2.1.

Tissue Model Geometry and Optical Properties

A two-layer model was established to simulate human epithelial tissue, which consists of a superficial epithelium and an underlying stroma. Figure 1 depicts the epithelial tissue model geometry, where the thickness of the epithelial layer and that of the stromal layer are fixed at 450 and 2050 μm, respectively. A thickness of 450 μm was chosen for the epithelial layer to approximate the thickness of the human cervical epithelium.⁷ The thickness of the stromal layer was set at 2050 μm to represent an infinitely thick tissue. This thickness is far greater than the probing depth of the fiber optic probes employed in this study. This has been verified using Monte Carlo simulations. The lateral dimension of the model was assumed to infinite relative to the fiber optic probe dimensions used in this study (100 to 1000 μm).

Figure 1

The epithelial tissue model geometry, where the thickness of the epithelial layer and that of the stromal layer are fixed at 450 and 2050 μm, respectively.

Table 1 lists the fluorescence efficiencies and optical properties (two optical property sets) designated for the epithelial and stromal layers in the epithelial tissue model. The fluorescence was simulated at an excitation-emission wavelength pair of 460 to 520 nm. The primary endogenous fluorophore in epithelial tissue at this excitation-emission wavelength pair is flavin adenine dinucleotide (FAD).^{2 8} The fluorescence measured at this excitation-emission wavelength pair has been shown to be able to discriminate neoplastic from nonneoplastic human cervical tissues.^{25 29} For both optical property sets, the fluorescence efficiencies of the epithelial and stromal layers at 460 to 520 nm were defined from the results of previous human cervical tissue studies.²⁵ The two different optical property sets were employed in these simulations to allow for a general assessment of the different probe geometries. Optical properties and refractive indices for set 1 were obtained from the publication by Liu and Ramanujam.²⁷ In this set, optical properties were identical for both epithelial and stromal layers. Optical properties in set 2 were obtained from the publication by Drezek et al.;²³ In this case, the epithelial layer and stromal layers have different absorption and scattering coefficients.

Table 1

2.2.

Illumination-Collection Geometries

Two illumination-collection geometries, the variable aperture (VA) and multidistance (MD) approaches, were employed to simulate fluorescence measurements from the epithelial tissue model. Figure 2 shows the schematic of the VA [Fig. 2(a)] and MD [Fig. 2(b)] probes. The VA probe has completely overlapping illumination and collection areas with variable diameters. In the MD approach, separate illumination and collection fibers are employed at a fixed separation on the tissue surface.

Figure 2

Schematic of the (a) variable aperture (VA) and (b) multidistance (MD) probes. The VA probe has completely overlapping illumination and collection areas with variable diameters. In the MD approach, separate illumination and collection fibers are employed at a fixed separation on the tissue surface.

Table 2 provides the characteristics of the simulated VA and MD probe geometries. In VA, the illumination and collection diameters are equal to each other and are varied from 100 to 1000 μm in 100-μm increments. It should be noted that in this probe geometry, the illumination and collection areas completely overlap. Three MD probe geometries were studied: MD1, MD2, and MD3. In MD2, both the illumination and collection diameters are set at 200 μm. In MD1, the illumination diameter is increased to 900 μm, with no change to the collection diameter (compared to MD2). In MD3, the collection diameter is decreased to 100 μm, with no change to the illumination diameter (compared to MD2). In the MD probe geometry, there is one illumination fiber and there are five adjacent collection fibers, configured in a linear array. In the MD probe geometry, the center-to-center distance for each illumination-collection fiber pair is the distance between the center of the illumination fiber and the center of the particular collection fiber. Both fiber optic probe geometries were evaluated for numerical apertures (NAs) of 0.22 and 0.37.

Table 2

2.3.

Monte Carlo Modeling

In this study, a modified, three-dimensional, weighted photon Monte Carlo code was employed to carryout fluorescence simulations on the theoretical model of human epithelial tissue using the VA and MD probe geometries. This code has been systematically validated by comparison of simulation results to experimental measurements on tissue phantom models for a range of optical properties representative of human epithelial tissues in the UV-visible spectrum and three different fiber optic probe geometries.³⁰ Two of the three fiber optic probe geometries are similar to MD1 and MD3. Details about the Monte Carlo simulation and its systematic validation are described in a companion manuscript, published in this issue.³⁰

2.4.

Monte Carlo Simulation Parameters

In each Monte Carlo simulation, the excitation photons were launched at random, uniformly distributed locations over a range of angles defined by the NA and over a circular illumination area. To simulate fluorescence emission in the medium, a rejection scheme was used to determine whether or not the absorbed fraction of a photon packet is reemitted as a fluorescent photon. The fluorescent photons escaping the medium from the top surface were collected over a circular area defined by the collection diameter and over a range of exit angles within the NA. The circular illumination and collection areas are equivalent to the cross-sectional areas of the illumination and collection fibers, respectively. Since the illumination and collection fibers were assumed to be in direct contact with the tissue surface, the refractive index of the medium above the tissue model was set to be 1.452 to simulate an optical fiber, and that of the medium below the tissue model was set at 1.0. To simulate a 3-D tissue geometry in the computational model, a cylindrical coordinate system was used, in which the axial dimension is perpendicular to the top surface of the medium and the radial dimension corresponds to any direction perpendicular to the axial dimension. The axial and radial grid sizes were set at 10 μm, and the numbers of axial and radial grids were both set at 250 to define the volume of interest in the tissue model.

In this study, a total of ten million photons were launched to provide a balance between simulation accuracy and computational time. All the simulations were run on a 1.6-GHz Pentium 4 computer with a Windows 2000 operation system. The running time varied from a few hours to approximately a whole day. MATLAB 5.3 was used to perform postsimulation data processing and statistical analysis.

2.5.

Analysis of the Simulation Results

The Monte Carlo simulation results were analyzed to enable comparison of the fluorescence measurements made with the VA and MD fiber optic probe geometries. A general summary of the comparison includes the following: total fluorescence detected, 80 probing depth, and sensitivity to the first (epithelial) layer. The total fluorescence detected was calculated by taking the ratio of the number of fluorescent photons detected by the collection fiber to the number of fluorescent photons generated within the epithelial tissue model. The 80 probing depth was defined as the depth within which 80 of the detected fluorescent photons originate. Here an 80 criterion was used to evaluate the probing depth, within which the majority of the detected fluorescent photons originate. The sensitivity to the first layer was defined as the ratio of the detected fluorescence from the first layer (within the depth of 450 μm) to the total detected fluorescence.

3.1.

Depth-Resolved Fluorescence Profiles

Figure 3 shows the percent fluorescence detected with the VA and MD probes as a function of depth in the tissue. The depth-wise distribution was calculated by summing the number of fluorescent photons over all radial positions at a specific depth, and then dividing by the total number of fluorescent photons generated within the tissue model. Both the VA and MD probes have illumination and collection diameters of 200 μm, and an NA of 0.22. The separation between the illumination and collection fibers in the MD probe is 200 μm. Evaluation of Fig. 3 indicates that μthe fluorescence originating in the epithelial layer dominates the total fluorescence detected with the VA probe, while that originating in the stromal layer dominates the fluorescence detected with the MD probe. For both probe geometries, there is a significant increase in the detected fluorescence beyond a depth of 450 μm, which is due to the higher fluorescence efficiency of the stromal layer (0.6) versus the epithelial layer (0.2).

Figure 3

The percent fluorescence detected with the VA and MD probes as a function of depth in the tissue. The depth-wise distribution was calculated by summing the number of fluorescent photons over all radial positions at a specific depth, and then dividing by the total number of fluorescent photons generated within the tissue model. Both the VA and MD probes have illumination and collection diameters of 200 μm and an NA of 0.22. The separation between the illumination fiber and the collection fiber in the MD probe is 200 μm.

3.2.

Variable Aperture Probe Geometry

Figures 4, 5, and 6 display the total fluorescence detected, the 80 probing depth, and the sensitivity to the first layer, respectively, for the variable aperture (VA) probe geometry. All the fibers have an NA of 0.22.

Figure 4

The total fluorescence detected from the epithelial tissue model with the VA probe (see Table 2, NA=0.22) . The total fluorescence detected was calculated by taking the ratio of the number of detected fluorescent photons to the number of fluorescent photons generated within the medium.

Figure 5

The 80 probing depth achieved in the epithelial tissue model with the variable aperture (VA) probe (see Table 2, NA=0.22) . The 80 probing depth is defined as the depth within which 80 of the detected fluorescent photons originate.

Figure 6

The sensitivity to the first layer in the epithelial tissue model achieved with the variable aperture probe (see Table 2, NA=0.22) . The sensitivity to the first layer is defined as the ratio of the detected fluorescence from the first layer (thickness of 450 μm) to the total detected fluorescence.

Figure 4 displays the total fluorescence detected from the epithelial tissue model with the VA probe. As the illumination/collection diameter increases from 100 to 1000 μm, the total fluorescence detected with VA probe increases from a minimum of 5E-4 to a maximum of 2.5E-3.

Figure 5 displays the 80 probing depth achieved in the epithelial tissue model with the VA probe. With the VA probe geometry, the 80 probing depth increases with the illumination/collection diameter from a minimum of ∼300 μm to a maximum of ∼750 μm.

Figure 6 displays the sensitivity to the first layer in the epithelial tissue model achieved with the VA probe. The sensitivity to the first layer of the VA probe decreases from a maximum of 90 to a minimum of 45 with an increase in the illumination/collection fiber diameter.

3.3.

Multidistance Probe Geometry

Figures 7, 8, and 9 display the total fluorescence detected, the 80 probing depth and the sensitivity to the first layer, respectively, for three multidistance (MD) probe geometries: MD1, MD2, and MD3. In each of the MD probe geometries, the linearly arranged adjacent collection fibers are labeled 1 through 5, with number 1 corresponding to the nearest collection fiber and number 5 corresponding to the outermost one. The x axis indicates the collection fiber number, rather than the center-to-center distance between each collection fiber and the illumination fiber, as the latter is different for the three MD probe geometries. All the fibers have an NA of 0.22.

Figure 7

The total fluorescence detected from the epithelial tissue model with the MD1, MD2, and MD3 probe geometries (see Table 2, NA=0.22) . The total fluorescence detected was calculated by taking the ratio of the number of detected fluorescent photons to the number of fluorescent photons generated within the medium. The linearly arranged adjacent collection fibers are labeled 1 through 5, with number 1 corresponding to the nearest collection fiber and number 5 corresponding to the outermost one.

Figure 8

The 80 probing depth in the epithelial tissue model achieved with the MD1, MD2, and MD3 probes (see Table 2, NA=0.22) . The 80 probing depth is defined as the depth within which 80 of the detected fluorescent photons originate. The linearly arranged adjacent collection fibers are labeled 1 through 5, with number 1 corresponding to the nearest collection fiber and number 5 corresponding to the outermost one.

Figure 9

The sensitivity to the first layer in the epithelial tissue model achieved with the MD1, MD2, and MD3 probes (see Table 2, NA=0.22) . The sensitivity to the first layer is defined as the ratio of the detected fluorescence from the first layer (thickness of 450 μm) to the total detected fluorescence. The linearly arranged adjacent collection fibers are labeled 1 through 5, with number 1 corresponding to the nearest collection fiber and number 5 corresponding to the outermost one.

Figure 7 displays the total fluorescence detected from the epithelial tissue model with the MD1, MD2, and MD3 probe geometries. The total fluorescence detected ranges from a maximum of 1.5E-4 to a minimum of 5E-6 as the center-to-center distance between the illumination and collection fibers increases. At small center-to-center distances (for example, collection fiber 1), MD2 exhibits the highest total fluorescence detected among the three, followed by MD3, then MD1. At larger center-to-center distances (for example, collection fibers 4 and 5), the total fluorescence detected is very similar for the three probes. These results indicate that for a fixed collection diameter, less fluorescence is detected if the area over which the illumination photons are launched is increased (MD1 versus MD2). For a fixed illumination diameter, less fluorescence is detected if the collection area is decreased (MD3 versus MD2). The effect of varying the illumination and/or collection diameter diminishes as the center-to-center distance is increased.

Figure 8 shows the 80 probing depth in the epithelial tissue model achieved with the MD1, MD2, and MD3 probes. For the three probe geometries employed, the 80 probing depth increases from a minimum of 700 μm to a maximum of 1200 μm, with an increase in the center-to-center distance between the illumination and collection fibers. MD1 has a greater probing depth than MD2, suggesting that an increase in the illumination diameter increases the probing depth. MD2 has a greater probing depth compared to MD3, indicating that increasing the collection diameter also increases the probing depth.

Figure 9 displays the sensitivity to the first layer in the epithelial tissue model achieved with the MD1, MD2, and MD3 probes. For all the three probe geometries, the sensitivity to the first layer ranges from a maximum of 40 to a minimum of 15. At small center-to-center distances (for example, collection fiber 1), the sensitivity to the first layer is highest for MD3, followed by MD2, then MD1. At large center-to-center distances (for example collection fibers 4 and 5), the sensitivity to the first layer is very similar for all three probe geometries. These results suggest that increasing the illumination or collection diameter decreases the sensitivity to the first layer. The effect of varying the illumination and/or collection diameter diminishes as the center-to-center distance is increased.

3.4.

Effect of Different Fiber Numerical Apertures

Table 3 shows the effect of two different fiber NAs (0.22 and 0.37) on the total fluorescence detected, the 80 probing depth, and the sensitivity to the first layer for the VA and MD2 probe geometries (see Table 2). The most significant change is observed in the total fluorescence detected, which is improved by a factor of 2 to 3 by increasing the NA from 0.22 to 0.37. The 80 probing depth is decreased only slightly when the NA is increased from 0.22 to 0.37. The sensitivity to the first layer does not change significantly as the fiber NA is increased from 0.22 to 0.37.

Table 3

3.5.

Effect of Optical Properties

Table 4 shows the effect of two different sets of optical properties (optical property sets 1 and 2, see Table 1) on the total fluorescence detected, the 80 probing depth, and the sensitivity to the first layer, for the VA and MD2 probe geometries (see Table 2) with an NA of 0.22. For convenience, the two sets of optical properties are denoted as tissue set 1 and tissue set 2, respectively. In tissue set 2, the absorption coefficient is lower in the first layer and the scattering coefficient is much higher in the second layer, relative to those in tissue set 1. The changes induced by different optical properties are different for the VA and MD2 probe geometries. In the case of the VA probe, the 80 probing depth is greater, while the total fluorescence detected and the sensitivity to the first layer is significantly lower for tissue set 2 compared to tissue set 1. In the case of MD2, the 80 probing is slightly lower for tissue set 2 relative to tissue set 1, except at the shortest center-to-center distance. The total fluorescence detected is slightly higher for tissue set 2. The sensitivity to the first layer is significantly decreased for tissue set 2 compared to tissue set 1. In summary, the most significant finding is that for both VA and MD2 probe geometries, sensitivity to the first layer is decreased when the absorption of the first layer is decreased and the scattering coefficient of the second layer is increased.

Table 4

3.6.

Comparison of VA and MD Probe Geometries

In summary, the VA and MD approaches have complementary characteristics. In Table 4, comparison of the VA and MD2 probe geometries indicates that for a fixed NA of 0.22 and for optical property set 1, the probing depth of the MD2 probe ranges from 750 to 1200 μm, while that of the VA probe ranges from 450 to 750 μm. At a similar probing depth of ∼750 μm for both the VA and MD2 probes, the total number of fluorescent photons detected by the VA probe is more than an order of magnitude greater than that detected by the MD2 probe. The sensitivity of the VA probe to the first layer ranges from 80 to 45, while that of the MD2 probe ranges from 30 to 15.

3.7.

Combined VA and MD Probe Designs

The work shown here suggests that a fiber optic probe design that combines the VA and MD configurations can maximize the sensitivity to both the epithelial and stromal layer of epithelial tissues. Figure 10 shows the cross-section of a simple fiber optic probe design that combines the complementary characteristics of the VA and MD approach. The probe consists of seven optical fibers, each with a diameter of 200 μm. Three illumination and collection geometries can be implemented. First, the central fiber 1 can be used for both illumination and collection (VA approach: illumination diameter=collection diameter=200 μm) . Second, fiber 1 and fiber ring 2 can be used for illumination and collection (VA approach: illumination diameter=collection diameter=600 μm) . Finally, fiber 1 can be used for illumination and fiber ring 2 can be used for collection (MD approach: illumination diameter=collection diameter=200 μm, center-to-center distance=200 μm) .

Figure 10

Cross-section of a simple fiber optic probe design that combines the complementary characteristics of the VA and MD approach. The probe consists of seven optical fibers, each with a diameter of 200 μm. Three illumination and collection geometries can be implemented. First, the central fiber 1 can be used for both illumination and collection (VA approach: illumination diameter=collection diameter=200 μm) . Second, fiber 1 and fiber ring 2 can be used for illumination and collection (VA approach: illumination diameter=collection diameter=600 μm) . Finally, fiber 1 can be used for illumination and fiber ring 2 can be used for collection (MD approach: illumination diameter=collection diameter=200 μm, center-to-center distance=200 μm) . All fibers have a numerical aperture (NA) of 0.22.

Table 5 shows the total fluorescence detected, the 80 probing depth, and the sensitivity to the first layer for the combined probe design shown in Fig. 10. The three different illumination and collection geometries allow the probing depth to vary such that at the smallest probing depth, the sensitivity to the first layer is maximized, while at the largest probing depth, the sensitivity to the second layer is maximized. At the intermediate probing depth, the probe samples both the first and second layer. The total fluorescence detected is lowest for the MD approach when one illumination and one collection fiber pair are simulated. In practice, this signal can be improved when a total of six collection fibers are used.

Table 5