2.1.

Cherenkov Lateral Resolution

A skin equivalent geometry based on a seven-layer skin model^11,12 was used to estimate the spread of Cherenkov emission. This model simulated a $2.5\mathrm{mm}\times 10\mathrm{mm}$ thin sheet of high-energy photos or electrons incident on the skin geometry and originated 0.2 m above the tissue volume. The minimum width of 2.5 mm chosen as this is the minimum MLC thickness available in commercial clinical linear accelerators (LINAC) and so provides the minimum beam lateral thickness available without a custom setup. A total of ${10}^7$ events were generated for each photon energy of 6 and 18 MV, as well as electron energies of 6 and 18 MeV, with these values being chosen based upon them being the minimum and maximum energies available on most clinical LINACs. The energy distribution of the photon beams is shown in Fig. 1(b). The photon simulations were split into 10 separate simulations, and the electron simulations were split into 100. Each simulation was given a unique random seed and executed using a cloud infrastructure.¹⁰ Each photon simulation required $\sim 30$ to 50 min to execute depending on the energy level, whereas each electron simulation required 15 to 30 min. The initial and final position of each optical Cherenkov emission was recorded.

Experimental measurements were collected with an intensified CMOS camera (C-Dose Research, DoseOptics LLC, Lebanon, NH) where a $3\mathrm{mm}\times 40\mathrm{mm}$ sheet of 6 and 18 MV photons was delivered into water in a clear plastic container with the water surface at isocenter. Using the $6\times 6$ electron beam collimator with a custom $3\mathrm{mm}\times 40\mathrm{mm}$ Cerrobend insert as a collimator, electron energies of 6, 9, 12, and 18 MeV were also imaged. The camera was positioned such that it was level with the surface of the water. A 500-nm short-pass filter (500FL07-50, Andover Corp, Andover NH) was attached to the front of a 50-mm $f/1.2$ lens. The camera was place on the couch $\sim 0.7\mathrm{m}$ from the water container. Images were processed using Python 3.7 and scikit-image 0.16.2.

2.2.

Limits of Depth Sensitivity and Detection

A model with tissue-equivalent geometry containing an inclusion with fluorescence contrast was defined, where the inclusion depth and primary excitation source were varied using input arguments. The multilayer tissue-equivalent geometry based on a seven-layer skin model^11,12 was combined with additional layers of adipose and muscle.^13–15 The surface dimensions for each layer were $10\mathrm{cm}\times 10\mathrm{cm}$, and the entire tissue geometry was 5 cm in depth (Fig. 2). The properties of the seven-layer skin model have been documented in previous publications^11,12 and are summarized in Fig. 2(b). Each layer has a specific density and mixture of predefined materials as well as optical properties $({\mu }_a,{\mu }_s,g,n)$ for wavelengths between 350 and 900 nm. A 1-cm diameter spherical inclusion was also defined with a set of optical properties and additional fluorescence absorption and emission characteristics, which most closely resemble the oxygen-sensitive luminescent compound PtG4,¹⁶ which has been used in many previous experimental studies.^1,4 This molecule has absorption peaks near 430 and 630 nm with luminescence emission near 770 nm, with a lifetime that is effected by the local oxygen concentration in tissue.

Fig. 2

A multilayer tissue model containing (a) a tumor-simulating inclusion is defined where (b) the average ${\mu }_{\mathrm{eff}}$ is shown for each layer-type. (c) The luminescent absorption and emission assigned to the tumor is provided as a contrast agent.

Simulations of a 1-cm square source with 0.97 deg divergence placed 0.9 m above the tissue geometry were run with ${10}^7$ optical photons (430 and 630 nm) and the same number of x-ray photons (6 and 18 MV). With the beam divergence, the total area of the incident events on the tissue surface is $\sim 4\mathrm{cm}\times 4\mathrm{cm}$. Tumor inclusion depths measured from the top of the tumor to the tissue surface were defined between 0 and 10 mm. A parallel world voxel geometry was defined with $1\mathrm{cm}\times 1\mathrm{cm}\times 10\mu \mathrm{m}$ voxels used to measure light fluence and for high-energy sources, dose deposited. Additional filters and detectors were defined to determine the position and wavelength of Cherenkov and fluorescence emissions starting in the tumor inclusion, exiting the tumor inclusion, and reaching the surface. Simulations for the 6- and 18-MV source were split into 10 simulations of ${10}^6$ events for each tumor inclusion depth, whereas the lower complexity of the 430- and 630-nm optical excitation simulations allowed for single ${10}^7$ event simulations to be executed in a short amount of time. Experimental comparison of the luminescent tumor geometry was not performed, but in vivo applications have been considered previously.^3–5

The spectral characteristics of the Cherenkov emissions in the tumor inclusion (Fig. 2) were compared to the absorption spectrum of compounds in the PhotoChemCAD database.^17,18 This database is publicly available and contains the absorption and emission spectra and quantum yield of many compounds. The entire database can be downloaded in the form of a text file. This file contains a list of chemicals and their properties and links to files containing the absorption, and emission spectra, as well as links to images of the compound’s chemical structure. A Python script was written to parse this text file and the corresponding absorptions files. All compounds with reported absorbance between 350 and 850 nm were considered for analysis. The Cherenkov spectra in the tissue, $I_{\mathrm{Ch},\text{tissue}}(l_i)$, was interpolated and resampled to match the reported absorption spectra of each compound $j,m_{a,j}(l_i)$. The product of these two spectra was integrated between the previously stated bounds and the result was multiplied by the quantum yield, ${\phi }_{QY}$, as described here

3.1.

Cherenkov Lateral Resolution

Text files recording the initial and final position of Cherenkov emissions were generated using filter detectors in the GAMOS simulations. While the simulation was a 3D geometry, the XZ positions were tabulated, effectively reducing the dimensionality of the data. The resulting photon counts generated from ${10}^7$ initial events are shown in Fig. 3. From these simulations, it can be observed there are $\sim 100\times$ more Cherenkov emissions generated due to the electron source. This is expected due to the higher energy of the electrons compared to the photon energy distribution and because each electron at this high energy level will result in numerous Cherenkov emissions, whereas high energy photons must first undergo a scattering event before electrons are freed. These simulations also indicate the electron source would have a wider penumbra. In the simulations, this effect is more pronounced in lower energy electron sources, mainly due to the shorter mean free path and higher likelihood of electron scattering, as has been shown.^19,20 The lower optical emissions in the first 1.5-mm of tissue are likely due to the higher absorption coefficients, whereas below this depth the volume is defined as adipose tissue.

Fig. 3

Cherenkov emissions recorded from simulations of (a) 2.5-mm wide photon source or (b) electron source in multilayer tissue volume.

Cherenkov imaging of water was performed as a comparison to the simulated results. Images were collected with both photons and electrons and results are shown in Fig. 4. From these images, it can be observed the photon source has largely similar distributions within the first 10 mm of water. However, the Cherenkov emission distributions of the electron sources are highly energy dependent.

Fig. 4

Experimental Cherenkov measurements of (a) photon and (b) and (c) electron beams in water.

The simulation data and experimental images were analyzed to determine the full width at half maximum (FWHM) for each for each millimeter of depth. The experimental and simulation data cannot be directly compared but show similar tends of larger FWHM for electron sources. The analysis for the simulations is shown in Fig. 5, where the electron sources have a wider FWHM as a function of depth, likely due to the increased probability of interaction. Even at depths beyond 5 mm there is minimal beam divergence observed for the photon source.

Fig. 5

Analysis of beam width as a function of depth for 2.5-mm wide photon (6 MV) and electron (6 MeV) sources. The average FWHM was calculated for each millimeter of depth in the tissue.

3.2.

Limits of Depth Sensitivity and Detection

Using detector filters to monitor the track of Cherenkov emissions, the spectral distribution can be monitored at various locations in the model. The spectral emissions are expected to follow a $1/{\lambda }^2$ distribution,²¹ which is generally observed in the tumor, with small increases at areas of lower attenuation, likely due to emissions originating outside the tumor and then being counted when entering the tumor [Fig. 6(a)]. As these emissions exit the tumor, another detector tabulated the spectral characteristics, showing a small peak around 480 nm while the majority is distributed beyond 600 nm, due to the longer mean free path in this spectral region. A similar long-pass filtering effect is seen at the surface, where the emissions are mainly in the red-NIR range. While the tumor fluorescence absorption is modeled after PtG4 [Fig. 2(c)], the $1/{\lambda }^2$ spectral distribution of the Cherenkov emissions must also be considered. This model provides the ability to determine the actual excitation wavelength distribution of the Cherenkov-excited luminescence, as shown in Fig. 6(a) (dotted-line).

Fig. 6

(a) The spectral distribution of optical emissions in a model with a tumor inclusion at depth of 2 mm, as detected in the tumor (light blue), exiting the tumor (orange), at the surface (red), or contributing to luminescent excitation (dotted indigo). (b) The deposited dose for 6 and 18 MV at depths into the tissue model and (c) the corresponding optical Cherenkov fluence, which is clearly affected by the tissue optical properties of each layer.

The Cherenkov emissions are related to the deposited dose which increases with depth into the tissue, where the maximum dose ($D_{\text{max}}$) is expected to be 1.5 cm for 6 MV and 3.5 cm for 18 MV photon beams which is similar to our simulation results [Fig. 6(b)]. While in a homogeneous medium, Cherenkov emissions are thought to be directly correlated with deposited dose, Fig. 6(c) shows how the higher attenuation of muscle and blood can greatly decrease the overall light fluence, which corresponds with previous studies of Cherenkov emissions in the presence of tissue optical properties.^22–24

As expected, these simulations of multilayer a tissue volume show the fluence rate for the 430-nm source drops significantly in under 1 mm, and the 630-nm source follows suit after a few millimeters [Fig. 7(a)]. The light gray vertical lines in Fig. 7(a) show the skin layer boundaries, with light red-shaded regions indicating blood networks in the skin, which correspond with sharp drops in fluence due to the high absorption of these layers. By placing a detector at the surface, all fluorescence emissions exiting the tissue volume could be counted. GAMOS has the ability to count the origination of all fluorescent photons and those exiting the tumor, which shows $\sim 90\%$ of the fluorescent emissions leave the tumor, but those reaching the tissue surface are much lower (0% to 23%) and dependent on tumor depth. In our model, at a tumor depth of 7 mm, just over 2% of fluorescent photons reach the surface for both 6 and 18 MV. A comparison of surface fluorescence emission intensity for excitation by either 430 nm, 630 nm optical, or a 6-MV x-ray source is provided in Figs. 7(b) and 7(c). A plot of the mean photon count at the surface, relative to the peak value observed by 630 nm excitation, is plotted by tumor depth [Fig. 7(b)], where the depth indicates the distance between the surface and the top of the 1-cm diameter inclusion. Here, it can be observed the 430-nm source has the poorest depth sensitivity of $\sim 250\mu \mathrm{m}$, while the 630-nm excitation source has improved depth sensitivity of $\sim 2\mathrm{mm}$, and in these simulations, the Cherenkov depth sensitivity is $\sim 7.5\mathrm{mm}$. The sharp drop in depth sensitivity appears to be limited by the absorption of the blood networks, which is $\sim 2\times$ higher in absorption at the fluorescence peak (770 nm) compared to the surrounding tissue. While the Cherenkov excitation shows the greatest depth sensitivity, the 430-nm excitation source provides the highest potential lateral resolution due to its short path length and resulting smaller tumor cross section [Fig. 7(c)].

Fig. 7

(a) The photon fluence due to external optical illumination or x-ray induce Cherenkov emissions at depth in tissue is compared to the corresponding normalized fluorescence detected at the surface, where (b) the blood networks (red vertical lines) introduce considerable attenuation. (c) 2D-histograms of the surface luminescence.

3.3.

Choice of Optimal Fluorescent Agents

To identify other potential fluorophores that would be ideal candidates for Cherenkov excitation, a computational ranking of fluorescent compounds was performed. These rankings, the product of the in vivo Cherenkov spectra, fluorescence absorption spectra, and quantum yield of each candidate compound are shown in Fig. 8.

Fig. 8

The Cherenkov-excitation ranking of the top 50 candidate compounds available in the PhotoChemCAD database. The chemical structure of the top three candidates is shown.

The PhotoChemCAD database organizes each compound into a chemical class, which are color-coded in the above figure, which presents the top 50 candidates. An alternative method of using a $1/{\lambda }^2$ spectral distribution for the Cherenkov emissions produces similar results where the ranking for a few of the compounds is rearranged by one to two places. These rankings do not take into account biocompatibility or lifetime which are generally on the order of nanoseconds for these compounds. The system does not consider the emissions spectra or how it would interact with tissue optical properties or detector quantum efficiency, although these could be implemented using the given data. The absorption spectrum of the top-ranked compounds is shown in Fig. 9.

Fig. 9

The absorption spectra of compounds with the highest Cherenkov-excitation ranking.

4.1.

Cherenkov Lateral Resolution

Electron sources are generally used to provide surface dose due to the increased probability of electron scatter resulting in short penetration depths. Since electrons are charged particles, as they travel through tissue they can exhibit three types of interactive forces: soft collisions, hard collisions, or Coulomb–force interactions. Soft collisions are the most common and occur when the incident electron passes at a considerable distance to an atom and can result in Cherenkov emissions.²⁵ In this case, the electron loses very little energy and continues in an undisturbed trajectory. With a hard collision, the incident electron interacts directly with an atom’s electron which is often ejected, often generating a characteristic x-ray.²⁵ In Coulomb–force interactions, the incident electron interacts primarily with an atom’s nucleus and is elastically scattered; however, in a small percentage of cases, an inelastic interaction occurs and the electron transfers most energy to the atom, resulting in an x-ray photon emission, also known as a bremsstrahlung emission.²⁵

The variety of photon and electron interactions with matter, which often cascade, results in a spreading of the Cherenkov emissions. Developing a model of the spread function is important to improve spatial localization for the delivered dose or for Cherenkov-excited scanned images. While this work demonstrates how simulations can be developed for developing these models, there are improvements that need to be made to the simulation before a deconvolution kernel with clinical utility can be defined. A very similar investigation has been previously conducted by Brost et al. that determined the Cherenkov scatter function in a multilayer tissue model for a number of LINAC energies.^8,26

In general, for scanning images utilizing shaped beams, photon sources are required due to the delivery mechanisms of LINACs. If shaped beams are not required, either photon or electron sources could be used to for wide-field excitation.

4.2.

Limits of Depth Sensitivity and Detection

A series of simulations were developed to better understand the limits of detection for a luminescent inclusion at varying depths in tissue. These simulations compared the light fluence from an external optical source as well as Cherenkov-emissions generated within the multilayer tissue model. While the purely optical simulation for measuring fluence could be performed in a package such as Monte Carlo multilayer,²⁷ the physics-engine required for Cherenkov emissions as well as the ability to simulate fluorescence is missing.

While Cherenkov emissions are correlated with deposited dose, these simulations show how tissue optical properties will influence the observed emissions. It is difficult to measure the spectral properties of Cherenkov emission inside tissue, and so these simulations provide insight on how tissue acts as a long-pass wavelength filter, allowing mainly red and NIR to pass to the surface for detection, even though the signal generated inside the tissue is broadband. While an 18-MV beam generates $\sim 2.5\times$ more Cherenkov emissions than the 6-MV counterpart, since the maximum dose occurs at 3.5 cm much of these optical photons are absorbed before reaching the tissue surface, which is in agreement with previous studies.^23,28

Cherenkov-excited luminescence was also compared to purely optical luminescence in these example simulations. It has been reported previously red or NIR light from Cherenkov emissions are actually the predominant wavelength available for luminescence excitation.²³ While our simulation was able to demonstrate this, it also shows that the UV-blue contribution is as important for the given compound’s excitation [Fig. 6(a)]. While it is well known 630-nm light will have a much higher penetration depth than 430 nm excitation, the complexity of Cherenkov emissions within tissue complicates depth estimates. In the present example, the 6-MV and 630-nm sources had largely similar luminescence reaching the surface when the tumor inclusion was 1 mm below the surface, but when the inclusion depth was moved to 5 mm, the Cherenkov excitation resulted in a surface luminescence over $10\times$ that of the 630-nm excitation. Models such as the one provided in this work could be help provide insight on how multimodal luminescence imaging could be used for improved depth discrimination.

While electron sources are not commonly used for Cherenkov-excited luminescence imaging, their depth-dose profile aligns well with the optical mean free path in tissue, where the energy could be used to adjust the depth of Cherenkov emissions. Since Cherenkov photons are generated along the path of high energy electrons as they pass through tissue, localizing the origin of excited emissions with high depth-resolution is challenging. A combination of multimodal optical and high-energy electron or photon excitation could be used to increase resolution along the $z$ axis. If imaging is not the primary application of Cherenkov excitation, and instead applications such as x-ray or Cherenkov-excited photodynamic activation are desired, then high energy photons would provide the highest depth penetrance.

A system for computational ranking potential compounds to be used in Cherenkov-excited luminescence imaging was demonstrated. While similar datasets are available for scintillators,²⁹ neither data sources consider long-lived phosphoresce ($>10\mu \mathrm{s}$). If the current available data were expanded and standardized to report lifetime and scintillation yield, the currently demonstrated method could easily be expanded to identify additional means of contrast, such as those described in our previous work.³⁰ In addition, if this functionality could be expanded to include triplet quantum yields in addition to fluorescence quantum yields, this computational search could be expanded to identify potential Cherenkov-excited or x-ray-excited photosensitizers. While many of the compounds identified by this work would not be appropriate for the time-delayed phosphorescent imaging as those used for oxygen estimations,^4,5 the basis demonstrates a method to quickly identify potential compounds based on empirical data. From the given data, a number of coumarins appear to be suitable for detection by Cherenkov-excitation. When the quantum efficiency of the photocathode is considered,³¹ a blue-sensitive camera is ideally suited to detect emissions from compounds such as Auramine O, coumarins, and curcumin, whereas with a red-sensitive photocathode Nile Blue, Perylenes, and Crystal violet are more appropriate.