Spatial distortion correction and crystal identification for MRI-compatible position-sensitive avalanche photodiode-based PET scanners

Abstract

Position-sensitive avalanche photodiodes (PSAPDs) are gaining widespread acceptance in modern PET scanner designs, and owing to their relative insensitivity to magnetic fields, especially in those that are MRI-compatible. Flood histograms in PET scanners are used to determine the crystal of annihilation photon interaction and hence, for detector characterization and routine quality control. For PET detectors that use PSAPDs, flood histograms show a characteristic pincushion distortion when Anger logic is used for event positioning. A small rotation in the flood histogram is also observed when the detectors are placed in a magnetic field. We first present a general purpose automatic method for spatial distortion correction for flood histograms of PSAPD-based PET detectors when placed both inside and outside a MRI scanner. Analytical formulae derived for this scheme are based on a hybrid approach that combines desirable properties from two existing event positioning schemes. The rotation of the flood histogram due to the magnetic field is determined iteratively and is accounted for in the scheme. We then provide implementation details of a method for crystal identification we have previously proposed and evaluate it for cases when the PET detectors are both outside and in a magnetic field. In this scheme, Fourier analysis is used to generate a lower-order spatial approximation of the distortion-corrected PSAPD flood histogram, which we call the 'template'. The template is then registered to the flood histogram using a diffeomorphic iterative intensity-based warping scheme. The calculated deformation field is then applied to the segmentation of the template to obtain a segmentation of the flood histogram. A manual correction tool is also developed for exceptional cases. We present a quantitative assessment of the proposed distortion correction scheme and crystal identification method against conventional methods. Our results indicate that our proposed methods lead to a large reduction in manual labor and indeed can routinely be used for calibration and characterization studies in MRI-compatible PET scanners based on PSAPDs.

Fig. 1

A single PET detector module from the UC Davis MRI-compatible PET scanner and flood histograms; (a) the PET detector module with an array of 8 × 8 LSO crystals coupled via optical fibers to a single 14 × 14 mm² PSAPD (reproduced from [4]), (b) flood histogram obtained for the detector when placed outside the 7T MRI scanner’s magnetic field, (c) flood histogram obtained for the same detector when placed inside the MRI scanner’s magnetic field

Fig. 2

Flood histograms after correction for effects of curved optical fibers; (a), (b) and (c) are for the PET detector when placed outside the 7T magnetic field, and (d), (e) and (f) are when the detector is placed in the magnetic field. (a) and (d) use Anger’s equations, (b) and (e) use Zhang’s method, and (c) and (e) use the proposed adaptive formulae with α = 0.7 and θ = 0°. All formulae are listed in in Table I

Fig. 3

Intensity compensation; (a) the flood histogram from Fig. 2(c) for comparison, (b) the smoothed image |k(x, y)|, (c) the intensity compensated image p(x, y), and (d) normalized intensity profiles obtained by summing (a) and (c) along the y dimension.

Fig. 4

Generation of the template image; (a) image q(x, y) determined by Fourier analysis, (b) the template image t(x, y), (d) segmentation w(x, y) of t(x, y) showing all 64 regions in pseudo-color

Fig. 5

Distortion corrected flood histograms with overlaid segmentation boundaries; (a) flood histogram when the PET detector was outside the magnetic field (α = 0.7, θ = 0°), (b) flood histogram generated from the same data set as in (a) but with Anger logic and segmented using the manual clicks on the peaks followed by the watershed method-based segmentation, (c) flood histograms when the PET detector was inside the 7T magnetic field (α = 0.7, θ = 21°). Segmented region boundaries are denoted by white lines. Slight mis-segmentations may happen for either case. Higher order polynomials may be used in our case to to approximate the deformation fields. We describe the trade-offs of this prospect in Section IV.

Fig. 6

Mean photopeak positions for all 64 crystals obtained using the segmentation in Fig. 5(b) and with the proposed automatic method (Fig. 5(a)). The error bars indicate the standard deviation over the five sets of data.

Fig. 7

Crystal-wise energy resolution (%) using manual segmentation and the proposed automatic method for the five sets of data. The error bars indicate standard deviation over the data sets.

Fig. 8

Total measured counts in each crystal after segmentation for the two methods. The error bars indicate standard deviation over the five data sets.