Joint Optimization of Collimator and Reconstruction Parameters in X-Ray Fluorescence Computed Tomography Using Analytical Point Spread Function and Model Observer

Objective: To jointly optimize collimator design and image reconstruction algorithm in X-ray Fluorescence Computed Tomography (XFCT) for imaging low concentrations of high atomic number (Z) elements in small animal models. Methods: Single pinhole (SPH) collimator and three types of multi-pinhole (MPH) collimators were evaluated. MPH collimators with 5, 7, and 9 pinholes using lead, stainless steel and brass were considered. A digital cylindrical phantom (0.5 mm³ voxels) of 25 mm diameter and 25 mm height with a central 5 mm diameter and 12.5 mm height cylindrical insert containing gold nanoparticles (2:1 insert: background concentration) was modeled. A 125 kVp, 2 mm Sn filtered x-ray spectrum (0.5 cGy/projection) for gold K-shell XFCT was considered. System matrices were implemented using analytical point spread functions (PSF) for each pinhole collimator. Poisson noise was added to the projection data (16 equiangular views) before image reconstruction using Maximum-Likelihood Expectation-Maximization (ML-EM) algorithm. Signal-present and signal-absent images were generated for the detection task performed by a channelized Hotelling observer (CHO) with 10 Dense Difference-of-Gaussian channels. The area under the curve (AUC) in receiver operating characteristic was used as the image quality metric. Results: A stainless steel focusing type MPH with 7 pinholes and 20 iterations of ML-EM provided the highest AUC. Conclusion: MPH collimators outperformed SPH collimators for XFCT and consistently high AUCs were observed with focusing type MPH designs with 7 pinholes. Significance: The combinations of collimator design and image reconstruction parameters that maximized AUC were identified, which could improve the performance of XFCT.

I. Introduction

Computed tomography (CT) is a common medical imaging modality which provides three-dimensional (3D) anatomical information and is routinely used for diagnosis, treatment planning and for monitoring of therapy response. CT also plays a major role in preclinical and small animal imaging. CT relies on measuring the differences in x-ray linear attenuation coefficients, but can be challenging to detect very low concentrations of high atomic number (Z) elements [1], [2]. In contrast, X-ray Fluorescence Computed Tomography (XFCT) relies upon detecting characteristic x-rays, such as those from K-shell or L-shell [3]–[6], enabling imaging and quantification of very low concentrations of high Z elements. Among imaging probes based on high-Z elements, gold nanoparticles (GNPs) conjugated with exogenous moieties targeting specific disease processes are of particular interest and can provide the molecular characteristics of such processes when properly imaged. Thus, the potential of XFCT for in vivo imaging of targeted high Z probes during pharmacologic and biodistribution studies using small animal models is being actively investigated.