2.1.

Tissue Model and Optical Properties

A two-layer cylindrical tissue model is used to represent human uterine-cervical epithelial tissue. The thickness of the epithelial (top) layer is set at $450\mathrm{\mu }\mathrm{m}$ to approximate the average thickness of the human uterine-cervical epithelium.³² The basal stromal layer is set at $10\mathrm{mm}$ , which is representative of a semi-infinite tissue layer underneath the epithelium. The cylindrical diameter of $20\mathrm{mm}$ is wide enough to encompass all photon paths collectible by our particular fiber geometries. The optical properties of the tissue model are based on the values reported by Collier, ³³ Chang, ³⁴ and Drezek ³ that were also adopted by Zhu, Liu, and Ramanujam,²² Wang, ²⁹ and Skala ³⁰ in their respective studies on epithelial tissue. The adopted scattering and absorption coefficients for the tissue model can be found in Figs. 1a and 1b , respectively. The anisotropy factors of the epithelium and stroma are 0.94 and 0.89, respectively, and are assumed to be constant according to our references.^{3, 34}

Fig. 1

(a) and (b) Optical properties of the normal and abnormal epithelial models are shown. The sectioned lines denote the properties of normal tissue; the triangular markers denote the epithelia and should be referenced to the primary axis on the left.

2.2.

Tissue Properties and Rationale

This study investigates the sensitivities of fiber probes to: 1. changes in tissue scattering properties and 2. changes in tissue absorption. As previously noted, epithelial dysplasia is linked to the growth of epithelial nuclei and the consequent increase of scattering. To explain, in human stratified epithelial tissue, a typical nucleus has a diameter of approximately $5\mathrm{\mu }\mathrm{m}$ , while the size can nearly double in cellular dysplasia. Cases involving an increase as large as $20\mathrm{\mu }\mathrm{m}$ in diameter have been reported. ^{2, 28, 35, 36, 37, 38, 39} These enlarged nuclei in the epithelial layer consequently increase the local scattering coefficients of the affected region. However, in advanced neoplasm, where degradation of collagen occurs in the stromal layer,^{40, 41, 42} a decrease in basal layer scattering has also been reported.^{43, 44} More importantly, such changes in tissue scattering result in differences in reflectance spectra, affecting detection of tissue pathology. Thus, the sensitivity and specificity of optical diagnostics applied to tissue may be enhanced where a given fiber geometry is able to identify the origins of detected spectra. From the perspective of tissue pathology then, it is important to understand how varying scattering properties of both epithelial and stromal layers may be better diagnosed with the angled fiber approach.

Three scattering scenarios are implemented in our tissue model. These scenarios take into account the development of tissue pathology relative to: 1. individual variations of the scattering coefficients of either the superficial or basal layer, and 2. simultaneous changes of tissue scattering in both layers. We use the scattering coefficients of the normal and abnormal cervical tissue as the boundary values of our model. Between these boundaries, three intermediate and equidistant points are designated as the transitional stages of tissue dysplasia. The scattering coefficients of the normal and abnormal tissue corresponding to both epithelial and stromal layers are shown in Fig. 1a. The three intermediate levels are omitted from the graph to avoid cluttering, but those values can be calculated as the weighted means (25/75, 50/50, and 75/25 percentage ratios) of the boundary values. This model does assume that the correlation between tissue pathology and scattering is linearly proportional. However, we believe it is justified in this particular study, since our primary aim focuses on investigating the capability of various fiber designs to differentiate, among reflectance spectra, the changes in layer-specific tissue properties. To emphasize the effect of tissue scattering, we keep the absorption coefficients of the tissue model constant and equal to those of the normal epithelial tissue.

With regard to tissue absorption, hemoglobin is perhaps the most dominant and relevant tissue chromophore. As such, accelerated metabolism and neovascularization associated with tissue neoplasia significantly affect the level of hemoglobin absorption in tissue;^{45, 46, 47} therefore, hemoglobin absorption is an important indicator of tissue pathology. However, it is generally believed that neovascularization usually does not appear at the onset of epithelial dysplasia, during which period most observable abnormalities are manifested in the epithelial layer. In addition, general hemoglobin absorption can pose a significant interference to the measurement of other physiological parameters, such as intrinsic tissue fluorescence and absorption due to nonhemoglobin chromophores. Notwithstanding these complications, our objective focuses on the performance of angular fiber geometry with respect to tissue absorption at different tissue pathological levels. Accordingly, spatially resolved spectroscopy provides an opportunity to separate layered-specific tissue absorption from the bulk measurement. Thus, for the superficially probing fiber geometry, it is desirable to have minimal perturbations in reflectance spectra due to hemoglobin absorption, while the deeply probing geometries are needed to increase the reflectance sensitivity to hemoglobin absorption in tissue.

Similar to the scattering scenarios, three absorption scenarios are implemented in the simulation model. This model takes into account isolated absorption variations of either the superficial or basal layer, as well as simultaneous changes of tissue absorption in both layers. Here, we use the absorption coefficients of the normal and abnormal cervical epithelial tissue as the boundary values [Fig. 1b].^{3, 34} Similar to the scattering scenarios, four intermediate points are selected as the transition states of tissue dysplasia. To emphasize the effect of tissue absorption, we use the scattering coefficients of the normal epithelial tissue as a constant parameter in the model.

2.3.

Fiber Geometries

Before starting the Monte Carlo simulation, solid fiber optics were computationally implemented in the simulation program to imitate realistic spatial configurations of fibers in a fiber probe. To execute this, a single illumination fiber, $100\mathrm{\mu }\mathrm{m}$ in diameter, is situated at the center of the tissue model, surrounded by a ring of 12 collection fibers, also $100\mathrm{\mu }\mathrm{m}$ in diameter and $300\mathrm{\mu }\mathrm{m}$ apart, as measured center-to-center from the source fiber. The collection fibers are evenly spaced and positioned concentrically about the illumination axis; each fiber is individually modeled as a solid 3-D object. The illumination fiber is invariantly oriented flush to the surface of the tissue model, and only the angular orientation of the collection fibers is investigated. Three collection angles, 0, 40, and $-20\mathrm{deg}$ , are implemented in this study. The negative angle denotes fiber rotation away from the illumination fiber. Differences in refractive indices and losses due to refraction are taken into account by the simulation program, based on the theoretical calculation of Fresnel’s refraction formula. The refractive indices of the fibers and tissue in our model are 1.5 and 1.37, respectively. The nominal numerical aperture of the fibers is 0.22, modeling after common multimode fiber optics, which translates to an effective numerical aperture of 0.16 inside the tissue model.

2.4.

Ray Tracing and TracePro Simulation

TracePro by Lambda Research (Littleton, Massachusetts) is the ray-tracing program used for the theoretical calculation of photon propagation in the tissue model. TracePro utilizes the well-established Monte Carlo solid modeling method to simulate photon interactions with tissue. The human interface of TracePro is similar to that of CAD, which allows users to create necessary geometric details of the model. Particulars about Monte Carlo modeling can be found in many published scientific texts. ^{48, 49, 50, 51, 52, 53}

In TracePro, illumination photons are guided through a perpendicularly oriented source fiber at the center of the tissue surface via an effective numerical aperture of 0.16, as noted before. An evaluation of simulation convergence had already been conducted prior to the initiation of this study. At that time, we ran ten groups of provisional simulations with increasing numbers of incident rays, and calculated the detected reflectance convergence. With a ray count of 10 million per wavelength, the maximum standard error among the ten trial simulations across the entire spectrum was no greater than 5%. Therefore, we determined that 10 million incident photons were sufficient to provide necessary simulation convergence. 40 million photons per wavelength are used in the final simulations to have extra data sampling. MATLAB version 7.0 by Mathworks, Incorporated (Natick, MA) is used for postsimulation data processing.

In this spectral simulation study, we are primarily interested in the reflectance spectra sampled under different tissue optical properties using the fiber geometries indicated earlier. Detected photons (simulated separately for each wavelength) and their remnant photonic weights (1 being the initial value) are summed to give the total detected reflectance at each simulated wavelength. The penetration depth $\left(Z_{max}\right)$ of a single photon is defined as the greatest axial displacement of photon propagation. Although $Z_{max}$ does not completely represent the spatial distribution of photons in tissue, since it only quantifies photon propagation in the axial direction, it is an appropriately indicative metric for the characterization of photon penetration in tissue and can be directly correlated to actual tissue depths. As the spatial metric, characterizing individual photons, is properly defined, its weighted average with respect to individual photons’ contribution to the overall reflectance is taken. This is done to give a proper valuation of the probing capability of the fiber probes as a whole. Let the weight of each detected photon be $\mathit{f}$ , the number of detected photons $\mathit{NP}$ , and the total reflectance $\mathit{R}$ . Then the expected value of probing depth at that wavelength is formulated as the following:

3.1.

Changes in Scattering Coefficients

Figures 2a, 2b, 2c show the reflectance detected by the 0-deg collection fibers at $300\text{-}\mathrm{\mu }\mathrm{m}$ SDSD when the scattering coefficients are varied in the epithelial, stromal, and both layers, respectively. The fluence values are referenced to the peak of the normal tissue’s spectra, so that the differences among the simulated reflectance spectra can be easily assessed. As the epithelial scattering increases nearly threefold from the normal to abnormal state, we expect to detect more early returning photons reemitted from the superficial layer. However, and contrary to our expectations, a slight downward trend in the detected reflectance is observed for the 0-deg collection fibers. Based on diminishing fluence levels, together with the opposing phenomenon of increasing superficial scattering, we conclude that the 0-deg fiber geometry may be predominantly sensitive to the basal stromal layer.

Fig. 2

(a), (b), and (c) Reflectance spectra detected by the 0-deg collection fibers when tissue scattering coefficients progress from the normal to abnormal conditions in the epithelial, stromal, and both layers, respectively; the values of fluence are referenced to the peak of the normal tissue.

Figures 3a, 3b, 3c depict the detected reflectance by the 40-deg collection fibers, and the optical properties of the tissue model are identical to those implemented previously. Contrary to the orthogonal fibers, this obliquely oriented fiber geometry accurately probes the epithelial layer, which is its expected target, and yields reflectance spectra consistent with the rising trend of the epithelial scattering, as epithelial dysplasia progresses. Additionally, the fluence levels and spectral structures of the reflectance curves shown in Figs. 3a and 3c are in general agreement. This indicates that the stromal variations additionally included in Fig. 3c do not significantly alter the results. At the same time, Fig. 3b corroborates this conclusion by demonstrating that variations in the stromal scattering only produce limited changes in the reflectance spectra, which are sampled with the 40-deg collection fibers.

Fig. 3

(a), (b), and (c) Reflectance spectra detected by the 40-deg collection fibers when tissue scattering coefficients progress from the normal to abnormal conditions in the epithelial, stromal, and both layers, respectively; the values of reflectance fluence are referenced to the peak of the normal tissue.

In Figs. 4a, 4b, 4c , where the reflectance spectra yielded by the $-20\text{-}\mathrm{deg}$ fibers are shown, we can see that the changes in epithelial scattering only produce limited perturbations on the spectra, whereas much more pronounced differences in the spectral fluence and structure are seen for the cases involving changes in stromal scattering properties.

Fig. 4

(a), (b), and (c) Reflectance spectra detected by the $-20\text{-}\mathrm{deg}$ collection fibers when tissue scattering coefficients progress from the normal to abnormal conditions in the epithelial, stromal, and both layers, respectively; the values of reflectance fluence are referenced to the peak of the normal tissue.

Quantitatively, Table 1 tabulates the “area under curve” (AUC) values of the spectra with various combinations of fiber angles and tissue scattering properties. The dataset of the normal tissue is designated as the reference and normalized to one. For fiber geometry insensitive to changes in the scattering property of a particular tissue layer, AUC should remain relatively unperturbed, while acute changes in AUC typically indicate a strong sensitivity to the particular layer under investigation. Neither the 0- nor $-20\text{-}\mathrm{deg}$ fibers yield significant differences in AUC when the epithelial layer is the sole subject of investigation. The $40\text{-}\mathrm{deg}$ fibers are particularly insensitive to the changes in stromal scattering, while significant changes in AUC are seen for the same fiber geometry as the epithelial model transforms from normal to abnormal. This strong correlation with the epithelial layer suggests that the 40-deg fibers have the potential to detect tissue pathology inside epithelia at an earlier time than the 0- and $-20\text{-}\mathrm{deg}$ fibers.

Table 1

Area under curve with respect to various combinations of tissue scattering properties and fiber geometry; values are normalized to the dataset of the normal tissue. Greater deviations from the normal tissue indicate strong fiber probing sensitivity and correlation to corresponding tissue layers.

In addition to the spectral relationship between the fiber geometry and tissue scattering, the probing depths of a fiber probe may also be affected by the changes in a tissue’s optical properties. Our simulation results show that the probing depths of all three fiber probes gradually increase with increasing wavelengths. This occurs because tissue is generally less scattering and absorptive at longer wavelengths. The trend of increasing probing depths with respect to longer wavelengths is consistent. Thus, for brevity, only two representative wavelengths (420 and $580\mathrm{nm}$ , representing the wavelengths on the shorter and longer ends of the spectrum, respectively) are shown. The selective wavelengths are indeed representative of the entire spectrum as regarding the penetration depths in tissue with respect to different fiber geometries. Table 2 tabulates the expected probing depths, as defined in Eq. 1, with respect to the combinations of fiber geometries and tissue scattering conditions discussed thus far, at wavelengths of 420 and $580\mathrm{nm}$ , respectively. In the parentheses following the expected probing depths, we include the standard deviations with respect to the computed means by Eq. 1. Mathematically, the standard deviations are a measure of distribution variation with respect to the mean values. In the context of this study, the standard deviations denote the spatial selectivity of the fiber probes. It must be noted that the standard deviations here should not be regarded as the level of convergence of the Monte Carlo simulations; instead, they should be viewed as the ranges of probing depths extended bilaterally from the expected probing depths.

Table 2

Mean and standard deviation of fiber probing depths with respect to various combinations of tissue scattering properties and fiber geometry; values are shown in the unit of μ m. The standard deviations enclosed in the parentheses represent the range of fiber probing depths extended bilaterally from the means.

3.2.

Changes in Absorption Coefficients

Although the tissue absorptions of both the epithelial and stromal layers are investigated, only the stromal absorption is presented here. Our simulations indicate that epithelial absorption coefficients only impose minuscule perturbations to the overall spectra. Using the metric AUC, we determine that the greatest difference in overall reflectance fluence among the simulated epithelial-only models is approximately 1%; thus, we are unable to make definitive discriminations among the spectra, since all spectra virtually overlap for all three configurations of fiber geometry. Since the thickness of the epithelial layer is small, the path lengths traversed by photons in the epithelial layer are most likely too small to create significant changes due to epithelial absorption. In addition, since the levels of variation in epithelial absorption associated with tissue pathology are considerably smaller in magnitude than those involving stromal absorption, we do not include epithelial absorption here.

Figures 5a, 5b, 5c show the reflectance spectra of the 0-, 40-, and $-20\text{-}\mathrm{deg}$ collection fibers, respectively; both the epithelial and stromal absorption coefficients sequentially transit from the normal to abnormal state. Comparing the spectra among the three subfigures, we see that the presence of hemoglobin absorption is the least evident in the spectra collected by the 40-deg fibers and the most evident for the $-20\text{-}\mathrm{deg}$ . fibers, as gauged by the reflectance fluence at the Soret $\left(420\mathrm{nm}\right)$ and Q-band (540 and $580\mathrm{nm}$ ) wavelengths. To quantify the sensitivity of the fibers to tissue absorption, we use the metric AUC to measure the change in overall reflectance with respect to varying tissue absorption, and these data are shown in Table 3 . Based on the numerical results shown in Table 3, it is clear that epithelial absorption properties have only very limited influence on the overall fluence levels of detected reflectance, while comparatively, stromal absorption is the main source of reflectance attenuation. Figure 6 specifically demonstrates the trend of decreasing AUC, as tissue absorption in both layers increases from normal to abnormal levels in tandem. The results suggest that the $-20\text{-}\mathrm{deg}$ fibers, by virtue of their deep probing depths, are more responsive to the changes in stromal absorption by showing 11 percentage points of variation in AUC. On the other hand, the 40-deg fibers only have about 2 percentage points of variation in the AUC metric.

Fig. 5

(a), (b), and (c) Reflectance spectra detected by the 0-, 40-, and $-20\text{-}\mathrm{deg}$ collection fibers, respectively, when tissue absorption coefficients progress from the normal to abnormal conditions in both layers; the values of reflectance fluence are referenced to the peak of the normal tissue.

Fig. 6

Normalized areas under curve calculated for the 0-, 40-, and $-20\text{-}\mathrm{deg}$ collection fibers, respectively, when tissue absorption coefficients progress from the normal to abnormal conditions in both layers; the values of AUC are referenced to those of the normal tissue.

Table 3

Area under curve with respect to various combinations of tissue absorption properties and fiber geometry; values are normalized to the dataset of the normal tissue. Greater deviations from the normal tissue indicate strong fiber probing sensitivity and correlation to corresponding tissue layers.

Table 4 shows another method of quantifying the fibers’ probing sensitivity to the stromal layer. This method measures the levels of reflectance depression at hemoglobin’s Soret wavelength $\left(420\mathrm{nm}\right)$ with respect to various combinations of tissue absorption properties and fiber geometries. Using the normal tissue model as the reference, we are able to assess the rate of reflectance attenuation at the Soret wavelength correlated to the transition of tissue absorption from the normal to abnormal states. This metric is particularly pertinent to the interpretation of hemoglobin absorption in the reflectance spectra: as hemoglobin concentration increases with angiogenesis in diseased tissue, further depressed reflectance fluence is seen with the 0- and $-20\text{-}\mathrm{deg}$ fibers, whereas only limited deviations are observable for the 40-deg fibers, which further confirm their insensitivity to hemoglobin interference using the 40-deg fiber geometry.

4.1.

Sensitivities to Changes in Layer Scattering

In this study, we investigate the sensitivity of reflectance spectroscopy to changes in tissue scattering properties when different fiber geometries are used. From the results collectively shown in Sec. 3.1, it is clear that changes in epithelial scattering coefficients are best detected by the 40-deg collection fibers, which produce the most discernable contrast among the simulated reflectance spectra, as the epithelial scattering coefficients increase from normal (low) to abnormal (high) levels [Fig. 3a]. At the same time, the 40-deg fibers are insensitive to changes in the stromal layer by yielding nearly identical reflectance spectra, regardless of the stromal scattering conditions [Fig. 3b]. In addition, the increase in epithelial scattering coefficients is accurately manifested in the reflectance spectra with the 40-deg fibers. More specifically, the fluence levels of the spectra consistently increase as the epithelial layer transforms from normal to abnormal. This is expected because, as the epithelial scattering coefficients increase nearly threefold, more photons should reemit from the superficial layer and increase the reflectance fluence. However, decreasing trends in the simulated reflectance are observed for the 0-deg collection fibers [Fig. 2a]. Diminishing fluence levels, together with the opposing phenomenon of increasing superficial scattering, indicate that this fiber geometry may be predominantly sensitive to the basal stromal layer. This is true because, with greater superficial scattering, it is likely that more photons are scattered and reemitted in shallow depths that are not detectable by the 0 collection fibers. Although the source-detector separation distance (SDSD) is quite small $\left(300\mathrm{\mu }\mathrm{m}\right)$ , the majority of early returning photons remains near the source fiber, which is outside the detection space of the collection fibers. Consequently, the increase in the superficially scattered rays does not contribute to the overall reflectance. By the same argument, the rise in superficial scattering should reduce the number of photons that reach the basal layer, where the 0-deg fibers gather the majority of reflectance signals. As a result, reductions in reflectance fluence are seen here. The suggestion that the 0-deg fibers are deeply probing is supported by the comparisons between Figs. 2b and 2c. Specifically, as tissue transforms from the normal to diseased states, the scattering coefficients of the basal stromal layer also decrease. Under these conditions, the detected reflectance correspondingly diminishes with the downward trend of stromal scattering. Furthermore, the reflectance spectra shown in Figs. 2b and 2c are similar in both magnitude and structure, which suggests the limited influence of epithelial scattering in the resultant spectra.

Similar to the 0-deg fibers, the resultant reflectance spectra simulated with the $-20\text{-}\mathrm{deg}$ fibers also demonstrate limited sensitivities to the changes in epithelial scattering properties. The negative prefix of the $-20\text{-}\mathrm{deg}$ fibers denotes an opposite rotation about the source fiber such that the angled fibers have their distal facets facing away from the illumination point. By blocking the intake of superficially scattered photons, this particular fiber geometry probes deeper into the tissue and, consequently, yields spectra that are more responsive to the changes in stromal tissue properties.

4.2.

Disparities between the 0 and –20–Deg Fibers

Although both the 0 and $-20\text{-}\mathrm{deg}$ fibers are expected to probe deeply into the tissue, we observe an interesting disparity in their reflectance spectra, as shown in Fig. 2a for the 0-deg fibers and Fig. 4a for the $-20\text{-}\mathrm{deg}$ fibers. In Fig. 2a, the fluence level decreases with increasing epithelial scattering coefficients. This may be attributed to both the loss of superficially scattered photons that are not detectable by the collection fibers, and consequent reduction in photons entering the stromal layer, as discussed previously. However, this effect does not seem to apply to the $-20\text{-}\mathrm{deg}$ fibers, which, in contrast, exhibit a gain in reflectance fluence as a result of increasing epithelial scattering. To further explain the apparent disparity between these two similarly deeply probing fiber geometries, we analyze the spatial distributions of the collected photons to gather more information about the photon collections of both fiber geometries. Beginning with the simplest representation of photon distributions in tissue, Fig. 7 demonstrates the depth-wise distribution of reflectance detected by the 0- and $-20\text{-}\mathrm{deg}$ fibers under low $(\mathrm{\mu }\mathrm{s}=4.82{\mathrm{mm}}^{-1})$ and high $(\mathrm{\mu }\mathrm{s}=14.2{\mathrm{mm}}^{-1})$ epithelial scattering coefficients that respectively represent the normal and abnormal epithelial scattering properties implemented in the tissue model. The horizontal axis is partitioned every $10\mathrm{\mu }\mathrm{m}$ , and the peak fluence is normalized to 1 to enable easy comparisons among the curves. These reflectance data are sampled at the 380-nm wavelength and verified to be representative of the general trends across the spectrum. The common responses to increasing epithelial scattering between the 0- and $-20\text{-}\mathrm{deg}$ fibers are the moderate rises in superficial reflectance from the epithelial layer, seen before the $450\text{-}\mathrm{\mu }\mathrm{m}$ mark on the abscissa, and leftward shifts of peak stromal reflectance to the epithelium-stroma interface. This explains the decrease in tissue probing depths, as the superficial layer becomes more scattering. However, the 0-deg fibers have a significant decline in stromal reflectance under the higher epithelial scattering condition, which, in effect, lowers the overall reflectance, despite the moderate increase in superficially scattered signal. Interestingly, the $-20\text{-}\mathrm{deg}$ fibers do not suffer the same loss in reflectance fluence as the 0-deg fibers. Instead, there is a gain of reflectance distributed in both epithelial and stromal layers for the $-20\text{-}\mathrm{deg}$ fibers with greater epithelial scattering.

Fig. 7

Depth-wise distribution of reflectance detected by the 0- and $-20\text{-}\mathrm{deg}$ collection fibers under low $(\mathrm{\mu }\mathrm{s}=4.82{\mathrm{mm}}^{-1})$ and high $(\mathrm{\mu }\mathrm{s}=14.2{\mathrm{mm}}^{-1})$ epithelial scattering conditions that respectively represent the normal and abnormal epithelial scattering properties implemented in our tissue models. The horizontal axis is partitioned into sections of $10\mathrm{\mu }\mathrm{m}$ , and the peak fluence is normalized to one.

The causes of the variations in the depth-resolved reflectance may be better understood when the lateral distributions of detected reflectance are analyzed. To illustrate this, Fig. 8 shows the density distribution of the collected photons with respect to the lateral distances measured from the illumination point when the photons reach their respective maximum probing depths in tissue. The $-20\text{-}\mathrm{deg}$ fibers, by virtue of their outwardly rotated facets, are able to detect photons farther away from the source fiber, as opposed to the 0-deg fibers, which primarily gather photons in the tissue volume between the source and collection fibers. The extended detection range of the $-20\text{-}\mathrm{deg}$ fibers may enable greater collection of the photons scattered in the stromal layer and thereby create a gain in the overall reflectance fluence.

Fig. 8

The lateral density distribution of detected reflectance, as measured from the center of the source fiber, as photons reach their respective maximum probing depths in tissue. Both instances of the 0- and $-20\text{-}\mathrm{deg}$ collection fibers under low $(\mathrm{\mu }\mathrm{s}=4.82{\mathrm{mm}}^{-1})$ and high $(\mathrm{\mu }\mathrm{s}=14.2{\mathrm{mm}}^{-1})$ epithelial scattering conditions, which respectively represent the normal and abnormal epithelial scattering properties, are demonstrated. The horizontal axis is partitioned into sections of $10\mathrm{\mu }\mathrm{m}$ .

Although Figs. 7 and 8 may reveal some important insights into the changes of reflectance distribution where tissue scattering is concerned, the information is, nonetheless, one dimensional. For better qualitative understanding of photon distribution in the tissue models, the maps of fluence distribution are used to provide simultaneous information about optical fluence and spatial distribution in both axial and radial directions, as shown in Figs. 9a, 9b, 9c, 9d . In these figures, the abscissa denotes the lateral positions of the moving photons in tissue, and the ordinate denotes the axial positions measured from the tissue surface. It should be noted that only the collected photons are shown in the maps; hence, the data provided in these figures do not account for photons that are lost or rejected by the collection fibers. For the 0-deg fibers [Figs. 9a and 9b], with greater epithelial scattering, the injected photons diverge quickly and lift the overall distribution toward the tissue surface. However, the fluence level near the epithelium-stroma interface has become less concentrated and thus results in a loss of detected reflectance from the same region. Similar observations can be made for the $-20\text{-}\mathrm{deg}$ fibers, with the exception that appreciable gains in both epithelial and total reflectance are observed where there is stronger epithelial scattering. When the tissue model employs the greater epithelial scattering coefficients, the $-20\text{-}\mathrm{deg}$ fibers detect more photons near the epithelium-stroma interface [Fig. 9d], whereas the lesser scattering epithelial layer leads to a less efficient reflectance gathering from the same region of the tissue [Fig. 9c]. To explain this phenomenon, we believe that the stronger epithelial scattering causes the incident photons to diverge more quickly and that this then results in a rise in reflectance carried by photons near the epithelium-stroma boundary. The radius of incident beam, expanded by the stronger epithelial scattering, seems to escape the effective detection region of the 0-deg collection fibers; consequently, we observe a decrease in detected fluence inside the stromal layer that overshadows the moderate gain in epithelial reflectance, and consequently results in a net loss in the overall reflectance. On the other hand, the expanded incident beam better illuminates the tissue space visible to the outwardly rotated $-20\text{-}\mathrm{deg}$ fibers, which consequently results in greater reflectance sampled from the tissue.

Fig. 9

(a) through (d) Internal fluence distribution in tissue for 0- and $-20\text{-}\mathrm{deg}$ fibers under low $(\mathrm{\mu }\mathrm{s}=4.82{\mathrm{mm}}^{-1})$ and high $(\mathrm{\mu }\mathrm{s}=14.2{\mathrm{mm}}^{-1})$ epithelial scattering conditions that respectively represent the normal and abnormal epithelial scattering properties implemented in our tissue models. The grid size is $10\times 10\mathrm{\mu }\mathrm{m}$ .

Table 4

Level of reflectance fluence at hemoglobin’s Soret wavelength (420nm) with respect to various combinations of tissue absorption properties and fiber geometry; values are normalized to the dataset of the normal tissue. Greater deviations from the normal tissue indicate strong fiber probing sensitivity to hemoglobin presence.

4.3.

Assessment of Probing Depths

In addition to the spectral relationship between the fiber geometry and tissue scattering, the probing depths of a fiber probe may also be affected by the changes in tissue scattering properties. For the 0-deg fibers, the increasing epithelial scattering shifts the proportionality of detected reflectance toward the surface and results in a trend of decreasing probing depths. However, a less intuitive result is that the reduction in the stromal scattering also increases the probing depths when the epithelial scattering remains constant. Conventionally, reduction in stromal scattering should decrease the amount of photons reemitted from the basal layer and shift the spatial emphasis to the superficial layer. In fact, while that may be true for some cases, our simulation data indicate that smaller stromal scattering coefficients allow photons to penetrate more deeply and travel greater distances in the tissue model before detection by the collection fibers. This prolonged tissue penetration may well offset the reduction of stromal reflectance in the calculation of probing depths [Eq. 1], and an increase in the calculated probing depths is therefore seen as associated with decreasing stromal scattering. Once the scattering transitions in both layers are combined, the probing depths are further reduced as tissue scattering conditions transform from normal to abnormal. The combination of high epithelial and low stromal scattering coefficients strongly diminishes the number of reflected rays from the basal layer and, consequently, further amplifies the reduction in probing depths, in spite of the prolonged penetration depths and path lengths of individual photons in the stromal layer.

Compared to the 0-deg fibers, the probing depths of the 40-deg fibers show a different dependence on the scattering properties of the tissue model, as the probing depths decrease in all three scenarios of tissue scattering. It should be recalled that moderately deeper depths are achieved with decreasingly intensive stromal scattering when the 0-deg fibers are used; however, in the instance of the 40-deg fibers, the probing depths are shifted toward the tissue surface under the same scattering conditions. According to the numerical results of our simulation, there is a significant reduction in the number of photons that penetrate to the region near the epithelium-stroma interface. In other words, there is a loss of reflectance that originates from the basal epithelium and top of the stroma. The exclusion of these moderately penetrating photons shifts the weight of reflectance distribution toward the surface. This loss can be elucidated by the scattering coefficients of the stroma, which acts as a background reflector underneath the epithelial layer. As the scattering coefficients of the stromal layer decrease, more photons are able to propagate into the deeper space of the tissue model and then exit outside the collecting region of the 40-deg fibers. These photons, however, are better sampled by the 0- or $-20\text{-}\mathrm{deg}$ collection geometry, as both result in a deeper distribution of detected reflectance. The probing depths of the $-20\text{-}\mathrm{deg}$ fibers trend in the same way as those of the orthogonal fibers, and are therefore not repeated here.

4.4.

Sensitivities to Changes in Absorption

Based on the spectra shown in Fig. 5, it is evident that hemoglobin, being the dominant chromophore in tissue, strongly affects the fluence levels and shapes of the reflectance spectra. In Fig. 5, the presence of hemoglobin absorption is the least evident in the spectra collected by the 40-deg fibers and the most evident for the $-20\text{-}\mathrm{deg}$ fibers, as gauged by the reflectance fluence at the Soret $\left(420\mathrm{nm}\right)$ and Q-band (540 and $580\mathrm{nm}$ ) wavelengths. As tissue absorption coefficients increase with increased tissue abnormality, the reflectance levels for all three fiber geometries correspondingly decrease. However, our data, as shown in Table 3, indicate that the 40-deg fibers are minimally affected by the changes in stromal absorption coefficients due to their highly selective probing sensitivity to the epithelial layer. On the other hand, the $-20\text{-}\mathrm{deg}$ fibers yield reflectance spectra for which the fluence levels are strongly sensitive to the increase in stromal absorption. These results indicate that the $-20\text{-}\mathrm{deg}$ fibers may be better utilized to target neovascularization in the stromal region, whereas the 40-deg fibers can better eliminate hemoglobin interference when only superficial epithelium is the target of interest.