This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18 degrees axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard "exact" 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time.

The quality of images reconstructed by statistical iterative methods depends on an accurate model of the relationship between image space and projection space through the system matrix The elements of the system matrix for the clinical Hi-Rez scanner were derived by processing the data measured for a point source at different positions in a portion of the field of view. These measured data included axial compression and azimuthal interleaving of adjacent projections. Measured data were corrected for crystal and geometrical efficiency. Then, a whole system matrix was derived by processing the responses in projection space. Such responses included both geometrical and detection physics components of the system matrix. The response was parameterized to correct for point source location and to smooth for projection noise. The model also accounts for axial compression (span) used on the scanner. The forward projector for iterative reconstruction was constructed using the estimated response parameters. This paper extends our previous work to fully three-dimensional. Experimental data were used to compare images reconstructed by the standard iterative reconstruction software and the one modeling the response function. The results showed that the modeling of the response function improves both spatial resolution and noise properties.

The purpose of this study was to apply a magnetic resonance (MR) imaging-compatible positron emission tomographic (PET) detector technology for simultaneous MR/PET imaging of the human brain and skull base. The PET detector ring consists of lutetium oxyorthosilicate (LSO) scintillation crystals in combination with avalanche photodiodes (APDs) mounted in a clinical 3-T MR imager with use of the birdcage transmit/receive head coil. Following phantom studies, two patients were simultaneously examined by using fluorine 18 fluorodeoxyglucose (FDG) PET and MR imaging and spectroscopy. MR/PET data enabled accurate coregistration of morphologic and multifunctional information. Simultaneous MR/PET imaging is feasible in humans, opening up new possibilities for the emerging field of molecular imaging.

A number of factors have to be considered for implementing an accurate attenuation correction (AC) in a combined MR-PET scanner. In this work, some of these challenges were investigated and an AC method based entirely on the MR data obtained with a single dedicated sequence was developed and used for neurological studies performed with the MR-PET human brain scanner prototype. Methods The focus was on the bone/air segmentation problem, the bone linear attenuation coefficient selection and the RF coil positioning. The impact of these factors on the PET data quantification was studied in simulations and experimental measurements performed on the combined MR-PET scanner. A novel dual-echo ultra-short echo time (DUTE) MR sequence was proposed for head imaging. Simultaneous MR-PET data were acquired and the PET images reconstructed using the proposed MR-DUTE-based AC method were compared with the PET images reconstructed using a CT-based AC. Results Our data suggest that incorrectly accounting for the bone tissue attenuation can lead to large underestimations (>20%) of the radiotracer concentration in the cortex. Assigning a linear attenuation coefficient of 0.143 or 0.151 cm−1 to bone tissue appears to give the best trade-off between bias and variability in the resulting images. Not identifying the internal air cavities introduces large overestimations (>20%) in adjacent structures. Based on these results, the segmented CT AC method was established as the “silver standard” for the segmented MR-based AC method. Particular to an integrated MR-PET scanner, ignoring the RF coil attenuation can cause large underestimations (i.e. up to 50%) in the reconstructed images. Furthermore, the coil location in the PET field of view has to be accurately known. Good quality bone/air segmentation can be performed using the DUTE data. The PET images obtained using the MR-DUTE- and CT-based AC methods compare favorably in most of the brain structures. Conclusion An MR-DUTE-based AC method was implemented considering all these factors and our preliminary results suggest that this method could potentially be as accurate as the segmented CT method and it could be used for quantitative neurological MR-PET studies.

Recently, shifted periodicities 1 modulo 3 and 2 modulo 3 have been identified in protein (coding) genes of both prokaryotes and eukaryotes with autocorrelation functions analysing eight of 64 trinucleotides (Arque`s et al., 1995). This observation suggests that the trinucleotides are associated with frames in protein genes. In order to verify this hypothesis, a distribution of the 64 trinucleotides AAA, . . . , TTT is studied in both gene populations by using a simple method based on the trinucleotide frequencies per frame. In protein genes, the trinucleotides can be read in three frames: the reading frame 0 established by the ATG start trinucleotide and frame 1 (resp. 2) which is the frame 0 shifted by 1 (resp. 2) nucleotide in the 5'-3' direction. Then, the occurrence frequencies of the 64 trinucleotides are computed in the three frames. By classifying each of the 64 trinucleotides in its preferential occurrence frame, i.e. the frame associated with its highest frequency, three subsets of trinucleotides can be identified in the three frames. This approach is applied in the two gene populations.Unexpectedly, the same three subsets of trinucleotides are identified in these two gene populations: T0 = X0 * {AAA,TTT} with X0 = {AAC,AAT,ACC,ATC,ATT,CAG,CTC,CTG,GAA,GAC,GAG, GAT,GCC,GGC,GGT,GTA,GTC,GTT,TAC,TTC} in frame 0, T1 = X1 * {CCC} in frame 1 and T2 = X2 * {GGG} in frame 2, each subset X0, X1 and X2 having 20 trinucleotides. Surprisingly, these three subsets have five important properties: (i) the property of maximal circular code for X0 (resp. X1, X2) allowing the automatical retrieval of frame 0 (resp. 1, 2) in any region of a protein gene model (formed by a series of trinucleotides of X0) without using a start codon; (ii) the DNA complementarity property C (e.g. C(AAC) = GTT): C(T0) = T0, C(T1) = T2 and C(T2) = T1 allowing the two paired reading frames of a DNA double helix simultaneously to code for amino acids; (iii) the circular permutation property P (e.g. P(AAC) = ACA): P(X0) = X1 and P(X1) = X2 implying that the two subsets X1 and X2 can be deduced from X0; (iv) the rarity property with an occurrence probability of X0 equal to 6 × 10 −8 ; and (v) the concatenation property with: a high frequency (27.5%) of misplaced trinucleotides in the shifted frames, a maximum (13 nucleotides) length of the minimal window to automatically retrieve the frame and an occurrence of the four types of nucleotides in the three trinucleotides sites, in favour of an evolutionary code.In the Discussion, the identified subsets T0, T1 and T2 replaced in the three two-letter genetic alphabets purine/pyrimidine, amino/ceto and strong/weak interaction, allow us to deduce that the RNY model (R = purine = A or G, Y = pyrimidine = C or T, N = R or Y) (Eigen & Schuster, 1978) is the closest two-letter codon model to the trinucleotides of T0. Then, these three subsets are related to the genetic code. The trinucleotides of T0 code for 13 amino acids: Ala, Asn, Asp, Gln, Glu, Gly, Ile, Leu, Lys, Phe, Thr, Tyr and Val. Finally, a strong...

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In positron emission tomography (PET) and single photon emission tomography (SPECT), attenuation correction is necessary for quantitative reconstruction of the tracer distribution. Previously, several attempts have been made to estimate the attenuation coefficients from emission data only. These attempts had limited success, because the problem does not have a unique solution, and severe and persistent "cross-talk" between the estimated activity and attenuation distributions was observed. In this paper, we show that the availability of time-of-flight (TOF) information eliminates the cross-talk problem by destroying symmetries in the associated Fisher information matrix. We propose a maximum-a-posteriori reconstruction algorithm for jointly estimating the attenuation and activity distributions from TOF PET data. The performance of the algorithm is studied with 2-D simulations, and further illustrated with phantom experiments and with a patient scan. The estimated attenuation image is robust to noise, and does not suffer from the cross-talk that was observed in non-TOF PET. However, some constraining is still mandatory, because the TOF data determine the attenuation sinogram only up to a constant offset.

Head motion is difficult to avoid in long PET studies, degrading the image quality and offsetting the benefit of using a high-resolution scanner. As a potential solution in an integrated MR-PET scanner, the simultaneously acquired MR data can be used for motion tracking. In this work, a novel data processing and rigid-body motion correction (MC) algorithm for the MR-compatible BrainPET prototype scanner is described and proof-of-principle phantom and human studies are presented. Methods To account for motion, the PET prompts and randoms coincidences as well as the sensitivity data are processed in the line or response (LOR) space according to the MR-derived motion estimates. After sinogram space rebinning, the corrected data are summed and the motion corrected PET volume is reconstructed from these sinograms and the attenuation and scatter sinograms in the reference position. The accuracy of the MC algorithm was first tested using a Hoffman phantom. Next, human volunteer studies were performed and motion estimates were obtained using two high temporal resolution MR-based motion tracking techniques. Results After accounting for the physical mismatch between the two scanners, perfectly co-registered MR and PET volumes are reproducibly obtained. The MR output gates inserted in to the PET list-mode allow the temporal correlation of the two data sets within 0.2 s. The Hoffman phantom volume reconstructed processing the PET data in the LOR space was similar to the one obtained processing the data using the standard methods and applying the MC in the image space, demonstrating the quantitative accuracy of the novel MC algorithm. In human volunteer studies, motion estimates were obtained from echo planar imaging and cloverleaf navigator sequences every 3 seconds and 20 ms, respectively. Substantially improved PET images with excellent delineation of specific brain structures were obtained after applying the MC using these MR-based estimates. Conclusion A novel MR-based MC algorithm was developed for the integrated MR-PET scanner. High temporal resolution MR-derived motion estimates (obtained while simultaneously acquiring anatomical or functional MR data) can be used for PET MC. An MR-based MC has the potential to improve PET as a quantitative method, increasing its reliability and reproducibility which could benefit a large number of neurological applications.