3.1.

Probe Preparation

A two-fiber side-firing probe was developed for steady-state diffuse reflectance measurements via the working channel of an endoscope, delivering and collecting light into/from the tissue at 90 deg relative to the axis of the fibers (Fig. 2). Two pieces of 620 μm diameter stainless steel rod were cut 12 mm long and one end of each was polished at a 45° angle to create a mirror. Two lengths of stainless steel tubing (inner diameter=660 μm, outer diameter=830 μm) were cut 8 mm long and a hole was made in each through one side of the tube wall using a 0.025 in. (635 μm diameter) end mill. The holes in the tubing were spaced 2 or 4.5 mm from the end for use as the source or the detector fiber, respectively. The polished steel rods were aligned inside the tubing such that the 45° mirror surface would reflect light through the hole. Two optical fibers (silica–silica, 600 μm core diameter, 3 m long; Ceramoptec Industries Inc., East Longmeadow, MA) were polished flat and one fiber was inserted through the open end of each tube. The optical fiber, rod/mirror, and tube were fixed in place by filling the internal spaces of the tube with clear epoxy (Epo-Tek 301; Epoxy Technology, Billerica, MA), and curing at 60 °C for 4 h. Excess rod was trimmed and filed to remove sharp edges. The source (with hole 2 mm from the end) and detector (with hole 4.5 mm from the end) were aligned side by side and bonded together by epoxy with the two holes facing toward the same side. The remaining 3 m optical fibers were inserted into Teflon tubing (PTFE 17LW; Zeus Industrial Products Inc., Orangeburg, SC). The tip of the probe was sealed with medical grade silicone glue and a 2 cm piece of heat-shrink Teflon tubing (14HS; Zeus Industrial Products Inc., Orangeburg, SC). The probe was sterilized with ethylene oxide gas prior to patient use.

Figure 2

Top and lower left: Photo and diagram of the two-fiber probe design for reflectance measurements. A 45° polished steel mirror directs source light from one 600 μm optical fiber 90° out the side of the fiber. A second mirror and fiber collect light for detection. Source-collector separation is 2.5 mm. Lower right: the probe is passed through working channel of an endoscope.

3.2.

Reflectance Measurements

Reflectance measurements of normal and cancerous esophagus, lung, and oral mucosa were taken with the reflectance system shown in Fig. 3. White light from a tungsten lamp (QTH6333, Oriel Instruments, Stratford, CT) was used as the source. The signal was detected with a diode array spectrophotometer (S2000, Ocean Optics Inc., Dunedin, FL). The fiber probe used was described in the previous section.

Figure 3

Reflectance system setup. Light from a tungsten lamp is guided through the two-fiber optical probe. Reflectance spectra is acquired with a spectrophotometer and recorded in a laptop.

During the clinical procedures the physician positioned the reflectance probe at normal sites (all patients) and tumor sites (PDT patients) according to his clinical evaluation of the tissue. Accurate positioning of the probe was possible due to maneuverability of the endoscope and the fact that a distinct spectrum (Fig. 4) was obtained when proper probe contact was achieved. Typical measurement-to-measurement variation on a single site was approximate 10%. Three sites were measured per patient/disease, and the reflectance spectra were later analyzed to determine the tissue optical properties. The endoscope illumination was turned off while the spectrum for a given site was acquired (200 ms acquisition time). The probe was calibrated by topical placement on an epoxy/titanium-dioxide solid phantom immediately after the procedure. The solid epoxy standard was previously calibrated with integrating sphere measurements and inverse adding-doubling^{8 23} modeling to specify its optical properties. Figure 4 shows the raw reflectance spectra for one of the patients. Lower intensities in the 500–600 nm range are due to blood absorption.

Figure 4

Typical reflectance raw data for three normal and three tumor sites of esophageal tissue (patient No. E1). A measurement of 2% intralipid is also shown for comparison.

3.3.

Empirical Forward Light Transport Model

The reflectance spectra used an empirical light transport function determined by experimental calibration of the reflectance probe with a matrix of tissue simulating phantom gels. This experimentally determined transport function behaves similar to that of diffusion theory with a mismatched air/tissue boundary, but accurately accounts for the performance of the actual probe device with its particular geometry and construction as described in the following sections.

3.3.1.

Preparation and calibration of the tissue phantom gel matrix

An 8×8 matrix of acrylamide gel tissue simulating phantoms was prepared using Intralipid (Liposin II, Abbott Laboratories, North Chicago, IL) as the scattering element and India ink (No. 4415, Higgs, Lewisburg, TN) as the absorber. The absorption coefficient of the stock ink was determined with an ultraviolet (UV)-visible spectrophotometer (model 8452A, Hewlett-Packard, Palo Alto, CA). A matrix of 64 gels was prepared with all combinations of eight different reduced scattering coefficients and eight different absorption coefficients. Samples were prepared to yield final Intralipid concentrations of 7%, 5%, 3.5%, 2.5%, 1.5%, 1.0%, 0.5%, and 0.25% (gram lipid/mL solution times 100%). Final range of the gels reduced scattering coefficient at 630 nm was 1–28 cm⁻¹. Different aliquots of India ink were added to yield final absorption coefficients of the gels at 630 nm of 0.01, 0.1, 0.4, 0.9, 1.6, 2.5, 4.9, and 6.4 cm⁻¹. Gels were prepared by adding aliquots of Intralipid, India ink, 45 mL of acrylamide solution (40% concentration) and water to a final volume of 100 mL (4 cm height by 5 cm diameter). The final gel was 18% acrylamide. Stock acrylamide was prepared by diluting 1.4 kg of acrylamide acid (BP170-100, 99%, electrophoresis grade, Fisher Scientific, Pittsburgh, PA) and 35 g of bis-acrylamide (BP171-25, Fisher Scientific, Pittsburgh, PA) in water (1:40 ratio) to create a final volume of 3.5 L (40% concentration). Samples were gelled by adding 0.4 g of ammonium persulfate (BP179-25, Fisher Scientific, Pittsburgh, PA) and 100 μL of TEMED (BP150-20, Fisher Scientific, Pittsburgh, PA) in each 100 mL sample. Figure 5 is a picture of the samples.

Figure 5

Picture of the 8×8 acrylamide gel matrix. Rows from top to bottom have final Intralipid concentrations of 7%, 5%, 3.5%, 2.5%, 1.5%, 1.0%, 0.5%, and 0.25%. Columns from left to right have final absorption coefficients at 630 nm of 0.01, 0.1, 0.4, 0.9, 1.6, 2.5, 4.9, and 6.4 cm⁻¹. All samples have 18% acrylamide gel concentration (see text) and a final volume of 100 mL.

Acrylamide did not change the absorbing properties of the added ink (as experimentally verified for an absorbing only gel), however, the scattering properties of the added Intralipid were assumed to change when added to the gels. This assumption was based upon experiments done with samples before and after gelling (data not shown). Optical properties of the final gel samples were determined by measuring the total reflectance with an 8 in. diam integrating sphere (IS-080, Labsphere Inc., North Sutton, NH). Samples were placed directly at the open port (1 in. diam) of the integrating sphere. Illumination of the sample was provided by a 600 μm diam optical fiber positioned inside the integrating sphere through a stainless steel tube 5 mm away from the sample, which yielded a 3 mm diameter spot at the sample surface. Total diffusely reflected light was collected with a 600 μm diam optical fiber positioned in another port of the sphere. A baffle was positioned between the two ports. The setup is shown in Fig. 6.

Figure 6

Setup of the integrating sphere used for calibration of the acrylamide samples. White light from a tungsten halogen lamp is guided through an 600 μm diam optical fiber positoned 5 mm away from the sample, inside the integrating sphere, forming a 3 mm diameter spot. Reflectance spectra is detected through a 600 μm diam optical fiber with a diode array spectrophotometer. Spectralon standards are used to calibrate the reflectance measurements.

Measurements of Spectralon standards (Labsphere Inc., North Sutton, NH) were taken to calibrate the sphere. Reduced scattering (μ_s ^′) and absorption (μ_a) coefficients were determined using a combination of the added-absorber²⁴ and adding-doubling^{8 23} methods to predict the total diffuse reflectance (R_i ^AD) for comparison with the measured total diffuse reflectance (R_i ^EXP ) in a least square minimization routine (Nelder-Mead simplex algorithm). Determination of the two parameters (μ_s ^′ and μ_a) with only one measurement of total diffuse reflectance is possible because of the knowledge of the added absorber to all samples. The minimization was done wavelength-by-wavelength using the samples with the five lowest ink concentrations (D_i ^ink =0, 0.0003, 0.0010, 0.0024, 0.0040, corresponding to 0.01, 0.1, 0.4, 0.9, and 1.6 cm⁻¹ at 630 nm, respectively) for each Intralipid concentration. Figure 7 shows a flow chart of the minimization.

Figure 7

Flow chart of the minimization process to determine the Intralipid absorption coefficient (μ_a0) and the reduced scattering coefficient (μ_s ^′) for each wavelength λ_j and for each Intralipid concentration. The samples with five lowest dilutions of ink (i=1–5) were used to determined μ_a0 and μ_s ^′. Least square minimization is performed between the reflectance calculated with adding-doubling and the reflectance experimentally measured. Effectively this finds the best μ_a0 and μ_s ^′ for each wavelength from five measurements on samples with the same scattering coefficient and known differences in absorption.

3.3.2.

Probe calibration

All 64 acrylamide gel samples and the epoxy/titanium-dioxide solid standard were measured with the probe. A drop of water aided optical coupling between the gel and the optical fiber probe. Measurement-to-measurement variation decreased from approximately 20% without optical coupling to less than 5% with optical coupling.

Reflectance measurements on samples (M_s) were normalized by the epoxy/titanium-dioxide (epoxy- TiO ₂) solid standard (M _std ). The final spectrum was the ratio M:

Eq. (4)

$$M(\lambda )=\frac{M_s\left(\lambda \right)}{M_{\text{std}}\left(\lambda \right)}=\frac{S\left(\lambda \right)R_s\left(\lambda \right){\eta }_s\left(\lambda \right)D\left(\lambda \right)}{S\left(\lambda \right)R_{\text{std}}\left(\lambda \right){\eta }_{\text{std}}\left(\lambda \right)D\left(\lambda \right)}=\frac{R_s\left(\lambda \right){\eta }_s\left(\lambda \right)}{R_{\text{std}}\left(\lambda \right){\eta }_{\text{std}}\left(\lambda \right)},$$

where S(λ) (W) is the light source power, D(λ) (counts/W) is the detector sensitivity, R_s(λ) (l/cm ²) is the optical transport into the medium and returning to the sample surface at the collection fiber, η_s(λ) (dimensionless) is the optical fiber collection efficiency for the sample, η _std (λ) (dimensionless) is the optical fiber collection efficiency for the standard, and R _std (λ) (dimensionless) is the reflectance of the epoxy/titanium-dioxide solid standard (0.65 at 630 nm).

The terms S (the source spectral response) and D (the detector spectral response) are the same for samples and standard measurements and do not vary within a measurement procedure and thus cancel in Eq. (4). The normalized measurement, M(λ), was multiplied by the reflectance of the standard [R _std (λ)] determined with the integrating sphere setup shown in Fig. 6 to yield the adjusted normalized measurement M^*(λ) [Eq. (5)]:

Eq. (5)

$$M^{*}(\lambda )=\frac{M_s(\lambda )}{M_{\text{std}}(\lambda )}{R}_{\text{std}}(\lambda )=R_s(\lambda )\frac{{\eta }_s(\lambda )}{{\eta }_{\text{std}}(\lambda )}\text{.}$$

The term M^* incorporated the actual light transport of the sample multiplied by the ratio between the optical fiber probe collection efficiency for the sample and the standard.

Each phantom gel yielded a spectrum of reflection values (λ=480–925 nm). With the knowledge of the optical properties of the samples from the integrating sphere measurements a light transport map was generated for each wavelength by interpolating the 64 normalized measurements [M^*(λ_i)] as follows:

1. (a) The 64 measurements for one wavelength (e.g., λ=630 nm) were plotted on a grid of absorption (μ_a) and reduced scattering (μ_s ^′) coefficients [Fig. 8(a)].

2. (b) A piecewise linear interpolation of the eight adjacent points in the reduced scattering dimension was made using the function interp1 in Matlab as shown in Fig. 8(b), i.e., M^*(μ_s ^′) at each of the eight known μ_a.

3. (c) The result of the linear interpolation was plotted on the same grid of absorption (μ_a) and reduced scattering (μ_s ^′) coefficients [Fig. 8(c)].

4. (d) The eight adjacent points in the absorption dimension were fitted with an exponential curve [Eq. (6)] as shown in Fig. 8(d):

   Eq. (6)

   $$M^{*}({\mu }_a,{\mu }_s^{\prime })=C_1({\mu }_s^{\prime })e^{-{\mu }_a{L}_1({\mu }_s^{\prime })}+C_2({\mu }_s^{\prime }),$$
   where the constants C₁, L₁, and C₂ are a function of the μ_s ^′.

5. (e) The resulting constants C₁, L₁, and C₂ (Fig. 9) were used with Eq. (6) to interpolate the remaining values in the transport map as shown in Fig. 8(e).

Figure 8

Creating the light transport maps used as forward model for the reflectance measurements. This is an example for one wavelength (630 nm). (a) Log base 10 of the normalized measurement M^* for the 64 samples at 630 nm displayed in a grid of absorption and reduced scattering coefficient. (b) Linear interpolation of the eight data points with the lowest μ_a in (a). (c) Log base 10 of the normalized measurement M^* obtained from the linear interpolation in (b). The points highlighted by the white line are shown in (d). (d) Exponential fit according to Eq. (6) of data highlighted in (c). (e) Light transport map at 630 nm constructed with the coefficients shown in Fig. 9 and Eq. (6).

Figure 9

Coefficients C₁, L₁, and C₂ used to reconstruct the map on Fig. 8 (630 nm). The coefficients were fitted to polynomials (lines) to speed the calculation of the light transport.

To speed the calculation of the light transport the coefficients C₁, L₁, and C₂ were fit to polynomial functions of orders 4, 15, and 15, respectively. The use of high order polynomial functions for L₁ and C₂ was necessary because of the rapid changes in these coefficients as a function of reduced scattering coefficients. Nevertheless, Fig. 9 shows that C₁, L₁, and L₂ were well-behaved functions of μ_s ^′. Fitted values beyond the limits of maximum and minimum coefficient values were discarded (shadow regions on Fig. 9).

3.4.

Modeling of Tissue Reflectance with the Empirical/Spectral Model

The analysis of reflectance assumes (1) that the reduced scattering coefficient of the tissue behaves as a power of the wavelength¹⁸ and (2) that a linear combination of chromophore spectra can fully approximate the absorption coefficient.¹⁸ Tissue absorption was modeled as a linear combination of water (μ_a ^water ), a background spectrum for dry bloodless tissue (μ_a ^dry ), and a variable blood volume fraction (f_v) of oxygenated and deoxygenated whole blood (μ_a ^oxy ,μ_a ^deoxy ) at an oxygen saturation (SO ₂). The fraction of water was kept fixed at 75%. In principle, the water content could be fit, but our system was not sufficiently sensitive in the 900–1000 nm spectral region where water strongly influences the spectra.

Tissue scattering can be represented by a simple expression, aλ^−b, that mimics the Mie scattering from larger tissues structures such as collagen fiber bundles, mitochondria, nuclei, and cells.²⁵ The Rayleigh scattering (∝λ⁻⁴) was neglected in this modeling effort because our spectra were acquired above 480 nm and were not sensitive to Rayleigh scattering. The absorption coefficient (μ_a) and reduced scattering coefficient (μ_s ^′) were specified as

Typical spectra for μ_a ^dry , μ_a ^water , and the μ_a ^oxy and μ_a ^deoxy for whole blood at 45% hematocrit are shown in Fig. 10.²⁶

Figure 10

Spectra of tissue chromophores used in Eq. (7). Oxy and deoxy spectra are for 45% hematocrit blood.

The absorption of dry tissue was assumed to behave as an exponential decay, as suggested by Saidi.²⁷ This approximation was used to represent the sum of the effect that all chromophores with Soret band in the UV-blue spectral region (e.g., collagen fibers, bilirubin, porphyrins, etc.) have on the absorption coefficient in the visible range.

Measurements on the solid standard made of epoxy, titanium dioxide (TiO ₂) and ink used to normalize the acrylamide gel phantoms (Sec. 3.3.2.) were taken to correct for day-to-day variations in the wavelength and magnitude dependence of the light source and detector sensitivity. As an example, normalized data from Fig. 4 is presented in Fig. 11.

Figure 11

Data from Fig. 4 normalized by the measurement of the epoxy standard (M _std ) and multiplied by the standard reflectance (R _std ) as an example of the normalization given by Eq. (6) to yield M^*.

In effect six parameters were determined from each reflectance spectrum by a least square minimization. The fitting process consisted of two phases. First, only the measurements at the isosbestic points (500, 530, 545, 570, 584, 796 nm) were used (so that oxygen saturation is unimportant) to determine a, b, blood fraction (f_v), A, and B. This produced a value for b that was held constant in the second fitting and optimized initial guesses for a, blood fraction (f_v), A and B. The second fitting allowed a, blood fraction (f_v), blood oxygen saturation (SO ₂), A and B to vary and used the entire reflection spectrum. Specifically,

3.5.

Validation of the Empirical Model with a Diffusion Model

Measurements of bovine muscle were made to validate the model. An in vitro tissue measurement was preferred to the use of phantoms composed of scatters such as intralipid or microspheres and absorbers such as India ink or other chemical chromophores because of the model dependence on the spectra of the tissue components (oxy and deoxy blood, water, etc.). Bovine muscle was bought fresh from the local abattoir and was approximately 24 h postmortem at the time of the measurements. Tissue was kept refrigerated and wrapped in plastic until the time of use. Three sites in three different samples were measured.

Optical properties of the samples were determined using the empirical model described in the previous sections and compared to optical properties determined by a wavelength-by-wavelength model using the total diffuse reflectance measurement (R_t) in conjunction to a spatially resolved steady-state diffuse reflectance measurement (R_d). The measurement R_t was done with the integrating sphere setup shown in Fig. 6. The measurement of R_d was made with an optical fiber probe composed of five 400 μm diam optical fibers linearly spaced 1.524 mm (0.060 in.) apart. The first fiber was used to illuminate the tissue with a white light tungsten lamp (QTH6333, Oriel Instruments, Stratford, CT). The remaining four fibers were connected to a four-channel diode array spectrophotometer (S2000, Ocean Optics Inc., Dunedin, FL). A measurement of the epoxy- TiO ₂ standard referred on Sec. 3.3.2 was taken to normalize the tissue measurements. This normalization was done to cancel the source and detector spectral variation. Optical properties were determined by fitting the experimental measurements R_t and R_d to adding-doubling^{8 24} and diffusion theory^{16 28} models, respectively, wavelength-by-wavelength, as follows:

3.6.

Patients

Patients undergoing endoscopic screening for esophageal diseases and patients undergoing photodynamic therapy for esophageal, lung, and oral cavity cancer treatment were recruited for the reflectance measurements. Consent to take part in the study was obtained from all patients. A study protocol was defined and approved by the Providence St. Vincent Medical Center IRB Committee. Detailed written and oral information on the study protocol was given to the patients prior to enrollment. The measurements increased the endoscopic procedure an average of 5 min.

A total of nine patients (Nos. N1–N9) undergoing the endoscopic procedures for screening purpose were recruited to set base line values for optical properties at clinically evaluated normal tissue sites. One measurement was taken at three different sites for each patient.

Four patients with esophageal tumors (Nos. E1–E4), two patients with lung tumors (Nos. L1–L2) and one patient with oral cavity tumors (No. O1) scheduled to receive standard FDA and off-label PDT treatment protocols were recruited for this study. All were intravenously injected with 2 mg/(kg body weight) of Photofrin II (Axcan Pharma Inc., Birmingham, AL) 48 h prior to activation by 630 nm laser light. Measurements of reflectance spectra were taken immediately prior to light treatment. Three clinically evaluated normal sites and three clinically evaluated tumor sites were measured per patient. Exception was lung patient No. L2, who had only two normal sites and three tumor sites measured due to time constraint.

4.1.

Bovine Muscle in vitro

Comparison between the optical properties of bovine muscle determined with the empirical/spectral model and by the wavelength-by-wavelength model (Sec. 3.5) is shown in Fig. 12. Figure 12(a) shows the average and standard deviations for μ_s ^′ (top) and μ_a (bottom) obtained with the two techniques for three different sites of one sample. Similar results are shown in Fig. 12(b) for all nine sites measured (three sites times three samples). These results illustrate how the analysis using the empirical/spectral model yielded a smooth spectrum for the reduced scattering coefficient while the analysis using the diffusion theory/wavelength-by-wavelength model allowed for cross talk between the absorption and scattering (seen as the influence of hemoglobin absorption in the reduced scattering coefficient spectrum). Note, however, that at longer wavelengths where hemoglobin absorption is low, the reduced scattering coefficient was similar for both methods.

Figure 12

Reduced scattering (μ_s ^′, top) and absorption (μ_a, bottom) coefficients determined for bovine muscle determined by the empirical/spectral model (diamonds) in comparison to the optical properties determined by the wavelength-by-wavelength model described in section 3.5 (circles). (a) Average and standard deviations for three different sites measured at one sample. (b) Average and standard deviations for all sites measured (three sites per sample for three different samples).

4.2.

Human Tissue in vivo

Figure 13 shows results of the empirical/spectral model for esophageal PDT patient No. E1 with plots of the experimental and predicted spectra for three normal sites [Figs. 13(a)–13(c)] and three tumor sites [Figs. 13(d)–13(f)]. Experimental curves in Figs. 13(a)–13(f) are the same shown in Fig. 9. Bloodless tissue curves are shown in black dashed lines, based on setting the factor f_v equal to zero for μ_a in Eq. (7) and determining the light transport using the bloodless tissue optical properties and Eq. (8). The values of a, b, f_v, SO ₂, A, and B are specified in the graphs for this patient and in Tables 1, 2, and 3 for sites measured in all patients (PDT and non-PDT). To obtain the optical properties one must use these numbers with Eqs. (7), (8), and (9). The normalized residual error [(predicted−experimental)/experimental] is also shown.

Figure 13

Normalized data for normal site 1–3 and tumor sites 1–3 of patient No. E1 in comparison to the predicted values (circles) determined using the fitted parameters a, b, f_v, SO ₂, A, and B shown, and Eqs. (7), (8), and (9). The percentage residual errors [(predicted−measured)/measured times 100%] are shown below each curve. Bloodless tissue curves are shown in black dashed lines, based on setting the factor f _v equal to zero for μ_a in Eq. (7). The system was not able to record data below 600 nm for tumor sites 2 and 3 because of strong blood absorption in that spectral range. Only data above 600 nm was used for fitting. Values of a, b, and B were assumed to be the same as those for tumor site 1 (see text).

Table 1

Table 2

Table 3

In some cases the blood content from tumor tissue was so high that zero reflectance was obtained in the 500–600 nm wavelength range. In these cases data were truncated below 600 nm and the same fitting algorithm was attempted. Without the data below 600 nm, the fitting for a and b (that describe the reduced scattering coefficient) and B (that describe the absorption of dry tissue) did not always converge to values that represented physiological values of μ_s ^′ and μ_a. Therefore, the values of a, b, and B were determined using the average of μ_s ^′ and μ_a ^dry from the other tumor sites for the same patient and the variables f_v, SO ₂, and A were fitted using the data above 600 nm. In the case of patient No. E1, just one tumor measurement (tumor site No. 1) did not have zero reflectance values in the 500–600 nm wavelength range. Thus, the values of a, b, and B for this tumor site were used to determine the other variables (f_v, SO ₂, and A) for tumor site Nos. 2 and 3. The sites where truncated data were used are highlighted in Table 3.

Calculated reduced scattering and absorption coefficients of normal and tumor sites for patient No. E1 are shown in Figs. 14(a) and 14(b), respectively. Reduced scattering coefficients for all three tumor sites are identical since the same values of a and b were assumed for all sites as explained earlier.

Figure 14

Optical properties of three normal sites and three tumor sites from patient No. E1. (Top) Reduced scattering coefficient. (Bottom) Absorption coefficient. Identical reduced scattering coefficients are obtained for all three tumor sites (see text).

Absorption and reduced scattering coefficients and the optical penetration depth (δ) at 630 nm are shown in Tables 1, 2, and 3 for all patients. Histograms of the optical penetration depth at 630 nm are shown in Fig. 15 for the normal, PDT normal and PDT tumor.

Figure 15

Histograms of the optical penetration depth at 630 nm in normal tissue for non-PDT and in normal and tumor tissue for PDT patients.

Mean and standard deviations for blood fraction (f_v), blood oxygen saturation (SO ₂), and reduced scattering coefficients (μ_s ^′), absorption coefficients (μ_a), and optical penetration depths (δ) at 630 nm are shown in Table 4.

Table 4

Two-sample t tests²⁹ were performed to compare results for normal esophageal tissue of non-PDT against normal tissue of PDT patients. t tests were also performed to compare normal against tumor sites for PDT patients. Significant difference was found between non-PDT normal and PDT normal tissue for f_v and SO ₂ with p values <0.03 and <0.01, respectively. No significant difference was found for the other parameters. Comparison between PDT normal and PDT tumor sites showed significant difference between all parameters except μ_s ^′ with p values <0.02, <0.003, <0.001, and <0.002 for f_v, SO ₂, μ_a, and δ, respectively.