phase-contrast diffuse optical tomography for in vivo breast imaging: a two-step method

Phase-contrast diffuse optical tomography forin vivo breast imaging: a two-step method

Ruixin Jiang,1 Xiaoping Liang,1 Qizhi Zhang,1 Stephen Grobmyer,2

Laurie L. Fajardo,3 and Huabei Jiang1,*1The J. Crayton Pruitt Family, Department of Biomedical Engineering, University of Florida,

Gainesville, Florida 32611, USA2Department of Surgery, University of Florida, Gainesville, Florida 32610, USA

3Department of Radiology, University of Iowa, Iowa City, Iowa 52242, USA

*Corresponding author: [email protected]

Received 19 December 2008; revised 4 July 2009; accepted 30 July 2009;posted 31 July 2009 (Doc. ID 105542); published 13 August 2009

We present a two-step reconstruction method that can qualitatively and quantitatively improve the re-construction of tissue refractive index (RI) distribution by phase-contrast diffuse optical tomography(PCDOT). In this two-step method, we first recover the distribution of tissue absorption and scatteringcoefficients by conventional diffuse optical tomography to obtain the geometrical information of lesions,allowing the incorporation of geometrical information as a priori in the PCDOT reconstruction using alocally refined mesh. The method is validated by a series of phantom experiments and evaluated using invivo data from 42 human subjects. The results demonstrate clear contrast of RI between the lesion andthe surroundings, making the image interpretation straightforward. The sensitivity and specificity fromthese 42 cases are both 81% when RI is used as an imaging parameter for distinguishing betweenmalignant and benign lesions. © 2009 Optical Society of America

OCIS codes: 170.3010, 170.3830.

1. Introduction

As the predominant conventional approach forbreast cancer detection, x-ray mammography haslow specificity and relatively lower sensitivity asthe breast density increases [1,2]. Among other con-ventional techniques that are being developed forimproving the diagnostic accuracy of breast cancer,magnetic resonance imaging has shown to be themost promising one, but it is costly [3] and thereforenot suitable for routine breast screening. Near-infrared light-based diffuse optical tomography(DOT) is emerging as a noninvasive and low cost al-ternative for breast cancer detection with its abilityto gain both structural and functional information ofbreast tissue. While DOT has shown high sensitivitytowards breast cancer detection, it has a limited

specificity [4–10]. While significantly improved spe-cificity may be acquired by imaging tissue absorptioncoefficient derived functional parameters [11], wehave expanded the ability of DOT by adding the pos-sibility of reconstructing tissue refractive index (RI)or phase contrast using diffusing light measure-ments [12]. A recent OCT study has shown that thereexists a significant contrast in RI between tumor andnormal tissues in an animal model [13].

We have recently reported an in vivo study of 35breast masses (11 malignant cases and 24 be-nign cases) from 33 patients conducted with phase-contrast DOT (PCDOT) [14]. The results obtainedfrom this study showed that malignant lesions gen-erally had a decreased RI while benign lesions exhib-ited an increased RI relative to the surroundingnormal tissue. A sensitivity of 81.8% and a specificityof 70.8% were obtained from this study. While asignificantly improved specificity was acquired by

0003-6935/09/244749-07$15.00/0© 2009 Optical Society of America

20 August 2009 / Vol. 48, No. 24 / APPLIED OPTICS 4749

PCDOT compared to conventional DOT, the rela-tively noisy RI distribution recovered sometimesmade it difficult to identify the lesion, making the im-age inspection observer dependent. The primary goalof the current work is to develop a two-step methodfor improving the quality of RI image reconstructionso that the image examination may be independentof the observer. In this two-step method, a locallyrefined finite-element mesh was created accordingto the reconstructed absorption/scattering imagesusing conventional DOT, followed by incorporationof the structural prior information into the itera-tive process for RI reconstruction. We validate andevaluate this method using both phantom and in vivodata.

2. Reconstruction Methods

A. Finite-Element Reconstruction Algorithm

As detailed in Ref. [9], a set of matrix equations for RIreconstruction based on the photon diffusion equa-tion considering spatially varying refractive indexcan be described as follows:

½A�fΦg ¼ fbg; ð1Þ

½A�f∂Φ=∂ng ¼ f∂b=∂ng − ½∂A=∂n�fΦg; ð2Þ

ðITI þ λLTLÞΔn ¼ ITðΦðmÞ −ΦðcÞÞ; ð3Þin which the elements of the matrix [A] areaij ¼

RVð−D∇ϕj ·∇ϕi þ ð2D=nÞ∇nk ·∇ϕi − μaϕjϕiÞdV ,

where the integrations are performed over the pro-blem domain V ; D ¼ 1=ð3ðμa þ μ0sÞÞ is the diffusioncoefficient, where μa and μ0s are the absorption andreduced scattering coefficient, respectively; ϕi and ϕjare locally spatially varying Lagrangian basis func-tions at node i and j, respectively; fbg is the sourcevector; I is the Jacobian matrix formed by ∂Φ=∂n atthe boundary measurement sites; λ is a scalar andL is the regularization matrix or filter matrix;Δn ¼ ðΔn1;Δn2;…;ΔnNÞT is the update vector forRI, where N is the total node number of the finite-element mesh used; ΦðmÞ ¼ ðΦðmÞ

1 ;ΦðmÞ2 ;…;ΦðmÞ

M ÞTand ΦðcÞ ¼ ðΦðcÞ

1 ;ΦðcÞ2 ;…;ΦðcÞ

M ÞT , where ΦðmÞi and

ΦðcÞi are the measured and calculated photon density

at i ¼ 1; 2;…;M boundary locations, respectively. Inthis algorithm, the n distribution is updated itera-tively through Eqs. (1)–(3) so that a weighted sumof the squared difference between the measuredand calculated photon density can be minimized. Dif-fusion and absorption coefficients are assumed con-stant during the RI reconstruction process in theprevious cases. For the two-step process describedin the following, the absorption and scatteringimages are reconstructed first, and then the spatialinformation defined from these images is taken toconstrain the spatial extent for RI recovery.

B. Adaptive Meshing

To generate a locally refined adaptive mesh, the ab-sorption and scattering images are first recon-structed by conventional DOT, where the lesionlocation/size can be confirmed in comparison withthe x-ray mammography or ultrasound. From theseimages, the maximum values (max) of absorption/scattering coefficients in the lesion/target area andthe minimum values (min) of absorption/scatteringcoefficients for the surroundings can be obtained.If the values of both absorption and scattering coeffi-cients at a nodal location are larger than minþv · ðmax−minÞ, where 0 < v < 1, then this node is la-beled as part of Region I; otherwise, the node is iden-tified as part of Region II. An element is split intofour smaller elements [Fig. 1(a)] if all three nodes as-sociated with this element are part of Region I, whilean element is divided into two smaller ones Fig. 1(b)]if only two nodes associated with this element arepart of Region I.

C. Incorporation of Structural Prior Information

The regularization matrix L included in Eq. (3) iscommonly taken as the identity matrix, and priorstructural information is iteratively incorporatedinto the reconstruction process through the spatiallyvarying regularization parameter λ [15,16]. Here weuse the logarithm-type regularization matrix, whichis constructed according to the prior information

Fig. 1. Geometry of split elements.

Fig. 2. Phantom geometry. R1 ¼ 50mm, R2 ¼ 5mm, d ¼ 14mm.

4750 APPLIED OPTICS / Vol. 48, No. 24 / 20 August 2009

obtained when generating the adaptive mesh. Thisregularization matrix can relax the smoothness con-straints at the interface of different regions so thatthe covariance of nodes within a region is basicallyrealized [17]. The elements of matrix L are

Lij ¼

8>><>>:

1 if i ¼ 1−1=NN1 if i; j⊂ region I−1=NN2 if i; j⊂ region II

0 if i; j⊂ others

; ð4Þ

where NN1 is the number of nodes within Region Iand NN2 is the number of nodes within Region II.The Jacobian matrix is reassembled according tothe region or tissue type that is associated with struc-tural priors.

3. Experiments

A. Phantom Experiments

Phantom experiments were conducted with a multi-spectral, multichannel DOT system, which was pre-viously described in detail [18]. For a 2D imagingexperiment, light from a diode laser at 775nm wastransmitted sequentially to 16 source points at thephantom surface through an optical switch, and dif-fusing light was detected by 16 photodiodes. A set of16 × 16measured data was then input into the recon-struction algorithm to generate a 2D cross-sectionimage of the phantom.

Four tissue-like phantom experiments were con-ducted with different contrasts in RI between the tar-get and the background. Tissue absorption (μa ¼0:007mm−1) and scattering (μ0s ¼ 1:0mm−1) were si-mulated for the background with India ink and In-tralipid, respectively. Agar powder (2%) was usedto solidify the mixed Intralipid–India ink solution.Thus the RI of the background was close to that ofwater (n ¼ 1:33 at 775nm). One 10mm diametertarget was placed off-center with various glucose con-centrations to mimic different RI contrasts [19]:

Fig. 3. (Color online) RI images reconstructed from phantom measurements without the two-step method, where the absorption andscattering coefficients were μa ¼ 0:007mm−1 and μ0

s ¼ 1:0mm−1, respectively, for both the background and the target. The target had(a) 1% glucose concentration (n ¼ 1:3312), (b) 2% glucose concentration (n ¼ 1:3332), (c) 3% glucose concentration (n ¼ 1:3353), and(d) 5% glucose concentration (n ¼ 3393)

Table 1. Values of RI and the Glucose Concentration Used in thePhantom Study

Glucose Concentration

1% 2% 3% 5%

RI 1.3312 1.3332 1.3353 1.3393


n ¼ 0:2105 · ½C� þ 1:3292; ð5Þ

where [C] is the concentration of the glucose solution.The values of the RI and their corresponding glucoseconcentrations used in this study are shown inTable 1. The geometry of the phantom is shown inFig. 2. A mesh of 717 nodes and 1368 triangular ele-ments was applied in the reconstruction.

B. Patient Examinations

The clinical study was approved by the institutionalreview board and was conducted in full compliancewith the accepted standards for research involvinghuman subjects. Signed informed consent from allstudy participants was obtained. In this study, 42breasts from 42 different patients (mean age 59;range from 32–82) were screened. Biopsy reportsdemonstrated 21 invasive carcinoma and 21 benignlesions. 29 patients were imaged by the same multi-channel photodiodes based system used for the phan-tom experiments described earlier [18], 9 patientswere examined by a multichannel photomultipliertube system [20] and 4 patients were screened bya single photomultiplier based scanning system [4].Data at one wavelength were used for the reconstruc-

tion, i.e., 775nm from the system described in [18]and 785nm from those described in [4,20].

4. Results and Discussion

Figures 3 and 4, respectively, present the recon-structed RI images for all four phantom cases with-out and with the two-step method. We see that theimages shown in Fig. 3 are qualitatively good interms of target location and size but have signifi-cantly overestimated RI values compared to theimages shown in Fig. 4. In addition, the imagesshown in Fig. 4 also exhibit a better recovered targetboundary relative to that shown in Fig. 3. To give aquantitative analysis of the two-step method, we cal-culated the relative errors of the recovered target RIvalue for the four cases and listed the results inTable 2. We found that the relative errors range from0.067% to 0.540%, which is significantly improvedcompared to that from our previous study [19]. We

Fig. 4. (Color online) RI images reconstructed from phantom measurements with the two-step method. The absorption and scatteringcoefficients were μa ¼ 0:007mm−1 and μ0

s ¼ 1:0mm−1 for both the background and the target. The target had (a) 1% glucose concentration(n ¼ 1:3312), (b) 2% glucose concentration (n ¼ 1:3332), (c) 3% glucose concentration (n ¼ 1:3353), and (d) 5% glucose concentration(n ¼ 1:3393).

Table 2. Comparison of the Actual and Recovered Values of the RIof the Target

Ideal 1.3312 1.3332 1.3353 1.3393Calculated 1.3354 1.3260 1.3362 1.3437Relative Error (%) 0.32 0.54 0.067 0.33


note that the calculated RI value for 2% glucoseconcentration deviates from the general trend, i.e.,instead of increasing RI from 1% to 2%, the calcu-lated value is decreased for this case. This deviationcould be caused by the measurement errors thatwere propagated into the reconstruction process.Reconstructed images of absorption, scattering

and RI from two representative clinical cases areshown in Figs. 5 and 6. The first case was a 66 yearold woman who had an invasive ductal carcinomathat measured 1:9 cm in maximal dimension. Boththe absorption and scattering images exhibit markedincrease in the region of the tumor [indicated byarrows in Figs. 5(a) and 5(b)], whereas the RI imageobtained without the two-step method [Fig. 5(c)]shows neither a clear increase nor decrease in the tu-mor area corresponding to that of the absorption/scattering images. Figure 5(d) gives the recon-structed RI image obtained using the two-step meth-od, where we see an identifiable decrease of RI at thetumor area (indicated by the arrow). The second casewas a 60 year old woman with a 9mm diameter be-nign nodule. Increased absorption and scatteringcoefficients are noticed in the lesion area [Fig. 6(a)and 6(b)], while the RI image without the two-step

method [Fig. 6(c)] demonstrates moderate contrastin the lesion area. The RI image using the two-stepmethod [Fig. 6(d)] presents a marked increase in thelesion.

We also calculated the sensitivity and specificityfor cancer detection for the 42 cases examined usinga prediction rule revealed in previous clinical studies[14]. In this prediction rule, a lesion will be diagnosedas malignant if its RI value is smaller than that of itssurroundings and its absorption and scattering coef-ficients are larger than its surroundings; otherwise itis a benign lesion. For the possible physiological rea-son behind this prediction rule, glucose metabolismin the tumor has been proved to be significantly in-creased compared to normal tissue in animal models[21], and as discussed in Ref. [12], we suspect the glu-cose consumption is higher in tumors and lower inbenign lesions. Using this rule, we found that thesensitivity (81%) is similar to that obtained pre-viously [14], but the specificity is significantly im-proved (81%) over the previous study (71%). Weconsider the PCDOT method to be a potential ap-proach to provide glucose metabolism information.In the current single-wavelength PCDOT algorithm,we made a first-order approximation that both

Fig. 5. (Color online) Reconstructed optical images for a 66 year old woman who had an invasive ductal carcinoma that measured 1:9 cmin maximal dimension. (a) Absorption coefficient image, (b) scattering coefficient image, (c) RI image recovered without the two-step meth-od, (d) RI image recovered with the two-step method.


absorption and scattering coefficients are being con-stant during the reconstruction process of RI. Infuture studies, we plan to adopt a multispectral re-construction method to simultaneously recover RIalong with other absorption derived chromophoressuch as oxy- and deoxyhemoglobin concentrations,which allows the study of combining glucose metabo-lism with blood volume and oxygen metabolism formore comprehensive diagnosis of breast cancer.

5. Conclusions

We have developed a two-step PCDOTmethod that isable to improve RI reconstruction qualitatively andquantitatively, making PCDOT a potentially obser-ver-independent approach for cancer diagnosis. Thismethod has been confirmed by phantom experimentsand 42 sets of clinical data. We expect to further eval-uate this method by using larger-scale clinical dataas well as applying this method for imaging otherorgans/diseases.

References1. E. A. Sickles, D. L. Miglioretti, R. Ballard-Barbash,

B. M. Geller, J. W. Leung, R. D. Rosenberg, R. S. Bindman,and B. C. Yankaskas, “Performance benchmarks for diagnostic

mammography,” Radiology (Oak Brook, Ill.) 235, 775–790(2005).

2. P. A. Carney, D. L. Miglioretti, B. C. Yankaskas,K. Kerlikowske, R. Rosenberg, C. Rutter, B. Geller,L. Abraham, S. Taplin, M. Dignan, G. Cutter, andR. B. Barbash, “Individual and combined effects of age, breastdensity, and hormone replacement therapy use on the accu-racy of screening mammography,” Ann. Intern. Med. 138,168–175 (2003).

3. D. A. Bluemke, C. A. Gatronis, M. H. Chen, G. Deangelis,N. Debruhl, S. Harms, S. Kobrunner, N. Hylton, C. Kuhl,C. Lehman, E. Pisano, P. Causer, S. Schnitt, S. Smazal,C. Stelling, P. Weatherall, and M. Schnall, “Magnetic reso-nance imaging of the breast prior to biopsy,” JAMA, J. Am.Med. Assoc. 292, 2735–2742 (2004).

4. H. Jiang, N. Iftimia, Y. Xu, J. Eggert, L. L. Fajardo, andK. Klove, “Near-infrared optical imaging of the breast withmodel-based reconstruction,” Acad. Radiol. 9, 186–194(2002).

5. V. Ntziachristos, A. G. Yodh, M. D. Schnall, and B. Chance,“MRI-guided diffuse optical spectroscopy of malignant and be-nign breast lesions,” Neoplasia 4, 347–354 (2002).

6. H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, andL. Fajardo, “Three dimensional optical tomographic imagingof breast in a human subject,” IEEE Trans. Med. Imaging20, 1334–1340 (2001).

7. M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Grat-ton, H. Jess, W. Mantulin, M. Seeber, P. Schlag, and

Fig. 6. (Color online) Reconstructed optical images for a 60 year old woman with a 9mm diameter benign nodule. (a) absorption coeffi-cient image, (b) scattering coefficient image, (c) RI image recovered without the two-step method, (d) RI image recovered with the two-stepmethod.


M. Kaschke, “Frequency-domain techniques enhance opticalmammography: Initial clinical results,” Proc. Natl. Acad.Sci. USA 94, 6468–6473 (1997).

8. D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke,C. Stroszczynski, R. Macdonald, P. Schlag, and H. Rinneberg,“Time-domain optical of breast tumors,” Appl. Opt. 42,3170–3186 (2003).

9. D. R. Leff, O. J. Warren, L. C. Enfield, A. Gibson, T. Athana-siou, D. K. Patten, J. Hebden, G. Z. Yang, and A. Darzi, “Dif-fuse optical imaging of the healthy and diseased breast: Asystematic review,” Breast Cancer Res. Treat. 108, 9–22(2008).

10. S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue,P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho,J. J. Gibson, and K. D. Paulsen, “Electromagnetic breastimaging: results of a pilot study in women with abnormalmammograms,” Radiology (Oak Brook, Ill.) 243, 350–359(2007).

11. B. Chance, S. Nioka, J. Zhang, E. F. Conant, E. Hwang,S. Briest, S. G. Orel, M. D. Schnall, and B. J. Czerniecki,“Breast cancer detection based on incremental biochemicaland physiological properties of breast cancers: a six-year,two-site study,” Acad. Radiol. 12, 925–933 (2005).

12. H. Jiang and Y. Xu, “Phase-contrast imaging of tissue usingnear-infrared diffusing light,” Med. Phys. 30, 1048–1051(2003).

13. A. Zysk, E. Chaney, and S. Boppart, “Refractive index of car-cinogen-induced rat mammary tumors,” Phys. Med. Biol. 51,2165–2177 (2006).

14. X. Liang, Q. Zhang, C. Li, S. Grobmyer, L. Fajardo, andH. Jiang, “Phase-contrast diffuse optical tomography: pilot re-sults in the breast,” Acad. Radiol. 15, 859–866 (2008).

15. A. Li, E. L. Miller, M. E. Kilmer, T. Brukilacchio, T. Chaves,J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. Moore, D. Kopans,and D. Boas, “Tomographic optical breast imaging guided bythree-dimensional mammography,” Appl. Opt. 42, 5181–5190(2003).

16. B. W. Pogue, T. O. McBride, J. O. Prewitt, U. L. Osterberg,and K. D. Paulsen, “Spatially variant regularization improvesdiffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).

17. Z. Yuan, Q. Zhang, E. S. Sobel, and H. Jiang, “Tomographic x-ray guided three-dimensional diffuse optical tomography ofosteoarthritis finger joint,” J. Biomed. Opt. 13, 047804 (2008).

18. C. Li, H. Zhao, B. Anderson, and H. Jiang, “Multispectralbreast imaging using a ten-wavelength, 64 × 64 source/detec-tor channels silicon photodiode-based diffuse optical tomogra-phy system,” Med. Phys. 33, 627–636 (2006).

19. X. Liang, Q. Zhang, and H. Jiang, “Quantitative reconstruc-tion of refractive index distribution and imaging of glucoseconcentration by using diffusing light,” Appl. Opt. 45,8360–8365 (2006).

20. N. Iftimia, X. Gu, Y. Xu, and H. Jiang, “A compact, parallel-detection diffuse optical mammography system,” Rev. Sci. In-strum. 74, 2836–2842 (2003).

21. J. J. Casciari, S. V. Sotirchaos, and R. M. Sutherland, “Varia-tions in tumor cell growth rates and metabolism with oxygenconcentration, glucose-concentration, and extracellular PH,”J. Cell. Phys. 151, 386–394 (1992).


phase-contrast diffuse optical tomography for in vivo breast imaging: a two-step method

Documents