###
^{197}Hg and ^{197m}Hg

Mercury-197 exists in two energy states [10]: a longer-lived ground state (^{197}Hg, half-life T_{1/2} = 64.1 h) and a shorter-lived excited state (^{197m}Hg, T_{1/2} = 23.8 h) separated by an energy difference of 299 keV. ^{197}Hg predominantly decays to stable ^{197}Au via electron capture, while ^{197m}Hg decays either to ^{197}Hg or ^{197}Au with respective branching ratios of 91 and 9%.

The ^{197(m)}Hg emission spectrum comprises a multitude of X-ray, conversion, and auger electron, as well as a few gamma emissions [10]. Dominant photon emissions are observed at energies of 70–80, 134, and 279 keV. The two higher energy contributions are exclusively associated with gamma emissions from ^{197m}Hg, while X-ray and gamma emissions from both isomers populate the low-energy domain. Given the difference in half-lives, one can thus expect the higher energy emissions to disappear over time. Figure 1 comprises the decay scheme and the most relevant emissions from ^{197m}Hg and ^{197}Hg.

Mercury-197 can be produced with a high specific activity (≈ 500 GBq/μmol) via (p,n) reactions on ^{197}Au [7], a reaction which creates both isomers in roughly equal proportions. The two samples used for this study were produced with 10 MeV cyclotron protons and measured on the order of 10 MBq in activity of both isomers together.

High-resolution spectroscopy was performed to determine sample purity and to exclude the presence of other nuclides from cyclotron target like ^{194}Au, ^{196}Au, or ^{198}Au. In particular, the presence of radioactive gold isotopes was found to be five orders of magnitude lower in activity than that of ^{197(m)}Hg. From gamma spectroscopy, a transferable activity ratio *R*_{
a
} of the two isomers (*R*_{
a
} = *A*(^{197}Hg)/*A*(^{197m}Hg)) was determined which can be evolved to different measurement times using the half-lives above.

### Camera model

The GATE (version 7.0) simulation toolkit [11] was used to model the BrightView SPECT system (Philips Healthcare, Best, the Netherlands). It utilizes two camera heads, each equipped with a 9.5-mm-thick NaI(Tl) scintillator measuring 40.6 cm axially by 54 cm trans-axially and instrumented with a 59-element PMT array. Camera heads were modeled as a succession of cuboidal layers, representing from the interior outwards: the collimator, an aluminum cover, the NaI crystal, an optical coupling, and a backscatter compartment (BSC), all encased in lead shielding. The BSC (thickness 150 mm, density 1.05 g/cm^{3}) simplifies the rather complicated geometry of the PMTs and associated readout electronics into a homogeneous volume whose material composition was taken from Rault et al. [12], who compare such a BSC with a more detailed geometric model with encouraging agreement. It is required for an accurate representation of photons which were scattered into the scintillator from material behind it, which is of particular importance in studies of ^{197(m)}Hg since maximally backscattered 279 keV gammas will be energetically indistinguishable from the direct 134 keV gamma signal.

Collimators were implemented as lead cuboids of the appropriate thickness, and collimator holes were introduced by placing hexagonal openings at intervals which result in the correct septal thickness as specified by the vendor [13]. The length, diameter of the circumscribed circle, and septal thickness of the LEHR collimator were 27.0, 1.22, and 0.152 mm, respectively. Corresponding parameters for the HEGP were 58.4, 3.81, and 1.730 mm.

Sources were modeled as volumes containing uniformly distributed mono-energetic point sources. Four energies were considered and simulated separately: 70, 77, 134, and 279 keV. Simulation results were then weighted according to the intensity per disintegration for each of the two isomers and the activity ratio at the time when measurements for comparison were taken. Simulated datasets could thus be matched to measurements taken at various times without the need for further simulation.

### Phantom measurements

Two measurement geometries were investigated: a planar and a tomographic setup. The former utilized a planar source imaged through a Pb-bar phantom (Von Gahlen, Zevenaar, the Netherlands) positioned directly on top of the collimator. The bar phantom comprises four quadrants of different modulation periods: 4, 6, 8, and 10 mm. The source was assembled by filling a 20-ml solution of [^{197(m)}Hg]HgCl_{2} in hydrochloric acid into a cell-culture flask measuring approx. 8 cm by 12 cm (Greiner Bio-One, Kremsmünster, Austria), where it formed a 4-mm layer when laying flat. Figure 2a,c illustrates the planar setup and the simulated geometry. Planar acquisitions were then recorded with a square matrix of 1024^{2} pixels measuring 0.314 mm (zoom factor 1.85). Acquisition durations and activity ratios were 151 min and 5.92, respectively, for the LEHR collimator and 165 min and 10.6 for the HEGP model.

The second arrangement uses a polymethyl-methacrylate (PMMA) slab resembling an abdominal section measuring roughly 30 cm by 20 cm by 8 cm (Fig. 2b,d). It contains three hollow cylindrical receptacles, which were loaded with source containers of varying diameter: an 11-ml vial (V11, inner diameter = 19 mm), a 25-ml vial (V25, diameter = 27 mm), and a thin syringe (SYR, diameter = 5 mm). These were filled with various activity concentrations of a sample of activity ratio *R*_{
a
} = 3.7. SPECT acquisitions were then performed with both heads facing one another, equipped with the LEHR collimator and rotating through 180° in 2° intervals held for 5 min each. The acquisition matrix consisted of 128^{2} pixels measuring 3.195 mm (zoom factor 1.46). Tomographic reconstruction was performed using the Astonish algorithm [14] supplied by the vendor which is an extension of OSEM incorporating corrections for collimator resolution at varying head radii. In order to reconstruct simulated and measured data in a uniform fashion, a dummy SPECT dataset was recorded with parameters matching those of the simulation. Simulation results were then embedded into this dataset, uploaded into the vendor-supplied workstation, and reconstructed using the same algorithm. Reconstruction parameters were two subsets and eight iterations in either scenario; scatter and attenuation correction was disabled because ^{197(m)}Hg is not listed in the nuclide database.

In order to validate the camera model, especially the BSC, it was necessary to record energy spectra. There was no direct way of obtaining them, but the camera’s acquisition terminal presents a crude spectrum display, a screen shot of which can be analyzed to obtain spectral data. This procedure is limited by the display resolution, which only allowed for a sampling of the spectra with a resolution of 1.05 keV on the energy axis and 45.5 on the count axis. Three separate energy windows were considered for evaluation, with centers and widths of 70 keV (30%), 135 keV (20%), and 280 keV (20%).

### Finite resolution modeling

Two components of system behavior could not be physically simulated by GATE, namely the energy and intrinsic spatial resolution. Both parameters can be considered by digitizer modules in the simulation to model the real behavior event by event. To accelerate the simulations, we considered energy and intrinsic spatial resolution afterwards by convolving the exact energy and position with related blurring functions. The energy blurring determined by measurements of the energy spectra of ^{197(m)}Hg and ^{131}I samples. The position and width of two dominant photon emissions from each nuclide were fitted using a model comprised of a Gaussian photo-peak on top of a linear background. These results yielded an energy calibration, as well as an energy-dependent resolution function. The energy resolution model was applied to simulation results in two different ways depending on the observable of interest. When examining energy spectra, the simulated spectra were convolved with Gaussian distributions of the appropriate width for the given energy. For investigations of imaging properties, on the other hand, the energies of detected photons and the camera’s ability to resolve them only have an impact on whether an event is registered in a particular energy window or not. The probability of such acceptance was computed as the overlap of the energy window and a cumulative distribution function taking its parameters from the energy resolution model. The event was then weighted accordingly. The intrinsic spatial resolution achieved at relevant ^{197(m)}Hg energies was investigated in the planar setup with its modulation patterns of different spatial frequency. Ultimately, an estimate of the line spread function (LSF) was obtained and later used to convolve the simulated images to incorporate the effects of a finite intrinsic spatial resolution. The modulation *M*(*ν*) of a periodic signal at frequency *ν* can be computed as the asymmetry in its maximal and minimal amplitude *M* = (*A*_{max} − *A*_{min})/(*A*_{max} + *A*_{min}). Evaluation of the ratio of image (*M*_{
i
}) to object modulations (*M*_{
o
}) yields the modulation transfer function (*MTF*), which is the LSF’s counterpart in the spatial frequency domain. Its total value can be decomposed into intrinsic and collimator parts as MTF_{sys}(*υ*) = MTF_{intr}(*υ*) × MTF_{coll}(*υ*) [15]. Exploiting this relation and recognizing that the measured MTF includes both components, while the simulation only includes the collimator part, one finds: MTF_{intr}(*υ*) = MTF_{sys}(*υ*)/MTF_{coll}(*υ*) = MTF_{data}(*υ*)/MTF_{sim}(*υ*), where MTF_{data} and MTF_{sim} are the measured and simulated MTF, respectively. Inserting the definition of modulation transfer (MTF(*υ*) = *M*_{
i
}(*υ*)/*M*_{
o
}(*υ*)) and assuming that object modulations are equivalent in the simulated and measured cases, one finally obtains

$$ {\mathrm{MTF}}_{\mathrm{intr}}\left(\upsilon \right)={M}_{i,\mathrm{data}}\left(\upsilon \right)/{M}_{i,\mathrm{sim}}\left(\upsilon \right) $$

(1)

Thus, by determining the image modulation in both measurement and simulation at the four spatial frequencies, the intrinsic MTF can be sampled. Ultimately, a width parameter is sought which can be used in a Gaussian blurring of the simulated images. Assuming the intrinsic spatial resolution to be isotropic, a Gaussian fit to the intrinsic LSF would provide just such a parameter. Hence, a Gaussian approximation of MTF_{intr}(*υ*) with width parameter *ω* is found, which can be Fourier transformed into an intrinsic LSF of width *σ*. The two width parameters are related by *σ* = 1/(2*πω*).

The whole sequence of creating simulation results is illustrated in Fig. 3.