2.1.

Tissue Phantoms

Tissue-mimicking phantoms that had varying amounts of absorption, scattering, and fluorophore concentrations were prepared. Hemoglobin (H0267, Sigma-Aldrich Co., St. Louis, MO) was used as the non-fluorescent absorber and 1-μm monodisperse polystyrene spheres (1-μm diameter, Catalog No. 07310, Polysciences, Warrington, PA) was used as the scatterer in tissue-mimicking phantoms following the procedures described in detail previously.^45,46 Mixing known volumes of stock hemoglobin (absorber) solution and microsphere suspensions in deionized (DI) water with stock fluorophore solution allowed accurate control of the final absorption, scattering, and fluorescence properties in each phantom. The absorption spectra of the stock ${\mathrm{HbO}}_2$ and stock fluorophore solutions [measured using a spectrophotometer (Cary 300, Varian, Inc.)] were used to determine the final absorption of the phantom, while the values of the reduced scattering coefficients in the phantoms were calculated from the Mie theory for spherical particles using freely available software.⁴⁷

Three distinct fluorophores were used in this study: Stilbene 3 (04200, Exciton, Dayton, Ohio) was used as an analog for NADH fluorescence,^22,48 2-NBDG (N13195, Invitrogen, Carlsbad, CA), and Rhodamine B (R6626, Sigma-Aldrich Co., St. Louis, MO) was used to represent fluorescence of TMR as their spectra are very similar.⁴⁹ The spectral range spanned by the fluorescence emission of these three fluorophores covers the three distinct absorption bands (soret, alpha, and beta bands) of the oxy hemoglobin (${\mathrm{HbO}}_2$) absorption spectrum. Since hemoglobin is the principal absorber in most human and animal tissues, these choices would also allow us to evaluate the effects of hemoglobin absorption on the detected fluorescence spectra. Figure 1 shows the emission spectra of these fluorophores (and NADH) along with the absorption spectrum of ${\mathrm{HbO}}_2$.

Fig. 1

(a) Normalized ${\mathrm{HbO}}_2$ absorption spectrum (Soret band region, 380 to 430 nm) along with emission spectra of NADH (340-nm exc.) and Stilbene (350-nm exc.), which are similar to each other, although the NADH fluorescence maximum is slightly red-shifted and (b) normalized ${\mathrm{HbO}}_2$ absorption spectrum (alpha-beta band region, 520 to 590 nm) with emission spectra of 2-NBDG (470-nm exc.) and Rhodamine B (545-nm exc.).

Six different sets of tissue phantoms containing one or more fluorophores were prepared. Table 1 summarizes the optical properties and fluorophore concentrations in the phantoms and the corresponding measurement parameters. The value of the optical absorption and scattering properties used here were based on our previous estimates of optical properties of murine tumors (${\mu }_a\approx 3.5{\mathrm{cm}}^{-1}$, ${\mu }_s^{\prime }\approx 10{\mathrm{cm}}^{-1}$, averaged between 350 to 650 nm).⁵⁰ Each phantom set contained two subsets: these two subsets either had two different ${\mathrm{HbO}}_2$ absorption levels with same scattering, or two levels of scattering with the same ${\mathrm{HbO}}_2$ absorption level. Each subset contained a phantom with increasing fluorophore concentrations through sequential additions of small volumes of fluorophore stock solution. Each phantom was identified through a code made up of an alphabet and two digits (A11 through F27). The alphabet denotes the main phantom set, the first digit represents the optical absorption (${\mu }_a$)/scattering (${\mu }_s^{\prime }$) level and last digit corresponds to the fluorophore concentration level in that subset (see Table 1). For each phantom set, the range of fluorophore concentrations in the two phantom subsets were identical; for example, both phantoms in the pairs A11 & A21, A12 & A22, A31 & A32, and A14 & A24 had the same fluorophore concentration, while phantoms A11 through A14 spanned a range of four different fluorophore concentrations. Phantom sets E and F contained two fluorophores, and therefore the concentrations of both fluorophores were increased simultaneously. Fluorophore solutions (containing only the fluorophore in water without any absorber and scatterer) with the same fluorophore concentrations as in the phantoms across each set were measured to get the measured intrinsic fluorescence free of absorption and scattering using the same illumination and collection geometry and instrument. These are referred to as the non-turbid fluorophore solution.

Table 1

Absorption, scattering, and fluorescence properties and measurement parameters within each phantom set. The listed optical properties represent the average value between 350 and 650 nm (* means excitation wavelength).

2.2.

In Vivo Murine Breast Cancer Model

All in vivo experiments were conducted according to a protocol approved by the Duke University Institutional Animal Care and Use Committee. Six- to eight-week-old female athymic nude mice (nu/nu, NCI, Frederic, MD) weighing 25 to 30 g were used in these studies. Animals were housed in an onsite housing facility with ad libitum access to food and water and standard 12-h light/dark cycles. All animal experiments were conducted during the day, and mice were fasted for six hours prior to optical measurements. Fasting ensured that glucose in the body did not compete with 2-NBDG uptake and good signal contrast from the tumor compared to normal tissue. A 4T1 murine breast cancer cell line was used to grow flank tumors in these mice. The 4T1 cells were transduced with retroviral siRNA to constitutively express the red fluorescence protein (RFP), DsRed. Each mouse received a subcutaneous injection of 750,000 cells in an injection volume of 100 μl. Flank tumors were monitored every other day and allowed to grow to a volume [$\pi /6\times \text{length}\times {(\text{breadth})}^2$] of $200{\mathrm{mm}}^3$. A total of eight tumor-bearing animals were divided into three groups and each group received 2, 4 or 6 mM of 2-NBDG (two animals in 2 mM group, three in 4 mM group, and three in 6 mM group). A volume of 100 μl of 2-NBDG was injected systemically through the tail-vein of the mouse.

2.3.

Optical Measurements

A commercial fluorometer (SkinSkan, J.Y. Horiba, Edison, NJ) coupled to a fiber-optic bundle was used for all the reflectance and fluorescence measurements. The instrument consists of a 150-W xenon lamp as the light source, dual excitation, and emission-grating monochromators, each having a fixed spectral band pass of 5 nm and an extended red photomultiplier tube (PMT) as the detector. Diffuse reflectance measurements were collected by synchronously scanning the excitation and emission monochromators across the wavelength range of interest. Fluorescence measurements were collected by fixing the source monochromator to provide the required excitation wavelength while scanning the detection monochromator over the desired spectral range (Table 1 shows both reflectance and fluorescence wavelengths for phantom measurement). The instrument coupled the excitation to the sample and collected detected light from the sample via a bifurcated fiber-optic probe bundle. The common (sample) end of the fiber probe had 59 individual fibers (with illumination and collection fibers having numerical apertures of 0.125 and 0.12, respectively) with each individual fiber having a core/cladding diameter of $200/245\mathrm{\mu m}$. The arrangement of the fibers within the optical probe is described in an earlier study.²⁵ Using forward Monte Carlo simulations as described in previous studies,^51,52 this probe was computed to have a sensing depth (defined as the maximum depth that 90% of diffusely reflected photons ever penetrated) of 1 to 3 mm for the range of optical properties listed in Table 1.

Single time repeated reflectance and fluorescence spectra were measured from both the phantom and animal models. Reflectance and fluorescence scans from the phantoms were obtained by placing the optical probe just beneath the surface of the liquid with the phantom being stirred using magnetic stirrers the entire time to prevent polystyrene spheres from settling. The optical measurement protocol for the animal tumors was as follows. The animals were anesthetized via Isoflurane breathing (1.5% Isoflurane gas mixed with oxygen) throughout the course of the optical measurements. Reflectance and fluorescence spectra were acquired sequentially from the tumor for 80 minutes (with a cycle time of 100 s) by gently pushing the probe to make contact with the tumor and stabilizing it using a clamp during the measurements. Reflectance spectra were acquired from 450 to 650 nm, and fluorescence emission spectra were acquired from 510 to 600 nm using excitation at 490 nm. An excitation wavelength of 490 nm was used rather than 470 nm as in 2-NBDG phantom studies to minimize endogenous FAD contribution. Prior to 2-NBDG injection, baseline reflectance and fluorescence spectra were measured from the tumor site. In both phantom and animal studies, the integration time of the photodetector was 0.1 s per wavelength for reflectance scans and 3 s per wavelength for fluorescence scans. All the measurements for both phantom and animal studies were acquired in a dark room.

Optical spectroscopy measurements on both the phantoms and animal models were conducted after adequate time was allowed for system warm up ($>30\min$) and under same probe-bending conditions to minimize their impact on the systematic errors reported in an earlier study.⁵³ Overall system throughput variation on different days was assessed by measuring the reflectance from a Spectralon reflectance standard SRS-99 (Labsphere Inc., North Sutton, NH) and the fluorescence from a Rhodamine standard slide (590-nm exc., 610 to 680-nm em.) on three different days. The coefficient of variance of the collected spectra (calculated as

2.4.

Inverse Monte Carlo Models for Reflectance and Fluorescence

The measured reflectance and system response calibrated fluorescence spectra for both phantom and pre-clinical studies were input into a series of scalable inverse Monte Carlo models. The scalable inverse Monte Carlo models for extracting optical properties and intrinsic fluorescence have previously been described and validated experimentally on optical tissue phantoms containing a single fluorophore.⁴¹ In order to correct the measured fluorescence spectrum, it is necessary to know the optical absorption and scattering properties of the medium, which are first extracted from the measured diffuse reflectance spectrum using the inverse Monte Carlo reflectance model.⁴⁰ These extracted optical properties are then used by the inverse Monte Carlo fluorescence model to remove the distortions in the measured fluorescence spectrum to provide the intrinsic fluorescence.^40,41 Figure 2 shows the inputs and outputs to the inverse MC reflectance and fluorescence models, which themselves are further deconstructed in Fig. 3.

Fig. 2

Input to and output from the inverse Monte Carlo model in phantom studies.

Fig. 3

Flowchart of inverse Monte Carlo reflectance and fluorescence models.

Figure 3 is a detailed flowchart of the model itself, with inputs in gray boxes and outputs in boxes with a dashed outline (“Measured Fluorescence” in the gray box means system response calibrated fluorescence). The reflectance model⁴⁰ consists of a forward and an inverse component. In the forward component, the wavelength-dependent absorption coefficients of the medium are calculated from the concentration of each absorber that is present in the medium and their corresponding wavelength-dependent extinction coefficients, while the wavelength-dependent reduced-scattering coefficients are calculated from scatterer size, density, and the refractive index of the scatterer and surrounding medium using Mie theory for spherical particles. The absorption and scattering coefficients are then used by the reflectance model to rapidly compute a modeled diffuse reflectance spectrum. The inverse component works by adaptively fitting the modeled diffuse reflectance to the measured tissue diffuse reflectance till the sum of squares error between the modeled and measured diffuse reflectance is minimized. A simulated and measured “reference” phantom with known optical properties is used to generate the calibration factor to put the experimental and simulated reflectance data on the same scale. The phantom reflectance spectra were calibrated to a reference phantom spectrum from the same phantom data set (phantom A14, B22, C21, D22, E12, F13 in each set) based on a previously used protocol,⁴⁵ i.e., the reference phantom should yield the lowest error when used to extract optical properties from the remaining phantoms in the same phantom data set. The reflectance spectra from the animals were calibrated to phantom F13 based on the same criteria. The concentrations of absorber, scatterer size, and density that match the measured reflectance are used to calculate the extracted optical properties.

The fluorescence model can be described by the following equation:

Once the intrinsic fluorescence is obtained, phantom fluorophore concentrations are estimated by using one phantom (calibration phantom) with known fluorophore concentration in each phantom set as a calibration standard to calculate fluorophore concentrations in other phantoms through a simple linear scaling relationship $\frac{I_{p(\mathrm{tar})}}{I_{P(\mathrm{cal})}}\times C_{\mathrm{cal}}$, where $I_{p(\mathrm{tar})}$ and $I_{p(\mathrm{cal})}$ are the fluorescence intensities at the peak wavelength of the intrinsic fluorescence for the target phantom and the calibration phantom, respectively and $C_{\mathrm{cal}}$ is the concentration of the calibration phantom. For phantom sets E and F, which contain two fluorophores, the two component spectra were separated first for both the target and the calibration phantom, after which the concentration of the target phantom was extracted through the simple scaling method described above. The two components in phantom set E can easily be separated as their spectra do not overlap, whereas the detailed method for component separation in phantom set F can be found in the results and discussion section. The speed for reconstruction of fluorophore concentration depends on the speed of the computer used as well as the number of iterations for reflectance fitting and the number of wavelengths in the reflectance and fluorescence spectra. For example, the speed for intrinsic fluorescence extraction of one animal (one reflectance and fluorescence spectrum) in this study is about 6.5 s (measured on a dual-core, 1.6-GHz machine) for 100 reflectance fits, 27 wavelengths in reflectance spectrum, and 19 wavelengths in fluorescence spectrum.

3.1.

Diffuse Reflectance Inversion

Optical absorption and scattering properties were extracted using the inverse reflectance Monte Carlo model from each measured phantom reflectance spectrum, and the errors in the extracted absorption and scattering coefficients were quantified as the root-mean square percent errors (across the spectrum) relative to the expected optical properties for each phantom and then averaging over all phantoms in phantom sets A through F. The mean errors and standard deviations in the extraction of optical properties were $11.35\pm 14.35\%$ for ${\mu }_a$ and $5.06\pm 4.83\%$ for ${\mu }_s^{\prime }$. The mean errors and standard deviations in the extraction of optical properties using the inverse reflectance Monte Carlo model in our previously published study were comparable for the same instrument and optical property range with accuracies of $12.48\%\pm 11.29\%$ for ${\mu }_a$ and $9.23\%\pm 7.50\%$ for ${\mu }_s^{\prime }$.⁴¹ The extracted ${\mu }_a$ takes into consideration the absorbance of both ${\mathrm{HbO}}_2$ and fluorophores, and the expected ${\mu }_a$ was also obtained by combining the absorption of both ${\mathrm{HbO}}_2$ and the fluorophores. Thus it was possible to compute the overall mean error in extraction of hemoglobin concentration in each phantom, which was $11.55\pm 12.75\%$.

3.2.

Intrinsic Fluorescence Extraction (Single Fluorophore Phantoms)

Figure 4 shows measured raw [Fig. 4(a) to 4(c)] and normalized [Fig. 4(d) to 4(f)] fluorescence spectra of two phantoms, from each of the two subsets in phantom sets A through D, along with the measured fluorescence of the corresponding fluorophore solution (fluorophore in water without any absorber and scatterer) that has the same fluorophore concentration as in the phantoms. The two phantoms chosen from each set had the same fluorophore concentration, but different optical properties. The solution fluorescence was measured using the same instrument and probe as for phantom measurement. Figure 4(a) shows the measured fluorescence from phantoms A13 and A23, while Fig. 4(b) and 4(c) show these data for phantoms B13 to B23, C12 to C22, and D12 to D22, respectively. Figure 4(c) shows the data for four phantoms, two each from phantom sets C or D as the fluorophores in these two sets are the same. The fluorophore concentrations in the four phantoms are the same while the optical properties are different. It can be seen from these figures that identical fluorophore concentrations yield varying magnitudes of emission intensities, depending on the optical properties of each phantom subset. Figure 4(d) to 4(f) show the same plots as in Fig. 4(a) to 4(c), except this time they were normalized to the peak value of the spectrum. A comparison of the turbid fluorescence spectra to the fluorescence measured in clear solution shows the impact of spectral distortions due to absorption and scattering.

Fig. 4

(a) to (b) Non-normalized measured fluorescence from two phantoms, each from a different sub-level in phantom set A (Stilbene) and B (Rhodamine), along with the measured fluorescence of the corresponding fluorophore solution that has the same fluorophore concentration as in the phantoms. (c) Non-normalized measured fluorescence from four phantoms, two each from set C (2-NBDG) or D (2-NBDG), along with the measured fluorescence of the corresponding fluorophore solution that has the same fluorophore concentration as in the phantoms. (d) to (f) Normalized measured fluorescence of the same plots as in (a) to (c). (Color online only.)

Figure 5(a) to 5(c) show the extracted intrinsic fluorescence from the inverse Monte Carlo model from all the phantoms in sets A through D, along with the measured intrinsic fluorescence from the non-scattering fluorophore solutions. The color indicates the same fluorophore concentration; i.e., for each color, there are two extracted intrinsic fluorescence spectra and one non-turbid fluorophore solution (dashed line: subset 1, solid line: subset 2, dotted line: fluorescence in non-turbid solution). Figure 5(a) to 5(b) show the data from phantom sets A and B while Fig. 5(c) shows the data from both phantom set C and D as the fluorophores in these two sets are the same. Figure 5(d) to 5(f) show the equivalent of Fig. 4(d) to 4(f), except this time the spectra from phantoms in each figure are the normalized extracted fluorescence. To get the magnitude of extracted fluorescence to match that of the non-turbid fluorophore solution, an S factor as mentioned above was determined by dividing the intensity of extracted intrinsic fluorescence spectrum (when S is set as default value of 1) to the intensity of the non-turbid fluorophore solution fluorescence. Compared with the spectra shown in Fig. 4, it is clear that the model corrects for both differences in magnitude and line shape among the two phantom spectra from each subset that have the same fluorophore concentration but different optical properties. The extracted intrinsic fluorescence spectra in Fig. 5(a) to 5(c) show that the model-corrected spectra had a similar shape and intensity as that measured from the fluorophore solution. Further, the extracted fluorescence for the two phantoms from each phantom subset indicates that the model was capable of extracting similar intensities in phantoms having the same fluorophore concentration but different optical properties.

Fig. 5

(a) to (c) Extracted intrinsic fluorescence from all phantoms in set A through D along with the measured intrinsic fluorescence from the corresponding non-turbid fluorophore solutions. (a) to (b) show the data for set A (Stilbene) and B (Rhodamine), and (c) shows the data from both sets C and D as the fluorophores in these two sets are the same (2-NBDG). The same color indicates the same fluorophore concentration. (d) to (f) show the equivalent of Fig. 4(d) to 4(f) for extracted fluorescence. (Color online only.)

To quantify the robustness of the extracted true intrinsic fluorescence spectrum, for each phantom set, the variance between the two fluorescence spectra from phantoms containing the same fluorophore concentration in the two phantom sub-sets before and after correction with the Monte Carlo model was assessed. The similarity between two spectra was computed using an $R^2$ metric, where $R^2$ was defined as 1-SSE/SST (SSE: sum of squares of remaining, SST: sum of squares of total). The SSE was given by $\sum _{i=1}^n{(X_i-Y_i)}^2$, and SST by $\max (\sum _{i=1}^n{(X_i)}^2,\sum _{i=1}^n{(Y_i)}^2)$, where $X$ and $Y$ are the two fluorescence spectra from phantoms with equal fluorophore concentrations in each phantom subset, and $i$ is the wavelength term. The $R^2$ value lies between 0 and 1, and indicates perfect agreement in the spectra when its value approaches 1. Table 2 lists the $R^2$ values across phantom set A through D between the two phantoms with equal fluorophore concentrations from each subset, before and after correction by the inverse Monte Carlo model. It is evident that the corrected spectra have much higher $R^2$ values relative to the measured, uncorrected spectra for all three fluorophores that span the UV-visible spectral range. The averaged $R^2$ value indicating shape resemblance was 0.988 here as compared with 0.989 in our previously published study.⁴¹

Table 2

Variance calculated using an R2 metric, between two fluorescence spectra with equivalent fluorophore concentrations but different absorption and scattering properties from the two phantom subsets before and after model correction. The variance was calculated specifically for regions where HbO2 causes distinct distortions (soret, alpha and beta bands); i.e., 410 to 430 nm in set A, 570 to 590 nm in set B, and both 530 to 550 nm and 570 to 590 nm in set C and D, respectively. Also provided in the parentheses are the concentration extraction errors for each phantom. “Cal” in the parentheses means the phantom is used as calibration phantom to calculate concentrations for other phantoms.

Ideally, it will be useful to have a method where the measured fluorescence spectrum from a turbid medium can be used to extract fluorophore concentrations. The extracted fluorescence spectrum in each phantom was converted into an extracted fluorophore concentration using a simple linear scaling relationship. For example, the fluorophore concentration of each phantom in phantom set A could be computed from the extracted intrinsic fluorescence spectrum if it was assumed that the fluorophore concentration of a single phantom within the set A11 to A24 was known. Figure 6(a) to 6(c) show the results of such a linear scaling relationship to extract the fluorophore concentration for all phantoms in phantom sets A through D by using the fluorophore concentrations in phantom A21, B21, and C21. The fluorophore concentrations can also be extracted with similar accuracy when other phantoms in each set are used as calibration standards. To be consistent the phantom with the lowest concentration in the second phantom subset of each phantom set was used for the purposes of calibration. The fluorophore concentrations in all phantoms are within fluorescence linear range in fluorophore solutions. Figure 6 indicates that extracted fluorophore concentration in each phantom is in good agreement with its true value across all phantom sets. It is to be noted that since phantom sets C and D had the same fluorophore and excitation wavelength, the extracted fluorophore concentrations in set D were obtained by using phantom C21 as calibration standard (the same as in set C), indicating that it was only necessary to have a corrected fluorescence spectrum measured once for a given fluorophore and excitation wavelength. The larger errors in phantom set D (especially in subset 2) compared with that in set C is likely due to the higher errors in the extracted optical properties in set D (6.40% for ${\mu }_a$ and 7.56% for ${\mu }_s^{\prime }$) compared with that in set C (2.44% for ${\mu }_a$ and 1.34% for ${\mu }_s^{\prime }$), which agrees with the findings that a wider range of scattering results in a higher extraction error of optical properties, which in turn causes higher extraction errors in the intrinsic fluorescence that is extracted using the scalable inverse Monte Carlo model of fluorescence.⁴⁵

Fig. 6

(a) to (b) shows the extracted fluorophore concentrations for each phantom (* and o) in sets A and B, using the extracted fluorescence spectrum of phantom A21 and B21 in each set as calibration standard. (c) Shows these data for set C and D (same fluorophore in these two sets) using the extracted fluorescence spectrum of phantom C21 as calibration standard. The extracted fluorophore concentrations of the non-turbid solutions ($\mathrm{\nabla }$) in each figure were determined using the measured solution fluorescence of the lowest concentration as calibration standard. The expected values are the true fluorophore concentration values. The dashed line in each figure indicates line of perfect agreement.

3.3.

Intrinsic Fluorescence Extraction (Multi-Fluorophore Phantoms)

Figure 7(a) and 7(b) show the measured [Fig. 7(a)] and extracted [Fig. 7(b)] fluorescence spectra from all the phantoms in set E along with measured fluorescence from the corresponding non-turbid fluorophore solutions, with the same color indicating the same fluorophore concentration. The intensity and shape differences in Fig. 7(a) between the two phantom spectra from each subset that have the same fluorophore concentration but different optical properties are corrected in Fig. 7(b).

Fig. 7

Measured (a) and extracted (b) fluorescence spectra from all the phantoms in set E along with measured fluorescence from the corresponding non-turbid fluorophore solutions. The same color indicates the same fluorophore concentration. (Color online only.)

Figure 8(a) and 8(b) show the extraction of fluorophore concentrations of both fluorophores in phantom set E using the extracted fluorescence spectrum from phantom E21 as the known calibration standard (390- to 550-nm region for Stilbene and 550- to 610-nm region for Rhodamine). Figure 8(c) and 8(d) show the same data using phantom A21 as the calibration standard for Stilbene concentration extraction and phantom B21 for Rhodamine concentration extraction. Given that the excitation wavelength used in phantom set E was different from that in phantom set A (for Stilbene) and B (for Rhodamine), the extracted concentrations in Fig. 8(c) and 8(d) were calculated through the relationship

Fig. 8

(a) to (b) shows the extracted Stilbene and Rhodamine concentrations for each phantom subset (* and o) in set E using the 390- to 550-nm (for Stilbene) and 550- to 610-nm (for Rhodamine) regions of the extracted fluorescence spectrum of phantom E21 as the calibration standard. Also shown in these two figures are the extracted fluorophore concentrations of the corresponding non-turbid solutions ($\mathrm{\nabla }$) using the fluorescence of the solution with the lowest concentration as calibration standard. (c) and (d) show the extracted Stilbene and Rhodamine concentrations for each phantom subset in set E using the extracted intrinsic fluorescence spectrum of phantom A21 (for Stilbene) and B21 (for Rhodamine), respectively, as the calibration standards. The expected values are the true fluorophore concentration values. The dashed line in each figure indicates line of perfect agreement.

Figure 9 shows measured [Fig. 9(a) and 9(b)] and extracted [Fig. 9(c) and 9(d)] fluorescence from phantoms with odd [Fig. 9(a) and 9(c)] and even [Fig. 9(b) and 9(d)] number fluorophore concentrations (-- and -) in set F along with a linear combination of the measured fluorescence (implemented in post-processing) from two separate non-turbid fluorophore solutions containing each of the fluorophores (:). The same color indicates the same fluorophore concentration. As in Fig. 7, the intensity and shape differences between the two measured phantom spectra from each subset that have the same fluorophore concentration but different optical properties are corrected in the extracted fluorescence spectra. Compared with Fig. 7, it is not as straightforward to differentiate the two fluorophores here due to their overlapping emission regions (550 to 620 nm). In Fig. 9(c) and 9(d), as the fluorophore concentration increases, the measured fluorescence of the non-turbid fluorophore solution combination deviates more from the two phantom extracted spectra that have the same fluorophore concentration (: compared with -- and -). This is likely due to the fact that extracted intrinsic fluorescence is corrected for fluorophore reabsorption, whereas this is not the case in the non-turbid fluorophore solution, where as the concentration of fluorophore increases there is significant reabsorption, which is not corrected for.

Fig. 9

(a) and (b) Measured fluorescence from phantoms with odd (a) and even (b) number fluorophore concentrations (-- and -) in set F along with a linear combination of the measured fluorescence (implemented in post-processing) from two separate non-turbid fluorophore solutions containing each of the fluorophores (:); (c) and (d) Equivalent of (a) and (b), the only difference is the measured fluorescence from the phantoms is substituted by the corresponding extracted fluorescence. The same color indicates the same fluorophore concentration. (Color online only.)

Since 2-NBDG emits between 500 to 550 nm with no emission from Rhodamine in this wavelength range, the measured fluorescence between 500 to 550 nm was assigned to 2-NBDG fluorescence, which can then be used to extrapolate the intensity over 550 to 620 nm (the intensity at 540 nm was used for this purpose and the intensity between 550 to 620 nm was calculated based on their relative intensity ratios to that at 540 nm from the normalized 2-NBDG spectrum). Rhodamine fluorescence was then obtained by subtracting the 2-NBDG component from the two-component fluorescence spectrum. Once the two component spectra were separated, their concentrations were extracted using appropriate calibration phantoms.

Figure 10(a) and 10(b) show the extraction of phantom fluorophore concentrations for both fluorophores from their separated extracted fluorescence spectrum using phantom F21 as the known calibration standard. Interestingly, the extracted intrinsic fluorescence has a much wider linear range than the measured non-turbid solution fluorescence. This is likely due to the fact that extracted intrinsic fluorescence is corrected for fluorophore reabsorption whereas that of the non-turbid fluorescence solution is not. Figure 10(c) and 10(d) show concentrations for both fluorophores using phantom C21 as the calibration standard for 2-NBDG and phantom B21 for Rhodamine. The fluorophore absorbance as well as photon energy differences were accounted for in the same way as mentioned previously when using B21 as calibration standard for Rhodamine concentration extraction since the excitation wavelengths are different between the two phantom sets. It is to be noted that the model in its current form does not account for fluorescence from one fluorophore as an excitation source for another; i.e., it does not separate Rhodamine fluorescence excited by NBDG fluorescence re-absorption from that excited by the instrument light source. The fluorescence of Rhodamine B in the target phantom is excited by both the instrument light source and NBDG fluorescence, while the reference phantom fluorescence is only excited by the light source of the instrument. Thus the extracted Rhodamine B concentration in Fig. 10(d) is higher than expected at higher concentrations partially because of reabsorption of NBDG fluorescence.

Fig. 10

(a) and (b) show the extracted 2-NBDG and Rhodamine concentrations for each phantom subset (* and o) in set F using separated 2-NBDG and Rhodamine fluorescence from the extracted fluorescence spectrum of phantom F21 as calibration standard. Also shown in these two figures are the extracted fluorophore concentrations of the corresponding non-turbid solutions ($\mathrm{\nabla }$) using the measured solution fluorescence of the lowest concentration as calibration standard. (c) and (d) show the extracted 2-NBDG and Rhodamine concentrations for each phantom subset in set F using the extracted fluorescence spectrum from phantom C21 (for 2-NBDG) and B21 (for Rhodamine), respectively, as the calibration standard. The expected values are the true fluorophore concentration values. The dashed line in each figure indicates line of perfect agreement.

3.4.

Pre-Clinical Pilot Study

Figure 11 shows measured and extracted fluorescence spectra at different time points for one mouse from the 6 mM 2-NBDG group. Figure 11(a) shows measured fluorescence spectra at four time points (baseline, t20, t40, and t60), and Fig. 11(b) shows the same data for the extracted fluorescence. The baseline fluorescence originates from RFP, while the fluorescence of the post-injection time points contains the contribution from both 2-NBDG and RFP. In both figures, fluorescence first increases after 2-NBDG injection and then decreases progressively as would be expected.⁴³ The fluorophore emission features/peaks (545 nm for 2-NBDG and 575 nm for RFP) can easily be observed from distortion corrected (extracted) intrinsic fluorescence as compared with that in measured fluorescence, where the peaks are affected by the alpha and beta bands absorption of ${\mathrm{HbO}}_2$.

Fig. 11

Measured (a) and extracted (b) fluorescence spectra of four time points (baseline, t20, t40, and t60) for one animal from the 6 mM 2-NBDG group. Baseline corresponds to the time point before 2-NBDG injection, and t20, t40, and t60 mean 20, 40, and 60 min post 2-NBDG injection. (Color online only.)

Figure 12(a) shows the measured fluorescence intensity change over time, and Fig. 12(b) shows the same data for extracted intrinsic fluorescence for all mice. Figure 12(c) shows the mean and standard deviation of measured fluorescence spectra for each dose group, and Fig. 12(d) shows the same data for extracted fluorescence. The 2-NBDG peak fluorescence wavelength (545 nm) was used at each time point for all plots. For a given 2-NBDG dose, the measured and extracted fluorescence first increase to a maximum and then decreases due to 2-NBDG uptake by the cells.⁴³ More importantly, there is a progressively increasing trend with increasing 2-NBDG dose in the extracted intrinsic fluorescence. However, this is much less significant in the raw fluorescence. The fluorescence measurements typically begin immediately after injection, which allows for the capture of both the rapid rise and fall off. There is one animal (dotted blue curve of 6 mM), however, that has different kinetics from the rest; i.e., the curve starts to decay almost immediately. This is due to the fact that there was a slight delay caused by probe movement, which prevented collected of data that shows the full extent of the rise.

Fig. 12

(a) shows the measured fluorescence intensity change over time for all mice, and (b) shows the same data for extracted fluorescence; (c) shows the mean and standard deviation of measured fluorescence spectra for each dose group, and (d) shows the same data for extracted fluorescence. Time point 0 is the time when 2-NBDG was injected. The legend indicates the injected 2-NBDG concentration. (Color online only.)

Figure 13 shows measured raw and extracted intrinsic fluorescence over injected 2-NBDG concentration for all mice. Figure 13(a) shows the scatter plot of measured fluorescence intensity as a function of injected 2-NBDG dose at three time points (t20, t40, and t60), and Fig. 13(b) shows the same data for extracted intrinsic fluorescence for all mice. The peak 2-NBDG fluorescence wavelength (545 nm) was used for each data point. The error bar indicates the standard deviation in each 2-NBDG concentration group. The $r$ value at the top of each figure is the Pearson’s linear correlation coefficient of the three doses at each time point and the coordinate origin (0,0). For a doubling or even tripling of the dose, the extracted fluorescence increases linearly while that of the measured fluorescence is non-linear with dose. Moreover, variations within the same dose group are smaller for intrinsic fluorescence than that for the measured fluorescence.

Fig. 13

(a) shows the scatter plot of measured fluorescence intensity over injected 2-NBDG concentration at three time points (t20, t40, and t60) for all the mice. (b) shows the same data for extracted fluorescence. The error bar shows the standard deviation among the mice in each 2-NBDG concentration group. The r value at the top of each figure indicates the linearity of the $y$ axis values over injected 2-NBDG concentrations (more linear when r approaches 1). t20, t40, and t60 mean 20, 40, and 60 min post-2-NBDG injection. (Color online only.)