PET iterative reconstruction incorporating an efficient positron range correction method

TL;DR: A method to correct for the positron range effect in iterative image reconstruction by including tissue-specific kernels in the forward projection operation was examined, resulting in sharper active region boundary definition, albeit with noise enhancement, and in the recovery of the true activity mean value of the hot regions.

Abstract: Positron range is one of the main physical effects limiting the spatial resolution of positron emission tomography (PET) images. If positrons travel inside a magnetic field, for instance inside a nuclear magnetic resonance (MR) tomograph, the mean range will be smaller but still significant. In this investigation we examined a method to correct for the positron range effect in iterative image reconstruction by including tissue-specific kernels in the forward projection operation. The correction method was implemented within STIR library (Software for Tomographic Image Reconstruction). In order to obtain the positron annihilation distribution of various radioactive isotopes in water and lung tissue, simulations were performed with the Monte Carlo package GATE [Jan et al. 2004 [1]] simulating different magnetic field intensities (0 T, 3 T, 9.5 T and 11 T) along the axial scanner direction. The positron range kernels were obtained for (68)Ga in water and lung tissue for 0 T and 3 T magnetic field voxellizing the annihilation coordinates into a three-dimensional matrix. The proposed method was evaluated using simulations of material-variant and material-invariant positron range corrections for the HYPERImage preclinical PET-MR scanner. The use of the correction resulted in sharper active region boundary definition, albeit with noise enhancement, and in the recovery of the true activity mean value of the hot regions. Moreover, in the case where a magnetic field is present, the correction accounts for the non-isotropy of the positron range effect, resulting in the recovery of resolution along the axial plane.

Summary

1. Introduction

• After its emission, the positron travels a finite distance interacting with the surrounding media.
• The length of its path depends on the energy of the positron, that has a characteristic emission spectrum dependent on the radiotracer.
• The photon-producing event therefore occurs outside the radioactive nucleus and the actual position of the radiotracer is different from the annihilation position.
• Simultaneous hybrid imaging using nuclear Magnetic Resonance tomography and Positron Emission Tomography (PET-MR) is expected to substantially improve the PET image resolution in the plane perpendicular to the static magnetic field of the scanner, due to the confined positron trajectory and particularly when inside a very strong magnetic field [2, 3, 4].
• This difference creates nonuniform resolution with an impact on the reconstructed radiotracer distribution.

1.2. Aim

• In this work the authors implement a method to take into account the positron range effect in iterative image reconstruction following the efficient approach proposed by Cal-Gonzalez [9] and Kraus [10].
• The presented correction method is suitable for every kind of scanner, although its practical utility would be more relevant for pre-clinical systems or organ-specific systems, given their highest spatial resolution.
• The implementation is compatible with and without the presence of a magnetic field and it is validated for material-variant and material-invariant positron range corrections [11].
• The correction method is implemented within STIR (Software for Tomographic Image Reconstruction, http://stir.sourceforge.net) that is one of the most common libraries for PET image reconstruction, such that it becomes available to several other investigators.

2.1. GATE simulations

• GATE simulations were performed to obtain the positron range annihilation distribution in water and lung tissue.
• The simulations were performed without and with a static and homogeneous magnetic field set along the PET scanner model’s axial direction for three different field strengths: 3 T, 9.5 T and 11 T. The Geant4 low energy package [12] was used for electromagnetic processes simulation.
• Approximately 105 annihilation events were simulated per configuration and the annihilation coordinates were obtained from the Geant4 output [13, 14].
• The positron end point coordinates were stored and used to create the blurring kernels, as described in the following paragraphs.

2.2. Correction method

• The version of STIR in which their method has been implemented is the 3.0.
• Changes have been made to the following codes: OSMAPOSLReconstruction.h: where a pointer to the so-called pre update filter is added; OSMAPOSLReconstruction.cxx: where a filtering of the current image es- timate is performed with the uploaded kernel inside the update estimate method, when a kernel is provided.
• The kernel is defined inside the parameter file that has to be given to the OSMAPOSL executable, that is an implementation of the OSEM algorithm (Ordered Subset Expectation Maximization [15]) and the type of filtering has to be set to Nonseparable Convolution Using Real DFT Image Filter.

2.3. Blurring kernels

• The blurring kernel ρ is a three dimensional matrix whose elements have values according to the number of events within the corresponding volume normalized by the total number of events.
• To obtain the kernels the annihilation coordinates were voxellized into a 3D matrix with element size equal to the voxel size of the reconstructed image and then normalized to sum up to 1.
• The 68Ga can be considered representative here due to its average energy emission properties, see Table 1.
• Two-dimensional planes of the lung tissue kernel are illustrated in Figure 1.

2.4.1. Phantoms

• The proposed method was evaluated using simulated data generated using STIR software [16] of acquisitions of the HYPERImage preclinical PET/MR scanner (diameter: 20.8 cm, length: 3.1 cm) [17].
• Simulations were done with and without additional Poisson noise.
• The reconstructed images of the water phantom are shown in Figure 4.
• The material-variant correction was applied on a phantom composed of water and lung tissue regions (activity contrast value respectively equal to 1 and 0.5).
• The effect of which has been evaluated with the material-invariant correction, was added to the ideal projection data.the authors.

3.1. GATE simulations

• Figure 2 shows one-dimensional histograms illustrating the number of positron annihilation events with respect to the distance from the origin, where the radioactive decay occurs.
• They show the effect of different magnetic field strengths on the annihilation coordinates x,y,z and on the distribution of the range for 68Ga.
• Figure 3 shows the mean positron range of the positron emitters as a function of the magnetic field in all simulated media.

3.2. Impact of noise and material-invariant correction for homogeneous phan-

• The images resulted from the material-invariant kernel reconstruction with the water phantom are shown in Figure 4.
• It can be seen that when the correction is applied there is improved recovery of the original radioisotope activity.
• Figure 5 shows the profiles for the water phantom with simulated Poisson noise and for the lung tissue phantom without simulated Poisson noise.
• The over-shoots noticeable in the line-profiles of the “true” data are caused by the PSF reconstruction (by modeling the positron range effect as a kernel the authors are performing resolution modeling, correcting for the contribution of the positron range to the overall degradation of the image), which is known to produce Gibbs artifacts at sharp intensity transitions inside the object.
• The related coefficient of variation, defined as CV = σ/ µ, which measures the extent of variability of the values in relation to the mean (i.e. the standard deviation of the selected region of interest over its mean) was also evaluated.

3.3. Material-invariant versus material-variant correction for multi-material phan-

• Line profiles were traced through the hot spot in the reconstructed images (as previously described) and are illustrated in Figure 6.
• They highlight that in both instances (displayed in the plot as “invar corr” and “var corr”) the use of the positron range correction yields sharper boundary definition, although resulting in edge artifacts.
• The mean, standard deviation and CV relative to the spherical hot spot are listed in Table 4.

4. Discussion

• In the absence of magnetic field the positron interactions result in random direction changes of its path, whereas when a magnetic field is applied the available direction change is reduced.
• This is in agreement with what has been reported in [3], where it is shown that the degree of reduction of the path traveled by the positron is proportional to the positron range of the isotope and to the magnetic field strength up to around 7T, where the extent of the reduction saturates.
• Moreover, when the material-variant correction is applied, the recovered radioactivity mean value increases considerably, as it can be observed by the values in Table 4, e.g. in the presence of magnetic field it ranges from the 55% in the case of the material-invariant correction to 92%.
• They suggest to choose a (maybe even inconsistent) projector/backprojector pair, suited for rapid computation, supported by further regularization methods to guide or stop the iteration process.

5. Conclusions

• The authors implemented a technique that accounts for the positron range effect in iterative reconstruction in STIR library.
• The method is independent of the existence of a magnetic field once the blurring kernels have been chosen for the correct combination of isotope, material and magnetic field strength.
• The evaluation of the proposed correction method was performed on simulated phantoms, in which a filtering process with the calculated kernels was used to emulate the positron range blurring.
• When a 3 T magnetic field is present, the application of the positron range correction can successfully correct for the non-isotropic resolution along the axial plane.
• With regard to the use of a material-variant kernel, the method performance in correspondence to the edges needs further investigation.

Figures

Figure 2: Histograms of the positron range and of the annihilation coordinates for 68Ga in water for different magnetic field strengths[14].

Table 2: Mean and CV relative to the small hot spot volume in the case of the water homogeneous phantom.

Table 3: Mean and CV relative to the small hot spot volume in the case of the lung tissue homogeneous phantom.

Table 1: Positron mean ranges (mm) for 18F (mean positron energy 250 keV ), 68Ga (mean positron energy 783 keV) and 82Rb (mean positron energy 1475 keV).

Figure 5: Line profiles: blue is the true phantom, black and red are relative to the blurred non-corrected and corrected phantom respectively. (a) and (b): big spot in water phantom with simulated noise. (c) and (d): small spot in the lung tissue phantom without simulated noise.

Figure 4: Transverse (on the left) and sagittal plane (on the right) of the water phantom with Poisson noise. (a) and (b): original phantom. (c) and (e): 0T, no correction. (d) and (f): 0T with correction. (g) and (i): 3 T, no correction. (h),(j): 3 T with correction.

Figure 1: 2D planes of the kernels relative to 68Ga in lung tissue.

Figure 3: Mean positron range versus magnetic field, for all simulated positron emitters, in water and lung tissue phantoms [14].

Table 4: Mean and CV values relative to the hot spot inside the lung region in the water and lung tissue phantom.

Figure 6: Line profiles through the hot spot inside the lung region that is surrounded by water (multi-material phantom). Top row is for 0 T and bottom row for 3 T. Blue line (true): simulated phantom. Black line (no corr): non corrected blurred phantom. Red line (invar corr): material-invariant correction. Green line (var corr): material-variant correction.

Frequently asked questions

Q1. What have the authors contributed in "Pet iterative reconstruction incorporating an efficient positron range correction method" ?

In this investigation the authors examined a method to correct for the positron range effect in iterative image reconstruction by including tissue-specific kernels in the forward projection operation. The use of the correction resulted in sharper active region boundary definition, albeit with noise enhancement, and in the recovery of the ∗Corresponding author Email address: ottavia. 

Q2. What are the future works in "Pet iterative reconstruction incorporating an efficient positron range correction method" ?

In the future the authors plan to extend this method to take into account the positron range behavior in correspondence to tissue borders and to incorporate the new developments in STIR library.