Numerical investigation of depth-sensitive diffuse reflectance and fluorescence measurements on murine subcutaneous tissue with growing solid tumors.

In most biomedical optical spectroscopy platforms, a fiber-probe consisting of single or multiple illumination and collection fibers was commonly used for the delivery of illuminating light and the collection of emitted light. Typically, the signals from all collection fibers were combined and then sampled to characterize tissue samples. Such simple averaged optical measurements may induce significant errors for in vivo tumor characterization, especially in longitudinal studies where the tumor size and location vary with tumor stages. In this study, we utilized the Monte Carlo technique to optimize the fiber-probe geometries of a spectroscopy platform to enable tumor-sensitive diffuse reflectance and fluorescence measurements on murine subcutaneous tissues with growing solid tumors that have different sizes and depths. Our data showed that depth-sensitive techniques offer improved sensitivity in tumor detection compared to the simple averaged approach in both reflectance and fluorescence measurements. Through the numerical studies, we optimized the source-detector distances, fiber diameters, and numerical apertures for sensitive measurement of small solid tumors with varying size and depth buried in murine subcutaneous tissues. Our study will advance the design of a fiber-probe in an optical spectroscopy system that can be used for longitudinal tumor metabolism and vasculature monitoring.


Introduction
Optical spectroscopy can leverage endogenous contrast or be coupled with appropriate indicators to provide functional information while allowing for high-dynamic measures of the tissue metabolism and its associated vasculature in vivo [1,2]. For example, both oxygenated and deoxygenated hemoglobin have broadband optical absorption spectra [3], which have been extensively used to quantify vascular oxygenation and hemoglobin concentration [4] with the use of diffuse reflectance spectroscopy techniques [5]. On the other hand, autofluorescence spectroscopy has been explored heavily to quantify tissue reduced nicotinamide adenine dinucleotide (NADH) and flavin adenine dinucleotide (FAD) [6,7] as an effective means to provide insights into the reduction-oxidation (redox) state to indicate the tissue metabolism status [8]. To quantify tumor metabolism directly and explicitly, exogenous fluorescence metabolic probes have been explored for in vivo tumor metabolism monitoring. For instance, we have developed novel techniques to quantify glucose uptake using glucose analog 2-NBDG [9] and mitochondrial membrane potential using TMRE [10] in tumor models in vivo [2,11]. The combination of diffuse reflectance and fluorescence spectroscopy has been reported frequently to quantify both tissue metabolism and vascular microenvironment in vivo in biological models [2,8,11].
In a typical optical spectroscopy setup, a fiber-probe consisting of single or multiple illumination and collection fibers was commonly used for the delivery of illuminating light and the collection of emitted light [12]. The fibers with small source-detector distances (SD) probe the superficial tissue layer while the fibers with large SD distances sense the deep tissue region [13,14]. To maximize the collected optical signal, the light intensities from all collection fibers were commonly combined and then sampled by an optical spectrometer [2]. However, such simple averaged-volume optical measurements may induce significant errors for in vivo tumor characterization as the superficial tissue layer over the tumor region could largely affect the optical tumor sensing capability. To increase the optical probing capability of a more deep-seated and larger target, larger SD was usually recommended in a diffuse reflectance setup with a sacrifice of collected optical signal strength [12][13][14][15][16][17]. This well-established guideline has been commonly adapted to optimize the fiber probe design for the detection of advanced tumors in different tissue models using diffuse reflectance spectroscopy. For example, Hennessy et al. [14] conducted a Monte Carlo study to demonstrate that the sampling depth of visible diffuse reflectance spectroscopy in a layered skin tumor model was around half of the SD. More recently, Greening et al. [13] conducted both phantom studies and in vivo animal studies to show that the sampling depth of visible diffuse reflectance spectroscopy in skin tissue was around half of the SD and the largest SD of 4 mm was examined. For the characterization of a semi-infinite or infinite target, the general guideline of increasing SD to maximize the sensing depth worked well as long as sufficient signals could be acquired. However, it may induce significant errors for early-stage tumor characterization, especially in longitudinal studies where the tumor size and depth vary with tumor stages, and a very early-stage tumor might be too small to be considered as a semi-infinite or infinite layer.
In our current study, we aimed to identify the most sensitive and practical probe design for a specific novel important application, i.e. in vivo optical characterization of a growing solid tumor in murine subcutaneous tumor models for longitudinal study in which the tumor size varies from tiny, to small, and to the middle. In vivo optical longitudinal monitoring of tumor biology becomes critical for translational cancer studies because it has the great potential to provide dynamic, quantitative measurements of both metabolism and the associated vascular endpoints of solid tumors under a variety of conditions in vivo. In addition to the examination of optimal SD values, we also investigated other key fiber parameters including fiber diameters and numerical apertures (NA) so that one may achieve high tumor detection sensitivity with decent signal levels for tumors at different stages. Moreover, we combined fluorescence and diffuse reflectance measurement in one platform, thus, one may identify the fiber probe design that works for the two types of measurements, enabling one quantify tumor metabolism and vasculature simultaneously on the same tissue region. To identify the optimal fiber geometries for tumor-sensitive diffuse reflectance and fluorescence measurement on murine subcutaneous tissue with growing solid tumors, our previously reported Monte Carlo code [18,19] was used to simulate both diffuse reflectance and fluorescence in a layered tissue model with a buried tumor-like target. Our study showed that the most tumor-sensitive SD varied with subcutaneous tumor stages. Specifically, the optimal SD distances for tiny subcutaneous tumors (< 3mm) were found to be ∼1.5 to 2.0 mm, while the best SD for small subcutaneous tumors (<6 mm) were found to be ∼2.5 to 3.0 mm, and the SD for middle subcutaneous tumors (>6 mm) were found to be ∼3. 0 mm or larger. Our data also showed that neither fiber diameters nor NA affect the tumor detection sensitivity when an optimal SD was used; however, both fiber diameter and fiber NA could significantly affect the collected signal strength. Our findings in this study will advance the design of tumor-sensitive fiber-probes to be used in an optical spectroscopy platform for longitudinal diffuse reflectance and fluorescence measurements on murine flank solid tumors.

Monte Carlo method and fiber probe geometry
A Monte Carlo code previously developed by us [18,19] was modified to simulate both diffuse reflectance and fluorescence in a layered tissue model with a buried tumor-like target. A spherical target with a specified radius and position was used to mimic an early stage solid tumor. The details and validation of the code have been reported elsewhere [20]. Twenty million photons were launched in all simulations as described below.
To compare the tumor detection sensitivities of depth-sensitive measurements and averaged spectroscopy measurements, the simple fiber-probe configuration with multiple SD distances as shown in Fig. 1 was examined. As illustrated in Fig. 1(a), the SD values were varied from 0.5 mm to 3.0 mm with an increment of 0.5 mm. A small SD was expected to probe the superficial tissue layer while a large SD is expected to sense the deep tissue region [13,14]. The summed value of the light intensities collected from all six collection fibers represent the averaged optical measurement, which was commonly used in a typical optical spectroscopy platform [2,11,21]. The values of the light intensity simulated from each of the specific collection fibers with different SD refer to the depth-sensitive optical measurements. Both illumination and collection fibers were perpendicular to the tissue surface as shown in Fig. 1(b). When the SD varied from 0.5 mm to 3.0 mm, the diameters of all fibers were fixed at 0.2 mm and the NA was set to be 0.22 in the simulations otherwise specified. The refractive indices of all fibers were set to 1.47. In addition to the examination of SD described above, we further investigated fiber diameter and NA for sensitive detection of a tiny tumor or a small tumor with a fixed tumor diameter. Note that the SD was fixed to be the optimized value for the finite small tumor models when different fiber diameters or NA values were studied. Specifically, the fiber diameters were varied from 0.1 mm, 0.2 mm, 0.4 mm, and 0.6 mm whenever it was practical to be implemented for a given SD, the fiber NA values were set to be 0.15, 0.22, 0.39, and 0.45 respectively.

Murine subcutaneous tumor models
In most existing tissue optical spectroscopy measurements, the sample was typically assumed to be a semi-infinite, homogenous tissue layer for data processing [2,11,21]. In order to mimic a practical optical spectroscopy measurement on skin tissue with a murine subcutaneous tumor, the simple homogenous layered tissue models as illustrated in Fig. 2(a) were used to simulate skin with advanced murine subcutaneous tumors. To simulate small tumors in a longitudinal tumor growth monitoring study, a finite tumor model shown in Fig. 2(b) consisting of a normal semi-infinite skin layer with a buried tumor-like spherical target was used. To ensure the fluorescence excitation light was always delivered to the central mass of the tumor, the center of the illumination fiber always overlapped with the vertical middle line of a spherical tumor target. In both the semi-infinite tumor model and finite tumor model, the tumor depth was set to be 0.7 mm or 1.0 mm according to previously reported murine skin thickness and subcutaneous tumor depths [13]. In the finite tumor model, the tumor diameters were varied based on their stages including a tiny tumor (<3 mm), a small tumor (<6 mm and >3 mm), and a middle tumor (> 6 mm) [22]. In all tissue models, the total thickness of the tissue was set to 15 mm.
The tissue optical properties including the absorption coefficient, scattering coefficient, and anisotropy used in our simulations were taken from previously published literatures [11,23,24] Table 1. A refractive index of 1.4 was used in both normal tissue and tumor tissue [23]. For diffuse reflectance measurement, the wavelength of 550 nm was used because: (1) It is within the typical light band for the extraction of vascular parameters; and (2) it is the excitation peak for the Tetramethylrhodamine ethyl ester (TMRE), a mitochondrial membrane potential fluorescence probe that we are interested in for our fluorescence measurement. For fluorescence simulations, the 550 nm light was used for excitation while the 585 nm light was used for emission given that the TMRE emission peak is around 585 nm. The quantum yield values for tumor region and normal tissue area were set to be 0.5 and 0.3 respectively according to our previous in vivo preclinical study in which we found that breast tumors have increased TMRE uptake compared to normal tissue [2].

Data analysis
The simulated diffuse reflectance intensities at 550 nm and fluorescence intensities at 585 nm were used to represent the collected optical signals. Because of the general interest in tumor detection, the tumor contrast was introduced to evaluate the optical probing sensitivity to a tumor. The tumor contrast of reflectance (TC R ) was defined as the percent deviation for weighted photon visiting frequency (WVF) which was calculated based on Eq. (1).
The WVF tumor refered to the weighted photon visiting frequency in the tumor region, while the WVF normal refered to the weighted photon visiting frequency in the normal tissue region. As reported previously [16], the WVF refered to the number of times that photons visit a region divided by the total attenuation coefficient at a given region. The WVF based TC R reflects the percentage of tumor region contribution to the total detected diffuse reflectance signals, thereby representing the tumor detection sensitivity. The tumor contrast of fluorescence (TC F ) was defined as the percent deviation for detected fluorescence generated from the tumor region to the total detected fluorescence generated from the entire tissue model which was calculated based on Eq. (2).
The F tumor refered to the fiber detected fluorescence signal contributed by the tumor region, while the F normal refered to the fiber detected fluorescence contributed by normal tissue region. A higher tumor contrast refered to a higher optical probe sensitivity to tumors as it represented that more signals from a tumor region could be captured [18]. Each simulation was repeated four times to generate error bars.
To quantify the optical sensing capability, the interrogation depth decribed previously [15] was used. The interrogation depth was the max depth that the detected photons can reach, which was approximately two times of the optical sensing depth which was defined as the depth that at least 50% photons can reach [13,14]. The interrogation depth of diffuse reflectance was obtained by examining the WVF distribution along the Z-axis direction [16], and interrogation depth of fluorescence was found by examining the function of surface measured fluorescence with the occurring position along the Z-axis introduced previously [25].

Depth-resolved diffuse reflectance and fluorescence measurements provided
improved tumor detection sensitivity compared to averaged optical measurements  showed TC R and TC F obtained from depth-resolved (dashed line) and averaged (solid line) measurements on semi-infinite tumor models with a tumor depth of 0.7 mm (thick line) and 1.0 mm (thin line), respectively. As introduced previously, the TC R was calculated based on the WVF, and TC F was obtained based on the fluorescence frequency. In both semi-infinite tumor models, both TC R and TC F were increased significantly when the SD was increased from 0.5 mm to 3.0 mm. TC R and TC F values obtained from the tumor models with a tumor depth of 0.7 mm were always higher than those from tumor models with a tumor depth of 1.0 mm. Figures 4(c)-4(d) showed simulated diffuse reflectance and fluorescence intensities from the tumor models with the corresponding SD values. Figures 4(e)-4(f) showed the log scale of simulated diffuse reflectance and fluorescence intensities as that in Figs. 4(c)-4(d). Both diffuse reflectance and fluorescence intensities dropped when SD was increased. Diffuse reflectance intensities from a tumor model with a tumor depth of 0.7 mm were generally lower than those from a tumor model with a tumor depth of 1.0 mm. In contrast, fluorescence intensities from a tumor model with smaller tumor depth were generally higher than that from a tumor model with larger tumor depth. All error bars in the curves were too small to see.  Figure 5 showed the WVF distribution and fluorescence frequency simulated from the finite tumor models with a spherical tumor that has different diameters. Both the WVF distribution and fluorescence frequency distribution showed that the optical interrogation depth was increased when SD was increased. Generally, the diffuse optical interrogation depth can reach up to 2 mm when the SD is equal or larger than 1.5 mm. In contrast, the fluorescence optical sensing depth may reach up to 3 mm when the SD is equal or larger than 1.5 mm. Interestingly, the fluorescence frequency distribution showed that the secondary peaks were likely caused by the tumor target that generated abundant fluorescence signals. Figure 6 showed TC R and TC F simulated from the finite tumor models with a spherical tumor that had a diameter of 1 mm, 2 mm, 3 mm, 5 mm, 6 mm, and 8 mm respectively. Figure 6(a) showed that the TC R did not change much when SD was changed if the tumor diameter was 1 mm. However, Figs. 6(b)-6(c) showed that the TC R for the 2-mm tumor model or 3-mm tumor model reached the maximum and then decreased when the SD was increased to certain thresholds. Figures 6(d)-6(f) showed that the TC R for small and middle tumors (>3 mm) was increased when SD was increased from 0.5 to 3 mm. Figure 6(g) showed that the TC F did not change much if the tumor diameter was 1 mm irrespective of any SD. In contrast, Figs. 6(h)-6(l) showed that the TC F was increased when SD was increased, and then reached their maximum when the SD reached a certain threshold. Based on Fig. 6, the optimal SD values that yielded the highest optical tumor contrast for detection of tiny tumors, small tumors, and middle tumors respectively were summarized in Table 2. Specifically, a SD of 1.5∼2.0 mm was recommended for diffuse reflectance and fluorescence measurement on tiny tumors, while a SD of 2.5∼3.0 mm was recommended for measurement on small tumors or middle tumors. For the 1-mm diameter tumor, the tumor contrasts were always less than 3%, which suggested that the tumor was too small to be detected by either diffuse reflectance or fluorescence spectroscopy.

3.3.
Size and numerical aperture of fibers did not affect the detection sensitivity of small tumors, but did affect the collected optical signal strength Figure 7 showed the effect of fiber size on the simulated tumor contrast and collected optical signals when the optimal SD of 3 mm was used for detection of a tumor with a diameter of  Figures 7(a)-7(d) showed that the source fiber size did not affect the tumor contrast nor collected diffuse reflectance intensities and fluorescence intensities. Figures 7(e)-7(f) showed that the detector fiber size did not affect the tumor contrast, but it did affect the collected diffuse reflectance intensities and fluorescence intensities. Specifically, the larger detector diameters yielded increased diffuse reflectance and fluorescence intensities. When the detection fiber diameter was increased from 0.1 mm to 0.6 mm, both the collected diffuse reflectance intensities and the collected fluorescence intensities were increased by 40 folds.

Discussion
Optical spectroscopy has the great potential to serve as an important tool for translational cancer studies. The commonly used average spectroscopy measurement [2] could result in low tumor detection sensitivity for small growing tumors. Therefore, depth-resolved measurement was necessitated in order to achieve improved tumor detection sensitivity. Large SD distance offers deeper sensing depth as reported previously [26,27]. Greening et al. conducted in vivo diffuse reflectance studyies on mice and found that SD over 2 mm could distinguish a significant difference in oxygen saturation between normal and small solid tumor (diameter is ∼ 6 mm) [13]. In this work, we examined the SD distances for small growing tumors (diameter varied from 1 mm to 8 mm) detection using both diffuse reflectance and fluorescence measurement.
Our simulations on semi-infinite layer tumor models showed that the large SD distances yielded higher tumor contrast but with lower signals for both diffuse reflectance and fluorescence measurement, which can be well explained by diffusion theory. A larger SD will lead to a deeper sensing depth within the semi-infinite tumor layer, which will monotonically increase the tumor contrast. Compared with depth-resolved measurements, the averaged measurement will display a compressed tumor contrast as it is a superposition of the all individual tumor contrasts within the combination. When the top layer becomes thicker, less percentage of the WVF and fluorescence frequency from tumor region will be collected, thus the overall tumor contrast will drop. This indicates that in a longitudinal study where the top layer thickness increases as the mouse grows, the performance of the averaged measurement will drop but the depth-resolved measurement may be able to provide flexibility to adapt to this change.
Our investigations on finite tumor models showed that a tiny tumor with a diameter of 1 mm might be too small to be detected by either diffuse reflectance or fluorescence. However, once the tumor diameters reached over 2 mm, a max tumor contrast can be achieved by adjusting the SD values. The tumor contrast from diffuse reflectance measurements on tiny tumors displayed a trapezoid pattern as SD distance increased. This trapezoid pattern suggested that a larger SD did not necessarily provide best tumor detection contrast for growing tiny tumors. TC R was increased with SD when tumor diameters are larger than 3 mm, while TC F was increased with SD when tumor diameters are larger than 2 mm when SD was increased from 0.5 mm to 3 mm. We observed that the TC R was always increased with SD for the small or middle tumor models (>5 mm). For these small or middle tumors models, the tumor diameter was larger than the SD values and the tumor can be treated as a semi-infinite layer for diffuse reflectance spectroscopy according to our former study [28]. In the semi-infinite tumor models, the ratio of reflectance signals from tumor region to that from non-tumor would be always increased with SD thereby the TC R was always increased with SD as shown in Fig. 9(a). However, if the tumor diameter was comparable or smaller than SD, the ratio of reflectance signals from tumor region to that from non-tumor may not be always increased with SD due to the tumor boundary effect as illustrated in Fig. 9(b). Because of this, it can be expected that the TC R would increase first and then decrease when the SD was increased from 1 mm to 3 mm for the tiny tumors with a diameter of 2 mm or 3 mm. In contrast, TC F was always increased with SD even for the tiny tumors, this was likely because the excited fluorescence was isotropic thus the tumor boundary effect was not obvious. This phenomenon further highlighted the importance of proper fiber geometry design for tiny tumor measurement in a longitudinal study. Fluorescence frequency distribution shown in Figs. 5(g)-5(l) showed a second peak in the depth region of 1-2 mm. This feature became more visible for larger tumor size and larger SD distance. This second peak was mainly caused by the sudden change of tissue optical properties, especially fluorescence properties at the spherical interface between normal tissue and tumor target. In contrast, the WVF distribution shown in Figs. 5(a)-5(f) did not display a remarkable second peak as that observed in fluorescence distribution. This was likely because the change of optical properties at the spherical interface only involved nonsignificant change of absorption coefficient and scattering coefficient. The above comparison also suggested that fluorescence measurement might be more sensitive for tumor detection compared to diffuse reflectance measurement.
Small tumors in mice with a diameter of ∼ 6 mm were commonly recommended for in vivo tumor metabolism characterization because these small tumors may retain the actual clinically relevant tumor micro-environment well, which was typically hypoxic but not yet starting to necrotize [22]. From the optical measurement perspective, small tumors with a dimeter of ∼ 6 mm were relatively easy to measure with an optical spectroscopy system. However, increasing evidence showed that the tumor metabolism and vasculature varied with tumor stages [2,22], thus it would be critical to be able to longitudinally monitor tumor metabolism and vasculature to comprehensively understand the tumor biology. Thanks to the advance of sensitive optical detectors and novel fiber probes, it was feasible to use optical spectroscopy to characterize tumors with smaller diameters. Our former study [2] demonstrated that the optical spectroscopy with a custom designed fiber probe could be sensitive enough to measure tiny tumors with a diameter of ∼3 mm. In our current study, the tumors were assumed to be spherical to simplify the simulations. The actual tumors might be not spherical when the tumors are either in early stage or advanced stage. However, we anticipated that the shape of tumor will minimally affect the trends of tumor contrast yielded from the current study irrespective of spherical or non-spherical tumors were used. This is because the tumor contrast value was mainly determined by the ratio of signals contributed from entire tumor region to that from the non-tumor region, which is primarily relying on the optically probed tumor volume rather than its shape.
Our numerical studies suggested a set of optimal SD distances as summarized in Table 2, in order to achieve the best tumor detection sensitivity for a longitudinal cancer study where the tumor size varied from tiny (< 3 mm), to small (3-6 mm), and to middle (> 6 mm). For a given tumor with a fixed size, we further optimized fiber diameter and NA when the optimal SD was used. Both tumor models with a 6-mm diameter small tumor (Figs. 7 and 8) and a 3-mm diameter tiny tumor (data not shown) were studied. It was interesting to notice that neither TC R nor TC F change much with fiber diameters. This was likely because the diffuse reflectance or fluorescence intensities could be scaled with baseline when the fiber diameters were changed, and the fiber diameter would influence both the baseline intensity and the tumor-sensed intensity of light. Our data showed that fiber diameters and NA value did not affect tumor contrast but did affect the collected diffuse reflectance and fluorescence intensities. Generally, larger diameter and NA of detection fiber but not illumination fiber yielded significantly increased optical signal. Along with optimal SD distances, the appropriate selection of detector fiber diameter and NA could be of significant value in improving signal-to-noise ratio during diffuse reflectance and fluorescence measurement, especially when detecting small tumors which yields lower tumor contrast. The practical application of our findings in this study is to provide valuable guidance to the probe design for diffuse and fluorescence measurement in longitudinal monitoring of murine subcutaneous tumors. For example, linearly arranged fiber probe consisting of one source fiber and three detection fibers (SD equals 1.5 mm, 2.5 mm and 3 mm), which are trifurcated and connected to one spectrophotometer, is suitable to detect solid tumors ranging from ∼2 mm to ∼8 mm. To obtain a stronger signal intensity and larger lateral sampling volume, a more advanced probe design that contains three rings of detection fibers concentrically arranged around several central source fibers can be fabricated to enable tumor-sensitive diffuse reflectance and fluorescence measurement in an in vivo longitudinal tumor monitoring study.

Conclusion
We numerically investigated the effect of fiber probe geometries to diffuse reflectance and fluorescence measurements on murine subcutaneous tissues with growing solid tumors that had diameters ranging from 1 mm to 8 mm. Our study showed that the most tumor-sensitive SD vary with subcutaneous tumor stages. The study also showed that neither fiber diameters nor NA would affect the tumor detection sensitivity when optimal SD distances were used; however, both fiber diameter and fiber NA could significantly affect the collected signal strength. Our results will advance the design of tumor-sensitive fiber-probes that could be adapted by a diffuse reflectance and fluorescence spectroscopy platform for in vivo longitudinal monitoring of tumor metabolism and vascularization.

Funding
University of Kentucky (Startup); National Institute of General Medical Sciences (P20GM121327).