2.1.

Measured Optical Properties of Mouse Lung

Optical properties of Mtb-infected mouse lung were measured experimentally to provide inputs into the computational and physical models. All animal experiments were approved by Texas A&M University Institutional Animal Care and Use Committee. Mice were infected by intratracheal instillation of ${10}^6$ CFU BCG. After 24 h of infection, mice were sacrificed, and the lungs were immediately excised. The excised lungs were placed in a well between two microscope slides. This well was created by curing a $\sim 1.5\mathrm{mm}$ layer of polydimethylsiloxane (PDMS) on a single microscope slide and using a custom biopsy punch to remove a 15-mm diameter section. Lungs were not sliced into thin sections because the organ had to be homogenized and plated for culture to quantify bacterial load. Lung reflectance and transmittance were measured at 535 and 730 nm wavelengths using an integrating sphere. The reduced scattering and absorption coefficients of excised mouse lungs were estimated using inverse adding-doubling method after collection of reflectance and transmittance values.²⁹ The resulting optical properties assume that the lungs remain well perfused and are fully deflated. Table 1 shows the optical properties of infected mouse lung for the two excitation wavelengths of interest: 535 nm for tdTomato fluorescent protein and 730 nm for REF substrate CNIR800.^17,18 Measured optical properties for the infected mouse lung are in the range of healthy human and piglet lung tissue optical properties in the literature.^30,31

Table 1

Absorption coefficients (μa) and reduced scattering coefficients (μs′) of infected mouse lung and validation phantoms at wavelengths of interest. Percent error between total flux measured experimentally with the phantom and simulated in the model.

2.2.

Airway and Lung Phantom

Optical phantoms were created from PDMS with India ink and titanium dioxide (${\mathrm{TiO}}_2$) to replicate the measured absorbing and scattering properties of lung tissue, respectively. Two separate phantoms were created to simulate the optical properties of the tissue at the two wavelengths of interest (Table 1). Phantom 535 contains 3 mg ${\mathrm{TiO}}_2$ and $7.5\mu \mathrm{L}$ India ink per gram of PDMS and approximates infected lung measured at 535 nm. Phantom 730 contains 2 mg ${\mathrm{TiO}}_2$ and $3.5\mu \mathrm{L}$ India ink per gram of PDMS and models the infected lung at 730 nm. Both phantoms were imaged at both illumination wavelengths to provide additional validation data for the computer model.

Structurally, the lung has a unique surface for internal illumination through the trachea. On the mesoscale, the airway branching results in a complex air–tissue interface where a stark contrast in refractive index between air and tissue will affect the transport of photons within the organ. The airway was included in both the computational and physical models of the physiological system to better evaluate the accuracy of the simulation to a biological environment. A fractal tree mock-airway was designed and printed out of a base-soluble material as an internal mold for the PDMS airway phantom. The preliminary structure shown in Fig. 3(a) was designed to be easily 3-D-printed in-house on a fused deposition modeling printer (Stratasys^®, Fortus360mc). This soluble structure was secured in a rectangular mold for pouring the PDMS and optical particle mixture. Upon curing, the mock airway was dissolved out of the phantom, leaving an airway void and a pathway for internal illumination of the solid rectangular block phantom. This method of incorporating complex geometry into a silicone matrix has previously been employed for designing flow systems for surgical training.³² 3-D printing is also becoming a popular method for fabricating phantom molds and for manufacturing the phantoms themselves.^33–35 The phantom fabrication methods used here are described in full detail by Durkee et. al.³⁶

Fig. 3

(a) 3-D models for photon transport in LightTools. The rectangular phantom used for validation studies has a four-generation fractal tree as a model airway. (b) The full-torso model of the mouse includes a more anatomically accurate model airway and lungs of comparable volume to that of a mouse. (d, e) The lung and heart are immersed in a cylindrical model of other soft tissues. The star in (b) is the location of the internal illumination source.

2.3.

Phantom Imaging

Imaging of the lung phantoms was performed in an IVIS Lumina II (PerkinElmer) whole-animal optical imaging system to validate the computer simulation of the analogous simplified model. For internal illumination, the IVIS illumination pathway was blocked, and a fiber ME light source was inserted into the airway void until the tip was in contact with the wall at the bifurcation.³⁷ The ME output power was set at $1\mu \mathrm{W}$ for both wavelengths. The IVIS emission filter wheel was set to “open” to collect the illumination light, and camera settings were set to automatic exposure. Total irradiance of the top surface of a phantom measured by the IVIS imaging system was compared with the simulation for 535- and 730-nm illumination studies.

2.4.

Mouse Torso Model

Once the simulation was validated using the simplified phantom, the airway structure within the simulation was updated to be more representative of the largest branches of the murine airway [Fig. 3(b)] based on computed tomography (CT) images.^38,39 The simulated lung was designed around the airway [Fig. 3(c)], with the general anatomy and size constraints of the mouse lung modeled after similar CT images.^39,40 In vivo, the lung is a dynamic and porous organ that scatters light much more effectively than solid tissue. Within the computational model, the lung properties can be adapted from the measured values of deflated lung to represent inflated lung at different points in the respiratory cycle. Here, we optimize the computational model to represent a point in the cycle indicative of passive respiration to analyze the illumination performance of external and internal illumination sources. The heart and other soft tissues are also represented [Figs. 3(d) and 3(e)] to more effectively model external illumination and to address photons scattered into the lung after traversing other tissues.

2.5.

Simulated Optical Properties of Inflated Lung

The optical properties of the lung were measured after excision, assuming the organ was deflated. In a living mouse, the lung will always have some level of inflation, with air making up at least 30% of the organ volume after expiration and up to 90% of the organ volume after inspiration.^41,42 The simulated optical properties can be mathematically manipulated to represent the scattering and absorption of an inflated lung, based on the optical properties of the deflated lung, and the alveolar size and density.³⁰

For this model, we assumed a constant alveolar diameter of $55\mu \mathrm{m}$.⁴³ Alveoli were assumed to be spherical in the calculation of the volume of a single alveolus, $V_{\text{alveolus}}$. A number density of alveoli were calculated based on mouse lung characteristics. First, because we have a static model, we assumed a constant level of inflation with air composing 80% of the organ volume. Using this inflation factor, $f_i$, and the properties listed in Table 2, the number of alveoli in the lung was calculated using

Table 2

Properties of inflated mouse lung used to calculate approximate optical properties.

The alveolar density

The absorption coefficient, ${\mu }_a$, of inflated lung was also adjusted because the path length available for absorption changes significantly with air in the tissue.³⁰ For the level of static inflation assumed in this model, only 20% of the total lung volume, $V_{\text{lung}}$, is actually tissue, $V_{\text{tissue}}$. With no absorption occurring in the air-space, the absorption coefficient is reduced accordingly by this factor,

2.6.

Heart and Other Soft Tissues

The heart is important in this simulation because of its high blood content and, therefore, high absorption in the visible range. While a majority of the photons contributing to the illumination profile of the lung come directly from the internal source, some fraction of the light will escape into the surrounding tissue. The properties of that tissue, including the heart, will determine how much the illumination of the lung is affected by its surroundings. The heart is assumed to be mainly an absorber, and the optical properties of partially oxygenated blood are used for the heart in this model (Table 3).⁵¹ The remaining tissue includes muscle, fat, skin, and bone; however, bone is not included in this model for simplicity. Overall optical properties for the collective “other soft tissues” are estimated based on values from the literature³¹ and are listed in Table 3. These values were used to determine the MFP and transmissivity ($T$) as inputs for the heart and other soft tissue materials. LightTools was set to interpolate values to determine the properties of material at wavelengths within the range listed in Table 3. If a wavelength simulated was out of the range listed, the value closest to that wavelength is used. For example, the optical properties of the heart at 535 nm were identical to those listed at 665 nm in Table 3.

Table 3

Optical properties for other soft tissues from Ref. 30.

2.7.

Illumination and Detection Parameters

The fiber bundle ME used for internal illumination has a divergence half angle of 20.5 deg, and experimental protocol specifies that the endoscope should be in contact with the tissue for imaging. This internal source was modeled as a point source with a divergence half angle of 20.5 deg to mimic the fiber bundle used in imaging experiments.^17,18 To model epi-illumination within the whole-body imaging system, dorsal and ventral external illumination sources were placed 20 mm away from the simulated phantom or torso and uniformly illuminated a plane located at the surface nearest to that source. Validation simulations were run with 1e6 photons with a source power of $1\mu \mathrm{W}$. All simulations of the mouse torso model were run in triplicate with 1e5 photons. External illumination simulation times ranged from 30 to 45 min, and internal illumination simulation times ranged from 3.5 to 4 h depending on source wavelength. External and internal sources at both wavelengths were set to 1 mW total power emitted.

Illumination of the lung was analyzed using average fluence rate in the lung and source efficiency, defined as average fluence rate in the lungs relative to average fluence rate in the entire simulated torso. Detection planes parallel to the coronal plane were placed at 0.5 mm intervals through the solid model of the torso to directly record photon flux, with bins of $0.1\mathrm{mm}\times 0.1\mathrm{mm}$ in each collection mesh. The complete detection matrix is $200\times 250\times 35$ elements, corresponding to a total of 1.75e6 elements ($8750{\mathrm{mm}}^3$).

Spatial distribution of the light within the lung was analyzed by fitting the average fluence rate in the detection planes to the exponential curve

3.1.

Validation of Computer Model with Lung Phantom Imaging

The measured optical properties of the phantoms and the accuracy of the simulation to reproduce the experimental IVIS imaging results are shown in Table 1. The simulation was able to replicate the total photon flux within 5.0% for both phantoms at both wavelengths. Figure 4 also demonstrates a similar irradiance profile between phantom imaging and the computational model for both wavelengths. After verifying agreement between the computational and physical models, we expanded on the computational model to better mimic the murine anatomy, as shown in Fig. 3. All results following verification are from this advanced model.

Fig. 4

Validation of the computational model with IVIS imaging of optical phantoms shows a similar irradiance profile at the phantom surface. Phantom 535 is shown here illuminated internally with (a) 535 nm and (c) 730 nm ME sources. The simulation replicates total flux output to the detector (Table 1) and the irradiance profile at (b) 535 and (d) 730 nm.

3.2.

External Illumination Versus Internal Illumination

As described earlier, the position of the mouse relative to an external illumination source has an effect on the signal collected from a fluorescent target within the lung. The 3-D illumination of the lung was analyzed for external illumination from the dorsal and ventral sides and for internal illumination. An internal source in contact with the tissue with a divergence half angle of 20.5 deg was used for the comparison between internal and external illumination.

Figure 3(e) shows a transverse view of the optical model, with the dorsal and ventral sides indicated. The asymmetry between dorsal and ventral causes a difference in the illumination profile of the lung [Figs. 5(a)–5(b) and 5(d)–5(e)]. Both positions yield an exponential decay in fluence rate with depth in the lung [Fig. 5(g)]. The decay constant, $b$, varies for both orientation of the external source and wavelength ($p<0.0001$) according to a comparison of fits of a nonlinear regression for each illumination strategy (Table 4). The difference in penetration depth of external illumination is most drastically affected by the heart, the main organ between the source and the lung in the ventral position. As a highly absorbing organ (due to blood content), the heart prevents a portion of the illumination from reaching the lungs, resulting in a lower $a$ parameter in the corresponding decay equations in Table 4.

Fig. 5

(a, d) Maximum intensity projections of the light distribution within the lung are shown for external illumination from the ventral side of the mouse, (b, e) external illumination from the dorsal side of the mouse, and (c, f) internal illumination. (a–c) A difference in penetration can be seen between the excitation wavelength for tdTomato and (d–f) the excitation wavelength for the REF NIR probe. All projections with epi-illumination are normalized to have the same maximum. In the internal illumination projections, all values above that maximum are set to that maximum to better represent the average fluence rate on the same scale. The average fluence rate within the lung decreases exponentially with distance away from the source for both (g) external illumination and (h) internal illumination. However, (g, h) the average fluence rate is higher throughout the lung with internal illumination.

Table 4

Decay of fluence rate within lung. Average power was fit to a decaying exponential: f(x)=a*exp(−b*x), where a is the initial average fluence rate at the detection plane nearest the source and b is the decay constant.

Internal illumination avoids the problem of traversing other tissues, and minimal light is lost to surrounding tissue. The illumination still decays exponentially with distance from the light source [Fig. 5(h), Table 4], but the efficiency of the light source at coupling light into the lung is much higher ($>60\%$), compared with less than 10% efficiency for either external illumination orientation at either wavelength (Table 5). The average fluence rate in the lung with the internal source is also significantly higher than external illumination when the sources have equal power ($p\ll 0.0001$).

Table 5

Ability of different illumination sources to couple light into the lung.

3.3.

Diffusing Fiber Internal Illumination Source

Simulations and previous animal experiments indicate that internal illumination is more efficient than external illumination in either position. To estimate the potential for further improvement in illumination of the lung, modifications to the internal source were designed and tested with the optical model. First, a 5-mm-long cylindrical light diffuser design was simulated [Fig. 6(a)]. Diffusing fibers can be designed to preferentially emit light radially or out the distal end of the diffuser.⁵² The percentage of power emitted from the distal end of the diffuser relative to the homogeneous radial emission along the length of the diffuser was varied from 10% to 100%. 100% power emitted from the tip of the diffuser is equivalent to the ME condition. All simulations were performed with the diffusing fiber tip in contact with the tissue at the tracheal bifurcation. As less power was emitted along the length of the diffuser, the efficiency of the source at coupling light into the lung increased, along with average fluence rate in the lung. Trends in efficiency and average fluence rate were similar across both wavelengths of interest [Figs. 6(d) and 6(g)].

Fig. 6

The fluence rate in the lung is sensitive to the parameters of the internal source, including (a) diffuser tip, (b) fiber position, and (c) divergence angle of the fiber. The efficiency of a fiber diffuser increases as more source power is emitted through the tip of the fiber rather than radially (d). The ME efficiency is more sensitive to (e) position than (f) divergence angle. (g–i) The average fluence rate in the lung follows similar trends to efficiency for all source manipulations.

3.4.

Positioning of Fiber Internal Illumination Source

The original internal source modeled off the ME specifications was simulated at different positions within the trachea to determine the effect of source placement on the illumination of the lung [Fig. 6(b)]. Starting with the internal source in contact with the tissue at the tracheal bifurcation (0 mm), the endoscope was moved away from the tissue surface, up to 6 mm offset, effectively pulling the endoscope out of the airway. As the internal source was moved away from the tracheal bifurcation [Fig. 6(e)], the efficiency increased moderately ($p\ll 0.0001$) until peaking near 2 mm distance from the bifurcation, then decreased below the initial efficiency at the tissue surface. In the region where efficiency hit a maximum, the simulation also indicated a maximum fluence rate within the lung [Fig. 6(h)].

3.5.

Divergence Angle of Fiber Internal Illumination Source

The final source manipulation simulated was the change of the divergence angle of the fiber bundle source [Fig. 6(c)]. The effects of the divergence angle on illumination were simulated for angles above and below the current design (20.5-deg half angle). The simulation results show an upward trend with increasing angle [Figs. 6(f) and 6(i)], with a slope of 0.021 and $0.039\mu \mathrm{W}/{\mathrm{mm}}^2/\mathrm{deg}$ divergence for NIR and visible wavelengths, respectively ($R^2>0.90$).

3.6.

Optimal Parameters of Internal Source

Illumination of the mouse lung was improved by independently changing the location and divergence of the internal source. The optimal source placement and optimal angle were combined to further improve the lung illumination. To find the optimal illumination, a divergence half angle of 40 deg and source locations of 0.7 and 1.7 mm away from the tracheal bifurcation were selected as inputs for the optical model. While these simulations show an improved illumination over the current experimental design, the optimal internal source parameters were achieved at the original 20.5-deg divergence half angle with the source placed 1.7 mm away from the tissue surface at the tracheal bifurcation (Table 6).

Table 6

Parameters and performance of optimized internal illumination. The bolded values are represented spatially in Fig. 7.

To illustrate the light distribution in the lungs, the fluence rate of each detection plane was combined into a 3-D representation of internal illumination of the lung at both wavelengths of interest. Maximum intensity projections for each orientation are shown in Figs. 7(a)–7(c) for 535 nm and Figs. 7(d)–7(f) for 730 nm illumination to describe the spatial variance in the fluence rate. Video 1 [Fig. 7(g)] of the complete rotating volumes at 535 nm (top) and 730 nm (bottom) show the dependence of fluence rate on the illumination wavelength due to the differences in optical properties.

Fig. 7

The 3-D illumination in the lung is shown for (a–d) 535 nm and (e–h) 730 nm. Maximum intensity projections of the fluence rate in (a, d) the coronal plane, (b, e) sagittal plane, and (c, f) transverse plane. A mask of the lung is also shown in each projection. (g) Video of the 3-D rendering of the illumination is shown for both wavelengths (Video 1, MP4, 8.3 MB [URL: https://doi.org/10.1117/1.JBO.23.7.071208.1]).

4.1.

Assumptions and Limitations of the Optical Model

The optical simulation was designed to analyze the 3-D illumination of a complex physiological system and optimize the illumination source and protocol for detection of optical targets in vivo. While the model is structurally and optically complex, it is important to note the assumptions and limitations of the optical model. An advanced phantom was designed to validate the ability of the optical model to replicate the boundary conditions of an internal airway and source placement within that airway. Due to manufacturing constraints, the airway modeled in the validation studies is less anatomically accurate than the airway in the full torso model. Assuming that this structural change does not affect the accuracy of the optical simulation, all tissue structure in the final model remains only an approximation of the natural anatomy.

While the porous tissue of the lung is approximated with the shifted scattering properties, in reality, the airway is continuous with the alveolar ducts and sacs. The boundary between the airway and the tissue might lead to some inaccuracy in the model, but it is assumed to be an underestimation of the diffusive properties of the lung. As the airway acts somewhat as a light guide, a continuous structure would likely yield a more uniform illumination. Unfortunately, modeling a structure of this complexity within a high-photon count Monte Carlo simulation is highly intensive computationally.

Simplifying all tissue except the lung and the heart into one bulk tissue layer might cause discrepancies in the model, particularly with the external illumination model. With fur unaccounted for on the external surface of the model, this model will overestimate the transmission of external illumination into the thoracic cavity. For internal illumination, the properties of this tissue layer have only a small effect on the illumination of the lung.

It is also important to note that both the internal and external power sources modeled are normalized to 1 mW. For animal experiments with this application, internal illumination power ranges from hundreds of microwatts to $\sim 1.3\mathrm{mW}$, and external illumination power is controlled by the IVIS software but can be estimated to range from milliwatts to watts depending on filters and lamp settings. The average fluence rate calculation, used as a measure for illumination, scales well with source power, and efficiency of the source will not change. Therefore, with a consistent source power of 1 mW, the results for changing source power are easily predictable. As an estimation, if we were to operate at the American National Standards Institute (ANSI) standard for maximum permissible exposure (MPE) for a collimated beam on skin, the source power would scale by this value relative to the area of incidence of the source on the tissue. The smaller area of incidence of the internal source therefore requires a lower power than the external source to fall below the ANSI standard. While neither source is actually collimated, we are using these values to demonstrate the scalability of this model. Table 7 shows these values with the internal source in contact with the tissue and the external source incident on the cylindrical model, creating the largest difference in source power achievable while normalizing irradiance to the ANSI standard. The external source power becomes $1000\times$ greater than the internal power. The corresponding average fluence rates for external illumination (Table 5) become roughly an order of magnitude higher than for internal illumination. However, as explained below, experimental limitations do not allow the external source to reach the same irradiance level as the internal source. If operation at the same irradiance levels was possible in the experimental setup, the efficiency rates and spatial distribution of light in the lung would remain poor for external illumination.

Table 7

Values relating source power in the simulations to ANSI standards for MPE of a collimated laser beam on skin for the wavelengths of interest.

Specifically for our application, the external source in the whole animal imaging system at the highest setting is roughly 3 to 8 mW, depending on the spectral filtering. This power is evenly distributed over the entire platform at the base of the chamber ($\sim 3500{\mathrm{cm}}^2$)⁵³ and not over the surface of the animal ($\sim 400{\mathrm{mm}}^2$). A higher, yet still very safe, irradiance is achieved with the internal source, which operates at $\sim 0.4$ to 1.3 mW. This power is incident on a much smaller area than the external source ($0.342{\mathrm{mm}}^2$). Using these values, the experimental irradiance ranges from 9 to $24\mu \mathrm{W}/{\mathrm{mm}}^2$ for the external source and 1200 to $3800\mu \mathrm{W}/{\mathrm{mm}}^2$ for the internal source, which is between two and three orders of magnitude difference. As stated earlier, the external source power would have to be about $1000\times$ greater than the internal source to achieve the same irradiance. The comparisons drawn in this paper with the two sources both at 1 mW of power are therefore on the appropriate scale for comparing with experimental data.

4.2.

External Illumination and Mouse Position

Previous animal experiments show a difference in fluorescence detected in different positions of the mouse in the imaging system, specifically in positioning the mouse ventrally or dorsally within the imaging system.¹⁸ Simulations of dorsal and ventral external illumination show that positioning the mouse dorsally with respect to the external imaging source more effectively couples the excitation light into the lung, supporting previous experimental results. The main explanation for this is the location of the heart within the thoracic cavity. At visible wavelengths, the heart and blood are highly absorbing. In the NIR, the heart does not absorb as much light, but it increases the path length that a photon must travel to arrive at the lung, increasing the likelihood that a photon is absorbed or scattered away from the lung. This model demonstrates the effect of the heart on ventral illumination. The simplification of all other biological tissues into one layer is an approximation, but it is anatomically similar from either side of the animal, incorporating skin, other soft tissue, and rib cage (not included in this model), which are all present both ventrally and dorsally.

4.3.

Optimal Illumination of the Mouse Lung

The goal of the internal illumination source is to better couple excitation light into the tissue of interest that may contain a fluorescent marker. For the specific application of detecting bacteria within the lung, there is no a priori knowledge about the location of the bacteria within the lungs of a given mouse. Diffuse, widespread illumination would therefore be an ideal tool for effectively detecting low numbers of bacteria within the lung. By simulating the physiology of the mouse and the optical system, the efficacy of different sources, different protocols, and even different animal positions can be analyzed without performing a large number of animal imaging experiments.

The fiber diffuser was determined to be a poor illumination source in the trachea due to its low efficiency of coupling light into the lung. While it did show a more uniform illumination of the lungs (data not shown), the light coupled into the lung was much lower than the current ME design. It is possible that a single lobe of the lung could be illuminated well by the fiber diffuser if the diffuser could be positioned deeper into the airway. In the current model, most of the power that was emitted along the length of the diffuser escaped through the trachea and into the surrounding tissue without ever reaching the lung. While positioning the diffuser deeper in the lung could remedy this, the current ME does not have the capability to steer the tip in the airway. The current fiber bundle diameter (0.66 mm) is close to the inner diameter of the trachea ($\sim 1.3\mathrm{mm}$), so there is also an anatomical size limitation with going much deeper in the mouse lung with these sources. Given a larger animal model, such experiments and corresponding simulations might be feasible.

The most effective manipulation of the internal illumination source was the placement of the source within the trachea. While the simulations indicate an enhanced illumination of the lung model, the effect of source placement in vivo may vary among animals. The airway will follow similar branching patterns in every mouse, but variability in animal size and lung development will likely hinder the reproduction of the simulation results in vivo. A change in the experimental protocol would still be recommended, as a small distance between the light source and tracheal bifurcation should show an increase in delivery of light to the lungs in any animal.

While changing the divergence angle of the source did not show the greatest increase in source efficiency or average fluence rate in the lung, it may be the best way to reproducibly enhance the illumination of the lung in animal experiments. An increase ($p\ll 0.0001$) in average fluence rate and coupling efficiency into the lung was found with the 40 deg half angle source relative to the current 20.5 deg half angle divergence of the microendoscope source. An increase of average fluence rate in the lung is expected to be more consistent with this change to the optical system than with an optimized experimental protocol regarding source placement.