1.

Introduction

The field of optical diagnostics has the potential to improve public health by providing rapid, minimally invasive disease detection with greater accuracy and less cost than current standards of care. One of the most promising approaches in this area is UV-VIS fluorescence spectroscopy, which has been demonstrated to be highly effective for a variety of applications including neoplasia detection.¹ While this technology is approaching clinical viability, it is likely that further developments may enhance diagnostic efficacy. Research on excitation and emission wavelengths and discrimination algorithms has elucidated issues relevant to system optimization. However, in spite of the myriad of fiber optic probe designs that have been implemented in prior studies,² the literature provides little information about the influence of device-tissue interface design on diagnostic efficacy or parameters that may influence disease diagnosis, such as signal origin and intensity.

In recent years, there has been rising interest in the role of device-tissue interface parameters. Studies on normal-incidence illumination-collection schemes have indicated that parameters such as fiber diameter, source-detector separation, and probe-tissue spacing strongly affect relative sensitivity to fluorophores in turbid media.^{3, 4, 5, 6, 7} These variations in spatial sensitivity have the potential to be exploited in vivo for targeting of specific tissue layers that are most diagnostically relevant, as suggested previously.^{8, 9}

Several prior studies of fiber optic probe design for Raman spectroscopy have investigated the use of fibers that are beveled to induce an optical deflection, such that excitation light enters the tissue at a non-normal angle to the surface.^{10, 11, 12} Similarly, beveled tip collection fibers detect light exiting tissue at an angle. For media with low turbidity, the location where illumination and collection cones overlap is interrogated in a highly selective manner. A simple illustration of this effect is shown in Fig. 1 . The top row of diagrams indicates how angled overlapping spot (e.g., single-fiber) probe geometries cause an increase in selectivity to the most superficial regions, whereas the second row indicates how angled nonoverlapping spot geometries could maximize selectivity to subsurface regions. These cases illustrate the basis of oblique geometry selectivity; however, scattering and absorption cause changes in the location and shape of the targeted region. It must also be noted that while Figs. 1(a), 1(b), 1(c) contain probe designs that are not realistic representations of true single-fiber angled probes, overlapping illumination and collection spots might be achieved through noncontact multifiber probes or free beam approaches.

Fig. 1

Illustration of illumination (solid lines) and collection (dashed lines) cones for normal- and oblique-incidence geometries. Darkened areas indicate the regions of overlap, and thus maximum sensitivity. Diagram in (c) indicates how illumination $\left({\theta }_i\right)$ and collection $\left({\theta }_c\right)$ angles were defined.

A prior investigation of angled fiber optic probe designs for fluorescence spectroscopy in epithelial tissue¹³ presented computational and in vivo results on the behavior of angled interface geometries. This study found that when an angled illumination fiber was used, the variations in relative sensitivity to epithelial and stromal layers obtained by changing illumination angle and fiber separation distance provided control over relative selectivity that was superior to that obtained using normal-incidence probes. Additionally, a recent study demonstrated the efficacy of an angled fiber approach to reflectance spectroscopy.¹⁴ While these results provide an initial proof of principle for a novel approach to optimizing depth-resolved selectivity of tissue fluorophores, and strong insights for a specific layered tissue geometry, numerous unresolved issues remain regarding the underlying light propagation mechanisms, variations in signal origin, and approaches for device optimization.

In this study, we perform a parametric computational investigation of the effect of a device-tissue interface with angled delivery and collection. The goals of this project were to characterize general trends in selectivity and signal intensity due to device parameters and optical properties, and to distill salient information on light-tissue interaction and device optimization from this data. Specifically, we have implemented a Monte Carlo model to simulate how variations in the illumination and collection angle, spot separation distance, and tissue optical properties influence the origin and intensity of detected fluorescence signals.

2.

Methods

Simulations were performed using a Monte Carlo model of fluorescence spectroscopy nearly identical to those used in our prior studies.^{3, 4} The major differences in the new model are: 1. variable angle of illumination and collection ( ${\theta }_i$ and ${\theta }_c$ , respectively, where both angles are defined with respect to normal incidence); 2. multiple collection geometries were specified for each delivery scheme; and 3. the detector was simulated as a single circular spot rather than a concentric ring (due to a lack of symmetry in many cases).

Given that a wide variety of device designs may be used to achieve an oblique-incidence probe interface (e.g., fibers in air or direct tissue contact, lenses, mirrors, cones, etc.), our intent was not to investigate the performance of a specific approach, but to investigate general light-tissue interactions for oblique-incidence geometries. Therefore, relatively simple illumination-collection geometries were implemented based on approaches from prior studies.^{3, 4, 12} Fiber numerical aperture was assumed to be 0.22. For each of the two oblique angles investigated, the illumination and collection cones were defined by a pair of angles relative to the normal to the tissue surface. The shallow angle case was defined by the angle pair $12.6∕31.6\mathrm{deg}$ and is referred to by its average angle, $22\mathrm{deg}$ . The sharper angle case was defined by the angle pair $35.0∕55.3\mathrm{deg}$ and is referred to by its average angle, $45\mathrm{deg}$ . Photons were launched in a uniform spatial distribution over a circular spot and in a uniform angular distribution through the specified cone angle. Simulations were performed with illumination and collection spots either in an overlapping geometry or with edge-to-edge separation distances $\left(L\right)$ of 0.025, 0.05, 0.1, 0.2, 0.4, or $0.75\mathrm{mm}$ .

Each photon absorbed in the tissue was converted to a fluorescence photon and propagated until absorbed or detected. Two assumptions are inherent in this simplified approach to the excitation-to-emission conversion process: 1. all absorption is due to a single fluorophore, and 2. the fluorophore has a quantum yield of 1.0. Therefore, signal intensities presented in the results show accurate trends but are not physically realistic in terms of absolute values. An important benefit of this approach is that it facilitates the calculation of realistic values for a wide range of situations through a simple multiplication of the simulated detected intensity by the fraction of total absorption due to the fluorophore $({\mu }_{a̱\mathrm{fl}}∕{\mu }_{a̱\text{total}})$ and the fluorophore quantum yield.

A homogeneous tissue region $5\times 5\times 4\mathrm{mm}$ $(\text{length}\times \text{width}\times \text{depth})$ was simulated. Since the probability of detecting photons that reached the edge of this region was minimal, such photons were terminated. Detected fluorescence photons were binned according to their emission location in a 2-D Cartesian matrix $\left(G[i,j]\right)$ , in which $i$ and $j$ correspond to the lateral and depth index of square bins measuring $0.025\mathrm{mm}$ on each side, and where $i$ is defined to be in the plane that bisects the illumination-collection spots (as seen in Fig. 1). This approach effectively provides integration of all fluorescence events over the out-of-plane dimension. The resulting fluorescence origin distribution describes device sensitivity as a function of location within the tissue. Depth-wise emission distributions were calculated by summing $G[i,j]$ over all $i$ , then normalizing the distribution to the total number of detected fluorescence photons.

The two sets of optical properties investigated are listed in Table 1 . These cases were chosen to provide biologically relevant absorption $\left({\mu }_a\right)$ and scattering $\left({\mu }_s\right)$ coefficients at two distinct attenuation levels. The entire superficial surface was assumed to have a refractive index of 1.45, which simulates a large probe that covers the tissue. The lateral and deep boundaries were index matched with the tissue at 1.37. One billion photons were used in each simulation to maximize distribution convergence for low collection efficiency cases while maintaining a marginally reasonable computation time of approximately $110\mathrm{h}$ on a $2.2\text{-}\mathrm{GHz}$ dual-processor workstation (Dell Incorporated, Round Rock, Texas).

Table 1

Tissue optical property cases.

3.

Results

Computational modeling results describing the effect of angled illumination-collection design on the intensity and origin of detected fluorescence are presented here. In all simulations performed, the geometry included one illumination and one collection spot, each having a diameter of $0.2\mathrm{mm}$ . For data presented in Fig. 2 , the illumination and collection spots overlapped completely. The remainder of the data presented here (Figs. 3, 4, 5, 6, 7 ) involves nonoverlapping cases with edge-to-edge spot separation distances $\left(L\right)$ from $0.025\text{to}0.75\mathrm{mm}$ .

Fig. 2

Depth-resolved graphs of the effect of illumination and collection angle on relative sensitivity for overlapping spot designs. Graphs present data for (a) low and (b) high attenuation cases. Label for each curve indicates type of illumination and collection geometry, respectively. Data have been normalized to total detected signal.

Fig. 3

Contour plots of the effect of illumination and collection angle on signal origin for the low attenuation case, where $L=0.1\mathrm{mm}$ . The illumination-collection geometries shown are: (a) ${\theta }_i=0\mathrm{deg}$ , ${\theta }_c=0\mathrm{deg}$ ; (b) ${\theta }_i=0\mathrm{deg}$ , ${\theta }_c=22\mathrm{deg}$ ; (c) ${\theta }_i=0\mathrm{deg}$ , ${\theta }_c=45\mathrm{deg}$ ; and (d) ${\theta }_i=45\mathrm{deg}$ , ${\theta }_c=45\mathrm{deg}$ . Scale represents the number of emission photons detected from each bin location. In all cases, the illumination fiber is on the left side.

Fig. 4

Effect of illumination and collection angle for nonoverlapping geometries where $L=0.1\mathrm{mm}$ . The four graphs represent two optical property sets and two illumination geometries: (a) low attenuation, ${\theta }_i=0\mathrm{deg}$ ; (b) low attenuation, ${\theta }_i=45\mathrm{deg}$ ; (c) high attenuation, ${\theta }_i=0\mathrm{deg}$ ; and (d) high attenuation, ${\theta }_i=45\mathrm{deg}$ . For each graph, three collection angles are presented as specified.

Fig. 5

Effect of spot separation distance $\left(L\right)$ for the low attenuation case. The five graphs represent different illumination-collection geometries: (a) ${\theta }_i=0\mathrm{deg}$ , ${\theta }_c=0\mathrm{deg}$ ; (b) ${\theta }_i=0\mathrm{deg}$ , ${\theta }_c=45\mathrm{deg}$ ; (c) ${\theta }_i=45\mathrm{deg}$ , ${\theta }_c=0\mathrm{deg}$ ; (d) ${\theta }_i=45\mathrm{deg}$ , ${\theta }_c=22\mathrm{deg}$ ; and (e) ${\theta }_i=45\mathrm{deg}$ , ${\theta }_c=45\mathrm{deg}$ . Note that a different set of separation distances were used in (e).

Fig. 6

Effect of illumination-collection spot separation distance $\left(L\right)$ for the high attenuation case. The four graphs represent four cases: (a) ${\theta }_i=0\mathrm{deg}$ and ${\theta }_c=0\mathrm{deg}$ ; (b) ${\theta }_i=0\mathrm{deg}$ and ${\theta }_c=45\mathrm{deg}$ ; (c) ${\theta }_i=45\mathrm{deg}$ and ${\theta }_c=0\mathrm{deg}$ ; and (d) ${\theta }_i=45\mathrm{deg}$ and ${\theta }_c=45\mathrm{deg}$ .

Fig. 7

Detected signal intensity as a function of probe design for (a) low attenuation ${\theta }_i=0\mathrm{deg}$ , (b) low attenuation, ${\theta }_i=45\mathrm{deg}$ , (c) high attenuation, ${\theta }_i=0\mathrm{deg}$ , and (d) high attenuation ${\theta }_i=45\mathrm{deg}$ .

Results for the overlapping spot cases are seen in Fig. 2. A design similar to the single fiber probes in our prior studies $({\theta }_i={\theta }_c=0\mathrm{deg})$ ^{3, 4} is represented with filled triangles. Changing ${\theta }_i$ or ${\theta }_c$ caused an increase in sensitivity to regions in the most superficial $50\text{to}100\mu \mathrm{m}$ . It is also worth noting that slightly greater selectivity—the ability to detect signals exclusively from a specific region—was achieved for ${\theta }_i=0\mathrm{deg}$ and ${\theta }_c=45\mathrm{deg}$ in comparison to the ${\theta }_i=45\mathrm{deg}$ and ${\theta }_c=0\mathrm{deg}$ geometry. This is seen as an increase in sensitivity for the very superficial regions and a corresponding decrease in deeper regions, and is likely due to differences in optical properties at the excitation and emission wavelengths, as well as differences in acceptance angle for the two detection geometries. Increasing attenuation caused an increase in selectivity to the superficial region, an effect that was most significant for the ${\theta }_i={\theta }_c=0\mathrm{deg}$ case. Most of these effects are explained by the diagrams in Figs. 1(a), 1(b), 1(c), which illustrate that the normal incidence case tends to collect fluorescence originating from a range of depths, yet when light is delivered or collected at an oblique angle, the cone overlap volume shrinks to a region close to the surface. 2-D plots are not provided in Fig. 3 for the overlapping probe geometry, because signal origin is limited to a very small region directly below the overlapping region and such graphs would not provide significant additional information than what is available in Fig. 2.

Spatially resolved fluorescence origin data are presented in Fig. 3 for the low attenuation case where the illumination-collection spot separation distance $\left(L\right)$ is $0.1\mathrm{mm}$ (edge-to-edge distance). For the ${\theta }_i={\theta }_c=0\mathrm{deg}$ geometry [Fig. 3(a)], detected photons originated over a large region from the tissue surface to $1.0\mathrm{mm}$ deep. This detection region resembles the crescent shape typical of light propagation in tissue. A significant amount of noise is seen in this graph due to the relatively low total signal and the fact that detected photons originated from a wide range of positions. Increasing ${\theta }_c$ to $22\mathrm{deg}$ [Fig. 3(b)] caused a decrease in noise and an increase in selectivity to a region $0.45\mathrm{mm}$ below the surface. Relative sensitivity to superficial regions decreased while sensitivity to the illumination-collection cone overlap zone seen in Fig. 1(e) increased. However, the higher sensitivity region is oval shaped, likely due to light scattering. For a ${\theta }_c=45\mathrm{deg}$ design [Fig. 3(c)], the location of greatest sensitivity was located about $0.2\mathrm{mm}$ below the surface and had sharper boundaries that were almost triangular, corresponding to the superficial edge of the overlap region. In both Figs. 3(b) and 3(c), the high-sensitivity region was almost directly below the illumination spot. When ${\theta }_i$ was increased to $45\mathrm{deg}$ [Fig. 3(d)], the high-sensitivity region moved to a location approximately halfway between the illumination and collection spots, as expected from Fig. 1(e). This change also caused an increase in selectivity, with very high sensitivity occurring in a circular region about $0.2\mathrm{mm}$ in diameter. While the location of this region is expected, the apparently circular shape is not, although this region is so small that its edges are distorted due to the size of the bins. The difference in signal intensity between these plots is an indication of the large changes in sensitivity that can occur as a result of device design.

1-D graphs of fluorescence signal origin for separated spot geometries are presented in Fig. 4. These data document the influence of illumination and collection angle as well as attenuation level. Changes in ${\theta }_i$ or ${\theta }_c$ had very similar affects, with increasing angles resulting in greater selectivity and a reduction in peak sensitivity depth. For example, the depth of the sensitivity peaks in Fig. 4(a) changed from $0.375\mathrm{mm}$ at ${\theta }_c=22\mathrm{deg}$ to $0.2\mathrm{mm}$ at ${\theta }_c=45\mathrm{deg}$ , while the corresponding full-width at half-maximum (FWHM) decreased from $0.425\text{to}0.225\mathrm{mm}$ . Exceptions to this trend were seen for high attenuation cases in Figs. 4(c) and 4(d), where shift in peak location was minimal as ${\theta }_c$ increases. It is also worth noting that minimal signal was detected from depths below $0.5\mathrm{mm}$ for the high attenuation cases, which may indicate the limit of probing depth for this technique, whereas significant signal can be obtained for the low attenuation case up to about $0.8\mathrm{mm}$ below the surface.

High attenuation results tended to produce sensitivity peaks that were greater and more superficial than their low attenuation counterparts, particularly for smaller angle geometries. Additionally, the widths of these peaks decreased with attenuation, for example, a change in FWHM peak width from $0.425\text{to}0.325\mathrm{mm}$ was produced for the ${\theta }_i=0\mathrm{deg}$ , ${\theta }_c=22\mathrm{deg}$ geometry. These changes were likely due to the reduction in photon penetration depth produced by the high attenuation case. However, the effect of attenuation on signal origin was reduced as ${\theta }_i$ or ${\theta }_c$ increased, to the point where for the ${\theta }_i=45\mathrm{deg}$ , ${\theta }_c=45\mathrm{deg}$ geometry, the peak height, width, and depth were very similar for both attenuation cases. This is likely a result of high angle geometries detecting excitation-emission photon pairs with shorter path lengths, therefore making these designs less susceptible to absorption-related effects.

The effect of $L$ on signal origin is shown for low and high attenuation cases in Figs. 5 and 6, respectively. These figures contain graphs representing different combinations of ${\theta }_i$ and ${\theta }_c$ . The greatest variations in signal origin distributions are produced for the low attenuation cases in Fig. 5. The normal-incidence case is represented in Fig. 5(a), and indicates a very homogeneous signal origin (and low signal level, which causes the high level of variability). As ${\theta }_i$ or ${\theta }_c$ are increased, the distributions become more selective to specific depth ranges; however, for each combination of angles, the separation distance has a strong effect on the location and selectivity of interrogation. Increasing separation distance caused increases in peak depth and width. For example, in Fig. 5(c), as $L$ increased from $0.025\text{to}0.4\mathrm{mm}$ , the peak sensitivity depth increased from 0.15 to 0.425, and the FWHM increased from 0.2 to 0.375. The separation distances in Fig. 5(e) are different than those in the remainder of Fig. 5 to investigate the potential for achieving high selectivity at greater depths. For the largest $L$ values investigated in Figs. 5(c), 5(d), 5(e) the peak sensitivity depths were 0.425, 0.35, and 0.375, and the FWHM values were 0.375, 0.275, and 0.3, respectively. These values indicate that the tradeoff between depth of peak sensitivity and selectivity can be modified using ${\theta }_i$ , ${\theta }_c$ , or $L$ ; however, several combinations of these parameters can be used to achieve relatively high selectivity at moderate depths. This tradeoff in depth of peak versus selectivity is likely a result of beam divergence due to the illumination and collection cones as well as scattering.

The high attenuation results in Fig. 6 show sensitivity peaks that are more superficial than in Fig. 5. For example, the $L=0.4\mathrm{mm}$ case for ${\theta }_i=45\mathrm{deg}$ , ${\theta }_c=45\mathrm{deg}$ has a maximum sensitivity depth of $0.175\mathrm{mm}$ , as opposed to the $0.225\text{-}\mathrm{mm}$ value for the corresponding geometry in Fig. 5(e). Additionally, the larger separation distance curves in Fig. 6 tend to show a rounded peak, possibly due to the higher level of scattering. These differences are most noticeable for larger $L$ values, and appear to decrease with $L$ . The sensitivity to deeper regions is minimal for the high attenuation case, indicating the difficulty of interrogating deep fluorophores. In general, the graphs in Fig. 6 show several common effects, including a shift in the location of subsurface peaks toward greater depths as $L$ is increased, although this effect is less than that seen for the low attenuation case, and quite minimal for the ${\theta }_i=0\mathrm{deg}$ case. Maximum sensitivity (peak height) showed a significant decrease with $L$ . Direct comparison between Figs. 6(b) and 6(c) indicate minimal differences, with the oblique-incidence collection case [Fig. 6(b)] providing slightly greater selectivity.

Detected fluorescence signal intensity data is presented in Fig. 7. These graphs contain data for the low attenuation [Figs. 7(a) and 7(b)] and high attenuation [Figs. 7(c) and 7(d)] cases and either ${\theta }_i=0\mathrm{deg}$ [Figs. 7(a) and 7(c)] or ${\theta }_i=45\mathrm{deg}$ [Figs. 7(b) and 7(d)]. Detected signal intensity decreased exponentially with illumination-collection spot separation distance ( $R^2$ values for these fits ranged from 0.97 to 0.99). While this relationship is similar to that found for normal-incidence probes in our prior study,⁴ simulation data from Skala ¹³ appear to indicate an approximately linear relationship between separation distance and detected signal when ${\theta }_i=45\mathrm{deg}$ and ${\theta }_c=0\mathrm{deg}$ , but an approximately exponential relationship for ${\theta }_i=0\mathrm{deg}$ and ${\theta }_c=0\mathrm{deg}$ , although no fitting data were provided. The source of this discrepancy is not known.

In general, increased illumination/detection angle caused an increase in detected signal. It is likely that this is due to the fact that larger angles reduce the depth of the subsurface overlap region. As a result, the average excitation-emission pathlength decreases as does the level of light absorption. The few exceptions to this trend occurred for the high attenuation/angled illumination case [Fig. 7(b)] as the ${\theta }_c$ was changed from $22\text{to}45\mathrm{deg}$ . The near equivalence in detected signal level for these two cases is likely due to the fact that the overlap regions for these two cases become similar as ${\theta }_c$ increases and $L$ decreases. One possible reason for the higher signal at ${\theta }_c=45$ and small $L$ values is that there is a smaller field of view represented by the $45\mathrm{deg}$ case based on the overlap area as opposed to that of the $22\mathrm{deg}$ case.

4.

Discussion

Depth-dependent variations in sensitivity to tissue fluorophores are strongly influenced by device-tissue interface parameters. By exploiting known variations, it may be possible to selectively interrogate individual tissue layers or determine the optical characteristics of tissue as a function of depth. Such abilities are particularly interesting in light of studies that indicate that disease progression can cause changes in the endogenous fluorescence characteristics and morphology of individual tissue layers.^{8, 9, 15} For example, fluorescence originating from the epithelial layer of cervical tissue has been shown to increase with neoplastic progression. This layer is on the order of $350\mu \mathrm{m}$ thick and contains three primary fluorophores—tryptophan, NADH, and FAD—of which the latter two are mitochondrial components. Fluorescence generated in the deeper stromal layer is primarily due to collagen and has been shown to decrease with disease onset. While the sensitivity distributions of normal-incidence designs have been investigated, it is likely that angled delivery and collection may enable further improvements in selective interrogation of tissue layers, such as the epithelium and stroma of cervical tissue. The unique insights provided by this study should improve understanding of basic light-tissue interaction effects, as well as provide insights on device design that are relevant to cervical cancer detection and a range of other public health issues.