Figure 1 shows the schematic configuration of the in-house-developed small animal multimodality image radiation therapy platform (SAMMI-RT) consisting of X-ray CT, FMT, and radiation treatment. The X-ray tube (COMET AG, Flmatt, Switzerland) has 1 mm and 5 mm focal spots for cone beam CT and irradiation, respectively. For fluorescence imaging, a fiber-coupled laser (785 nm, full width at half maximum: 1 nm, output power: 20 mW) was collimated as a 2-mm-diameter light spot to excite the fluorescent nanoparticles in small animals. A neutral filter (OD=2, Thorlab, Newton, NJ, USA) and a fluorescence filter (832 nm, full width at half maximum: 37 nm, block-band OD>10, Semrock, Rochester, NY, USA) were installed in front of the CCD (quantum efficiency 95%, Andor, Belfast, Northern Ireland) to collect excitation and fluorescent images, respectively. A home-built geometrical calibration method was performed to rigorously register optical images onto CT coordinate (29). CT provides anatomical information used to construct three-dimensional mesh for FMT reconstruction. Previous study demonstrated that FMT could localize tumor and guide focal radiation delivery with submillimeter accuracy. More detail description about SAMMI-RT can be referred to (9, 30).

All the animal experiments were conducted under the protocols approved by the institutional animal care and use committee. We first conducted an in vivo experiment to demonstrate the reliability of our background subtraction method in a stringent situation, where the target fluorescence might be overlapped or overwhelmed with the strong fluorescence either from another target or from the background. To mimic this stringent situation for in vivo fluorescence imaging, a female athymic nude mouse (Harlan, Indianapolis, IN, USA) with orthotopic MDA-MB-231 breast tumor was intramurally injected with gold nanorods (GNRs, length: 38 nm, dimeter: 10 nm, excitation wavelength: 788 nm, emission wavelength: 808 nm, NanopartZ, Loveland, CO, USA). According to our experience based on several preliminary experiments, one hour post the intratumoral injection, a large majority of GNRs extravasated from the MDA-MB-231 breast tumor and accumulate in the bladder. In this scenario, the targets of interest are both tumor and bladder, however, the tumor fluorescence will be overwhelmed with the bladder fluorescence. To verify the accuracy of the proposed background subtraction method, after fluorescence imaging experiments on SAMMI-RT, this mouse was euthanized and dissected for organ fluorescence imaging on Kodak In Vivo Multispectral Imaging system (Carestream Health, New Haven, CT, USA).

Then, we carried out in vivo active-targeting imaging experiments on white mice (BALB/c, Jackson laboratory, Bar Harbor, ME, USA). Compared to nude mice, white mice show additional hair-induced artifacts on fluorescence imaging. Therefore, white mice bearing breast tumors were implemented to further demonstrate the feasibility and robustness of our background subtraction method. To grow the orthotopic breast tumor on these immunocompetent mice, 5×10⁵ 4T1 cells were injected into the mammary fat pad of 4-week female white mice (n=10). Two weeks after tumor cell implantation, the fluorescent PLGA-anti-EGFR nanoparticles (300 µL, 10 mg/ml) were administrated via tail-vein injection after the mice were anesthetized with 2% isoflurane. Figure 2A shows the schematic structure of homemade PLGA-anti-EGFR nanoparticle, where the nanoparticle size is 262.9 ± 80.5 nm and the fluorescence excitation and emission wavelengths are 780 nm and 820 nm. Figure 2B compares the longitudinal tumor fluorescence intensity (on Kodak In Vivo Multispectral Imaging system) following the injection of active (anti-EGFR) and passive (IgG) targeting PLGA nanoparticles. The active targeting nanoparticles demonstrated enhanced tumor accumulation and long retention; peak appeared at 1 day after intravenous injection. Therefore, imaging experiments on SAMMI-RT were performed one day following PLGA-anti-EGFR injection. Then, the mouse was intravenously administered 200 µL iodinated contrast agent Iopamidal (1000 mg/kg body weight, Bracco Diagnostics, Princeton, NJ, USA) for contrast CT to delineate tumor. About 1 minute after Iopamidol injection, we began CT scan followed by fluorescence imaging. The white mice (n=10) were shaved around the abdominal region, before fluorescence imaging.

We take a fluorescence image in PLGA-anti-EGFR fluorescence imaging as a representative example to illustrate the necessity of background subtraction. Because contrast CT can delineate tumor, tumor region can be distinctly identified on the fluorescence image after geometric registration. As shown in Figure 3A , the fluorescence emanating from the tumor (left solid circle) is overwhelmed by the nonspecific signal from the gut (right dotted circle). Hence, it is difficult to directly identify tumor only from raw fluorescence image. The measured excitation distribution (shown in Figure 3B ) exhibits large dynamic range, under the trans-illumination by a point source indicated in Figure 3C . The dotted circle region on Figure 3A was near the excitation source, therefore received much more excitation than the tumor area. In addition, the low absorption of the near-transparent bladder that localized around the dotted circle region may further enhance the transmission of light. Additionally, it is noteworthy that the two rectangle regions in Figure 3B correspond to the high-intensity excitation light reflecting from the residual hair (right rectangle) and the transparent animal holder (left rectangle), respectively. Although the fluorescence filter can highly attenuate the excitation light (OD >10), small fraction of excitation light still leaked through the fluorescence filter, as shown in the rectangle regions in Figure 3A . And in Figure 3A , the signal in the dotted circle region is much stronger than that in the rectangle region, which is opposite to the correspondent distribution in Figure 3B . This means that the signal in the dotted circle in Figure 3A was not caused by the excitation leakage, but mainly attributed to the fluorescence emitted by the nonspecific uptake of PLGA-anti-EGFR nanoparticles in the surrounding tissues.

We classify the internal fluorophores both exogenous and endogenous into two parts: baseline (homogeneous distribution), target (heterogeneous distribution). Therefore, the surface fluorescence signals Flu(i, j) can be defined as:

Where Flu_baseline and Flu_target denotes the surface fluorescence from baseline and target fluorophores. Flu_leak denotes the excitation leakage passing through fluorescence filter, (i, j) indicates the pixel position on CCD-measured image with matrix size L×L. The proposed method in this study is developed based on the fact that the near-infrared light in biological tissues at excitation and fluorescence wavelengths separated by short Stokes shift has similar optical characteristics and follows strongly correlated propagation patterns (31). Take adipose tissue for an example, the absorption (μ_a ) and reduced scattering (μ’_s ) coefficients are 0.029 cm^-1 and 11.10 cm^-1 as well as 0.031 cm^-1 and 10.77 cm^-1, calculated at the excitation (785 nm) and fluorescence (832 nm) wavelengths in this study.

Additionally, when exciting the fluorophores within the biological tissues, the generated fluorescence signal is linearly proportional to the excitation intensity and the internal fluorophore concentration. Therefore, the distribution of excitation field Exc(i, j) can be used to approximate the fluorescence distribution.

where Exc(i,j) is the measurable excitation image. P_baseline and P_target (i, j) denote the weighting coefficients of baseline (i.e. homogenous distributed) and target (i.e. heterogenous distributed) fluorophores in the imaged animal. Because the baseline fluorophores are homogenously distributed, P_baseline is position independent. In contrast, for the heterogeneously distributed target fluorophores, the value of P_target depends on the position (i,j). Moreover, the excitation leakage part in fluorescence measurement can be written as:

where coefficient P_leak accounts for the filter leakage ratio of the illumination light. Substituting Eqs. (2) and (4) to Eq. (1), we obtain:

Equation (5) indicates that the “background fluorescence” induced by the homogenous baseline fluorophore and filter leakage, i.e. the first term on the right side of the Eq. (5), has the similar distribution pattern as excitation image. This fraction of fluorescence can be estimated by calculating the correlation between the collected fluorescence (Flu(i, j)) and excitation (Exc(i, j)) images, where P_corr denotes the correlation coefficient. The linear minimum mean square error (LMMSE) estimation was adopted to calculate P_corr :

Therefore, Eq. (6) is used to maximize background fluorescence, thus extracting the target fluorescence that is overwhelmed with the background fluorescence. The scalar P_corr is derived by:

Because P_corr is position independent, LMMSE is expressed in the form of vectors, where Flu _1×L ² and Exc_1×L ² denote the reshaped 1-dimension vectors of the measured 2-dimension fluorescence image Flu_L×L and excitation image Exc_L×L E x c L 2 × 1 T denotes the transposition of vector Exc_1×L ² . Finally, the corrected target fluorescence distribution F l u t a r g e t c o r r is calculated as:

It should be noted that the background subtraction through Eq. (6) is based on the distribution of measured fluorescence and excitation fields which have different scales of signal intensity. Therefore, before using Eq. (7), the fluorescence and excitation images are respectively normalized to their own maximum. As shown in Figure 3B , the reflection artifact induced by mouse fur corresponds to the maximum of the excitation image. Therefore, the normalization to this high-intensity artifact (i.e., right square region in Figure 3B ) can severely impact the true distribution of excitation photons transmitting though tissues. To eliminate the effect of reflection artifacts on the normalization and optimally subtract the background fluorescence, an Adaptive Mask-based Background Subtraction (AMBS) strategy is further implemented in a workflow as shown in Figure 4 .

In the first step, based on the normalized raw fluorescence and excitation images, preliminary background subtraction is conducted through Eqs. (6)-(8) to get the subtraction coefficient P c o r r 1 and the corrected fluorescence distribution F l u t a r g e t c o r r 1 . In steps 2 and 3, a mask is generated by binarizing the first-round correction F l u t a r g e t c o r r 1 and only keeping pixels with non-zero values. As is shown in the Step 3 of Figure 4B , with the use of mask, the reflection artifacts and high-intensity background region can be filtered out. Compared with the original excitation image (Step 1 in Figure 4B ), the masked excitation image (Step 3 in Figure 4B ) exhibits more detailed transmission field on the animal surface, rendering an optimized background subtraction. In step 4, a further background subtraction is conducted based on the masked fluorescence and excitation images, to get a new coefficient P c o r r   2 and corrected fluorescence distribution F l u t a r g e t   c o r r 2 . In step 5, we select the final residual fluorescence from F l u t a r g e t c o r r 1 and F l u t a r g e t c o r r 2 . As shown in Eq. (5), the subtraction coefficient P_corr denotes the percentage of background in the fluorescence measurement. To avoid over-subtraction, we choose the corrected image with a smaller P_corr .

Coupled diffusion equation with Robin-type boundary condition was employed to model the propagation of near-infrared light in highly scattering media (32). The surface fluorescence measurement Φ f l u ( r d ⇀ , r s ⇀ ) detected at position r d ⇀ due to excitation spot located at r s ⇀ can be written as (33):

where Green’s function G 0 e x c ( r 1 ⇀ , r s ⇀ ) describes the propagation of excitation light from a source to a point r 1 ⇀ in the medium. Similarly, Green’s function G 0 f l u ( r d ⇀ , r 1 ⇀ ) denotes the propagation of fluorescence light emanating from fluorophore at r 1 ⇀ to a detector r d ⇀ . Calibration factor S ^flu accounts for the unknown gain and attenuation factors of the optical system. v is the speed of light in the medium. D ^flu is the diffusion coefficient of medium at fluorescence wavelength. After discretizing the imaging domain generating from the 3D CT surface, the FMT reconstruction problem can be formulated as the following matrix equation (34, 35):

where W denotes the weight matrix mapping the relationship between the 2D fluorescence measurement Φ ^flu and the 3D internal fluorophore distribution . The discrete cosine transform based L1-norm regularization algorithm was employed to solve the Eq. (10) for FMT reconstruction, and its detailed description can be referred to (36). Raw and AMBS corrected fluorescence images were respectively employed in Eq. (10), to investigate the performance of AMBS in FMT reconstruction improvement.

To evaluate the performance of the proposed method, we introduce the tumor-to-background ratio (TBR) based on the profile traversing tumor center on the 2D fluorescence image. The TBR indicates the contrast of the mean fluorescence intensity inside (mFluⁱⁿ ) and outside (mFlu^out ) of the tumor region on the profile:

Tumor center offset (TCO) and tumor volume overestimation (TVO) were used to quantitatively evaluate the performance of FMT respectively reconstructed using raw and background-corrected fluorescence images. TCO indicates the Euclidean distance between the tumor center (x, y, z) recovered in the FMT and the true center (x₀, y₀, z₀ ) obtained from the contrast CT:

TVO denotes the percentage of over-estimated tumor volume in FMT (V_FMT-V_CT ) relative to the true tumor volume V_CT :

It’s noteworthy that, in the example ( Figure 3 ), the strong background fluorescence originated from the regions which have low absorption characteristic and locate near the excitation light source. If target of interest resides in these regions, our method can still effectively suppress the background fluorescence and extract the target signal, which is illustrated through the following GNR fluorescence imaging experiment. Figure 5A shows the raw and AMBS-corrected fluorescence images, before and after intertumoral GNR injection. The excitation location is indicated on Figure 5B . Owing to the low absorption of the bladder, more autofluorescence and possibly unfiltered excitation light will penetrate through this region. Without effective background subtraction, it is difficult to determine if there were GNRs in the tumor or bladder, since the fluorescence images appeared similar between the pre- and post-injection raw images ( Figure 5A , column 1). And the tumor was not clearly visible in the raw post-GNR fluorescence image. Based on the AMBS correction, we can reliably identify if there exits GNRs in the imaged body. And by effectively subtracting the background fluorescence, AMBS clearly extracted the GNR fluorescence emanating from both tumor and bladder ( Figure 5A , column 2), which can be directly validated through the organ fluorescence image acquired on Kodak In Vivo multispectral Imaging System ( Figure 5C ). Additionally, the highlighted GNR fluorescence in tumor and bladder, as shown in Figure 5C , can also be treated as the benchmark to validate the accuracy of FMT reconstruction. Figure 5D shows that FMT reconstruction using the raw fluorescence images can only recover the GNRs accumulated in the bladder, due to the overly strong bladder fluorescence signal. In contrast, FMT reconstruction using AMBS-corrected fluorescence images recovered the GNRs accumulated in both the breast tumor and bladder ( Figure 5E ), bolstering that our proposed background subtraction strategy can improve the reliability of FMT, even when the target signal is overwhelmed by strong background.

As an example, Figure 6 shows the contrast CT slices of 2 (out of 10) mice bearing breast tumors of different sizes. The large tumor (4 mm diameter) was clearly delineated through the enhanced tumor edge. The small tumor (1.5 mm), however, demonstrated minimal contrast enhancement, and was identified only from its morphological appearance. In this study, the tumor contoured from contrast CT was treated as the benchmark to verify the accuracy of AMBS in tumor identification.

Figure 7A shows the raw and AMBS-corrected fluorescence images for the 10 white mice bearing 4T1 tumors of different sizes (top half: ≥ 4mm; bottom half:< 4mm). The first column shows the fluorescence images of the mice bearing 4-mm and 1.5-mm tumors (as indicated in Figure 6 ). Since the optical and CT coordinates are geometrically registered, the true tumor location shown in CT can be precisely projected onto the fluorescence images. The red circles on Figure 7 indicate the tumor region acquired from CT. As shown in the raw fluorescence images, the tumor fluorescence (circle region) mixes up with the nonspecific background fluorescence with large dynamic range, complicating the tumor detection. In contrast, all the tumor fluorescence signals were effectively extracted in the corrected fluorescence, validating the feasibility and robustness of the proposed AMBS method. Compared with the raw fluorescence images, corrected fluorescence images show significantly higher tumor-to-background contrast, which is beneficial to early-stage small tumor detection. As examples, Figures 7B, C show the normalized profiles plotted along the dotted lines (shown in Figure 7A , column 1) across the tumor regions. The profiles quantitatively demonstrate that the strong artifacts (indicated by the signal peaks) outside of the tumor region is effectively suppressed. In addition, the tumor sizes in the corrected fluorescence images are much closer to the truth than that in the raw fluorescence images.

To further quantitatively demonstrate the effectiveness of the developed approach, the tumor-to-background ratios for all the 10 experiments were calculated from the profiles traversing the tumor centers in Figure 7A , based on Eq. (11). Student’s t-test analysis result in Figure 8 suggests that the proposed strategy significantly (P<0.05, N=10) improved the tumor-to-background contrast.

Figure 9A shows the 3D FMT results reconstructed using the AMBS-corrected fluorescence images, for the same example mice shown in Figure 6 . The FMT and CT coordinates are physically registered in our system through rigorously geometrical calibration (29). The red line denotes the mouse contour used for FMT reconstruction. The match between the FMT contour and CT animal surface confirmed the accuracy of our geometrical calibration. The dotted line delineates the tumor edge obtained from contrast CT. A good coincidence of the tumor localization and tumor volume was observed between FMT and CT in all three orthogonal views, indicating that FMT with AMBS-corrected fluorescence images can accurately recovery the tumors even for the small tumor. The last row in Figure 9A displays the 3D rendering of FMT reconstruction fused with the CT bony anatomy. Figure 9B shows the FMT results reconstructed using the raw fluorescence images. Because the tumor fluorescence is surrounded by the strong background fluorescence (as shown in the raw fluorescence images in Figure 7 ), the FMT tumor volume in Figure 9B is much larger than the truth, especially for the small 1.5 mm tumor. And the high-intensity fluorescence in the bladder region (as shown in Figure 7 , raw 2D fluorescence image of 4-mm tumor) induced the false-positive 3D-FMT target recovery in bladder (marked as arrows in Figure 9B ).

Figures 9C, D illustrate the comparison between the FMT respectively reconstructed from corrected and raw fluorescence images, in terms of tumor center offsets and tumor volume overestimation. After background subtraction, the accuracy of FMT reconstruction regarding both tumor localization and tumor volume was significantly improved (P<0.05, N=10).