A scanning focus nuclear microscope with multi-pinhole collimation

The proposed SFNM imaging system consists of a focusing MPH collimator made of gold with a total of 42 round knife-edge pinholes, each having an opening angle of 10° (see figures 1(b), (c)). These 0.05 mm diameter pinholes focus on a 0.5 mm diameter central field of view (CFOV). The object is scanned through this focus to obtain data from various projection angles for each point in the object using a scanning focus method (Vastenhouw and Beekman 2007).

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The MPH collimator has a rectangular shape with a wall thickness of 30 mm and can be mounted on a U-SPECT/CT or a VECTor/CT imaging system (MILabs B.V., the Netherlands) (van der Have et al 2009, Goorden et al 2013). It projects on one of the system's large-area gamma detectors (NaI(Tl) crystal). The gamma detector has a 3.5 mm intrinsic spatial resolution with 10% full width at half-maximum (FWHM) energy resolution at 140 keV (^99mTc). The distances from the centre of the CFOV to the collimator's surface, to the pinhole's centre and to the detector's surface are 1.5 mm, 2 mm and 210 mm, respectively, which leads to a large pinhole magnification factor of 104.

For comparison with SFNM, we considered two SPH collimator designs (table 1), of which the CFOV size, collimator thickness and collimator-to-detector distance are the same as in SFNM (figure 1(a)). In the SPH1 design, we adjusted the pinhole diameter (0.35 mm) to match the sensitivity to that of the SFNM, whereas in the SPH2 design we set the pinhole diameter to the same value as that used in the SFNM (0.05 mm). The sensitivity was determined by Monte Carlo simulations (details in section 2.2) of a 0.3 mm thick disc-shaped uniform ^99mTc activity distribution with the diameter of the CFOV. The disc lies in the XY plane. The sensitivity was then calculated by taking the fraction of the number of detected photons over the total number of photon emissions.

For the SPH designs, we both show direct detector projection (projected images) and reconstructed images obtained with the same scanning focus method as described for the SFNM (synthetic images).

For the proposed SFNM system and SPH approach, simulation data were generated using the Monte Carlo Simulation package Geant4 Application for Tomographic Emission (GATE), version 8.0. The GATE application was run in a CentOS 6.6 computer cluster with 250 processors running in parallel. To simulate photon paths through the collimator and in the detector, physics processes were defined by the 'physics list builder' mechanism in GATE, which includes but is not limited to photoelectric effect, Compton scatter, Rayleigh scatter, bremsstrahlung, electron ionisation and positron annihilation. To simulate the detector geometry, a NaI scintillator was created in GATE using a $497.4\,\mathrm{mm}\times 410.6\,\mathrm{mm}\times 9.5\,\mathrm{mm}$ rectangular box, which was placed as shown in figure 1(c).

STL files of the proposed focused MPH collimator and the SPH collimators were prepared using computer-aided design software (OpenSCAD), with the required pinhole diameter and collimator material. We assumed a MPH aperture made of gold to limit the pinhole edge penetration of gamma radiation. GATE outputs the total deposited energy in the scintillator and the interaction time of each gamma photon, along with the energy-weighted average interaction location in the scintillator. Photon interaction locations were sampled on a pixel grid with pixels of size 1.072 mm × 1.072 mm, the same as the pixel size of the real detectors used in the U-SPECT/CT or VECTor/CT imaging system (MILabs B.V., the Netherlands). The photopeak window was set to a 20% width at 140 keV.

The Derenzo resolution phantom simulated in this study has six sectors containing rod diameters ranging from 0.02 mm to 0.07 mm (figure 2). In each sector, the distance between the centres of two adjacent rods is twice the rod diameter. The rod length is 0.3 mm. The rods were defined in GATE using analytical cylinders, meaning that there was no voxelisation effect.

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First, the phantom was simulated with SPH2 at one central bed position, assuming that it contained either 40 kBq of ¹²⁵I or ^99mTc and that it was scanned for 2 h to assess the effect of increasing photon energy with this SPH.

Then, the phantom was simulated, assuming that it contained ^99mTc at three activity levels (40 kBq, 8 kBq and 4 kBq in the whole phantom), and a 2 h acquisition was assumed. For the projected image with the SPH, the phantom was placed at the centre of CFOV and projections at a single position were acquired. For the synthetic images with both collimators, the Derenzo phantom was scanned at nine bed positions separated by a 0.25 mm step size in the XY plane.

A mouse ankle joint phantom was derived from a real CT image of a mouse ankle joint having a voxel size of 0.08 mm. The mouse ankle phantom contained a realistic activity concentration of 336 MBq ml⁻¹ of ^99mTc, which we inferred from experimental mouse data (Nguyen et al 2020b). The phantom had a volume of 3.76 mm × 2.48 mm × 3.00 mm. For the synthetic images, the phantom was simulated assuming a scan time of either 1 h or 4 h and 693 bed positions separated by a 0.125 mm step in the XY plane. The time step was equal for all bed positions. For the projected image with the SPH for the comparison in figure 6, the area viewed by the pinhole at the centre of the system (0.5 mm diameter) is smaller than the phantom size; therefore, the mouse ankle phantom was moved in the Z direction 15 mm away from the pinhole such that the whole mouse ankle could be observed through the pinhole. In this case, the pinhole magnification is 13.5 times.

The acquired simulated projection data at multiple object positions were used collectively in image reconstruction. For image reconstruction, a system matrix was generated for the SFNM collimator using an in-house developed ray-tracing code that takes into account pinhole edge penetration and the spatial resolution and depth of interaction in the detector, but excludes scatter (Goorden et al 2016). For this ray-tracing simulation, the position, orientation and linear attenuation coefficients of the collimator (4.26 ${{\rm{mm}}}^{-1}$) and detector (0.245 ${{\rm{mm}}}^{-1}$) relevant for 140 keV energy were provided as input. To generate a reasonable system matrix size for fast image reconstruction, only the gamma photon paths that have at least a 4% probability of passing through the collimator material were included. A lower cut-off will lead to a matrix with many more elements, and a longer computation time for the matrix and image reconstruction. We found that for 140 keV, the cut-off of 4% resulted in approximately 96% of the photon flux being modelled, and this cut-off was sufficiently small in this case. Decay correction was included to account for the change in the activity in the object during the scan.

Images were reconstructed using a similarity-regulated ordered-subset expectation-maximisation (SROSEM) algorithm (Vaissier et al 2016) with the maximum number of subsets set to 128. All images presented in this work were reconstructed with a voxel size of 0.02 mm. A voxel size of 0.01 mm did not improve the resolution further but dramatically increased computation time; therefore, it was not used. Gaussian filters of 0.04 and 0.14 mm FWHM were applied to the reconstructed images of the Derenzo phantom and mouse ankle, respectively. From these reconstructed images, synthetic planar images were generated by adding slices up to 0.3 mm and 3 mm for the Derenzo phantom and mouse ankle, respectively. The reconstruction iteration numbers were chosen to maximise the contrast-to-noise ratio (CNR; equations (1)–(2)) for the Derenzo images or to minimise the normalised root mean squared error (NRMSE) for the mouse ankle images.

Scatter correction was applied using the triple energy window method (Ogawa et al 1991) in a model-based approach (Bowsher et al 1992, King et al 1997). For this purpose, two side windows, each having a width equal to 25% of the width of the photopeak window, were set. The scatter estimate was then smoothed by a Gaussian filter having a standard deviation of five pixels and then added to the forward projection in each iteration during reconstruction.

For the SPH, the projection images shown in figures 4 and 6 were post-processed using Gaussian filters having FWHMs of 0.04 mm and 0.14 mm multiplied with a magnification factor of 104 and 13.5 for the Derenzo phantom and the mouse ankle joint phantom, respectively. The synthetic images with the SPH were obtained in the same way as with the SFNM. The obtained images were resampled with a 1.58 times smaller pixel size using bicubic interpolation and plotted with the pseudocolour ('pcolor') function in MATLAB to avoid a pixelation effect.

For the obtained resolution phantom image, CNR was calculated in the same way as in Walker et al (2014) by drawing regions of interest (ROIs) with red circles indicating the regions with activity and blue circles indicating the background regions (figure 2). ROIs had a diameter of 0.9 times the diameter of the rods. We defined the contrast (${C}_{s}$) and noise (${N}_{s}$) of rod sector $s$ as follows:

$$\begin{eqnarray}&&{C}_{s}=\displaystyle \frac{\overline{{I}_{s}}-\overline{{B}_{s}}}{\overline{{I}_{s}}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{N}_{s}=\displaystyle \frac{\sqrt{{\sigma }_{{I}_{s}}^{2}+{\sigma }_{{B}_{s}}^{2}}}{\overline{I{B}_{s}}},\end{eqnarray} \tag{ 2 }$$

where $\overline{{I}_{s}}$ and $\overline{{B}_{s}}$ are the mean intensity over the activity regions (${I}_{s}$) and background regions (${B}_{s}$) of sector $s,$ respectively. ${\sigma }_{{I}_{s}}$ and ${\sigma }_{{B}_{s}}$ are standard deviations over ${I}_{s}$ and ${B}_{s},$ respectively, and $\overline{I{B}_{s}}$ is the mean intensity over all ROIs of sector $s.$ Then the CNR of each rod sector was defined as ${C}_{s}/{N}_{s},$ and the average of the CNRs over sectors with 0.04, 0.05 and 0.06 mm diameter rods was taken as an image quality assessment (reported in figure 4). Sector 0.07 mm with only one rod and sectors 0.02 mm and 0.03 mm with non-discernible rods were excluded from this calculation.

Figure 3 demonstrates the image degradation due to pinhole edge penetration when increasing the photon energy from 30 keV to 140 keV. Figure 4 shows the synthetically generated planar images of the Derenzo resolution phantom obtained by summing slices of the reconstructed images across the whole phantom length of 0.3 mm, as well as the projected images only for the SPH. The results show a clear advantage of SFNM over using a SPH collimator at a matched sensitivity. The achieved image resolution is 0.04 mm with SFNM, whereas in both the SPH projected and synthetic images with matched sensitivity the rods are not discernible. When compared at equal physical pinhole diameters, the improvement in image resolution by applying SFNM is still significant. In this case, the SFNM images contain far less background and image noise than the SPH2 projected images, and visualise the rods better than the SPH2 synthetic images. This can also be seen on the profiles through different rod sectors (figure 5). The SFNM also gives the highest CNRs of the obtained Derenzo images among the presented methods.

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Figure 6 demonstrates the imaging capability of SFNM compared with the SPH cameras for the mouse ankle joint phantom. The synthetic image generated using SFNM clearly shows the anatomical structure of the mouse ankle and the best NRMSE among the presented methods.