2.1.

Empirical Ratiometric Model

A first-order approximation of intrinsic fluorescence spectra can be obtained by dividing the fluorescence spectra by diffuse reflectance spectra recorded at the same anatomical location to some variable power.¹⁸ This approximation can be expanded to remove the distortions by dividing the fluorescence spectra by integrated diffuse reflectance spectra recorded at both absorption band and emission band with a variable power, which has been used for rapid extraction of pPIX fluorophore.¹⁹ We further developed this technique for rapid extraction of intrinsic 2-NBDG and TMRE fluorescence by dividing the fluorescence spectra by reflectance intensities recorded at excitation and emission peak with a pair of system-dependent power, using the following equation:

2.2.

Tissue-Mimicking Phantom Experiment

We created tissue-mimicking fluorescence phantoms to evaluate the empirical method for rapid quantification of metabolic probes. 20% intralipid (Sigma-Aldrich) was used to mimic tissue scattering. Dehydrated human hemoglobin powder (H0267, Sigma-Aldrich) was used as a major absorber in the phantoms. TMRE and 2-NBDG were used as fluorophores. Phosphate buffered saline $1\times$ (Fisher Scientific) was used to suspend the scattering intralipid, hemoglobin, and fluorophores for the liquid fluorescence phantoms. The optical properties of the phantoms were designed based on the formerly reported optical properties of mice skin.²⁰ Specifically, the tissue-mimicking phantoms had the following average absorption coefficients and reduced scattering coefficients (400 to 600 nm): ${\mu }_a=[1.5,3.0,4.5]{\mathrm{cm}}^{-1}$ and ${\mu }_s^{\prime }=[4.5,9.0,13.5]{\mathrm{cm}}^{-1}$. For every single set of absorption and scattering phantom, either 2-NBDG or TMRE was added at biologically relevant concentrations to mimic the fluorophore uptake in tissues. Specifically, the 2-NBDG was varied from 0 to $9\mu \mathrm{M}$ by every $3\mu \mathrm{M}$, and the TMRE was varied from 0 to 300 nM by every 100 nM based on our former in vivo studies.¹¹ All baseline absorption and scattering phantoms (no fluorophore) had the same starting volume of 5 mL, then a stock of $15\mu \mathrm{L}$ 2-NBDG or TMRE was added sequentially to create the fluorescence phantoms with the designed fluorophore concentrations. Each phantom was vibrated well to ensure homogeneity before the optical measurements. Totally, 27 sets of fluorescence phantoms were made for each fluorescent probe. Independently, two sets of liquid phantoms consisting of either 2-NBDG or TMRE only but with the same set of concentrations were made and used as control references for future comparison.

2.3.

Spectroscopy System and Optical Measurement

A portable spectroscopy system based on a Solis™ white LED (400 to 900 nm, SOLIS-3C, Thorlabs) and a compact visible spectrometer (FLAME-T-VIS-NIR, Ocean Optics) was used for diffuse reflectance and fluorescence measurements. A low-cost fiber probe (BF19Y2HS02, Thorlabs) with 10 illumination fibers and 9 collection fibers was used for light delivery and collection. Two bandpass filters were used in the illumination channel to generate appropriate excitations for 2-NBDG and TMRE. Specifically, a bandpass filter of 450 nm (25 nm bandwidth) was used to excite 2-NBDG as its excitation peak is around 470 nm, whereas a bandpass filter of 549 nm (25 nm bandwidth) was used to excite TMRE because its excitation peak is around 550 nm. In the collection end, two long-pass filters (515 nm for 2-NBDG, and 575 nm for TMRE) were used for fluorescence measurement. No filter was used in the collection channel for diffuse reflectance measurement thus diffuse reflectance in a wide range (400 to 900 nm) was measured for future correction; however, one neutral density filter ($\mathrm{OD}=2.0$) was installed on the diffuse reflectance illumination channel to protect the spectrometer from overexposure. Two cage filter wheels (CFW6, Thorlabs) were installed on the excitation branch and emission branch, allowing a fast switch among three measurement channels: diffuse reflectance, 2-NBDG fluorescence, and TMRE fluorescence. Both diffuse reflectance and fluorescence spectra were measured on every single set of fluorescence phantom by loading the fiber probe into the middle level of a phantom. The integration time was set as 50 ms for diffuse reflectance and 5 s for fluorescence measurement. After all optical measurements on the phantoms were completed, reference spectra on a diffuse reflectance standard puck (20%, Spectralon, Labsphere) and a fluorescence standard puck (USF210-010, LabSphere) were collected for future calibration.

2.4.

Data Analysis

All diffuse reflectance and fluorescence spectra were calibrated using a 20% reflectance standard (Spectralon, Labsphere) and a fluorescence standard (USF 210-010, LabSphere), respectively. Specifically, the diffuse reflectance spectra measured on samples were calibrated for the wavelength-dependent response by normalizing them to the diffuse reflectance spectrum measured on the reflectance standard. The fluorescence spectral intensities were normalized to the output excitation power quantified by the fluorescence standard, to account for the wavelength-dependent variation of the excitation light intensity. The empirical ratiometric model was implemented in MATLAB (MathWorks, Natick, Massachusetts, USA) for spectral data processing. The optimal parameter set for the pair of powers $[\alpha ,\beta ]$ that could converge the fluorescence spectra from different absorption–scattering combinations but the same fluorophore concentration was found for the selected correction wavelengths or wavelength bands. Specifically, the relative variation of corrected fluorescence in the selected group of phantoms with the same fluorophore concentrations was minimized using the empirical model. The nonlinear multivariable optimization function, fmincon from the MATLAB optimization toolbox, was used to find the optimal parameter set $[\alpha ,\beta ]$. Once the optimal parameter set $[\alpha ,\beta ]$ was found from the selected group of phantoms (15 from 27 phantoms), the whole set of fluorescence spectral data (15 sets of training phantoms plus 12 sets of validation phantoms) was processed and compared with the control references obtained from the control phantoms. The mean percent errors were calculated for the comparison between the corrected fluorescence $F_{\mathrm{corr}}$ with reference set. We further estimated the concentrations of the metabolic probes based on the corrected fluorescence spectra intensities at their corresponding emission peaks. The estimated concentrations were then compared with their corresponding true values using Pearson’s test.

3.1.

Attenuation Correction for 2-NBDG Fluorescence

Figure 1 shows the attenuation correction for 2-NBDG fluorescence using the empirical model. Diffuse reflectance intensities at the excitation source peak (450 nm) and the emission peak (550 nm) with optimized powers were used for the fluorescence correction. Figure 1(a) shows the representative diffuse reflectance spectra for the phantoms with different absorption coefficients (top) and scattering levels (bottom). Figure 1(b) shows the representative raw fluorescence spectra measured on the turbid fluorescence phantoms. Spectra in the same color but different line styles have the same fluorophore concentrations but different absorptions or scattering levels. The spectra with the same line style but different colors had the same absorption-scattering levels but different fluorescent probe concentrations. The graphs in Fig. 1(b) show significant distortions on the fluorescence spectra caused by either absorption or scattering, which were reflected by the huge percent errors. Figure 1(c) shows the representative corrected fluorescence spectra using the empirical model. The comparison between the corrected fluorescence spectra and the true references spectra (solid curves) demonstrates the high accuracy of the empirical model. Specifically, the percent errors were reduced to 3.2% (absorption group) and 4.3% (scattering group). When the model was used to correct the whole set of phantom data, the average percentage error was reduced from 80% to 6%.

Fig. 1

The empirical model with a pair of single wavelengths for accurate attenuation removal in 2-NBDG phantoms. ${\lambda }_{\mathrm{ex}}=450\mathrm{nm}$, ${\lambda }_{\mathrm{em}}=550\mathrm{nm}$, the parameter set $[\alpha ,\beta ]=[5.96,-6.44]$. (a) Optical properties of phantoms; (b) diffuse reflectance spectra; (c) raw fluorescence; and (d) corrected fluorescence of phantoms with fixed reduced scatterings but different absorption coefficients (top) and fixed absorption but different reduced scatterings (bottom).

Due to the general interest in metabolic probe concentration quantification in tissue for cancer research, we estimated the 2-NBDG concentrations based on the corrected fluorescence spectra intensities. Figure 2 shows the quantitative comparison between the corrected fluorescence peak intensities and true 2-NBDG concentrations using the processed spectral data. In Fig. 2(a), a linear fit to the corrected fluorescence peak intensities versus 2-NBDG concentrations yielded a coefficient of determination $R^2$ of 0.999 and $p\text{-}\text{value}<0.0001$, indicating the high performance of the method. Figure 2(b) shows the quantitative comparison between the optically estimated 2-NBDG concentrations with the expected true concentrations. High correlation and accuracy were achieved and demonstrated by the coefficient value and $p$-value.

Fig. 2

(a) Correlation between the corrected fluorescence intensities at 550 nm and true 2-NBDG concentrations; (b) comparison between the optically 2-NBDG concentrations and their corresponding true concentrations; (c) Bland–Altman plot for data shown in (a); and (d) Bland–Altman plot for (b). LoA represents limits of agreement, which are defined as the mean difference $\pm 1.96\mathrm{SD}$ of differences. “Mean diff” represents mean difference.

To further popularize the general use of the empirical model for spectral data processing, we also explored the potentially available wavelength bandwidths and wavelength bands based on the commonly used optical bandpass filters. Figure 3 shows the effect of wavelength bandwidth on the model’s accuracy for 2-NBDG extraction when the central wavelength (CWL) bands for diffuse reflectance were set to be the excitation peak (450 nm) and emission peak (550 nm). Figure 3(a) shows the minimal effect of wavelength bandwidth on performance of the empirical model when the wavelength bands were changed from 5 to 40 nm. However, a larger bandwidth of the optical filters typically would provide enhanced optical signals. Figure 3(b) shows the corresponding powers for each combination of the wavelength bandwidths. Generally, the absolute values of these power decreased slightly when the bandwidths were increased.

Fig. 3

(a) The effect of wavelength bandwidth on the mean percent error of the empirical model for 2-NBDG extraction, and the CWLs were fixed to be 450 and 550 nm. (b) The corresponding parameter set $[\alpha ,\beta ]$ for the combination of different wavelength bandwidths.

Figure 4 shows the effect of the CWL of diffuse reflectance filters on the accuracy of the empirical model for 2-NBDG correction when the bandwidth of the diffuse reflectance filters is set to 10 nm. The curves with different colors represent the selection of different CWL of filters (${\mathrm{CWL}}_{\mathrm{ex}}$ or ${\mathrm{CWL}}_{\mathrm{ex}}$) for diffuse reflectance collection. Figure 4(a) shows a minimal effect of diffuse reflectance filters’ CWL on the performance of the empirical model when the ${\mathrm{CWL}}_{\mathrm{ex}}$ of diffuse reflectance was set to 440 or 450 nm; however, the accuracy decreases considerably when ${\mathrm{CWL}}_{\mathrm{ex}}$ was changed to 470 and 490 nm, especially when the ${\mathrm{CWL}}_{\mathrm{em}}$ is set to 530 nm.

Fig. 4

(a) The effect of CWL band of diffuse reflectance collection on the mean percent error of the empirical model for 2-NBDG extraction when bandwidth is fixed at 10 nm. (b) The corresponding powers $[\alpha ,\beta ]$ for the combination of different CWLs.

3.2.

Attenuation Correction for TMRE Fluorescence

The attenuation corrections on TMRE spectra are presented in the same manner as the corrections for 2-NBDG spectra. Diffuse reflectance intensities at the excitation peak (550 nm) and the emission peak (580 nm) with an optimized power pair are used for TMRE correction. Similarly, Fig. 5(a) shows the representative diffuse reflectance spectra for the phantoms with different absorption and scattering levels in the range of 520 to 650 nm. The representative raw TMRE fluorescence spectra measured on turbid phantoms in Fig. 5(b) show significant distortions caused by either absorption or scattering, which are reflected by the percent errors of 73.6% and 80.1%, respectively. The comparison between the corrected fluorescence spectra and the true references spectra (solid curves) in Fig. 5(c) show the high performance of the empirical model for distortion removal. The errors were reduced to 4.7% (absorption group) and 3.2% (scattering group), respectively, as shown in Fig. 1(c). To validate the empirical model for TMRE correction, we prepared additional phantoms with lower TMRE concentrations (15 to 50 nM) and absorption or scattering levels at different days. When the same set of powers are used to correct the validation phantom data, an average percent error of 5% for the whole set of data was achieved.

Fig. 5

The empirical model with a pair of single wavelengths for accurate attenuation correction in TMRE phantoms. ${\lambda }_{\mathrm{ex}}=550\mathrm{nm}$, ${\lambda }_{\mathrm{em}}=580\mathrm{nm}$, the parameter set $[\alpha ,\beta ]=[-10.25,10.58]$. (a) Optical properties of phantoms; (b) diffuse reflectance spectra; (c) raw fluorescence; and (d) corrected fluorescence of phantoms with fixed reduced scatterings but different absorption coefficients (top) and fixed absorption but different reduced scatterings (bottom).

Figure 6 shows the quantitative comparison between the corrected fluorescence peak intensities and reference TMRE concentrations using the corrected spectra data. In Fig. 6(a), a linear fit to the corrected fluorescence intensities versus TMRE concentrations yields a coefficient of determination $R^2$ of 0.999 and $p\text{-}\text{value}<0.0001$, indicating the high performance of the empirical correction. Figure 6(b) shows the quantitative comparison between the optically estimated TMRE concentrations with the expected true values. High accuracy is achieved and demonstrated by the low percent error values.

Fig. 6

(a) Correlation between the corrected fluorescence intensities at 580 nm and true TMRE concentrations; (b) comparison between the optically TMRE concentrations and their corresponding true concentrations; (c) Bland–Altman plot for data shown in (a); and (d) Bland–Altman plot for (b). LoA represents limits of agreement, which are defined as the mean difference $\pm 1.96\mathrm{SD}$ of differences. Mean diff represents mean difference.

Figure 7 shows the effect of wavelength bandwidth on the accuracy of the empirical model for TMRE extraction when the CWL bands for diffuse reflectance are set to the excitation peak (550 nm) and emission peak (580 nm). Figure 7(a) shows a minimal effect of wavelength bandwidth on the performance of the empirical model for TMRE extraction when the wavelength bands are changed from 5 to 40 nm except for the wavelength band of 20 nm. Figure 7(b) shows the corresponding powers for each combination of the wavelength bandwidths. No clear trend is observed on these power values, however, the absolute values of each set of the power $\alpha$ and $\beta$ were close to each for all combinations as observed in Fig. 3.

Fig. 7

(a) The effect of wavelength bandwidth on the mean percent error of the empirical model for TMRE extraction, the CWLs are fixed at 550 and 580 nm. (b) The corresponding parameter set $[\alpha ,\beta ]$ for the combination of different wavelength bandwidths.

Figure 8 shows the effect of the CWL of diffuse reflectance filters on the accuracy of the empirical model for TMRE correction when the bandwidth of the diffuse reflectance filters is set to 10 nm. The curves with different colors represent the selection of different CWLs of diffuse reflectance filters (${\mathrm{CWL}}_{\mathrm{ex}}$ or ${\mathrm{CWL}}_{\mathrm{ex}}$). The data in Fig. 8(a) show a minimal effect of diffuse reflectance filters’ CWL on the performance of the empirical model no matter the selection of ${\mathrm{CWL}}_{\mathrm{em}}$ and ${\mathrm{CWL}}_{\mathrm{ex}}$ for diffuse reflectance filters except the case of 570 nm. Fig. 8(b) shows the corresponding powers for each combination of ${\mathrm{CWL}}_{\mathrm{em}}$ and ${\mathrm{CWL}}_{\mathrm{ex}}$. Generally, the absolute power values decrease when the bandwidths increase, the absolute values of each pair of the powers were close to each for all combinations as observed previously.

Fig. 8

(a) The effect of CWL band of diffuse reflectance filter on the mean percent error of the empirical model for TMRE extraction, the bandwidth is fixed at 10 nm. (b) The corresponding powers $[\alpha ,\beta ]$ for the combination of different CWLs.