Three-dimensional diffuse optical mammography with ultrasound localization in a human subject

. We describe an approach that combines clinical ultrasound and photon migration techniques to enhance the sensitivity and information content of diffuse optical tomography. Measurements were performed on a postmenopausal woman with a single 1.8 3 0.9 cm malignant ductal carcinoma in situ approximately 7.4 mm beneath the skin surface (UCI IRB protocol 95-563). The ultrasound-derived information about tumor geometry enabled us to segment the breast tissue into tumor and background regions. Optical data was obtained with a multifrequency, multiwavelength hand-held frequency-domain photon migration backscattering probe. The optical properties of the tumor and background were then computed using the ultrasound-derived geometrical constraints. An iterative perturbative approach, using parallel processing, provided quantitative information about scattering and absorption simultaneously with the ability to incorpo-rate and resolve complex boundary conditions and geometries. A three to four fold increase in the tumor absorption coefﬁcient and nearly 50% reduction in scattering coefﬁcient relative to background was observed ( l 5 674, 782, 803, and 849 nm). Calculations of the mean physiological parameters reveal fourfold greater tumor total hemoglobin concentration @ Hb tot # than normal breast (67 m M vs 16 m M) and tumor hemoglobin oxygen saturation (SOx) values of 63% (vs 73% and 68% in the region surrounding the tumor and the opposite normal tissue, respectively). Comparison of semi-inﬁnite to heterogeneous models shows superior tumor/background contrast for the latter in both absorption and scattering. Sensitivity studies assessing the impact of tumor size and refractive index assumptions, as well as scan direction, demonstrate modest effects on recovered properties.


Introduction
The unique functional information and deep tissue penetration provided by near-infrared ͑NIR͒ light makes it well suited for characterizing and imaging breast tumors. However, optical contrast elements associated with malignant and benign lesions as well as normal breast tissue physiological fluctuations are poorly understood. Consequently, NIR transillumination techniques that do not separate light absorption from scattering may not provide sufficient diagnostic information to be clinically useful. In order to address this issue, time-and frequency-domain photon migration ͑PM͒ techniques have been developed to facilitate quantitative tissue analysis and separation of tissue absorption and scattering properties in vivo. When multiwavelength time-or frequency-domain photon migration ͑FDPM͒ are combined with tomographic techniques, such as diffuse optical tomography ͑DOT͒, then it is possible to construct low-resolution ͑0.5-1 cm͒ functional images of intrinsic tissue physiology; e.g., tissue hemoglobin ͑total, oxy-, and deoxyforms͒, oxygen saturation, blood volume fraction, water content, fat content, and cellular structure.
In order to perform DOT, measurements of remitted diffuse light intensity and time-of-flight ͑or photon density wave phase and amplitude͒ are made on the boundary of the tissue, and are then used to reconstruct the absorption and scattering optical properties of the underlying medium. A variety of methods have been developed for DOT. These include fits to analytic solutions, 1-3 backprojection methods, 4-7 diffraction tomography in k-space, [8][9][10][11][12][13][14] perturbation approaches, [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] elliptic systems method ͑ESM͒, [31][32][33] and a direct method. 34 All of these approaches have various advantages and disadvantages. Simple boundary conditions and geometries reduce computational cost and increase speed, but also reduce quantitative information about the system. On the other hand, DOT reconstructions are sensitive to many parameters including complex internal geometry of tissues, and at a high computational cost provide access to this information. In this article we employ an iterative perturbative approach that yields quantitative information about scattering and absorption simultaneously, and has the ability to resolve complex boundary conditions and geometries. However, the method is slow and computationally expensive, especially in threedimensions ͑3D͒. Therefore, we have implemented the algorithm using parallel processing to reduce the computational processing time.
Our reconstruction is enhanced by the use of clinical ultrasound measurements to locate the tumor and assess its size. Using this information about tumor geometry, we segment the breast into two regions: tumor and background. Our data is derived at multiple frequencies using a simple, hand-held backscattering probe that contains relatively few sourcedetector separations. 35 This scheme of combining ultrasound and optical information has been suggested as a means to improve breast tumor diagnostics and an instrument employing these modalities simultaneously has been demonstrated in phantoms. 36 To our knowledge, this work represents the first in vivo investigation along these lines.
The optical properties of the tumor and background are computed based on the data and the geometrical constraints. We compare our results to analytic models in order to demonstrate the utility of image segmentation for quantitative tumor spectroscopy. Factors that influence the recovered properties, such as tumor size, refractive index, and scan direction are examined. Finally, the resultant optical properties are used to calculate tumor and normal tissue hemoglobin content and hemoglobin oxygen saturation in order to gain insight into the relationship between optical and physiological changes associated with malignant tumor growth.

FDPM Instrument
FDPM instrumentation and theoretical background have been described in detail. 35 Briefly, the core component of the FDPM apparatus is a network analyzer ͑Hewlett Packard, model 8753C͒, which is used to produce modulation swept from 300 kHz to 1 GHz ͓20 dBm radio-frequency ͑rf͒ output͔. rf from the network analyzer is serially superimposed ͓via the alternating-current ͑ac͒ switch͔ on the direct current of up to eight different diode lasers ͑e.g., 674, 782, 803, 849, 894, and 956 nm͒ using individual bias tees ͑model 5575 A, Picosecond Pulse Labs͒ and an rf switch ͑model 8768 K, Hewlett Packard͒. 100-m-diam gradient-index fibers are used to couple each light source to an 8ϫ8 optical multiplexer ͑model GP700, DiCon Instruments͒. The 8ϫ8 optical multiplexer allows for up to eight different diode laser light sources and eight different optical fiber positions.
Light is launched onto the tissue ͑or test object͒ using the above-mentioned unique wavelengths and one source fiber. An avalanche photodiode ͓͑APD͒, Hamamatsu, model C5658͔ is used to detect the diffuse optical signal that propagates through the biological tissue. Both the APD and probe end of the source optical fiber are fabricated into a hand-held probe. The probe is in direct contact with the patient and can be scanned over the surface. The optical power coupled into the tissue averages approximately 10-30 mW. Measurement time depends on the precision required, the number of sweeps performed, and rf optical switch times. For human subject studies, approximately 0.1 s is used to sweep over the entire 1 GHz band of modulation frequencies. However, total elapsed time for four diodes ͑typically 12-16 sweeps/diode͒, data transfer, display, and source switching is approximately 40 s. Most components, including the network analyzer, rf optical switches, diode power supplies, and temperature of diode mounts are controlled by computer using virtual instrument software ͑LabView, National Instruments͒.

Measurements
Experiments were performed under the guidelines of UC Irvine IRB-approved protocol No. 95-563. The patient was a 67 year old postmenopausal woman with a single palpable mass approximately 7.4 mm beneath the skin surface in the upper outer quadrant of the left breast. Histological examination following surgical biopsy and prebiopsy ultrasound revealed a roughly 1.8ϫ0.9 cm ductal carcinoma in situ ͑DCIS͒ ͑malignant tumor͒. Ultrasound images along the sagittal and axial planes supplied geometry and location information about the tumor ͑see Figure 1͒. The location, dimension, and depth of the tumor are reported in Table 1.  Table 1 Elliptical tumor geometry: a is along the y axis (sagittal), b is along the x axis (axial), c is along the z axis, zc is the depth of the center of the tumor below the skin surface. Relative positioning of the tumor to the source-detector pairs can be seen in Figure 1. This information was then used to center the optical measurement pad over the tumor. Here we have assumed that the ultrasound-defined margins are the same as the optical margins. This assumption could be incorrect, if alterations due to neovascular density and tissue inflammatory response occur beyond the ultrasound-defined tumor region and are detected optically, but not ultrasonically. Optical measurements were performed by placing the FDPM probe on both a normal and a tumor-containing breast. Data were acquired using the hand-held scanning probe placed in 10 discrete locations covering a 2ϫ2 cm grid mapped onto the breast surface ͑Figure 2͒. The probe sourcedetector ͑s-d͒ pair was fixed at 2.5 cm in separation and the probe was placed on the tissue with the source and detector bracketing the tumor. Photon migration data were acquired by moving the probe in 0.5 cm increments along inferiorsuperior and medial-lateral paths. Repeat measurements immediately above tumor center were obtained at least 3 times. Both normal and tumor-containing breasts were studied.
Sequential scans of the same location following probe removal and replacement revealed no significant variation ͑Ͻ5%͒ in optical properties. Normal tissue measurements were acquired in the same manner from a symmetric site on the opposite, uninvolved breast ͑Figure 3͒. Phase and amplitude data ͑represented by ᮀ and A, respectively͒ obtained from tumor measurements are shown in Figure 4. We only utilized frequencies below 400 MHz due to high frequency noise. Additionally, the wavelengths 894 and 956 nm suffered from modulation artifacts and were not employed.

Diffuse Optical Mammography Segmentation and Analytic Schemes
The segmentation and semi-infinite analytic fits are accomplished using diffusion theory in the frequency domain to describe the propagation of light in breast tissue. 37 The equation is with the following boundary condition: D(r) is the diffusion coefficient and is equivalent to 1/3 s (r)Ј. s Ј(r) and a (r) are the scattering and absorption coefficients respectively. ⌽(r,) is the diffuse photon density, is the frequency modulation, and c is the speed of light in the media. S(r,) is the source term, approximated as a Ϫ1.440n Ϫ2 ϩ0.170n Ϫ1 ϩ0.668ϩ0.063n, 38 and n is equal to n in /n out , the index of refraction mismatch at the tissue/air interface boundary. All iterative perturbative approaches follow a similar algorithm. First, the optical properties are estimated. Second, the forward problem ͓Eq. ͑1͔͒ is solved. Third, a 2 ͑i.e., 2 where NM is the number of measure-

Fig. 2
Source-detector pair locations along the sagittal (left, the horizontal measurements) and axial (right, the vertical measurements) planes centered with respect to the tumor. The 0h position is the source-detector pair centered over the tumor for the horizontal measurements, 0v is similar but for the vertical measurements. Med refers to medial, i.e., towards the middle of the body, and lat refers to lateral, i.e., towards the side of the body. u refers to up, which is towards the head and d refers to down, i.e., towards the feet. The tumor geometrical constants a and b are listed in Table 1.
ments, ⌽ m is the measured data, and ⌽ c is the numerically calculated data͒ is calculated and convergence is checked. Fourth, the inverse problem is setup ͑i.e., the Jacobian is de-termined͒. Fifth, the optical property perturbations are solved for ͑i.e., the inverse problem is solved͒. Finally, the optical properties are updated and a return to the second step occurs. Within these approaches there are a couple of methods to solving the forward problem and for determining the Jacobian ͓for a review see Ref. 39͔. Additionally, there have been a variety of methods developed for solving the inverse problem. [40][41][42][43][44][45][46][47][48] We have chosen to follow a Green's function ͑or adjoint͒ method. [15][16][17][18]27,28 The inverse problem, therefore, is formulated in the following way:

Fig. 3
Measurements for each optical wavelength over the entire modulation frequency range for the normal breast. Source-detector pairs along sagittal planes (left, horizontal measurements) have blue for 10 med, green for 5 med, red for 0h, cyan for 5 lat, and magenta for 10 lat; along axial planes (right) vertical measurements have blue for 10d, green for 5d, red for 0v, cyan for 5u, and magenta for 10u. See Figure 1, for detector positioning. Measurements over 400 MHz suffer from systematic noise and the 894 and 956 nm wavelengths have significant artifacts below 400 MHz also. These measurements, therefore, are not used in the semi-infinite analytic fits.
or in matrix form: where r d is the position of the detectors, ⌽ m refers to the measurements, ⌽ c are the calculated values, ⌽ s ϭ⌽ m Ϫ⌽ c , and J is the Jacobian. The Green's function satisfies the following adjoint problem: The equations are solved numerically utilizing a finite difference method. The tumor location and geometry are used to segment the inverse problem into two regions, tumor and background, over which the volume integrals in Eq. ͑3͒ are computed. Equation ͑4͒ is then solved for the absorption perturbations ⌬ a o ͑background͒ and ⌬ a t ͑tumor͒ and for the diffusion perturbations ⌬Do ͑background͒ and ⌬Dt ͑tumor͒. The diffusion perturbations are easily transformed into scattering perturbations using the following equation: Two assumptions were necessary to attempt the segmentation. First the different tumor information from the ultrasound images were averaged together to give a single estimate of the size and location. Second, it was assumed that the tumor was symmetric; this assumption removed any dependence on the relative position of the sources and detectors to the tumor. Additionally, it reduced the number of forward and adjoint problems, five source-detector positions became three independent positions along a given direction, see Figure 2.
The algorithm is depicted in Figure 5. The initial estimates for the optical properties are based on a semi-infinite homogeneous analytic fit. Each box containing ⌽ or G represents a three-dimensional finite-difference computation for those variables ͓i.e., a solution to Eq. ͑1͒ or ͑5͒, respectively͔. These computations for each source/detector position and for each frequency are done in parallel. The building of the Jacobian and its solution are done on a single processor. The solution of Eq. ͑4͒ is found using simultaneous iterative reconstruction technique ͑SIRT͒. The algorithm iterates until convergence is achieved.
The size of the domain was approximated to be 8 cm ϫ8 cmϫ4 cm, with a grid size resolution of 0.125 cm. The number of forward problem solutions for horizontal or vertical simulations was 18 (6 frequenciesϫ3 source positions), equivalent to the number of adjoint problem solutions. These simulations took approximately 3 min/iteration on 19 processors. The number of forward problem solutions for both directions was 36 (6 frequenciesϫ6 source positions), equivalent to the number of adjoint problem solutions. These simulations took 6 min/iteration on 19 processors.
The source strength, an unknown experimental quantity, is removed from the analysis by normalizing the data with a single frequency measurement ͓i.e., ⌽ m (r, i ) ϭ⌽ m (r, i )/⌽ m (r, o ), where o i ͔. A series of numerical tests were conducted on this segmented reconstruction approach using the experimental geometry and we found that six frequencies ͑including o ͒ were adequate to yield good leastsquares fits for a single source-detector pair.
The semi-infinite homogeneous analytic fits are done by iteratively fitting to the semi-infinite analytic solution where r 1 ϭͱ͑xϪx s ͒ 2 ϩ͑yϪy s ͒ 2 ϩ͑zϪz s ͒ 2 , , ͑ x s ,y s ,z s ͒ is the source location and z b is defined as 1/␣. The fitting was done by using a Taylor series expansion of ⌽(r,) with respect to the optical properties, that is, where the derivatives are easily determined from Eq. ͑6͒. The same six frequencies are used in the segmented reconstruction. Additionally, because we are fitting to a homogeneous solution here, the measurements for the different positions are averaged together as they all share the same source-detector separation and are not supplying additional positional information to the semi-infinite solution.

Semi-infinite Analytic
The results from the homogeneous semi-infinite analytic fits for the normal breast are listed in Table 2 and for the breast  with the lesion in Table 3. The v 2 values validate the goodness of fit since the values are 1.5 or less. The number of degrees of freedom ͑DOF͒ is the number of source-detector pairs (10 or 5)ϫnumber of frequencies ͑74͒-the number of parameters ͑two for semi-infinite and four for segmented re-construction͒. Generally, for testing goodness of fit one would want the values to lie between 1.5 and 0.5, when the values are less than 0.5 it is generally believed that the noise was overestimated.
In Figure 6, the homogeneous semi-infinite analytic optical properties for both breasts are plotted versus wavelength. The absorption coefficient shows an increase of approximately 48% from the normal breast, consistent with the presence of the tumor. The scattering coefficient exhibits a decrease of ϳ11% for the horizontal measurements and an increase of ϳ11% for the vertical measurements from the normal breast.
Using both sets of measurements, the average difference between the breasts is less than 1% for the scattering coefficient. These semi-infinite analytic results provide a simple and fast way of determining the presence of a tumor, however the optical properties are clearly insufficient for further diagnosis of the tumor. Therefore, we have advanced the reconstruction by assuming the presence of a tumor with the geometry provided by the ultrasound images.

Segmented Reconstruction
The segmented reconstruction parameters are listed in Table 4 along with the parameters for a series of sensitivity studies. The optimal estimate of all the parameters is the base case. The results of the segmented reconstruction fit for the base case are listed in Table 5. For all four wavelengths, the tumor properties had increased absorption, on average 3.4ϫ the background, and decreased scattering, on average 0.41ϫ the background. The (2) are again very good, in fact the segmented reconstruction values are improved compared to those  Table 2) and the breast with lesion (solid triangles, see Table 3). Table 4 Simulation parameters for the base case and the sensitivity studies. Direction is the set of measurements used for the given simulation, a is the y-axis length of the tumor, b is the x-axis length of the tumor, c is the z-axis length of the tumor, and zc is the center of the tumor below the skin surface. n in /n out is the index mismatch between the tissue (n in ) and the air (n out ). The base case is the optimal choice of the listed parameters. The sensitivity studies focus on directional sensitivity of the measurements (horizontal and vertical), size of the tumor (bigger and smaller), and the index mismatch of the tissue-air interface (greater and less).  Overall, the optical properties of the tumor show dramatic contrast with both normal tissue and tumor-breast background. The increase in a is due to hemoglobin absorption; the principal NIR-absorbing component of highly vascular tumors. Previous in vivo studies suggest that tumors can display two to fivefold higher blood volume fractions than uninvolved breast tissue. [49][50][51] Our segmentation scheme reveals substantially higher tumor/background contrast than observed using a homogeneous semi-infinite analytical model that averages properties over a large volume. In addition, the reduced scattering ( s Ј) values in the tumor were, on average, about half those of normal tissue. This feature suggests the core of the tumor has a low cellular and/or extracellular matrix density. Interestingly, since fluid content also provides contrast for ultrasound images, combining optical and ultrasound observations indicates the tumor core is likely to be a necrotic, bloodfilled region dominated by particles that have low scattering cross sections and/or low density ͑compared to normal, welldifferentiated breast tissue͒. This view coincides well with histopathology data showing the tumor to be poorly differentiated and malignant.

Experiment
Further diagnostic insight is provided by calculating the physiological properties of normal breast, tumor, and tumor breast outside the tumor region. Assuming the principal absorbers are oxy-and deoxyhemoglobin ͑HbOx and Hb, re-spectively͒, least squares fits of calculated a values ͑from Tables 2 and 5 for normal and tumor breast, respectively͒ to molecular extinction coefficients for each component at the four measured wavelengths 1 can be used to determine ͓HbOx͔, ͓Hb͔, and percentage hemoglobin saturation (SOx ϭ100ϫ͓HbOx͔/͓Hb tot ͔; and ͓Hb tot ͔ϭ͓Hb͔ϩ͓HbOx͔).
These results, summarized in Figure 7, show clear differences between tumor and normal tissue. Most dramatic is the approximately fourfold increase in total hemoglobin content at the tumor ͑67 M͒ vs normal tissue ͑16 M͒. Hemoglobin contrast is reduced to a factor of 2.6 when the tumor site and surrounding tumor-containing breast tissue ͑25.5 M͒ are compared. SOx values are lower at the tumor site ͑63%͒ vs normal ͑68%͒ and surrounding tumor-containing breast ͑73%͒. Differences are likely due to the oxygen extraction demands of rapidly proliferating, metabolically active tumor cells. The reduced saturation value at the tumor is consistent with the measured elevation in tumor hemoglobin, since both blood and oxygen are required to sustain tumor growth. Others have measured similar elevated tumor hemoglobin concentration and low SOx values noninvasively with photon migration techniques. 48,49 Interestingly, both total hemoglobin and SOx values are slightly elevated in the tumor-containing surrounding breast versus the contra-lateral normal side. This suggests that physiological changes occur beyond the ultrasound-designated tumor margin that are detectable with light. For example, a high blood flow, well-vascularized region could extend beyond the ultrasound-defined tumor dimension. This observation is consistent with the notion of a hypoxic, necrotic tumor core surrounded by a wellvascularized, normoxic cortex that provides the leading edge for growth. Table 4 lists the parameters for a series of sensitivity studies. We examined the sensitivity of the optical properties to measurement direction, tumor size, and boundary condition. Measurement direction had two options: horizontal ͑along the axial plane͒ or vertical ͑along the sagittal plane͒. Tumor size was enlarged by 10% along each major axis or was decreased by 10% along each major axis. The boundary condition was either based on an index mismatch of 1.333 or 1.40.

Measurement direction
These results tested the sensitivity of the calculated optical properties to the direction that the measurements were taken. Figure 8͑a͒ lists optical property and 2 values for the four parameter fits. Some of the 2 values are increased relative to the semi-infinite fit. This is caused by the symmetry assumption and is minimized when using both measurement sets together. The tumor absorption was on average 4.1ϫ the background for the horizontal and 2.3ϫ the background for the vertical. The tumor scattering for the horizontal was on average 0.3ϫ the background and 0.55ϫ for the vertical. The base case values lie directly inbetween these values illustrating the impact of minimizing the error between the two directions.
The sensitivity can best be depicted by a bar graph showing the average percentage change from the base case for each of the four parameters, see Figure 8͑b͒. The background properties decreased from the base case for the horizontal measurements ϳ10% and increased for the vertical ϳ15%. The tumor properties showed more sensitivity to the vertical direction, especially the scattering ͑ϳ45%͒. Finally, the base case optical properties were more similar to the horizontal optical properties, indicating that the base case segmented reconstruction fits were more sensitive to the horizontal measurements than the vertical. This is consistent with the vertical measure- ments being more sensitive to the symmetry assumption for the tumor geometry. This is clear since the vertical measurement set is aligned with the major axis of the ellipse. Therefore the vertical measurement set will be more sensitive to the tumor optical properties than the horizontal measurement set.

Tumor size
This study observed the impact of changing the size of the tumor on the optical properties. Figure 9͑a͒ lists the results from the segmented reconstruction fit. The 2 values are smaller than the base case for the larger tumor, implying that the optical tumor margins might in fact be larger than was estimated from the ultrasound. The tumor absorption was about 3.0ϫ the background for the larger size and about 3.75ϫ for the smaller size. The tumor scattering was about 0.46ϫ the background for the larger size and about 0.39ϫ for the smaller size. Figure 9͑b͒ shows the average over the wavelengths for the percentage change from the base case for the tumor size sensitivity. Overall, the size sensitivity is quite reduced from the directional sensitivity. The background properties did not change significantly from the base case. However, the tumor properties showed greater sensitivity; particularly the absorption increasing or decreasing when size decreased and increased, respectively. The volume change ͑⌬VϭVЈϪV, where VЈ is the new volume and V is the base case volume͒ of the tumor is directly related to the change in ⌬ a ( a t Ϫ a o) as follows: ⌬ a Јϭ⌬ a /(1ϩ⌬V/2V). ⌬ s Ј also changed with volume; increasing when the volume increased ϳ6% and decreasing when the volume decreased ϳ3%, however there was no clear functional relationship between the two parameters.

Index mismatch
This last study focused on changing the index mismatch at the tissue-air interface, essentially testing the importance of the boundary condition assumption. Figure 10͑a͒ lists the results from the segmented reconstruction fit. The 2 values are very similar for all cases of the index mismatch parameter, including the base case. The tumor absorption was on average 3.4ϫ the background for both mismatch indices. The tumor scatter-  Table 4 for parameters. (b) Average percentage change of the segmented reconstruction optical properties over the four optical wavelengths from the base case to the horizontal measurement set simulation (left four bars) and the vertical measurement set simulation (right four bars). The horizontal measurement set simulations show less change from the base case than the vertical set measurement simulations. This is consistent with the horizontal measurement set being less sensitive to the symmetry assumption of the tumor than the vertical measurement set. Fig. 9 (a) Tumor size sensitivity segmented reconstruction results. Bigger refers to an increase in tumor size and smaller refers to a decrease in tumor size, see Table 4 for parameters. (b) Average percentage change of the segmented reconstruction optical properties over the four optical wavelengths from the base case to the bigger tumor size simulation (left four bars) and the smaller tumor size simulation (right four bars). The tumor optical properties had the most sensitivity, specifically its absorption coefficient. As the tumor increased its absorption decreased and its scattering increased, when the tumor decreased the opposite occurred. Additionally, the v 2 values for the bigger tumor size were slightly less than the base case values. This implies that the tumor was optically larger than the ultrasound size.
ing was on average 0.4ϫ the background for both mismatch indices. These factors are very similar to the base case factors. Figure 10͑b͒ shows the average percentage change from the base case for the index mismatch simulations ͑over the four wavelengths͒. The sensitivity of the optical properties was very small and all the properties were affected ϳ1.5% or less. This indicates that this assumption did not affect our solution.

Conclusions
Semi-infinite homogeneous analytic fits are very useful for providing a gross determination of tumor optical properties. However, significant physiological information in tumors and surrounding tissues may be lost in this averaging procedure. Our use of ultrasound localization with diffuse optical mammography provides improved optical information about the tumor and background tissue. From this reconstruction, a sharp contrast in the optical properties was readily determined. A three to fourfold increase in the absorption coefficient and nearly 50% reduction in scattering coefficient, relative to background, were found. These values are consistent with expected properties of a highly vascularized tumor with a blood-filled, necrotic core. Physiological property calculations confirm this view, revealing fourfold greater tumor hemoglobin concentration than normal breast ͑67 vs 16 M͒ and low tumor SOx values of 63% ͑vs 73% and 68% in the region surrounding the tumor and the opposite normal tissue, respectively͒. Comparison of the semi-infinite results from the normal breast to the background properties of the lesioncontaining breast yields further information about tissues surrounding the tumor. They suggest that alterations in vascular density and tissue inflammatory response occur beyond the ultrasound-defined tumor margins.
A series of sensitivity studies were conducted to ascertain the relative importance of some of our basic assumptions. A test of measurement direction revealed that the assumption of tumor symmetry in shape and orientation was quite sensitive, but its impact was minimized when using both horizontal and vertical measurement sets together. In a test of the tumor size estimate, an increase in tumor size resulted in better model fits. This suggests that the tumor may be larger when defined by light than by ultrasound.
Although our analysis is reported only for a single subject, frequency domain-DOT images obtained from this hand-held probe reveal new tumor diagnostic criteria and substantially enhanced contrast in both absorption and scattering. The increase in measured absorption and decrease in scattering at the tumor versus surrounding tissue further underscores a key practical benefit to our quantitative approach. Ultimately, the combination of hand-held ultrasound and optical probes may allow rapid, functional characterization of subcutaneous inhomogeneities. We expect this information will be particularly useful in screening pre-and perimenopausal women with radiographically dense breast tissue, where distinguishing between malignant and benign lesions and understanding effects of therapies and disease progression can be highly problematic. Fig. 10 (a) Index mismatch sensitivity segmented reconstruction results. 1.4 refers to the index mismatch at the tissue-air interface to be 1.4 and 1.333 refers to the index mismatch at the tissue-air interface to be 1.333. (b) Average percentage change of the segmented reconstruction optical properties over the four optical wavelengths from the base case to the 1.40 tissue-air interface index mismatch simulation (left four bars) and the 1.333 tissue-air interface index mismatch simulation (right four bars). Overall the index mismatch did not impact our results, suggesting that the optical properties are not very sensitive to this parameter. Additionally, the v 2 values were similar for all cases of the index mismatch parameter supporting the finding that this parameter did not affect our results.