title: Assessment of a three-dimensional line-of-response probability density function system matrix for PET.
abstract: To achieve optimal PET image reconstruction through better system modeling, we developed a system matrix that is based on the probability density function for each line of response (LOR-PDF). The LOR-PDFs are grouped by LOR-to-detector incident angles to form a highly compact system matrix. The system matrix was implemented in the MOLAR list mode reconstruction algorithm for a small animal PET scanner. The impact of LOR-PDF on reconstructed image quality was assessed qualitatively as well as quantitatively in terms of contrast recovery coefficient (CRC) and coefficient of variance (COV), and its performance was compared with a fixed Gaussian (iso-Gaussian) line spread function. The LOR-PDFs of three coincidence signal emitting sources, (1) ideal positron emitter that emits perfect back-to-back γ rays (γγ) in air; (2) fluorine-18 (¹⁸F) nuclide in water; and (3) oxygen-15 (¹⁵O) nuclide in water, were derived, and assessed with simulated and experimental phantom data. The derived LOR-PDFs showed anisotropic and asymmetric characteristics dependent on LOR-detector angle, coincidence emitting source, and the medium, consistent with common PET physical principles. The comparison of the iso-Gaussian function and LOR-PDF showed that: (1) without positron range and acollinearity effects, the LOR-PDF achieved better or similar trade-offs of contrast recovery and noise for objects of 4 mm radius or larger, and this advantage extended to smaller objects (e.g. 2 mm radius sphere, 0.6 mm radius hot-rods) at higher iteration numbers; and (2) with positron range and acollinearity effects, the iso-Gaussian achieved similar or better resolution recovery depending on the significance of positron range effect. We conclude that the 3D LOR-PDF approach is an effective method to generate an accurate and compact system matrix. However, when used directly in expectation-maximization based list-mode iterative reconstruction algorithms such as MOLAR, its superiority is not clear. For this application, using an iso-Gaussian function in MOLAR is a simple but effective technique for PET reconstruction.
authors.affiliation: Department of Nuclear Medicine, University at Buffalo, SUNY, Buffalo, NY 14214, USA. rutaoyao@buffalo.edu
authors.forename: Rutao
authors.initials: R
authors.lastname: Yao
authors.forename: Ranjith M
authors.initials: RM
authors.lastname: Ramachandra
authors.forename: Neeraj
authors.initials: N
authors.lastname: Mahajan
authors.forename: Vinay
authors.initials: V
authors.lastname: Rathod
authors.forename: Noel
authors.initials: N
authors.lastname: Gunasekar
authors.forename: Ashish
authors.initials: A
authors.lastname: Panse
authors.forename: Tianyu
authors.initials: T
authors.lastname: Ma
authors.forename: Yiqiang
authors.initials: Y
authors.lastname: Jian
authors.forename: Jianhua
authors.initials: J
authors.lastname: Yan
authors.forename: Richard E
authors.initials: RE
authors.lastname: Carson
mesh_terms: D000818:Animals; D021621:Imaging, Three-Dimensional / Q000379:methods*; D009010:Monte Carlo Method; D019047:Phantoms, Imaging; D017785:Photons; D049268:Positron-Emission Tomography / Q000295:instrumentation / Q000379:methods*; D011336:Probability; D012680:Sensitivity and Specificity