2.1.

Description of Tissue Phantoms

The excitation-emission wavelength pair to be investigated was chosen to be (460, 520 nm). This wavelength pair falls within a spectral region, where the absorption coefficient of tissues is comparable to the scattering coefficient.^{12 18} Furthermore, they are close to the excitation- emission maxima of two important fluorophores. One is flavin adenine dinucleotide (FAD), which is an endogenous fluorophore in tissue with an excitation-emission maximum of (450, 535 nm).¹⁹ The other is a widely used molecular reporter of gene expression, green fluorescent protein (GFP), with an excitation-emission maximum near (460, 520 nm).²⁰ The optical properties of the phantom models at 460 and 520 nm were selected to be the representative of human epithelial tissues.^{12 18} The absorption coefficient was varied from 1.3 to 31.8 cm ⁻¹, and the scattering coefficient was varied from 50 to 225 cm ⁻¹.

India ink (Super Black India Ink, The Speedball Art Products Company, Statesville, North Carolina) was chosen as the absorber since the ratio of its absorption coefficients at 460 and 520 nm is very similar to that of human epithelial tissues. The absorption coefficient of India ink, diluted by a factor of 1000 in distilled water, was measured using an absorption spectrophotometer (Cary 300, Varian, Australia) and quantified using Beer’s law.

Figure 1 shows the absorption coefficient of pure India ink over the UV-visible spectrum. The absorption coefficient at a particular wavelength is linearly proportional to the concentration of India ink according to Beer’s law, which greatly facilitates the calculation of appropriate concentrations for a particular absorption coefficient. To achieve a desired absorption coefficient in the phantom model, pure India ink was diluted by an appropriate dilution factor, and the absorption coefficient of the final concentration was verified again using the absorption spectrophotometer.

Figure 1

Absorption coefficient of pure India ink over the UV-visible spectrum.

Polystyrene spheres with a diameter of 1.053 μm and a refractive index of 1.6 (Polysciences Incorporated, Warrington, Pennsylvania) were chosen as the scatterer because they have a uniform and well-characterized particle size distribution, as well as low absorption and fluorescence at the excitation and emission wavelengths employed in this study. According to Durkin, Jaikumar, and Richards-Kortum,²¹ the absorption coefficient of 0.625 polystyrene spheres with a diameter of 1.05 μm and a refractive index of 1.56 is about 0.50 cm ⁻¹ at wavelengths between 400 and 600 nm. The wavelength-dependent scattering coefficient of a specific fractional volume of polystyrene spheres, with a known diameter and refractive index, was predicted by use of the Mie theory.²² These calculations were verified by comparing our results to experimentally measured values in the publication by Durkin, Jaikumar, and Richards-Kortum.²¹

Figure 2 shows the scattering coefficient of polystyrene spheres suspended in distilled water with a fractional volume of 2.6, 1.053-μm diameter and a refractive index of 1.6 over the UV-visible spectrum. The scattering coefficient of polystyrene spheres is linearly proportional to its concentration for the concentration used and wavelength ranges of interest according to our calculations, which greatly facilitates the calculation of appropriate concentrations of the suspension for a particular scattering coefficient. To achieve a desired scattering coefficient in the phantom model, the fractional volume of polystyrene spheres was diluted by an appropriate dilution factor.

Figure 2

Scattering coefficient of polystyrene spheres with a fractional volume of 2.6 in distilled water, 1.053-μm diameter, and refractive index of 1.6 over the UV-visible spectrum.

The fluorophore used in the tissue phantom experiments was FAD, which is one of the endogenous fluorophores present in human epithelial tissues as mentioned previously. The concentration of FAD to be used in the tissue phantoms was selected to be such that its absorption coefficient is at least one order of magnitude lower than the smallest absorption coefficient contributed by India ink in the tissue phantom models at both the excitation and emission wavelengths. The absorption coefficient spectrum of FAD in distilled water was measured at various concentrations using the absorption spectrophotometer. A concentration of 7-μM FAD yielded an absorption coefficient of 0.108 cm ⁻¹ at 460 nm, and 0.001 cm ⁻¹ at 520 nm, which are at least one order of magnitude lower than the lowest absorption coefficient of India ink (∼1.2 cm ⁻¹) in the tissue phantom model at both the excitation and emission wavelengths. Therefore, the concentration of FAD in all the phantom models was fixed at 7 μM.

Two sets of tissue phantoms were prepared for the experimental measurements of fluorescence and diffuse reflectance. In the first set of phantoms (group 1), the scattering coefficient and fluorophore concentration were fixed at 110.4 cm ⁻¹ and 7 μM, respectively, while the absorption coefficient was varied from 1.204 to 31.704 cm ⁻¹. In the second set of phantoms (group 2), the absorption coefficient and the fluorophore concentration were fixed at 10.709 cm ⁻¹ and 7 μM, respectively, and the scattering coefficient was varied from 50 to 225 cm ⁻¹. Tables 1 and 2 show the concentrations of each component and corresponding optical properties in tissue phantom groups 1 and 2, respectively. It should be noted that all the phantoms contained 7-μM FAD.

Table 1

Table 2

After the optical properties of interest were established, the lateral and depth dimensions of the tissue phantom models were determined. Specifically, a Monte Carlo simulation was carried out for a homogeneous semi-infinite medium, in which the optical properties were set to be the smallest absorption coefficient (1.2 cm ⁻¹) and largest scattering coefficient (225 cm ⁻¹) employed in the tissue phantom models. These optical properties were chosen to maximize the fluence distribution in the medium. The dimensions of the medium were increased until the photon interactions with boundaries were negligible. A diameter of 1 cm and a depth of 0.5 cm were determined to be the minimum required dimensions of tissue phantom models.

Cylindrical plastic bottles with a height of 5 cm and a diameter of 2 cm (Plastic Snap Cap Vial, distributed by Fisher Scientific) were used as containers for the phantoms. The phantoms were filled up to a height of 3 cm in the containers. A diameter of 2 cm and a depth of 3 cm were sufficient to meet the requirements of a semi-infinite homogeneous medium as determined previously.

2.2.

Instruments and Fiber Optic Probes for Fluorescence and Diffuse Reflectance Measurements

Three types of fluorometers with three different kinds of fiber optic probes were used in this study. Figure 3 shows the cross-sectional views of the common ends of three fiber optic probes employed to measure the fluorescence, and in most cases the diffuse reflectance, of the tissue phantom models. The filled area represents the illumination fiber(s) and the unfilled area represents the collection fiber(s). It should be noted that the collection fibers in Fig. 3(c) are round, although they appear slightly elliptical. The configuration of illumination and collection fibers in each fiber optic probe and a description of the corresponding instruments are provided next.

Figure 3

Cross-section views of the common ends of three fiber optic probes employed to measure the fluorescence, and in most cases the diffuse reflectance, of the tissue phantom models. The filled area represents the illumination fiber(s) and the unfilled area represents the collection fiber(s). Note that the collection fibers in (c) are round, although they appear slightly elliptical.

The first instrument (Fluorolog-3, J.Y. Horiba Incorporated, New Jersey) incorporates a 450-W Xenon lamp, a photomultiplier tube (PMT), and double excitation and emission scanning monochromators. The corresponding fiber optic probe (a) [see Fig. 3(a)] has a central illumination fiber with a core/cladding diameter of 200/245 μm, surrounded by a concentric ring composed of nine collection fibers, each with a core/cladding diameter of 100/130 μm. The distance between the center of the illumination fiber and the center of each collection fiber is 187.5 μm. The numerical aperture (NA) of all fibers is 0.22.

The second instrument (Skinscan, J.Y. Horiba Incorporated, New Jersey) comprises a 150-W Xenon lamp, a PMT, and double excitation and emission scanning monochromators. The corresponding fiber optic probe (b) [see Fig. 3(b)] has a collection core with a diameter of 1.52 mm surrounded by an illumination ring, with an outer diameter of 2.18 mm. Both the illumination ring and collection core are composed of 31 individual fibers, each with a core/cladding diameter of 200/245 μm. This fiber optic probe differs from the one described previously with respect to the illumination and collection geometries (here the outer ring is used for illumination and the central core for collection, while in the previous probe the central fiber is used for illumination and the surrounding ring for collection) and the effective illumination and collection areas.

The third custom-built instrument consists of a 450-W xenon lamp (FL-1039, J.Y. Horiba Incorporated, New Jersey) coupled to a scanning double excitation monochromator (Gemini 180, J.Y. Horiba Incorporated, New Jersey), a filter wheel, an imaging spectrograph (Triax 320, J.Y. Horiba Incorporated, New Jersey) and a CCD camera (CCD 3000, J.Y. Horiba Incorporated, New Jersey). The common end of the corresponding fiber optic probe (c) [see Fig. 3(c)] consists of an illumination core with a 1180 μm diameter (made up of 19 fibers, each with a core/cladding diameter of 200/245 μm), and three surrounding concentric rings of collection fibers (each ring has 12 fibers and each fiber has a core/cladding diameter of 200/245 μm). The NA of all fibers is 0.22. The output of the three concentric rings of collection fibers on the CCD chip can be spatially separated, thereby allowing for optical spectroscopic measurements to be made at three source-detector separations simultaneously. This fiber optic probe design is similar to that described in Fig. 3(a), in that both of them consist of a central illumination core surrounded by one or several concentric rings of collection fibers. However, the illumination core here is much larger than that used previously, and there are three collection rings instead of one in this fiber optic probe. The distances between collection rings and the geometrical center of the probe are 735, 980, and 1225 μm, respectively, and these separations are much larger than that in the fiber optic probe shown in Fig. 3(a).

Table 3 provides the integration time and the excitation and emission bandpasses for fluorescence and diffuse reflectance measurements with each fiber optic probe and corresponding instrument. The procedure of the measurement is the same for all instruments and fiber optic probes and are described as follows. The fluorescence measurements were made at an excitation-emission wavelength pair of (460, 520 nm) and the diffuse reflectance was measured at 460 nm. The background fluorescence of each tissue phantom (containing the absorber and scatterer only) was measured before the addition of the fluorophore FAD. Then the fluorescence and diffuse reflectance of each phantom was measured after the addition of FAD. Each measurement was performed three times. The dark current of the instrument was measured prior to the diffuse reflectance measurements. The background fluorescence was subtracted from the experimental fluorescence measurement, and the dark current was subtracted from the experimental diffuse reflectance measurement. In the end, the three background-subtracted fluorescence measurements and the three dark current-subtracted diffuse reflectance measurements were averaged. During the course of the measurements, the probes were immersed a few millimeters into the phantoms to ensure that there was no air gap between the probe tip and the phantoms. The phantoms were stirred during the course of each experimental measurement to prevent polystyrene spheres from settling down at the bottom of containers.

Table 3

2.3.

Monte Carlo Simulations

3.1.

Results for Fiber Optic Probe Geometry (a)

Figure 4 shows the fluorescence measured from a tissue phantom groups 1 and (b) tissue phantom group 2 with fiber optic probe geometry (a) [see Fig. 3(a)] and the corresponding Monte Carlo simulation results. The number closest to each data point in Fig. 4(a) is the absorption coefficient at the excitation wavelength (460 nm), and the number closest to each data point in Fig. 4(b) is the scattering coefficient at the excitation wavelength (the same format has been used in Figs. 5 through 9). The absorption and scattering coefficients at the emission wavelength (520 nm) are lower than those at the excitation wavelength by 16 and 6, respectively, for all data points. Each experimental data point has been normalized by the sum of all experimental data points, and each simulation data point has also been normalized by the sum of all simulation data points. This method of normalization sets the area under the curve to unity and facilitates comparison between the computational and experimental results. The error bar represents variation in three consecutive measurements from each phantom, which is too small to be clearly observed at most points.

Figure 4

Fluorescence measured from tissue phantom group 1 and tissue phantom group 2 with fiber optic probe geometry (a) [see Fig. 3(a)] and the corresponding Monte Carlo simulation results. The number closest to each data point in Fig. 4(a) is the absorption coefficient at the excitation wavelength of 460 nm, and the number closest to each data point in Fig. 4(b) is the scattering coefficient at the excitation wavelength. The absorption and scattering coefficients at the emission wavelength (520 nm) are lower than that at the excitation wavelength by 16 and 6, respectively, for all data points. Each experimental data point has been normalized by the sum of all experimental data points, and each simulation data point has also been normalized by the sum of all simulation data points. The error bar represents the variation in three consecutive measurements from each phantom.

Figure 5

Normalized fluorescence measured from tissue phantom group 1 and tissue phantom group 2 with fiber optic probe geometry (b) [see Fig. 3(b)] and corresponding Monte Carlo simulation results. The number closest to each data point in Fig. 5(a) is the absorption coefficient at the excitation wavelength of 460 nm, and the number closest to each data point in Fig. 5(b) is the scattering coefficient at the excitation wavelength. Each experimental data point has been normalized by the sum of all experimental data points, and each simulation data point has also been normalized by the sum of all simulation data points. The error bar represents the variation in three consecutive measurements from each phantom.

Figure 9

Radial distribution of the normalized (a) fluorescence and (b) diffuse reflectance measured from tissue phantom group 1 with fiber optic probe geometry (c) [Fig. 3(c)] and the corresponding Monte Carlo simulation results. The three center-to-center distances are 735, 980, and 1225 μm, respectively, which correspond to the distance from the center of the inner, middle, and outer collection rings, respectively, to the center of fiber optic probe (c). The fluorescence/diffuse reflectance radial profiles are shown only for the cases of the four smallest absorption coefficients in tissue phantom group 1. The absorption coefficient corresponding to that at wavelength 460 nm is indicated above the corresponding data points. The data points for simulation results are denoted by individual markers. The three experimentally obtained data points have been interpolated and connected by smoothed curves to facilitate comparison between the computational and experimental results and also to easily distinguish them. The curves are spaced out on the y axis for clarity. Each data point has been normalized by the sum of all three data points in the same dataset.

Figure 4(a) indicates that the fluorescence intensity decreases with an increase in the absorption coefficient. The percent error was calculated for each data point. and it is defined as the ratio of the difference between computational and experimental values (numerator) to the experimental value (denominator). and then multiplied by a factor of 100. The lowest percent error is 0.3 (for μ_a=14.427 cm ⁻¹) and the highest is 14.4 (for μ_a=21.236 cm ⁻¹) . Figure 4(b) shows that the fluorescence intensity increases as the scattering coefficient is increased. The lowest percent error is 0.1 (for μ_s=125 cm ⁻¹) and the maximum percent error is 6.0 (for μ_s=75 cm ⁻¹) . There is good agreement between the computational and experimental results over the range of absorption and scattering coefficients employed in these phantom studies.

3.2.

Results for Fiber Optic Probe Geometry (b)

Figure 5 shows the normalized fluorescence measured from (a) tissue phantom group 1 and (b) tissue phantom group 2 with fiber optic probe geometry (b) [see Fig. 3(b)] and the corresponding Monte Carlo simulation results. The trends shown in the normalized fluorescence in Figs. 5(a) and 5(b) are similar to those observed in Fig. 4(a) and 4(b), respectively. In Fig. 5(a), the lowest percent error is 1.1 (for μ_a=14.427 cm ⁻¹) , and the highest is 28.6 (for μ_a=21.236 cm ⁻¹) . In Fig. 5(b), the lowest percent error is 0.02 (for μ_s=225 cm ⁻¹) , and the maximum error is 8.1 (for μ_s=50 cm ⁻¹) . The percent errors observed for this probe geometry are greater than those observed for fiber optic probe geometry (a).

Figure 6 shows the normalized diffuse reflectance measured from tissue phantom group 1 and tissue phantom group 2 with fiber optic probe geometry (b) [see Fig. 3(b)] and the corresponding Monte Carlo simulation results. Both curves have been normalized in the same manner as described previously. The trends in the diffuse reflectance measurements are similar to those observed in the fluorescence measurements. In Fig. 6(a), the lowest percent error is 3.3 (for μ_a=1.312 cm ⁻¹) , and the highest is 22.4 (for μ_a=19.191 cm ⁻¹) , excluding the last data point. At the last data point, the percent error is 49.2 (for μ_a=31.812 cm ⁻¹) , but the signal intensity at this point is too small to be reliable. In Fig. 6(b), the lowest percent error is 0.67 (for μ_s=150 cm ⁻¹) , and the maximum percent error is 27.5 (for μ_s=50 cm ⁻¹) . The percent error for the diffuse reflectance data is higher than that for the fluorescence data obtained using the same fiber optic probe.

Figure 6

Normalized diffuse reflectance measured from tissue phantom group 1 and tissue phantom group 2 with fiber optic probe geometry (b) [see Fig. 3(b)] and corresponding Monte Carlo simulation results. The number closest to each data point in Fig. 6(a) is the absorption coefficient at an excitation wavelength of 460 nm, and the number closest to each data point in Fig. 6(b) is the scattering coefficient at the excitation wavelength. Each experimental data point has been normalized by the sum of all experimental data points, and each simulation data point has also been normalized by the sum of all simulation data points. The error bar represents the variation in three consecutive measurements from each phantom.

3.3.

Results for Fiber Optic Probe Geometry (c)

In the previous results it can be seen that the agreement between the computational and experimental results is significantly better for tissue phantom group 2, where the scattering coefficient is varied, than that for tissue phantom group 1. Furthermore, these results do not significantly depend on the fiber optic probe geometry. Thus, in the remaining section, only the results corresponding to tissue phantom group 1 are presented.

Figure 7 shows the normalized fluorescence measured from tissue phantom group 1 with fiber optic probe geometry (c) [see Fig. 3(c)] and corresponding Monte Carlo simulation results. Fiber optic probe (c) contains three independent collection fiber rings with different distances relative to the geometrical center of the illumination core. Thus, there are three pairs of curves in this figure, which correspond to the fluorescence collected by the (a) inner, (b) middle, and (c) outer rings, respectively. The trends of the fluorescence in Figs. 7(a), 7(b), and 7(c) are similar to those seen in Figs. 4(a) and 5(a). In Fig. 7(a), the lowest percent error is 2.0 (for μ_a=5.286 cm ⁻¹) , and the highest is 20.4 (for μ_a=31.812 cm ⁻¹) . In Fig. 7(b), the lowest percent error is 2.6 (for μ_a=1.312 cm ⁻¹) , and the highest percent error is 42.4 (for μ_a=31.812 cm ⁻¹) . In Fig. 7(c), the lowest percent error is 0.7 (for μ_a=1.312 cm ⁻¹) , and the highest error is 54.8 (for μ_a=14.427 cm ⁻¹) . The percent errors observed for the inner collection ring [Fig. 7(a)] are comparable to those observed for fiber optic probes (a) and (b). However, the percent errors for the middle and outer collection rings [Figs. 7(b) and 7(c)] are significantly greater than those observed for fiber optic probes (a) and (b).

Figure 7

Normalized fluorescence measured from tissue phantom group 1 with fiber optic probe geometry (c) [see Fig. 3(c)] and the corresponding Monte Carlo simulation results. Fiber optic probe (c) contains three independent collection fiber rings with different distances relative to the geometrical center of the illumination core, thus there are three pairs of curves in this figure, which correspond to the fluorescence collected by (a) inner, (b) middle, and (c) outer rings, respectively. The number closest to each data point is the corresponding absorption coefficient at the excitation wavelength of 460 nm. Each experimental data point has been normalized by the sum of all experimental data points, and each simulation data point has also been normalized by the sum of all simulation data points. The error bar represents the variation in three consecutive experimental measurements from each phantom.

Figure 8 shows the normalized diffuse reflectance measured from tissue phantom group 1 with fiber optic probe geometry (c) [see Fig. 3(c)] and corresponding Monte Carlo simulation results. The diffuse reflectance curves shown in Figs. 8(a), 8(b), and 8(c) display similar trends with those observed in Fig. 6(a). In Fig. 8(a), the lowest percent error is 5.3 (for μ_a=1.312 cm ⁻¹) , and the highest is 39.5 (for μ_a=31.812 cm ⁻¹) . In Fig. 8(b), the lowest percent error is 5.4 (for μ_a=21.236 cm ⁻¹) , and the maximum error is 25.2 (for μ_a=2.025 cm ⁻¹) . Moreover, the simulated data at μ_a=1.312 cm ⁻¹ is believed to be a random error, since the diffuse reflectance intensity at this point is expected to be greater than that at μ_a=2.025 cm ⁻¹. In Fig. 8(c), the lowest percent error is 2.6 (for μ_a=2.025 cm ⁻¹) , and the maximum percent error is 32.9 (for μ_a=31.812 cm ⁻¹) . The percent errors observed here are greater than those observed for diffuse reflectance measurements with fiber optic probe (b), and are also greater than those of the corresponding fluorescence results obtained with the same fiber optic probe geometry.

Figure 8

Normalized diffuse reflectance measured from tissue phantom group 1 with fiber optic probe geometry (c) [see Fig. 3(c)] and the corresponding Monte Carlo simulation results. Fiber optic probe (c) contains three independent collection fiber rings with different distances relative to the geometrical center of the illumination core, thus there are three pairs of curves in this figure, which correspond to the diffuse reflectance collected by the (a) inner, (b) middle, and (c) outer rings, respectively. The number closest to each data point is the corresponding absorption coefficient at an excitation wavelength of 460 nm. Each experimental data point has been normalized by the sum of all experimental data points, and each simulation data point has also been normalized by the sum of all simulation data points. The error bar represents the variation in three consecutive experimental measurements from each phantom.

Figure 9 shows the radial distribution of the normalized fluorescence and diffuse reflectance measured from tissue phantom group 1 with fiber optic probe geometry (c) [see Fig. 3(c)] and corresponding Monte Carlo simulation results. The three center-to-center distances are 735, 980, and 1225 μm, respectively, which correspond to the distance from the center of the inner, middle, and outer collection rings, respectively to the center of fiber optic probe (c). The fluorescence/diffuse reflectance radial profiles are shown only for the four smallest absorption coefficients of tissue phantom group 1. The absorption coefficient corresponding to that at the excitation wavelength 460 nm is indicated on top of each curve. The curves are spaced out on the y axis for clarity. Each data point within a curve has been normalized by the sum of all three data points. In addition, the three experimentally obtained data points on each curve have been interpolated and connected by a curve to facilitate comparison between the computational and experimental results. The fluorescence and diffuse reflectance decrease with increasing center-to-center distance. The percent error increases as the absorption coefficient increases. As observed previously, the fluorescence data show better agreement between the computational and experimental results compared to the diffuse reflectance data.

3.4.

Summary of Minimum/Maximum Percent Error Between Computational and Experimental Results

Table 6 summarizes the minimum/maximum percent errors and corresponding optical properties (at an excitation wavelength of 460 nm) for the normalized fluorescence data obtained from tissue phantom group 1 and tissue phantom group 2. In Table 6, the maximum percent error increases from fiber optic probe (a), to probe (b), to probe (c). Furthermore, the maximum percent error increases as the center-to-center distance is increased in fiber optic probe (c). In general, the maximum percent error occurs at absorption coefficient values greater than 20 cm ⁻¹. In Table 7, the maximum percent error occurs at scattering coefficient values smaller than 75 cm ⁻¹. The maximum percent errors are greater between the computational and experimental results for tissue phantom group 1 (see Table 6) compared to those for tissue phantom group 2 (see Table 7).

Table 6

Table 7

Table 8 and 9 summarizes the minimum/maximum percent errors and corresponding optical properties (at the wavelength 460 nm) for the normalized diffuse reflectance obtained from tissue phantom group 1 and tissue phantom group 2. In general, the trends observed for the normalized diffuse reflectance data are similar to those observed for the normalized fluorescence data, with the exception at the middle collection ring of fiber optic probe (see Table 8).

Table 8

Table 9