Abstract

We present a robust simulation technique to model the time-reversed ultrasonically encoded (TRUE) technique for deep-tissue imaging. The pseudospectral time-domain (PSTD) algorithm is employed to rigorously model the electromagnetic wave interaction of light propagating through a macroscopic scattering medium. Based upon numerical solutions of Maxwell’s equations, the amplitude and phase are accurately accounted for to analyze factors that affect the TRUE propagation of light through scattering media. More generally, we demonstrate the feasibility of modeling light propagation through a virtual tissue model of macroscopic dimensions with numerical solutions of Maxwell’s equations.

© 2014 Optical Society of America

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  1. Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun.3, 928 (2012).
  2. X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011).
    [CrossRef] [PubMed]
  3. K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics6(10), 657–661 (2012).
    [CrossRef] [PubMed]
  4. J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt.18(2), 025004 (2013).
    [CrossRef] [PubMed]
  5. S. H. Tseng, “PSTD Simulation of optical phase conjugation of light propagating long optical paths,” Opt. Express17(7), 5490–5495 (2009).
    [CrossRef] [PubMed]
  6. S. H. Tseng, “Investigating the Optical Phase Conjugation Reconstruction Phenomenon of Light Multiply Scattered by a Random Medium,” IEEE Photon. J.2(4), 636–641 (2010).
    [CrossRef]
  7. Q. H. Liu, “Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm,” IEEE Trans. Geosci. Rem. Sens.37(2), 917–926 (1999).
    [CrossRef]
  8. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag.44(12), 1630–1639 (1996).
    [CrossRef]
  9. Y. Huang, C. Tsai, W. Ting, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” In Review.
  10. A. Taflove and S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method (Artech House, 2000).
  11. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
    [CrossRef] [PubMed]

2013 (1)

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt.18(2), 025004 (2013).
[CrossRef] [PubMed]

2012 (2)

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun.3, 928 (2012).

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics6(10), 657–661 (2012).
[CrossRef] [PubMed]

2011 (1)

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011).
[CrossRef] [PubMed]

2010 (1)

S. H. Tseng, “Investigating the Optical Phase Conjugation Reconstruction Phenomenon of Light Multiply Scattered by a Random Medium,” IEEE Photon. J.2(4), 636–641 (2010).
[CrossRef]

2009 (1)

2007 (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

1999 (1)

Q. H. Liu, “Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm,” IEEE Trans. Geosci. Rem. Sens.37(2), 917–926 (1999).
[CrossRef]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag.44(12), 1630–1639 (1996).
[CrossRef]

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

Choi, W.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

Cui, M.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics6(10), 657–661 (2012).
[CrossRef] [PubMed]

Dasari, R. R.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

DiMarzio, C. A.

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt.18(2), 025004 (2013).
[CrossRef] [PubMed]

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun.3, 928 (2012).

Fang-Yen, C.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

Feld, M. S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

Fiolka, R.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics6(10), 657–661 (2012).
[CrossRef] [PubMed]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag.44(12), 1630–1639 (1996).
[CrossRef]

Hollmann, J. L.

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt.18(2), 025004 (2013).
[CrossRef] [PubMed]

Horstmeyer, R.

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt.18(2), 025004 (2013).
[CrossRef] [PubMed]

Huang, Y.

Y. Huang, C. Tsai, W. Ting, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” In Review.

Judkewitz, B.

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun.3, 928 (2012).

Liu, H.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011).
[CrossRef] [PubMed]

Liu, Q. H.

Q. H. Liu, “Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm,” IEEE Trans. Geosci. Rem. Sens.37(2), 917–926 (1999).
[CrossRef]

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

Si, K.

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics6(10), 657–661 (2012).
[CrossRef] [PubMed]

Ting, W.

Y. Huang, C. Tsai, W. Ting, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” In Review.

Tsai, C.

Y. Huang, C. Tsai, W. Ting, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” In Review.

Tseng, S. H.

S. H. Tseng, “Investigating the Optical Phase Conjugation Reconstruction Phenomenon of Light Multiply Scattered by a Random Medium,” IEEE Photon. J.2(4), 636–641 (2010).
[CrossRef]

S. H. Tseng, “PSTD Simulation of optical phase conjugation of light propagating long optical paths,” Opt. Express17(7), 5490–5495 (2009).
[CrossRef] [PubMed]

Y. Huang, C. Tsai, W. Ting, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” In Review.

Wang, L. V.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011).
[CrossRef] [PubMed]

Wang, Y. M.

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun.3, 928 (2012).

Xu, X.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011).
[CrossRef] [PubMed]

Yang, C.

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt.18(2), 025004 (2013).
[CrossRef] [PubMed]

Yang, C. H.

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun.3, 928 (2012).

IEEE Photon. J. (1)

S. H. Tseng, “Investigating the Optical Phase Conjugation Reconstruction Phenomenon of Light Multiply Scattered by a Random Medium,” IEEE Photon. J.2(4), 636–641 (2010).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag.44(12), 1630–1639 (1996).
[CrossRef]

IEEE Trans. Geosci. Rem. Sens. (1)

Q. H. Liu, “Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm,” IEEE Trans. Geosci. Rem. Sens.37(2), 917–926 (1999).
[CrossRef]

J. Biomed. Opt. (1)

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt.18(2), 025004 (2013).
[CrossRef] [PubMed]

Nat. Commun. (1)

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun.3, 928 (2012).

Nat. Methods (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods4(9), 717–719 (2007).
[CrossRef] [PubMed]

Nat. Photonics (2)

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011).
[CrossRef] [PubMed]

K. Si, R. Fiolka, and M. Cui, “Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation,” Nat. Photonics6(10), 657–661 (2012).
[CrossRef] [PubMed]

Opt. Express (1)

Other (2)

Y. Huang, C. Tsai, W. Ting, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” In Review.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the finite-difference time-domain method (Artech House, 2000).

Supplementary Material (3)

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» Media 2: MOV (621 KB)     
» Media 3: MOV (2296 KB)     

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Figures (9)

Fig. 1
Fig. 1

PSTD simulation of the TRUE technique. In the TRUE technique, a virtual light source (yellow arrow) is formed inside the scattering medium where the incident light (yellow dashed lines) and incident ultrasound (purple dashed lines) overlaps and light is frequency-shifted by the ultrasound pulse. Light reaching the OPC region (blue shaded-area) is phase-conjugated and back-propagates towards the virtual source. The PSTD simulation region is surrounded by an APML absorbing boundary condition (pink shaded area) to model an isolated system.

Fig. 2
Fig. 2

(Media 1) Simulation of the back-propagation of phase-conjugated light originating from a finite-width, CW plane wave virtual light source. A CW Gaussian beam (wavelength λ = 532 nm, beam width = 10 μm) impinging a scattering medium is simulated. The 200-μm-by-300-μm scattering medium consists of 676 randomly positioned, 5-μm-diameter dielectric (n = 1.2) cylinders. Snapshots at various instances depicting light propagation through the scattering medium are shown: (a) 5000 time steps (0.25 ps), (b) 20000 time steps (1.00 ps), and (c) 40000 time steps (2.00 ps). (d): a 30um-by-30um zoomed-in view of (c). (e) The intensity profile of the back-propagated light reaching the virtual light source (green line) is compared to light just emitted from the virtual light source (black thin line) with a root-mean-square error of 7.8%.

Fig. 3
Fig. 3

(Media 2) Simulation of the propagation of phase-conjugated light originating from the speckle-like virtual light source. The speckle-like virtual source is modeled as an aggregate of 4 randomly positioned 0.66-μm-diameter point light sources. The 200-μm-by-300-μm scattering medium consists of 676 randomly positioned, 5-μm-diameter dielectric (n = 1.2) cylinders. Snapshots at various instances depicting light propagation through the scattering medium are shown: (a) 5000 time steps (0.25 ps), (b) 20000 time steps (1.00 ps), and (c) 40000 time steps (2.00 ps). (d): a 30um-by-30um zoomed-in view of (c). (e) The intensity profile of the back-propagated light reaching the virtual light source (blue line) is compared to light just emitted from the virtual light source (black thin line) with a root-mean-square error of 9.0%.

Fig. 4
Fig. 4

Light delivery of various virtual light sources at various frequencies (100 THz to 563 THz) is compared. We simulate TRUE light propagation through a 200-μm-by-300-μm scattering medium consisting of 676 randomly positioned, 5-μm-diameter dielectric (n = 1.2) cylinders. Light delivery from a speckle-like virtual light source is compared to a single, coherent plane wave light source of various widths: w = 0.67 μm, 2 μm, 5, μm, 10 μm, and 20 μm. The root-mean-square (RMS) error of back-propagated light is compared to the original emitted light. Simulation results show insignificant differences for the effectiveness of the speckle-like virtual light source and a coherent, finite-width plane wave virtual light source.

Fig. 5
Fig. 5

Simulation of a CW, phase-conjugated light (wavelength λ = 1 μm) back-propagating (from right to left) through a scattering medium of various densities. The 200-μm-by-300-μm scattering medium consists of N randomly positioned, 5-μm-diameter dielectric (n = 1.2) cylinders: (a) N = 200, (b) N = 400, (c) N = 600. The phase-conjugated light back-propagates through the scattering medium and converges at the virtual light source. Intensity of light back-propagating through the scattering medium is depicted.

Fig. 6
Fig. 6

Varying the density of the scattering medium. The amplitude profile of the phase-conjugated light reaching the target position (as shown in Fig. 5) is compared for various N (number of dielectric cylinders within the scattering medium). Each profile is normalized by its maximum value; from bottom to top: N = 0, 100, 200, 600, and 676. For a denser scattering medium, the amount of light reaching the target position decreases.

Fig. 7
Fig. 7

Varying radius of constituent scatterers of a scattering medium. We simulate TRUE light propagation through 600-μm-by-600-μm scattering media consisting of uniform scatterers with refractive index n = 1.2 and radius r, r ranging from 1.2 to 18 μm. The amplitude profile of the phase-conjugated light reaching the target position is compared to the original intensity profile of light emitted from the virtual light source. The root-mean-square error for various radius r is calculated. The error is insensitive to the size of the scatterers.

Fig. 8
Fig. 8

Varying the width of the OPC region. A CW Gaussian beam (wavelength λ = 1 μm, beam width = 10 μm) impinging a scattering medium is simulated. The percentage of scattered light being phase-conjugated is increased by increasing the span of the OPC region. The time-reversed light profile reaching the target position is compared. To compare the width, each profile is normalized by its maximum value. Width of the OPC region from bottom to top is: 50 μm, 100 μm, 200 μm, and 300 μm. With increased amount of phase-conjugated light, the signal-to-background ratio increases.

Fig. 9
Fig. 9

(Media 3) (Top): Simulation of TRUE light propagating through a 1000-μm-by-1000-μm virtual tissue model consisting of ~670 cells. The 2-D virtual tissue model is constructed based upon a HT29 cell. (Bottom): The time-reversed light profile (playback scenario) is compared with the forward scenario light profile. Both field profiles were measured at the center of the simulation space. (Inset-figure): A 80-μm-by-80-μm zoomed-in view of back-propagated light converging at the virtual light source.

Equations (2)

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{ E x | i }=| F 1 {j k x F{ E i }},
E i = e ( y y 0 σ y ) 2 cos[k(x x 0 )ωt],

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