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Time-gated viewing studies on tissuelike phantoms

Berg, R; Andersson-Engels, Stefan; Jarlman, O; Svanberg, Sune

Published in:Applied Optics

DOI:10.1364/AO.35.003432

Published: 1996-01-01

Link to publication

Citation for published version (APA):Berg, R., Andersson-Engels, S., Jarlman, O., & Svanberg, S. (1996). Time-gated viewing studies on tissuelikephantoms. Applied Optics, 35(19), 3432-3440. DOI: 10.1364/AO.35.003432

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Time-gated viewingstudies on tissuelike phantoms

R. Berg, S. Andersson-Engels, O. Jarlman, and S. Svanberg

A time-gated technique to enhance viewing through highly scattering media such as tissue isdiscussed. Experiments have been performed on tissuelike plastic phantoms to determine thepossibilities and limitations of the technique. The effects of the time-gate width and the localization,size, and optical properties of hidden objects have been studied. A computer model to simulate lightpropagation in tissue is also presented. The predictions of the model are compared with experimentalresults.Key words: Medical diagnostics, time-gated viewing, tissue optics, transillumination, scattering

media, diffusion equation, numerical modeling. r 1996 Optical Society of America

1. Introduction

The challenge of looking through highly scatteringmaterials such as tissue by the use of low-energyphotons is a growing field of interest.1 The task hasbeen promoted by a desire to develop a method toperform screening for breast cancer with safe dosesof optical radiation instead of potentially harmfulionizing x rays.2,3 The wavelength region of inter-est is approximately 650–1300 nm, where transmis-sion through tissue is highest.4 The dilemma en-countered when breast imaging is performed atthese wavelengths is that the dominating attenua-tion process is scattering. This leads to blurredimages and poor resolution. Typical values for thescattering coefficient µs of tissue in this wavelengthregion are in the range of 5–50 mm21. This rangeimplies that the main number of photons that havetraveled through a few centimeters of tissue havebeen scattered several thousand times.Several new techniques to improve optical tissue-

transillumination imaging are under develop-ment.1,5,6 The new modalities can be divided intotwo major groups: time- and frequency-domainmethods. The time-domain methods are based on

irradiating the tissue with ultrashort laser pulsesand on using time-resolved detection of the transmit-ted light. An enhanced image of objects locateddeeply inside the tissue can be accomplished by theuse of the very first arriving photons only. Theyhave traveled the straightest and shortest paththrough the tissue and thus give a higher spatialresolution. Different methods of performing time-resolved detection have been used. One techniqueis based on holographic detection, in which the firsttransmitted photons are gated out by the use of thecoherent interference between this light and a gatepulse on a holographic plate.7,8 This technique im-plies, as a result of the demand of coherence, that thefirst light exiting the tissue is coherent with the laserpulse. Light delayed because of multiple scatteringin the tissue has lost the coherence and thus contrib-utes to an undesirable background. This back-ground makes this technique not useful in practicefor transilluminating tissues of some centimeters inthickness. The imaging technique developed byInaba et al.9 is also dependent on the coherence of thetransmitted light. Other techniques are based onultrafast gating by the use of different types ofnonlinear optical phenomena, such as second-har-monic generation,10 the optical Kerr effect,11 stimu-lated Raman amplification,12 or upconversion.13These techniques require lasers with high peakpowers to drive the nonlinear optical device. Time-resolved detection can also be attained with fastelectronic devices. The streak camera gives a tem-poral resolution of the order of 1–10 ps, depending onthe operational mode, and it has been used by somegroups for tissue zc transillumination studies.14,15

R. Berg, S. Andersson-Engels, and S. Svanberg are with theDepartment of Physics, Lund Institute of Technology, P.O. Box118, S-221 00 Lund, Sweden; O. Jarlman is with the Departmentof Diagnostic Radiology, Lund University Hospital, S-221 85Lund, Sweden.Received 20 July 1995; revised manuscript received 2 January

1996.0003-6935@96@193432-09$10.00@0r 1996 Optical Society of America

3432 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

In this paper we present research performed usingtime-correlated single-photon counting as the detec-tion technique.5,16 This modality has a temporalresolution of roughly 30–100 ps and a wide dynamicrange.The frequency-domain approach for tissue transil-

lumination is based on irradiation of the sample withintensity-modulated light and detection of the de-modulation of the amplitude and the change of phaseof the exiting light.17,18 As light sources rf-modu-lated diode lasers and mode-locked lasers have beenused. The detection is based on heterodyne orfrequency-mixing actions.The time- and frequency-domain techniques can

also be used for tissue characterization.19 By analy-sis of the temporal dispersion of the transmitted orbackscattered light, the optical properties of thetissue can be determined. These properties areinteresting, e.g., for photodynamic therapy or tissuediagnostics. Tissue oxygenation can also be deter-mined with these techniques.20,21Conventional transillumination breast imaging

1diaphanography2 is based on the detection of tumorsbecause of their elevated absorption, which is causedby the increased blood supply that many tumorshave. However, we have shown that the time-gated, as well as the frequency-domain, technique ismuch more sensitive to the scattering coefficientthan to the absorption coefficient.22 In this paperwe show the ability of our system to detect tumorphantoms, depending on their size and localizationin the tissue phantom. The effects of the opticalproperties of the hidden object are also studiedexperimentally, and we verify our experimental datausing a numerical model developed at our depart-ment.23 The model is also used to expand the studyof the optical properties beyond the experimentaldata.

2. Materials and Methods

A. Experimental Setup

The experimental arrangement used for time-resolved transillumination is illustrated in Fig. 1.The light source was a mode-locked argon-ion laserpumping a dye laser. The pulse length from the dyelaser was measured with an autocorrelator to be 6ps. The dye laser was equipped with a cavitydumper 1and its driver2, making it possible to alterthe repetition rate from the laser. In all the experi-ments reported in this paper the repetition rate was10 MHz and the wavelength 670 nm. The averagepower was approximately 50 mW. The laser lightirradiated the sample, and the transmitted light wascollected on the opposite side by a clear-cut 600-µm-diameter optical fiber. The light exiting the fiberwas focused onto the detector through an interfer-ence filter to reduce the influence of ambient light.The time-correlated single-photon counting detec-tion technique was employed. A fast detector1Hamamatsu, Model R1564U-07 MCP-PMT2 was

used. The signal for each detected photon wasamplified with a fast amplifier, fed through a con-stant fraction discriminator, and worked as a startsignal for the time-to-amplitude converter. The stopsignal was taken from the cavity-dumper driver unitthrough an amplifier and a constant-fraction dis-criminator, to the time-to-amplitude converter.The output voltage from the time-to-amplitude con-verter was fed to a multichannel analyzer, in whichthe temporal histogramswere assembled. The tem-poral-response function for the system was approxi-mately 70 ps 1FWHM2. To compensate for any driftphenomena in the system, a small part of theincident light was reflected off by a glass slide anddirected to the detector through an optical fiber,providing a reference peak in time. The referencepeak is located in time when it does not interferewith the light exiting the sample. The curves wereread out to a PC for on-line evaluation. The com-puter also controlled the scanning over the sampleby means of stepping motors.

B. Tissue Phantom

The tissue phantom in all experiments consisted of awhite, highly scattering plastic called Delrin 1Du-Pont2. We estimated the optical properties of theplastic by fitting an experimental time-dispersioncurve of light transmitted through a homogeneousslab with the solution to the diffusion equationpresented by Patterson et al.24 Figure 2 shows thetemporal-dispersion curve obtained when a 30-mm-thick slab of Delrin was transilluminated 1filled-squares curve2. The figure also shows the fit to theanalytical model 1solid curve2, from which the opticalproperties were extracted. The optical propertieswere µs8 5 2.3 mm21 and µa 5 0.002 mm21 3µs8 is theeffective scattering coefficient, i.e., 11 2 g2 3 µs, whereg is the scattering anisotropy coefficient 1the averageof the cosine of the scattering angle2, µa is

Fig. 1. Diagram of experimental setup used in the time-gatedviewing experiments. Const. Fract. Discr., constant fractiondiscriminator; Ref., reference; Amp., amplifier.

1 July 1996 @ Vol. 35, No. 19 @ APPLIED OPTICS 3433

the absorption coefficient4. The plastic is thus ahighly scattering medium with low absorption. Weused 5-mm-thick slabs of the plastic. Holes of differ-ent sizes were drilled into the plastic to act as tumorphantoms. The holes were either empty or filledwith liquid to simulate different optical properties ofthe tumor. Stacking the slabs of plastic yieldeddifferent thicknesses for the model and positions ofthe tumor. Silicon oil with the same refractiveindex as the plastic was used between the plasticslabs to reduce the effect of any air pockets.

C. Computer Model

Two frequently used techniques for modeling near-infrared light fluence in tissue are Monte Carlosimulations25 and analytical or numerical solutionsof the diffusion approximation to the Boltzmanntransport equation.26,27 The basis for the MonteCarlo technique is tracing a large number of photonpaths that traverse the tissue from the photonsource through a multiple-scattering medium to thephoton detector. The scattering events within thetissue are determined by a probability function thatmatches the scattering coefficient. At each scatter-ing event a part of the ray, determined by theabsorption coefficient, is absorbed. The scatteringangle is given by the scattering phase function. AMonte Carlo algorithm can simulate the photon fluxaccurately for a wide range of geometries and opticalparameters of the tissue slab. Monte Carlo simula-tions, however, require a high computer capacity toobtain statistically good, quality data. The diffu-sion equation can be derived from the transportequation if the coherent radiance is neglected andthe diffuse radiance is assumed to be only linearlydependent on the direction of the photon velocity.With this approximation, and the further assump-tion that the rate of change in the photon flux ismuch smaller than the reduced collision rate multi-plied by the photon flux, the Boltzmann transportequation can be simplified to yield the diffusion

equation:

n

c

≠f1r, t2

≠t2 =3D=f1r, t24 1 µaf1r, t2 5 S1r, t2, 112

where f1r, t2 is the diffuse photon fluence rate, c isthe speed of light in vacuum, n is the refractive indexof the tissue, D is the diffusion coefficient, i.e., D 5331µa 1 11 2 g2µs24 21, and S1r, t2 is the photon source.In Eq. 112 the tissue is characterized with an absorp-tion and a scattering coefficient 1µa and µs, respec-tively2 and the mean cosine of the scattering function1g2. This approximation is valid if µs11 2 g2 : µa forthe photon fluence rate at a distance from the sourceand some time after an impulse source injection.We are interested in the light fluence rate far fromthe source but within a relatively short time windowfollowing the irradiation pulse. In this situationthe diffusion approximation may not be accurate.However, here we are interested in qualitative ratherthan quantitative behavior, and thus this approxima-tion should be acceptable for the study of the relativesensitivity of the fluence rate to variations in absorp-tion and scattering coefficients inside a turbid me-dium.This equation can be solved analytically in certain

simple geometries. For our studies, we chose to usea numerical solution of the diffusion approximation.This model allows us to vary freely both the scatter-ing and the absorption coefficient within the slab andto compare weak signals without problems withphoton statistics. The diffusion equationwas trans-lated to a difference equation for finite steps of the x,y, z, and t variables, and a generalized Crank–Nicholson algorithm for three dimensions, the alter-nating-direction implicit method, was employed.28This method solves each spatial dimension sepa-rately using a third of a time step for the x, y, and zdimensions, respectively. The resulting equationfor the x dimension is

fxyzt11@3

2 fxyzt

5cDt

3nD23Dx11@2yz1fx11yz

t11@32 fxyz

t11@32

2 Dx21@2yz1fxyzt11@3

2 fx21yzt11@32

1 Dxy11@2z1fxy11zt

2 fxyzt 2

2 Dxy21@2z1fxyzt

2 fxy21zt 2

1 Dxyz11@21fxyz11t

2 fxyzt 2

2 Dxyz21@21fxyzt

2 fxyz21t 24

2cDt

6nµa1fxyz

t1 fxyz

t11@32, 122

where fxyzt is the fluence rate in the matrix element

1x, y, z2 at time t, Dt is the time step, D is the step sizein x, y, and z, and Dx11@2yz is the average of thediffusion coefficient in the matrix elements 1x, y, z2and 1x 1 1, y, z2. Similar equations are obtained for

Fig. 2. Temporal-dispersion data: The filled squares form atypical experimental time-dispersion curve, obtained when 30mm of Delrin plastic were transilluminated. The solid curve is afit to the analytical solution of the diffusion equation, giving theoptical properties of the plastic 1µs8 5 2.3 mm21 and µa 5 0.002mm212.

3434 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

the y and z dimensions. To solve for the x dimensionrequires that a tridiagonal system of equations besolved for every y and z coordinate.

3. Results

A. Gate Width

To measure the effects of the time-gate width weused a 30-mm-thick slab of Delrin with a 5-mm-diameter hole. The hole was located in the middleof the slab and was empty. We performed a scantransversally to the direction of the hole with 1 mmbetween every measuring point. The total scanlength was 30 mm. The lower part of Fig. 3 showsthe measurement geometry. The recording timewas 10 s@point. The upper part of Fig. 3 shows aplot of the light intensity in a 230-ps-long gatedivided by the total amount of light detected. Thistime gate corresponds to a light intensity of 0.1% ofthe total light for regions far from the hole. Thisdivision is done to minimize the influence of someartifacts, such as intensity variations in the laserand dirt on the sample surfaces. As can be seenthere is more early light detected in the region of thehole than beside it. This effect has been shown inprevious studies and is due to the low scatteringcoefficient in the hole.22 To quantify this effect inthe scan obtained, we fitted it to a Gaussian curve.

It turns out that the scan obtained fits a Gaussiancurve quite well. The letters in the figure denotecertain features of the curve: A is the relativeamount of light obtained in regions far from theempty hole; B is the relative amount of light in theempty-hole region; andC is the FWHMof the peak inthe obtained scan. In Fig. 4 it is shown how theseparameters change when the time-gate width ischanged. Figure 41a2 shows the relative amount oflight obtained at different gate widths 1A2. The gatestarts when the signal starts to rise. Figure 41b2shows the relative contrast, i.e., B@A. As can beseen, the shorter the time gate, the higher thecontrast. Figure 41c2 shows the FWHM 1C2 of thescan, and Fig. 41d2 shows the residual from theleast-squares fit of the Gaussian curve and the scan,i.e., this curve shows the noise. As can be seen thenoise is low down to an ,250-ps time-gate width, atwhich point the noise starts to rise. When weevaluated the experimental curves discussed in thefollowing sections, we chose a time-gate window thatstarts at the value of the signal as it begins to rise upto where the noise 3Fig. 41d24 has become low. Wechose a time gate of 230 ps, which also corresponds tothat 0.1% of the total light reading the detector thatfalls into this gate if measured at a position far fromthe empty hole.

B. Effects of Hole Size

A series of scans with different hole sizes wasperformed to determine the spatial resolution of thesystem. The geometry and size of the phantom wasexactly as described in Section 3.A. The diameter ofthe empty hole in the middle of the slab was alteredbetween 8 and 3 mm. Figure 5 shows the relativecontrast B@A and the FWHM C of the differentscans. As the plot shows, the hole can be seen downto a size of,4mm. The curves comprise an averageof five scans and include error bars. Clearly thecontrast is highly dependent of the size of the hole,but the FWHM is not.

C. Effects of Hole Position

We also wanted to study the influence of the positionof the hole in the phantom. Figure 6 shows therelative contrast B@A and the FWHM C as functionsof the hole position. As Fig. 6 illustrates, the hole ismost difficult to detect when it is located in themiddle of the phantom.

D. Numerical Modeling

The numerical computer model was compared withexperimental results to verify the model. For thenumerical solutions calculated in this study a 1x 5 31,y 5 31, z 5 202 matrix was used. This size of thematrix is sufficient to give a reliable result.29 Toobtain a time-dispersion curve, which is approxi-mately 6 ns long, we required a computer time of 10min on a 150-MHz Digital Equipment CompanyAlpha PC. Experimental scanswere performed overa 30-mm-thick slab of Delrin with a 5-mm-diameterhole in the middle. The hole was filled with a mix of

Fig. 3. Diagram of the geometry used during transilluminationof the tissue phantoms 1lower image2. The curve 1upper plot2shows the relative amount of light detected in the time-gatewindow used. The letters A, B, and C represent the detectedrelative light intensity within the time gate and the change of thelight intensity that is due to the hidden object when the phantomis scanned.

1 July 1996 @ Vol. 35, No. 19 @ APPLIED OPTICS 3435

Intralipid 1Kabi Pharmacia2 as a scatterer and alaser dye 1Rh 700, Lambda Physik2 as an absorber.To avoid an influence from fluorescence in the dye, afilter that transmitted only the laser wavelength wasplaced in front of the detector. The optical proper-ties of the two constituents were estimated sepa-rately with a simple narrow-beam experiment ondiluted samples of each constituent. The scatteringcoefficient of Intralipid was estimated to 601 6 85mm21 for 1 g@ml pure Intralipid. The g factor wastaken from the literature to be 0.7.30 The laser dyewas mixed to a stock solution with an absorptioncoefficient of µa 5 1.47mm21, which was then dilutedto the appropriate concentration. Figure 7 shows atypical scan in which the optical properties of themixture were estimated to be µs8 5 0.56 mm21 andµa 5 0.029 mm21, i.e., the cylinder-shaped hole hadlower scattering and higher absorption than thesurrounding Delrin 1µs8 5 2.3 mm21, µa 5 0.002mm212. The numerical model was used to simulatethe same type of scan. The solid curveswith squaresin Figs. 7 show the experimental results and thedashed curves with triangles the results obtainedwith the numerical model. The curves in Fig. 71a2show the first 230 ps of light, and those in Fig. 71b2

1a2

1b2

1c2

1d2

Fig. 4. Plots of the influence of the time-gate width when a30-mm-thick tissue phantom 1µs8 5 2.3 mm21 and µa 5 0.002mm212 containing a 5-mm hole in the middle is transilluminated:1a2 The relative 1Rel.2 amount of lightA detected as a function of thewidth of the gate window. 1b2 The contrast 1B@A2 in the detectionof the hidden object. 1c2 The FWHM C in the detection of thehidden object. 1d2 The residual between the experimental curveand the Gaussian fit. The 230-ps gate used during evaluation ofthe experimental curves is also indicated in 1a2 and 1d2.

Fig. 5. Experimental curves obtained from the transillumina-tion of a 30-mm-thick tissue phantom 1µs8 5 2.3 mm21 andµa 5 0.002 mm212 containing holes of varying sizes located in themiddle of the phantom. The diagram shows the relative contrastB@A 1solid curve2 and the FWHM C 1dashed curve2 as functions ofthe hole size.

Fig. 6. Experimental curves obtained by transillumination of a30-mm-thick tissue phantom 1µs8 5 2.3 mm21, µa 5 0.002 mm212containing a 4-mm hole at different distances from the surface atwhich the light enters the phantom. The diagram shows therelative contrast B@A 1triangles2 and the FWHM C 1squares2 asfunctions of the hole position.

3436 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

show the total light intensity obtained at eachmeasurement point. As can be seen the amount oftotal light decreases when the scan passes over thecylinder because of the increased absorption, whereasthe time-gated light intensity increases because ofthe lower scattering in the cylinder.Because of the rather low resolution of the numeri-

cal model, it is not possible to simulate a 5-mmcylindrical hole. It has to be simulated with a5-voxel cross in cross section. In the Boltzmanntransport equation, fromwhich the diffusion approxi-mation is derived, the description of the fluence flowin and out of a voxel is given by the partial derivativein space multiplied by the surface area of the voxel.This is transformed with Gauss’ theorem into avolume integral:

r =f1r, t2dS 5 e Df1r, t2dV. 132

Looking more carefully at Eq. 122we can see that alsoin the numerical model the flow into a voxel isproportional to the gradient of the fluence times thesurface area of the voxel, whereas the absorption

scales with the volume of the voxel. To describe the5-mm hole in the model correctly, one must choosethe surface area of the 5-voxel cross to be the same asthat of the cylindrical holes. Thus the volume willnot be correct, but this is solved when the absorptioncoefficient of the hole is scaled a factor correspondingto the difference in volume. In our model the differ-ence was D 5 1.5 mm, thus the circumference of the5-voxel hole is 18 mm, compared with the real holecircumference of 15.7 mm. The difference in vol-ume is 1.75; thus the absorption of the hole isincreased by this factor in our model as comparedwith the estimated absorption of the experimentalliquid.The experiment was repeated for nine different

combinations of the optical properties of the liquidwith µs8 5 0.56, 2.3, 9.0mm21 and µa 5 0.0018, 0.015,0.029 mm21. Figure 8 shows a comparison betweenthe experimental and numerical-model results.The figure shows the ON–OFF contrast, i.e., the ratioof light detected during the first 230 ps when themeasurement is performed through the sample inthe region of the hole, divided by the amount of lightdetected in the same timewindowwhen themeasure-ment is performed through the sample perpendicu-lar to the surface, 15 mm from the vertical planecontaining the cylindrical hole 3Fig. 81a24. Thus, avalue larger than 1 representsmore early light in thehole region, and a value less than 1 represents lessearly light detected from that region. The symbolsrepresent the experimental data, with error bars.

1a2

1b2

Fig. 7. Comparison between the experimental results and thenumerical computer model of the transillumination of a 30-mm-thick tissue phantom containing a 5-mm hole filled with a liquidthat has a lower scattering coefficient and a higher absorptioncoefficient than the phantom: 1a2 the first light detected in a230-ps time gate, and 1b2 the total light intensity obtained as afunction of the scan position.

Fig. 8. Relative contrastB@A, i.e., the amount of light in a 230-pstime-gate window for a measurement over the hole, B, divided bythe amount of light detected in the same time window for ameasurement 15 mm beside the hole, A, as a function of theeffective scattering coefficient µs8 of the liquid in the hole: 1a2 Thesymbols represent the experimental data, and the curves repre-sent the numerical-model data for different values of the absorp-tion coefficient µa of the liquid in the hole. 1b2 The experimentalratio in the total light intensity for the two measuring sites.

1 July 1996 @ Vol. 35, No. 19 @ APPLIED OPTICS 3437

Three different sets of data represent the differentabsorption coefficients of the liquid in the hole.Data are shown for various scattering coefficients ofthe liquid in the hole as well. The results show agood agreement between the experimental data andthe data obtained with the numerical model. Thereis some difference at low scattering, but in thisregion the gradient of the curve is steep, making itsensitive to small variations in the scattering coeffi-cient. Figure 81b2 shows the ratio B@A in the totallight intensity for the experimental data.A set of simulations were performed with the

optical properties of the bulk material being closer tothose of real tissue 1µs8 5 1.1 mm21 and µa 5 0.05mm212. The optical properties of the 5-voxel cross-approximated cylinder were altered between valuesof µs8 5 0.2–2.2 mm21 and µa 5 0.005–0.1 mm21.Figure 9 shows a calculated surface plot represent-ing the same ON–OFF contrast that was described forFig. 8. The axes at the bottom represent the differ-ent absorption and scattering coefficients of thehidden cross-approximated cylinder. It should benoted that, in the region where scattering is low andabsorption is high, the diffusion approximation isprobably not valid because scattering is only of theorder of 2–3 times larger than absorption.

4. Discussion

Optical techniques for tissue diagnostics providesome characteristics thatmake them potential candi-dates for future clinical use. Light diagnostics isnonintrusive, and the radiation in the visible andnear-infrared regions is not harmful. As for all newmodalities, it is most interesting to evaluate such

techniques in cases for which the existing techniquesare not so well suited. For the purpose of breast-tumor detection, conventional x-ray mammographydetects most tumors well. This technique has, how-ever, some less attractive features.The ionizing radiation used is connected with

some small risk for patients in terms ofmutagenicity.This risk is of special interest to the discussion ofscreening large populations for breast tumors. Itwould therefore be of great advantage if one couldfind an alternative method that diagnoses breasttumors with the same accuracy but without this risk.There is also an interest in developing new diagnos-tic techniques to be used as a complement to conven-tional x-ray mammography, as this technique, afterall, is not able to identify all tumors. It has beenshown that it is difficult to detect some tumor types,e.g., comedo structures, with conventional mammog-raphy, especially in the dense breast tissue of youngwomen.31 Optical transillumination imaging mightbe a technique that could be developed to serve anyof these purposes.Time-resolved detection in optical transillumina-

tion imaging is used for two purposes: it permitsimaging with an improved spatial resolution andalsomakes it possible to utilize the scattering proper-ties of the tissue in the diagnostics, so that one is notlimited to differences in the absorption coefficientonly.Our experiments show that the influence of scatter-

ing is very high during time-gated viewing. Figure4 shows that an object with a scattering coefficientdifferent from the surrounding medium could bedetected by the use of time-resolved detection tech-

Fig. 9. Surface plot representing the same ON–OFF contrast that was described for Fig. 81a2. The axes at the bottom represent thedifferent absorption and scattering coefficients of the hidden, cross-approximated cylinder. The optical properties of the bulk materialwere µs8 5 1.1 mm21 and µa 5 0.05 mm21.

3438 APPLIED OPTICS @ Vol. 35, No. 19 @ 1 July 1996

niques. This would not be possible in the steady-state case. Furthermore, in the geometry used herean increased spatial resolution can be achieved as aresult of the suppression of multiple-scattered light.Our experiment shows that it is possible to detectsubcentimeter features, with scattering propertiesthat differ from their surroundings, inside a highlyscattering phantom with a thickness realistic formammography. This result is in agreement withthose reported by others.32 The phantomwe used isa worst-case condition for transillumination: thescattering is higher and the absorption lower thanfor breast tissue. Figure 5 shows that the relativecontrast of a hole in the center of the phantom wasdependent on the hole size. Ahole less than approxi-mately 4 mm could not be detected. The FWHM ofthe detected peak was rather constant for the differ-ent hole diameters. We believe that this consis-tency reflects the highest spatial resolution detect-able in this time window with the use of a phantomthat has the high scattering coefficient of Delrin.We also show that the location of the lesion inside thevolume is of great importance to the possibility of itsdetection 1see Fig. 62. The closer the lesion is to oneof the borders, the easier it is to detect. Thisrelation is also found in traditional diaphanography.It is shown that our computer model works well to

solve the diffusion equation numerically, making itpossible to study the influence of inhomogenities intissue 1Figs. 7 and 82. In Fig. 81b2 it can be seen thatthe total light intensity is insensitive to variations inthe scattering coefficient. On the other hand, thesensitivity to variations in the absorption coefficientseems to be approximately the same for the gatedand the total light. Figure 9 shows the possibility ofdetection of a hidden lesion, depending on the differ-ences in the optical properties between the bulktissue and the lesion. Note that there is a line inFig. 9 across the surface, representing a value of 1,where there is no contrast between the lesion regionand the region located 15 mm from the lesion.Thus, the use of the time-gated technique gives riseto some critical combinations of the scattering andabsorption coefficients of the lesion when it cannot bedetected. This limitation could be circumvented bythe use of a more sophisticated evaluation proce-dure, for instance, using several time gates or usingthe whole time-dispersion curve for data evaluation.Even though we use a time gate that is rather long

compared with other time-gating techniques, weshow that we can increase the spatial resolution, ascompared with cw techniques, and detect objectswith a wide range of scattering properties. Becauseof this long time gate, which means that a relativelybig fraction of the total light is used in detection 1inthis case approximately 0.1%2, the total acquisitiontime for each sample position could be short. Toimprove the technique and to be able to furthershorten the acquisition time, it would be desirablefor an evaluation procedure to make use of the wholetime-dispersion curve.

A method to reduce the influence of scattering intissue would be to use longer wavelengths, i.e.,1000–1300 nm, for which tissue scattering is lowerbut for which water absorption has not yet becomesignificant.33 In this wavelength region differencesin optical properties between malignant and normaltissues have, to our knowledge, not yet been investi-gated. Absorption will be much more important inthis region than for shorter wavelengths, making iteasier to obtain a good spatial resolution. But, ifthe scattering properties constitute the diagnosticcriteria for detecting tumors, it is probably better towork at shorter wavelengths.A general condition for the success of the optical

techniques is, of course, that there are differences inthe optical properties between healthy and malig-nant tissues. Some studies have been performed,but they are normally performed in vitro.34 Furtherstudies on tissue optical parameters are required topermit speculation in more detail of the future use ofthe optical techniques described here.

This research was supported by the Swedish Re-search Council for Engineering Sciences 1TFR2, theSwedish Medical Research Council 1MFR2, and theSwedish Natural Science Research Council 1NFR2.

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