Time efficient scatter correction in Time-Of-Flight PET image reconstruction

INTRODUCTION
As is well known, quantitative combined PET/MR imaging depends on accurate MR-based attenuation correction (MRAC). While a mostly satisfactory state of affairs has been reached today, problems persist regarding segmentation errors including unsatisfactory bone identification and residual systematic differences in comparison to PET/CT. Alternative or complementary strategies for attenuation correction (AC), therefore, are of considerable relevance. In this context, Maximum Likelihood reconstruction of Attenuation and Activity (MLAA) is one of the most promising approaches but, as A. Rezaei et al. have shown [1], Time-Of-Flight (TOF) image reconstruction is then required to eliminate possible ”crosstalks” between the estimated activity and attenuation distribution. We are aiming at implementation of MLAA for the Philips Ingenuity-TF PET/MR scanner as part of our previously developed Tube of response High resolution OSEM Reconstruction (THOR), see ref [2]. As a prerequisite we are currently modifying THOR to make full use of the available TOF information. The most critical point in this context is accurate and computational efficient TOF Scatter Correction (TOF-SC). Here, we report on our approach to solving this issue.

METHODS
One possible implementation of TOF-SC uses a straight forward extension of Watson’s well-known Single Scatter Simulation (SSS) algorithm [3] but this approach results in about an order of magnitude increase of computational burden compared to standard SSS. Alternatively, one can use standard SSS to estimate the number of scattered events in each Line Of Response (LOR) and use an additional algorithm to estimate the shape of the time distribution of scattered events within each LOR (scatter mask). To integrate TOF-SC into our THOR reconstruction, three different approaches to scatter mask calculation have been investigated which are modifications/improvements of key ideas from article [4]:
A. Simple scatter scaling
This approach assumes that scattered and unscattered events have identical time distribution within each single LOR.
B. Attenuation based SC
In this approach the object is modeled as a set of “scatter points” which are generated by SSS. Each scatter point is then also assumed to be a scatter source. For each detector pair and scatter point the geometric path difference from scatter source to both detectors is calculated and an effective position of the scattered event within the corresponding LOR is determined. By repeating this procedure for a large number of scatter points and post-processing the results by smoothing or using a TOF-binning technique one can compute the required scatter mask.
C. Attenuation and activity based SC
While approach B allows to properly handle the shape of the attenuating object it does not take into account the given activity distribution. To fix this issue scatter sources and scatter points should be separated. To do this in a simple and fast way we introduce a small set of “emission points” for approximation of the given activity distribution. The activity distribution/object is then described as superposition of suitable 3D Gaussian distributions around these emission
points. Calculation of the scatter masks is similar to the previous approach, but now scatter sources are determined as projections of emission points onto straight lines connecting selected scatter point and detectors. In this approach the intensity of each source is proportional to the intensity of corresponding emission point and decreases according to a Gaussian as a function of the distance between them.

RESULTS
All three approaches have been integrated into our THOR reconstruction and tested in phantom and patient studies. Simple scatter scaling (approach A) does not yield quantitatively correct scatter distributions for big objects such as whole body phantoms. Attenuation based SC (approach B) does not have this problem due to proper handling of the object shape, but notable artifacts appear in the presence of high-contrast such as in the pelvis/bladder region. The combined attenuation and activity based algorithm (approach C) is able to eliminate part of the latter artifacts but requires more computation time.

CONCLUSION
Our preliminary results indicate that attenuation based SC might be the best compromise between computation time and image quality for a wide range of applications. A more detailed investigation of the efficiency and accuracy of the implemented TOF-SC methods is currently in progress.

REFERENCES
[1] A. Rezaei, M. Defrise, G. Bal, C. Michel, M. Conti, C. Watson, and J. Nuyts, “Simultaneous reconstruction of activity and attenuation in time-of-flight PET.” IEEE transactions on Medical Imaging, vol. 31, no. 12, pp. 2224–33, dec 2012.
[2] A. Lougovski, F. Hofheinz, J. Maus, G. Schramm, E. Will, J. van den Hoff, and J. van den Hoff, “A volume of intersection approach for on-the-fly system matrix calculation in 3D PET image reconstruction,” Physics in Medicine and Biology, vol. 59, no. 3, pp. 561–577, feb 2014.
[3] C. C. Watson, “Extension of Single Scatter Simulation to Scatter Correction of Time-of-Flight PET,” IEEE Transations on Nuclear Science, vol. 54, no. 5, pp. 1679–1686, 2007.
[4] M. Conti, B. Bendriem, M. Casey, M. Chen, F. Kehren, C. Michel, and V. Panin, “First experimental results of time-of-flight reconstruction on an LSO PET scanner.” Physics in medicine and biology, vol. 50, no. 19, pp. 4507–4526, oct 2005.