2.1.

Instrumentation

The DRS probe (FiberTech Optica, Kitchener, Ontario, Canada) consists of a brass ferrule tip of 6.35 mm in diameter and 50 mm in length (Fig. 1). Five multimode optical fibers ($\mathrm{NA}=0.22\pm 0.02$, high-OH for wavelength range 190 to 1200 nm) are arranged in a slit line along the tip of the brass ferrule, with one fiber serving as the source fiber and the remaining four fibers serving as the detector fibers. SDSs are 0.75, 2.00, 3.00, and 4.00 mm. These optical fibers were included to sample into the subcutaneous murine tumor at increasing sampling depths. The source fiber as well as the 2.00-, 3.00-, and 4.00-SDS fibers (FiberTech Optica, SUV400/440PI) consist of a $400/440\mu \mathrm{m}\pm 2\%$ silica core/cladding with a $470\mu \mathrm{m}\pm 5\%$ polyimide jacket. The 0.75-mm SDS fiber (FiberTech Optica, SUV200/220PI) consists of a $200/220\mu \mathrm{m}\pm 2\%$ silica core/cladding with a $245\mu \mathrm{m}\pm 5\%$ polyimide jacket.

Fig. 1

The DRS probe showing (a) distal optics, (b) dimensions of the optical fibers within the probe tip, and (c) proximal optics showing several legs of the DRS probe, spectrometers, and lamp.

The total length of the DRS probe is 1.00 m. The distal (common) end of the probe is 0.67-m long, and fibers are secured within a 4.8-mm outer diameter black PVC-coating monocoil. The proximal (legs) end of the probe is 0.33 m in length, and each individual fiber is secured within a 3.0-mm outer diameter black PVC monocoil terminating in subminiature version A (SMA) connectors, reinforced with strain relief, to be attached to the lamp or spectrometers.

A 20W tungsten-halogen lamp (Ocean Optics, HL-2000-HP) provided broadband light (360 to 2400 nm) to the $400\text{-}\mu \mathrm{m}$ core source fiber. One spectrometer (Ocean Optics, USB2000+VIS-NIR-ES) with a Sony ILX511B 2048-element linear silicon CCD array collected diffusely reflected light from the 0.75- and 2.00-mm SDSs. A second spectrometer (Ocean Optics, FLAME-S) with a Sony ILX511B 2048-element linear silicon CCD array collected diffusely reflected light from the 3.00- and 4.00-mm SDSs. The spectral resolution of the system [Eq. (1)] was calculated as

2.2.

Animal Model

The study was approved by the University of Arkansas Institutional Animal Care and Use Committee (IACUC #18060). CT26 (ATCC^®, CRL-2638^™), a murine colon carcinoma cell line derived from the Balb/c mouse strain, was maintained in Roswell Park Memorial Institute (RPMI)-1640 medium (ATCC^®, 30-2001^™) supplemented with 10% fetal bovine serum (ATCC^®, 30-2020), 1% antibiotic antimycotic solution (Sigma-Aldrich, A5955-100ML), and 0.2% amphotericin B/gentamicin (Thermo Fisher Scientific, R015010). Third passage (P3) CT26 cells were used throughout the study.²²

Ten female Balb/c mice were (strain: 000651, The Jackson Laboratory, ME) aged 9 weeks were housed in groups of three in three cages in the Small Animal Facility at the University of Arkansas. The facility was maintained at $23°\mathrm{C}\pm 1°\mathrm{C}$ and 40% to 60% humidity on a 12:12 h light–dark cycle. Food (8640, Teklad) and water were provided ad libitum. All nine mice acclimated for 7 days after arrival prior to the study start. After 1 week of acclimation, the left flanks of the 10-week-old Balb/c mice were shaved, and Nair was applied for 1 min to locally remove hair. Then, $1\times {10}^5$ CT26 cells in sterile saline were injected subcutaneously into the left flank.^23–25 Tumor allografts grew until they reached a volume of $200{\mathrm{mm}}^3$, after which the tumor underwent DRS measurements.

2.3.

Tumor Allograft Geometry

After performing DRS measurements of Balb/c-CT26 tumor allografts at a volume of $200\pm 50{\mathrm{mm}}^3$, mice were euthanized via cervical dislocation under 4.0% isoflurane and 1 L/min oxygen. Tumors were dissected, placed in OCT and flash frozen in isopentane in liquid nitrogen, and stored at $-80°\mathrm{C}$ for up to 1 week. Tumors cut into $6\text{-}\mu \mathrm{m}$ sections using a cryostat (Leica Biosystems CM1860) and stained with hematoxylin (VWR 100504-404) and eosin (VWR 10143-130) (H&E). H&E-stained tissue sections were imaged with a microscope (Nikon Eclipse Ci) with a 4X/0.25 NA objective and field of view (FOV) of $2.9\times 2.2\mathrm{mm}$. Tumors often exceeded this FOV (i.e., a perfectly spherical tumor at a volume of $200{\mathrm{mm}}^3$ would have a diameter of $\sim 7.4\mathrm{mm}$). Therefore, images were taken of the entire tumor cross section and stitched together using a commercial panoramic image stitching software (Microsoft, Image Composite Editor) (Fig. 2). Thickness of the epidermis, dermis/hypodermis, and fascia was calculated from H&E images calibrated to a 1951 USAF resolution test target (Thorlabs, R1DS1P). All nine CT26 tumors were measured to determine average and standard deviation. Calculating tissue thickness overlying the subcutaneous tumor was important to determine which layers were sampled by each SDS of the DRS probe (Fig. 2).

Fig. 2

The subcutanous Balb/c-CT26 colon tumor allograft showing (a) the DRS probe in contact with the tumor, (b) an H&E-stained transverse section of tumor with overlying tissue layers (scale bar = 1 mm, $E$, epidermis; $D$, dermis; $F$, fascia; and $T$, tumor), and (c) a representation of light transport through the murine subcutaneous tumor allograft at each of the four SDSs (0.75, 2.00, 3.00, and 4.00).

2.4.

Optical Phantoms

To establish a relationship between optical properties, diffuse reflectance, and sampling depth in the LUT model, liquid calibration phantoms were generated with known ${\mu }_s^{\prime }$ and ${\mu }_a$. Calibration phantoms were constructed using distilled water as the solvent. The scattering agent was $1.00\text{-}\mu \mathrm{m}$-diameter polystyrene microspheres (07310-15, Polysciences) and the associated ${\mu }_s^{\prime }$ was calculated using Mie theory. The absorbing agent was teal India ink (11BY, Salis International). The ${\mu }_a$ was calculated by measuring a diluted solution of teal India ink in distilled water using a spectrophotometer (5102-00, PerkinElmer) and the Beer–Lambert Law.^18–20,26

A $5\times 3$ (15 total) set of calibration phantoms was created, corresponding to five scattering ranges and three absorbing ranges (Fig. 3). Five of the 15 phantoms were considered “scattering-only” and contained only polystyrene microspheres without India ink. Distilled water and polystyrene microspheres were mixed inside 7-mL scintillation vials (66022-300, VWR) to yield a ${\mu }_s^{\prime }$ of 2.7, 3.8, 5.4, 7.6, and $10.9{\mathrm{cm}}^{-1}$ at a reference of 630 nm to span a ${\mu }_s^{\prime }$ range of 2 to $15{\mathrm{cm}}^{-1}$ from 450 to 900 nm. The remaining 10 calibration phantoms contained both polystyrene spheres and teal India ink. Five of the 12 phantoms had a peak ${\mu }_a$ of 3.0 at $632{\mathrm{cm}}^{-1}$ and the final five phantoms had a peak ${\mu }_a$ of 10 at $632{\mathrm{cm}}^{-1}$. Thus, calibration phantoms spanned a ${\mu }_s^{\prime }$ range of 2 to $15{\mathrm{cm}}^{-1}$ and a ${\mu }_a$ range of 0 to $10{\mathrm{cm}}^{-1}$ from 450 to 900 nm. These ranges span the optical property range of interest for subcutaneous Balb/c-CT26 tumor allografts.^10,27,28

Fig. 3

Calibration phantoms were made with distilled water, polystyrene microspheres, and teal India ink to span ${\mu }_s^{\prime }$ and ${\mu }_a$ ranges between (a) 2 to $15{\mathrm{cm}}^{-1}$ and (b) 0 to $10{\mathrm{cm}}^{-1}$, respectively, while validation phantoms were made with distilled water, polystyrene microspheres, and bovine hemoglobin to span ${\mu }_s^{\prime }$ and ${\mu }_a$ ranges between (c) 4 to $19{\mathrm{cm}}^{-1}$ and (d) 0 to $8{\mathrm{cm}}^{-1}$, respectively.

To validate the relationship between optical properties and diffuse reflectance in the LUT model, liquid validation phantoms were generated with known ${\mu }_s^{\prime }$ and ${\mu }_a$, respectively. Using these validation phantoms, accuracy of the LUT model could be established by comparing known ${\mu }_s^{\prime }$ and ${\mu }_a$ (expected values) to the ${\mu }_s^{\prime }$ and ${\mu }_a$, respectively, generated by the LUT model (experimental). Validation phantoms were constructed similar to calibration phantoms but used bovine hemoglobin (H2625, Sigma-Aldrich) as the absorbing agent. Bovine hemoglobin was used to better simulate biological tissue absorption.

A $3\times 3$ (9 total) set of validation phantoms was created, corresponding to three scattering ranges and three absorbing ranges (Fig. 3). Polystyrene microspheres were added such that phantoms yielded a ${\mu }_s^{\prime }$ of 5.2, 8.5, and $13.5{\mathrm{cm}}^{-1}$ at a reference of 630 nm to span a ${\mu }_s^{\prime }$ range of 4 to $19{\mathrm{cm}}^{-1}$ from 450 to 900 nm. Bovine hemoglobin was added such that phantoms yielded a ${\mu }_a$ of 0 to $1.8{\mathrm{cm}}^{-1}$, 0 to $3.6{\mathrm{cm}}^{-1}$, and 0 to $8.1{\mathrm{cm}}^{-1}$, respectively.

2.5.

Lookup Tables for Diffuse Reflectance

The DRS probe was placed in each liquid calibration phantom, so it was completely submerged at 2 cm from the bottom of the 7-mL scintillation vial. Broadband DRS data (450 to 900 nm) were recorded at each SDS (0.75, 2.00, 3.00, and 4.00 mm) with integration times of 100, 200, 300, and 400 ms, respectively, to yield a SNR of at least 15 dB. Five spectra were averaged for all measurements. Spectra were converted to absolute diffuse reflectance values²¹ by calibrating with a Spectralon^® 20% diffuse reflectance standard (SRS-20-010, Labsphere), which accounts for the spectral shape and daily intensity fluctuations of the halogen lamp. Diffuse reflectance calibration [Eq. (2)] was calculated as

LUTs were generated for each SDS by plotting absolute diffuse reflectance ($R$) against ${\mu }_s^{\prime }$ and ${\mu }_a$ and then interpolating between raw data points to create a smooth mesh for ${\mu }_s^{\prime }$ between 4 and $12{\mathrm{cm}}^{-1}$, and ${\mu }_a$ between 0 and $-8{\mathrm{cm}}^{-1}$ (Fig. 4). This optical property range accounts for all expected ${\mu }_s^{\prime }$ and ${\mu }_a$ in murine tissue in the wavelength range of interest (450 to 900 nm).²⁷

Fig. 4

(a–d) LUTs were created for each SDS (0.75, 2.00, 3.00, and 4.00 mm) using diffuse reflectance spectra from calibration phantoms that were then (e–h) interpolated to create a continuous mesh for ${\mu }_s^{\prime }$ values between 4 and $12{\mathrm{cm}}^{-1}$ and ${\mu }_a$ values between 0 and $8{\mathrm{cm}}^{-1}$.

2.6.

Validation of Lookup-Table Inverse Model

Once LUTs were constructed (Fig. 4), the accuracy of the LUTs needed to be quantified. In other words, for a single spectrum, how closely do the experimental optical properties (determined by the LUT model) match the expected optical properties?

The DRS probe was placed in each liquid bovine Hb-based validation phantom, so it was completely submerged 2 cm from the bottom of the 7-mL scintillation vial. Broadband DRS data (450 to 900 nm) were recorded at each SDS (0.75, 2.00, 3.00, and 4.00 mm) with integration times of 100, 200, 300, and 400 ms, respectively, to yield an SNR of at least 15 dB. Five spectra were averaged for all measurements. Spectra were converted to absolute diffuse reflectance values by calibrating with a Spectralon^® 20% diffuse reflectance standard and background noise subtraction as previously described.

Experimental ${\mu }_s^{\prime }$ and ${\mu }_a$ were calculated using the damped least-squares nonlinear fitting method, appropriate for least squares curve fitting. This method will be, henceforth, referred to as the LUT inverse model fit and was based on the constraining equation for ${\mu }_s^{\prime }$ [Eq. (3)] and ${\mu }_a$ [Eq. (4)]. The constraining equation for ${\mu }_s^{\prime }$ is

Table 1

Boundary conditions for quantifying optical properties of validation phantoms.

After initial conditions were set, the LUT inverse model fit performed up to $1\times {10}^4$ iterations until the sum of squares (${\chi }^2$) were minimized²¹ between the fitted reflectance and measured reflectance. All phantom DRS spectra underwent a final quality control step. If ${\chi }^2$ was $>5\%$, data were discarded (Fig. 5).

Fig. 5

The LUT inverse model of diffuse reflectance fit is based on the damped least-squares nonlinear fitting method, with the goal of outputting ${\mu }_s^{\prime }$ and ${\mu }_a$, as well as contributing parameters from the constraining equations such as scattering exponent and absorber concentration.

Percent errors for ${\mu }_s^{\prime }$ and ${\mu }_a$ were calculated by comparing the expected optical properties derived from Mie theory and the Beer–Lambert law to experimental optical properties derived from the LUT inverse model fit. Average percent error was then calculated by averaging the percent error at each wavelength (450 to 900 nm) for each validation phantom (nine phantoms). Percent errors were always positive values; thus, overestimating and underestimating optical properties produced positive errors that did not cancel out. The LUT was considered accurate when average percent errors for ${\mu }_s^{\prime }$ and ${\mu }_a$ were each $<10\%$, a standard cutoff across the literature.^{18,20,32–35}

2.7.

Optical Properties from Balb/c-CT26 Tumor Allografts

After validation of the LUTs, spectra were collected from Balb/c-CT26 tumor allografts $200\pm 50{\mathrm{mm}}^3$ in diameter ($n=9$), as well as immediately adjacent tissue from the same mouse. Mice were not anesthetized during data collection. The DRS probe was placed in direct contact with the tissue. Broadband DRS data (450 to 900 nm) were recorded at each SDS (0.75, 2.00, 3.00, and 4.00 mm) with integration times of 100, 200, 300, and 400 ms, respectively, to yield an SNR of at least 15 dB. Five spectra were averaged for all measurements. Spectra were converted to absolute diffuse reflectance values by calibrating with a Spectralon® 20% diffuse reflectance standard and background noise subtraction as previously described.

The optical properties were quantified in a similar manner to validation phantoms, using the LUT inverse model fit based on the damped least squares nonlinear fitting method.³⁶ Quantifying in vivo ${\mu }_s^{\prime }$ relied on the same constraining equation as validation phantoms [Eq. (3)]. Next, assuming hemoglobin as the only in-vivo absorber from 450 to 900 nm, the constraining equation [Eq. (5)] for ${\mu }_a$ was equated as

Table 2

Boundary conditions for quantifying optical properties of Balb/c-CT26 tissue.

After initial conditions were set, the LUT inverse model fit performed up to $1\times {10}^4$ iterations until the sum of squares (${\chi }^2$) were minimized between the fitted reflectance and measured reflectance. Using the constraining equations for in-vivo tissue, ${\mu }_s^{\prime }$ at 630 nm, THC, and ${\mathrm{StO}}_2$ were quantified as functions of tissue types (normal versus tumor) and SDS. Optical properties were compared between normal and tumor tissues for each SDS. The significance threshold was set at 0.05. All in-vivo DRS spectra underwent a final quality control step. If ${\chi }^2$ was $>5\%$, data were discarded (Fig. 5). Artifacts due to mouse movement during data collection could potentially cause a high ${\chi }^2$ between the fitted reflectance and measured reflectance. Significance of optical properties between tissue types (healthy and tumor) and SDS (0.75, 2.00, 3.00, and 4.00) was determined using a two-way mixed ANOVA. The significance level was set at 0.05.

2.8.

Sampling Depth of Diffuse Reflectance Spectroscopy Probe into Tissue

The next goal was to quantify sampling depth for each SDS as a function of ${\mu }_s^{\prime }$ and ${\mu }_a$. In other words, once ${\mu }_s^{\prime }$ and ${\mu }_a$ have been quantified via the LUT inverse model, at what depth into tissue are these optical properties being measured?

To quantify sampling depth, a $5\times 3$ (15 total) set of calibration phantoms were constructed.¹⁸ Each of these phantoms was placed into a 5-mL beaker (Fig. 6) with a highly absorbing (${\mu }_a>100{\mathrm{cm}}^{-1}$) black phantom layer, made with (poly)-dimethylsiloxane (PDMS) and black India ink at the bottom. It was assumed that any photon contacting this layer would be attenuated. The ${\mu }_a$ of the black layer was calculated using a spectrophotometer and the Beer–Lambert Law. Additionally, the black layer contained no scattering agent. Contributions from specular reflection at the interface between the black layer and calibration phantoms were negligible (data not shown) as there is a minimal mismatch between the PDMS and liquid phantoms.^14,18

Fig. 6

Sampling depth was quantified by (a–d) taking DRS measurements of calibration phantoms at $50\text{-}\mu \mathrm{m}$ increments between 0 and 3 mm from a highly absorbing (${\mu }_a>100{\mathrm{cm}}^{-1}$) phantom layer. (e) Reflectance (R) increased as distance between the probe and black layer increased, shown for calibration phantom #7 at the 3.00-mm SDS as an example. (f) Sampling depth ($D$) was defined when the SDS is most sensitive to the black layer, which occurs when 50% of photons reach the black layer. (g) Sampling depth ($D$) was then quantified at the $50\text{-}\mu \mathrm{m}$ increment at each wavelength.

The probe was placed in direct contact with the black layer [Figs. 6(a)–6(d)]. Using a mechanical translation stage equipped with a micrometer scale (LNR25M, Thorlabs), the probe was raised from the black layer in $50\text{-}\mu \mathrm{m}$ increments from 0 to 3 mm. DRS measurements, from 450 to 900 nm, were taken at each $50\text{-}\mu \mathrm{m}$ step at each SDS of 0.75, 2.00, 3.00, and 4.00 mm at integration times of 100, 200, 300, and 400 ms, respectively, to yield an SNR of at least 15 dB. As the optical properties of the calibration phantoms were known, a relationship was established between ${\mu }_s^{\prime },{\mu }_a$, and reflectance at various sampling depths. As the probe increased in distance from the black layer, reflectance increased, then leveled [Fig. 6(e)]. At each wavelength, the probe was most sensitive to changes in optical properties when 50% of photons reached the black layer [Fig. 6(f)]. When this process was repeated at each wavelength, a relationship between sampling depth and wavelength was established [Fig. 6(g)]. Therefore, sampling depth ($\lambda$) was defined at the most sensitive $50\text{-}\mu \mathrm{m}$ increment.

Three-dimensional (3-D) plots were generated for each SDS by plotting sampling depth ($D$) against ${\mu }_s^{\prime }$ and ${\mu }_a$ and then interpolating between raw data points to create a smooth mesh for ${\mu }_s^{\prime }$ between 4 and $12{\mathrm{cm}}^{-1}$, and ${\mu }_a$ between 0 and $8{\mathrm{cm}}^{-1}$. This optical property range accounts for all expected ${\mu }_s^{\prime }$ and ${\mu }_a$ in murine tissue in the wavelength range of interest (450 to 900 nm). Once optical properties were calculated using the LUT inverse model, sampling depth was quantified. Significance of sampling depth between tissue types (healthy and tumor) and SDS (0.75, 2.00, 3.00, and 4.00) was determined using a two-way mixed ANOVA. The significance level was set at 0.05.

3.1.

Tumor Allograft Geometry by Tissue Type

Tumors were dissected, cut into $6\text{-}\mu \mathrm{m}$ sections, and H&E stained. Three primary tissue types were visualized above the subcutaneous tumor (Fig. 7): the epidermis, dermis/hypodermis, and fascia. In female Balb/c-CT26 tumor allografts ($n=9$), the epidermis was $0.22\text{-}\pm 0.05\text{-}\mathrm{mm}$ thick, the base of the dermis was $0.71\pm 0.11\mathrm{mm}$ from the surface, and the base of the fascia was $1.00\pm 0.15\mathrm{mm}$ from the surface, respectively.

Fig. 7

To acquire optical properties from the subcutaneous tumor, broadband light from the DRS probe needed to penetrate past the fascia, located $1.00\pm 0.15\mathrm{mm}$ from the surface. Values are mean ± SD. (scale bar = 1 mm).

3.2.

Validation of Lookup-Table Inverse Model

The reflectance from each validation phantom at each SDS, with known ${\mu }_s^{\prime }$ and ${\mu }_a$, was plotted against the LUT created from the calibration phantoms (Fig. 8). Percent errors were acceptable if $<10\%$ for both ${\mu }_s^{\prime }$ and ${\mu }_a$.

Fig. 8

Reflectance from bovine Hb-based validation phantoms (red) was plotted against the LUTs (grayscale grid) for each SDS of (a) 0.75, (b) 2.00, (c) 3.00, and (d) 4.00 mm.

Average percent errors for ${\mu }_s^{\prime }$ were 2.9%, 4.7%, 2.2%, and 2.8% for the 0.75-, 2.00-, 3.00-, and 4.00-mm SDSs, respectively. Average percent errors for ${\mu }_a$ were 9.1%, 9.6%, 9.6%, and 9.2% for the 0.75-, 2.00-, 3.00-, and 4.00-mm SDSs, respectively. Thus, all percent errors were below 10% (Fig. 9).

Fig. 9

Percent errors for comparing experimental optical properties (from LUT inverse model fit) and expected (known) optical properties were below 10% for all SDS of (a, e) 0.75, (b, f) 2.00, (c, g) 3.00, and (d, h) 4.00 mm. The LUT inverse model fit more accurately extracted (a-d) ${\mu }_s^{\prime }$ (percent errors $<5\%$) compared WITH (e–h) ${\mu }_a$. Black dots represent raw data. Red lines indicate a perfect fit with 0% error. Gray background represents the acceptable 10% error.

3.3.

Sampling Depth in Balb/c-CT26 Allografts

Following DRS measurements of calibration phantoms overlying a highly absorbing PDMS layer, 3-D plots were generated for each SDS by plotting sampling depth ($D$) against ${\mu }_s^{\prime }$ and ${\mu }_a$ and then interpolating between raw data points to create a smooth mesh. Sampling depths were valid for ${\mu }_s^{\prime }$ between 4 and $12{\mathrm{cm}}^{-1}$, and ${\mu }_a$ between 0 and $8{\mathrm{cm}}^{-1}$ (Fig. 10). Lowest sampling depth occurred at the highest optical properties (${\mu }_s^{\prime }=12{\mathrm{cm}}^{-1}$, ${\mu }_a=8{\mathrm{cm}}^{-1}$) and highest sampling depth occurred at the lowest optical properties (${\mu }_s^{\prime }=4{\mathrm{cm}}^{-1}$, ${\mu }_a=0{\mathrm{cm}}^{-1}$). Based on this, sampling depths ranged between 0.37 and 1.10 mm, 0.72 and 1.76 mm, 0.92 and 2.08 mm, and 1.16 and 2.25 mm for the 0.75-, 2.00-, 3.00-, and 4.00-mm SDSs, respectively, indicating sampling depth increased as SDS increased. Subcutaneous tumors were located $1.00\pm 0.15\mathrm{mm}$ or deeper below the skin surface; thus, broadband light from the DRS probe needed to penetrate at least 1.15 mm into tissue to sample tumor optical properties. With regard to the colormap in Fig. 10, red coloring indicates sampling depth $\le 1.15\mathrm{mm}$, which was the average thickness, plus one standard deviation, of the overlying skin and fascia of the subcutaneous Balb/c-CT26 tumor. Yellow coloring indicates sampling depth between 1.15 and 1.45 mm, with peak yellow occurring at 1.30 mm, which was the average thickness, plus two standard deviations. Green coloring indicates sampling depth $\ge 1.45\mathrm{mm}$, which was the average thickness plus three standard deviations. Thus, yellow and green coloring represent optical properties in which tumor tissue was sampled.

Fig. 10

Raw sampling depth data (a–d) was plotted for each SDS and then (e–h) interpolated into a mesh. Sampling depth increased as SDS increased.

3.4.

Balb/c-CT26 Allograft Wavelength-Dependent Optical Properties

Next, DRS measurements were collected from Balb/c-CT26 tumor allografts ($n=9$) $200\pm 50{\mathrm{mm}}^3$ in diameter, as well as immediately adjacent normal flank tissue from the same mouse. The LUT inverse model fit analyzed the spectra to output ${\mu }_s^{\prime }(\lambda )$ and ${\mu }_a(\lambda )$ (Fig. 11). Based on the relationship between ${\mu }_s^{\prime }$, ${\mu }_a$, and sampling depth (Fig. 10), sampling depth was quantified as a function of wavelength. In general, as SDS increased, ${\mu }_s^{\prime }(\lambda )$ decreased, ${\mu }_a(\lambda )$ increased, and sampling depth increased for both normal and tumor tissues.

Fig. 11

Average optical properties and sampling depth for (a–c) normal Balb/c flank tissue and (d–f) subcutaneous Balb/c-CT26 tumor allografts showing (a, d) ${\mu }_s^{\prime }$, (b, e) ${\mu }_a$, and (c, f) sampling depth. As SDS increased, ${\mu }_s^{\prime }$ decreased, ${\mu }_a$ increased, and sampling depth increased for both tissue types. Values are mean ± SD.

3.5.

Balb/c-CT26 Allograft Diffuse Reflectance Spectroscopy-Derived Physiological Parameters

After comparing wavelength-dependent optical properties as a function of SDS, key physiological optical parameters were extracted and compared for normal and tumor tissues (Fig. 12).

Fig. 12

Average (a) ${\mu }_s^{\prime }$ at 630 nm, (b) THC, (c), ${\mathrm{StO}}_2$, and (d) sampling depth for normal (dark gray) and tumor (light gray) tissue. The ${\mu }_s^{\prime }$ was comparable between normal and tumor tissues and decreased as SDS increased. The THC was comparable between normal and tumor tissues and increased as SDS increased. The ${\mathrm{StO}}_2$ in tumor tissue was significantly decreased compared with normal tissue for SDSs longer than 0.75 mm. Additionally, ${\mathrm{StO}}_2$ decreased as SDS decreased. The sampling depth was comparable between normal and tumor tissues and increased as SDS increased. Values are mean ± SD. Significance is indicated by ^*($p<0.05$).

The ${\mu }_s^{\prime }$ at 630 nm decreased as SDS increased [Fig. 12(a)], as shown in Fig. 11. For the 0.75-, 3.00-, and 4.00-mm SDSs, differences in ${\mu }_s^{\prime }$ were insignificant between normal and tumor tissues. In the 2.00-mm SDS, ${\mu }_s^{\prime }$ was significantly lower in tumor tissue ($p=0.02$) compared with normal tissue but only by $0.49{\mathrm{cm}}^{-1}$.

The THC, measured in $\mathrm{mg}/\mathrm{mL}$, increased as SDS increased [Fig. 12(b)]. This was also indicated by the observed increased ${\mu }_a(\lambda )$ magnitude shown in Fig. 11. For the 0.75-, 2.00-, and 4.00-mm SDSs, differences in THC were insignificant between normal and tumor tissues. In the 3.00-mm SDS, THC was significantly lower in normal tissue ($p=0.03$) compared with tumor tissue but only by $0.64\mathrm{mg}/\mathrm{mL}$. The THC rose from $\sim 1.4\mathrm{mg}/\mathrm{mL}$ in the 0.75-mm SDS to $\sim 6.8\mathrm{mg}/\mathrm{mL}$ in the 4.00-mm SDS for both tissue types.

The ${\mathrm{StO}}_2$ remained constant as SDS increased in normal tissue [Fig. 12(c)]; however, ${\mathrm{StO}}_2$ decreased as SDS increased in tumor tissue, indicating increasing hypoxia at increased depths within the tumor microenvironment. The ${\mathrm{StO}}_2$ quantified by the short 0.75-mm SDS was significantly higher ($p<0.01$) than the ${\mathrm{StO}}_2$ quantified by all longer SDSs. Furthermore, there was no significant difference in ${\mathrm{StO}}_2$ between normal and tumor tissues in the 0.75-mm SDS. However, tumor tissue expressed significantly decreased ${\mathrm{StO}}_2$ compared with normal tissue for SDSs of 2.00, 3.00, and 4.00 mm.

In Fig. 12(d), sampling depth was quantified at the first $Q$-band of hemoglobin at 542 nm, where the lowest sampling depth would occur. In normal tissue, sampling depth was $0.66\pm 0.04$, $1.22\pm 0.11$, $1.55\pm 0.12$, and $1.64\pm 0.12\mathrm{mm}$ at 542 nm for the 0.75-, 2.00-, 3.00-, and 4.00-mm SDSs, respectively. In tumor tissue, sampling depth was $0.66\pm 0.03$, $1.30\pm 0.09$, $1.49\pm 0.14$, and $1.65\pm 0.05\mathrm{mm}$ at 542 nm for the 0.75-, 2.00-, 3.00-, and 4.00-mm SDSs, respectively. There was no significant difference ($p>0.05$) comparing sampling depth in normal versus tumor tissue. For both normal and tumor tissues, sampling depth increased significantly ($p<0.01$) at longer SDSs of 2.00, 3.00, and 4.00 mm compared with the shorter 0.75-mm SDS.