mr water quantitative priors improves the accuracy of optical breast imaging

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 1, JANUARY 2011 159

MR Water Quantitative Priors Improves theAccuracy of Optical Breast Imaging

Colin M. Carpenter*, Brian W. Pogue, Shudong Jiang, Jia Wang, Brian A. Hargreaves, Rebecca Rakow-Penner,Bruce L. Daniel, and Keith D. Paulsen

Abstract—Magnetic resonance (MR) guided optical breastimaging is a promising modality to improve the specificity ofbreast imaging, because it provides high-resolution quantitativemaps of total hemoglobin, oxygen saturation, water content,and optical scattering. These properties have been shown todistinguish malignant from benign lesions. However, the opticaldetection hardware required for deep tissue imaging has poorspectral sensitivity which limits accurate water quantification; thisreduces the accuracy of hemoglobin quantification. We presenta methodology to improve optical quantification by utilizing theability of Dixon MR imaging to quantitatively estimate water andfat; this technique effectively reduces optical crosstalk betweenwater and oxyhemoglobin. The techniques described in this paperreduce hemoglobin quantification error by as much as 38%, asshown in a numerical phantom, and an experimental phantom.Error is reduced by as much 20% when imperfect MR waterquantification is given. These techniques may also increase con-trast between diseased and normal tissue, as shown in breast tissuein vivo. It is also shown that using these techniques may permitfewer wavelengths to be used with similar quantitative accuracy,enabling higher temporal resolution. In addition, it is shown thatthese techniques can improve the ability of MRI to quantify waterin the presence of bias in the Dixon water/fat separation.

Index Terms—Breast cancer, diffuse optics, image reconstruc-tion, magnetic resonance (MR).

I. INTRODUCTION

M AGNETIC resonance (MR) guided diffuse opticalbreast imaging generates spatial maps of tissue oxyhe-

moglobin (HbO), deoxyhemoglobin (Hb), water fraction, lipid

Manuscript received June 07, 2010; accepted August 03, 2010. Date ofpublication September 02, 2010; date of current version December 30, 2010.This work was supported by the Department of Defense Pre-doctoral TrainingFellowship 503298, the National Cancer Institute grants 5P01CA080139 and2R01CA069544, and the Center for Advanced Magnetic Resonance Tech-nology at Stanford, P41 RR009784. Asterisk indicates corresponding author.

*C. M. Carpenter was with the Thayer School of Engineering, DartmouthCollege, Hanover, NH 03755 USA. He is now with the Department of RadiationOncology, School of Medicine, Stanford University, Stanford, CA 94305 USA(e-mail: [email protected]).

B. W. Pogue, S. Jiang, and K. D. Paulsen are with the Thayer School of En-gineering, Dartmouth College, Hanover, NH 03755 USA (e-mail: [email protected]; [email protected]; [email protected]).

J. Wang was with the Thayer School of Engineering, Dartmouth College,Hanover, NH 03755 USA. He is now with the Department of Radiology, MayoClinic, Rochester, MN 55905 USA (e-mail: [email protected]).

B. W. Hargreaves, R. Rakow-Penner, and B. L. Daniel are with the Depart-ment of Radiology, Stanford University School of Medicine, Stanford, CA94305 USA (e-mail: [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMI.2010.2071394

fraction, and optical scattering amplitude (ScA) and scatteringpower (ScP) [1]–[3], at a higher resolution than standalone op-tical imaging [4], [5]. From these quantities, the more clinicallyrelevant values of total hemoglobin andoxygen saturation fraction (HbO/HbT) can be calculated, whichhave been shown in standalone optical imaging to exhibit highcontrast between normal and diseased tissue [6]–[8], as well asbetween malignant and benign lesions [9]–[11].

Optical imaging determines tissue contents (chromophores)by reconstructing for the absorption and scatter properties atmultiple wavelengths and fitting for tissue contents using theirspectral signatures, known a priori. Light in the near infrared(NIR) is highly attenuated in thick tissue, and may decreaseby seven orders of magnitude through the breast. This largedynamic range often necessitates imaging with photomulipliertube (PMT) detectors (gain of in this study). However, thecurrent state-of-the-art PMTs for detection of near infrared lighthave nonuniform spectral sensitivity, and are ill-suited to mea-sure wavelengths greater than about 850 nm, due to their useof multialkali photocathodes, which have reduced sensitivity inthe NIR spectrum.

The omission of wavelengths greater than 850 nm leads toerrors in water quantification [12] because the water spectrumis similar to oxyhemoglobin across the sensitivity range of thePMTs, as shown in Fig. 1 [13]. Previous studies have shownthe limitations of poor spectral sampling within optical imaging.Franceschini et al. [14] determined that with two wavelengths inthe NIR (715 and 825 nm), oxygenation was overestimated by15% in typical brain tissue. This error increased as tissue prop-erties were modified to match known tumor tissue estimates.Cerussi et al. [15] found that water errors caused by imagingwith three wavelengths of 672, 806, and 849 nm could induceerrors as high as 60% and 10% in total hemoglobin and oxy-genation, respectively, in a diseased breast in vivo compared toimaging using the broadband NIR spectrum.

To correct for water quantification errors and the associatedcrosstalk between it and hemoglobin, investigators have as-sumed water values [16], [17], or calculated the water contentfrom scattering power [17]. These techniques are suboptimalbecause water concentration in the breast varies both spatiallyand quantitatively between individuals, and scatter power mea-surements are sensitive to structural tissue property changesthat may be independent of water concentration.

An effective way to remove water/hemoglobin crosstalk isto determine water concentration using another modality thatis more accurate. Towards this goal, this paper investigates theuse of Dixon MR water/fat separation [18] as prior information

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160 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 1, JANUARY 2011

Fig. 1. (a) Tissue absorption spectra for typical breast tissue optical propertiesof �� HbO, �� Hb, and 60% water. (b) Tissue absorption spectra inthe sensitivity region of the PMTs. Note the spectral similarity between oxyhe-moglobin (HbO) and water.

for the optical reconstruction to provide water quantification.MR water/fat separation has been proposed previously by Li etal. [19] to structurally guide the optical reconstruction. Othermethods to incorporate the MR anatomical information into theoptical reconstruction have used T1-weighted gadolinium con-trast enhanced images [20]. The spatial prior has been eitherincorporated as a cost-term in the reconstruction objective func-tion [19], [21], [22], or as an absolute structural bound [23], [24].This study expands on the utility of MR within optical breastimaging by presenting a means to use the MR for quantitativeguidance of the reconstruction, through the use of quantitativewater priors.

II. METHODS

A. MR-Guided Optical Image Formation

MR-guided optical imaging creates images of tissue compo-nents by sampling tissue absorption and scattering propertiesat several wavelengths in the near infrared range. The systeminstrumentation to perform optical imaging has been describedpreviously [5]. Briefly, 16 13-m-long optical fiber bundleswhich operate in transmit or receive mode are coupled to thebreast tissue through a custom-designed optical fiber holder.NIR light is frequency modulated at 100 MHz and transmittedthrough the tissue sequentially through each fiber bundle. Theamplitude attenuation and phase shift of light emitted fromthe tissue are measured with PMTs attached to the distal endof the remaining 15 fibers. These data are input into a lightpropagation model to determine the optical absorption andscattering coefficients for tissue at each wavelength.

Hemoglobin species, water, and lipid content can be com-puted from optical absorption by solving a linear system thatmaps the tissue optical absorption coefficients at multiple wave-lengths to tissue content concentrations, given by

(1)

where are the absorption coefficients in tissue which are de-pendent on wavelength , and are well-known molar extinc-tion coefficients which quantify the optical absorption of tissuecomponents with respect to concentration for each wavelengthin the set of measured wavelengths. Hemoglobin optical absorp-tion depends on the concentration of red blood cells in the bloodplasma (i.e., the hematocrit) and the concentration of blood inthe tissue. Water and lipid absorption is determined by the rela-tive percentages of these components compared to pure (100%)water and lipid. The reduced optical scattering coefficient is rep-resented by . It can be decomposed into scattering amplitudeand scattering power by fitting at multiple wavelengths to theform

(2)

This is done with a least squares method (lsqlin, MATLAB,Mathworks Natick, MA). Scattering depends on tissue mi-crostructure [25]; the analysis of scattering is beyond the scopeof this work.

Light propagation through the breast can be modeled with thelossy diffusion equation [26], which is solved numerically viathe finite element method [27], [28]. Images of the tissue prop-erties are formed using a model-based reconstruction approach,utilizing the generalized least squares framework [29]. This op-timization problem minimizes the difference between modeleddata and experimental data, with a constraint on contrast that isphysiologically relevant. The objective function is

(3)

where is the tissue property vector for discrete tissue voxels

is the difference between the photon propagation modeland the experimental measurements , and and areweighting functions based on the data noise and chromophoreconcentrations, respectively. is determined from a systemnoise characterization, and incorporates several factorsbased on typical tissue contrasts [3], [9], edge-preservingfilters [30], and the water/fat weighting proposed herein. Thisparameter estimation problem is nonlinear and must be solvediteratively to achieve high quantitative accuracy. Equation (3)is linearized for iterative solving as follows:

(4)

where the model data, , can be approximated with a first-order Taylor series

(5)

Here, (the partial derivative of with respect to ) is knownas the Jacobian sensitivity matrix, as has been formulated pre-viously [31], [32]

(6)

CARPENTER et al.: MR WATER QUANTITATIVE PRIORS IMPROVES THE ACCURACY OF OPTICAL BREAST IMAGING 161

where are the simulated measurements of amplitude andphase ( with this instrument) calculated from the cur-rent estimate of the optical properties, and is the number ofunknowns (e.g., nodes in a finite element mesh).

The optimization procedure begins by calculating an initialguess, , for each parameter by fitting the data to a lightpropagation model for a homogeneous volume to determine theaverage tissue properties [33]. In this study, fat is ignored be-cause its contribution to the optical absorption spectra between660 and 850 nm is negligible. The initial guess of the tissueproperty vector, is therefore

(7)

Next, the heterogeneous tissue properties are determined bycalculating an update to the parameters. The update equation is

(8)where is the iteration number.

To improve chromophore quantification and accuracy, inte-rior tissue boundaries, determined by MR, can be incorporatedinto the image reconstruction [5]. The various methods to incor-porate this a priori information have been described elsewhere[34]. Here, a region-based reconstruction scheme is used to de-termine average optical properties in each MR-defined region(adipose tissue, fibroglandular tissue, and suspect lesions) [23].

B. Separating Water and Fat With MR

There are several different approaches to separate water andfat signals in the MR. These methods are based on the protonchemical shift, where differences in the local electronic environ-ment of lipids and water cause differences in the resonant fre-quency of protons that are exposed to an external magnetic field.The Dixon-type sequences, originally developed by Dixon [18]and Glover et al. [35], sample the magnetic signal at multipleecho times and enable the decomposition of the total signal intowater signal and lipid signal. Since the signal in MRI is dom-inated by the proton density of these two constituents, images ofwater and fat percentage can be calculated simply by taking theratio of either component to the total signal [36]. These methodsare the most quantitatively accurate water/fat sequences becausethey are less sensitive to magnetic field inhomogeneities com-pared to other methods.

In this study the IDEAL (Iterative Decomposition of waterand fat with Echo Asymmetry and Least-squares estimation)sequence was used, which improves the signal-to-noise ratio(SNR) of the Dixon sequence by sampling at echo times whichminimize the effects of noise [37]. IDEAL imaging improves onDixon imaging by enabling the choice of echo times which max-imize SNR. This sequence has been shown to have extremelyhigh lipid quantification accuracy in the liver [38] and ex vivoswine samples [39]. Bernard et al. [40] found a 3.7% mean dif-ference in lipid quantification between IDEAL and MR spec-troscopy, the “gold standard,” and concluded that the IDEALMR sequence was the best sequence of the available methods toprovide quantitative water and fat images.

Fig. 2. Comparison of the spectral dependency of MR and NIR optics on waterand fat. Because the signal contributions from water and fat can be isolated,percent water and fat calculated by MR will in principle be the same percentagesdetermined by optics (Optical spectrum obtained from van Veen et al.).

C. Correlation of Water and Fat Between Optical and MRImaging

It is critical for the methods presented in this work that thewater and fat measured by the MR are the same substances thatare measured optically. In principle, optical and MR imagingare sensitive to different characteristics of water and lipids;whereas optical imaging is sensitive to the electronic atomicstructure, MR imaging is sensitive to the proton resonance,which is affected by local magnetic shielding. However, for agiven voxel of tissue, these modalities both determine water andlipid volume fractions, which are equivalent. This separation isshown pictorially in Fig. 2.

The total signal detected by MR in a unit of tissue consistingof protons only associated with water and fat is [37]

(9)

where , are the signals from water and fat, respectively,are differences in frequency between the known spec-

trum of water and lipids, shown in Fig. 2(a), and the frequency ofthe measurement, and is the time of the measurement (i.e., theecho time). Water and fat are separated in the IDEAL sequenceby measuring the changes in the signal at a distinct number ofecho times, and decomposing (9) for water and fat signal. Mostimportantly, the IDEAL sequence and reconstruction removecontributions due to local field inhomogeneities (offsets), . Acomprehensive detailing of this procedure is given in [37].

The signal calculated for each component is

(10)

where is either water, , or fat, , is the proton density,is a scaling factor, which depends on coil sensitivity [41], and

is a relaxation factor which is dependent on tissue relaxationparameters and sequence selection. The coil sensitivity factoris difficult to determine in practice; however, this is not criticalsince the goal is to separate the signal into water and fat frac-tions. Additionally, for a small tip angle (used in this work), thecontributions from the different are minimal—these can be


set equal. Therefore, normalizing the signal in (10) by andassuming uniform proton density gives the relative fraction ofwater and fat

(11)

In optical imaging, light absorption from a voxel of tissue isdue to the concentration of water, lipids, and hemoglobin. How-ever, water and lipids make up the great majority of the tissuevolume. Since water and lipids make up nearly 100% of thevolume of breast tissue, one constituent may be determined bysubtracting the percentage of the other from 100%. This allowsthe determination of lipid fraction without the need for its inclu-sion in the spectroscopic system of equations, given by (1).

Merritt et al. [42] investigated the correlation between waterand fat measured optically and by a three-point Dixon MRsequence in water and soybean oil emulsion phantoms. Theyfound an agreement of 0.97 in water, and 0.99 in lipid. Thedifference in water fraction between the modalities was highest,5% and 8%, when water percentages were at the extremes ofwater fraction in tissue, at 10% and 100%, respectively.

D. Methods to Incorporate MR Water and Fat Into ImageReconstruction

In this work, quantitative MR water/fat separation is incor-porated into the optical reconstruction using two methods: thedirect substitution method, and the joint weighted estimationmethod. For both methods, quantitative water and fat fractionsfrom MR are substituted into the initial guess, , whereasthe other parameters are computed from an optical calibrationroutine [33], mentioned above. An example of an all-optical ini-tial guess from the patient imaged in Section III-D is shown inFig. 3(a), whereas the initial guess using the MR water image isshown in Fig. 3(b). In this work, lipids are ignored since theirspectral contribution to the optical signal for the PMTs used inthis system is insignificant. Lipid signals are used to determinewater concentration in the MR sequences, and are ignored forthe MR/optical reconstruction. Once water images are formed,lipid images can be calculated simply by subtracting the waterfraction from 1.0, if desired.

1) Direct Substitution of Water and Fat: If it is assumed thatthe MR water and fat information is perfectly accurate, thesevalues can be substituted directly into the objective function.Thus, the Water estimate in the tissue property vector, , can bereplaced with the MR water estimate, , which is thewater fraction calculated via MR.

The water fraction is fixed throughout the reconstruction,since it is assumed to be estimated accurately by MR. Thus,the water contribution to the Jacobian may be removed duringmatrix inversion. The Jacobian is modified to

(12)

Its dimensions are reduced. The tissue property vector duringmatrix inversion is reduced to

Fig. 3. The initial guess determined by (a) optics alone, and (b) optics includingthe MR water image, from the patient imaged in this study.

After the update is calculated, the water estimate from MRis inserted back into the tissue property vector to calculatethe data/model misfit. This formulation has several advantages.First and foremost, the water is forced to be a more accuratevalue for water fraction, which ensures that hemoglobin/watercrosstalk is reduced. Additionally, the inversion is more stablebecause of the reduction in the number of unknowns.

2) Joint Weighted Estimation of Water and Fat: A concernwith the direct substitution method is in the assumption that theMR quantitative information is perfect. Even in MR sequencesthat are quantitatively accurate in phantoms, effects from T1 re-laxation, inhomogeneous Rf excitation, and spectral deviationsfrom the assumed spectral signatures will lead to inaccuracies.These errors in MR estimation will corrupt not only the MRmeasured water, but also other parameters because of similari-ties in the optical absorption spectrum. The joint weighted esti-mation (JWE) method estimates tissue properties using both op-tical and MR information jointly. Since both datasets are avail-able, bias in water estimation in one modality will have smallerdetriments to parameter recovery. In contrast to the direct substi-tution approach, this method uses the full Jacobian in the imagereconstruction.

The advantage of this method is that the weighting functioncan be adjusted to control the expected contrast of the water andfat. This weighting function depends on the expected accuracyof the ability of the MR to separate water and fat. These quanti-ties are incorporated into the parameter weighting function

(13)

where each of the tissue content weight submatrices,(where are the chromophores), contains the variance, orcontrast bound, of each of the parameters on the diagonal,and the covariance, or spatial interdependence of the parame-ters on the off-diagonal. The weighting functions for ,

, , and incorporate the known physiologically


possible contrasts of oxyhemoglobin, deoxyhemoglobin, scat-tering amplitude, and scattering power, respectively, extractedfrom the literature [3], [9], [43]. These values are describedin more detail in Yalavarthy et al. [29] The water weightingfunction, , incorporates the known accuracy of theMR water quantification measurement at each voxel (denotedwith subscript)

(14)

In this approach, as opposed to the direct substitution ap-proach, the tissue property vector is

for each calculation of the update equation. The initial guess,is the same as that used for the direct substitution ap-

proach (7). In this method, the MR water is used only for theprior estimate of the water—it is not used to fix the water valuethroughout the reconstruction, as in the direct substitution ap-proach. This formulation allows a joint determination of water,and therefore maintains the dimensions of the Jacobian. Thisweighting function in is input into the objective function of (3).In this work, the covariances were set to zeros, as covarianceof the water voxels between each tissue region were assumedto be independent. The variance of the MR water quantificationcan be determined via phantom experiments, as performed byBernard et al. [40].

III. RESULTS

A. Effects of MR Water-Guidance on Errors Caused byInsufficient Spectral Sampling

In any spectroscopy problem, insufficient spectral samplingwill lead to errors in separation of the different componentsdue to measurement noise. In optical imaging, the use of fewerwavelengths leads to greater errors in chromophore estima-tion. In particular, fewer wavelengths is expected to increasecrosstalk between water and oxyhemoglobin, as measurementnoise will have a greater impact on their spectral separation.

This section investigates error due to hemoglobin/watercrosstalk with differing numbers of wavelengths. Thewater-guided reconstruction algorithms described abovewere compared to a reconstruction which omitted MR water/fatinformation. Reconstructions were performed with ensemblesof 3, 4, 5, and 6 wavelengths typically used in optical tomog-raphy [1], [44] (chosen from 661 nm, 761 nm, 785 nm, 808 nm,826 nm, 849 nm).

A simulated test problem was created from a breast MR scan,shown in Fig. 4. A finite element mesh was created from theMR images, segmented, and used to generate noisy data (5%Gaussian noise in amplitude, 5 Gaussian noise in phase). A

Fig. 4. Test problem used in this simulation study. Total hemoglobin in thetumor was set at 0.04 mM, a 2:1 contrast over the background fibroglandulartissue. Oxygen saturation was 50% in the tumor, and 70% in the background.These values are within the range of contrast found between healthy tissue andinvasive ductal carcinomas [1]. Data with 5% white noise in AC amplitude and5 white noise in phase was generated from this geometry.

TABLE ITISSUE PROPERTIES USED IN THE SIMULATION STUDY OF FIG. 4

5-mm-diameter tumor was embedded in the fibroglandular re-gion of a segmented coronal breast MR slice. The diameter ofthe domain was mm. The contrast added to the breast wastypical of recovered breast properties [2], [20], and is shown inTable I. A separate reconstruction mesh, made from the samevolume but with slightly fewer nodes was used to reconstructtissue properties. The oxyhemoglobin concentration error wasdetermined for various wavelength sets for different numbers ofwavelengths. For three wavelengths , five sets of dif-ferent wavelengths were used. Similarly, five sets wereused for four wavelengths, five sets were used for five wave-lengths, and one set for six wavelengths. The error percentage,

, reported for each of wavelengths was averaged over theensembles of wavelength sets, according to

(15)

where and are the recovered (estimated)and true oxyhemoglobin concentrations, respectively.

Fig. 5 shows the error in oxyhemoglobin concentration of thevarious reconstructions. The mean from each set is plotted, aswell as error bars indicating standard deviations for each set.Omitting MR water yields average errors of 38%, 18%, 9%,and 2% for 3, 4, 5, and 6 wavelengths, respectively, whereasincluding MR water yields average errors of 1%, 2%, 2%, and1%. It is apparent that using MR water information with ei-ther method, even with a mere three wavelengths, gives superioroxyhemoglobin concentration quantification compared to omit-ting MR water, as all are within 2%.

B. Influence of MR Water/Fat Separation Constraint onCrosstalk

It is important to study the effects of errors in MR quantifi-cation on these methods, as MR water quantification is not ex-pected to be perfect. Imperfect water estimation, if rigidly en-forced to incorrect values, will lead to errors in oxyhemoglobin


Fig. 5. Oxyhemoglobin error in terms of the means and standard deviationsfor all wavelength sets with and without water quantification. Error in HbOdecreases with additional wavelengths because of the improved spectral sam-pling, which in turn leads to more accurate separation between water and oxy-hemoglobin. Comparatively, the direct substitution method gives superior quan-tification, even with three wavelengths.

concentration. With sufficiently large errors in MR water, in-cluding this information may lead to poorer estimation than ex-cluding the water information altogether. This section investi-gates this effect.

Datasets were formed from the previous test problem ofSection III-A, using ensembles of three-wavelengths. This caserepresents the worst-case scenario for spectral separation, wherethere are only three datasets for the three unknowns of oxy-hemoglobin concentration, deoxyhemoglobin concentration,and water concentration. While the true water concentrationwas fixed, the initial water estimation used in the initial guess,

, for the MR water guided reconstructions was perturbedby varying amounts, from 0% to 35%. The joint weightedestimation approach incorporated the bound of the MR errorinto , as described in Section II-D. Fig. 6 displayserrors in oxyhemoglobin concentration as a function of errorsin MR water quantification; means and standard deviations forall sets are plotted. As expected, if the MR water quantificationis accurate, using MR water guidance results in lower errorsin oxyhemoglobin concentration than if MR water is ignored.However, these results suggest that if MR water quantificationis worse than about 22%, including MR water directly is detri-mental to the optical reconstruction, even compared to omittingthis information entirely. On the other hand, using the jointweighted estimation approach yields a superior estimate whenthere are biases in MR water for all investigated perturbations.

Fig. 7 examines the recovered water values using the twowater-guided methods. This shows the increased errors in waterestimation as the prior water concentration is increasingly per-turbed. In the direct substitution case water error increases lin-early, as this method fixes the water concentration to its erro-neous prior estimate. In contrast, the joint weighted estimationapproach improves the water estimate. Thus, this method maybe beneficial in applications where obtaining highly accuratewater or lipid concentrations with MR is difficult because ofanatomically-induced field inhomogeneity or time constraints.

Fig. 6. Oxyhemoglobin error in terms of means and standard deviations forall wavelength sets with respect to error in the water estimates. Error in oxy-hemoglobin increases as MR water quantification error increases. In this case,simulations were performed using three-wavelength sets. Error is shown as themean with error bars indicating standard deviation. In these cases, if MR waterquantification was within 20% error, using MR water guidance provided a ben-efit (lower error). In all cases, using a weighted estimate achieved the best quan-tification (within error bounds).

Fig. 7. Recovered water error in terms of the means and standard deviations forall wavelength sets with respect to errors in the water estimates. Comparison ofrecovered errors in water quantification between the direct substitution approachversus the joint weighted estimation approach.

C. Experimental Validation in a Breast Tissue-SimulatingPhantom

A gelatin (G2625, Sigma), tissue-simulating phantom wasused to test the methodology of using MR water/fat priors. Thisphantom had a 24 mm gelatin inclusion with 2:1 contrast in totalhemoglobin. It was made following techniques described else-where [21], [45], [46]. The optical properties of this phantomare shown in Table II. Optical properties are quantified in termsof total hemoglobin and oxygen satura-tion (Sat), because the blood oxygenation was not measured (al-though it was nearly fully oxygenated), and these properties arearguably more interesting clinically.

1) Measurement of Water Concentration in Gelatin: To de-termine the water content in the gelatin, measurements were per-formed using both a UV-VIS-NIR spectrophotometer (Varian


TABLE IITRUE CONCENTRATIONS IN THE BACKGROUND AND REGION OF INTEREST

(ROI) IN THE GELATIN PHANTOM. SCATTER AMPLITUDE AND SCATTER POWER

WERE HOMOGENEOUS, BUT UNKNOWN (UK)

Fig. 8. Methods used to compute percent water in gelatin consisted of (a) NIRspectrophotometry, and (b) DIXON MR. In both cases, pure water was used asa reference to determine the water content of the gelatin (labeled here as “gel”).

Cary, Varian, Palo Alto, CA) and an MR water/fat separationgradient echo DIXON technique.

Optical absorbance data was collected by placing water andthe prepared gelatin into sample cuvettes and measuring theirspectra with a spectrophotometer. These spectra were calibratedwith a blank cuvette. The spectral absorbance for water and thegelatin phantom are shown in Fig. 8(a). A power law fit wasperformed on the gelatin data to remove the offset due to scattersignal from the gelatin. Using pure water as a reference, it wasdetermined with this method that the gelatin contained 87%water.

To measure the water content in gelatin with MR, water-fatseparated MR images (2D GRASS, ms,

ms, flip angle ) of phantomscontaining varying amounts of water and soybean oil wereacquired. These phantoms were blended together by adding1% Tween (Sigma–Aldrich, St. Louis, MO) and mixing on theblender’s high setting for 3 min. The well-mixed phantomshad a milky consistency. These phantoms were poured into acylindrical mold to form phantoms with water concentrationsof: 0%, 25%, 50%, 75%, and 100%. The gelatin mixture waspoured into a sixth hole, and allowed to cool. The signals fromthe resulting water images were normalized to the signal ofthe phantom containing 100% water. Using this method, it wasdetermined that the gelatin phantom had a water concentrationof 90%.

2) Reconstruction Results From the Gelatin Phantom: Cal-ibrated data from six wavelengths (661, 761, 785, 808, 826,849 nm) were used to reconstruct images of chromophoreconcentrations with water-guided and non-water-guided re-constructions. To again investigate the effects of poor spectralsampling, reconstructions were performed with varying num-bers of wavelengths. Specifically, three reconstructions usedthree wavelengths of data (one with 661, 785, and 849 nm,one with 661, 761, and 785 nm, and one with 661, 785, and826 nm), two reconstructions used four wavelengths (one with661, 761, 785, 849, and one with 661, 761, 785, 808) one

Fig. 9. Comparison of reconstructions of three wavelengths of 661, 785, and826 nm with and without water priors. (a) Target true values, (b) non-water-guided reconstruction, and (c) water-guided reconstruction. (d) Errors in oxyhe-moglobin of water guided versus nonwater guided reconstructions for differentnumbers of wavelengths.

reconstruction used five wavelengths (661, 761, 785, 808, 826),and one used the full six wavelength dataset. For the MR waterguided methods, water was input exactly (88.5%, averagedfrom the spectrometer and DIXON methods), as determinedabove. Since the water-guided reconstructions give the sameresult with 0% error in water, only the JWE approach wasused in this section. Example optical image reconstructions areshown in Fig. 9(a)–(c) for the wavelength set of 661, 785, and826 nm. Absolute percent errors are shown in Fig. 9(d).

As expected, when the MR water image is used, errors in totalhemoglobin decrease compared to the non-water-guided tech-nique, especially when using three or four wavelengths. As morewavelengths are included in the reconstruction, the non-water-guided case converges to the water guided-case. These recon-struction results show that utilizing the MR water informationyields a more accurate estimation of total hemoglobin (statis-tical significance: , one-tailed two-sample t-test).

D. In Vivo Results in a Human Breast

A 47-year-old woman with an invasive ductal carcinoma ofthe left breast was imaged postbiopsy. MR images were takenin the coronal plane, including a gradient echo T2-weightedsequence [Fig. 10(b)] and a spoiled gradient echo IDEALwater/fat sequence. Anatomical boundaries of the fibroglan-dular tissue and suspect lesion were manually segmented undersupervision of the radiologist (B. Daniel). Gadolinium-en-hanced images were collected 11 days prior to the imagingsession according to the clinical breast protocol at StanfordUniversity Medical Center [Fig. 10(a)]. IDEAL water/fat sep-aration images in the plane of the optical fibers are shown inFig. 10(c) and (d). Three reconstructions were performed: onewithout water-guidance, one with water-guidance using thedirect substitution method, and one with the JWE approachwith MR water accuracy of 3.7%. This value was taken from[40], which used the same commercially available Fat/Waterimaging sequence.

The optical image results are shown Fig. 11. Without eitherMR-water method, the tumor hemoglobin was estimated at0.035 mM compared to 0.026 mM in the fibroglandular and0.016 mM in the adipose tissue. Comparing the quantitativeMR water image with the all-optical estimatation, the watercontent is underestimated. Oxygen saturation was highest in


Fig. 10. (a) T1-W Gadolinium MR image of the affected breast (b) T2 weightedimage in the coronal plane of the optical fibers. Tumors are identified with thered arrows. Images of water (c) and lipid (d) IDEAL MR images.

Fig. 11. (a) In vivo image reconstructions of a diseased breast without MRwater guidance priors. (b) Image reconstruction using the direct substitutiongives the highest tumor to background contrast. (c) Image reconstruction usingthe joint weighted estimation approach yields higher contrast than ignoringwater quantitative priors, but less contrast than the direct substitution method.

the tumor at 70%, slightly above the oxygen saturation in thefibroglandular and adipose tissue, both around 60%.

By including MR water values via the direct substitutionmethod, total hemoglobin was estimated to be 0.039 mM in thetumor, and 0.019 mM and 0.015 mM in the fibroglandular andadipose tissues, respectively. Because the direct method moreaccurately estimates water at 60%, oxyhemoglobin estimatesare lower, which results in more hemoglobin contrast betweenthe fibroglandular tissue and the tumor tissue. The effect ofincluding MR water priors via this method increased tumor tofibroglandular total hemoglobin contrast by 42%, to 103%.

The joint weighted estimation approach led to total hemo-globin recovery of 0.031 mM, while fibroglandular and adiposewere 0.018 mM and 0.017 mM, respectively. This led to anincrease in contrast compared to excluding water priors of7%. The decrease in contrast in total hemoglobin of the JWEmethod versus the direct method could likely be attributed tothe decrease in water in the fibroglandular tissue by 5%, from60.2% to 54.9%, and no significant change in water content inthe tumor tissue.

IV. DISCUSSION AND CONCLUSION

MR-guided optical imaging offers the ability to characterizetissue properties that may provide significant benefit to theidentification and classification of lesions. One advantage ofusing MR guidance compared to standalone optical imagingis its ability to provide anatomical boundaries; this topic hasbeen previously investigated in the literature. Structural infor-mation enables several improvements: a more accurate lightpropagation model is formed by better delineating the air/tissueboundary [47], optical fiber positions relative to the tissue areidentified with higher accuracy [5], and interior boundariesmay be incorporated [4], [21], [22]. Incorporating anatomicalMR information has been shown to improve a fundamentallimitation of optical imaging—spatial resolution [48]. In thiswork, we have shown that the MR may provide further aid tooptical imaging through its spectral capabilities, which improvea practical limitation—suboptimal optical detection hardware.

This study shows that including MR water/fat separation canyield significant improvement in hemoglobin quantification. Ina simulated complex case with added noise, inputting the cor-rect quantity of water through these techniques yielded nearlya 40% reduction in oxyhemoglobin error when imaging with asfew as three wavelengths. This error was demonstrated in Figs. 6and 7 to be dependent on water bias, due to poor spectral sam-pling of the water (compare the near-linear increase in recoveredwater bias in Fig. 7 with oxyhemoglobin bias in Fig. 6). Thesenumerical phantoms suggest that these methodologies are lesssensitive to data noise, which is the dominant cause of errorswhen de-convolving spectra with a minimal number of samples(wavelengths).

In a tissue-simulating experimental phantom, including theMR water prior in the image reconstruction yielded hemoglobinquantification improvements of near 40% when imaging withthree wavelengths.

In imaging a patient with breast cancer, it was found that he-moglobin contrast between the tumor and the background tissuewas increased when MR quantitative water information was in-corporated. Since the all-optical water estimation led to an un-derestimation of the water content compared to the MR, thisreconstruction may have led to an overestimation in total hemo-globin in the fibroglandular tissue because of crosstalk. Thus,the ignoring the MR water information led to reduced tumor tobackground contrast.

These results also demonstrate that large MR water quantifi-cation errors will result in poorer tissue recovery with a con-strained water-guided reconstruction than if MR water is ig-nored. By incorporating the known variance of the MR sequence


(here varied between 2.5% and 35%) into the reconstruction,the joint-weighted estimate algorithm recovered tissue proper-ties with up to 20% less error. This method is critical when thereis a high degree of magnet inhomogeneity, such as cases wherepatient size or patient position in the breast coil degrades imagequality. Thus, in cases where the water/fat separation is expectedto be poor, the joint weighted estimation method is more appro-priate.

An important outcome from this work is the demonstrationthat incorporating MR water quantification may alleviate theneed to add more than the 3 wavelengths required to resolveHbO, Hb, and Water. Figs. 5 and 9 demonstrated this capability.This has significant utility for increasing temporal resolution,as adequate accuracy may be achieved with fewer wavelengths.These results imply that adding additional wavelengths in en-dogenous optical imaging mainly serves to improve water quan-tification, thereby indirectly aiding hemoglobin quantification.However, this observation must be put into the context of thesystem, both in terms of spectral capabilities and noise perfor-mance. Clearly, a system which has poor accuracy in detectingthe wavelengths most sensitive to hemoglobin (e.g., 661, 761,and 785 nm) will suffer from poor quantification in hemoglobinregardless of whether or not MR water quantification is utilized.

As multimodality instruments become more common in theclinic, a unique benefit is if they offer complimentary infor-mation. Combining MR and optical provides benefits to eachmodality; while MR can improve on the inherent limitations ofoptical imaging, optical contrasts may improve the informationcontent of MR. Imaging of water and fat quantities is a goodexample of the synergy that can exist between these modalities.

REFERENCES

[1] B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, S. K. Os-terman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobintomography with diffuse near-infrared spectroscopy: Pilot results in thebreast,” Radiology, vol. 218, no. 1, pp. 261–6, 2001.

[2] B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C.Kogel, T. Tosteson, J. B. Weaver, S. P. Poplack, and K. D. Paulsen,“Imaging breast adipose and fibroglandular tissue molecular signaturesusing hybrid MRI-guided near-infrared spectral tomography,” Proc.Nat. Acad. Sci., vol. 103, pp. 8828–8833, 2006.

[3] T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Gi-ammarco, B. Chance, and A. G. Yodh, “Bulk optical properties ofhealthy female breast tissue,” Phys. Med. Biol., vol. 47, no. 16, pp.2847–2861, 2002.

[4] R. L. Barbour, H. L. Graber, J. Chang, S. S. Barbour, P. C. Koo, andR. Aronson, “MRI-guided optical tomography: Prospects and compu-tation for a new imaging method,” IEEE Comp. Sci. Eng., vol. 2, no. 4,pp. 63–77, 1995.

[5] B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, C.Kogel, M. Doyley, J. B. Weaver, and S. P. Poplack, “Magnetic res-onance-guided near-infrared tomography of the breast,” Rev. Sci. In-strum., vol. 75, no. 12, pp. 5262–5270, 2004.

[6] D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, M. Moller, C.Stroszczynski, J. Stossel, B. Wassermann, P. M. Schlag, and H. Rin-neberg, “Concentration and oxygen saturation of haemoglobin of 50breast tumours determined by time-domain optical mammography,”Phys. Med. Biol., vol. 47, no. 9, pp. 1165–1181, 2004.

[7] X. Intes, “Time-domain optical mammography softscan initial results,”Acad. Radiol., vol. 12, no. 8, pp. 934–947, 2005.

[8] 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 breast imaging: Results of a pilot study in womenwith abnormal mammograms,” Radiology, vol. 243, no. 2, pp. 350–9,2007.

[9] A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. Tromberg,“In vivo absorption, scattering, and physiologic properties of 58 ma-lignant breast tumors determined by broadband diffuse optical spec-troscopy,” J. Biomed. Opt., vol. 11, no. 4, 2006.

[10] R. Choe, S. D. Konecky, A. Corlu, K. Lee, T. Durduran, D. R. Busch,B. Czerniecki, J. Tchou, D. L. Fraker, A. DeMichele, B. Chance, E.Putt, M. D. Schnall, M. A. Rosen, and A. G. Yodh, “Differentiationof benign and malignant breast lesions by in-vivo three-dimensionaldiffuse optical tomography,” Cancer Res., vol. 69, no. 2, p. 102S, 2009.

[11] C. M. Carpenter, S. Jiang, S. Srinivasan, B. W. Pogue, and K. D.Paulsen, “MRI-guided near-infrared spectroscopy of breast tumors,”Medicamundi, vol. 53, no. 1, pp. 28–34, 2009.

[12] A. Corlu, T. Durduran, R. Choe, M. Schweiger, E. M. Hillman, S. R.Arridge, and A. G. Yodh, “Uniqueness and wavelength optimization incontinuous-wave multispectral diffuse optical tomography,” Opt. Lett.,vol. 28, no. 23, pp. 2339–41, 2003.

[13] R. van Veen, H. Sterenborg, A. Pifferi, A. Torricelli, and R. Cubeddu,in OSA Annu. BIOMED Topical Meeting, Miami, FL, 2004, p. SF4.

[14] M. Franceschini, S. Fantini, A. Cerussi, B. Barbieri, B. Chance, andE. Gratton, “Quantitative spectroscopic determination of hemoglobinconcentration and saturation in a turbid medium: Analysis of the effectof water absorption,” J. Biomed. Opt., vol. 2, no. 2, pp. 147–153, 1997.

[15] A. E. Cerussi, D. Jakubowski, N. Shah, F. Bevilacqua, R. Lanning, A.J. Berger, D. Hsiang, J. Butler, R. F. Holcombe, and B. J. Tromberg,“Spectroscopy enhances the information content of optical mammog-raphy,” J. Biomed. Opt., vol. 7, no. 1, pp. 60–71, 2002.

[16] Q. Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans,R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combinedoptical imaging and mammography of the healthy breast: Optical con-trast derived from breast structure and compression,” IEEE Trans. Med.Imag., vol. 28, no. 1, pp. 30–42, Jan. 2009.

[17] T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S.Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infraredtomography: A case study in compensating for water and lipid contentin hemoglobin imaging of the breast,” J. Biomed. Opt., vol. 7, no. 1,pp. 72–9, 2002.

[18] W. T. Dixon, “Simple proton spectroscopic imaging,” Radiology, vol.153, pp. 189–194, 1984.

[19] A. Li, G. Boverman, Y. Zhang, D. Brooks, E. Miller, M. Kilmer, Q.Zhang, E. Hillman, and D. Boas, “Optimal linear inverse solution withmultiple priors in diffuse optical tomography,” Appl. Opt., vol. 44, no.10, 2005.

[20] C. M. Carpenter, B. W. Pogue, S. J. Jiang, H. Dehghani, X. Wang, K. D.Paulsen, W. A. Wells, J. Forero, C. Kogel, J. B. Weaver, S. P. Poplack,and P. A. Kaufman, “Image-guided spectroscopy provides molecularspecific information in vivo: MRI-guided spectroscopy of breast cancerhemoglobin, water, and scatterer size,” Opt. Lett., vol. 32, no. 8, pp.933–935, 2007.

[21] B. Brooksby, S. Jiang, H. Dehghani, B. W. Pogue, K. D. Paulsen, J. B.Weaver, C. Kogel, and S. P. Poplack, “Combining near infrared tomog-raphy and magnetic resonance imaging to study in vivo breast tissue:Implementation of a laplacian-type regularization to incorporate MRstructure,” J. Biomed. Opt., vol. 10, no. 5, pp. 050504-1–050504-10,2005.

[22] M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomog-raphy with a priori anatomical information,” Phys. Med. Biol., vol. 12,pp. 2837–2858, 2005.

[23] H. Dehghani, B. W. Pogue, J. Shudong, B. Brooksby, and K. D.Paulsen, “Three-dimensional optical tomography: Resolution insmall-object imaging,” Appl. Opt., vol. 42, no. 16, pp. 3117–28, 2003.

[24] C. Carpenter, S. Srinivasan, B. Pogue, and K. Paulsen, “Method-ology development for three-dimensional MR-guided near infraredspectroscopy of breast tumors,” Opt. Express, vol. 16, no. 22, pp.17903–17914, 2008.

[25] I. R. Bigio, S. G. Bown, G. Briggs, C. Kelley, S. Lakhani, D. Pickard,P. M. Ripley, I. G. Rose, and C. Sanders, “Diagnosis of breast cancerusing elastic-scattering spectroscopy: Preliminary clinical results,” J.Biomed. Opt., vol. 5, no. 2, pp. 221–228, 2000.

[26] M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation ofoptical radiation in tissue II. Optical properties of tissues and resultingfluence distributions,” Lasers Med. Sci., vol. 6, pp. 379–390, 1990.

[27] S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite-element approach for modeling photon transport in tissue,” Med. Phys.,vol. 20, no. 2, pp. 299–309, 1993.

[28] K. D. Paulsen and J. Hjiang, “Spatially varying optical property re-construction using a finite element diffusion equation approximation,”Med. Phys., vol. 22, no. 6, pp. 691–701, 1995.


[29] P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen,“Weight-matrix structured regularization provides optical generalizedleast-squares estimate in diffuse optical tomography,” Med. Phys., vol.34, no. 6, pp. 2085–98, 2007.

[30] X. Intes, C. Maloux, M. Guven, T. Yazici, and B. Chance, “Diffuseoptical tomography with physiological and spatial a priori constraints,”Phys. Med. Biol., vol. 49, pp. N155–N163, 2004.

[31] S. R. Arridge and M. Schweiger, “Photon-measurement density func-tions. Part 2: Finite-element-method calculations,” Appl. Opt., vol. 34,pp. 8026–8037, 1995.

[32] A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge,E. M. Hillman, and A. G. Yodh, “Diffuse optical tomography with spec-tral constraints and wavelength optimization,” Appl. Opt., vol. 44, no.11, pp. 2082–93, 2005.

[33] T. O. McBride, B. W. Pogue, U. L. Osterberg, and K. D. Paulsen,“Strategies for absolute calibration of near infrared tomographic tissueimaging,” Adv. Exp. Med. Biol., vol. 530, pp. 85–99, 2003.

[34] C. M. Carpenter and B. W. Pogue, “Diffuse optical spectroscopy withmagnetic resonance imaging,” in Translational Multimodality OpticalImaging, F. S. Azar and X. Intes, Eds. Boston, MA: Artech, 2008.

[35] G. H. Glover and E. Schnieder, “Three-point dixon technique for truewater/fat decomposition with B0 inhomogeneity correction,” Magn.Reson. Med., vol. 18, no. 2, 1991.

[36] S. J. Graham, P. L. Stanchev, J. O. A. LloydSmith, M. J. Bronskill, andD. B. Plewes, “Changes in fibroglandular volume and water content ofbreast tissue during the menstrual cycle observed by MR imaging at1.5 T,” J. Magn. Reson. Imag., vol. 5, no. 6, pp. 695–701, 1995.

[37] S. Reeder, N. Pelc, M. Alley, and G. Gold, “Multi-coil Dixon chem-ical species separation with an iterative least squares method,” Magn.Reson. Med., vol. 51, pp. 35–45, 2004.

[38] B. Guiu, R. Loffroy, J. P. Cercueil, and D. Krause, “Multiecho MRimaging and proton MR spectroscopy for liver fat quantification,” Ra-diology, vol. 249, no. 3, p. 1081, 2008.

[39] H. H. Hu and K. S. Nayak, “Quantification of absolute fat mass usingan adipose tissue reference signal model,” J. Magn. Reson. Imag., vol.28, no. 6, pp. 1483–1491, 2008.

[40] C. P. Bernard, G. P. Liney, D. J. Manton, L. W. Turnbull, and C. M.Langton, “Comparison of fat quantification methods: A phantom studyat 3.0 T,” J. Magn. Reson. Imag., vol. 27, no. 1, pp. 192–197, 2008.

[41] Z. P. Liang and P. C. Lauterbur, Principles of Magnetic ResonanceImaging a Signal Processing Perspective. New York: IEEE Press,2000.

[42] S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. E. Cerussi, A.J. Durkin, B. J. Tromberg, and O. Nalcioglu, “Comparison of waterand lipid content measurements using diffuse optical spectroscopy andMRI in emulsion phantoms,” Technol. Cancer Res. Treatment, vol. 2,no. 6, pp. 563–9, 2003.

[43] S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho,J. G. Chambers, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In-terpreting hemoglobin and water concentration, oxygen saturation, andscattering measured by near-infrared tomography of normal breast invivo,” Proc. Nat. Acad. Sci. USA, vol. 100, no. 21, pp. 12349–12354,2003.

[44] V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, “ConcurrentMRI and diffuse optical tomography of breast after indocyanine greenenhancement,” Proc. Nat. Acad. Sci. USA, vol. 97, no. 6, pp. 2767–72,2000.

[45] B. W. Pogue and M. S. Patterson, “Review of tissue simulating phan-toms for optical spectroscopy, imaging and dosimetry,” J. Biomed.Opt., vol. 11, no. 4, 2006.

[46] J. Wang, S. C. Davis, S. Srinivasan, S. D. Jiang, B. W. Pogue, andK. D. Paulsen, “Spectral tomography with diffuse near-infrared light:Inclusion of broadband frequency domain spectral data,” J. Biomed.Opt., vol. 13, no. 4, p. 041305, 2008.

[47] A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilaccio, T. Chaves, J. Stott,Q. Zhang, T. Wu, M. Choriton, R. H. Moore, D. B. Kopans, and D.A. Boas, “Tomographic optical breast imaging guided by three-dimen-sional mammography,” Appl. Opt., vol. 42, no. 25, pp. 5181–5190,2003.

[48] P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. J.Jiang, and K. D. Paulsen, “Structural information within regularizationmatrices improves near infrared diffuse optical tomography,” Opt. Exp.,vol. 15, no. 13, 2007.

mr water quantitative priors improves the accuracy of optical breast imaging

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