Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry Roland Bays, Georges Wagnie ` res, Dimitri Robert, Daniel Braichotte, Jean-Franc ¸ois Savary, Philippe Monnier, and Hubert van den Bergh A noninvasive method to measure the optical properties of a diffusing and absorbing medium is described. Based on the spatially resolved measurement of diffuse reflectance at the sample surface, this method is particularly suitable for investigating the in vivo optical properties of biological tissues endoscopically in a clinical context. The sensitivity of the measurement is discussed, and two optical probes for two different clinical applications are presented. Preliminary measurements are performed on a nonbiological medium, which illustrate the possibilities of the proposed method. Finally, we report on in vivo measurements of the optical properties of the human esophageal wall at 630 nm. Key words: Diffuse reflectance, tissue optics, optical probe, optical properties, scattering. r 1996 Optical Society of America 1. Introduction Knowledge of radiant energy fluence rate distribu- tion in living tissue is useful to analyze and under- stand the photobiological, photophysical, and photo- chemical processes that occur in such a medium. In the photodynamic therapy 1PDT2 of cancers, 1–4 for which the therapeutic effect is, among other param- eters, determined by the radiant energy density 1 J@cm 3 2 absorbed by a photosensitizer, this knowl- edge is particularly useful in determining the light dose for safe and effective treatment. 5,6 Inaccurate light dosimetry, for example, in the case of early squamous cell carcinomas located in the esophagus or the tracheobronchial tree, can induce severe medi- cal complications such as perforation of the organ wall 1fistula2 or stenosis. Accurate light dosimetry requires a well-con- trolled illumination of the treated surface. Several types of light distributor, suited to the geometry of different treated sites, have been developed for this purpose. 7–10 The various therapeutic conditions 1light distributor and site geometry2 and the variabil- ity of light propagation in the tissues between organs and between patients make the accurate determina- tion of the optical dose by a totally heuristic ap- proach difficult. In this perspective, we have searched for a noninvasive method to obtain, in vivo and endoscopically, the necessary optical parameters for the description of light propagation in the mucosa of hollow organs at wavelengths of interest in PDT. Numerous models based on the diffusion approxi- mation of the transport equation 11,12 have been de- scribed in the literature over the last few years. In these models, light propagation in a macroscopi- cally homogeneous medium is characterized by only three parameters: 112 absorption coefficient μ a 1mm 21 2, defined so that 1 2 exp12μ a z2 is the probabil- ity for a photon to be absorbed in path length z; 122 reduced scattering coefficient μ s 8 1mm 21 2, which de- fines the probability of the photon to be scattered in path length z, when the scattering is described by an isotropic phase function; 132 refractive index n tissue . In the case of an anisotropic scattering medium, such as in biological tissue, this description is appro- priate if one takes μ s 8 5 μ s 11 2 g2, where μ s is the anisotropic scattering coefficient, the inverse of the mean-free path between two scattering events and g, the so-called anisotropy parameter, is the average cosine of the scattering angle. This approach sup- poses the validity of the similarity principle that R. Bays, G. Wagnie ` res, D. Robert, D. Braichotte, and H. van den Bergh are with the Institute of Environmental Engineering, Swiss Federal Institute of Technology, CH-1015 Lausanne, Swit- zerland. J.-F. Savary and P. Monnier are with the Ear, Nose, and Throat Division, Centre Hospitalier Universitaire Vaudois Hospi- tal, CH-1011 Lausanne, Switzerland. R. Bays is also with the University of Toronto, Medical Science Building, Room 7345, 8 Taddle Creek Road, Toronto, Ontario M5S 1K9, Canada. Received 6 September 1995. 0003-6935@96@101756-11$06.00@0 r 1996 Optical Society of America 1756 APPLIED OPTICS @ Vol. 35, No. 10 @ 1 April 1996
Transcript
Clinical determination of tissue optical propertiesby endoscopic spatially resolved reflectometry
Roland Bays, Georges Wagnieres, Dimitri Robert, Daniel Braichotte,Jean-Francois Savary, Philippe Monnier, and Hubert van den Bergh
A noninvasive method to measure the optical properties of a diffusing and absorbing medium isdescribed. Based on the spatially resolved measurement of diffuse reflectance at the sample surface,this method is particularly suitable for investigating the in vivo optical properties of biological tissuesendoscopically in a clinical context. The sensitivity of the measurement is discussed, and two opticalprobes for two different clinical applications are presented. Preliminary measurements are performedon a nonbiological medium, which illustrate the possibilities of the proposedmethod. Finally, we reporton in vivomeasurements of the optical properties of the human esophageal wall at 630 nm.Key words: Diffuse reflectance, tissue optics, optical probe, optical properties, scattering. r 1996
Optical Society of America
1. Introduction
Knowledge of radiant energy fluence rate distribu-tion in living tissue is useful to analyze and under-stand the photobiological, photophysical, and photo-chemical processes that occur in such a medium.In the photodynamic therapy 1PDT2 of cancers,1–4 forwhich the therapeutic effect is, among other param-eters, determined by the radiant energy density1J@cm32 absorbed by a photosensitizer, this knowl-edge is particularly useful in determining the lightdose for safe and effective treatment.5,6 Inaccuratelight dosimetry, for example, in the case of earlysquamous cell carcinomas located in the esophagusor the tracheobronchial tree, can induce severemedi-cal complications such as perforation of the organwall 1fistula2 or stenosis.Accurate light dosimetry requires a well-con-
trolled illumination of the treated surface. Severaltypes of light distributor, suited to the geometry of
R. Bays, G. Wagnieres, D. Robert, D. Braichotte, and H. van denBergh are with the Institute of Environmental Engineering,Swiss Federal Institute of Technology, CH-1015 Lausanne, Swit-zerland. J.-F. Savary and P. Monnier are with the Ear, Nose, andThroat Division, Centre Hospitalier Universitaire Vaudois Hospi-tal, CH-1011 Lausanne, Switzerland. R. Bays is also with theUniversity of Toronto, Medical Science Building, Room 7345, 8Taddle Creek Road, Toronto, Ontario M5S 1K9, Canada.Received 6 September 1995.0003-6935@96@101756-11$06.00@0r 1996 Optical Society of America
different treated sites, have been developed for thispurpose.7–10 The various therapeutic conditions1light distributor and site geometry2 and the variabil-ity of light propagation in the tissues between organsand between patients make the accurate determina-tion of the optical dose by a totally heuristic ap-proach difficult. In this perspective, we havesearched for a noninvasive method to obtain, in vivoand endoscopically, the necessary optical parametersfor the description of light propagation in themucosaof hollow organs at wavelengths of interest in PDT.Numerous models based on the diffusion approxi-
mation of the transport equation11,12 have been de-scribed in the literature over the last few years.In these models, light propagation in a macroscopi-cally homogeneous medium is characterized by onlythree parameters: 112 absorption coefficient µa1mm212, defined so that 1 2 exp12µaz2 is the probabil-ity for a photon to be absorbed in path length z; 122reduced scattering coefficient µs8 1mm212, which de-fines the probability of the photon to be scattered inpath length z, when the scattering is described by anisotropic phase function; 132 refractive index ntissue.In the case of an anisotropic scattering medium,such as in biological tissue, this description is appro-priate if one takes µs8 5 µs11 2 g2, where µs is theanisotropic scattering coefficient, the inverse of themean-free path between two scattering events and g,the so-called anisotropy parameter, is the averagecosine of the scattering angle. This approach sup-poses the validity of the similarity principle that
states that two kinds of scattering event, with differ-ent anisotropy parameters, give the same light distri-bution if they have the same reduced scatteringcoefficient µs8. Both the similarity principle anddiffusion models are not exact, and their precisionmust be assessed in each case.13–16 These modelsare, however, generally accurate if the medium isvery diffusing, i.e., µs8 : µa, and if the light distribu-tion is studied far enough away from the lightdistributor and boundaries, typically at a distancegreater than the effective mean-free path, the latterbeing defined as mfp8 5 1µs8 1 µa221. One particulardiffusion model parameter is often suited to describelight propagation in diffusing media. This param-eter, the so-called effective attenuation coefficientµeff, is obtained from the other two optical coefficientsby the relation11
µeff 5 33µa1µa 1 µs8241@2. 112
From the three parameters defined above, it ispossible to obtain a more accurate description of thelight propagation in tissue with solutions of thetransport equation for simple experimental condi-tions or with numerical simulation techniques suchas Monte Carlo simulations.17,18 In the latter case,Henyey–Greenstein19 and Rayleigh–Gans13,20 phasefunctions are often used to describe the tissue aniso-tropic scattering. Typical values of g range between0.7 and 0.99 1Ref. 162 in the case of soft tissue in thedomain of wavelengths of interest, i.e., between 500and 900 nm. The similarity relation is especiallyvalid in this narrow interval.Therefore, the three parameters µs8, µa, and ntissue
enable the characterization of light propagation insoft tissue in a satisfactory way for numerous appli-cations. In addition, the refractive index of thetissue normally falls in a relatively narrow range,typically between 1.33 and 1.5 1Ref. 212 for thewavelengths of interest here.Several measurement techniques have been stud-
ied to obtain the effective scattering coefficient µs8and absorption coefficient µa in a noninvasive way.Among others, one canmention the pulsed photother-mal radiometry method,22 the acoustical method,23the time-resolved reflectance method,24 the fre-quency-domain reflectance method,25 and the spa-tially resolved steady-state diffuse reflectancemethod.26–30 Themeasurement technique describedhereafter is based on the last method mentionedabove. The concept is illustrated schematically inFig. 1. The tissue sample is locally illuminated by acollimated beam of unpolarized, monochromatic andcontinuous light. Part of the light, which has en-tered the tissue and has not been absorbed, isreemitted at the surface by diffuse reflection. Thesteady-state spatial distribution of this light aroundthe illumination spot, detected at the surface, can beused to determine the tissue optical properties.Several approaches are possible to define the
relationship between the spatial distribution of the
diffuse reflectance and the optical parameters for amacroscopically homogeneous medium. The firstone is experimental and consists of measuring thespatial diffuse reflectance of media with knownoptical properties. This approach takes into ac-count the probe characteristics and in particular theperturbations induced by the probe on the observedquantities. However, the determination of optimalmeasuring conditions 1geometry of the probe, etc.2 isdifficult in this way. Moreover, this method re-quires the production of numerous optical phantomswith different optical and geometric properties.Another method is based on numerical Monte Carlosimulations.17,18 This can be an accurate techniqueto study light propagation in a diffusing medium.The advantage of such a numerical technique is topermit light distribution shaping in complex experi-mental conditions. This approach has similar ad-vantages as the first one, without the problem ofhaving to create optical phantoms. This secondmethod has been used by Groenhuis et al.28 in thecase of a not very diffusing medium, which is ratherpoorly described by analytical models. Finally, thecurrently most widely used method is based onanalytical models and especially on diffusion mod-els.27–32 These models describe the diffuse reflec-tance distribution of highly diffusing media underrelatively simple experimental conditions that areusually difficult to satisfy in practice.In order to study light propagation in human
dental enamel 1<2 mm thick2, Groenhuis et al.27,28presented a model that can be used to describe thelight intensity distribution in a tissue slab of arbi-trary thickness and refractive index. The surfacewas assumed to be smooth and was illuminated by anarrow collimated light beam. The diffusion ap-proximation was used to determine the relativediffuse reflectance distribution at the tissue surface,especially its radial variation R1r2 as a function ofdistance r from the light source. R1r2was given by
R1r2 5 oi51
`
CiliK01lir2. 122
Parameters Ci and li depend on the optical andgeometric properties of the tissue sample and on the
Fig. 1. Principle of the tissue optical property measurementbased on the observation of diffuse reflectance at different dis-tances from the light source.
illumination beam radius.27 K0 is the modified Bes-sel function. Groenhuis et al. estimated that, intheir application, i.e., dental enamel of 2-mm thick-ness and wavelengths between 500 and 700 nm, themodel can be simplified, especially when the detec-tion is performed far away from the light source1r : 1@µeff2:
R1r2 < D1r21@2 exp12D2r2. 132
The Groenhuis et al. measurement algorithm con-sists therefore of determining constants D1 and D2from the full model 3Eq. 1224 or from Monte Carlosimulations performed with different optical param-eters, tissue thicknesses, and refractive indices.These calculated values of D1 and D2 are thencompared with those obtained by fitting the experi-mental measurement with the simplified model 3Eq.1324.To avoid absolute measurement of diffuse reflec-
tance, which is difficult to perform experimentally,Wilson and Patterson29 proposed a measurementtechnique based on the spatial variation of theln3R1r24 derivative. They showed that this relativemeasurement is strongly correlated to the reducedtotal interaction coefficient µt8 5 µa 1 µs8 close to thelight source and to the effective attenuation coeffi-cient µeff far away from the light source 1see Fig. 22.The diffusion model used by Wilson and Patterson isless complex than the Groenhuis et al. model. Itdescribes the radial distribution of diffuse reflec-tance in the case of an optically infinite tissuethickness and an infinitely narrow collimated beam.This model enables one to apply nonlinear least-square fitting algorithms to obtain iteratively thebest estimation of µeff and µt8 from the R1r2 measure-ment. Farrell et al. also tested a correlation tech-nique based on the use of a neural network in orderto reduce measurement time and sensitivity to mea-surement noise.33 The measurement probe pro-posed by Wilson and Patterson is clinically used forexternal tissue investigation only.One major problem in the medical application of
the diffuse reflectance technique is the great diver-sity of clinical experimental conditions 1optically thinor thick tissue sample, small hollow organs, etc.2.Actually, conditions have so far been defined by onesimple analytical model and were difficult to obtain
Fig. 2. Determination of optical parameters based on spatialvariation of the slope of ln3R1r24.
during an in vivomeasurement. In the absence of ageneral and accurate analytical model to describediffuse reflectance, we propose hereafter a techniquethat allows flexibility of the experimental conditionsas well as accuracy of measurement. This tech-nique allows mixing of the different previously men-tioned approaches to link diffuse reflectance andoptical properties, i.e., analytical models 1even com-plex2, Monte Carlo simulations, and the experimen-tal approach. The measurement method, althoughbased on complex diffusion models or Monte Carlosimulations, gives the necessary information formedical application in a time compatible with theclinical schedule.The sensitivity of the proposed method is strongly
dependent on the optical and geometric properties ofthe sample. A study of this sensitivity is presented,allowing us to determine the limitations of themeasurement technique and to deduce some condi-tions to obtain an optimal probe design. Two probesfor endoscopic measurements have been developedfor two different clinical applications. In vivo re-sults obtained in the esophagus are presented.
2. Measurement Technique
A. Method
Our technique to determine tissue optical param-eters in a clinical context from diffuse reflectance isbased on the measurement of the spatial variation ofthe ln3R1r24 derivative. The full Groenhuis et al.analytical model 3Eq. 1224 and Monte Carlo simula-tions are used to describe this. In the Groenhuis etal. diffusion model, there is no limitation to tissuethickness, but it should remainmuch larger than theeffective photon mean-free path. Optically, thesample has to be macroscopically homogeneous andisotropic. The surroundingmediummust be nondif-fusing with matching or mismatching boundary con-ditions, assuming a smooth surface. The light sourceis collimated and can have any chosen diameter.The accuracy of the Groenhuis et al. model wasassessed by using Monte Carlo simulations.30 Inparticular, it was necessary to evaluate the influenceof both the diffusion approximation and the similar-ity principle that have been assumed in order to dealwith the tissue anisotropic scattering. The simu-lated medium was mainly diffusing, i.e., µs8 . µa.Simulations were performed with several phasefunctions having the same anisotropy factor g, whichin general is between 0.7 and 0.99. Results showedthat the ln3R1r24 derivative is well described by theanalytical model whatever the scattering phase func-tion, i.e., the relative error is less than 2% as long asthe observation position is sufficiently distant fromthe light source, i.e., r:mfp8. In the vicinity of theincident collimated beam, the diffusion approxima-tion is no longer valid. Here Monte Carlo calcula-tions must be used instead of diffusion models.However, the similarity principle is also no longervalid whereas the mean number of scattering events
of the light measured at the tissue surface decreases.This can be compensated for by using the MonteCarlo simulation when the scattering phase functionis well defined and known. The absolute value ofR1r2 is strongly dependent on the phase function, andthe relative error does not decrease at larger dis-tances from the light source. The error is especiallylarge in the case of small albedo. These resultsemphasize that measurement techniques based ondetermining the absolute value of R1r2 should beavoided.The Groenhuis et al. diffusion model is not a
simple function of radial distance and optical proper-ties and is therefore difficult to invert; thus, it doesnot allow for a direct analytical expression for thetissue optical parameters. Classical correlationtechniques are also difficult to apply and are time-consuming. Moreover, under specific conditions1r 9 mfp8 or µs8 # µa2, Monte Carlo simulations, atime-consuming technique, must be used to describediffuse reflectance accurately. Regarding these con-siderations, the following clinically usable algorithmof measurement has been developed. The slope ofln3R1r24 is measured at only two distances from thelight source. As it has been already pointed out byWilson and Patterson29 and as we show below, if themeasurement position is close to the source, theslope of ln3R1r24 is primarily sensitive to reducedscattering coefficient µs8, and if this position is faraway from the illumination spot, the slope is closelyrelated to effective attenuation coefficient µeff.Consequently, it is possible to define a one-to-onecorrespondence between slopes of ln3R1r24 measuredat two distances from the light source and therelevant optical parameters. The optimal choice ofthese two measurement positions will be discussedhereafter. The optical parameters can then be ob-tained from the measured quantities by a graphicmethod. The principle of this technique consists ofdetermining the slopes of ln3R1r24 at both observationpositions using the full Groenhuis et al. model 3Eq.1224 or Monte Carlo simulation with different opticalparameters. Sample slab thickness and refractiveindex are selected. The calculated slopes are shownin a diagram such as that in Fig. 3. One can achieveextraction of optical parameters by locating themeasured slopes in the diagram. From µs8 and µeff,absorption coefficient µa can be obtained through Eq.112. A calibration procedure that consists of measur-ing media with known optical properties can also beused to complete and to improve the accuracy of thediagram.A major difficulty in designing a probe for a
particular clinical application is the choice of twomeasurement positions. This choice determines therange of optical properties measurable with suffi-cient accuracy. A limitation of this technique is theloss of sensitivity when the tissue sample is opticallythin. To investigate these two issues, the followingstudy of the measurement sensitivity is proposed.
B. Sensitivity
The sensitivity of the measurement method dependson several experimental conditions such as sampleoptical properties, sample thickness, chosen detec-tion positions and can strongly vary as a function ofthese parameters. The diagram used to determinethe optical properties from the measured slopesclearly exposes the sensitivity as a function of sampleoptical properties and can be used during the mea-surement to estimate the reliability of the results.The influence of other parameters such as samplethickness 1see Fig. 42 or sample refractive index 1seeFig. 52 can also be studied by the superposition ofdiagrams. In particular, this permits an estimationof the consequence of inaccurate knowledge of thesetwo parameters. To help design a probe for a par-
Fig. 3. Slopes of ln3R1r24 at two distances from the light source asa function of optical properties. The slopes were calculated usingthe Groenhuis et al. diffusionmodel. In this example, the samplethickness is 15 mm and the relative refractive index is 1.35,indicating an internal specular reflectance rd of 49% for anisotropic radiance distribution and a smooth surface.
Fig. 4. Slopes of ln3R1r24 at two distances from the light source,calculated for two different sample thicknesses, namely, 5 1s2 and15mm 1d2. The relative refractive index is 1.35 1rd 5 49%2. Thisfigure shows the influence of the thickness on the measuredquantities and on the measurement sensitivity.
ticular application, it is however useful to considerthe following analytical development.We define sensitivity Sµeff as the ratio between a
relative variation of the measured quantity, i.e., theslope of ln3R1r24, and a relative variation of µeff whenµs8 is kept constant. The same definition is used forSµs8. In other words, if m is the slope of ln3R1r24, Sµeffand Sµs8 are defined by
Sµeff5 0
Dm
m
Dµeffµeff
0µs85const
> 0µeffm
≠m
≠µeff 0µs85const
,
Sµs85 0
Dm
m
Dµs8
µs80µeff5const
> 0µs8m≠m
≠µs80µeff5const
. 142
From these quantities one can determine at bothmeasurement positions r1 and r2 the relative changeof m that is due to relative changes in both opticalparameters:
Em1r12 > Sµs81r12Eµs8
1 Sµeff1r12Eµeff
, 15a2
Em1r22 > Sµs81r22Eµs8
1 Sµeff1r22Eµeff
, 15b2
where
Em1ri2 5Dm1ri2
m1ri2, Eµi
5Dµiµi
.
By solving relations 15a2 and 15b2, an estimation of themaximal relative error of the optical parameters
Fig. 5. Slopes of ln3R1r24 at two distances from the light sourcecalculated for two relative refractive indices, namely, 1.5 1s2 and1.35 1d2, i.e., with, respectively, 60% and 49% of internal specularreflectance. The sample thickness is 15 mm. These relativerefractive indices can be considered as the utmost values observedat the tissue–air boundary for soft living tissues.21 In the case ofoptically thick samples, it appears that boundary conditions donot affect the determination of effective attenuation coefficientµeff.
that is due to a relative error in the measurement ofm can be obtained:
Eµs8>
1
Sµs81r12Sµeff
1r22 2 Sµeff1r12Sµs8
1r22
3 3Sµeff1r22Em1r12 2 Sµeff
1r12Em1r224, 16a2
Eµeff>
1
Sµs81r12Sµeff
1r22 2 Sµeff1r12Sµs8
1r22
3 32Sµs81r22Em1r12 1 Sµs8
1r12Em1r224. 16b2
The principle of measurement assumes, and itcan be verified to be usually true from Fig. 6, thatSµs81r12Sµeff 1r22: Sµeff 1r12Sµs81r22. In this case, relations16a2 and 16b2 can be simplified to
Eµs8>
1
Sµs81r12
Em1r12 2
Sµeff1r12
Sµs81r12Sµeff
1r22Em1r22, 17a2
Eµeff>
2Sµs81r22
Sµs81r12Sµeff
1r22Em1r12 1
1
Sµeff1r22
Em1r22. 17b2
As the absorption coefficient is obtained throughEq. 112, the maximal relative error in µa is deter-mined by
Eµa>
1
2µaµs8
1 1
Eµs81
21µaµs8 1 122µaµs8
1 1
Eµeff. 182
Fig. 6. Sensitivities of the determination of µs8 and µeff as afunction of the distance between the light beam and the position ofthe measurement. Sensitivity Sµeff has been calculated withseveral effective attenuation coefficients µeff typically observed insoft living tissues at wavelengths of interest in PDT.34 The Sµeffplot is shaded between the upper limit given by µs8 5 0.5 mm21
and the lower limit given by µs8 5 4 mm21. Sensitivity Sµs8 hasbeen estimated for different values of µs8. The Sµs8 plot is shadedbetween the upper limit given by µeff 5 0.1 mm21 and the lowerlimit given by µeff 5 2 mm21.
For specific cases we obtain the following expres-sions: If µs8 : µa,
Eµa< Eµs8
1 2Eµeff. 192
If µs8 < µa,
Eµa< 1@3Eµs8
1 4@3Eµeff. 1102
It appears that the relative error in µa is strongerthan the relative error in each of the other opticalparameters with a predominantly diffusing mediumsuch as living soft tissue.To evaluate relations 162 and 172, sensitivities Sµeff
and Sµs8 have to be estimated as a function of themeasurement position. First, the simple case of anoptically thick sample with matching boundary con-ditions is considered. In this situation, the diffu-sion model proposed by Patterson et al.31 and theGroenhuis et al. model give comparable results.As the first model has a more simple form, it can beused to evaluate sensitivities. With the Pattersonet al. model, the relative diffuse reflectance can bedescribed as follows:
R1r2 <z02p
exp32µeffŒz02 1 r24
z02 1 r2 1µeff 11
Œz02 1 r22 , 1112
with
z0 5 1@µs8. 1122
The slope of ln3R1r24 is then given by
m1r2 5d
drln3R1r24 5 2µeff
r
Œz02 1 r2
22r
z02 1 r22
r1z02 1 r2223@2
µeff 11
Œz02 1 r2
. 1132
Figure 6 shows the sensitivities Sµeff and Sµs8 as afunction of the measurement distance from the lightsource. These sensitivities have been evaluatedwith different optical properties. As can be seen inFig. 6, the sensitivity of the determination of µs8 isstrongly dependent on the measurement position.The sensitivity of µeff is close to 1 for most tissueoptical properties, as long as the measurement posi-tion is far enough away from the light source.From this sensitivity study it appears that the first
measurement position has to be chosen as close aspossible to the light source. However, as it has beenpreviously pointed out, the similarity principle con-cerning the phase function can no longer be assumedif the measurement position is too close to the lightsource. In this situation, diffuse reflectance can nolonger be evaluated by optical parameters µeff and µs8only. This limitation does not depend on the model
used to describe diffuse reflectance 1diffusion model,Monte Carlo simulation, or experimental model2.As a rule, the first measurement position has to bechosen at a distance greater than 1@µs8. To improvethe sensitivity of µeff, the second measurement posi-tion has to be selected as far as possible from thelight source. However, on the other hand, the dis-tance between light source and detector is limited bythe signal-to-noise ratio, which depends on the instru-mentation. Moreover, in some clinical applications,the size of the probe is limited by the measurementsite geometry and@or by the volume of the tissuesample.From Fig. 6 and Eqs. 162, the maximal relative
error in each optical parameter can be estimated as afunction of measurement error in the slope of ln3R1r24that can be attained with a particular probe design.A sample of finite thickness is now considered.
Once again the sensitivity of the determination of µeffis maximal if the slope is measured at a largedistance from the light source. However, this sensi-tivity decreases in thin samples. Indeed, in opti-cally thin samples, the spatial distribution of diffusereflectance is determined to a large degree by theboundary conditions. In a thin slab slope m, mea-sured at a large distance from the illuminationsource, is defined in the Groenhuis et al.model by
m 5 l1 5 Œk12 1 µeff2, 1142
where k1 is the first nontrivial root of the followingequation:
tan1k1d2 52hk1
h2k12 2 1, 1152
where
h 52
31µa 1 µs82
11 1 rd2
11 2 rd2, 1162
d is the sample thickness, rd is the internal specularreflectance35 < 21.4399ntissue22 1 0.7099ntissue21 10.6681 1 0.0636ntissue 1in the case of a boundary withrelative refractive index close to 1.352, and ntissue isthe relative tissue refractive index.The maximum sensitivity Sµeff
max, i.e., the sensitiv-ity of determination of µeff observed at a largedistance from the light source, can then be defined
Sµeffmax < 0
µeffm
≠m
≠µeff 0µs85const
<µeff2
k12 1 µeff2
1if µs8 : µa2. 1172
From Eq. 1152 it appears that k1 increases whenthickness d decreases. Consequently, Sµeff
max alsodecreases. It is now interesting to determine thesmallest sample thickness dmin that enables one to
This relation is true as long as the validity of thediffusion model is true. Namely, the thickness hasto be at least larger than the effective mean-freepath, i.e., dmin . 1@1µa 1 µs82. The result is shown inFig. 7 for the case of Sµeff
max* 5 50%.This loss of sensitivity in thin samples can reduce
the possibilities of applying the technique for thestudy of stratified or thin tissue layers. However, itcan be shown using a similar approach that thesensitivity in the determination of µs8 is only slightlymodified by the sample thickness if the observationposition is close enough to the light source.
C. Instrumentation
The first noninvasive probe30 was designed to allowin vivo clinical measurements to be made duringendoscopic procedures in hollow organs such as theesophagus. A schematic view of this probe is shownin Fig. 8, and the experimental setup is illustrated inFig. 9. The probe consists mainly of two opticalfibers 1AS200-2802. The first fiber is fixed in theprobe and guides the monochromatic illuminationlight from the light source 1cw Ar1, He–Ne, or dyelaser2 to the tissue surface. The second optical fiberis movable and measures the backscattered light atdifferent distances from the illumination spot. Theprobed light is guided to a photomultiplier 1Hama-matsu R9552, where the signal was amplified byusing a lock-in technique. A monochromator isinserted between the fiber and the photomultiplierin order to avoid as much as possible significantinterference from the tissue autofluorescence. One
Fig. 7. Minimal sample thickness in order to obtain a maximalsensitivity for µeff of 0.5.
can perform fiber displacement using a computer-controlled motor. The probe surface that is in con-tact with the tissue is a blackened glass mask with36 small holes arranged in increments of 0.76 mm.Through these holes, the detection optical fiberprobes the diffusely reflected light. In this way,each hole defines one measurement of R1r2, theposition of which is accurately known. The dis-tance between the light spot and the first hole is 3.5mm. This first noninvasive probe based on a scan-ning optical fiber has the advantage of enabling goodwavelength flexibility, spectral control of the de-tected light, and a broad measurement domain.Furthermore, high sensitivity and dynamics can beobtained without a calibration procedure.The second prototype has been designed to mea-
sure the optical properties of the esophagus ingeometric conditions identical to those used in PDT.Indeed, for PDT in the esophagus we developed acylindrical light distributor7 with different diam-eters, generally 15–20 mm. Such diameters aresuited to distend and to smooth the esophageal wallin order to obtain a uniform and well-defined lightdistribution at the surface of the organ. The dila-tion of the esophagus wall induces a change of tissueoptical properties. This effect must be taken intoaccount for accurate light dosimetry in PDT. Thesecond prototype of a noninvasive probe is shown inFig. 10. This design for endoscopic measurement issomewhat similar to that proposed by Wilson andPatterson for external applications.29
Fig. 8. Schematic view of the noninvasive probe for measuringtissue optical parameters.
Fig. 9. Schematic diagram of the experimental setup for thenoninvasive optical probe.
Afirst optical fiber 1AS 200@2802 with a small 10.212numerical aperture 1NA2, supplies a quasi-collimatedlight beam at the tissue surface. The radiant powerat the end of the optical fiber is typically 15 mW.This value is not large enough for generating athermal effect. Six polymer optical fibers 1PFU-FB500 Toray2 were used to collect the backscatteredlight at different distances from the light source.These fibers have a large acceptance angle 10.46 NA2.The distances between the illumination spot and thedetection optical fiberswere determined by the follow-ing conditions. In our application, wemeasured theoptical properties of the esophageal wall mainly at514 and 630 nm. Both wavelengths are of interestin PDT with the photosensitizers used at present inour and other ear, nose, and throat clinics. Prelimi-nary ex vivo measurements have shown that theoptical properties of the esophageal tissue are typi-cally µs8 5 1 mm21 for both wavelengths, and µeff is 1or 0.3 mm21 at 514 and 630 mm, respectively.Based on these values and the sensitivity argumentsproposed in Subsection 2.B, we selected themeasure-ment distances that are shown in Fig. 11. In thepreliminary in vivo measurements we used the firsttwo optical fibers to determine, at both wavelengths,the slope of the diffuse reflectance close to the lightsource. The next two optical fibers allowed us todetermine the second slope at 514 nm. Finally, thelast two fibers were considered for the measurementof the second slope at 630 nm. Of course, othercombinations of the six light intensity measurementdistances can be used in order to optimize thesensitivity in the case of other optical propertiesand@or to increase the signal-to-noise ratio.
3. Experimental Results
A. Measurements with White Polyoxymethylene Samples
Measurements with white polyoxymethylene 1POM2samples were performed with the first prototype
Fig. 10. Schematic view of the second noninvasive prototypeprobe, which was developed for in vivo measurement in theesophagus in the red 1630 nm2 and in the green 1514 nm2. Thedilator facilitates the insertion of the probe into the esophagus.
Fig. 11. Measurement positions in the second probe.
probe and illustrate the possibilities and limitationsof the proposed technique. They were made withwhite POM samples of several thicknesses. Thewavelength was 633 nm 1He–Ne laser2. Figure 12shows radial distributions of diffusely reflected lightat the sample surface. The influence of the samplethickness is obvious. In Fig. 13, diagrams thatcorrespond to the different thicknesses concernedare superimposed and the slopes measured fromeach sample are plotted.With the thicker sample 120 mm2, optical param-
eters are easily estimated: µeff < 0.075 mm21, µs8 <0.6 mm21. From Eq. 112 one can then obtain µa <0.003 mm21. Sensitivities of the determination ofµeff and µs8 are, respectively, 21% and 32%. Theseresults are in agreement with the study of sensitivitypresented in this paper. Indeed, with a slope mea-surement made at a distance of 20 mm from the lightspot and in the range of optical parameters consid-
Fig. 12. Radial distribution of diffusely reflected light at 633 nmmeasured at the surface of white POM samples of differentthicknesses. These measurements were performed with the firstprobe.
Fig. 13. Diagram that was used to determine optical parametersof white POM samples of different thicknesses. The model datawere obtained from the Groenhuis et al. diffusion model.Measurements were determined from the radial distribution ofdiffusely reflected light at 633 nmmeasured with the first probe.
ered, the sensitivity of µeff with an optically thicksample would be less than 40% of the maximalsensitivity 1see Fig. 62. However, from Fig. 7 itappears that the maximal sensitivity is lowered by afactor of 2, if the thickness of the sample is close to 25mm. The sensitivity of µs8 predicted from Fig. 6 isclose to 30% at a distance of 4.2 mm from theillumination spot and is not significantly modified bythe slab thickness in the range of thicknesses consid-ered here 1see Fig. 122.When the sample thickness decreases, the diffuse
reflectance distribution is more determined by theboundary conditions. The sensitivity consequentlydecreases, as is apparent from Fig. 13, and, inparticular, the sensitivity associated with the slopemeasurement at a large distance from the illumina-tion spot. The optical parameters can still be evalu-ated from the measurement of the 10-mm-thicksample, but the sensitivity of µeff is weak. Thesensitivity of µs8 is relatively constant. It becomesdifficult to determine µeff accurately from the mea-surement of the 6- and 3-mm-thick samples. Asthis example illustrates, the graph correlation tech-nique enables rapid evaluation of the reliability ofthe measurement procedure.It is important to emphasize that white POM and
living tissue have different optical properties at 633nm. POM is a simple optical phantom with stableand reproducible properties, but its absorption isparticularly weak at 633 nm. Therefore, thick-nesses considered in this example and loss of sensitiv-ity are not comparable with those observed in livingtissues. The thickness that induces a decrease by afactor of 2 of the sensitivity of µeff is approximately 25mm with POM at 633 nm 1see Fig. 72. In the case ofsoft living tissues, this thickness is typically betweenapproximately 2 and 6 mm at this wavelength,depending on the type of tissue, and decreases toapproximately 1 mm at 514 nm.
B. In vivo Measurements with Biological Tissues
Preliminary in vivo measurements were performedin patients with the first probe at 630 and 514 nm onthe inner wall of the oral cavity. Another semi-invasive technique was applied on the same patients.This second technique consisted of measuring thespace irradiance in the tissue by means of a smallisotropic detector.30 Consistent results were ob-tained with these two techniques.36 The buccalcavity was selected as the model for the esophagealwall. Indeed, the mucous membrane that linesthese two organs is similar, and the buccal cavityallows for good accessibility.In vivo measurements were performed with the
second prototype probe at 630 and 514 nm in theesophagus of patients. As mentioned in Section 1,an accurate knowledge of light distribution in theesophageal wall is particularly interesting in PDT toavoid severe medical complications such as perfora-tions of this wall 1fistula2.5 These measurementswere done on noninjected patients to avoid a limita-tion on tissue illumination duration and therefore to
allow numerous measurements of the same spot inthe esophagus. For each patient, several measure-ments were performed in different areas. Resultsobtained at 630 nm are shown in Fig. 14. The largevariance of the measured values was also observedat 514 nm and is probably due to the real variance oftissue optical properties and to some measurementerrors, in particular, those induced by tissue inhomo-geneities in the esophagus. This topic is discussedhereafter.
4. Discussion
The proposed noninvasive measurement techniqueis based on the observation of spatial distribution ofdiffuse reflectance at two positions only. It has beenshown that the sensitivity of this method stronglydepends on the choice of measurement positions, onthe optical properties of the medium, and on samplethickness. The graphic method for determiningoptical parameters enables a rapid and simple evalu-ation of this sensitivity. Furthermore, this methodalso enabled us to estimate the consequential effectsof measurement errors on the optical parameters.These errors have several origins. The first and
main origin is the discrepancy between a real tissuesample and its ideal model taken for our measure-ments. In particular, macroscopic optical homoge-neity is nonexistent in the wall of a real organ. Partof the variance observed in the in vivo measure-ments in the esophagus is probably due to thisproblem. The presence of small inhomogeneitiesclose to one of the detection fibers, such as a narrowblood vessel, might induce a significant error. Theinfluence of this effect can be reduced by performingseveral measurements at different locations. An-other kind of inhomogeneity occurs in stratifiedtissues. Indeed, histological layers, in general, ex-hibit different optical properties. In the esophagus,the wall is particularly thin5 1typically 2.1 mm thickunder our measurement conditions2. It is composedof mainly two kinds of tissue: a first layer ofconnective tissue 1approximately 0.8 mm thick2 and asecond layer of muscle 1approximately 1.3 mm thick2.Moreover, the esophagus is surrounded by differentkinds of tissue, such as fatty tissue, muscle, andlarge blood vessels whose optical properties can bedifferent. This problem has not been resolved until
Fig. 14. In vivo measurement performed at 630 nm in a humanesophagus; 51 measurements were done on 11 patients with thesecond probe.
now, and we have assumed similar optical propertiesthroughout the whole tissue sample.A second source of errors is the model that de-
scribes the relationship between microscopic opticalparameters and the observed quantities. The preci-sion of this model is limited, in our case, by theapproximations used to resolve the transport equa-tion and by the validity of the similarity principle.This source of errors can be partially eliminated byusing Monte Carlo simulations.Instrumentation is the third source of measure-
ment errors. First, it induces systematic errors.Indeed, the probe cannot be used tomeasure interest-ing quantities precisely under the model conditions,either because the probe induces a perturbation onthe observed light distribution, or the measuredsignal is not exactly the signal described by themodel, for example, resulting from the measurementof diffuse radiance on a limited solid angle. Thesesystematic errors can be significantly reduced byusing the calibrated experimental procedure men-tioned above, i.e., measurements on optical phan-toms or the method based on Monte Carlo simula-tions. Finally, instrumentation induces statisticalerrors. Part of these errors is determined by opticaldetection noise. The relative error in the determina-tion of slopes with the second probe that is due to thisnoise is estimated to be less than 2% by measure-ments on optical phantoms with homogeneous andstable properties. The large variance of the mea-surements in the esophagus is apparently not in-duced by this effect.
5. Conclusion
In the medical field in which light is used for therapyand diagnosis, there is a need for information on theoptical properties of living tissues in order to beefficient and safe. To be relevant, these opticalproperties have to be measured in situ. Conse-quently, the measurement technique must generallybe noninvasive and applicable in different experimen-tal geometries 1narrow hollow organs, optically thinor thick tissue sample, etc.2. Moreover, thismeasure-ment has to be performed in a sufficiently short timeto be compatible with the clinical schedule.The measurement of diffuse reflectance is an
interesting noninvasive way to obtain informationabout optical properties. The lack of a general andaccurate analytical model to analyze the diffusereflectance was a limitation for the clinical applica-tion of this technique. The solution proposed hereis based on a relative measurement of the diffusereflectance at two distances from the light sourceonly. This approach is not limited to only oneanalytical model, but allows one to choose the bestmodel for the considered experimental conditions1diffusion model, Monte Carlo simulations, or opticalphantoms with known optical properties2.With the approach that we have outlined, themain
difficulty encountered when one designs a probe for aparticular application is the choice of the two mea-surement positions. For this purpose, a study of
the measurement sensitivity is a first step. It hasbeen shown that this sensitivity is dependent on themeasurement positions and that these positionshave to be chosen according to the range of opticalproperties in view. We have also pointed out thedecrease of sensitivity when the sample thicknessdecreases, and how this decrease can be predicted.Two different prototype probes have been devel-
oped. The first was dedicated for general-purposemeasurement over a large range of optical param-eters, whereas the second was specially designed tomeasure optical properties in the esophagus at twowavelengths of interest in PDT. Preliminary re-sults obtained at 514 and 630 nm have given usefulinformation for optimizing the PDT of early superfi-cial cancers in this organ. Large variance, probablya result of the optical heterogeneities of the tissueconsidered, has been observed in the esophagus,whereas such fluctuations have not been observedwith other living tissues such as muscle.
The authors are grateful to the Swiss FondsNational, Centre Hospitalier Universitaire Vaudois,Ecole Polytechnique Federale de Lausanne, Univer-site de Lausanne program of collaboration in biomedi-cal technology, the Swiss National Priority Programin Optics, and Ciba-Geigy for financial support.
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