Isotope independent determination of PET/CT modulation transfer functions from phantom measurements on spheres

A PET/CT system's imaging capabilities are best described by its point spread function (PSF) in the spatial domain or equivalently by its modulation transfer function (MTF) in the spatial frequency domain. Knowing PSFs or MTFs is a prerequisite for many numerical methods attempting to improve resolution and to reduce the partial volume effect. In PET/CT, the observed PSF is a convolution of the system's intrinsic imaging capabilities including image reconstruction (PSF₀) and the positron range function (PRF) of the imaged β⁺ emitting isotope. A PRF describes the non-Gaussian distribution of β⁺ annihilation events around a hypothetical point source. The main aim was to introduce a new method for determining a PET/CT system's intrinsic MTF (MTF₀) from phantom measurements of hot spheres independently of the β⁺ emitting isotope used for image acquisition. Secondary aim was to examine non-Gaussian and nonlinear MTFs of a modern iterative reconstruction algorithm.

PET/CT images of seven phantom spheres with volumes ranging from 0.25 to 16 ml and filled either with ¹⁸F or with ⁶⁸Ga were acquired and reconstructed using filtered back projection (FBP). MTFs were modeled with linear splines. The spline fit iteratively minimized the mean squared error between the acquired PET/CT image and a convolution of the thereof derived PSF with a numerical representation of the imaged hot phantom sphere. For determining MTF₀, the numerical sphere representations were convolved with a PRF, simulating a fill with either ¹⁸F or ⁶⁸Ga. The MTFs determined by this so-called MTF fit method were compared with MTFs derived from point source measurements and also compared with MTFs derived with a previously published PSF fit method. The MTF fit method was additionally applied to images reconstructed by a vendor iterative algorithm with PSF recovery (Siemens TrueX).

The MTF fit method was able to determine ¹⁸F and ⁶⁸Ga dependent MTFs and MTF₀ from FBP reconstructed images. Root-mean-square deviation between fit determined MTFs and point source determined MTFs ranged from 0.023 to 0.039. MTFs from Siemens TrueX reconstructions varied with size of the imaged sphere.

MTF₀ can be determined regardless of the imaged isotope, when using existing PRF models for the MTF fit method presented. The method proves that modern iterative PET/CT reconstruction algorithms have nonlinear imaging properties. This behaviour is not accessible by point source measurements. MTFs resulting from these clinically applied algorithms need to be estimated from objects of similar geometry to those intended for clinical imaging.