Scatter correction in 3-D PET

High accuracy multiple scatter modelling for 3D whole body PET

A new technique for modelling multiple-order Compton scatter which uses the absolute probabilities relating the image space to the projection space in 3D whole body PET is presented. The details considered in this work give a valuable insight into the scatter problem, particularly for multiple scatter. Such modelling is advantageous for large attenuating media where scatter is a dominant component of the measured data, and where multiple scatter may dominate the total scatter depending on the energy threshold and object size. The model offers distinct features setting it apart from previous research: (1) specification of the scatter distribution for each voxel based on the transmission data, the physics of Compton scattering and the specification of a given PET system; (2) independence from the true activity distribution; (3) in principle no scaling or iterative process is required to find the distribution; (4) explicit multiple scatter modelling; (5) no scatter subtraction or addition to the forward model when included in the system matrix used with statistical image reconstruction methods; (6) adaptability to many different scatter compensation methods from simple and fast to more sophisticated and therefore slower methods; (7) accuracy equivalent to that of a Monte Carlo model. The scatter model has been validated using Monte Carlo simulation (SimSET).

Scatter modelling and compensation in emission tomography

In nuclear medicine, clinical assessment and diagnosis are generally based on qualitative assessment of the distribution pattern of radiotracers used. In addition, emission tomography (SPECT and PET) imaging methods offer the possibility of quantitative assessment of tracer concentration in vivo to quantify relevant parameters in clinical and research settings, provided accurate correction for the physical degrading factors (e.g. attenuation, scatter, partial volume effects) hampering their quantitative accuracy are applied. This review addresses the problem of Compton scattering as the dominant photon interaction phenomenon in emission tomography and discusses its impact on both the quality of reconstructed clinical images and the accuracy of quantitative analysis. After a general introduction, there is a section in which scatter modelling in uniform and non-uniform media is described in detail. This is followed by an overview of scatter compensation techniques and evaluation strategies used for the assessment of these correction methods. In the process, emphasis is placed on the clinical impact of image degradation due to Compton scattering. This, in turn, stresses the need for implementation of more accurate algorithms in software supplied by scanner manufacturers, although the choice of a general-purpose algorithm or algorithms may be difficult.

Iterative reconstruction algorithms in nuclear medicine

Iterative reconstruction algorithms produce accurate images without streak artifacts as in filtered backprojection. They allow improved incorporation of important corrections for image degrading effects, such as attenuation, scatter and depth-dependent resolution. Only some corrections, which are important for accurate reconstruction in positron emission tomography and single photon emission computed tomography, can be applied to the data before filtered backprojection. The main limitation for introducing iterative algorithms in nuclear medicine has been computation time, which is much longer for iterative techniques than for filtered backprojection. Modern algorithms make use of acceleration techniques to speed up the reconstruction. These acceleration techniques and the development in computer processors have introduced iterative reconstruction in daily nuclear medicine routine. We give an overview of the most important iterative techniques and discuss the different corrections that can be incorporated to improve the image quality.

A 2D/3D hybrid PET scanner with rotating partial slice-septa and its quantitative procedures

This paper presents a PET scanner capable of acquiring projection data in three-dimensional (3D) and two-dimensional (2D) modes simultaneously. The scanner has rotating partial slice-septa, and coincidence events are stored as 2D data or as 3D data depending on whether the lines of response are collimated by the septa or not. 68Ge/Ga rod sources can be set on the rotating septa, and a transmission scan for attenuation correction is performed in the 2D mode. The scanner allows simultaneous 3D-emission/2D-transmission scanning or post-injection transmission scanning with little cross-talk. A blank scan for detector normalization is also performed with the rotating rod sources in the 2D mode, from which we can derive the normalizing factors in both modes. The 3D/2D difference method is available for scatter correction, even in a dynamic study where the source distribution is changing. A 'summation method' is proposed as a new image reconstruction algorithm, in which the high- and low-frequency components of images are reconstructed from the 3D and 2D data respectively. In this method, most of the scatter contribution in the 3D data is removed by high-pass filtering, not by subtracting estimated scatter distribution, and hence the method is expected to be robust for scatter from outside the axial field of view. Computer simulations revealed that the rotating partial septa offer a single-scatter to true ratio similar to that of the conventional full septa if the depth of the partial septa is properly lengthened, with a small increase in multiple scattering.

Energy-based scatter correction for 3-D PET scanners using NaI(T1) detectors

Earlier investigations with BGO positron emission tomography (PET) scanners showed that the scatter correction technique based on multiple acquisitions with different energy windows are problematic to implement because of the poor energy resolution of BGO (22%), particularly for whole-body studies. We believe that these methods are likely to work better with NaI(TI) because of the better energy resolution achievable with NaI(TI) detectors (10%). Therefore, we investigate two different choices for the energy window, a low-energy window (LEW) on the Compton spectrum at 400-450 keV, and a high-energy window (HEW) within the photopeak (lower threshold above 511 keV). The results obtained for our three-dimensional (3-D) (septa-less) whole-body scanners [axial field of view (FOV) of 12.8 cm and 25.6 cm] as well as for our 3-D brain scanner (axial FOV of 25.6 cm) show an accurate prediction of the scatter distribution for the estimation of trues method (ETM) using a HEW, leading to a significant reduction of the scatter contamination. The dual-energy window (DEW) technique using a LEW is shown to be intrinsically wrong; in particular, it fails for line source and bar phantom measurements. However, the method is able to produce good results for homogeneous activity distributions. Both methods are easy to implement, are fast, have a low noise propagation, and will be applicable to other PET scanners with good energy resolution and stability, such as hybrid NaI(TI) PET/SPECT dual-head cameras and future PET cameras with GSO or LSO scintillators.

Investigation of scattered radiation in 3D whole-body positron emission tomography using Monte Carlo simulations

The correction of scattered radiation is one of the most challenging tasks in 3D positron emission tomography (PET) and knowledge about the amount of scatter and its distribution is a prerequisite for performing an accurate correction. One concern in 3D PET in contrast to 2D PET is the scatter contribution from activity outside the field-of-view (FOV) and multiple scatter. Using Monte Carlo simulations, we examined the scatter distribution for various phantoms. The simulations were performed for a whole-body PET system (ECAT EXACT HR+, Siemens/CTI) with an axial FOV of 15.5 cm and a ring diameter of 82.7 cm. With (without) interplane septa, up to one (two) out of three detected events are scattered (for a centred point source in a water-filled cylinder that nearly fills out the patient port), whereby the relative scatter fraction varies significantly with the axial position. Our results show that for an accurate scatter correction, activity as well as scattering media outside the FOV have to be taken into account. Furthermore it could be shown that there is a considerable amount of multiple scatter which has a different spatial distribution from single scatter. This means that multiple scatter cannot be corrected by simply rescaling the single scatter component.

A method for calibrating three-dimensional positron emission tomography without scatter correction

Calibration for three-dimensional positron emission tomography (3D PET) using a uniform cylinder and cross-calibration with aliquots requires correction for scatter and attenuation. Thus the accuracy of the calibration is dependent on the scatter correction method, and on the applicability of the scatter correction for different regions of the body. A method has been developed which provides a calibration which does not require correction for scatter or attenuation, making it generally applicable and independent of the scatter correction. The method has been previously described for measurement of the absolute sensitivity of tomographic devices. This approach has been extended to give a calibration of the PET camera "in air" in units of kBq/pixel. The reconstructed images are multiplied by this factor to give accurate activity concentrations, after attenuation and scatter correction. The method has been used with a fully 3D filtered backprojection (reprojection) algorithm and iterative convolution-subtraction scatter correction on data from an ECAT 953B. Using this method 3D PET images have been calibrated to within +/-5% accuracy, but this is highly dependent on the accuracy of the scatter correction. The method described here is practical and provides a means of calibrating a 3D PET system without the need for correction for scatter or attenuation of the calibration data.

Correction for scatter in 3D brain PET using a dual energy window method

A method for scatter correction using dual energy window acquisition has been developed and implemented on data collected with a brain-PET tomograph operated in the septa retracted, 3D mode. Coincidence events are assigned to (i) an upper energy window where both photons deposit energy between 380 keV and 850 keV or (ii) a lower energy window where one or both photons deposit within 200 keV and 380 keV. Scaling parameters are derived from measurements of the ratios of counts from line sources due to scattered and unscattered events in the two energy windows in head-sized phantoms. A scaled subtraction of the two energy windows produces a distribution of scatter which is smoothed prior to subtraction from the upper energy window. In phantoms, the correction was found to restore the uniformity, contrast and linearity of activity concentration. Relative activity concentrations were restored to within 7% of their true values in a multicompartment phantom. The method was found to provide accurate correction for scattered events arising from activity outside the direct detector field of view. In a three-compartment phantom containing water, 18F and 11C scanned in dynamic, multiframe mode, the half-lives of the two isotopes were restored to within 2% of their true value.

Bayesian reconstruction of PET images: methodology and performance analysis

We describe a practical statistical methodology for the reconstruction of PET images. Our approach is based on a Bayesian formulation of the imaging problem. The data are modelled as independent Poisson random variables and the image is modelled using a Markov random field smoothing prior. We describe a sequence of calibration procedures which are performed before reconstruction: (i) calculation of accurate attenuation correction factors from re-projected Bayesian reconstructions of the transmission image; (ii) estimation of the mean of the randoms component in the data; and (iii) computation of the scatter component in the data using a Klein-Nishina-based scatter estimation method. The Bayesian estimate of the PET image is then reconstructed using a pre-conditioned conjugate gradient method. We performed a quantitation study with a multi-compartment chest phantom in a Siemens/CTI ECAT931 system. Using 40 1 min frames, we computed the ensemble mean and variance over several regions of interest from images reconstructed using the Bayesian and a standard filtered backprojection (FBP) protocol. The values for the region of interest were compared with well counter data for each compartment. These results show that the Bayesian protocol can produce substantial improvements in relative quantitation over the standard FBP protocol, particularly when short transmission scans are used. An example showing the application of the method to a clinical chest study is also given.

Model-based scatter correction for fully 3D PET

A method is presented that directly calculates the mean number of scattered coincidences in data acquired with fully 3D positron emission tomography (PET). This method uses a transmission scan, an emission scan, the physics of Compton scatter, and a mathematical model of the scanner in a forward calculation of the number of events for which one photon has undergone a single Compton interaction. The distribution of events for which multiple Compton interactions have occurred is modelled as a linear transformation of the single-scatter distribution. Computational efficiency is achieved by sampling at rates no higher than those required by the scatter distribution and by implementing the algorithm using look-up tables. Evaluation studies in phantoms with large scatter fractions show that the method yields images with quantitative accuracy equivalent to that of slice-collimated PET in clinically useful times.