In this paper, we extend the gradient vector flow field for robust variational segmentation of vector-valued images. Rather than using scalar edge information, we define a vectorial edge map derived from a weighted local structure tensor of the image that enables the diffusion of the gradient vectors in accurate directions through the 4D gradient vector flow equation. To reduce the contribution of noise in the structure tensor, image channels are weighted according to a blind estimator of contrast. The method is applied to biological volume delineation in dynamic PET imaging, and validated on realistic Monte Carlo simulations of numerical phantoms as well as on real images.
Positron emission tomography (PET) data are typically reconstructed with maximum likelihood expectation maximization (MLEM). However, this method suffers from positive bias due to the non-negativity constraint. This is particularly problematic for tracer kinetic modeling analysis of dynamic PET studies. Two reconstruction methods with bias reduction properties that do not use strict Poisson optimization are presented and studied in this work. They are compared to each other, to filtered backprojection (FBP), and to MLEM. The first method is an extension of the so-called NEGML algorithm. This algorithm is based on a modified Poisson distribution that replaces the original function by a Gaussian distribution for low count data points. This modified likelihood function is optimized by a gradient ascent approach. The point of transition between the Gaussian and the Poisson regime is a parameter of the model. The second method, AML, is a simplification of the ABMLmethod proposed by Byrne. ABML has parameters A and B, which represent the lower and upper bounds for the reconstructed image. AML is the ABML algorithm with upper bound B set to infinity. AML with negative A has bias reduction properties. AML for different choices of A is studied. The parameter of both algorithms determines the effectiveness of the bias reduction. It was found that the parameter should be chosen large enough to ensure bias-free images. This means that both algorithms become more similar to a least squares algorithm, which turned out to be necessary to obtain bias-free reconstructions. This comes at the cost of increased variance. Nevertheless, both NEGML and AML have lower variance compared to FBP. Furthermore, it was observed that the way randoms are handled has a large influence on the bias in the images. Reconstruction with smoothed randoms results in lower bias compared to reconstruction with unsmoothed randoms or randoms precorrected data. However, NEGML and AML results are both bias-free for large values of their parameter.
PET is a promising technique for in vivo treatment verification in hadrontherapy. Three main PET geometries dedicated to in-beam treatment monitoring have been proposed in the literature: the dual-head PET geometry, the OpenPET geometry and the slanted-closed ring geometry. The aim of this work is to characterize the performance of two of these dedicated PET detectors in realistic clinical conditions. Several configurations of the dual-head PET and OpenPET systems were simulated using GATE v6.2. For the dual-head configuration, two aperture angles (15° and 45°) were studied. For the OpenPET system, two gaps between rings were investigated (110 and 160 mm). A full-ring PET system was also simulated as a reference. After preliminary evaluation of the sensitivity and spatial resolution using a Derenzo phantom, a real small-field head and neck treatment plan was simulated, with and without introducing patient displacements. No wash-out was taken into account. 3D maps of the annihilation photon locations were deduced from the PET data acquired right after the treatment session (5 min acquisition) using a dedicated OS-EM reconstruction algorithm. Detection sensitivity at the center of the field-of-view (FOV) varied from 5.2% (45° dual-head system) to 7.0% (full-ring PET). The dual-head systems had a more uniform efficiency within the FOV than the OpenPET systems. The spatial resolution strongly depended on the location within the FOV for the ? = 45° dual-head system and for the two OpenPET systems. All investigated architectures identified the magnitude of mispositioning introduced in the simulations within a 1.5 mm accuracy. The variability on the estimated mispositionings was less than 2 mm for all PET systems.
Iterative reconstructions in positron emission tomography (PET) need a model relating the recorded data to the object/patient being imaged, called the system matrix (SM). The more realistic this model, the better the spatial resolution in the reconstructed images. However, a serious concern when using a SM that accurately models the resolution properties of the PET system is the undesirable edge artefact, visible through oscillations near sharp discontinuities in the reconstructed images. This artefact is a natural consequence of solving an ill-conditioned inverse problem, where the recorded data are band-limited. In this paper, we focus on practical aspects when considering image-based point-spread function (PSF) reconstructions. To remove the edge artefact, we propose to use a particular case of the method of sieves (Grenander 1981 Abstract Inference New York: Wiley), which simply consists in performing a standard PSF reconstruction, followed by a post-smoothing using the PSF as the convolution kernel. Using analytical simulations, we investigate the impact of different reconstruction and PSF modelling parameters on the edge artefact and its suppression, in the case of noise-free data and an exactly known PSF. Using Monte-Carlo simulations, we assess the proposed method of sieves with respect to the choice of the geometric projector and the PSF model used in the reconstruction. When the PSF model is accurately known, we show that the proposed method of sieves succeeds in completely suppressing the edge artefact, though after a number of iterations higher than typically used in practice. When applying the method to realistic data (i.e. unknown true SM and noisy data), we show that the choice of the geometric projector and the PSF model does not impact the results in terms of noise and contrast recovery, as long as the PSF has a width close to the true PSF one. Equivalent results were obtained using either blobs or voxels in the same conditions (i.e. the blobs density function being the same as the voxel-based PSF). From a practical point-of-view, the method can be used to perform fast reconstructions based on very simple models (compared to sinogram-based PSF modelling), producing artefact-free images with a better compromise between noise and spatial resolution than images reconstructed without or with under-estimated PSF. Besides, the method inherently limits the spatial resolution in the reconstructed images to the intrinsic one of the PET system.
18F-fluorodeoxyglucose positron emission tomography (18FDG PET) has become an essential technique in oncology. Accurate segmentation and uptake quantification are crucial in order to enable objective follow-up, the optimization of radiotherapy planning, and therapeutic evaluation. We have designed and evaluated a new, nearly automatic and operator-independent segmentation approach. This incorporated possibility theory, in order to take into account the uncertainty and inaccuracy inherent in the image. The approach remained independent of PET facilities since it did not require any preliminary calibration. Good results were obtained from phantom images [percent error =18.38% (mean) ± 9.72% (standard deviation)]. Results on simulated and anatomopathological data sets were quantified using different similarity measures and showed the method was efficient (simulated images: Dice index =82.18% ± 13.53% for SUV =2.5 ). The approach could, therefore, be an efficient and robust tool for uptake volume segmentation, and lead to new indicators for measuring volume of interest activity.
Accurate modeling of system response and scatter distribution is crucial for image reconstruction in emission tomography. Monte Carlo simulations are very well suited to calculate these quantities. However, Monte Carlo simulations are also slow and many simulated counts are needed to provide a sufficiently exact estimate of the detection probabilities. In order to overcome these problems, we propose to split the simulation into two parts, the detection system and the object to be imaged (the patient). A so-called virtual boundary that separates these two parts is introduced. Within the patient, particles are simulated conventionally. Whenever a photon reaches the virtual boundary, its detection probability is calculated analytically by evaluating a multi-dimensional B-spline that depends on the photon position, direction and energy. The unknown B-spline knot values that define this B-spline are fixed by a prior pre- simulation that needs to be run once for each scanner type. After this pre-simulation, the B-spline model can be used in any subsequent simulation with different patients. We show that this approach yields accurate results when simulating the Biograph 16 HiREZ PET scanner with Geant4 Application for Emission Tomography (GATE). The execution time is reduced by a factor of about 22 x (scanner with voxelized phantom) to 30 x (empty scanner) with respect to conventional GATE simulations of same statistical uncertainty. The pre-simulation and calculation of the B-spline knots values could be performed within half a day on a medium-sized cluster.
In (18)F-FDG PET, tumors are often characterized by their metabolically active volume and standardized uptake value (SUV). However, many approaches have been proposed to estimate tumor volume and SUV from (18)F-FDG PET images, none of them being widely agreed upon. We assessed the accuracy and robustness of 5 methods for tumor volume estimates and of 10 methods for SUV estimates in a large variety of configurations.
Geant4 Application for Emission Tomography (GATE) is a widely used, well-validated and very versatile application for Monte Carlo simulations in emission tomography. However, its computational performance is poor, especially for voxelized phantoms, partly due to the use of a very general particle tracking algorithm. In this work, two methods are proposed to reduce the time spent on particle tracking in the phantom: a newly introduced regular navigation algorithm of Geant4 and fictitious interaction tracking (also known as Woodcock tracking) for photons. The speed-up introduced by the two methods was investigated by simulating a PET acquisition with the Allegro/GEMINI GXL PET/CT scanner. The simulation was based on a clinical head-and-neck [(18)F]FDG PET/CT scan. The total time spent for the simulation (including initialization, particle tracking and signal processing) was obtained for seven settings corresponding to different tracking options. All seven methods led to very close results with regard to the total number of detected coincidences (less than 0.5% differences), and trues, scatter and random fractions. Acceleration factors of approximately 2.7 (14 x 14 x 9 voxels) to 27.6 (378 x 378 x 243 voxels) were obtained in comparison with the fastest available tracking available in GATE 3.1.2.
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