Abstract

In the present contribution we investigate the images of CW diffusely reflected light for a point-like source, registered by a CCD camera imaging a turbid medium containing an absorbing lesion. We show that detection of μa variations (absorption anomalies) is achieved if images are normalized to background intensity. A theoretical analysis based on the diffusion approximation is presented to investigate the sensitivity and the limitations of our proposal and a novel procedure to find the location of the inclusions in 3D is given and tested. An analysis of the noise and its influence on the detection capabilities of our proposal is provided. Experimental results on phantoms are also given, supporting the proposed approach.

© 2014 Optical Society of America

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2013 (1)

B. Tavakoli and Q. Zhu., “Two-step reconstruction method using global optimization and conjugate gradient for ultrasound-guided diffuse optical tomography,” J. Biomed. Opt.18(1), 16006 (2013).
[CrossRef]

2012 (2)

2011 (5)

S. Gioux, A. Mazhar, B. T. Lee, S. J. Lin, A. Tobias, D. J. Cuccia, A. Stockdale, R. Oketokoun, Y. Ashitate, E. Kelly, M. Weinmann, N. J. Durr, L. A. Moffitt, A. J. Durkin, B. J. Tromberg, and J. V. Frangioni, “First-in-human pilot study of a spatial frequency domain oxygenation imaging system,” J. Biomed. Opt.16(8), 086015 (2011).
[CrossRef] [PubMed]

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

D. Grosenick, A. Hagen, O. Steinkellner, A. Poellinger, S. Burock, P. Schlag, H. Rinneberg, and R. Macdonald., “A multichannel time-domain scanning fluorescence mammograph: performance assessment and first in vivo results,” Rev. Sci. Instrum.82, 024302 (2011).
[CrossRef] [PubMed]

H. Di Rocco, D. Iriarte, M. Lester, J. Pomarico, and H. F. Ranea-Sandoval., “CW Laser transilluminance in turbid media with cylindrical inclusions,” Int. J. Light Electron Opt.122, 577–581 (2011).
[CrossRef]

E. B. Aksel, A. N. Turkoglu, A. E. Ercan, and A. Akin., “Localization of an absorber in turbid semi - infinite medium by spatially resolved continuous - wave diffuse reflectance measurements,” J. Biomed. Opt.16(8), 086010 (2011).
[CrossRef] [PubMed]

2010 (2)

J. Liu, A. Li, A. E. Cerussi, and B. J. Tromberg., “Parametric diffuse optical imaging in reflectance geometry,” IEEE J. Sel. Topics Quantum Electron16(3), 555–564 (2010).
[CrossRef]

N. Carbone, H. Di Rocco, D. Iriarte, and J. Pomarico., “Solution of the direct problem in turbid media with inclusions using Monte Carlo simulations implemented on graphics processing units: new criterion for processing transmittance data,” J. Biomed. Opt.15(3), 035002 (2010).
[CrossRef]

2009 (2)

R. Ziegler, B. Brendel, A. Schiper, R. Harbers, M. van Beek, H. Rinneberg, and T. Nielsen., “Investigation of detection limits for diffuse optical tomography systems: I. Theory and experiment,” Phys. Med. Biol.54, 399–412 (2009).
[CrossRef]

S. Gioux, A. Mazhar, D. J. Cuccia, A. J. Durkin, B. J. Tromberg, and J. V. Frangioni, “Three-dimensional surface profile intensity correction for spatially modulated imaging,” J. Biomed. Opt.14(3), 034045 (2009).
[CrossRef] [PubMed]

2008 (2)

A. Bassi, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg., “Spatial shift of spatially modulated light projected on turbid media,” J. Opt. Soc. Am. A25(11), 2833–2839 (2008).
[CrossRef]

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys.35(6), 2443–2451 (2008).
[CrossRef] [PubMed]

2007 (3)

E. M. Hillman., “Optical brain imaging in vivo: techniques and applications from animal to man,” J. Biomed. Opt.12(5), 051402 (2007).
[CrossRef] [PubMed]

A. Hagen, O. Steinkellner, D. Grosenick, M. Möller, R. Ziegler, T. Nielsen, K. Lauritzen, R. Macdonald, and H. Rinneberg., “Development of a multi-channel time-domain fluorescence Mammograph,” Proc. SPIE6434, 64340Z (2007).
[CrossRef]

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg., “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast-equivalent phantoms and optical mammograms,” Phys. Rev. E76(6), 061908 (2007).
[CrossRef]

2006 (1)

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt.11(4), 044005 (2006).
[CrossRef] [PubMed]

2005 (6)

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol.50, R1–R43, (2005).
[CrossRef] [PubMed]

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Med. Phys.32(4), 1128–1139 (2005).
[CrossRef] [PubMed]

C. H. Schmitz, D. P. Klemer, R. Hardin, M. S. Katz, Y. Pei, H. L. Graber, M. B. Levin, R. D. Levina, N. A. Franco, W. B. Solomon, and R. L Barbour., “Design and implementation of dynamic near-infrared optical tomographic imaging instrumentation for simultaneous dual-breast measurements,” Appl. Opt.44(11), 2140–2153 (2005).
[CrossRef] [PubMed]

G. Yu, T. Durduran, G. Lech, C. Zhou, B. Chance, E. R. Mohler, and A. G. Yodh, “Time-dependent blood flow and oxygenation in human skeletal muscles measured with noninvasive near-infrared diffuse optical spectroscopies,” J. Biomed. Opt.10(2), 024027 (2005).
[CrossRef] [PubMed]

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol.50(11), 2519–2542 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg., “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

2004 (2)

T. Durduran, G. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, J. Wang, C. Zhou, and A. G. Yodh, “Diffuse optical measurement of blood flow, blood oxygenation, and metabolism in a human brain during sensorimotor cortex activation,” Opt. Lett.29(15), 1766–1768 (2004).
[CrossRef] [PubMed]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, G. M. Danesini, and R. Cubeddu, “Bulk optical properties and tissue components in the female breast from multiwavelength time-resolved optical mammography,” J. Biomed. Opt.9(6), 1137–1142 (2004).
[CrossRef] [PubMed]

2003 (1)

X. Intes, J. Ripoll, Yu Chen, S. Nioka., A.G. Yodh, and B. Chance., “In vivo continuous-wave optical breast imaging enhanced with indocyanine green,” Med. Phys., 30(6) 1039–1047, (2003).
[CrossRef] [PubMed]

2001 (1)

A. Torricelli, A. Pifferi, P. Taroni, E. Giambattistelli, and R. Cubeddu., “In vivo optical characterization of human tissue from 610 to 1010 nm by time resolved reflectance spectroscopy,” Phys. Med. Biol.46(8), 2227–2237 (2001).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

V. Nziachristos, X. Ma, and B. Chance., “Time correlated single photon counting imager for simultaneous magnetic resonance and near infrared mammography,” Rev. Sci. Instrum.69, 4221–4233 (1998).
[CrossRef]

S. R. Arridge and W. R. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett.23, 882–884 (1998).
[CrossRef]

1997 (2)

1996 (2)

X. D. Zhu, S. Wei, S. C. Feng, and B. Chance, “Analysis of a diffuse-photon-density wave in multilpe-scattering media in the presence of a small spherical object,” J. Opt. Soc. Am. A23(3), 494–499 (1996).
[CrossRef]

X. D. Li, M. A. OLeary, D. A. Boas, B. Chance, and A. G. Yodh., “Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications,” Appl. Opt.35(19), 3746–3758 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

’t Hooft, G. W.

Akin., A.

E. B. Aksel, A. N. Turkoglu, A. E. Ercan, and A. Akin., “Localization of an absorber in turbid semi - infinite medium by spatially resolved continuous - wave diffuse reflectance measurements,” J. Biomed. Opt.16(8), 086010 (2011).
[CrossRef] [PubMed]

Aksel, E. B.

E. B. Aksel, A. N. Turkoglu, A. E. Ercan, and A. Akin., “Localization of an absorber in turbid semi - infinite medium by spatially resolved continuous - wave diffuse reflectance measurements,” J. Biomed. Opt.16(8), 086010 (2011).
[CrossRef] [PubMed]

Amyot, F.

Ardeshirpour, Y.

Arridge, S.

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol.50(11), 2519–2542 (2005).
[CrossRef] [PubMed]

Arridge, S. R.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Med. Phys.32(4), 1128–1139 (2005).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol.50, R1–R43, (2005).
[CrossRef] [PubMed]

S. R. Arridge and W. R. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett.23, 882–884 (1998).
[CrossRef]

Ashitate, Y.

S. Gioux, A. Mazhar, B. T. Lee, S. J. Lin, A. Tobias, D. J. Cuccia, A. Stockdale, R. Oketokoun, Y. Ashitate, E. Kelly, M. Weinmann, N. J. Durr, L. A. Moffitt, A. J. Durkin, B. J. Tromberg, and J. V. Frangioni, “First-in-human pilot study of a spatial frequency domain oxygenation imaging system,” J. Biomed. Opt.16(8), 086015 (2011).
[CrossRef] [PubMed]

Barbour., R. L

Bassi, A.

Bearman, G. H.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

Binder, D. K.

J. R. Weber, D. J. Cuccia, W. R. Johnson, G. H. Bearman, A. J. Durkin, M. Hsu, A. Lin, D. K. Binder, D. Wilson, and B. J. Tromberg, “Multispectral imaging of tissue absorption and scattering using spatial frequency domain imaging and a computed-tomography imaging spectrometer,” J. Biomed. Opt.16(1), 011015 (2011).
[CrossRef] [PubMed]

Boas, D. A.

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys.35(6), 2443–2451 (2008).
[CrossRef] [PubMed]

X. D. Li, M. A. OLeary, D. A. Boas, B. Chance, and A. G. Yodh., “Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications,” Appl. Opt.35(19), 3746–3758 (1996).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of optics (Cambridge Unversity Press, 1999).
[CrossRef]

Brendel, B.

R. Ziegler, B. Brendel, A. Schiper, R. Harbers, M. van Beek, H. Rinneberg, and T. Nielsen., “Investigation of detection limits for diffuse optical tomography systems: I. Theory and experiment,” Phys. Med. Biol.54, 399–412 (2009).
[CrossRef]

Burnett, M. G.

Burock, S.

D. Grosenick, A. Hagen, O. Steinkellner, A. Poellinger, S. Burock, P. Schlag, H. Rinneberg, and R. Macdonald., “A multichannel time-domain scanning fluorescence mammograph: performance assessment and first in vivo results,” Rev. Sci. Instrum.82, 024302 (2011).
[CrossRef] [PubMed]

Butler, J.

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt.11(4), 044005 (2006).
[CrossRef] [PubMed]

Carbone, N.

N. Carbone, H. Di Rocco, D. Iriarte, and J. Pomarico., “Solution of the direct problem in turbid media with inclusions using Monte Carlo simulations implemented on graphics processing units: new criterion for processing transmittance data,” J. Biomed. Opt.15(3), 035002 (2010).
[CrossRef]

Cerussi, A.

T. O’ Sullivan, A. Cerussi, D. Cuccia, and B. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt.17(7), 071311 (2012).

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt.11(4), 044005 (2006).
[CrossRef] [PubMed]

Cerussi, A. E.

J. Liu, A. Li, A. E. Cerussi, and B. J. Tromberg., “Parametric diffuse optical imaging in reflectance geometry,” IEEE J. Sel. Topics Quantum Electron16(3), 555–564 (2010).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Schema of the experimental setup. A CW NIR diode laser illuminates a semi-infinite turbid medium with inclusions. A small tilt angle, α, is used to avoid Fresnel reflections and a CCD camera images the medium.

Fig. 2
Fig. 2

Geometry used (not to scale). We considered a thick slab, which can be taken as semi - infinite. This schema is a front view of the slab, as seen from the camera. The laser impinges at coordinates (x = 0, y = 0, z = 0). The camera is focused at the plane z = 0, which is the plane of the Figure, and a region of extension Dx × Dy is imaged onto the CCD.

Fig. 3
Fig. 3

Illustration of the principle of the method by theoretical calculations. An absorbing (μaInc = 4μa0) spherical inclusion, ϕInc = 1.0 cm was placed at a depth zInc = 1.0 cm and at xInc = 5 cm from the laser illumination point.

Fig. 4
Fig. 4

Theoretical profiles obtained using Eq. (1) for an absorbing spherical inclusion (μaInc = 4μa0, ϕInc = 1.0 cm) located at different depths, zInc and at several distances from the laser, xInc. a) zInc = 0.6cm, b) zInc = 1.0cm.

Fig. 5
Fig. 5

Modulation (M) map obtained by the theory as a function of both, the inclusion’s radius (rInc) and the inclusion’s depth (zInc). The inclusion is assumed to be a sphere placed at xInc = 2.0 cm from the illumination point. (a) μaInc = 4μa0; (b) μaInc = 2μa0.

Fig. 6
Fig. 6

Illustration of the approach used to locate the inclusion in 3D. a) Illustrates the principle for finding the in plane location of the inclusion for the illumination point at coordinates (xs, ys). This produces at (xd, yd) a blurred image of the inclusion, which is actually located at (xInc, yInc). b) Shows how to retrieve the depth of the inclusion once the average values of the in plane coordinates, (Inc, ȳInc), are known. The plane of this Figure is the one defined by the z axis and the line joining the illumination point and the image. See text for a detailed explanation.

Fig. 7
Fig. 7

Schematic representation (at scale) of the solid phantom used in the experiment. The inclusion is located at (xInc, yInc, zInc) = (9 cm, 9 cm, 1 cm). The dark spot indicated by ”L” is the illumination point and the phantom can be rotated around the point indicated by ”C”.

Fig. 8
Fig. 8

a) Raw image of the phantom at position j = 180° as seen by the camera. b) Result of dividing the image in a) by the average of all 18 images. c) Same as in b) after Fourier filtering.

Fig. 9
Fig. 9

Comparison of the experimental profile with theory using the camera offset value Ioff = 497. In addition, the theoretical profile is shown for the situation of background correction (Ioff = 0). For both simulations the standard deviation intervals are indicated by the black solid and dashed lines

Fig. 10
Fig. 10

Result of applying the criterion of Section 2.6 to two ratio images. a) Corresponding to the case of the phantom rotated by 180° and b) corresponding to the phantom rotated by 140°. Values of the profiles are obtained by averaging all pixels in each column of the region delimited by the dashed contour. Threshold values, T, for different significance levels, are shown as horizontal lines. Inclusion is considered to be “detected” at positions at which the average values are below threshold. White crosses indicate the true position of the laser, and the white dots indicate the actual position of the inclusion inside the phantom.

Fig. 11
Fig. 11

Line profiles for three different distances (1cm, 2cm and 3cm) of the 1cm spherical inclusion from the illumination spot. a) Experimental result for a depth of zInc = 1cm obtained by averaging 25 lines of the ratio image. The dashed and the dotted line show the corresponding detection thresholds for significance levels of αFP = 10−2 and 10−4, respectively. b) Theoretical result for the parameters of the experiment in a). c) Theoretical result for an increased depth of the inclusion (zInc = 1.5cm).

Tables (1)

Tables Icon

Table 1 Result of applying our algorithm to the solid phantom. Nominal values for the inclusion location are (xInc, yInc, zInc) = (9 cm, 9 cm, 1 cm). Errors are given as the standard deviation of the measured values.

Equations (15)

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P ( x , y ) = I ( x , y ) / I 0 ( x , y )
J 0 ( r s , r d ) = A 0 4 π [ ( κ + 1 r 1 ) z 0 exp ( κ r 1 ) r 1 2 + ( κ + 1 r 2 ) ( 2 z e + z 0 ) exp ( κ r 2 ) r 2 2 ] ,
J out ( r s , r d , r Inc ) = J 0 ( r s , r d ) + J Inc ( r s , r d , r Inc )
J Inc ( r s , r d , r Inc ) = D c z d { Φ Inc inf ( r s 1 , r d , r Inc ) Φ Inc inf ( r s 2 , r d , r Inc ) + Φ Inc inf ( r s 1 , r d , r Inc * ) Φ Inc inf ( r s 2 , r d , r Inc * ) }
Φ Inc inf ( r s , r d , r Inc ) = B m k m ( κ | r d r Inc | ) P m ( cos θ ) ,
Φ Inc inf ( r s , r d , r Inc ) [ q r d + p r d r d 3 ( 1 + κ | r d r Inc | ) ] exp ( κ | r d r Inc | )
P ( x ) = J out ( r s , r d , r Inc ) J 0 ( r s , r d ) = 1 + J Inc ( r s , r d , r Inc ) J 0 ( r s , r d )
( x ¯ Inc , y ¯ Inc ) = ( j = 1 N x Inc j N , j = 1 N y Inc j N )
z ¯ Inc = j = 1 N z Inc j N .
B ( r , r s , r d ) = [ exp ( κ | r r s 1 | ) | r r s 1 | exp ( κ | r r s 2 | ) | r r s 2 | ] × [ exp ( κ | r d r | ) | r d r | exp ( κ | r d r * | ) | r d r | ] .
J 0 ( r s , r d ) A 0 4 π 2 ( z e + 1 / μ s ) ( 1 + κ ρ ) exp ( κ ρ ) ρ 3 .
I k N = I k + N k + I off ,
σ I = n a 2 + ( n p I k N I off ) 2 + ( n r ( I k N I off ) ) 2 .
T ( α F P ) = θ 0 2 k σ erf 1 ( 1 2 α F P ) .
σ P ( x ) = P ( x ) n a 2 + n p 2 A J out + n r 2 A 2 J out 2 ( A J out + I off ) 2 + n a 2 + n p 2 A J 0 + n r 2 A 2 J 0 2 ( A J 0 + I o f f ) 2 .

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