Breast cancer is the leading cause of cancer death forwomen. Optical imaging of the breast can providespectroscopic information on breast tissue and can-cers not obtainable from conventional x-ray mam-mography. Absorption of near-infrared light bybreast tissue is caused mainly by oxyhemoglobin anddeoxyhemoglobin, water, and lipids. Optical mam-mography allows one to determine hemoglobin con-centration and blood oxygen saturation of breasttumors from absorption coefficients measured at se-lected wavelengths.1 Thus optical mammographymight supplement existing breast imaging tech-niques by characterizing lesions in suspicious cases,resulting in a reduction of the number of unnecessarybiopsies. Further clinical applications may includethe monitoring of therapeutic effects of neoadjuvantchemotherapy and, eventually, risk-group screening.
D. Grosenick �[email protected]�, H. Wabnitz, R. Mac-donald, and H. Rinneberg are with the Physikalisch-TechnischeBundesanstalt, Abbestrasse 2-12, 10587 Berlin, Germany; K. T.Moesta, J. Mucke, C. Stroszczynski, and P. M. Schlag are with theRobert-Rossle-Klinik, Charite, Humboldt-Universitat zu Berlin,Lindenberger Weg 80, 13125 Berlin, Germany.
Received 1 September 2002; revised manuscript received 6 No-vember 2002.
One focus of recent work on optical mammographyis spectroscopic investigation of breast tissue in vivoto study the physiology of the breast, the dependenceof optical properties on hormonal status, and age-dependent changes. These investigations use time-domain,2 frequency-domain,3 or cw4 experimentalmethods at a large number of wavelengths and allowone to determine tissue composition reliably. Onthe other hand, such measurements were restrictedto a small number of selected locations; i.e., mam-mograms cannot be readily obtained in this way.Tromberg et al.1 have shown that near-infraredspectroscopy allows one to characterize known le-sions situated close to the surface of the breast byusing a handheld probe.
The development of imaging techniques representsanother direction of recent work on optical mammog-raphy. The advantage of recording an image of theentire breast is paid for by losses in spectral informa-tion. On the other hand, this approach reveals thespatial distribution of the optical properties of thewhole breast. The first imaging systems were basedon the frequency-domain approach with a single mod-ulation frequency.5–7 However, it is difficult to sep-arate absorption from scattering reliably by thisapproach. Recent developments of time-correlatedsingle photon-counting techniques enabled us tobuild the first time-domain scanning mammographand to confirm the feasibility of time-domain optical
mammography for selected cases.8 At present, ef-forts are underway to increase the number of wave-lengths employed in laser-pulse scanningmammographs to increase spectral information con-tained in optical mammograms.9,10 Apart fromscanning mammographs, several groups are pursu-ing tomographic techniques to obtain three-dimensional images of the breast. A cwtomographic instrument was built at the Philips com-pany and was successfully applied to case studies.11
However, the method used did not allow scattering tobe separated from absorption. Currently, tomo-graphic frequency-domain and time-domain instru-ments are being tested in vivo.12,13 Anotherapproach combines contrast-agent-enhanced diffuseoptical tomography with magnetic resonance imag-ing of the breast to use a priori morphological infor-mation for analysis of optical data.14 Recently a fastoptical imager was developed that allows one to de-tect physiological changes on a subsecond timescale.15
It is our aim in our current work to assess thepotential of scanning laser-pulse mammography andto understand the origin of contrast in optical mam-mograms, in particular between cancers and healthytissue or benign lesions. To this end, a clinical trialwas started. Here we report initial results obtainedfor the first group of 35 patients suspected to havebreast cancer. Optical mammograms were derivedfrom photon counts in selected time windows of mea-sured distributions of times of flight of transmittedphotons as well as from optical properties estimatedby means of diffusion theory. Optical mammogramsare compared retrospectively with x-ray and mag-netic resonance mammograms. On the basis of ab-sorption coefficients measured at two opticalwavelengths, tumors are characterized by hemoglo-bin concentration and blood oxygen saturation.Furthermore, tumor scattering and absorption coef-ficients are compared with those of surroundinghealthy tissue �bulk values�, and similarities of tumoroptical properties with glandular tissue are empha-sized. In addition, we discuss the limits associatedwith the dual-wavelength approach and present cor-relation plots �scatter plots� as a tool to improve thedetectability of tumors.
2. Experiment
A. Laser-Pulse Mammograph
We used a laser-pulse scanning mammograph8 thatmeasures distributions of times of flight of scatteredphotons through the female breast at a large numberof scan positions. The breast is gently compressedbetween two parallel glass plates. The mammo-graph was equipped with two picosecond laser diodes�PDL-800, PicoQuant, Berlin�, and optical mammo-grams were recorded simultaneously at 670 and 785nm �see Fig. 1�. The average output power of eachlaser was adjusted to 2 mW at a repetition rate of 40MHz; the pulse durations were 100 ps �670 nm� and400 ps �785 nm�. Both pulse trains were multi-
plexed in time; transmitted photons were collected bya 4-mm-diameter fiber bundle �numerical aperture0.54, Schott Mainz� and detected by a fast photomul-tiplier with a transit time spread of �110 ps �H6279,Hamamatsu Photonics�. The source fiber and detec-tor fiber bundle were arranged face to face andscanned in tandem. The photomultiplier signal wasprocessed with a high-throughput time-correlatedsingle-photon counting system �SPC-300, Becker &Hickl, Berlin�. Photon count rates of up to 1 MHzallowed us to collect data of sufficient statistical ac-curacy within 100 ms at each scan position. At astep size of 2.5 mm, typically 1000–2000 scan posi-tions were sampled, and optical mammograms wererecorded along craniocaudal and mediolateral projec-tions within 3–5 min each. When the response func-tion of the mammograph was measured, care wastaken to completely fill the aperture of the receivingfiber bundle by placing a thin diffuser �sheet of whitepaper� in front of the receiving fiber bundle.
B. Analysis of Time Windows
In optical mammograms contrast between differenttypes of tissue is based on differences in their absorp-tion and scattering coefficients. When measure-ments are taken in the transmission geometry,absorbing inhomogeneities essentially cause an over-all decrease of the amplitude of the distribution oftimes of flight, and scattering inhomogeneitiesmainly influence photons with rather short trajecto-ries.16,17 If photon counts are analyzed in a late timewindow, absorbers can be imaged directly, whereasphoton counts in an early time window are sensitiveto changes in both absorption and, in particular, scat-tering. For time-window analysis8 of the distribu-tion N�x, y, t� of times of flight measured at position�x, y�, 10 consecutive time windows each containingthe same number of photon counts were derived froman average distribution Nave�t� of times of flight. Togenerate Nave�t�, we determined the median of times
Fig. 1. Schematic diagram of laser-pulse scanning mammograph.
of flight from N�x, y, t� at all scan positions of a givenmammogram and averaged over those distributionsN�x, y, t� with a mean time of flight larger than themedian value. In this way we excluded distribu-tions measured close to the edges of the breast, wherethe mean time of flight is reduced because of a lowerthickness. Such analyses were carried out at eachwavelength separately. We selected the eighth timewindow as the late time window, since it had beenobserved previously that optical mammograms basedon this time window are rather insensitive towardedge effects.8 After normalizing photon counts inthis time window with respect to that of the averagedistribution Nave�t�, we obtained the quantity N8�x,y�. On the other hand, normalized photon countsN1�x, y� of the first time window and normalized totalintegrals Ntot�x, y� were derived from distributionsNcorr �x, y, t� corrected for edge effects. To this end,the measured distributions N�x, y, t� were re scaled toconstant breast thickness by application of the algo-rithms described in Ref. 8.
C. Determination of Tissue Optical Properties
To derive optical mammograms displaying �effective�absorption and reduced scattering coefficients of thetissue, we used the diffusion theory of photon trans-port. To this end the breast was modeled as a semi-infinite slab of constant thickness dgap to account forthe finite size of the breast �see Fig. 2�a��. At eachscan position the tissue was assumed to be homoge-neous. Consequently this approach yields absorp-tion and scattering coefficients averaged along theline of sight between source and detector fiber or,more precisely, averaged over the particular volumeof the tissue sampled by the photons. The analytical
solution for the time-dependent photon flux densityrelating to the homogeneous semi-infinite slab wasderived from the solution for the infinite slab18,19 byintroduction of a set of lateral mirror light sourcesleading to the additional factor 1 � exp � � �a � ze�
2��Dct��. Extrapolated boundary conditions were used,with ze denoting the location of the extrapolatedboundary.20 It follows that the distance a�x, y� be-tween the scan position �x, y� and the lateral boundaryhas to be known. The distance a�x, y� represents theperpendicular from the scan position �x, y� to the cor-responding plane parallel to z and tangential to thebreast boundary �Fig. 2�b��. The quantity a�x, y� wasnot readily available from the experiment, since thescanner reversed its direction when the count rate ex-ceeded a preselected value. In this way the edges ofthe breast were never reached or even passed by thescanning transmitting and receiving fibers. There-fore we derived the distance a�x, y� from the �true�thickness d�x, y� of the breast, assuming the breast tohave an elliptically shaped radial cross section close toits edge �Fig. 2�b�� with the major axis being twice theminor axis �dgap�, yielding
a� x, y� � dgap�1 � �1 �d2� x, y�
dgap2 �1�2� . (1)
The thickness d�x, y� of the breast was estimatedfrom the mean time of flight, as discussed in Ref. 8.At those locations �x, y� where the tissue completelyfilled the gap between both glass plates �d�x, y� �dgap�, a�x, y� amounts to dgap, and the results of theanalysis essentially coincide with those for the infi-nite homogeneous slab. It should be noted that the�true� thickness d�x, y� enters the analysis onlythrough the determination of a�x, y�, and a constantbreast thickness dgap is used in the model.
To determine absorption and reduced scatteringcoefficients a �x, y� and s�x, y�, the model was fittedto measured distributions of times of flight. Beforethey were compared with experimental data, theoret-ical values were convolved with the measured instru-ment response function. As mentioned inSubsection 2.B, absorbing inhomogeneities embed-ded in an otherwise homogeneous medium essen-tially cause a decrease of the amplitude of thedistribution of times of flight, whereas scattering in-homogeneities also change the shape of the distribu-tion. When an absorbing inhomogeneity is treatedwithin the homogeneous model, a strong correlationis observed between a and the amplitude scalingfactor used in converting theoretical photon flux den-sity to measured photon counts. To suppress thiscorrelation we divided the fitting procedure into sev-eral consecutive steps.
First the analytical solution corresponding to thehomogeneous infinite slab was fitted to the averagedistribution of times of flight Nave �see Subsection2.B� with a, s, and the origin t0 of the time axisbeing free parameters. Before the �2 sum was cal-culated, the theoretical curve was scaled to have thesame integral as the measured distribution of times
Fig. 2. �a� Cross section of semi-infinite slab. �b� Idealized shapeof breast, used to derive distance a�x, y� from thickness d�x, y� �seeEq. �1��; a�x, y� is the perpendicular from the scan position �x, y� tothe corresponding plane parallel to z and tangential to the breastboundary.
of flight. From this step of the fitting procedure weobtained the average �bulk� optical properties a,0and s,0 of the breast, time zero t0, and the amplitudescaling factor A0. During the following steps t0 waskept fixed.
As the next step the analytical solution correspond-ing to the homogeneous semi-infinite slab was fittedto the experimental data at each scan position �x, y�,with the absorption coefficient a�x, y�, the reducedscattering coefficient s�x, y�, and the scaling factorA�x, y� being free parameters. The reduced scatter-ing coefficients s�x, y� obtained from these fits wereused to generate optical mammograms. However,spatial changes in absorption are essentially con-tained in the spatial variations of the scaling factorsA�x, y�. Therefore, to derive absorption coefficients,we performed a third fit with a�x, y� as the sole freeparameter by using s�x, y� obtained in the secondstep and setting A�x, y� � A0 at each scan position.The absorption coefficients obtained in this way wererather free of edge effects; i.e., photon losses throughthe sides of the compressed breast were sufficientlytaken into account by the semi-infinite slab geometry.In contrast, the decreasing thickness of the breastclose to its edges resulted in considerably decreasedreduced scattering coefficients. This observationcan be understood from the solution of the diffusionequation for a homogeneous slab. A change in slabthickness is compensated by a change in s whendistributions of times of flight are analyzed, whereasa remains unaffected. We found empirically thatthe reduced scattering coefficients s�x, y� essen-tially follow the thickness profile of the breast. Asan example, Fig. 3 shows the reduced scattering co-efficients s�x, y� as a function of the correspondingthickness d�x, y� of a tumor-bearing breast. Theopen symbols illustrate the result of a least-squaresfit to the leading edge of a Gaussian profile. Thisempirical relation was used to rescale the reducedscattering coefficients s�x, y� from thickness d�x, y�to dgap before optical mammograms were generated.Our empirical approach was found to give better re-
sults than using a semi-infinite homogeneous slab ofthickness d�x, y� when theoretical data were fitted todistributions of times of flight.
Absorption of breast tissue at the wavelengthsused in our mammograph ��1 � 670 nm, �2 � 785 nm�is determined mainly by oxyhemoglobin and deoxy-hemoglobin and by water, whereas the contributionof lipids can be neglected. To derive the concentra-tions cHbO2
and cHb of oxyhemoglobin and deoxyhe-moglobin as well as the corresponding blood oxygensaturation in tissue Y � cHbOH2
�ctHb with total hemo-globin concentration ctHb � cHbO2
� cHb, we used thefollowing equation:
a��i� � �cHbεHb��i� � cHbO2εHbO2
��i��ln 10
� H2 Oa,H2 O��i�,
i � 1, 2 . (2)
Because mammograms were taken at only two wave-lengths, the volume fraction H2O of water was as-sumed to be 30% and independent of position.Although these assumptions represent an oversim-plification and water content of breast tissue dependson many factors, a value of 30% seems to be reason-able.21,22 The extinction coefficients εHb��i� andεHbO2
��i� were taken from Ref. 23, and the absorptionof water from Ref. 24.
3. Clinical Protocol
The mammograph was installed in a clinical environ-ment; measurements on patients were performed ac-cording to the approval of the local ethics committee,and informed consent was obtained from each pa-tient. In a first trial phase we investigated a groupof 35 patients with suspect lesions of the breast lead-ing to histological assessment. The first 7 patientswere examined at 785 nm only; the remaining 28patients were examined at both wavelengths. Opti-cal mammograms were taken of both breasts incraniocaudal and mediolateral projections. In onecase, only an oblique projection was recorded becausethe suspect region was close to the axilla and coulddefinitely not be accessed by the laser radiation byuse of our standard projection directions. All pa-tients underwent x-ray mammography and, in themajority of cases, magnetic resonance �MR� mam-mography.
It is our aim in this study to understand the originof contrast in optical mammograms by comparingthem with x-ray and MR mammograms and with theresults of pathohistology. To this end, we derivedoptical mammograms based on early and late timewindows �Subsection 4.A� as well as optical mammo-grams displaying effective absorption and reducedscattering coefficients �Subsection 4.B�. From effec-tive absorption coefficients, hemoglobin concentra-tion and blood oxygen saturation were estimated.In addition, optical mammograms of the unsuspi-cious contralateral breast were recorded as a refer-ence.
Fig. 3. Reduced scattering coefficients s�x, y� versus thicknessd�x, y� for all pixels �solid squares� of a mammogram �patient 9, leftbreast, mediolateral, 670 nm� and corresponding fit to leading edgeof a Gaussian pulse shape �open circles�.
For each patient investigated, we generated opticalmammograms by plotting normalized reciprocal pho-ton counts 1�N1, 1�N8, and 1�Ntot versus scan posi-tion �x, y�. These images were compared with thecorresponding craniocaudal and mediolateral x-raymammograms, and, if available, with MR mammo-grams. Comparison was performed qualitatively byvisual inspection of the images based on contrast andlocation of the lesions. In 3 of the 35 cases a com-parison was not possible for technical reasons �1 in-strumental failure and 2 patients not submitted tohistological assessment�. Among the remaining 32cases standard clinical examination and histopathol-ogy showed that 26 patients had developed breastcancer, whereas in 6 cases there was no carcinoma
present. In 14 of the 26 cases, cancers could be de-tected in optical mammograms in both projections;for 3 additional patients cancers were found in oneprojection only, and optical mammograms of the re-maining 9 patients did not reveal the tumor at all. Atumor was considered to be visible in optical mam-mograms provided an area of noticeably altered �low-er� transmittance was present that was compatible insize and location with x-ray and MR mammogramsand with the results of histopathology.
In Table 1 all 14 tumors are listed that were visiblein both projections. Patient 1 is included in thistable, although optical mammograms were recordedin craniocaudal projection only. Generally, tumortype and size were taken from histology after sur-gery. Quantitative values for tumor contrast C weredetermined according to C � �N�tumor�-N�bulk���N�bulk� with N denoting N8 or N1 and N�tumor�
Table 1. Patients with Tumor Visible in Optical Mammograms �Both Projections�
Case AgeTumorTypea
TumorSize Proj.b
N8 N1
Other Lesions or Tissueswith High Contrast inOptical Mammograms
�1 �2 �1 �2
Cc Vd C V C V C V
1 43 IDC 2.5 cm cc n.a. n.a. �0.53 �� n.a. n.a. �0.51 �� Blood vessels
aIDC, invasive ductal carcinoma; ILC, invasive lobulary carcinoma; ITLC, invasive tubololobulary carcinoma.bProjections: cc, craniocaudal; ml, mediolateral.cContrast score, defined as C � �N�tumor�-N�bulk���N�bulk� with N denoting N8 or N1.dVisibility score of tumor, classified according to �, not visible; ���, weakly visible; �, clearly visible, worse than other lesions or
structures; ��, clearly visible, equal to other lesions or structures; ���, dominantly visible ��1 � 670 nm, �2 � 785 nm�; n.a., notapplicable.
taken as average over nine pixels at the location ofthe tumor. Contrast defined in this way is a mea-sure of the visibility of the tumor in those cases onlywhen the mammogram has a homogeneous appear-ance apart from the tumor. However, this is nottrue for mammograms with inhomogeneities otherthan the tumor. Therefore we introduced a visibilityscore based on visual inspection of the optical mam-mograms. This score ranges from “tumor not visi-ble” to “tumor dominantly visible” �see footnote ofTable 1�. As can be seen from the score, all tumorswere visible in mammograms based on reciprocalnormalized photon counts N8, except that for patient22. In each case N8 was reduced at the location ofthe tumor. This observation is explained by an in-creased absorption of the tumor tissue because ofincreased vascularization.25 In the majority of casescontrast was found to be larger at 670 nm than at 785nm. In one case �12, craniocaudal view� the tumorwas visible at the shorter but not at the infraredwavelength. It is well known that edge effects canbe effectively suppressed by use of ratios of corre-sponding optical mammograms recorded simulta-neously at two wavelengths.6 However, weobserved that contrast between tumor and surround-ing tissue was often decreased and washed out inratio images compared with optical mammogramsbased on a single wavelength, in particular in medio-lateral projections.
In one case �22� the tumor was visible only in op-tical mammograms based on the first time window�N1�. Either this tumor was associated with achange in scattering but not in absorption, or theoverlying tissue cancelled out changes in absorption.In two other cases �9 and 24� N1 mammograms ex-hibited the tumor at a higher contrast than did N8mammograms. This observation can be explainedby an increase in the scattering coefficient of thesetumors with respect to the surrounding tissue. Aslisted in Table 1, further inhomogeneities were visi-ble, such as blood vessels, mammary gland, the nip-ple, or mastopathies, each resulting in reducedtransmittance. In one case a cyst was observed,leading to increased transmittance because of re-duced scattering.
In the following, three cases listed in Table 1 arediscussed in more detail: �i� a tumor embedded inmore or less homogeneous tissue �9�, �ii� a tumorembedded in highly inhomogeneous tissue �12�, and�iii� a cyst �5�. Figure 4 shows optical mammogramsof both breasts of patient 9 based on reciprocal nor-malized photon counts 1�N8 at 670 nm. This pa-tient had a large invasive ductal carcinoma in her leftbreast. In the craniocaudal view the tumor isclearly visible at �x, y� � ��2 cm, 2.5 cm� and appearsas a region of reduced transmittance �Fig. 4�a��.There is another region of reduced transmittance inthe upper right part of Fig. 4�a�, representing thenipple. In addition, a superficial blood vessel can beseen as a vertical narrow line. The tumor is alsoclearly visible in the mediolateral view at �x, y� � �0.5cm, �3.75 cm� �Fig. 4�c��. Transmittance is slightly
reduced in the lower part of the breast compared withthe upper part. This is probably caused by themammary gland; in the upper part, fatty tissue dom-inates. A similar gradient can be observed in themediolateral view of the right �healthy� breast �Fig.4�d��. In the craniocaudal view of the right breast�Fig. 4�b�� a superficial blood vessel runs from top tobottom on the left-hand side. Images based on thefirst time window �N1� show the tumor at slightlyhigher contrast but do not reveal additional lesions.
In Fig. 5 optical mammograms of patient 12 areshown; they are based on reciprocal normalized pho-ton counts 1�N8 at 670 nm and compared with MR
Fig. 4. Optical mammograms of patient 9 based on reciprocalnormalized photon counts 1�N8�x, y� at 670 nm. �a� Left breast,craniocaudal, with tumor centered at �x, y� � ��2 cm, 2.5 cm�; �b�right breast, craniocaudal; �c� left breast, mediolateral, with tumorcentered at �x, y� � �0.5 cm, �3.75 cm�; �d� right breast, mediolat-eral.
mammograms recorded without and with contrastagent. This patient had an invasive ductal carci-noma in her left breast. In the optical mammogram�craniocaudal view, Fig. 5�a�� of this breast the cen-tral part ��2 cm, 2.5 cm� and the lower left part ��5cm, 0 cm� close to the chest wall appear to be stronglyabsorbing. The MR mammogram displayed in Fig.5�e� was recorded by a T2-weighted spin echo se-quence without contrast agent and represents atransversal plane containing the tumor, which is in-dicated by the arrows. It should be noted that theMR image is mirrored with respect to the standardcraniocaudal projections of x-ray and optical mam-mography. Fatty tissue appears bright in this im-age and glandular tissue dark. The subtractionimage �Fig. 5�f �� after intravenous injection of Gd-DTPA �gadolinium-diethylene triamine pentaaceticacid� shows the tumor image to be enhanced. Theinsert in Fig. 5�f � displays the signal kinetics derivedfrom the tumor area, with a typical plateau indicativeof malignancy. A comparison of Figs. 5�a� and 5�e�suggests that the lesion in the optical mammogram
close to the chest wall is the tumor, whereas thesecond, centrally located inhomogeneity is attributedto glandular tissue. The latter inhomogeneityshows strongly increased contrast in the opticalmammogram based on N1 and therefore exhibits bothincreased absorption as well as increased scatteringcompared with the surrounding tissue. The rightpart of this breast �Fig. 5�a�� is rather transparentbecause of fatty tissue, consistent with the MR mam-mogram �Fig. 5�e��. Apart from the tumor, thecraniocaudal view of the right �healthy� breast �Fig.5�b�� is more or less symmetrical to the optical mam-mogram of the left breast �Fig. 5�a��. The sameholds true for the MR image �Fig. 5�e��.
The optical mammograms in mediolateral projec-tion �Figs. 5�c�, 5�d�� reveal a reduced transmittanceof the lower parts of both breasts that is due to glan-dular tissue. The tumor is observed in the medio-lateral projection �Fig. 5�c�� at �x, y� � �0.25 cm, �3cm� and is associated with reduced transmittance.The contrast between tumor and surrounding tissueis comparatively poor at 785 nm. In particular, at
Fig. 5. �a�–�d� Optical and �e�, �f � MR mammograms of patient 12. Optical mammograms display reciprocal normalized photon counts1�N8 �x, y� at 670 nm. �a� Left breast, craniocaudal, with tumor centered at �x, y� � ��5 cm, 0 cm�; �b� right breast, craniocaudal; �c� leftbreast, mediolateral, with tumor centered at �x, y� � �0.25 cm, �3 cm�; �d� right breast, mediolateral; �e� MR mammogram �transversal crosssection�, T2-weighted spin echo sequence, tumor in left breast marked by arrows; �f � subtraction image after intravenous injection ofGd-DTPA with tumor area enhanced. Insert, signal kinetics of tumor area with typical plateau indicative of malignancy.
this wavelength the tumor cannot be detected in thecraniocaudal optical mammogram �not shown� with-out prior knowledge. We explain this outcome byassuming a lower blood oxygen saturation in the tu-mor compared with the surrounding tissue; i.e., de-oxyhemoglobin contributes more strongly toabsorption by the tumor, resulting in an enhancedcontrast at the lower wavelength.
As an example, Fig. 6 displays mammograms of apatient �5� who carried a cyst of �3-cm diameter aswell as a tumor in her left breast. The tumor isclearly visible in the 1�N8 images and is located inthe craniocaudal projection �Fig. 6�a�� at �x, y� � ��3cm, 2.5 cm� and in the mediolateral view �Fig. 6�d�� at�x, y� � �3 cm, �4.5 cm�. Images displaying recipro-cal normalized photon counts 1�N1 of this breast�Figs. 6�b� and 6�e�� exhibit similar contrast betweentumor and surrounding tissue, indicating that thetumor is essentially an absorber. Furthermore, thecyst can be detected in Figs. 6�b� and 6�e� by its in-creased transmittance, which is due to a smallerreduced scattering coefficient. Although transmit-
tance of the cyst is larger by a factor of �5, contrastis only moderate, since in Figs. 6�b� and 6�e� recipro-cal values of N1 are plotted to highlight regions ofdecreased transmittance. When N1 values are plot-ted �Figs. 6�c� and 6�f ��, the cyst is conspicuouslyvisible whereas the tumor can hardly be detected.
Table 2 lists all tumors that were visible in only oneprojection. One of these tumors �patient 8� was sit-uated close to the chest wall and was most likelyoutside the area scanned in the craniocaudal projec-tion. In the two other cases �patients 21 and 23� thetumor was possibly masked by glandular tissue; i.e.,contrast between tumor and glandular tissue was toosmall for the tumors to be detected in the mediolat-eral projection.
Table 3 specifies the nine tumors that were missedaltogether in optical mammograms displaying �in-verse� photon counts with criteria of reduced trans-mittance in selected time windows. Furthermore,none of these tumors could be detected in mammo-grams based on effective absorption and reducedscattering coefficients. As is known from histopa-
Table 2. Patients with Tumor Visible in Optical Mammograms �One Projection Only�
Case Age Founda Tumor TypeTumor Size
�cm�Possible Reason for MissingTumor in Other Projection
8 ml Invasive tubulary carcinoma 1.4 Outside of scan area21 56 cc Invasive ductal carcinoma 1.5 Masked by glandular tissue23 47 cc Invasive ductal carcinoma 1.6 Masked by glandular tissue
aProjections: cc, craniocaudal; ml, mediolateral.
Fig. 6. �a�–�c� Craniocaudal and �d�–�f � mediolateral optical mammograms of left breast of patient 5 based on normalized photon countsat 785 nm. �a� Late time window, 1�N8�x, y�, tumor centered at �x, y� � ��3 cm, 2.5 cm�; �b� early time window, 1�N1 �x, y�; �c� N1 �x, y�,cyst centered at �x, y� � (�2.5 cm, 0 cm�; (d) 1�N8 �x, y�, tumor centered at �x, y� � (3 cm, �4.5 cm�; (e) 1�N1�x, y�; (f) N1�x, y�, cyst centeredat �x, y� � �0.5 cm, �0.5 cm�.
thology, the tumors were of sufficient �moderate tolarge� size to be detected by optical mammography,provided their scattering and absorption propertiesdiffered sufficiently from those of the surroundingtissue. In three cases �patients 4, 13, and 18� wepresume that the tumors were masked by dense glan-dular tissue. In one case �patient 7� the tumor wassituated close to the axilla and in two cases �patients10 and 13� close to the chest wall and therefore wasmost likely outside the scan area. One patient �18�had a rare tumor �lymphoma�, and another patient�33� a ductal carcinoma in situ. This tumor was notseen in the optical mammograms probably because ofmissing neovascularization. In the optical mammo-grams of the remaining two patients �26 and 28� weobserved several areas of reduced transmittance,none of which could be correlated with the tumorsvisible in the x-ray mammograms.
For illustration, Fig. 7 displays x-ray and opticalmammograms of patient 26; the optical mammo-grams were based on reciprocal normalized photoncounts 1�N8 at 670 nm. The x-ray mammograms�Figs. 7�a�, 7�d�� show the tumor of diameter 1 cm�indicated by white arrows� to be located in the lowerinner quadrant of the right breast. There is verylittle absolute contrast in radiological density be-tween tumor and surrounding tissue, and the diag-nosis is based on fine morphological features�spiculated margins� of the tumor. From the loca-tion of the tumor in the x-ray mammograms we ex-pect it to appear in the optical mammogram atapproximately �x, y� � ��0.5 cm, 3 cm� in the cranio-caudal view �Fig. 7�b�� and at �x, y� � ��1.75 cm, �1cm� in the mediolateral view �Fig. 7�e��. However, atthese locations we did not observe any reduced trans-mittance in the optical mammograms at either wave-
Table 3. Patients with Tumor Missed in Optical Mammograms �Both Projections�
Case Age Tumor Type Tumor Size �cm� Possible Reason for Missing Tumor
4 43 Medullary carcinoma 1.7 Masked by glandular tissue7 63 Invasive ductal carcinoma 2.5 Too close to axilla
10 58 Invasive ductal carcinoma 1.6 Too close to chest wall13 48 Invasive ductal carcinoma 0.8 Masked by glandular tissue18 60 Lymphoma Masked by glandular tissue19 58 Invasive ductal carcinoma 1.1 Too close to chest wall26 49 Invasive ductal carcinoma 1.0 Unclear28 65 Invasive ductal carcinoma 1.6 Unclear33 60 Ductal carcinoma in situ 3 No neovascularization
Fig. 7. �a�, �d� X-ray mammograms and �b�, �c�, �e�, �f � optical mammograms of patient 26 based on reciprocal normalized photon counts1�N8�x, y� at 670 nm. The tumor is located in the right breast. �a� Right breast craniocaudal, position of tumor indicated by arrows; �b�right breast craniocaudal; �c� left breast craniocaudal; �d� right breast mediolateral, position of tumor indicated by arrows; �e� right breastmediolateral; �f � left breast mediolateral.
length. On the other hand, the opticalmammograms �Figs. 7�b�, 7�c�, 7�e�, 7�f �� of bothbreasts exhibit reduced transmittance at severalother locations. From histological examination ofsurgical specimens of the tumor-bearing right breastit is known that the lesion at �x, y� � ��3 cm, 1 cm��mediolateral� and �x, y� � �2 cm, 4 cm� �craniocaudal�is a fibrocystic mastopathy. At the shorter wave-length the fibrocystic mastopathy exhibits highercontrast than at the longer wavelength. For thehealthy left breast the cause for the reduced trans-mittance close to the nipple �craniocaudal view� andin the lower part �mediolateral view� is not known.
B. Optical Properties of Breast Tissue and Tumors
To derive optical properties of different types ofbreast tissue and of tumors, we analyzed distribu-tions of times of flight of photons by using the homo-geneous model described in Subsection 2.C. Webegin our discussion with bulk optical properties a,0and s,0 obtained from the first step of our fittingprocedure. In Fig. 8 the reduced scattering and theabsorption coefficients at 785 nm are plotted versusthose at 670 nm for each patient. Each data point isthe average of the values deduced from the cranio-caudal and the mediolateral projections. It is well
known that the reduced scattering coefficients ofbreast tissue depend on wavelength according to
s��� � a��b , (3)
approximately, on the basis of Mie scattering.2,26,27
For the ratio of reduced scattering coefficients at twowavelengths one obtains
s��2�
s��1�� ��2
�1��b
. (4)
The data shown in Fig. 8�a� suggest that the scatter-ing coefficients s,0�785 nm� depend linearly ons,0�670 nm�. This observation indicates that acommon scatter power b can be used as an approxi-mation for all patients. The solid line in Fig. 8�a�represents a linear fit of Eq. �4� to the data, yieldinga value of the scatter power b � 0.91 � 0.07 averagedover the patients investigated. Scatter power isknown to vary with the type of tissue. Cubeddu etal.2 reported values of scatter power between 0.9and 1.2 deduced from measurements at different po-sitions of the same breast. Cerussi et al.3 obtainedscatter power from spectroscopic investigations onindividual subjects ranging from �0.4 up to 1.6.These authors observed the scatter power to dependon body mass index and on the age of the women, bothaffecting the ratio of fatty to glandular tissue. Thevalue of b � 0.91 given above represents an averageover all patients and hence over different types oftissue. It falls within the ranges for the scatterpower reported in the literature.
The linear relationship between the average ab-sorption coefficients a,0�785 nm� and a,0�670 nm�that is evident from Fig. 8�b� can be easily under-stood. Considering two wavelengths, we obtainfrom Eq. �2�
a��2� � m�a��1� � H2Oa,H2O��1��
� H2Oa,H2O��2� , (5)
where the slope m,
m�Y� ��YεHbO2
��2� � �1 � Y�εHb��2��
�YεHbO2��1� � �1 � Y�εHb��1��
, (6)
depends on blood oxygen saturation Y only. In Fig.8�b� the solid line corresponds to a fit of Eq. �5� to thedata, excluding the four data points furthest to theright-hand side. These four data points correspondto measurements on two patients with conspicuoussuperficial blood vessels, strongly influencing the av-erage coefficients a,0���. The fit of Eq. �5� to thedata yields mean values for blood oxygen saturation�Y � �74 � 3�%� and for the volume fraction of water� H2O � �25 � 11�%� within the ranges expected.The latter result is consistent with the assumptionmade above for the volume fraction of water. On theother hand, the large uncertainty of H2O indicatesthat the water fraction may vary considerably frompatient to patient. We note in passing that the sec-ond term in the square brackets in Eq. �5� could be
Fig. 8. �a� Average reduced scattering coefficients �bulk values�s,0 and �b� absorption coefficients a,0 at 785 nm versus those at670 nm. Data refer to patients 7–35 �left and right breasts�;estimated error bars to �5% of bulk values.
neglected, since the absorption coefficient of water atthe shorter wavelength �a,H2O�670 nm� � 0.0043cm�1� is considerably smaller than the correspondingvalue at the longer wavelength �a,H2O�785 nm� �0.0252 cm�1�. Neglecting the second term, the valuefor blood oxygen saturation remains essentially thesame, and the water fraction drops slightly to 21%.
Table 4 lists the bulk optical properties averagedover all breasts that were investigated at both wave-lengths. In addition, the mean values of the totalhemoglobin concentration ctHb and of the blood oxy-gen saturation Y are given that were calculated foreach patient from a,0 �670 nm� and a,0 �785 nm� byuse of Eq. �2� assuming H2O � 30%. Also includedin Table 4 are the scatter power b, the results for the
blood oxygen saturation Y, and the water fraction H2O deduced from Figs. 8�a� and 8�b�, respectively.Blood oxygen saturations obtained by both methodsagree within error limits, and the water fraction de-duced from Fig. 8�b� is consistent with the assumedwater fraction H2O � 30%. Generally, all resultsare within the expected range and correspond to find-ings reported by other authors.2,28
In the following we discuss tumor optical proper-ties. To generate optical mammograms displayingthe spatial distributions of optical properties, effec-tive absorption and reduced scattering coefficientswere derived at each scan position. Again, assum-ing the volume fraction of water in the tissue to be30%, the corresponding concentrations of oxyhemo-globin and deoxyhemoglobin and blood oxygen satu-ration were calculated from Eq. �2�. As an example,Figs. 9�a� and 9�b� show optical mammograms repre-senting absorption and reduced scattering coeffi-cients, respectively, at 670 nm for the tumor-bearingbreast of patient 9 �compare Fig. 4�. At the locationof the tumor, �x, y� � ��2 cm, 2.5 cm�, absorption isremarkably higher, whereas the reduced scatteringcoefficient hardly differs from that of the surroundingtissue. The superficial blood vessel running verti-cally and the nipple are characterized by increasedabsorption, too. The same structures appear in themammogram displaying total hemoglobin concentra-tions �Fig. 9�c��; i.e., an increased absorption corre-sponds to an increased hemoglobin content. The
Table 4. Ensemble Averages �Patients 7–35� of Bulk Optical Properties,Bulk Physiological Parameters, Scatter Power b and Water Fraction
mammogram in Fig. 9�d� represents blood oxygensaturation in tissue. Reduced oxygen saturation oc-curs at the location of the tumor and at the nipple.When the volume fraction of water is varied within areasonable range �10%–50%�, the numerical values ofthe quantities displayed in Figs. 9�c� and 9�d� change,but images remain qualitatively the same. In gen-eral, the visibility of the tumor was found to be worsein mammograms representing absorption coefficientsor physiological parameters such as total hemoglobinconcentration and blood oxygen saturation �Fig. 9�than in mammograms based on reciprocal normal-ized photon counts in the late time window �Fig. 4�.
We derived average optical properties of the tumorin all cases for which the tumor was detected in op-tical mammograms. To this end, we calculated themean over nine pixels of the corresponding mammo-gram at the center of the tumor. In Fig. 10 resultsare given for all patients for whom measurementswere performed at both wavelengths. Figures 10�a�and 10�b� show the tumor absorption and reducedscattering coefficient, respectively, normalized to thecorresponding bulk values. In all cases absorptionof the tumor is larger than that of the bulk; the in-crease in the effective absorption coefficients rangesfrom 10% to 150%. It should be noted, however, thatbecause of partial volume effects this difference isunderestimated by the homogeneous model. It canbe seen from Fig. 10�a� that the absorption ratio is
larger at 670 nm than at 785 nm. Reduced scatter-ing coefficients exhibit a more complex behavior.For some tumors we observed stronger, for others aweaker scattering. Generally, relative changes inscattering between tumor and surrounding tissue aresmaller than for absorption.
Figures 10�c� and 10�d� show differences in totalhemoglobin concentration and in blood oxygen satu-ration between the tumor and the corresponding bulkvalues. In all cases the hemoglobin concentration ofthe tumor is larger than that of the bulk. On theother hand, blood oxygen saturation is lower or ap-proximately unchanged in the majority of cases, butthere is one exception �patient 25� with a stronglyincreased blood oxygenation saturation of the tumor.For each patient, Fig. 11 correlates blood oxygen sat-uration with total hemoglobin concentration derivedfrom bulk values a,0 at both wavelengths. In addi-tion, Fig. 11 includes values for all tumors detectedretrospectively. There is a large overlap betweenvalues of normal breast tissue and of tumors, and noglobal thresholds can be found to discriminate tu-mors from healthy tissue. In contrast, Figs. 10�c�and 10�d�, which display changes rather than abso-lute values, are suited for characterizing and possiblyfor discriminating tumors.
The preceeding discussion refers to effective opticalproperties derived from the homogeneous model. Asmentioned above, effective optical properties gener-
Fig. 10. �a� Effective absorption coefficients and �b� reduced scattering coefficients of tumors of selected patients normalized to bulkvalues. Corresponding changes in �c� total hemoglobin concentration ctHb and �d� blood oxygen saturation Y with respect to bulk values.Error bars were derived assuming a 5% uncertainty of the absorption and reduced scattering coefficients.
ally underestimate differences in optical propertiesbetween tumor and surrounding tissue because ofpartial volume effects. To obtain true differences,inhomogeneous models have to be employed. Forselected patients, Fig. 12 compares bulk optical prop-erties, effective optical properties of the tumor, andtumor optical properties derived from diffraction ofphoton density waves by a spherical inhomogene-ity.8,29,30 Whereas effective absorption coefficientsof the tumors exceed those of the bulk by only 10%–20%, absorption coefficients of the tumor obtainedfrom diffraction of photon density waves are largerthan those of the bulk by a factor of two to three. Inthe same way, reduced scattering coefficients derivedfrom diffraction of photon density waves are signifi-cantly different from bulk values for patients 9 and11, whereas effective reduced scattering coefficientsof the tumor are equal to bulk values within errorlimits. It follows that tumor detection will be im-proved considerably when inhomogeneous modelsare used to derive optical properties from measured
distributions of times of flight of photons. Gener-ally, the model of diffraction of photon density wavesby a spherical object embedded in an otherwise ho-mogeneous medium requires the size, shape, and lo-cation of the tumor to be known. For the three casesshown in Fig. 12 this information was derived fromhistology and x-ray and MR mammograms. Inmany cases the diffraction model is not applicable, inparticular when the tumor is located too close to theedges of the breast, when its shape cannot be approx-imated reasonably by a sphere, or when the tumorand the surroundings are very inhomogeneous. Insuch cases numerical models such as finite elementmethods used to integrate the diffusion equationmight be more appropriate.
We conclude this section by deriving optical prop-erties of specific kinds of breast tissue other thantumors. As indicated in Table 1, glandular tissueand mastopathic changes were visible at high con-trast in several optical mammograms. As a matterof fact, some tumors were even missed because theywere masked by glandular tissue. To derive the op-tical properties of glandular tissue we selected caseswith a large contrast between glandular and fattytissue in optical mammograms. Allocation of themammary gland was achieved by comparison of op-tical mammograms with x-ray and MR mammo-grams. In each case we determined the mean of theabsorption or reduced scattering coefficients overnine pixels at the center of the glandular tissue. Inthe same way we derived optical properties of mas-topathies and of fatty regions of the breast. In Figs.13�a� and 13�b� the reduced scattering and the ab-sorption coefficients at 785 nm are plotted versusthose at 670 nm.
The reduced scattering coefficients of fatty andglandular tissue �Fig. 13�a�� scatter over the samerange, whereas mastopathies show comparably largereduced scattering coefficients. The slope in Fig.13�a� is similar for all three types of tissue. A com-parison of the reduced scattering coefficients of fattyand glandular tissue of the same patient shows thats of glandular tissue is slightly larger by �5% thanthat of fatty tissue. The results reported in Refs.31–33 support our findings. Absorption coefficients�Fig. 13�b�� are smallest for fatty tissue, ranging from0.02 to �0.04 cm�1 at both wavelengths. Mastopa-thies are found to have larger absorption coefficients,and the highest values of a are observed for glandu-lar tissue. Moreover, glandular tissue and mastop-athies are characterized by much larger absorption at670 nm than at 785 nm. The absorption coefficientsof fatty and glandular tissue are consistent with theresults reported by Suzuki et al.,32 who investigatedoptical properties of breast tissue at 753 nm in vivo.Investigations of tissue absorption performed invitro31,33 showed decreased absorption for glandulartissue compared with fat, most likely because of miss-ing blood. Heusmann et al.34 reported increasedtotal hemoglobin concentration and increased watercontent in mastopathies compared with the sur-rounding normal tissue. This result is consistent
Fig. 11. Scatter plot of blood oxygen saturation versus total he-moglobin concentration, derived from effective absorption coeffi-cients. Data refer to patients with tumors clearly visible inoptical mammograms.
Fig. 12. Bulk optical properties s,0 and a,0, effective tumoroptical properties �EFF�, and tumor optical properties obtainedfrom diffraction of photon density waves �PDW� for selected casesat 785 nm. �a� Reduced scattering coefficients; �b� absorption co-efficients. Error bars correspond to an uncertainty of �5% �ho-mogeneous model� and �10% �PDW�.
with the increased absorption of mastopathies thatwe observed.
It follows from our investigations that absorptionproperties of glandular tissue are rather similar tothose of tumors. Hence, tumors embedded in glan-dular tissue might be masked and indistinguishablefrom the surrounding tissue, at least at the two wave-lengths employed in our mammograph.
C. Scatter plots
To gain more insight into differences between tumorand surrounding tissue, we correlated selected quan-tities available for each pixel of a particular opticalmammogram in two-dimensional scatter plots. Forillustration, in Figs. 14�a�–14�c� we show such dia-grams plotting oxygen saturation versus hemoglobinconcentration or absorption �reduced scattering� at785 nm versus absorption �reduced scattering� at 670nm. Data refer to the craniocaudal projection of theleft breast of patient 9 �compare Fig. 4�. In theseplots each symbol corresponds to one pixel of theoptical mammogram. Data points appearing in theupper right part of Figs. 14�a�–14�c� correspond toscan positions close to the edges of the breast. Forthese positions the considerable scatter of the datareflects the residual influence of edge effects aftercorrection. When we tag the area of the tumor in theoptical mammogram �see Fig. 14�d��, we obtain the
open symbols in Figs. 14�a�–14�c�. In Fig. 14�a� thetumor is found in the lower right-hand part of thescatter plot, reflecting its decreased blood oxygen sat-uration and increased total hemoglobin concentra-tion �compare Fig. 9�. In the absorption plot �Fig.14�b�� the tumor appears as a small concentratedregion, whereas in Fig. 14�c� the scattering coeffi-cients of the tumor are distributed over a larger partof the scatter plot. These observations indicate thatin the case considered here the scattering coefficientsare not suited for differentiating between tumor andhealthy tissue. In contrast, absorption coefficientsat two wavelengths and hemoglobin concentrationcorrelated with oxygen saturation are significant pa-rameters.
Moreover, we performed a reverse analysis; i.e., wetagged all pixels in the lower right quadrant of theoxygen saturation versus hemoglobin concentrationscatter plot and marked these pixels in the opticalmammogram. Two separate self-contained regionswere obtained in this way, corresponding to the nip-ple and to the tumor. For all patients this approachwas applied to scatter plots representing blood oxy-gen saturation versus total hemoglobin concentra-tion. In this way those tumors could be identified inoptical mammograms that were characterized byboth increased hemoglobin concentration and de-creased oxygen saturation �compare Figs. 10�c�,10�d��. However, our method did not work reliablyfor those cases in which the oxygen saturation of thetumor did not remarkably differ from that of the sur-rounding tissue �see Fig. 10�d��.
It should be noted that a horizontal line �Y � con-stant� in the scatter plot of oxygen saturation versushemoglobin concentration corresponds to a straightline in the absorption plot �see Fig. 14�b�� with theslope m given by Eq. �6�. Performing an analysis forall pixels of Fig. 14�b� corresponding to patient 9 sim-ilar to that for Fig. 8�b� representing results fromdifferent patients, we derived average values of H2Oand Y for the particular breast under discussion.We observed rather large differences in the averagevalues of H2O and Y for the various projections ofboth breasts of the same patient. This observationindicates that the assumption of a spatially indepen-dent water fraction over the whole breast is a roughapproximation. It follows that the shape of the scat-ter plot in Fig. 14�b� is primarily caused by contribu-tions from different types of tissue.
Scatter plots can also be used to compare thetumor-bearing breast with the corresponding healthybreast. To this end, we superimposed the scatterplot of the healthy breast onto that of the diseasedbreast to find self-contained regions of outliers rep-resenting the tumor. This approach worked in somecases �e.g., patient 9� but failed for other patients.
The different methods of reverse analysis of scatterplots discussed above were applied unsuccessfully tothose cases for which the tumor could not be detectedin the first place in optical mammograms represent-ing early and late time windows �26, 28�. Probablyin these cases either the tumors did not sufficiently
Fig. 13. Optical properties of fatty tissue, glandular tissue, andmastopathies for selected patients: Reduced scattering coeffi-cients �a� and absorption coefficients �b� at 785 nm versus those at670 nm. Error bars correspond to a typical uncertainty of 5%.
differ in hemoglobin concentration and oxygen satu-ration derived from effective optical properties, orcontrast between tumor and healthy tissue was toosmall compared with the biological variability of thesurrounding tissue.
5. Conclusion
We performed a preclinical study of optical mammog-raphy on 35 patients suspected to have breast cancerby using a dual-wavelength laser pulse mammographto record mammograms in craniocaudal and medio-lateral projections. From 26 histologically con-firmed cancers, 17 cancers were visible in opticalmammograms based on photon counts in selectedtime windows. The majority of tumors detected �14�were visible in both projections. There are severalpossible reasons for missing the tumor altogether inthe remaining 9 cases. Some of these tumors werelocated close to the axilla or to the chest wall andwere outside the scanning range of our laser pulsemammograph. Furthermore, we observed that op-tical properties of breast tumors are rather similar tothose of glandular tissue, and some of the tumors
missed were probably masked by the mammarygland. However, two tumors of moderate size thatwere missed in both projections possibly had opticalproperties too close to those of the surrounding tissueto be detected, or contrast might have been cancelledby our use of effective optical properties.
Effective absorption and reduced scattering coeffi-cients were derived by use of a homogeneous modelfrom distributions of times of flight measured at eachscan position. Absorption coefficients obtained attwo wavelengths were converted into total hemoglo-bin concentration and blood oxygen saturation, as-suming a water content of 30%. All tumors detectedin optical mammograms exhibited increased absorp-tion and increased total hemoglobin concentrationcompared with the surrounding healthy tissue.Moreover, blood oxygen saturation in tumors was re-duced in the majority of cases. Because of partialvolume effects, differences between tumor opticalproperties derived from measured distributions oftimes of flight with a homogeneous model and bulkvalues are grossly underestimated. However, effec-tive optical properties derived at each scan position
Fig. 14. Scatter plots of selected parameters taken from mammograms of patient 9 �left breast, craniocaudal; compare Fig. 4�a��. Eachdata point corresponds to a particular scan position. �a� Blood oxygen saturation versus total hemoglobin concentration; �b� absorptioncoefficients at 785 nm versus those at 670 nm; �c� reduced scattering coefficients at 785 nm versus those at 670 nm; �d� optical mammogram,1�N8�x, y�. Open squares correspond to the tumor area tagged in the optical mammogram.
allow one to generate two-dimensional images of ab-sorption and scattering. To deduce more realisticvalues of tumor optical properties, inhomogeneousmodels such as random-walk theory35 or diffraction ofphoton density waves by a spherical inhomogeneity30
should be employed. Furthermore, by scanning onetransmitting and several receiving optical fibers ar-ranged in fan geometry rather than a transmitting–receiving fiber pair arranged on-axis, one canmeasure transmittance under selected oblique pro-jection angles. In this way information can be ob-tained about the position of the inhomogeneity alongthe compression direction.
Scatter plots based on a pixelwise analysis of indi-vidual mammograms are a powerful tool for visual-izing correlations between characteristic quantitiesderived from time-resolved transmittance. Scatterplots allow one to select specific areas of mammo-grams by exploiting the spectral information con-tained in measured distributions of times of flight ofphotons taken at several wavelengths.
We conclude that the potential of scanning laserpulse mammography has not yet been fully exploredand will be increased by performance of multiwave-length, multiprojection measurements together withadvanced methods of data analysis by means of in-homogeneous models.
Part of this work was supported by the EuropeanCommission, contract QLG1-CT-2000-00690.
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