Fluorescence modeling of in vivo optical detection of Mycobacterium tuberculosis.

Tuberculosis is one of the deadliest infectious diseases worldwide. New tools to study pathogenesis and monitor subjects in pre-clinical studies to develop treatment regimens are critical for progress. We developed an improved optical system for detecting bacteria in lungs of mice using internal illumination. We present a computational optical model of the full mouse torso to characterize the optical system. Simulated theoretical limits for the lowest detectable bacterial load support the experimental improvements with an internal illumination source, and suggest that protocol improvements could further lower the detection threshold.


Introduction
In 2016, tuberculosis (TB) was the ninth leading cause of death worldwide and the deadliest disease caused by a single infectious agent. Despite efforts to improve disease diagnosis and treatment and minimize transmission, there were over 10 million new cases of TB in 2016, including an estimated 600,000 cases of multidrug-resistant TB (MDR-TB) [1]. In the past decade, improved diagnostic methods have been developed for more rapid and accurate diagnosis of TB, but many of these tests cannot discern between the drug-susceptible and drug-resistant strains of Mycobacterium tuberculosis (Mtb), the causative agent of TB [2]. Also, only one of these tests-the Xpert MTB/RIF assay-has been shown to aid in the diagnosis of pediatric TB. Children under five have a higher mortality rate from TB, making early and accurate diagnosis imperative for effective treatment and survival [3].
Addressing the TB epidemic requires a multi-prong approach including development of new diagnostics and therapies, methods for minimizing transmission of Mtb, and research into the complex pathogenesis of the disease. Optical sensing and imaging has been used to observe disease pathogenesis in small animal models and in preliminary studies for the development of antibiotic treatment regimens [4][5][6][7][8]. Here, we evaluate two methods for optical detection of viable bacteria (Fig. 1). First, Mtb can be transfected with a fluorescent vector so that the bacteria produce the tdTomato fluorescent protein ( Fig. 1(a)). Because the bacteria itself is fluorescent in this case, there is no baseline fluorescence from an exogenous probe. However, the excitation and emission wavelengths of tdTomato lie in the visible range ( Fig. 1(c)), and biological tissue has a high optical attenuation and high tissue autofluorescence (TAF) in the visible range. This physiological limitation will reduce the signal to noise ratio (SNR) of any in vivo detection system.
Another method for detecting viable bacteria is through reporter enzyme fluorescence (REF) technology, using an exogenous fluorescent probe. Xie et. al. have developed a fluorescent probe excited in the near infrared (NIR) that is sensitive to a specific set of mycobacteria expressing a class C beta-lactamase, including Mtb [9]. This fluorogenic probe is made up of an NIR fluorophore connected to a quencher by a lactam ring. When the molecule is intact, the fluorescence is quenched. However, if the molecule comes into contact with the beta-lactamase Mycobacterium tuberculosis can be optically detected using genetic modification to express a fluorescent protein (a), or via a molecular beacon probe that is sensitive to an enzyme found on mycobacteria (b). The fluorescent protein modeled is tdTomato, with an excitation peak at 535 nm and an emission peak at 585 nm (c). The reporter enzyme fluorescent probe contains IRDye 800CW that is excited and emits in the NIR (d).
on the surface of a bacterium, the probe is cleaved, and the emission of the fluorophore will no longer be quenched ( Fig. 1(b), (d)). This method has two main advantages: 1) biological tissue is less autofluorescent and less attenuating in the NIR spectral region, so a higher SNR is possible; and 2) because this method can detect wild-type bacteria, there is potential for translation to a clinical diagnostic tool. However, this sensing method also has challenges. The probe enters the bloodstream and is broken down by the body, so a baseline signal exists without the presence of bacteria. Also, an exogenous probe will have a pharmacokinetic time scale of efficacy [4,6], unlike imaging transfected bacteria that have no time-dependence on signal intensity.
Recently, the incorporation of an internal illumination source placed in the airway of a mouse during whole-animal imaging has improved the sensitivity of optical detection for both of the previously mentioned detection schemes to be within the range of physiologic doses of bacteria [6,10]. Previously, a high detection threshold of ∼10 5 colony forming units (CFU) [5] limited use of these optical tools to monitor reduction of infection below this threshold along the course of treatment. The use of a fiber microendoscope for intravital illumination has shown a reduction of detection threshold to ∼10 3 CFU in the visible spectrum (tdTomato-transfected mycobacteria) [10] and ∼10 2 CFU in the NIR (exogenous bacteria-sensing probe) [6]. These detection thresholds were measured with intravital illumination in the airway and external detection, and while this method works for experiments with small animal imaging, internal fluorescence collection with the microendoscope could help to translate this method to a clinical diagnostic tool. Figure 2 details the various geometries used for intravital and external illumination in small animal imaging experiments.
Here, we use a comprehensive radiative transport model to characterize intravital excitation and external detection and predict fluorescence detection performance. This model allows us to 1) explore the effect of TAF on SNR in the different wavelength regimes and 2) model both widespread and localized infections and predict detection capabilities for each. Methods for in vivo optical detection of Mycobacterium tuberculosis. A whole-body animal imaging system is used for external illumination and fluorescence detection with the animal in both the ventral and dorsal positions (a). Internal illumination is accomplished by incorporating a fluorescence microendoscope (ME) into the whole-body imaging system (b). Using the microendoscope for internal illumination, fluorescence is detected either using the animal imaging system (a) or internally through the fiber microendoscope (b). Separate endoscopes are used for visible and NIR fluorescence excitation. A laser diode (730 nm) or LED (535 nm) light source is passed through a collimating lens (CL) and excitation filter (EX), then reflected off of a dichroic mirror (DM) into an objective lens (OL), which focuses the beam onto the proximal end of the fiber bundle. Fluorescence collected with the fiber bundle is filtered with an emission filter (EM) and imaged with a CCD camera for internal detection.

Methods
The computational model was developed in LightTools Illumination software (Synopsys Inc.), building on our previous illumination model [11]. The model incorporates the anatomy of a small animal with appropriate internal structures and optical properties. The airway structure was enhanced by adding an airway surface liquid layer that contributes to light transport to the lungs. The fluorescence contributions include tdTomato or REF fluorescence from the bacteria as signal and tissue autofluorescence that generates unwanted background and reduces SNR. Illumination and detection schemes incorporate whole-animal imaging and a microendoscope.

Mouse torso anatomy
The simulated mouse torso is composed of four components: bulk tissue, heart, lung, and a mucosal lining of the airway. The bulk tissue layer is representative of soft tissue, dermis, epidermis, subcutaneous fat, and muscle. Absorption and reduced scattering coeffecients were estimated along the spectrum through a ratiometric calculation from the tissue properties published in the literature [12]. The heart is modeled as a spherical organ with the optical properties of hemoglobin at a healthy (97%) oxygen saturation level, with the values pulled directly from the LightTools biological materials library [13]. Optical properties of the inflated lung are estimated through a combination of ex vivo measurements of tissue and Mie scattering for inflated alveoli, which is discussed in detail in the following section. Tissue optical properties for each layer of the model are listed in Table 1.

Airway surface liquid
Anatomically, this model builds upon the previous model through the addition of the airway surface layer (ASL), a liquid layer lining the transport and respiratory airways in the lung [14,15].
In the large scale branching structure, the ASL is modeled as a 100 µm thick layer coating the inner surface of the airway ( Fig. 3(a), (b)). At the alveolar level, the ASL is modeled through a multi-layer Mie scattering model. The alveoli are modeled as coated spheres with a 1 µm thick ASL shell [16]. The overall scattering and absorption coefficients are calculated from the measured tissue properties and the calculated alveolar scattering. Figure 3(c)-3(d) show the effect of this layer on the illumination of the lung. In these 10 5 photon simulations, the internal source was placed at the tracheal bifurcation, in contact with the ASL (Fig. 3(c)) or tissue ( Fig. 3(d)). The ASL has a "piping" effect on the illumination light when the source is in contact with this liquid layer. Modeling the ASL changes the spatial distribution of light in the parenchyma, therefore it is included as a fourth layer within this model.

Tissue autofluorescence
Tissue autofluorescence (TAF) is included in the fluorescence model, because it is integral for determining the SNR of the integrated imaging system. A single population of fluorescent particles was used to approximate all sources of autofluorescence in the torso. The emission spectra, conversion efficiency, and absorption cross section for these simulated fluorophores were taken from literature values at excitation wavelengths ranging from blue (480 nm) to NIR (800 nm) at 20 nm intervals [17]. Because ∼80% of the lung layer is modeled as air (due to the Mie scattering calculations), the concentration of TAF fluorophores in the lung layer was set to be one order of magnitude less than in the bulk layer. The values for the concentration of TAF particles were based off of the total flux collected from uninfected control mice in previous animal experiments [6,10]. The simulated TAF spectra shown in Fig. 4(a) and Fig. 4(b) are zero-padded at the lower wavelengths to provide a reference point for ideal spectral unmixing, because at these lower wavelengths, we can assume all signal is bacterial signal. This will not be possible to calculate for in vivo experiments, but provides a theoretical limit for the fluorescence detection capabilities of the optical system. Figure 4(c) demonstrates the difference in TAF intensity between the visible and NIR excitation sources, which is due to the wavelength-dependent conversion efficiencies which are defined and extrapolated from Zellweger et. al. [17].

Bacteria fluorescence
Two different bacteria detection schemes are modeled: 1) tdTomato-transfected mycobacteria and 2) an exogenous fluorogenic probe that is sensitive to the Mtb beta-lactamase enzyme. Without incorporating detailed information on the pharmacokinetics of the exogenous probe or the rate of conversion from the quenched to excitable state in vivo, we assume for this model that imaging occurs at a post-administration time point and probe dose that is equivalent to the quantum yield of the transfected bacteria. With this assumption, the conversion rate of a photon reaching a bacterium is the same between the two detection schemes, and the difference in signal collection comes from the underlying radiative transport phenomena at the excitation and emission wavelengths. Simulated fluorescence spectra for the tdTomato fluorescent protein and the IRDye 800CW fluorophore found on the NIR probe are shown in black in Fig. 4(a) and Fig. 4(b), respectively.

Pulmonary infection models
The simplest pulmonary infection model is a widespread infection model. In this model, each infectious dose (1-10 7 CFU) is distributed evenly throughout the lung volume. The fluorescent particles are defined as a single fluorescent molecule. However, fluorescent protein expression in a transfected bacterium gives a baseline fluorescence level associated with 1 CFU that cannot be attributed to a single molecule [18,19]. For the widespread fluorescence model, the expression at an equilibrium point was assumed to be 1000 molecules per bacterium. For the larger infectious doses, assuming an even distribution of molecules is a valid assumption because the bacteria are highly concentrated in the lung at high doses (>10 4 CFU). However, this assumption becomes invalid for lower numbers of bacteria. Therefore, the infection was also modeled as a bolus of fluorescent particles, mimicking a lesion containing multiple fluorescent bacteria or even a single bacterium. Not only does this better represent a low bacteria load, it also better represents the early stages of human pathogenesis, when Mtb is contained by the immune system in a localized granuloma. Localizing the infection to a bolus of fluorescent particles also allows us to analyze the sensitivity of the integrated imaging system to the location of the bacteria within the lung.

Spectral unmixing of simulated bacteria signal and tissue autofluorescence
The largest source of noise during in vivo detection of pathogenic bacteria is TAF. Fluorescent molecules endogenous to the animal have an emission response to stimulation with light, especially within the visible spectrum. Spectral unmixing mathematically separates the animal TAF signal from desired bacteria signal assuming the signal from a given pixel is a linear combination of bacteria fluorescence and TAF. In this radiative transport model, the spectra of the TAF and the fluorophore are both inputs to the model, and TAF is uniform throughout each layer. Given the assumption that collected signal is a linear combination of the TAF and bacterial fluorescence, we can quantify the signal from each population of fluorophores. All fluorescence signal is collected on a 2D simulated detector and summed at each wavelength to achieve a single fluorescence spectrum. The spectral content of this signal is compared to the input spectra for bacteria fluorescence and TAF to give the total flux for each population of fluorophores at the location of the simulated detector.

Illumination and fluorescence detection parameters in the infection model
Fluorescence collection was simulated in multiple imaging conditions including every combination of illumination and fluorescence collection at external ventral, external dorsal, and internal positions of the source and detector (Fig. 2). The external illumination source was placed 20 mm from the central plane of the simulated torso with a power output for all wavelengths of 1 mW, which is within the range of illumination for whole-animal fluorescence imaging systems with very sensitive cameras. Previous work shows that, at this scale, the dosage to the lung scales linearly with power [11]. Simulation results can therefore be easily scaled to represent specific experimental parameters. The source was modeled as a point source with the power evenly distributed across the central cranio-caudal plane of the mouse model. External signal was collected at a plane tangent to the dorsal or ventral surface of the torso. To mimic the collection with the whole-animal imaging system CCD camera for external detection, the angle of acceptance at this plane was limited to 25°. A microendoscope is modeled as a point source with a divergence half angle of 20.5°for internal illumination within the airway. Experimentally, placing the microendoscope in the same location in each animal is extremely difficult due to inter-animal anatomical variability. Additionally, we previously showed that the illumination of the lung by the microendoscope was dependent on source location [11]. To more accurately represent the experimental procedure, signal collection was modeled with "pseudo-random" placement of the microendoscope. This "pseudo-random" placement assumes that the experimentalist can have millimeter precision in placing the microendoscope, and that the projection angle of the source can divert within roughly 5°in any direction from the central axis of the animal. Internal signal was collected at a plane corresponding with the location of the internal illumination source. This sensing plane was limited to a 0.66 mm diameter with a 20.5°acceptance angle, simulating the collection capabilities of a fiber microendoscope [6,10,20]. The source wavelength was set to 535 nm and 730 nm for tdTomato and NIR probe simulations, respectively. Fluorescence collection was filtered to have a central wavelength of 585 nm for tdTomato and 775 nm for NIR probe simulations. All excitation and emission filters had a 20 nm spectral bandwidth.
For both internal and external fluorescence collection, irradiance was recorded on simulated detection planes in W/mm 2 . To compare simulations across a range of bacterial loads, total photon flux was calculated by integrating irradiance over the plane.

Results
All fluorescence simulations were run on a desktop computer (6 core Intel i7 processor, 3.3 GHz, 72 GB RAM) using LightTools Illumination Software (Synopsys, Inc.). Each simulation was run with 1 × 10 6 photons. Simulation times ranged from roughly 1 to 8 hours, depending on wavelength, position, and illumination and detection geometries. Internal illumination with external detection had the longest simulation time. Tissue autofluorescence simulations (Fig. 5) and internal source placement simulations (Fig. 6) were run a single time, with error estimates calculated from the number of photons at the detector.

Tissue autofluorescence and illumination strategy
Tissue autofluorescence (TAF) is a severely limiting factor in these experiments due to inter-animal variability and the long pathlength of the excitation and emission light in the tissue. Because there is not positional symmetry in the animal, the TAF will vary with the illumination and signal collection method. Simulations confirmed positional and spectral dependence for TAF photon flux. Figure 5 shows TAF simulations at the two excitation wavelengths of interest for epi-and trans-illumination in whole-animal imaging (Fig. 5(a)), and using the microendoscope for internal illumination with microendoscope internal detection, dorsal external detection, and ventral external detection (Fig. 5(b)). While external illumination yields a higher detected TAF signal with visible wavelengths, detected TAF signal is higher in the NIR with internal illumination (ventral detection: p < 0.005, dorsal detection: p < 0.05, internal detection: p = 0.2578 (NS)). Table 2 shows that the ratio of TAF at 730 nm to TAF at 535 nm is preserved for illumination direction (ventral or dorsal) rather than external illumination/detection strategy (epi-v. transillumination). Simulations of internal illumination of an uninfected mouse predict that collected TAF will be greater in the NIR compared to the tdTomato spectral region for each detection position. This demonstrates the competing relationship between photon path length and TAF spectral absorption within these two spectral regions.

Total fluorescence signal and internal source placement
Because the internal source is also a microendoscope capable of collecting fluorescence, this microendoscope could potentially be used as real-time feedback to the experimentalist to optimize source placement before taking images, given a correlation between the signal at the scope tip and the externally detected fluorescence. To test this theory, we compared the fluorescence collected at the fiber tip to dorsally collected fluorescence. The fluorescence recorded on the dorsal detector and the internal detector from each pseudo-random internal source location is shown for 10 3 CFU in the tdTomato range, and 10 4 CFU in the NIR range ( Fig. 6(b)). Representative trends are shown at a single inoculation dose in each wavelength regime. No correlation was found between the internally and externally detected signals for any dose (0-10 7 CFU) in either wavelength regime, indicating that the internal sensor cannot be used to optimize the internal source location for maximum signal at an external detector.

Fluorescence signal and effective NA
Previous work investigating the spatial distribution of light in the lung from an internal illumination source showed a slightly enhanced illumination of the lung tissue with an internal illumination source having a greater divergence angle [11]. To evaluate potential enhancement of fluorescence signal collection with a microendoscope with a higher divergence angle, we compared a source with a 40°divergence angle to the 20.5°divergence angle source. The acceptance angle of the internal sensor was held constant to observe signal changes solely due to the broader divergence of the source. The source and detector were placed at three random locations within the area of interest for each angle at each inoculation level. In most cases, there was no significant enhancement in the average fluorescence collected. The 40°source was significantly better (p < 0.005) at detecting 100 CFU in the NIR range. There was no consistent change in standard deviation across all groups between the 40°and the 20.5°source. Therefore, there is also no change in the robustness of the optical system with a higher divergence source because the inter-measurement variability is also not reduced.

Theoretical limits of optical detection of murine pulmonary infection
First, we examine the total fluorescence (bacterial signal and TAF) simulated for each illumination condition. Figure 6 shows the total flux due to fluorescence simulated for dorsal (a, c), ventral (b, d), and internal (e) detection in each wavelength regime. By comparing the total fluorescence collected, it is possible to compare results prior to any experimental post-processing. Spectral unmixing of bacterial signal and TAF is less reliable without an internal control for each animal, so total fluorescence collected provides a lower bound for system performance. System performance will be quantified through two metrics: 1) detection threshold, referring to the lowest bacterial load which yields a significant increase in signal above the control population (CFU = 0), and 2) the sensitivity of the system above this threshold, specifically the change in collected signal per unit change in CFU.
In the tdTomato spectral region, total simulated fluorescence for bacterial loads below 10 6 CFU were not significantly different from control mice (CFU = 0, not shown in Fig. 6) for any combination of external detection and external illumination, as shown by the shaded regions in Fig. 6(a)-(b). However, internal illumination in this spectral range demonstrated a reduction in this detection threshold for both dorsal and ventral fluorescence collection, denoted by the dashed lines in Fig. 6(a)-(b).
In the NIR spectral region, internal illumination showed further improvement over external illumination methods, reducing the threshold from 10 5 to 10 3 CFU in both collection positions (Fig. 6(c)-(d)). Simulations of internal fluorescence detection with internal illumination showed further decrease in the detection threshold, with total fluorescence collection in mice inoculated with over 100 CFU showing a significant difference from control mice (Fig. 6(e)).
These simulations indicate that for both external detection methods, the spectral region is the determining factor in the detection threshold, with all tdTomato simulations predicting a pre-unmixing detection threshold between 10 5 and 10 6 CFU and all NIR probe simulations predicting a pre-unmixing detection threshold between 10 4 and 10 5 CFU. Internal illumination with external detection also shows spectrally dependent detection thresholds prior to spectral unmixing, with tdTomato simulations yielding a threshold between 10 4 and 10 5 CFU and NIR simulations between 10 2 and 10 3 CFU. However, both tdTomato and NIR simulations give the same detection threshold with internal fluorescence detection, between 10 2 and 10 3 CFU.
Through simulations, we can also estimate the amount photon flux solely due to bacterial fluorescence, allowing for approximations of theoretical detection thresholds of the system given optimal spectral unmixing for each animal. Similar to the total simulated fluorescence, the unmixed simulated fluorescence varies with wavelength, animal position, and illumination method (Fig. 7). For internal illumination simulations, the average unmixed bacterial signal from 3 random placements of the internal source were used to more accurately simulate experimental conditions. External illumination simulations were run in triplicate, with static source and detector positions. Table 3 compares the modeled detection thresholds for all illumination and detection positions for tdTomato-transfected mycobacteria and the exogenous NIR probe. Simulations of infection with a bacterial load lower than 100 CFU show 0 photons from the tdTomato emission spectrum reaching the detector, with the exception of one ventral collection trial and one dorsal collection trial, which are assumed to be a statistical anomalies due to the low (< 50) photon count on the simulated detector. A linear regression shows that dorsal collection is more sensitive to CFU for internal illumination (Table 4).  We can assume that tissue attenuation is the limiting factor in delivering excitation photons to the bacteria and allowing transmission of emission photons outside of the body. Given the location of the heart, which is highly absorbing along the visible spectrum, a correlation between fluorescence signal and CFU is more likely to be achieved by imaging the mouse in the dorsal position. This model also shows a correlation between signal and CFU at the microendoscope tip (Fig. 7, Table 4). The slope of these linear regressions demonstrate the sensitivity of the imaging system to bacterial load. The data here is spectrally unmixed; however, the current microendoscope design does not have multiple emission filters, so microendoscope detection does not currently have the capability of reaching these limits. A spectrometer could be incorporated in the system in place of the camera to gain spectral information from an infected mouse.
As mentioned earlier, the widespread infection model is more accurate for high bacterial loads than low loads. Infection with a small number of bacteria can be better represented by a bolus of fluorescence corresponding to the bacterial load. Localizing the infection to a bolus of fluorescent particles allows us to analyze the sensitivity of the integrated imaging system to the location of the bacteria within the lung. We have modeled this cavitation to represent 10 2 -10 3 CFU, and placed this "lesion" at five points in the lung. None of these locations or bacterial loads yielded a fluorescence signal statistically greater than control, indicating that the optical system is limited by tissue attenuation at low bacteria loads. This model limits the scope placement to

Sensitivity ([photons/sec]/CFU) R 2 Sensitivity ([photons/sec]/CFU) R 2
Internal illumination 2 × 10 5 0.993 1 × 10 6 0.9784 the tracheal bifurcation. Without the ability to steer the endoscope deeper into the lungs, it is highly improbable that this system could get a high enough power density of excitation light to a cavitation or single CFU to produce a detectable signal in a mouse model of infection.

Simulated fluorescence and spectral unmixing
Simulations with tissue autofluorescence show that the TAF spectrum and total signal both vary with illumination strategy. A two-layer model of lung and bulk material (data not shown) produce red-shifted TAF spectra for internal and trans-illumination (detecting opposite the illumination source), with the spectral shift dependent on the thickness of the bulk tissue layer. This is consistent in both spectral regions we investigated. Contrarily, the simulated TAF signal from epi-illumination (detecting from the same side as the illumination source) are consistent for a given illumination wavelength, regardless of the thickness of the bulk tissue layer. TAF spectral signal will vary between animals due to animal size and illumination method, indicating the need for an internal control for each animal. Notably, the structurally-complex simulation of the mouse torso showed that integrated TAF signal is higher for internal illumination with NIR light than with a 535 nm source (tdTomato excitation wavelength). This was not consistent with the trans-illumination model, which showed higher TAF in the visible range, consistent with the epi-illumination model. A possible explanation for this is the tissue attenuation of the initial tissue of contact. In the external illumination cases, the increased TAF is the dominating factor because the rate of attenuation of the excitation light in the bulk tissue layer. However, with internal illumination, the initial tissue of contact is the lung, which is a highly perfused and highly scattering layer. Both visible and NIR light is highly scattered, but visible light is absorbed at a higher rate due to the hemoglobin content. Therefore, the NIR light is more efficient at reaching the lung/bulk tissue boundary than visible light. This can be explained numerically by understanding TAF trend for internal illumination with internal detection, (Fig. 5(b)), is the relationship between the likelihood of tissue absorption and conversion efficiency of TAF at each wavelength. Both tissue types (lung and bulk tissue) have both a higher attenuation and higher TAF in the visible compared to the NIR. TAF particles were consistent throughout all layers of the model, and a 535 nm photon is ∼4x more likely to be converted to TAF than a 730 nm photon (Fig. 4(c)). In the bulk tissue layer, a 535 nm photon is only ∼2x more likely to be absorbed than a 730 nm photon over a given path length. Therefore, in the bulk layer, visible photons will still produce more TAF than their NIR counterparts. However, in the lung, a 535 nm photon is ∼5.7x more likely to be absorbed than a 730 nm photon. With this factor increasing over the relative likelihood of producing fluorescence (4x), NIR excitation light will lead to more TAF than visible light.
Investigations of source manipulations did not suggest any improvement in fluorescence signal. Simulations of internal illumination showed that a broader divergence angle would result in more effective illumination of the lung [11]. However, this did not reliably translate into a significant improvement in collected fluorescence. For one condition, a higher divergence angle even performed significantly worse than the current source design. Also, using the microendoscope camera to find the ideal internal source position did not prove to be helpful without spectral unmixing, a post-processing technique. The total signal collected on the endoscope camera did not correlate with the signal collected on the external camera. However, the endoscope camera can still be used to ensure that the internal illumination source is in contact with the tissue, providing some feedback in reproducible source placement between animals.
In the simulations of murine infection, spectral unmixing improved the detection threshold by 1 to 3 orders of magnitude for external illumination methods (Table 3). However, because internal illumination overall yields less TAF signal, the results from spectral unmixing were not as significant, with one condition even predicting an increase in the detection threshold after spectral unmixing. This relationship can be explained by fluorophore crosstalk. A fraction of the photons emitted from the excited bacteria will excite simulated TAF fluorophores before exiting the torso. At low bacterial loads, the TAF signal is already much higher than the bacterial signal. With crosstalk further increasing the collected TAF, the apparent detection threshold increases. Experimentally, if an animal were to be imaged with a red-shifted source as a reference, the TAF from this image will be related to the overall TAF. The red-shifted source would minimize crosstalk between TAF and bacteria, allowing for an internal control. This could possibly decrease the detection threshold farther than the simulations suggest, because an increase in local TAF could be attributed to interaction between bacterial signal and TAF.

Strengths and weaknesses of this model
The simulation of pulmonary infection supports results from previous animal experiments. Although previously published simulations suggest that a higher divergence angle would improve illumination, this enhancement does not propagate to an improved threshold of detection for CFU in either the preliminary or advanced fluorescence models of infection. Here, we examine the limitations and assumptions of the fluorescence models, and discuss where these assumptions falter and how they might misrepresent in vivo infection.
One of the simplifications of this model is that TAF is consistent throughout the torso and shows no regional dependence. Also, TAF intensity was not varied between trials. Animals show high variability in their TAF, between subjects and spatially within the same animal. However, to develop an internal control for each animal experimentally, adding a secondary, spectrally separated illumination source would allow for a 2D TAF "map" for a given animal, which could be extrapolated to the spectral region of interest. Each animal could therefore serve as its own control, and spectral unmixing could better approach the theoretical limits determined in this work. Fluorescence detection would become limited solely by tissue attenuation, and not by a high background (TAF) signal.
A considerable limitation of the current model is the representation of anatomy. First, the mock torso does not have a fur layer. This issue is most likely not a major concern for internal illumination, mainly because the illumination light is attenuated by the time it reaches the outside of the animal. On the emission end of the process, the fur would act as a diffusing layer, mainly redirecting the emission light, but also absorbing and generating TAF. The redirection of the emission light will reduce overall signal collected and SNR, possibly raising the detection threshold for bacteria. For external illumination, this fur layer would have a more significant effect. Illumination light would be reflected and scattered before entering the mouse, lowering the power density of excitation light reaching the lung. The attenuation of any resulting emission would be the same as the internal illumination case. The lack of this fur layer leads to a discrepancy between the fluorescence model and previous experiments for both epi-and trans-illumination techniques. Figure 7 shows the detection threshold of epi-and trans-illumination to be comparable to internal illumination and a signal correlation with CFU down to this threshold, which disagrees with past experiments. It is possible that with ideal spectral unmixing, these external illumination methods could reach the simulated values, but the fur of the animal generates too much reflection and TAF for the bacteria signal to be pulled out. Essentially, by not modeling this fur layer, we are modeling a system with much less background noise than occurs during in vivo imaging experiments.
This model also does not account for inter-animal variability. The simplified geometry is assumed to be close to the average mouse, but variability in airway branching, animal weight, and relative lung size would affect system performance. Also, some mice simply have higher TAF. The model assumes the same TAF for each trial, which is not the case in vivo. If a mouse has a higher metabolism or is more stressed than the others in its cohort, it could have a vastly different TAF intensity, and even a different spectrum. TAF also varies across the animal. The ears, feet, and tail of the mouse have minimal fur, and yield a different TAF spectrum. In animal experiments, this makes spectral unmixing more difficult, because the spectrum used for unmixing does not necessarily fit for all pixels. For this model, we used a single fluorophore population to represent general TAF. This will again result in the model predicting lower noise and background relative to animal imaging.

Improving experimental setup and protocol
These simulations suggest that for murine models of infection, microendoscope detection should have a similar detection threshold to internal illumination and external collection experiments. However, the current microendoscope collects fluorescence on a CCD camera with a single emission filter corresponding to the peak wavelength of bacterial fluorescence, 585 nm for tdTomato-transfected bacteria or 775 nm for the exogenous NIR probe. Either multiple filters or a spectrometer would need to be added to the setup to collect spectral information. Although the unmixed simulated data do not show a reliable improvement in the detection threshold compared to the raw data, spectral information could help the post-processing, especially if an internal control for TAF is incorporated.
The internal control for TAF suggested earlier is imaging with a red-shifted source to minimize fluorophore crosstalk between the bacteria and the TAF generated by this second source. In the simulations, there is a reliable relationship between the TAF when imaged at different wavelengths (Fig. 5). In an animal, this information could be used to extrapolate the TAF from the red-shifted source to what would be expected from an uninfected animal at the wavelength corresponding to excitation of the bacteria-associated fluorophore. This would improve the current post-processing method because a local increase in TAF could be associated with fluorophore crosstalk between excited tdTomato or NIR probe and the background fluorescence of resident tissue. However, because TAF in an animal is dependent on which molecules are present locally, and the simulations generalize TAF, this relationship may not hold in vivo. If this relationship is not confirmed experimentally, the TAF internal control would still provide information about the relative intensity of the TAF for a given animal, which would aid in spectral unmixing.

Potential application for human disease
Here, we use a comprehensive radiative transport model to characterize the current optical system in a murine model of infection. However, this model has the potential to be expanded to predict the performance of an optical detection system as a diagnostic tool in children. Unlike the tdTomato-transfected Mtb system modeled, the bacteria-sensing NIR probe simulated in this model has the potential to be extended to a human diagnostic tool in tandem with the optical system. Tuberculosis manifests differently in children than adults, due to underdeveloped immune responses [21]. Also, children under 5 years old lack the ability to expectorate effectively, causing difficulties in acquiring samples for sputum culture, which is the gold standard for diagnosis [22]. A minimally invasive optical detection system would serve as an ideal tool for earlier diagnosis of TB in children, ideally reducing the high mortality rate in that age group. Future work involves extrapolating this model to replicate the anatomy of a young child to test the feasibility of optical detection of mycobacteria in children.

Summary
A fluorescence model of bacterial infection was developed to determine the physiological limitations of optical detection of pathogenic bacteria. The simulation revealed nuances in TAF signal related to the illumination method used to excite bacteria-associated fluorophores. This information about TAF and its dependence on illumination method changes the post-processing techniques used for each imaging method, and clearly demonstrates that each illumination method should have a unique spectral unmixing process. Previous animal experiments confirm the simulation detection thresholds of bacteria for internal and external illumination methods. The simulations also imply that the current spectral unmixing methods could be improved if animal-specific TAF can be collected or inferred. The simulations improve understanding of the relationship between the infection, the animal (TAF), and the optical system by allowing manipulation of variables not possible during in vivo imaging experiments.

Funding
National Institutes of Health, National Institute of Allergy and Infectious Diseases (R01 AI104960); National Science Foundation, Directorate for Engineering (CBET-1254767).