Richards-Kortum, "Light scattering from cells: finite-difference time-domain simulations and goniometric measurements," Appl. Opt. 38(16), 3651-3661 (1998).

A. Dunn and R. Richards-Kortum, "Three-dimensional computation of light scattering from cells," IEEE J. Sel. Top. Quantum Electron. 2(4), 898-905 (1996).

Dunn, A. K.

Gan, X.

Gauthier, R.

Geisbauer, M.

M. Oheim, D. J. Michael, M. Geisbauer, D. Madsen, and R. H. Chow, "Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches," Adv. Drug Del. Rev. 58(7), 788-808 (2006).
[CrossRef]

Gu, M.

Heckenberg, N. R.

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, "Numerical Modelling of Optical Trapping," Comp. Phys. Comm. 142, 468-471 (2001).
[CrossRef]

Heifetz, A.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

Jiang, Y.

W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53(18), 2691-2700 (2006).
[CrossRef]

Kim, H.

Kim, S.

Kimura, M.

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1(2), 200-211 (1996).
[CrossRef]

Koenig, K.

C.-Y. Dong, K. Koenig, and P. So, "Characterizing point spread functions of two-photon fluorescence microscopy in turbid medium," J. Biomed. Opt. 8(3), 450-459 (2003).
[CrossRef]

Kunte, D.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

Lee, B.

Li, X.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

X. Li, A. Taflove, and V. Backman, "Recent progress in exact and reduced-order modeling of light-scattering properties of complex structures," IEEE J. Sel. Top. Quantum Electron. 11(4), 759-765 (2005).

Lim, Y.

Liu, C.

C. Liu and C. E. Capjack, "Effects of cellular fine structure on scattered light pattern," IEEE Trans. Nanobiosci. 5(2), 76-82 (2006).
[CrossRef]

Liu, H.

H. Liu, B. Beauvoit, M. Kimura, and B. Chance, "Dependence of tissue optical properties on solute-induced changes in refractive index and osmolarity," J. Biomed. Opt. 1(2), 200-211 (1996).
[CrossRef]

Liu, Y.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

Madsen, D.

M. Oheim, D. J. Michael, M. Geisbauer, D. Madsen, and R. H. Chow, "Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches," Adv. Drug Del. Rev. 58(7), 788-808 (2006).
[CrossRef]

Mertz, J.

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, "Two-photon microscopy in brain tissue: parameters influencing the imaging depth," J. Neurosci. Methods 112(2), 205 (2001).
[CrossRef]

Michael, D. J.

M. Oheim, D. J. Michael, M. Geisbauer, D. Madsen, and R. H. Chow, "Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches," Adv. Drug Del. Rev. 58(7), 788-808 (2006).
[CrossRef]

Mullaney, P. F.

A. Brunsting and P. F. Mullaney, "Differential Light Scattering from Spherical Mammalian Cells," Biophys. J. 14(6), 439 (1974).
[CrossRef]

Mur, G.

G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. 23(4), 377-382 (1981).
[CrossRef]

Nieminen, T. A.

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, "Numerical Modelling of Optical Trapping," Comp. Phys. Comm. 142, 468-471 (2001).
[CrossRef]

Oheim, M.

M. Oheim, D. J. Michael, M. Geisbauer, D. Madsen, and R. H. Chow, "Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches," Adv. Drug Del. Rev. 58(7), 788-808 (2006).
[CrossRef]

M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, "Two-photon microscopy in brain tissue: parameters influencing the imaging depth," J. Neurosci. Methods 112(2), 205 (2001).
[CrossRef]

Pan, S.

W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53(18), 2691-2700 (2006).
[CrossRef]

Peng, C.

Pradhan, P.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

Richards-Kortum, R.

R. Drezek, A. Dunn, and R. Richards-Kortum, "Light scattering from cells: finite-difference time-domain simulations and goniometric measurements," Appl. Opt. 38(16), 3651-3661 (1998).

A. Dunn and R. Richards-Kortum, "Three-dimensional computation of light scattering from cells," IEEE J. Sel. Top. Quantum Electron. 2(4), 898-905 (1996).

Rogers, J. D.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

Roy, H. K.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

Rubinsztein-Dunlop, H.

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, "Numerical Modelling of Optical Trapping," Comp. Phys. Comm. 142, 468-471 (2001).
[CrossRef]

Sendur, I.

So, P.

C.-Y. Dong, K. Koenig, and P. So, "Characterizing point spread functions of two-photon fluorescence microscopy in turbid medium," J. Biomed. Opt. 8(3), 450-459 (2003).
[CrossRef]

Strickler, J.

W. Denk, J. Strickler, and W. Webb, "2-Photon Laser Scanning Fluorescence Microscopy," Science 248(4951), 73-76 (1990).
[CrossRef]

Subramanian, H.

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W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53(18), 2691-2700 (2006).
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H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

I. R. Capoglu, A. Taflove, and V. Backman, "Generation of an incident focused light pulse in FDTD," Opt. Express 16(23), 19,208-19,220 (2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-19208.

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W. Sun, S. Pan, and Y. Jiang, "Computation of the optical trapping force on small particles illuminated with a focused light beam using a FDTD method," J. Mod. Opt. 53(18), 2691-2700 (2006).
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M. Oheim, E. Beaurepaire, E. Chaigneau, J. Mertz, and S. Charpak, "Two-photon microscopy in brain tissue: parameters influencing the imaging depth," J. Neurosci. Methods 112(2), 205 (2001).
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Opt. Express (4)

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Proc. National Acad. Sci. (1)

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, "Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells," Proc. National Acad. Sci. 105(51), 20,118-20,123 (2008).

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Figures (12)

Fig. 1.
Fig. 1.

Example Slice of 3D 3 Cell Geometry used in FDTD Model. Axes are in microns. Vertical dotted lines represent focal depths in parametric study.

Fig. 2.
Fig. 2.

Three dimensional representation of 3 Cell Geometry used in FDTD Model.

Fig. 3.
Fig. 3.

Examples of recorded steady-state optical intensity data (log(I) shown). (a) Incident optical intensity data. Focal depth of 42 µm. (b) Total optical intensity data for incident case in (a). (c) Total optical intensity data for incident focal depth of 22 µm

Fig. 4.
Fig. 4.

Beam profiles along axial and radial directions. Includes profiles of data in Figs. 3b and 3c

Fig. 5.
Fig. 5.

Fluorescence excitation signals for case of cells containing only small organelles and no nucleus.

Fig. 6.
Fig. 6.

Fluorescence excitation signals for case of cells containing a nucleus and small organelles.

Fig. 7.
Fig. 7.

Radial FWHM for case of cells containing only small organelles and no nucleus.

Fig. 8.
Fig. 8.

Radial FWHM for case of cells containing a nucleus and small organelles.

Fig. 9.
Fig. 9.

Three dimensional views of scattering geometry for 3 cell and 27 cell cases

Fig. 10.
Fig. 10.

Examples of recorded steady-state optical intensity data (log(I) shown). (a) Total optical intensity data for 3 cell case. (b) Total optical intensity data for 27 cell case

Fig. 11.
Fig. 11.

Three dimensional views of geometry for 3 cell and 27 cell cases with optical intensity data

Fig. 12.
Fig. 12.

Beam profiles for 12 µm and 42 µm focal depths in the case of 3 cells and 27 cells

Equations (4)

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×Hscat=ε0εrEscatt+ε0(εr1)Einct
A e(xμ)22σ2
FWHM=2σ 2ln(2)
I2P=VI2dVVfocI2dVΣiΣjΣkIi,j,k2Δx3

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