Evaluation of image reconstruction algorithms encompassing Time-Of-Flight and Point Spread Function modelling for quantitative cardiac PET: Phantom studies

Background

To perform kinetic modelling quantification, PET dynamic data must be acquired in short frames, where different critical conditions are met. The accuracy of reconstructed images influences quantification. The added value of Time-Of-Flight (TOF) and Point Spread Function (PSF) in cardiac image reconstruction was assessed.

Methods

A static phantom was used to simulate two extreme conditions: (i) the bolus passage and (ii) the steady uptake. Various count statistics and independent noise realisations were considered. A moving phantom filled with two different radionuclides was used to simulate: (i) a great range of contrasts and (ii) the cardio/respiratory motion. Analytical and iterative reconstruction (IR) algorithms also encompassing TOF and PSF modelling were evaluated.

Results

Both analytic and IR algorithms provided good results in all the evaluated conditions. The amount of bias introduced by IR was found to be limited. TOF allowed faster convergence and lower noise levels. PSF achieved near full myocardial activity recovery in static conditions. Motion degraded performances, but the addition of both TOF and PSF maintained the best overall behaviour.

Conclusions

IR accounting for TOF and PSF can be recommended for the quantification of dynamic cardiac PET studies as they improve the results compared to analytic and standard IR.

Appendix

The Reconstruction Algorithms

All the iterative algorithms used in this work were provided by the scanner manufacturer. They are all based on a 3D-OSEM algorithm, with all the relevant corrections implemented in the iterative scheme as

$$ I_{n}^{i + 1} = \frac{{I_{n}^{i} }}{{\sum\limits_{m} {H_{m,n} M_{m} } }}\sum\limits_{m} {\frac{{H_{m,n} M_{m} P_{m} }}{{M_{n} \sum\limits_{{n^{\prime}}} {H_{{m,n^{\prime}}} I_{{n^{\prime}}}^{i} + A_{m} } }}} , $$

where I ⁱ⁺¹ _n and I ⁱ _n are the values of the nth image pixel of the images I at the ith + 1 and ith iteration. P _m is the mth sinogram element, M _m is a matrix accounting for all the multiplicative correction to be applied to the mth sinogram element (normalisation, dead-time and attenuation) and A is the matrix of the additive corrections accounting for random and scatter coincidences. The matrix H account for the system geometry, which represent the probability for a photon emitted from the nth image pixel to be recorded in the mth projection bin.

The PSF modelling is achieved by modifying the H operator to H′ such that $H^{\prime}_{m,n} = \sum\limits_{k} {D_{m,k} H_{k,n} } ,$ where D represents the detector response model. Note that the PSF has been implemented as a spatially variant model in the sinogram domain.

The iterative algorithms, including TOF, have a basic implementation, like the OSEM counterpart, but the events are weighted according to the TOF probability distribution by a TOF kernel T, which estimates the contribution from each voxel n, to the time bin t of the projection bin m considered

$$ I_{n}^{i + 1} = \frac{{I_{n}^{i} }}{{\sum\limits_{m,t} {H_{m,n} M_{m} T_{n,t} } }}\sum\limits_{m,t} {\frac{{H_{m,n} M_{m} P_{m} T_{n,t} }}{{M_{n} \sum\limits_{{n^{\prime}}} {H_{{m,n^{\prime}}} T_{{n^{\prime},t}} I_{n'}^{i} + A_{m,t} } }}} . $$

The multiplicative corrections and the PSF implementation work as in the non-TOF case while the additive correction requires TOF to be taken into consideration (i.e., the random coincidences are split equally between each time bin, while the scatter distribution is time dependent).

Scatter coincidences are iteratively estimated using a 3D model-based scatter simulation30 that computes the fraction of the single scatter, following a convolution procedure is used to estimate multiple scatter, finally scaling the results to the emission tails. For TOF reconstruction, the same procedure is used but the simulation account for the distribution along the temporal dimension. Random coincidences are estimated from detectors single count rates.

The RP algorithm we used was also provided by the scanner vendor. The filters were based on what described by Kinahan and Rogers.5 Scatter and random coincidences were estimated with the same algorithms as for OSEM and, subsequently, subtracted from the sinogram.

The TOF-FORE-FBP algorithm was implemented off-line by our group using a research-tool software provided under a research collaboration with GEMS which uses the same routines as in the PET scanner. The implementation it is based on the work by Defrise et al24 for the TOF implementation of FORE and the TOF-FBP procedure uses the same filter described by Conti et al25 to reconstruct the rebinned 2D-TOF sinograms. Scatter coincidences were simulated in the same way of the TOF iterative algorithms in 3D. Once estimated, scatter and random coincidences were subtracted from the 3D-TOF sinograms. Subsequently, the sinogram was corrected for detector geometry, dead-time, normalisation and attenuation. Finally, the 3D data were rebinned to 2D using FORE, before the TOF-FBP reconstruction.