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Contributions to quantitative dynamic contrast-enhanced MRIGarpebring, Anders January 2011 (has links)
Background: Dynamic contrast-enhanced MRI (DCE-MRI) has the potential to produce images of physiological quantities such as blood flow, blood vessel volume fraction, and blood vessel permeability. Such information is highly valuable, e.g., in oncology. The focus of this work was to improve the quantitative aspects of DCE-MRI in terms of better understanding of error sources and their effect on estimated physiological quantities. Methods: Firstly, a novel parameter estimation algorithm was developed to overcome a problem with sensitivity to the initial guess in parameter estimation with a specific pharmacokinetic model. Secondly, the accuracy of the arterial input function (AIF), i.e., the estimated arterial blood contrast agent concentration, was evaluated in a phantom environment for a standard magnitude-based AIF method commonly used in vivo. The accuracy was also evaluated in vivo for a phase-based method that has previously shown very promising results in phantoms and in animal studies. Finally, a method was developed for estimation of uncertainties in the estimated physiological quantities. Results: The new parameter estimation algorithm enabled significantly faster parameter estimation, thus making it more feasible to obtain blood flow and permeability maps from a DCE-MRI study. The evaluation of the AIF measurements revealed that inflow effects and non-ideal radiofrequency spoiling seriously degrade magnitude-based AIFs and that proper slice placement and improved signal models can reduce this effect. It was also shown that phase-based AIFs can be a feasible alternative provided that the observed difficulties in quantifying low concentrations can be resolved. The uncertainty estimation method was able to accurately quantify how a variety of different errors propagate to uncertainty in the estimated physiological quantities. Conclusion: This work contributes to a better understanding of parameter estimation and AIF quantification in DCE-MRI. The proposed uncertainty estimation method can be used to efficiently calculate uncertainties in the parametric maps obtained in DCE-MRI.
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Modelování v perfusním MR zobrazování / Modelling in perfusion MR imagingVálková, Hana January 2014 (has links)
This thesis deals with the magnetic resonance perfusion data analysis especially DCEMRI. In its introduction the thesis describes the problem of DCE-MRI data aquisition, the necessity of appropriate contrast agent and basic principles of perfusion analysis. The dynamic behavior of contrast agent vascular distribution can be described by arterial input function (AIF). The shape of the curves close to the area of interest is affected by dispersion which is called vascular transport function (VTF) due to the distribution of the contrast agent to the region of interest. Finally the tissue residual function describes system behavior of tissue. The practical part of the diploma thesis is aimed at implementation of model curves AIF, VTF and TRF. Furthermore, a simulation program was created for easy manipulation with introduced models moreover the program is used to perform an estimation of perfusion parameters based on nonblind deconvolution. The method is validated on synthetic data and illustrated on clinical data of the renal cell carcinoma patient.
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Estimation de la fonction d’entrée en tomographie par émission de positons dynamique : application au fluorodesoxyglucose / Estimation of the input function in dynamic positron emission tomography applied to fluorodeoxyglucoseJouvie, Camille 06 December 2013 (has links)
La tomographie par émission de positons (TEP) est une méthode d’imagerie fonctionnelle, utilisée en particulier lors du développement de nouveaux médicaments et pour imager les tumeurs. En TEP, l’estimation de la concentration plasmatique artérielle d’activité du traceur non métabolisé (nommée « fonction d’entrée ») est nécessaire pour l’extraction des paramètres pharmacocinétiques. Ceux-ci permettent de quantifier le comportement du traceur dans les tissus, ou plus précisément le traitement du traceur par les tissus. Cette thèse constitue une contribution à l’étude de la fonction d’entrée, par l’élaboration d’une méthode d’estimation de la fonction d’entrée peu invasive à partir des images TEP et de prélèvements veineux. L’exemple du traceur FDG (analogue du glucose) dans le cerveau humain a été choisi. La méthode proposée repose sur la modélisation compartimentale de l’organisme : elle déconvolue le modèle à trois compartiments utilisé pour le FDG. L’originalité de la méthode repose sur trois points : l’utilisation d’un grand nombre de régions d’intérêt ; l’utilisation d’un grand nombre de jeux de trois régions d’intérêt différentes; une estimation itérative. Pour la validation de la méthode, un soin particulier a été porté à la simulation d’images TEP (simulation d’acquisition, reconstruction, corrections) de plus en plus réalistes, depuis une image simple simulée avec un simulateur analytique jusqu’à une image la plus proche possible de la réalité, simulée avec simulateur Monte-Carlo. Une chaîne de pré-traitement (segmentation des IRM associés, recalage entre images TEP et IRM et correction de l’effet de volume partiel par une variante de la méthode de Rousset) a ensuite été appliquée à ces images afin d’extraire les cinétiques des régions d’intérêt, données d’entrée de la méthode d’estimation de la fonction d’entrée. L’évaluation de la méthode sur différentes données, simulées et réelles, est présentée, ainsi que l’étude de la sensibilité de la méthode à différents facteurs tels que les erreurs de segmentation, de recalage, de mesure de l’activité des prélèvements sanguins. / Positron Emission Tomography (PET) is a method of functional imaging, used in particular for drug development and tumor imaging. In PET, the estimation of the arterial plasmatic activity concentration of the non-metabolized compound (the "input function") is necessary for the extraction of the pharmacokinetic parameters. These parameters enable the quantification of the compound dynamics in the tissues. This PhD thesis contributes to the study of the input function by the development of a minimally invasive method to estimate the input function. This method uses the PET image and a few blood samples. In this work, the example of the FDG tracer is chosen. The proposed method relies on compartmental modeling: it deconvoluates the three-compartment-model. The originality of the method consists in using a large number of regions of interest (ROIs), a large number of sets of three ROIs, and an iterative process. To validate the method, simulations of PET images of increasing complexity have been performed, from a simple image simulated with an analytic simulator to a complex image simulated with a Monte-Carlo simulator. After simulation of the acquisition, reconstruction and corrections, the images were segmented (through segmentation of an IRM image and registration between PET and IRM images) and corrected for partial volume effect by a variant of Rousset’s method, to obtain the kinetics in the ROIs, which are the input data of the estimation method. The evaluation of the method on simulated and real data is presented, as well as a study of the method robustness to different error sources, for example in the segmentation, in the registration or in the activity of the used blood samples.
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Feasibility Study of Phase Measurements of the Arterial Input Function in Dynamic Contrast Enhanced MRIMarklund, Sandra January 2009 (has links)
<p> </p><p>Acquired data from dynamic contrast enhanced MRI measurements can be used to non-invasively assess tumour vascular characteristics through pharmacokinetic modelling. The modelling requires an arterial input function which is the concentration of contrast agent in the blood reaching the volume of interest as a function of time. The aim of this work is testing and optimizing a turboFLASH sequence to appraise its suitability for measuring the arterial input function by measuring phase.</p><p>Contrast concentration measurements in a phantom were done with both phase and relaxivity techniques. The results were compared to simulations of the experiment conditions to compare the conformance. The results using the phase technique were promising, and the method was carried on to in-vivo testing. The in-vivo data displayed a large signal loss which motivated a new phantom experiment to examine the cause of this signal reduction. Dynamic measurements were made in a phantom with pulsatile flow to mimic a blood vessel with a somewhat modified turboFLASH sequence. The conclusions drawn from analyzing the data were used to further improve the sequence and this modified turboFLASH sequence was tested in an in-vivo experiment. The obtained concentration curve showed significant improvement and was deemed to be a good representation of the true blood concentration.</p><p>The conclusion is that phase measurements can be recommended over relaxivity based measurements. This recommendation holds for using a slice selective saturation recovery turboFLASH sequence and measuring the arterial input function in the neck. Other areas of application need more thorough testing.</p><p> </p>
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Feasibility Study of Phase Measurements of the Arterial Input Function in Dynamic Contrast Enhanced MRIMarklund, Sandra January 2009 (has links)
Acquired data from dynamic contrast enhanced MRI measurements can be used to non-invasively assess tumour vascular characteristics through pharmacokinetic modelling. The modelling requires an arterial input function which is the concentration of contrast agent in the blood reaching the volume of interest as a function of time. The aim of this work is testing and optimizing a turboFLASH sequence to appraise its suitability for measuring the arterial input function by measuring phase. Contrast concentration measurements in a phantom were done with both phase and relaxivity techniques. The results were compared to simulations of the experiment conditions to compare the conformance. The results using the phase technique were promising, and the method was carried on to in-vivo testing. The in-vivo data displayed a large signal loss which motivated a new phantom experiment to examine the cause of this signal reduction. Dynamic measurements were made in a phantom with pulsatile flow to mimic a blood vessel with a somewhat modified turboFLASH sequence. The conclusions drawn from analyzing the data were used to further improve the sequence and this modified turboFLASH sequence was tested in an in-vivo experiment. The obtained concentration curve showed significant improvement and was deemed to be a good representation of the true blood concentration. The conclusion is that phase measurements can be recommended over relaxivity based measurements. This recommendation holds for using a slice selective saturation recovery turboFLASH sequence and measuring the arterial input function in the neck. Other areas of application need more thorough testing.
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Modelování a analýza signálů v zobrazování perfúze magnetickou rezonancí / Modeling and Signal Processing in Dynamic Contrast Enhanced Magnetic Resonance ImagingKratochvíla, Jiří January 2018 (has links)
The theoretical part of this work describes perfusion analysis of dynamic contrast enhanced magnetic resonance imaging from data acquisition to estimation of perfusion parameters. The main application fields are oncology, cardiology and neurology. The thesis is focused on quantitative perfusion analysis, specifically it contributes to solving of the the main challenge of this method – correct estimation of the contrast-agent concentration sequence in the arterial input of the region of interest (arterial input function). The goals of the thesis are stated based on literature review and on the expertise of our group. Blind deconvolution is selected as the method of choice. In the practical part of this thesis, a new method for arterial input function identification based on blind deconvolution is proposed. The method is designed for both preclinical and clinical applications. It was validated on synthetic, preclinical and clinical data. Furthermore, possibilities of the longer temporal sampling provided by blind deconvolution were analyzed. This can be used for improved spatial resolution and possibly for higher SNR. For easier deployment of the proposed methods into clinical and preclinical use, a software tool for perfusion data processing was designed.
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PHARMACOKINETIC MODELING OF DYNAMIC MR IMAGING IN THE KNEE OF CHILDREN WITH JUVENILE RHEUMATOID ARTHRITISWORKIE, DAGNACHEW WALELIGN 14 July 2005 (has links)
No description available.
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Quantification of cerebral blood flow with 15O-water PET : A comparison study between PET/CT and PET/MR and two different blood sampling instrumentsEriksson, Amanda January 2021 (has links)
Cerebral blood flow quantification is a vital diagnostic tool for disease monitoring and used for diagnosing a variation of pathological conditions. The human brain requires roughly about 20 % of the total cardiac output to sustain normal functioning, hence the perfusion of blood is an important factor to deliver oxygenated blood. The golden standard for quantifying the cerebral blood flow follows by measurement with dynamic positron emission tomography of 15O-labelled water modelled by tracer kinetic compartments. For implementation, knowledge of an input function must exist which is in general being sampled through arterial cannulation of the radial artery with a continuous sampling instrument. The core of this thesis is to establish if two sampling instruments contradicts in comparison to each other when sampling the data to the input function. In total 22 subjects underwent a 10-minute dynamic 15O-labeled water brain PET scan on two imaging modalities PET/CT and PET/MR. Continuous arterial sampling was performed either by a Veenstra on PET/CT or a Swisstrace on PET/MR during a baseline scan. In two subjects the two sampling instruments were coupled in series and imaged solely on the PET/CT. Cerebral blood flow analysis was done comparing varying dispersion times, the two imaging modalities compared each other and comparing the calculated and measured blood flows obtained through this study with the values obtained prior. To be able to compare the values showing inconsistency to the values obtained through this thesis, a comparison between two different iterative reconstruction methods was done. Here the method of ordered subsets expectation maximum was compared to a Bayesian penalized-likelihood method. To further compare the two sampling instruments an image derived input function was constructed and compared with the blood sampled input function. The results showed that there was no significant difference between measured cerebral blood flow between the two imaging modalities with the currently used reconstruction method based on Bayesian penalized likelihood but presented in the earlier data there was an inconsistency. A dispersion analysis with variation on the external dispersion time shows that if the time was chosen to low or to high compared to the standard time used it introduced distorted fitted models of the activity curves. This distortion creates further errors in the calculation of the cerebral blood flow, however with the analysis the standard dispersion time could be confirmed as an accurate fit. Subjects imaged with the two sampling instruments in series showed no significant difference except for the measured values on Veenstra to be slightly higher. Lastly the correlation between the image derived input function and the blood sampled input function showed poorly performance. Only a R2 value of 0.42 was achieved on the PET/CT while a meagre R2 value of 0.18 was achieved on the PET/MR. Although the correlation was poorly, the plotted activity curves from the two functions showed a representable appearance between each other. / Kvantifiering av det cerebrala blodflödet är ett nödvändigt diagnostiskt verktyg som används för att kontrollera och diagnostisera en variation av patologiska sjukdomstillstånd. Den mänskliga hjärnan kräver kring 20 %av den totala produktionen från hjärtat för att upprätthålla normal funktion, följaktligen är perfusion av blod en viktig faktor för att distribuera syrerikt blod runt om i kroppen. Den gyllene standarden för kvantifiering av det cerebrala blodflödet följer som undersökning med dynamisk positron emission tomografi av 15O-märkt vatten, modellerat med kinetisk kompartment teori. För att kunna implementera detta måste information om en input-funktion erhållas, generellt erhålls detta genom att blod tags genom arteriell kanylering av antingen den radiella artären med ett kontinuerligt samplings instrument. Målet med detta arbete är att fastställa om två samplings instrument motsäger varandra vid mätning av data till input-funktionen. Totalt deltagande är 22 patienter som genomgick en 10-minuters dynamisk 15O-märkt vatten PET undersökning av hjärnan på två bildtagningsmodaliteter PET/CT och PET/MR. Kontinuerlig blodtagning genomfördes antingen med en Veenstra sampler instrument på PET/CT eller en Swisstrace sampler instrument på PET/MR tillsammans med en baseline undersökning. Vid två undersökningar seriekopplades de två instrumenten och patienterna blev endast undersökta vid PET/CT. För ytterligare kunna utvärdera de två instrumenten, konstruerades en bild framtagen input-funktion som sedan kunde jämföras med den blod samplade input-funktionen. Cerebrala blodflödes analyser gjordes med olika dispersions tider, även för att kunna jämföra de två bildtagningsmodaliteterna mot varandra och jämföra erhållna värden framtagna under denna studie med en tidigare studie. För att kunna jämföra avvikelserna i de uppmätta värdena har även två olika rekonstruerings metoder studerats. Resultaten visar ingen signifikant skillnad mellan de uppmätta cerebrala blodflödena mellan de två bildtagningsmodaliteterna rekonstruerade med den nuvarande standarden. Dispersions analysen med varierande extern dispersions tid visar att om tiden är för kort eller för lång jämfört med standardtiden, introduceras en osann anpassning av aktivitets kurvorna. Denna förvrängning av datat resulterar till fler avvikelser i beräkningarna av blodflödet, likväl var det möjligt att bekräfta standardtiderna som används. Patienter som undersöktes med instrumenten i seriekoppling visade ingen signifikant skillnad förutom att det uppmättes en aningens högre värden hos patienter med Veenstra som blod sampler. Slutligen, korrelationen mellan den bild framtagna input-funktionen och den blod samplade input-funktionen visade ett dåligt resultat. Endast ett R2 värde på 0.42 erhölls för PET/CT medan endast ett R2 värde på 0.18 på PET/MR erhölls. Trotts att korrelationen var dålig, visade de plottade aktivitets kurvorna ett representativt utseende mellan de två typerna av input funktion.
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IRM de perfusion T1 dans le cancer de la prostate, analyse quantitative et étude de l’impact de la fonction d’entrée artérielle sur les capacités diagnostiques des paramètres pharmacocinétiques / Dynamic Contrast Enhanced - MRI of prostate cancer : quantitative analysis and study of the impact of arterial input function selection on the diagnosis accuracy of the pharmacokinetic parametersAzahaf, Mustapha 15 December 2015 (has links)
La séquence d’IRM de perfusion pondérée T1 après injection de Gadolinium (Gd), appelée dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) fait partie du protocole d’IRM multiparamétrique (IRM-mp) réalisée pour le bilan d’extension du cancer prostatique (CaP). Le rationnel pour l’utilisation de cette séquence est d’une part le rôle capital de la néoangiogénèse dans le développement et la dissémination du CaP et d’autre part la possibilité d’imager l’angiogénèse in vivo et de façon non invasive. L’analyse quantitative nécessite un post-traitement multi-étapes complexe, dont le principe repose sur la modélisation pharmacocinétique (PC) de la biodistrubtion du Gd. Elle permet de calculer des paramètres PC reflétant la perméabilité capillaire et/ou la perfusion. Dans le CaP, ces paramètres PC ont montré leur potentiel pour évaluer l’agressivité tumorale, le pronostic, l’efficacité d’un traitement et/ou pour déterminer la dose efficace d’une nouvelle molécule anti-angiogéniques ou antivasculaires en cours de développement. Néanmoins, ils manquent de reproductibilité, notamment du fait des différentes techniques de quantifications utilisées par les logiciels de post-traitement.Nous avons développé au sein du laboratoire un outil de quantification capable de calculer une cartographie T1(0) à partir de la méthode des angles de bascule variables, nécessaire pour convertir les courbes du signal en courbe de concentration du Gd (Ct); de déterminer la fonction d’entrée artérielle (AIF – arterial input function) dans l’artère fémorale (Indivuduelle – Ind) ou lorsque cela n’était pas possible, d’utiliser une AIF issue de la littérature, telle que celle de Weinmann (W) ou de Fritz-Hansen (FH) ; et d’utiliser deux modèles PC, celui de Tofts et celui de Tofts modifié. Le logiciel a été validé sur des données simulées et sur une petite série clinique.Nous avons ensuite étudié l’impact du choix de la fonction d’entrée artériel sur les paramètres PC et notamment sur leur capacité à distinguer le CaP du tissu sain. 38 patients avec un CaP (>0,5cc) de la zone périphérique (ZP) ont été rétrospectivement inclus. Chaque patient avait bénéficié d’une IRM-mp sur laquelle deux régions d’intérêt (RI) : une tumorale et une bénigne ont été sélectionnées en utilisant une corrélation avec des cartes histo-morphométriques obtenues après prostatectomie radicale. En utilisant trois logiciels d’analyse quantitative différents, les valeurs moyennes de Ktrans (constante de transfert), ve (fraction du volume interstitiel) and vp (fraction du volume plasmatique) dans les RI ont été calculées avec trois AIF différentes (AIF Ind, AIF de W et AIF de FH). Ktrans était le paramètre PC qui permettait de mieux distinguer le CaP du tissu sain et ses valeurs étaient significativement supérieures dans le CaP, quelque soit l’AIF ou le logiciel. L’AIF de W donnait des aires sous les courbes ROC (Receiver Operating Characteristic) significativement plus grandes que l’AIF de FH (0.002≤p≤0.045) et plus grandes ou égales à l’AIF Ind (0.014≤p≤0.9). L’AIF Ind et de FH avaient des aires sous les courbes ROC comparables (0.34≤p≤0.81). Nous avons donc montré que les valeurs de Ktrans et sa capacité à distinguer CaP du tissu sain variaient significativement avec le choix de l’AIF et que les meilleures performances étaient obtenues avec l’AIF de W. / Dynamic contrast enhanced (DCE)-MRI is a T1 weighted sequence performed before, during and after a bolus injection of a contrast agent (CA). It is included in the multi-parametric prostate MRI (mp-MRI) protocol using to assess the extent of prostate cancer (PCa). The rationale for using DCE-MRI in PCa is that on one hand angiogenesis has been shown to play a central role in the PCa development and metastasis and on the other hand that DCE-MRI is a non invasive method able to depict this angiogenesis in vivo. The quantitative analysis of DCE-MRI data is a complex and multi-step process. The principle is to use a pharmacokinetic (PK) model reflecting the theoretical distribution of the CA in a tissue to extract PK parameters that describe the perfusion and capillary permeability. These parameters are of growing interest, especially in the field of oncology, for their use in assessing the aggressiveness, the prognosis and the efficacy of anti-angiogenic or anti-vascular treatments. The potential utility of these parameters is significant; however, the parameters often lack reproducibility, particularly between different quantitative analysis software programs.Firstly, we developed a quantitative analysis software solution using the variable flip angle method to estimate the T1 mapping which is needed to convert the signal-time curves to CA concentration-time curves; using three different arterial input functions (AIF): an individual AIF (Ind) measured manually in a large artery, and two literature population average AIFs of Weinmann (W) and of Fritz-Hansen (FH); and using two PK models (Tofts and modified Tofts). The robustness of the software programs was assessed on synthetic DCE-MRI data set and on a clinical DCE-MRI data set. Secondly, we assessed the impact of the AIF selection on the PK parameters to distinguish PCa from benign tissue. 38 patients with clinically important peripheral PCa (≥0.5cc) were retrospectively included. These patients underwent 1.5T multiparametric prostate MR with PCa and benign regions of interest (ROI) selected using a visual registration with morphometric reconstruction obtained from radical prostatectomy. Using three pharmacokinetic (PK) analysis software programs, the mean Ktrans, ve and vp of ROIs were computed using three AIFs: Ind-AIF, W-AIF and FH-AIF. The Ktrans provided higher area under the receiver operating characteristic curves (AUROCC) than ve and vp. The Ktrans was significantly higher in the PCa ROIs than in the benign ROIs. AUROCCs obtained with W-AIF were significantly higher than FH-AIF (0.002≤p≤0.045) and similar to or higher than Ind-AIF (0.014≤p≤0.9). Ind-AIF and FH-AIF provided similar AUROCC (0.34≤p≤0.81).We have then demonstrated that the selection of AIF can modify the capacity of the PK parameter Ktrans to distinguish PCa from benign tissue and that W-AIF yielded a similar or higher performance than Ind-AIF and a higher performance than FH-AIF.
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Etude de faisabilité de l'estimation non-invasive de la fonction d'entrée artérielle B+ pour l'imagerie TEP chez l'homme / Feasibility study of the non-invasive estimation of the b+ arterial input function for human PET imagingHubert, Xavier 08 December 2009 (has links)
Cette thèse traite de l'estimation de la concentration dans le sang artériel de molécules marquées par un radioélément émettant des positons. Cette concentration est appelée « fonction d'entrée artérielle B+ ». Elle doit être déterminée dans de nombreuses analyses en pharmacocinétique. Actuellement, elle est mesurée à l'aide d'une série de prélèvements artériels, méthode précise mais nécessitant un protocole contraignant. Des complications liées au caractère invasif de la méthode peuvent survenir (hématomes, infections nosocomiales).L'objectif de cette thèse est de s'affranchir de ses prélèvements artériels par l'estimation non-invasive de la fonction d'entrée B+ à l'aide d'un détecteur externe et d'un collimateur. Cela permet la reconstruction des vaisseaux sanguins afin de discriminer le signal artériel du signal contenu dans les autres tissus avoisinants. Les collimateurs utilisés en imagerie médicale ne sont pas adaptés à l'estimation de la fonction d'entrée artérielle B+ car leur sensibilité est très faible. Pour cette thèse, ils sont remplacés par des collimateurs codés, issus de la recherche en astronomie. De nouvelles méthodes pour utiliser des collimateurs à ouverture codée avec des algorithmes statistiques de reconstruction sont présentées.Des techniques de lancer de rayons et une méthode d'accélération de la convergence des reconstructions sont proposées. Une méthode de décomposition spatio-temporelle est également mise au point pour estimer efficacement la fonction d'entrée artérielle à partir d'une série d'acquisitions temporelles.Cette thèse montre qu'il est possible d'améliorer le compromis entre sensibilité et résolution spatiale en tomographie d'émission à l'aide de masques codés et d'algorithmes statistiques de reconstruction ; elle fournit également les outils nécessaires à la réalisation de tellesreconstructions. / This work deals with the estimation of the concentration of molecules in arterial blood which are labelled with positron-emitting radioelements. This concentration is called “ B+ arterial input function”. This concentration has to be estimated for a large number of pharmacokinetic analyses. Nowadays it is measured through series of arterial sampling, which is an accurate method but requiring a stringent protocol. Complications might occur during arterial blood sampling because this method is invasive (hematomes, nosocomial infections).The objective of this work is to overcome this risk through a non-invasive estimation of B+ input function with an external detector and a collimator. This allows the reconstruction of blood vessels and thus the discrimination of arterial signal from signals in other tissues.Collimators in medical imaging are not adapted to estimate B+ input function because their sensitivity is very low. During this work, they are replaced by coded-aperture collimators, originally developed for astronomy.New methods where coded apertures are used with statistical reconstruction algorithms are presented. Techniques for analytical ray-tracing and for the acceleration of reconstructions are proposed. A new method which decomposes reconstructions on temporal sets and on spatial sets is also developped to efficiently estimate arterial input function from series of temporal acquisitions.This work demonstrates that the trade-off between sensitivity and spatial resolution in PET can be improved thanks to coded aperture collimators and statistical reconstruction algorithm; it also provides new tools to implement such improvements.
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