2.1.

Experimental Measurements and Analysis

Chicken breast samples were imaged in an IVIS Spectrum small animal optical imaging system (Perkin Elmer), as has been described in Ref. 20. In the center of the imaging field, we placed a 0.5-mL Eppendorf vial containing either $1\mu \mathrm{Ci}$ of ${}^{99\mathrm{m}}\mathrm{Tc}$-methylene diphosphate or $84\mu \mathrm{Ci}$ adenosine 5’-triphosphate [$\gamma \text{-}{}^{32}\mathrm{P}$]. ${}^{32}\mathrm{P}$ is a $\beta$ emitter with endpoint energy of 1710.66 keV, sufficient to produce Cerenkov light in tissue, whereas ${}^{99\mathrm{m}}\mathrm{Tc}$ is a $\gamma$ emitter that is not expected to produce Cerenkov light.²⁰ A layer of black paper was added around the Eppendorf tube to block any light generated in the source. A slice of uniform chicken breast, 6-mm thick and 20-mm wide, was cut and placed $\sim 5\mathrm{mm}$ from the radiation source. Spectral data were captured by using 18 20-nm bandpass filters, ranging from 500 to 840 nm. Each spectral image was generated from a 300-s exposure, with a binning of 16, f/1, and field of view of 6.6 cm.

The luminescence image was analyzed in Living Image 4.5 (Perkin Elmer) with the following corrections applied: dark background subtraction, flat field correction, cosmic correction, and lens distortion correction. The cosmic correction algorithm removes any signal spikes due to particles directly interacting with the CCD. Spectral data were captured for four ROIs (regions of interest), two corresponding to the tissue (signal) and two corresponding to background regions. The ROI locations are shown in Fig. 1. Note that the entire field of view is not shown and that the source is located at the edge of the image. For only the ${}^{99\mathrm{m}}\mathrm{Tc}$ images, a smoothing of $5\times 5$ was applied.

Fig. 1

ROIs for the experimental and simulation data. (a) Merged white light photograph and luminescence image for ${}^{32}\mathrm{P}$, 500-nm filter. (b) The merged photograph and luminescence image for ${}^{99\mathrm{m}}\mathrm{Tc}$, for the 500-nm filter. (c) The geometry and ROIs as used in the simulation.

Two additional measurements were performed without radioactive sources. We placed a sample of chicken breast in the IVIS system and acquired the luminescence spectrum, acquiring each filter for 300 s with binning of 16, f/1, and field of view of 13.6 cm. One corner of the chicken sample displayed a higher signal value, so one ROI was placed over this area, another ROI was placed over a different region of the chicken breast, and a third ROI was placed over a background region. We also captured the fluorescence spectra from the chicken breast sample using an excitation filter of 430 nm and the full set of 18 emission filters in the IVIS. For the fluorescence measurement, we used automatic (variable) acquisition times, a binning of 8, f/2, and field of view of 13.6 cm.

2.2.

Geant4 Simulation

We constructed the simulation model using Geant4 version 10.02.p02.³¹ The Penelope low-energy physics model was used for electromagnetic processes and the Cerenkov and scintillation processes were both enabled. The G4RadioactiveDecay process was used with the default settings of enabling the atomic relaxation module and internal conversion module. The tissue volume was constructed as a triangular prism with a thickness of 6.0 mm and a hypotenuse of 35.4 mm. The NIST material G4_MUSCLE_SKELETAL_ICRP, default density of $1.04\mathrm{g}/{\mathrm{cm}}^3$, provided the elemental composition of the chicken breast tissue. The radioactive source was modeled as a cylinder with a radius of 3.0 mm and a height of 11.0 mm, filled with liquid water. The liquid was surrounded by a layer of plastic (polypropylene) 0.8-mm thick. The optical properties of the plastic and water were not defined so that no photons would be generated in those materials. The center of the radioactive sample was placed 5.75 mm from the edge of the tissue sample to approximate the experimental setup. Radioactive decays of either ${}^{32}\mathrm{P}$ or ${}^{99\mathrm{m}}\mathrm{Tc}$ (142.6832 keV excitation) were generated randomly in the water volume. Subsequent $\beta$ decays of the long-lived ${}^{99}\mathrm{Tc}$ ground-state were disabled.

The simulation results were written to two files. One file contained all energy deposits in the tissue material which were later processed to create dose maps. The second file recorded all photons that impacted a surface 0.1 mm above the top of the tissue. The photons’ momentum vector, creation process, and location were all recorded for later processing. No imaging system was explicitly modeled, instead an angular threshold (30 deg) was applied to exclude photons that would not possibly reach a camera, while maintaining high statistics. Each simulation represents the detected photons from 100,000,000 decays of ${}^{32}\mathrm{P}$ or 1,000,000,000 decays of ${}^{99\mathrm{m}}\mathrm{Tc}$.

2.3.

Validation

We validated the basic optical simulation and parameter conversion using two simple geometries and optical parameters, previously used by other techniques.^38–41 One model (hereafter referred to as model 1) used a 0.02-cm-thick slab with a width of 20 cm in each direction. The index of refraction of the slab was defined as 1.0, to match the index of the surrounding air. The absorption coefficient (${\mu }_a$) was set to $10.0{\mathrm{cm}}^{-1}$, the scattering coefficient (${\mu }_s$) was set to $90.0{\mathrm{cm}}^{-1}$, and the anisotropy ($g$) for the Henyey–Greenstein model was specified as $g=0.75$. Photons were incident normal to the surface and reflected photons were counted for 5 runs of 1,000,000 events each. A second model (model 2) utilized a quasi-infinite geometry, with slab dimensions of 20 cm on each side. The same values of ${\mu }_a$ and ${\mu }_s$ were used, but with $n=1.5$ and $g=0$.

2.4.

Optical Parameters of Chicken Breast

The optical properties of chicken breast were compared for different reported measurements. We identified four studies that measured ${\mu }_a$ and ${\mu }_s$ for chicken breast. Marquez et al.⁴² used oblique-incidence reflectometry for wavelengths between 400 and 800 nm and investigated the differences based on muscle fiber orientations. The work of Honda et al.⁴³ focused on the changes in optical properties after laser treatment, but provided an untreated baseline from 350 to 1000 nm using the integrating-sphere technique. Adams et al.⁴⁴ also used the integrating-sphere technique to investigate optical properties responding to thermal changes, over a range of 500 to 1000 nm. Sun and Wang⁴⁵ also used oblique-incidence reflectometry but only considered a wavelength of 650 nm. Because the Geant4 model requires the parameters to be defined over the entire optical spectrum, this measurement cannot be used in the simulation.

All models are shown in Fig. 2, including the different muscle fiber orientations. Note that while Sun and Wang reports two measurements, corresponding to two fiber orientations, the difference is negligible on the scale of the plot, so only one is shown. The absorption coefficient is significantly higher in the Ref. 43 measurement, but all spectral measurements of ${\mu }_a$ show similar shapes. There is relatively good agreement between most measurements for ${\mu }_s$, though Sun and Wang measure a significantly lower value.

Fig. 2

Different optical parameters for chicken breast as reported in the literature. The hatched regions are outside the filters used in the IVIS. (a) All models for ${\mu }_a$ and (b) a view which better distinguishes the majority of models but excludes Honda et al.

In order to define the parameters in Geant4, we must convert the absorption coefficients to lengths and specify the spectra in terms of photon energy. The absorption length ${\ell }_a$ was calculated as the inverse of the absorption coefficient $({\mu }_a)$

The standard Geant4 optical photon scattering process uses a double Henyey–Greenstein model.⁴⁶ The required parameters include the scattering length (defined as a function of energy) and single values for a forward scattering anisotropy constant ($g_f$), backward anisotropy constant ($g_b$), and a parameter $f$ (between 0 and 1) that defines the relative fraction of the forward to backward model. While this parameterization is different from the typical Henyey–Greenstein model,⁴⁷ it simplifies to the traditional model if $g_f=g$ and $f$ is set to 1.0. The published parameters are typically in terms of the reduced scattering coefficient ${\mu }_s^{\prime }$, which can be converted to the scattering length (${\ell }_s$) by accounting for the anisotropy $g$

Geant4 will kill a photon, or generate errors, if a photon enters a region in which the optical properties are not defined for its energy. In order to ensure that a consistent wavelength range was used (490 to 850 nm), any optical parameter data outside of the wavelength range was truncated. Data for the end points were generated by duplicating the values at the closest defined point. Geant4 used a spline model to generate values at intermediate points, except for the absorption length, where a linear interpolation was used to avoid unphysical negative values.

The index of refraction for chicken breast was reported in Sun and Wang as $1.397\pm 0.002$ for the parallel orientation and $1.407\pm 0.003$ for the vertical orientation. Marquez et al. reported an index of refraction of 1.37. The report of Sun and Wang was the only one to include a measured value for Mie anisotropy $g=0.99$. Adams et al. used $g=0.97$ and $n=1.4$, though they state these are based on the measurements of Sun and Wang. In the simulation, we used $n=1.37$ and $g=0.99$.

2.5.

Analysis

We typically present experimental measurements of emission spectra as fractional spectral components. The average radiance from the signal ROI (either near or far) was corrected by subtracting the average of the two background ROIs. The individual spectral values were normalized by dividing the sum of all values. Error bars are not shown on the measurements from ${}^{32}\mathrm{P}$ due to the standard deviation being dominated by the variation in intensity over the near and far ROIs, as can be seen in Fig. 1. In order to compare the simulated spectra with the experimentally measured spectra, each simulated data point was centered on the IVIS filter value and included photons within $\pm 10\mathrm{nm}$. The spectra were typically normalized to have an integral of 1. A second approach was to compare the ratio of the far to the near ROI for each wavelength. While the resulting shape is very unlike the actual detected spectrum, this cancels any individual filter miscalibrations. We defined the simulation ROIs to have similar sizes and placements to the ${}^{32}\mathrm{P}$ experimental ROIs so that the changes in emission spectrum and intensity would be comparable.

We generated line profiles from the simulation and experimental data to quantify the spatial distribution of light, independent of spectrum. Experimental line profiles were calculated from an open-filter image in the Living Image software, using a line width of 2 pixels. Five lines were drawn with different orientations, each passing somewhere through the region of apparent maximum. The peak values of each line were aligned, corresponding to the edge, and then we calculated the mean and standard deviation for each position. We generated the line profiles for the simulation data by considering photons detected $\pm 1\text{pixel}$ from the axis perpendicular to the edge and passing through the center of the source. A line profile of the simulated dose was similarly constructed by considering all energy deposits within the same $\pm 1\text{pixel}$ region for all heights in the tissue.

2.6.

Generation of Radioluminescence in Geant4

The radioluminescence process was modeled using the Geant4 scintillation method, which has been extensively used for modeling scintillating detectors.^48,49 In brief, scintillation light is generated in Geant4 based on the energy lost by a particle in a single step in a given material, where the material has a characteristic light yield $Y$ in terms of photons/MeV. The energy of the photons is generated based upon a user-entered spectrum, with an initial photon position that is uniform along the particle’s path and with an isotropic direction. The number of photons varies based upon a Poisson distribution, with an optional broadening parameter needed for doped scintillator materials.⁴⁶

The scintillation model requires an emission spectrum and yield, which have not been studied previously for chicken breast. Initially, we ran the simulation with a luminescence emission that is uniform in wavelength. This was used to observe the impact of the absorption and scattering parameters on the detected spectrum. Our IVIS measurements for ${}^{99\mathrm{m}}\mathrm{Tc}$ in chicken breast were used to estimate the radioluminescence spectrum. The average background signal for each wavelength was subtracted from the value measured in the near ROI to construct the signal spectrum (${\mathcal{L}}_{\mathrm{sig}}$). The simulated measurement in the near ROI (${\mathcal{L}}_{\text{flat},\text{out}}$) and signal spectra were both normalized to have a maximum value of one. A new luminescence spectrum ${\mathcal{L}}_{\text{in}}(\lambda )$, used in further simulations, was calculated by

3.1.

Validation of Geant4 Optical Model

Table 1 compares the simulation to past results for the two tested models. The measured reflectance in Geant4 is in good agreement, demonstrating the validity of the Geant4 optics models and our conversion process.

Table 1

Validation of Geant4 optical model.

3.2.

Comparison of Chicken Breast Tissue Optical Parameters to Experimental Data

Figure 3 shows the impact of the different tissue optical parameter models on the simulation results, when only a Cerenkov emission from ${}^{32}\mathrm{P}$ is considered. In the near ROI, shown in (a), the Cerenkov spectrum from each of the models is in relatively good agreement with the experimentally measured ${}^{32}\mathrm{P}$ data. In the far ROI, (b), each model shows a relatively similar shape for the light emitted, but the relatively intensity varies. All models predict less light at the far ROI than is measured, though the model of Adams et al. results in values most similar to the experimental measurement.

Fig. 3

(a) Spectral comparison between ${}^{32}\mathrm{P}$ experimental results in the near ROI and the Cerenkov spectrum from different optical parameter models in the simulation. (b) The ratio of photons measured in the far ROI, compared to the near ROI, for the experimental measurement and the different optical models.

From Fig. 3(b), it appears that all models underestimate the light measured at farther distances. In conjunction with Fig. 2, this could be used to infer that ${\mu }_a$ for our sample was lower than these models predicted. In particular, Adams et al. note that their spectrophotometer and integrating sphere system is unable to provide accurate measurements of ${\mu }_a$ below $0.05{\mathrm{cm}}^{-1}$. Another possibility is that this difference is due to the curvature of the tissue sample, which was not included in the simulation.

While no model correctly predicts the absolute ratio of light in the far to near ROIs, we can focus on the wavelength dependence of the ratio. The models have a similar trend, notably that short wavelengths are more attenuated at the far ROI than longer wavelengths. This trend is reflected in the experimental data, but the experimental and simulated results do not reflect the same trend for the longest wavelengths. The difference in shape in the NIR region in the far ROI will be addressed through introducing the radioluminescence model. For the subsequent simulations, we have used the optical parameters of Adams et al.

We ran additional simulations (results not shown) with variations on the model of Adams et al. We tested whether small changes in the anisotropy or index of refraction had a significant effect on the spectrum or relative light seen between near and far ROIs. No significant difference was seen between $g=0.99$ and $g=0.90$. Similarly, another simulation showed no significant difference for $n=1.37$ versus $n=1.4$.

3.3.

Luminescence Spectrum from ^99mTc

Figure 4(a) shows the experimentally measured spectra from ${}^{99\mathrm{m}}\mathrm{Tc}$ in tissue and from the chicken breast with no radioactive sources present. The signal from ${}^{99\mathrm{m}}\mathrm{Tc}$ in chicken breast is low, but consistently above the diffuse background in the presence of ${}^{99\mathrm{m}}\mathrm{Tc}$ and above the background measured in chicken without a source present. The background signal (in the presence of ${}^{99\mathrm{m}}\mathrm{Tc}$) is likely due to scattered light in air, demonstrating that blue light is more strongly scattered than NIR light. It is unlikely to be due to radiation interacting in air, given that one background ROI is much closer to the source [as shown in Fig. 1(b)] but the spectral signals are statistically equivalent. Compared to the luminescence measurement without ${}^{99\mathrm{m}}\mathrm{Tc}$, the ${}^{99\mathrm{m}}\mathrm{Tc}$-radiated chicken has a noticeable increase at both edges of the spectrum.

Fig. 4

Spectral profiles from ${}^{99\mathrm{m}}\mathrm{Tc}$ radioluminescence. (a) The experimentally measured luminescence spectra with and without the presence of ${}^{99\mathrm{m}}\mathrm{Tc}$. Standard deviations on each measurement are $50\mathrm{p}/\mathrm{s}/{\mathrm{cm}}^2/\mathrm{sr}$. (b) The simulated spectrum that would be measured from a flat luminescence profile, and the calculated emission spectrum predicted to match the experimental spectrum (near ROI) shown in part (a).

The $\gamma$ decay of ${}^{99\mathrm{m}}\mathrm{Tc}$ is not expected to produce any Cerenkov emission, so the signal measured in Fig. 4(a) must be due to a non-Cerenkov radioluminescence process. While ${}^{99\mathrm{m}}\mathrm{Tc}$ has rare $\beta$ decays, the decay probability is ${10}^{-5}$ for an endpoint energy of 436.3 keV and $2.6\times {10}^{-5}$ for an endpoint energy of 346.7 keV,⁵⁰ rendering it unable to produce significant Cerenkov light. In 1,000,000,000 decays of ${}^{99\mathrm{m}}\mathrm{Tc}$, no Cerenkov photons were produced in the simulation.

The dashed line in Fig. 4(b) shows the detected spectrum in the simulation, for a flat radioluminescence emission spectrum. The deviations largely correlate with the wavelength dependencies in the tissue optical parameters. The solid line shows the calculated emission spectrum, where a significant source of the fluctuations are statistical fluctuations in the experimental data.

Figure 5 shows the spectrum of the radioluminescence process from ${}^{99\mathrm{m}}\mathrm{Tc}$ after the near ROI has been used to estimate the needed emission spectrum. Because the near ROI was explicitly used to generate the radioluminescence emission, the agreement between experiment and simulation is not surprising. However, the far ROI provides a test of the optical parameters as the photons propagate through a greater distance of tissue.

Fig. 5

The experimentally measured and simulation spectra from ${}^{99\mathrm{m}}\mathrm{Tc}$ using the optical properties of Adams et al. (a) The near ROI and (b) the far ROI. Error bars represent $\pm 1\sigma$, propagated from the standard deviation in the measured radiance.

3.4.

Fluorescence Spectrum of Chicken Breast

Our measured emission from chicken breast from the 430-nm excitation is shown in Fig. 6. Multiple features are visible, with peaks around 520, 600, and 640 nm. This is largely in agreement with the turkey spectrum in Ref. 51, though their measurement used an excitation of 382 nm. Note that there is no significant emission in the NIR, which is expected due to the low autofluorescence from many tissue chromophores and other biological molecules in these wavelengths.⁵²

Fig. 6

Fluorescence of chicken breast with an excitation wavelength of 430 nm. The background corresponds to a region off the chicken breast while the two ROIs show the variation in one piece of tissue. Error bars are the standard deviation of the signal over the ROI.

3.5.

Spectral and Spatial Profiles for ³²P with Radioluminescence

Figure 7 shows the experimental and simulation results for the spectral measurements in the near and far ROIs for decays of ${}^{32}\mathrm{P}$. The simulation model includes both Cerenkov light and the scintillation-based radioluminescence model. The scintillation yield parameter controls how many scintillation photons are generated, while the number of Cerenkov photons remains fixed. Hence, by varying the scintillation yield, we see a difference in the total simulated photon spectrum due to the differences in shapes of the two spectra. A yield of $0\text{photons}/\mathrm{MeV}$ corresponds to the detected spectrum from Cerenkov alone. While the $10\text{photons}/\mathrm{MeV}$ yield is a better match to the experimental data in the near ROI, it does not provide sufficient light in the NIR region of the far ROI. The $30\text{photons}/\mathrm{MeV}$ values overestimate the NIR contribution in the near ROI but are a better match in the far ROI.

Fig. 7

Comparison of the measured spectrum from ${}^{32}\mathrm{P}$ and the simulation results, for the near (a) ROI and far (b) ROI. The simulation results differ by the scintillation yield parameter used.

Finally, Fig. 8 shows line profiles of light for an open filter image of ${}^{32}\mathrm{P}$. The simulation results show that the luminescence light falls off faster than the corresponding Cerenkov light, as shown in (a). The lateral plot shows that the detected light does not provide an accurate measure of the dose in the tissue, but it is important to remember that the dose is due to an external radiation source. Both the scintillation and Cerenkov light curves reflect a slower fall-off than the dose curve. The disagreement between simulated and experimental light measurements is likely due to the curvature of the chicken breast sample that is not reflected in the simulation geometry. Figure 8(b) compares the changes in overall shape (the curves are normalized to have the same area) due to different yield values for the scintillation response. The changes are very small, indicating that the lateral light distribution is not an effective way to constrain the presence of a non-Cerenkov luminescence component.

Fig. 8

Light intensity (open filter) as a function of position from the edge. Error bars represent $\pm \sigma$ from five similarly placed line profiles. (a) Comparison between different light production processes, dose, and experimental data. The curves are normalized to have the same maximum values. (b) The change in lateral profile due to varying the scintillation yield parameter, where the integral of each curve has been normalized to 1.