Previous attempts to estimate attenuation correction factors using only PET emission data have had limited success. Now, researchers in Belgium have demonstrated that for time-of-flight (TOF) PET scanners, it is possible to estimate this attenuation, except for a constant, using just the TOF emission data.

"Compared to traditional PET scanners, measurement of time-of-flight provides additional information on the spatial distribution of the injected radioactive tracer," explained Michel Defrise, from Vrije Universiteit Brussel. "Specifically, it yields an approximate localization of each decaying positron along the line of response linking the two detectors. This additional information turns out to be sufficient to determine both the attenuation image and the emission image."

Writing in Physics in Medicine & Biology, Defrise and colleagues Ahmadreza Rezaei and Johan Nuyts from Katholieke Universiteit Leuven develop a simple analytic method for estimating the attenuation sinogram and demonstrate the feasibility of their approach on a software phantom (Phys. Med. Biol. 57 885).

Analytic approach

The attenuation sinogram (a Radon transform of the attenuation image) is basically a map of the probability of attenuation for each photon path through the tissues that comprise the scanned object. It is used to correct the PET sinogram, without which, the reconstructed PET image will be quantitatively inaccurate and may also exhibit structural inaccuracies.

The researchers begin by proving the theorem that for TOF PET, "the emission data determine the φ and s derivatives of the attenuation sinogram, for all φ and s values in the region containing activity" (where φ and s are the transaxial sinogram coordinates). They then develop an analytical algorithm to estimate the gradient of the attenuation sinogram from 2D TOF emission data, following the logic of the proof of this theorem.

To assess the viability of this method, the team performed a 2D TOF simulation using a software phantom comprising regions of tissue, bone, lung and air, with known attenuation coefficients. TOF-PET data were generated by sampling the phantom's activity and attenuation images and using forward projection to obtain PET sinograms.

The researchers used the abovementioned analytical algorithm to estimate the gradient of the attenuation sinogram, and then employed the iterative Landweber algorithm to estimate the attenuation sinogram from its gradient.

The final step in this method involves determining the arbitrary offset associated with this estimated attenuation sinogram. This constant can be estimated if the initial PET image can be segmented, and attenuation coefficients are available in at least some of the segmented regions. For the phantom example, the researchers employed simple thresholding to obtain a region containing mostly tissue and bone, and used the known attenuation coefficient of tissue.

This process enabled calculation of the final estimated attenuation sinogram. "If the offset is known and the data is noise free, the match is accurate to a few per cent for the specific case study in the paper," said Defrise. "The accuracy, of course, degrades with increasing noise."

For illustration, the authors also present the reconstructed attenuation image. However, they point out that no reconstruction of the attenuation image is needed for PET attenuation correction. Although not shown in this paper, Defrise says that the final attenuation-corrected PET emission image also shows good accuracy.

The authors note that implementing their analytic method for simulated data demonstrates the practical impact of this approach. They also suggest that the use of iterative algorithms will likely lead to significantly superior results.

"We are now working on iterative methods for solving this problem, which take into account the Poisson nature of the measurement noise," Defrise told medicalphysicsweb. "We are also working towards extending the analytical results presented in this paper to three dimensions."

Related articles in PMB
Time-of-flight PET data determine the attenuation sinogram up to a constant
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