Robust Framework for PET Image Reconstruction Incorporating System and Measurement Uncertainties

In Positron Emission Tomography (PET), an optimal estimate of the radioactivity concentration is obtained from the measured emission data under certain criteria. So far, all the well-known statistical reconstruction algorithms require exactly known system probability matrix a priori, and the quality of such system model largely determines the quality of the reconstructed images. In this paper, we propose an algorithm for PET image reconstruction for the real world case where the PET system model is subject to uncertainties. The method counts PET reconstruction as a regularization problem and the image estimation is achieved by means of an uncertainty weighted least squares framework. The performance of our work is evaluated with the Shepp-Logan simulated and real phantom data, which demonstrates significant improvements in image quality over the least squares reconstruction efforts

Topics in image reconstruction for high resolution positron emission tomography

Les problèmes mal posés représentent un sujet d'intérêt interdisciplinaire qui surgires dans la télédétection et des applications d'imagerie. Cependant, il subsiste des questions cruciales pour l'application réussie de la théorie à une modalité d'imagerie. La tomographie d'émission par positron (TEP) est une technique d'imagerie non-invasive qui permet d'évaluer des processus biochimiques se déroulant à l'intérieur d'organismes in vivo. La TEP est un outil avantageux pour la recherche sur la physiologie normale chez l'humain ou l'animal, pour le diagnostic et le suivi thérapeutique du cancer, et l'étude des pathologies dans le coeur et dans le cerveau. La TEP partage plusieurs similarités avec d'autres modalités d'imagerie tomographiques, mais pour exploiter pleinement sa capacité à extraire le maximum d'information à partir des projections, la TEP doit utiliser des algorithmes de reconstruction d'images à la fois sophistiquée et pratiques. Plusieurs aspects de la reconstruction d'images TEP ont été explorés dans le présent travail. Les contributions suivantes sont d'objet de ce travail: Un modèle viable de la matrice de transition du système a été élaboré, utilisant la fonction de réponse analytique des détecteurs basée sur l'atténuation linéaire des rayons y dans un banc de détecteur. Nous avons aussi démontré que l'utilisation d'un modèle simplifié pour le calcul de la matrice du système conduit à des artefacts dans l'image. (IEEE Trans. Nucl. Sei., 2000) );> La modélisation analytique de la dépendance décrite à l'égard de la statistique des images a simplifié l'utilisation de la règle d'arrêt par contre-vérification (CV) et a permis d'accélérer la reconstruction statistique itérative. Cette règle peut être utilisée au lieu du procédé CV original pour des projections aux taux de comptage élevés, lorsque la règle CV produit des images raisonnablement précises. (IEEE Trans. Nucl. Sei., 2001) Nous avons proposé une méthodologie de régularisation utilisant la décomposition en valeur propre (DVP) de la matrice du système basée sur l'analyse de la résolution spatiale. L'analyse des caractéristiques du spectre de valeurs propres nous a permis d'identifier la relation qui existe entre le niveau optimal de troncation du spectre pour la reconstruction DVP et la résolution optimale dans l'image reconstruite. (IEEE Trans. Nucl. Sei., 2001) Nous avons proposé une nouvelle technique linéaire de reconstruction d'image événement-par-événement basée sur la matrice pseudo-inverse régularisée du système. L'algorithme représente une façon rapide de mettre à jour une image, potentiellement en temps réel, et permet, en principe, la visualisation instantanée de distribution de la radioactivité durant l'acquisition des données tomographiques. L'image ainsi calculée est la solution minimisant les moindres carrés du problème inverse régularisé.Abstract: Ill-posed problems are a topic of an interdisciplinary interest arising in remote sensing and non-invasive imaging. However, there are issues crucial for successful application of the theory to a given imaging modality. Positron emission tomography (PET) is a non-invasive imaging technique that allows assessing biochemical processes taking place in an organism in vivo. PET is a valuable tool in investigation of normal human or animal physiology, diagnosing and staging cancer, heart and brain disorders. PET is similar to other tomographie imaging techniques in many ways, but to reach its full potential and to extract maximum information from projection data, PET has to use accurate, yet practical, image reconstruction algorithms. Several topics related to PET image reconstruction have been explored in the present dissertation. The following contributions have been made: (1) A system matrix model has been developed using an analytic detector response function based on linear attenuation of [gamma]-rays in a detector array. It has been demonstrated that the use of an oversimplified system model for the computation of a system matrix results in image artefacts. (IEEE Trans. Nucl. Sci., 2000); (2) The dependence on total counts modelled analytically was used to simplify utilisation of the cross-validation (CV) stopping rule and accelerate statistical iterative reconstruction. It can be utilised instead of the original CV procedure for high-count projection data, when the CV yields reasonably accurate images. (IEEE Trans. Nucl. Sci., 2001); (3) A regularisation methodology employing singular value decomposition (SVD) of the system matrix was proposed based on the spatial resolution analysis. A characteristic property of the singular value spectrum shape was found that revealed a relationship between the optimal truncation level to be used with the truncated SVD reconstruction and the optimal reconstructed image resolution. (IEEE Trans. Nucl. Sci., 2001); (4) A novel event-by-event linear image reconstruction technique based on a regularised pseudo-inverse of the system matrix was proposed. The algorithm provides a fast way to update an image potentially in real time and allows, in principle, for the instant visualisation of the radioactivity distribution while the object is still being scanned. The computed image estimate is the minimum-norm least-squares solution of the regularised inverse problem

Positron emission tomography-based assessment of metabolic gradient and other prognostic features in sarcoma

Intratumoral heterogeneity biomarkers derived from positron emission tomography (PET) imaging with fluorodeoxyglucose (FDG) are of interest for a number of cancers, including sarcoma. A range of radiomic texture variables, adapted from general methodologies for image analysis, has shown promise in the setting. In the context of sarcoma, our group introduced an alternative model-based approach to the measurement of heterogeneity. In this approach, the heterogeneity of a tumor is characterized by the extent to which the 3-D FDG uptake pattern deviates from a simple elliptically contoured structure. By using a nonparametric analysis of the uptake profile obtained from this spatial model, a variable assessing the metabolic gradient of the tumor is developed. The work explores the prognostic potential of this new variable in the context of FDG-PET imaging of sarcoma. A mature clinical series involving 197 patients, 88 of whom have complete time-to-death information, is used. Texture variables based on the imaging data are also evaluated in this series and a range of appropriate machine learning methodologies are then used to explore the complementary prognostic roles for structure and texture variables. We conclude that both texture-based and model-based variables can be combined to achieve enhanced prognostic assessments of outcome for patients with sarcoma based on FDG-PET imaging information

Multimodality Quantitative Assessments of Myocardial Perfusion Using Dynamic Contrast Enhanced Magnetic Resonance and 15O-Labeled Water Positron Emission Tomography Imaging

Kinetic modeling of myocardial perfusion imaging data allows the absolute quantification of myocardial blood flow (MBF) and can improve the diagnosis and clinical assessment of coronary artery disease (CAD). Positron emission tomography (PET) imaging is considered the reference standard technique for absolute quantification, whilst oxygen-15 (15O)-water has been extensively implemented for MBF quantification. Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) has also been used for MBF quantification and showed comparable diagnostic performance against (¹⁵ O)-water PET studies. We investigated for the first time the diagnostic performance of two different PET MBF analysis softwares PMOD and Carimas, for obstructive CAD detection against invasive clinical standard methods in 20 patients with known or suspected CAD. Fermi and distributed parameter modeling-derived MBF quantification from DCE-MRI was also compared against (15O)-water PET, in a subgroup of six patients. The sensitivity and specificity for PMOD was significantly superior for obstructive CAD detection in both per vessel (0.83, 0.90) and per patient (0.86, 0.75) analysis, against Carimas (0.75, 0.65) and (0.81, 0.70), respectively. We showed strong, significant correlations between MR and PET MBF quantifications (r = 0.83 - 0.92). However, DP and PMOD analysis demonstrated comparable and higher hemodynamic differences between obstructive versus (no, minor, or non)-obstructive CAD, against Fermi and Carimas analysis. Our MR method assessments against the optimum PET reference standard technique for perfusion analysis showed promising results in per segment level and can support further multimodality assessments in larger patient cohorts. Further MR against PET assessments may help to determine their comparative diagnostic performance for obstructive CAD detection

Incorporating accurate statistical modeling in PET: reconstruction for whole-body imaging

Tese de doutoramento em Biofísica, apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2007The thesis is devoted to image reconstruction in 3D whole-body PET imaging. OSEM ( Ordered Subsets Expectation maximization ) is a statistical algorithm that assumes Poisson data. However, corrections for physical effects (attenuation, scattered and random coincidences) and detector efficiency remove the Poisson characteristics of these data. The Fourier Rebinning (FORE), that combines 3D imaging with fast 2D reconstructions, requires corrected data. Thus, if it will be used or whenever data are corrected prior to OSEM, the need to restore the Poisson-like characteristics is present. Restoring Poisson-like data, i.e., making the variance equal to the mean, was achieved through the use of weighted OSEM algorithms. One of them is the NECOSEM, relying on the NEC weighting transformation. The distinctive feature of this algorithm is the NEC multiplicative factor, defined as the ratio between the mean and the variance. With real clinical data this is critical, since there is only one value collected for each bin the data value itself. For simulated data, if we keep track of the values for these two statistical moments, the exact values for the NEC weights can be calculated. We have compared the performance of five different weighted algorithms (FORE+AWOSEM, FORE+NECOSEM, ANWOSEM3D, SPOSEM3D and NECOSEM3D) on the basis of tumor detectablity. The comparison was done for simulated and clinical data. In the former case an analytical simulator was used. This is the ideal situation, since all the weighting factors can be exactly determined. For comparing the performance of the algorithms, we used the Non-Prewhitening Matched Filter (NPWMF) numerical observer. With some knowledge obtained from the simulation study we proceeded to the reconstruction of clinical data. In that case, it was necessary to devise a strategy for estimating the NEC weighting factors. The comparison between reconstructed images was done by a physician largely familiar with whole-body PET imaging

Advanced perfusion quantification methods for dynamic PET and MRI data modelling

The functionality of tissues is guaranteed by the capillaries, which supply the microvascular network providing a considerable surface area for exchanges between blood and tissues. Microcirculation is affected by any pathological condition and any change in the blood supply can be used as a biomarker for the diagnosis of lesions and the optimization of the treatment. Nowadays, a number of techniques for the study of perfusion in vivo and in vitro are available. Among the several imaging modalities developed for the study of microcirculation, the analysis of the tissue kinetics of intravenously injected contrast agents or tracers is the most widely used technique. Tissue kinetics can be studied using different modalities: the positive enhancement of the signal in the computed tomography and in the ultrasound dynamic contrast enhancement imaging; T1-weighted MRI or the negative enhancement of T2* weighted MRI signal for the dynamic susceptibility contrast imaging or, finally, the uptake of radiolabelled tracers in dynamic PET imaging. Here we will focus on the perfusion quantification of dynamic PET and MRI data. The kinetics of the contrast agent (or the tracer) can be analysed visually, to define qualitative criteria but, traditionally, quantitative physiological parameters are extracted with the implementation of mathematical models. Serial measurements of the concentration of the tracer (or of the contrast agent) in the tissue of interest, together with the knowledge of an arterial input function, are necessary for the calculation of blood flow or perfusion rates from the wash-in and/or wash-out kinetic rate constants. The results depend on the acquisition conditions (type of imaging device, imaging mode, frequency and total duration of the acquisition), the type of contrast agent or tracer used, the data pre-processing (motion correction, attenuation correction, correction of the signal into concentration) and the data analysis method. As for the MRI, dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a non-invasive imaging technique that can be used to measure properties of tissue microvasculature. It is sensitive to differences in blood volume and vascular permeability that can be associated with tumour angiogenesis. DCE-MRI has been investigated for a range of clinical oncologic applications (breast, prostate, cervix, liver, lung, and rectum) including cancer detection, diagnosis, staging, and assessment of treatment response. Tumour microvascular measurements by DCE-MRI have been found to correlate with prognostic factors (such as tumour grade, microvessel density, and vascular endothelial growth factor expression) and with recurrence and survival outcomes. Furthermore, DCE-MRI changes measured during treatment have been shown to correlate with outcome, suggesting a role as a predictive marker. The accuracy of DCE-MRI relies on the ability to model the pharmacokinetics of an injected contrast agent using the signal intensity changes on sequential magnetic resonance images. DCE-MRI data are usually quantified with the application of the pharmacokinetic two-compartment Tofts model (also known as the standard model), which represents the system with the plasma and tissue (extravascular extracellular space) compartments and with the contrast reagent exchange rates between them. This model assumes a negligible contribution from the vascular space and considers the system in, what-is-known as, the fast exchange limit, assuming infinitely fast transcytolemmal water exchange kinetics. In general, the number, as well as any assumption about the compartments, depends on the properties of the contrast agent used (mainly gadolinium) together with the tissue physiology or pathology studied. For this reason, the choice of the model is crucial in the analysis of DCE-MRI data. The value of PET in clinical oncology has been demonstrated with studies in a variety of cancers including colorectal carcinomas, lung tumours, head and neck tumours, primary and metastatic brain tumours, breast carcinoma, lymphoma, melanoma, bone cancers, and other soft-tissue cancers. PET studies of tumours can be performed for several reasons including the quantification of tumour perfusion, the evaluation of tumour metabolism, the tracing of radiolabelled cytostatic agents. In particular, the kinetic analysis of PET imaging has showed, in the past few years, an increasing value in tumour diagnosis, as well as in tumour therapy, through providing additional indicative parameters. Many authors have showed the benefit of kinetic analysis of anticancer drugs after labelling with radionuclide in measuring the specific therapeutic effect bringing to light the feasibility of applying the kinetic analysis to the dynamic acquisition. Quantification methods can involve visual analysis together with compartmental modelling and can be applied to a wide range of different tracers. The increased glycolysis in the most malignancies makes 18F-FDG-PET the most common diagnostic method used in tumour imaging. But, PET metabolic alteration in the target tissue can depend by many other factors. For example, most types of cancer are characterized by increased choline transport and by the overexpression of choline kinase in highly proliferating cells in response to enhanced demand of phosphatidylcholine (prostate, breast, lung, ovarian and colon cancers). This effect can be diagnosed with choline-based tracers as the 18Ffluoromethylcholine (18F-FCH), or the even more stable 18F-D4-Choline. Cellular proliferation is also imaged with 18F-fluorothymidine (FLT), which is trapped within the cytosol after being mono phosphorylated by thymidine kinase-1 (TK1), a principal enzyme in the salvage pathway of DNA synthesis. 18F-FLT has been found to be useful for noninvasive assessment of the proliferation rate of several types of cancer and showed high reproducibility and accuracy in breast and lung cancer tumours. The aim of this thesis is the perfusion quantification of dynamic PET and MRI data of patients with lung, brain, liver, prostate and breast lesions with the application of advanced models. This study covers a wide range of imaging methods and applications, presenting a novel combination of MRI-based perfusion measures with PET kinetic modelling parameters in oncology. It assesses the applicability and stability of perfusion quantification methods, which are not currently used in the routine clinical practice. The main achievements of this work include: 1) the assessment of the stability of perfusion quantification of D4-Choline and 18F-FLT dynamic PET data in lung and liver lesions, respectively (first applications in the literature); 2) the development of a model selection in the analysis of DCE-MRI data of primary brain tumours (first application of the extended shutter speed model); 3) the multiparametric analysis of PET and MRI derived perfusion measurements of primary brain tumour and breast cancer together with the integration of immuohistochemical markers in the prediction of breast cancer subtype (analysis of data acquired on the hybrid PET/MRI scanner). The thesis is structured as follows: - Chapter 1 is an introductive chapter on cancer biology. Basic concepts, including the causes of cancer, cancer hallmarks, available cancer treatments, are described in this first chapter. Furthermore, there are basic concepts of brain, breast, prostate and lung cancers (which are the lesions that have been analysed in this work). - Chapter 2 is about Positron Emission Tomography. After a brief introduction on the basics of PET imaging, together with data acquisition and reconstruction methods, the chapter focuses on PET in the clinical settings. In particular, it shows the quantification techniques of static and dynamic PET data and my results of the application of graphical methods, spectral analysis and compartmental models on dynamic 18F-FDG, 18F-FLT and 18F-D4- Choline PET data of patients with breast, lung cancer and hepatocellular carcinoma. - Chapter 3 is about Magnetic Resonance Imaging. After a brief introduction on the basics of MRI, the chapter focuses on the quantification of perfusion weighted MRI data. In particular, it shows the pharmacokinetic models for the quantification of dynamic contrast enhanced MRI data and my results of the application of the Tofts, the extended Tofts, the shutter speed and the extended shutter speed models on a dataset of patients with brain glioma. - Chapter 4 introduces the multiparametric imaging techniques, in particular the combined PET/CT and the hybrid PET/MRI systems. The last part of the chapter shows the applications of perfusion quantification techniques on a multiparametric study of breast tumour patients, who simultaneously underwent DCE-MRI and 18F-FDG PET on a hybrid PET/MRI scanner. Then the results of a predictive study on the same dataset of breast tumour patients integrated with immunohistochemical markers. Furthermore, the results of a multiparametric study on DCE-MRI and 18F-FCM brain data acquired both on a PET/CT scanner and on an MR scanner, separately. Finally, it will show the application of kinetic analysis in a radiomic study of patients with prostate cancer

Quantitative PET-CT Perfusion Imaging of Prostate Cancer

Functional imaging of 18F-Fluorocholine PET holds promise in the detection of dominant prostatic lesions. Quantitative parameters from PET-CT Perfusion may be capable of measuring choline kinase activity, which could assist in identification of the dominant prostatic lesion for more accurate targeting of biopsies and radiation dose escalation. The objectives of this thesis are: 1) investigate the feasibility of using venous TACs in quantitative graphical analysis, and 2) develop and test a quantitative PET-CT Perfusion imaging technique that shows promise for identifying dominant prostatic lesions. Chapter 2 describes the effect of venous dispersion on distribution volume measurements with the Logan Plot. The dispersion of venous PET curves was simulated based on the arterio-venous transit time spectrum measured in a perfusion CT study of the human forearm. The analysis showed good agreement between distribution volume measurements produced by the arterial and venous TACs. Chapter 3 details the mathematical implementation of a linearized solution of the 3-Compartment kinetic model for hybrid PET-CT Perfusion imaging. A noise simulation determined the effect of incorporating CT perfusion parameters into the PET model on the accuracy and variability of measurements of the choline kinase activity. Results indicated that inclusion of CT perfusion parameters known a priori can significantly improve the accuracy and variability of imaging parameters measured with PET. Chapter 4 presents the implementation of PET-CT Perfusion imaging in a xenograft mouse model of human prostate cancer. Image-derived arterial TACs from the left ventricle were corrected for partial volume and spillover effects and validated by comparing to blood sampled curves. The PET-CT Perfusion imaging technique produced parametric maps of the choline kinase activity, k3. The results showed that the partial volume and spillover corrected arterial TACs agreed well with the blood sampled curves, and that k3max was significantly correlated with tumor volume, while SUV was not. In summary, this thesis establishes a solid foundation for future clinical research into 18F-fluorocholine PET imaging for the identification of dominant prostatic lesions. Quantitative PET-CT Perfusion imaging shows promise for assisting targeting of biopsy and radiation dose escalation of prostate cancer

Attenuation compensation in cerebral 3D PET: effect of the attenuation map on absolute and relative quantitation

It is generally well accepted that transmission (TX)-based non-uniform attenuation correction can supply more accurate absolute quantification; however, whether it provides additional benefits in routine clinical diagnosis based on qualitative interpretation of 3D brain positron emission tomography (PET) images is still the subject of debate. The aim of this study was to compare the effect of the two major classes of method for determining the attenuation map, i.e. uniform versus non-uniform, using clinical studies based on qualitative assessment as well as absolute and relative quantitative volume of interest-based analysis. We investigated the effect of six different methods for determining the patient-specific attenuation map. The first method, referred to as the uniform fit-ellipse method (UFEM), approximates the outline of the head by an ellipse assuming a constant linear attenuation factor (μ=0.096cm−1) for soft tissue. The second, referred to as the automated contour detection method (ACDM), estimates the outline of the head from the emission sinogram. Attenuation of the skull is accounted for by assuming a constant uniform skull thickness (0.45cm) within the estimated shape and the correct μ value (0.151cm−1) is used. The usual measured transmission method using caesium-137 single-photon sources was used without (MTM) and with segmentation of the TX data (STM). These techniques were finally compared with the segmented magnetic resonance imaging method (SMM) and an implementation of the inferring attenuation distributions method (IADM) based on the digital Zubal head atlas. Several image quality parameters were compared, including absolute and relative quantification indexes, and the correlation between them was checked. The qualitative evaluation showed no significant differences between the different attenuation correction techniques as assessed by expert physicians, with the exception of ACDM, which generated artefacts in the upper edges of the head. The mean squared error between the different attenuation maps was also larger when using this latter method owing to the fact that the current implementation of the method significantly overestimated the head contours on the external slices. Correlation between the mean regional cerebral glucose metabolism (rCGM) values obtained with the various attenuation correction methods and those obtained with the gold standard (MTM) was good, except in the case of ACDM (R 2=0.54). The STM and SMM methods showed the best correlation (R 2=0.90) and the regression lines agreed well with the line of identity. Relative differences in mean rCGM values were in general less than 8%. Nevertheless, ANOVA results showed statistically significant differences between the different methods for some regions of the brain. It is concluded that the attenuation map influences both absolute and relative quantitation in cerebral 3D PET. Transmission-less attenuation correction results in a reduced radiation dose and makes a dramatic difference in acquisition time, allowing increased patient throughpu