The aim of this thesis is to develop a study of numerical simulation finalized to optimize the use of PET imaging in dosimetry for hadron therapy applications. In particular, the analysis concentrated on the phenomenon of organ motion, which represents an important limitation to the accuracy of image reconstruction. Hadron therapy is a technique performed in oncology that is characterized by a particle beam (protons and carbon ions) extremely precise, selective and accurate. The interest towards this kind of therapy is constantly increasing because, unlike conventional radiotherapy, it allows to preserve healthy tissues and to concentrate the dose in proximity of the injured area, at any depth it is located. The high selectivity of hadron therapy requires the definition of an accurate treatment plan, therefore it becomes necessary the verification of the treatment administered. The definition of treatment plans starts with the acquisition of CT (Computed Tomography) images, on which the target lesion is identified. It is essential that the patient is placed inside the treatment room in a way that permits the localization of the target planned in the reference image. Afterwards, the treatment control is realized through PET imaging, a solution that allows to obtain an in-situ and non-invasive tridimensional monitoring of the dose application. The use of PET in dosimetry is allowed by the nuclear interactions between delivered particles and atomic nuclei of the tissues irradiated. The interaction of hadrons with the surrounding tissues determines the production of β+ positron, which constitute the base of PET imaging. The most utilized particles are protons and carbon ions; although the protons-nuclei interactions are halved with respect to the carbon ions-nuclei ones, both can be deployed in dosimetry. Interaction β+-electrons leads to annihilation, a phenomenon through which two γ photons are emitted with an energy of 511 KeV and an angle of 180°. Coincidence detectors that equip the PET scanner consent to identify the line along which the event of annihilation takes place, therefore the reconstructed PET image results correlated with the dose administered. PET with dosimetric purposes encompasses two different modalities: in-beam, that requires PET detectors inside the treatment room, and off-line, that is based on acquisitions made with hybrid scanners PET/CT immediately after the treatment. Nevertheless, PET in-beam generates a signal which is more intense and more correlated to the dose distribution. In PET acquisitions it is necessary to take into account the phenomenon of organ motion, as it determines a degradation of the spatial resolution of the reconstructed image. Organ motion can spread over a long time scale, namely between different treatment sessions, or along a short time scale, which means during the same treatment session (effect of physiological movements such as respiration). Movement artifacts induced by respiratory movements are much relevant in the thoracic abdominal district, and they cause blurring effects and loss of contrast due to the displacement of the radioactive emission source. To solve this problem PET acquisitions are realized according to the list mode, through which it is possible to divide the respiratory cycle of the patient in various temporal phases; PET acquisitions belonging to every phase of the cycle are then reorganized. The main problem related to this kind of acquisition is the loss of counting statistics. This can be overcome during the application of reconstruction algorithms, tools aimed at elaborating images associated to every phase of the respiratory cycle (acquired in list mode) to generate an image compensated for the movement. Reconstruction algorithms with movement compensation are based on the definition of a movement model that reproduces the deformation of every gate with respect to the reference gate. The movement model is generally obtained from CT acquisitions made by hybrid scanners PET/CT. The compensation for the movement can be applied either before or after, or during the reconstruction itself. “Post-reconstruction” optimization refers to the application of the movement model in the image domain, “intra-reconstruction” indicates that the optimization is contemporaneous with the reconstruction of the compensated image and “pre-reconstruction” consists in the application of the movement model in the sinogram domain. The novel algorithm taken into account in this thesis belongs to this category. Movement compensation in the image domain is based on the reconstruction of images associated with every gate; a reference image is then defined, and it is calculated a movement model that expresses the transformations to be applied to the image of each gate so that it can be superimposed to the reference image. In order to increase the counting statistics the images obtained from the operation of warping are eventually summed. Differently, algorithms applying the movement compensation in the sinogram domain are based on the application of the movement model to sinograms of each gate obtained with 4D PET. After the warping phase, sinogram are summed and a final sinogram compensated for the movement is generated. In literature this kind of optimization strategy is defined for rigid deformation only. The state of the art in the movement compensation in 4D PET comprehends an intra-reconstruction algorithm called 4D-MLEM. It consists in an iterative reconstruction algorithm that, at every iteration, applies a multiplicative update that is function of the estimation error of the sinogram of interest. It applies both direct and inverse deformation of every respiratory phase with respect to the reference phase. Although this method represents the best 4D PET optimization strategy, it is strongly affected by the inverse inconsistency of the registration with deformation: the application of direct deformation, followed by the inverse one, does not lead to the starting image. In this thesis it is generated a geometrical phantom characterized by low counting statistics and low spatial frequency content, in order to reproduce the typical features of dosimetry PET images and to evaluate the accuracy of the optimization strategy. These strategies are also applied to the anthropomorphic phantom 4D PET-CT NCAT, which is characterized by high counting statistics and high spatial content. In addition a Poisson’s noise is applied to the sinograms of both phantoms to evaluate the proposed strategies in different conditions of SNR (Signal Noise Ratio). In the simulations made with the dosimetry phantom the motion model is generated artificially, so that the deformation associated to each voxel of the image are defined along the three spatial directions. The deformation field (vector field) is defined according to two warping modalities: push-forward, which permits to obtain a direct deformation that defines the displacement to be applied to the fixed image (or reference image) to get the moving image, and pull-back, which provides an inverse deformation that defines the displacement to be applied to the moving image to get the fixed one. By definition, the direct deformation field represented by the push-forward warping coincides with the one represented by the pull-back warping. On the other hand the motion model of NCAT phantom is calculated starting from a registration with deformation of 4D CT images co-registered with PET images. In particular, it is derived from an open source software called Plastimatch, which implements a registration with deformation procedure and defines a vector field based on the pull-back warping method. Warping methods have been applied in the sinogram domain according to the point-based interpretation of the projection model, which defines the sinogram as a linear combination of point sinograms weighted by I_k coefficients. In PET images a point is defined as an emissive source whose dimensions are inferior or equal to the voxel. The activity of this emissive source should be sufficiently high to describe a sinusoidal line in the sinogram domain. On the basis of this correspondence, whose “duality” has been evaluated quantitatively, it has been formulated and developed the innovative “pre-reconstruction” optimization method. The geometric phantom is defined to compare results obtained with the pre-reconstruction warping strategy to those resulting from the application of 4D-MLEM algorithm, which is considered gold-standard in quantification. Pre-reconstruction strategy is based on the conversion of the motion model from the image domain to the sinogram domain, so that it is possible to apply vector fields directly to sinograms of interest. The vector field is applied to sinograms associated with breathing phases generated by acquisitions PET 4D. Deformed sinograms are then summed to gain a motion compensated sinogram, which are reconstructed according to the two reconstruction algorithms considered: SVD e MLEM. The conversion of motion model from the image domain to the sinogram domain generates an intrinsic error which determines a decay in the accuracy of the proposed strategy. The error is evaluated during the quantification of results through the generation of standard error matrices, that permit to quantify the error committed along each LOR in terms of displacement (pixels). This strategy is successively compared to 4D-MLEM algorithm, from which it has been preventively eliminated the issue of the inverse deformation inconsistency. For this reason 4D-MLEM can be considered the gold-standard of quantification. The deformation field is applied using the same vector field to calculate both direct deformation (warping push-forward) and inverse deformation (warping pull-back). However this procedure generates additional inconsistencies caused by the presence of holes and overlaps in the push-forward method, and inconsistencies due to the fact that pull-back method does not take into account the activity in the moving image (and does not guarantee the conservation of total activity during the warping). Quantification of results of the application of such strategies to the geometric phantom in different conditions of SNR generates comparable values, demonstrating that the strategy proposed can represent a valid alternative to 4D-MLEM method. Moreover, results achieved with the NCAT phantom are comparable, but it is necessary to consider that the application of the algorithms occurs in unfavorable conditions and that 4D-MLEM method is applied without eliminating the problem of the inverse inconsistency of the vector field. Results also highlight a high noise sensitivity of SVD reconstruction algorithm, demonstrating its scarce applicability in a real context. Furthermore, it is evaluated the “duality” of the vector field application in the image domain and in the sinogram domain, by implementing a post-reconstruction method in both domains according to the concept of point. The motion compensated image is obtained with the reconstruction algorithms MLEM and SVD, even if the latter reveals to be too sensitive to the Poisson’s noise level considered. The “duality” is demonstrated in low SNR conditions as well, showing the validity of the pre-reconstruction method hypothesis. Currently, pre-reconstruction strategies cause greater interest with respect to post-reconstruction ones, particularly in the context of 4D PET dosimetry in hadron therapy. The validation of the proposed pre-reconstruction strategy and 4D-MLEM in a real setup would consent to realize a comparison between the two, evaluating the degree of the different artifacts introduced by the methods. It is however necessary to keep in mind that 4D-MLEM introduces inaccuracies at each iteration, whereas pre-reconstruction strategy introduces them only when the algorithm is applied. For this reason it is reasonable expecting that, in a real context, pre-reconstruction method performances could be not only comparable, but even better than those of 4D-MLEM.
In questo lavoro di tesi è stato sviluppato uno studio di simulazione numerica, finalizzato all’ottimizzazione dell’utilizzo della PET a scopo dosimetrico per applicazioni di adroterapia. In particolare sono stati analizzati fenomeni di organ motion, che costituiscono un grande limite all’accuratezza della ricostruzione delle immagini. L’adroterapia è una tecnica impiegata in ambito oncologico, caratterizzata da un fascio di particelle (protoni e ioni carbonio) estremamente preciso, selettivo e accurato. L’interesse verso questo tipo di terapia è in continua crescita, in quanto a differenza della radioterapia convenzionale permette di preservare i tessuti sani e di concentrare la dose in prossimità della zona in cui è localizzata la lesione, a qualsiasi profondità essa si trovi. L’elevata selettività della terapia adronica rende indispensabile la definizione di un piano di trattamento accurato e di conseguenza, diventa auspicabile la verifica del trattamento somministrato. La definizione del piano di trattamento viene eseguita a partire dall’acquisizione di immagini CT (Computed Tomography), su cui si individua la lesione target della terapia. È indispensabile che il paziente venga posizionato all’interno della sala di trattamento, in modo tale da localizzare il target pianificato nell’immagine di riferimento. La verifica del trattamento viene poi effettuata attraverso l’utilizzo dell’imaging PET, che permette di realizzare un monitoraggio tridimensionale in situ non invasivo della dose somministrata. L’utilizzo della PET in dosimetria è reso possibile dalle interazioni nucleari tra i proiettili e i nuclei atomici dei tessuti. L’interazione delle particelle adroniche con i tessuti circostanti determina la produzione di positroni β+, che costituiscono la base del sistema di imaging PET. Le particelle adroniche più utilizzate sono i protoni e gli ioni carbonio; nonostante le interazioni protoni-nuclei siano due volte inferiori rispetto alle interazioni ioni carbonio-nuclei, entrambi possono essere impiegati a scopo dosimetrico. I positroni β+ interagiscono con gli elettroni e determinano il fenomeno dell’annichiliazione, in cui vengono emessi due fotoni γ aventi un angolo di 180° e un’energia pari a 511 KeV. I rilevatori posti in coincidenza di cui è provvisto lo scanner PET permettono di individuare la linea in cui si è verificato l’evento di annichilazione. L’immagine PET ricostruita risulta quindi correlata alla dose somministrata. La PET a scopo dosimetrico viene utilizzata secondo due diverse modalità: in-beam, che prevede la presenza dei rilevatori PET all’interno della sala di trattamento, e off-line, che si basa su acquisizioni effettuate con scanner ibridi PET/CT immediatamente dopo la somministrazione del trattamento. Tuttavia la PET in-beam genera un segnale più intenso e maggiormente correlato alla distribuzione della dose. Nelle acquisizioni PET è necessario tenere in considerazione il fenomeno di organ motion, in quanto determina un degrado della risoluzione spaziale dell’immagine ricostruita. L’organ motion si può verificare su una scala temporale lunga, cioè tra sessioni di trattamento differenti, o su una scala temporale breve, cioè all’interno della stessa sessione di trattamento (effetto di fenomeni fisiologici come la respirazione). Gli artefatti da movimento indotti da movimenti respiratori sono piuttosto rilevanti nel distretto toraco-addominale, e causano effetti di blurring e perdita di contrasto dovuti al movimento della sorgente di emissione radioattiva. Per risolvere tale problematica le acquisizioni PET vengono effettuate in modalità list mode, attraverso la quale è possibile suddividere il ciclo respiratorio del paziente in varie fasi temporali. Le acquisizioni PET relative a ogni fase del ciclo respiratorio vengono poi riordinate. La problematica principale legata a questo tipo di acquisizione è la perdita di statistica di conteggio. Tale problema può essere risolto in fase di applicazione degli algoritmi di ricostruzione, il cui scopo è la generazione di un’immagine compensata per il movimento a partire dalle immagini relative a ogni fase del ciclo respiratorio, acquisite in modalità list mode. Gli algoritmi di ricostruzione con compensazione per il movimento si basano sulla definizione di un modello di movimento che esprima la deformazione di ogni gate rispetto al gate di riferimento. Il modello di movimento generalmente viene ricavato a partire dalle acquisizioni CT effettuate dagli scanner ibridi PET/CT. La compensazione per il movimento può essere applicata sia prima che dopo, o contemporaneamente alla ricostruzione stessa. Si definisce ottimizzazione “post-ricostruzione” quando l’applicazione del modello di movimento avviene nel dominio immagine, “intra-ricostruzione” se contemporanea alla ricostruzione dell’immagine compensata per il movimento e si può definire “pre-ricostruzione” quando avviene nel dominio del sinogramma. A quest’ultima categoria appartiene l’algoritmo innovativo preso in considerazione in questo lavoro di tesi. La compensazione per il movimento nel dominio immagine si basa sulla ricostruzione delle immagini relative a ogni gate; si definisce un immagine di riferimento e si calcola un modello di movimento che esprima le trasformazioni da applicare all’immagine relativa a ogni gate affinché possa essere sovrapposta all’immagine di riferimento. Per aumentare la statistica di conteggio, le immagini risultanti dall’operazione di warping vengono poi sommate. Gli algoritmi che effettuano la compensazione per il movimento nel dominio sinogramma si basano invece sull’applicazione del modello di movimento ai sinogrammi relativi a ogni gate acquisito dalla 4D PET. Dopo la fase di warping si sommano i sinogrammi e si genera un sinogramma compensato per il movimento. In letteratura questo tipo di strategia di ottimizzazione è definita soltanto per deformazioni rigide. Allo stato dell’arte la compensazione per il movimento nella 4D PET viene effettuata da un algoritmo intra-ricostruzione definito 4D-MLEM. Si tratta di un algoritmo di ricostruzione iterativo che ad ogni iterazione applica un aggiornamento moltiplicativo funzione dell’errore di stima del sinogramma d’interesse, applicando la deformazione diretta e inversa di tutte le fasi respiratorie rispetto alla fase di riferimento ad ogni iterazione. Sebbene rappresenti la migliore strategia di ottimizzazione PET 4D, esso è pesantemente affetto dall’inconsistenza inversa della registrazione con deformazione: l’applicazione della deformazione diretta, seguita da quella inversa, non conduce all’immagine di partenza. In questo lavoro di tesi è stato generato un fantoccio geometrico costituito da una bassa statistica di conteggio e da un basso contenuto di frequenza spaziale, con lo scopo di simulare le caratteristiche tipiche delle immagini di dosimetria PET, e valutare l’accuratezza delle strategie di ottimizzazione proposte. Tali strategie sono state applicate anche al fantoccio antropomorfo 4D PET-CT NCAT, costituito da un’elevata statistica di conteggio e un elevato contenuto di frequenza spaziale. Ai sinogrammi di entrambi i fantocci è stato poi aggiunto un rumore di Poisson, con lo scopo di poter valutare le strategie proposte in differenti condizioni di SNR (Signal Noise Ratio). Nelle simulazioni effettuate con il fantoccio dosimetrico il modello di movimento è stato generato artificialmente, in modo tale da definire la deformazione associata a ogni singolo voxel dell’immagine lungo le tre direzioni. Il campo di deformazione (vector field) è stato definito secondo due modalità di warping: push-forward, che permette di ottenere una deformazione diretta che definisce lo spostamento da applicare all’immagine fixed (o di riferimento) per ottenere l’immagine moving, e pull-back, che permette di ottenere una deformazione inversa che definisce lo spostamento da applicare all’immagine moving per ottenere la fixed. Per definizione, il campo di deformazione diretto espresso secondo il push-forward coincide con il campo di deformazione espresso secondo il pull-back. Il modello di deformazione del fantoccio NCAT è stato invece calcolato a partire da una registrazione con deformazione di immagini 4D CT co-registrate con immagini PET. Esso viene ricavato attraverso il software open surce Plastimatch, che implementa una procedura di registrazione con deformazione definendo un vector field basato sul metodo di warping pull-back. I metodi di warping sono stati applicati nel dominio sinogramma, secondo l’interpretazione point-based del modello di proiezione, che definisce il sinogramma come la combinazione lineare di sinogrammi point pesati dai coefficienti I_k. Nelle immagini PET una point è definita come una sorgente emissiva di dimensioni inferiori o uguali alle dimensioni del voxel, la cui attività sia sufficientemente elevata da poter descrivere una linea sinusoidale nel dominio del sinogramma. Sulla base di questa corrispondenza, la cui “dualità” è stata valutata quantitativamente, è stato formulato e sviluppato l’innovativo metodo di ottimizzazione “pre-ricostruzione”. Il fantoccio geometrico è stato definito per confrontare i risultati ottenuti dalla strategia di warping pre-ricostruzione rispetto all’applicazione dell’algoritmo 4D-MLEM, gold-standard della quantificazione. La strategia pre-ricostruzione si basa sulla conversione del modello di movimento dal dominio immagine al dominio sinogramma, in modo tale da poter applicare i vector field direttamente ai sinogrammi d’interesse. Il vector field viene applicato ai sinogrammi relativi alle fasi respiratorie generati a partire da un’acquisizione PET 4D. I sinogrammi deformati vengono poi sommati per ottenere un sinogramma compensato per il movimento, che viene poi ricostruito in accordo ai due algoritmi di ricostruzione considerati: SVD e MLEM. La conversione del modello di movimento dal dominio immagine al dominio sinogramma genera però un errore intrinseco che determina un degrado dell’accuratezza della strategia proposta. Tale errore è stato valutato in fase di quantificazione dei risultati attraverso la generazione di matrici standard error, che permettono di quantificare l’errore commesso in corrispondenza di ogni LOR, in termini di spostamento (pixel). Tale strategia è stata poi confrontata all’algoritmo 4D-MLEM, da cui è stata preventivamente eliminata la problematica relativa all’inconsistenza della deformazione inversa. Per questo motivo la strategia 4D-MLEM può essere considerata gold-standard della quantificazione. Il campo di deformazione è stato applicato utilizzando lo stesso vector field per calcolare sia la deformazione diretta (warping push-forward) che la deformazione inversa (warping pull-back). Tuttavia questa procedura genera ulteriori inconsistenze dovute alla presenza di holes e overlaps nel metodo push-forward e inconsisenze dovute al fatto che il metodo pull-back non tiene in considerazione l’attività presente sull’immagine moving (e non garantisce la conservazione dell’attività totale durante il warping). La quantificazione dei risultati ottenuti dall’applicazione di tali strategie al fantoccio geometrico in differenti condizioni di SNR ha generato dei valori confrontabili, dimostrando che la strategia di warping pre-ricostruzione proposta può rappresentare una valida alternativa al metodo 4D-MLEM. Anche i risultati ottenuti nel fantoccio NCAT risultano confrontabili, ma bisogna tenere in considerazione che in questo caso l’applicazione degli algoritmi è avvenuta in condizioni sfavorevoli, e che il metodo 4D-MLEM è stato applicato senza eliminare il problema dell’inconsistenza in senso inverso del vector field. I risultati hanno inoltre evidenziato l’elevata sensibilità al rumore dell’algoritmo di ricostruzione SVD, dimostrando la scarsa applicabilità di tale algoritmo in un contesto reale. È stata valutata la “dualità” dell’applicazione del vector field nel dominio immagine e nel dominio sinogramma, implementando un metodo post-ricostruzione sia nel dominio immagine che nel dominio sinogramma, secondo il concetto di point. L’immagine compensata per il movimento è stata ottenuta in accordo agli algoritmi di ricostruzione MLEM e SVD, nonostante quest’ultimo si riveli ancora una volta troppo sensibile al livello di rumore di Poisson considerato. La dualità è stata dimostrata anche in condizioni di SNR molto sfavorevoli, comprovando la validità dell’ipotesi del metodo pre-ricostruzione. Le strategie pre-ricostruzione suscitano attualmente un maggior interesse rispetto ai metodi post-ricostruzione, specialmente nell’ambito della dosimetria PET 4D in adroterapia. La validazione in un contesto reale della strategia pre-ricostuzione proposta e del 4D-MLEM permetterebbe di realizzare un confronto tra tali metodi, valutando l’entità dei differenti artefatti introdotti da entrambi. È tuttavia necessario considerare che il 4D-MLEM introduce delle inaccuratezze ad ogni iterazione implementata, mentre la strategia pre-ricostruzione le introduce solo nel momento in cui viene applicato l’algoritmo. Per questo motivo è ragionevole aspettarsi che, in un contesto reale, le performance del metodo pre-ricostruzione proposto possano essere non solo comparabili, ma addirittura migliori rispetto all’algoritmo 4D-MLEM.
Ottimizzazione dell'imaging 4D PET : studio comparativo su simulazioni numeriche di dosimetria PET per il dose delivery control in adroterapia
CASANOVA, CLAUDIA
2010/2011
Abstract
The aim of this thesis is to develop a study of numerical simulation finalized to optimize the use of PET imaging in dosimetry for hadron therapy applications. In particular, the analysis concentrated on the phenomenon of organ motion, which represents an important limitation to the accuracy of image reconstruction. Hadron therapy is a technique performed in oncology that is characterized by a particle beam (protons and carbon ions) extremely precise, selective and accurate. The interest towards this kind of therapy is constantly increasing because, unlike conventional radiotherapy, it allows to preserve healthy tissues and to concentrate the dose in proximity of the injured area, at any depth it is located. The high selectivity of hadron therapy requires the definition of an accurate treatment plan, therefore it becomes necessary the verification of the treatment administered. The definition of treatment plans starts with the acquisition of CT (Computed Tomography) images, on which the target lesion is identified. It is essential that the patient is placed inside the treatment room in a way that permits the localization of the target planned in the reference image. Afterwards, the treatment control is realized through PET imaging, a solution that allows to obtain an in-situ and non-invasive tridimensional monitoring of the dose application. The use of PET in dosimetry is allowed by the nuclear interactions between delivered particles and atomic nuclei of the tissues irradiated. The interaction of hadrons with the surrounding tissues determines the production of β+ positron, which constitute the base of PET imaging. The most utilized particles are protons and carbon ions; although the protons-nuclei interactions are halved with respect to the carbon ions-nuclei ones, both can be deployed in dosimetry. Interaction β+-electrons leads to annihilation, a phenomenon through which two γ photons are emitted with an energy of 511 KeV and an angle of 180°. Coincidence detectors that equip the PET scanner consent to identify the line along which the event of annihilation takes place, therefore the reconstructed PET image results correlated with the dose administered. PET with dosimetric purposes encompasses two different modalities: in-beam, that requires PET detectors inside the treatment room, and off-line, that is based on acquisitions made with hybrid scanners PET/CT immediately after the treatment. Nevertheless, PET in-beam generates a signal which is more intense and more correlated to the dose distribution. In PET acquisitions it is necessary to take into account the phenomenon of organ motion, as it determines a degradation of the spatial resolution of the reconstructed image. Organ motion can spread over a long time scale, namely between different treatment sessions, or along a short time scale, which means during the same treatment session (effect of physiological movements such as respiration). Movement artifacts induced by respiratory movements are much relevant in the thoracic abdominal district, and they cause blurring effects and loss of contrast due to the displacement of the radioactive emission source. To solve this problem PET acquisitions are realized according to the list mode, through which it is possible to divide the respiratory cycle of the patient in various temporal phases; PET acquisitions belonging to every phase of the cycle are then reorganized. The main problem related to this kind of acquisition is the loss of counting statistics. This can be overcome during the application of reconstruction algorithms, tools aimed at elaborating images associated to every phase of the respiratory cycle (acquired in list mode) to generate an image compensated for the movement. Reconstruction algorithms with movement compensation are based on the definition of a movement model that reproduces the deformation of every gate with respect to the reference gate. The movement model is generally obtained from CT acquisitions made by hybrid scanners PET/CT. The compensation for the movement can be applied either before or after, or during the reconstruction itself. “Post-reconstruction” optimization refers to the application of the movement model in the image domain, “intra-reconstruction” indicates that the optimization is contemporaneous with the reconstruction of the compensated image and “pre-reconstruction” consists in the application of the movement model in the sinogram domain. The novel algorithm taken into account in this thesis belongs to this category. Movement compensation in the image domain is based on the reconstruction of images associated with every gate; a reference image is then defined, and it is calculated a movement model that expresses the transformations to be applied to the image of each gate so that it can be superimposed to the reference image. In order to increase the counting statistics the images obtained from the operation of warping are eventually summed. Differently, algorithms applying the movement compensation in the sinogram domain are based on the application of the movement model to sinograms of each gate obtained with 4D PET. After the warping phase, sinogram are summed and a final sinogram compensated for the movement is generated. In literature this kind of optimization strategy is defined for rigid deformation only. The state of the art in the movement compensation in 4D PET comprehends an intra-reconstruction algorithm called 4D-MLEM. It consists in an iterative reconstruction algorithm that, at every iteration, applies a multiplicative update that is function of the estimation error of the sinogram of interest. It applies both direct and inverse deformation of every respiratory phase with respect to the reference phase. Although this method represents the best 4D PET optimization strategy, it is strongly affected by the inverse inconsistency of the registration with deformation: the application of direct deformation, followed by the inverse one, does not lead to the starting image. In this thesis it is generated a geometrical phantom characterized by low counting statistics and low spatial frequency content, in order to reproduce the typical features of dosimetry PET images and to evaluate the accuracy of the optimization strategy. These strategies are also applied to the anthropomorphic phantom 4D PET-CT NCAT, which is characterized by high counting statistics and high spatial content. In addition a Poisson’s noise is applied to the sinograms of both phantoms to evaluate the proposed strategies in different conditions of SNR (Signal Noise Ratio). In the simulations made with the dosimetry phantom the motion model is generated artificially, so that the deformation associated to each voxel of the image are defined along the three spatial directions. The deformation field (vector field) is defined according to two warping modalities: push-forward, which permits to obtain a direct deformation that defines the displacement to be applied to the fixed image (or reference image) to get the moving image, and pull-back, which provides an inverse deformation that defines the displacement to be applied to the moving image to get the fixed one. By definition, the direct deformation field represented by the push-forward warping coincides with the one represented by the pull-back warping. On the other hand the motion model of NCAT phantom is calculated starting from a registration with deformation of 4D CT images co-registered with PET images. In particular, it is derived from an open source software called Plastimatch, which implements a registration with deformation procedure and defines a vector field based on the pull-back warping method. Warping methods have been applied in the sinogram domain according to the point-based interpretation of the projection model, which defines the sinogram as a linear combination of point sinograms weighted by I_k coefficients. In PET images a point is defined as an emissive source whose dimensions are inferior or equal to the voxel. The activity of this emissive source should be sufficiently high to describe a sinusoidal line in the sinogram domain. On the basis of this correspondence, whose “duality” has been evaluated quantitatively, it has been formulated and developed the innovative “pre-reconstruction” optimization method. The geometric phantom is defined to compare results obtained with the pre-reconstruction warping strategy to those resulting from the application of 4D-MLEM algorithm, which is considered gold-standard in quantification. Pre-reconstruction strategy is based on the conversion of the motion model from the image domain to the sinogram domain, so that it is possible to apply vector fields directly to sinograms of interest. The vector field is applied to sinograms associated with breathing phases generated by acquisitions PET 4D. Deformed sinograms are then summed to gain a motion compensated sinogram, which are reconstructed according to the two reconstruction algorithms considered: SVD e MLEM. The conversion of motion model from the image domain to the sinogram domain generates an intrinsic error which determines a decay in the accuracy of the proposed strategy. The error is evaluated during the quantification of results through the generation of standard error matrices, that permit to quantify the error committed along each LOR in terms of displacement (pixels). This strategy is successively compared to 4D-MLEM algorithm, from which it has been preventively eliminated the issue of the inverse deformation inconsistency. For this reason 4D-MLEM can be considered the gold-standard of quantification. The deformation field is applied using the same vector field to calculate both direct deformation (warping push-forward) and inverse deformation (warping pull-back). However this procedure generates additional inconsistencies caused by the presence of holes and overlaps in the push-forward method, and inconsistencies due to the fact that pull-back method does not take into account the activity in the moving image (and does not guarantee the conservation of total activity during the warping). Quantification of results of the application of such strategies to the geometric phantom in different conditions of SNR generates comparable values, demonstrating that the strategy proposed can represent a valid alternative to 4D-MLEM method. Moreover, results achieved with the NCAT phantom are comparable, but it is necessary to consider that the application of the algorithms occurs in unfavorable conditions and that 4D-MLEM method is applied without eliminating the problem of the inverse inconsistency of the vector field. Results also highlight a high noise sensitivity of SVD reconstruction algorithm, demonstrating its scarce applicability in a real context. Furthermore, it is evaluated the “duality” of the vector field application in the image domain and in the sinogram domain, by implementing a post-reconstruction method in both domains according to the concept of point. The motion compensated image is obtained with the reconstruction algorithms MLEM and SVD, even if the latter reveals to be too sensitive to the Poisson’s noise level considered. The “duality” is demonstrated in low SNR conditions as well, showing the validity of the pre-reconstruction method hypothesis. Currently, pre-reconstruction strategies cause greater interest with respect to post-reconstruction ones, particularly in the context of 4D PET dosimetry in hadron therapy. The validation of the proposed pre-reconstruction strategy and 4D-MLEM in a real setup would consent to realize a comparison between the two, evaluating the degree of the different artifacts introduced by the methods. It is however necessary to keep in mind that 4D-MLEM introduces inaccuracies at each iteration, whereas pre-reconstruction strategy introduces them only when the algorithm is applied. For this reason it is reasonable expecting that, in a real context, pre-reconstruction method performances could be not only comparable, but even better than those of 4D-MLEM.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/47101