STIR: software for tomographic image reconstruction release 2

We present a new version of STIR (Software for Tomographic Image Reconstruction), an open source object-oriented library implemented in C++ for 3D positron emission tomography reconstruction. This library has been designed such that it can be used for many algorithms and scanner geometries, while being portable to various computing platforms. This second release enhances its flexibility and modular design and includes additional features such as Compton scatter simulation, an additional iterative reconstruction algorithm and parametric image reconstruction (both indirect and direct). We discuss the new features in this release and present example results. STIR can be downloaded from http://stir.sourceforge.net

Expectation maximization (EM) algorithms using polar symmetriesfor computed tomography(CT) image reconstruction

We suggest a symmetric-polar pixellation scheme which makes possible a reduction of the computational cost for expectation maximization (EM) iterative algorithms. The proposed symmetric-polar pixellation allows us to deal with 3D images as a whole problem without dividing the 3D problem into 2D slices approach. Performance evaluation of each approach in terms of stability and image quality is presented. Exhaustive comparisons between all approaches were conducted in a 2D based image reconstruction model. From these 2D approaches, that showing the best performances were finally implemented and evaluated in a 3D based image reconstruction model. Comparison to 3D images reconstructed with FBP is also presented. Although the algorithm is presented in the context of computed tomography (CT) image reconstruction, it can be applied to any other tomographic technique as well, due to the fact that the only requirement is a scanning geometry involving measurements of an object under different projection angles. Real data have been acquired with a small animal (CT) scanner to verify the proposed mathematical description of the CT system.This work was supported by the Spanish Plan Nacional de Investigacion Cientifica, Desarrollo e Innovacion Tecnologica (I+D+I) under Grant, FIS2010-21216-CO2-01, Valencian Local Government under Grant Nos. PROMETEO 2008/114 and APOSTD/2010/012. The authors would like to thank Brennan Holt for checking and correcting the text.Rodríguez Álvarez, MJ.; Soriano Asensi, A.; Iborra Carreres, A.; Sánchez Martínez, F.; González Martínez, AJ.; Conde, P.; Hernández Hernández, L.... (2013). Expectation maximization (EM) algorithms using polar symmetriesfor computed tomography(CT) image reconstruction. Computers in Biology and Medicine. 43(8):1053-1061. https://doi.org/10.1016/j.compbiomed.2013.04.015S1053106143

Bayesian Approach for dimensionality reduction of compartmental model parameters of the PET [18F]FDG tracer

openPositron Emission Tomography (PET) con [18F]FDG (Fluorodeossiglucosio) è una tecnica di imaging nucleare ampiamente utilizzata in oncologia. Ha un ruolo cruciale nell'esaminare i processi fisiologici e patofisiologici in vivo, consentendo la misurazione quantitativa dei cambiamenti biochimici nel corpo. Ciò facilita la rilevazione di anomalie nel metabolismo dei tessuti d'interesse. Per stabilire una connessione tra i segnali PET e i processi biochimici interni, è richiesto l'utilizzo di un modello compartimentale. La stima dei parametri può essere eseguita a livello di regione di interesse (ROI) o a livello di voxel, sfruttando appieno la risoluzione spaziale dello scanner PET. In situazioni specifiche, ad esempio nello studio di una lesione, le informazioni fornite dall'analisi a livello di ROI potrebbero non essere sufficienti, e sarebbe richiesta un'analisi a livello di voxel. La sfida risiede nel tipo di segnale ottenuto a livello di voxel, caratterizzato da un basso rapporto segnale-rumore (SNR), in contrasto al segnale ottenuto dall'analisi a livello di ROI. Attualmente, i metodi comunemente utilizzati per la stima dei microparametri a livello di ROI non sono altrettanto efficaci a livello di voxel, a causa del basso SNR. Approcci semplificati, come il metodo grafico di Patlak, sono applicabili, ma generano parametri con informazioni fisiologiche meno dettagliate. Pertanto, c'è la necessità di un approccio in grado di produrre risultati affidabili a livello di voxel. Una soluzione potrebbe essere negli stimatori Bayesiani, che sfruttano informazioni a priori per performare meglio in presenza di dati rumorosi. Tuttavia, la stima dei microparametri nel modello è basata sull'assunzione di disporre di una funzione di input priva di rumore. Questo richiede tipicamente campionamenti arteriali, che possono essere scomodi e gravosi per il paziente. Un'alternativa è la Image-derived Input Function (IDIF), che estrae la funzione di input direttamente dall'immagine PET, utilizzando le arterie carotidi interne (ICA) o le arterie carotidi comuni (CCA), con correzioni applicate per correggere i Partial Volume Effect (PVE). Questa tesi si concentra sull'esplorazione di un approccio bayesiano per consentire una stima adeguata dei microparametri a livello di voxel. In particolare, è stato utilizzato il metodo di stima Maximum A Posteriori (MAP). Nella nostra implementazione, le informazioni a priori derivano dalle stime a livello di ROI, con l'obiettivo finale di ottenere stime precise a livello di voxel. Inoltre, la stima MAP è stata testata con un vincolo su un parametro del modello, il k3, basato sulla stima voxel-wise di Ki ottenuta utilizzando l'analisi grafica di Patlak, per ridurre ulteriormente la complessità. Inoltre, è stata esaminata l'influenza dell'utilizzo di diverse funzioni di input estratte da diverse ROI vascolari in questo studio. L'analisi è stata eseguita su un dataset composto da 10 soggetti affetti da glioma sottoposti ad una acquisizione con tracciante [18F]FDG su un sistema PET/MR presso l'Ospedale Universitario di Padova. Per valutare l'affidabilità dei risultati ottenuti con la stima MAP, le mappe parametriche sono state confrontate con quelle ottenute utilizzando un altro approccio bayesiano, ovvero il Variational Bayes (VB). Le stime a livello di voxel ottenute dai due diversi metodi presentano una correlazione elevata. Per quanto riguarda la funzione di input, osserviamo che si ottengono stime simili utilizzando l'IDIF delle ICA con correzione del PVE o utilizzando l'IDIF delle CCA senza alcuna correzione. Questo approccio apre la strada a futuri studi sulla gestione dei dati rumorosi in relazione all'errore di misura e sull'ispezione dell'influenza dei vincoli sul calcolo a posteriori del parametro k3.Positron Emission Tomography (PET) with [18F]FDG (Fluorodeoxyglucose) is a nuclear imaging technique widely utilized in oncology. It plays a crucial role in examining physiological and pathophysiological processes in vivo, enabling the quantitative measurement of biochemical changes in the body. This facilitates the detection of anomalies in the metabolism of tissues of interest. To establish a connection between PET signals and internal biochemical processes, compartmental modeling is required. Parameter estimation can be performed either at region-of-interest (ROI) level or at the voxel level, fully exploiting the PET scanner spatial resolution. In specific situations, for example when studying a lesion, the information provided by ROI level analysis may not be enough, and a voxel level analysis would be required. The challenge lies in the type of signal obtained at the voxel level, characterized by a low Signal-to-Noise Ratio (SNR), in contrast to regional analysis. Currently, commonly employed methods for microparameter estimation at ROI level are not equally effective at the voxel level, due to the low SNR. Simplified approaches, such as the Patlak Graphical method, are available, but they generate parameters with less detailed physiological information. Therefore, there is a need for an approach able to produce reliable voxel-level results. A solution may be found in Bayesian approaches, which leverage a priori information to perform better in the presence of noisy data. Nevertheless, microparameter estimation in the model is based on the assumption of having a noise-free Input function. This typically requires arterial sampling, which can be uncomfortable and burdensome for the patient. An alternative is the Image-Derived Input Function (IDIF), which extracts the Input function directly from the PET image, using the Internal Carotid Arteries (ICA) or the Common Carotid Arteries (CCA), with corrections applied for Partial Volume Effect (PVE). This thesis focuses on exploring a Bayesian approach to enable adequate voxel-level microparameter estimation. Specifically, the Maximum a Posteriori (MAP) estimation method is employed. In our implementation, the prior information is derived from ROI-level estimates with the ultimate goal of obtaining precise voxel-level estimates. Additionally, the MAP estimation was tested with a constraint on a model parameter, k3, based on the voxel-wise Ki estimate obtained using Patlak's graphical analysis, to further reduce complexity. Furthermore, the impact of using different input functions extracted from different vascular ROIs was examined in this study. The analysis was performed on a dataset consisting of 10 subjects affected by glioma who underwent [18F]FDG acquisition on a PET/MR system at the University Hospital of Padova. To assess the reliability of the results obtained with the MAP, the parametric maps were compared to the ones obtained using another bayesian approach, i.e. the Variational Bayes (VB). Voxel-level esimates coming from the two different methods exhibit a high correlation. As for the input function, we observe that similar estimates are obtained when using ICA's IDIF with PVE correction or when using CCA's IDIF without any correction. This approach opens doors for future research in handling data fitting with respect to measurement error and examining the influence of constraints on the posterior calculation of the k3 parameter

Kinetic Modelling in Human Brain Imaging

Geneeskunde en GesondheidswetenskappeKerngeneeskundePlease help us populate SUNScholar with the post print version of this article. It can be e-mailed to: [email protected]

4D-PET reconstruction using a spline-residue model with spatial and temporal roughness penalties

4D reconstruction of dynamic positron emission tomography (dPET) data can improve the signal-to-noise ratio in reconstructed image sequences by fitting smooth temporal functions to the voxel time-activity-curves (TACs) during the reconstruction, though the optimal choice of function remains an open question. We propose a spline-residue model, which describes TACs as weighted sums of convolutions of the arterial input function with cubic B-spline basis functions. Convolution with the input function constrains the spline-residue model at early time-points, potentially enhancing noise suppression in early time-frames, while still allowing a wide range of TAC descriptions over the entire imaged time-course, thus limiting bias. 
 Spline-residue based 4D-reconstruction is compared to that of a conventional (non-4D) maximum a posteriori (MAP) algorithm, and to 4D-reconstructions based on adaptive-knot cubic B-splines, the spectral model and an irreversible two-tissue compartment ('2C3K') model. 4D reconstructions were carried out using a nested-MAP algorithm including spatial and temporal roughness penalties. The algorithms were tested using Monte-Carlo simulated scanner data, generated for a digital thoracic phantom with uptake kinetics based on a dynamic [18F]-Fluromisonidazole scan of a non-small cell lung cancer patient. For every algorithm, parametric maps were calculated by fitting each voxel TAC within a sub-region of the reconstructed images with the 2C3K model. 
 Compared to conventional MAP reconstruction, spline-residue-based 4D reconstruction achieved >50% improvements for 5 of the 8 combinations of the 4 kinetics parameters for which parametric maps were created with the bias and noise measures used to analyse them, and produced better results for 5/8 combinations than any of the other reconstruction algorithms studied, while spectral model-based 4D reconstruction produced the best results for 2/8. 2C3K model-based 4D reconstruction generated the most biased parametric maps. Inclusion of a temporal roughness penalty function improved the performance of 4D reconstruction based on the cubic B-spline, spectral and spline-residue models.&#13

Stochastic Optimisation Methods Applied to PET Image Reconstruction

Positron Emission Tomography (PET) is a medical imaging technique that is used to pro- vide functional information regarding physiological processes. Statistical PET reconstruc- tion attempts to estimate the distribution of radiotracer in the body but this methodology is generally computationally demanding because of the use of iterative algorithms. These algorithms are often accelerated by the utilisation of data subsets, which may result in con- vergence to a limit set rather than the unique solution. Methods exist to relax the update step sizes of subset algorithms but they introduce additional heuristic parameters that may result in extended reconstruction times. This work investigates novel methods to modify subset algorithms to converge to the unique solution while maintaining the acceleration benefits of subset methods. This work begins with a study of an automatic method for increasing subset sizes, called AutoSubsets. This algorithm measures the divergence between two distinct data subset update directions and, if significant, the subset size is increased for future updates. The algorithm is evaluated using both projection and list mode data. The algorithm’s use of small initial subsets benefits early reconstruction but unfortunately, at later updates, the subsets size increases too early, which impedes convergence rates. The main part of this work investigates the application of stochastic variance reduction optimisation algorithms to PET image reconstruction. These algorithms reduce variance due to the use of subsets by incorporating previously computed subset gradients into the update direction. The algorithms are adapted for the application to PET reconstruction. This study evaluates the reconstruction performance of these algorithms when applied to various 3D non-TOF PET simulated, phantom and patient data sets. The impact of a number of algorithm parameters are explored, which includes: subset selection methodologies, the number of subsets, step size methodologies and preconditioners. The results indicate that these stochastic variance reduction algorithms demonstrate superior performance after only a few epochs when compared to a standard PET reconstruction algorithm

Inverse Problems in data-driven multi-scale Systems Medicine: application to cancer physiology

Systems Medicine is an interdisciplinary framework involving reciprocal feedback between clinical investigation and mathematical modeling/analysis. Its aim is to improve the understanding of complex diseases by integrating knowledge and data across multiple levels of biological organization. This Thesis focuses on three inverse problems, arising from three kinds of data and related to cancer physiology, at different scales: tissues, cells, molecules. The general assumption of this piece of research is that cancer is associated toa path ological glucose consumption and, in fact, its functional behavior can be assessed by nuclear medicine experiments using [18F]-fluorodeoxyglucose (FDG) as a radioactive tracer mimicking the glucose properties. At tissue-scale, this Thesis considers the Positron Emission Tomography (PET) imaging technique, and deals with two distinct issues within compartmental analysis. First, this Thesis presents a compartmental approach, referred to as reference tissue model, for the estimation of FDG kinetics inside cancer tissues when the arterial blood input of the system is unknown. Then, this Thesis proposes an efficient and reliable method for recovering the compartmental kinetic parameters for each PET image pixel in the context of parametric imaging, exploiting information on the tissue physiology. Standard models in compartmental analysis assume that phosphorylation and dephosphorylation of FDG occur in the same intracellular cytosolic volume. Advances in cell biochemistry have shown that the appropriate location of dephosphorylation is the endoplasmic reticulum (ER). Therefore, at cell-scale, this Thesis formalizes a biochemically-driven compartmental model accounting for the specific role played by the ER, and applies it to the analysis of in vitro experiments on FDG uptake by cancer cell cultures obtained with a LigandTracer (LT) device. Finally, at molecule-scale, this Thesis provides a preliminary mathematical investigation of a chemical reaction network (CRN), represented by a huge Molecular Interaction Map (MIM), describing the biochemical interactions occurring between signaling proteins in specific pathways within a cancer cell. The main issue addressed in this case is the network parameterization problem, i.e. how to determine the reaction rate coefficients from protein concentration data