Summary
List of abbreviations
Résumé
Acknowledgements
1. Introduction
1.1 Medical imaging techniques
1.2 Positron Emission Tomography in medical imaging
1.3 The aim of this work
2. Positron Emission Tomography : Physics and Instrumentation
2.1 The physical principles of PET
2.1.1 Positron emission and annihilation
2.1.2 Positron emitting radiopharmaceuticals
2.1.3 Interaction of photons with matter
2.1.3.1 Photoelectric absorption
2.1.3.2 Incoherent (Compton) scattering
2.1.3.3 Coherent (Rayleigh) scattering
2.1.3.4 Pair production
2.1.3.5 The linear attenuation coefficient
2.1.4 Types of coincidence events
2.2 Design configurations of PET tomographs
2.3 Scintillation detectors for PET
2.4 2D and 3D PET data acquisition
2.5 Towards quantitative 3D PET
2.6 Innovative developments in PET instrumentation
3. Algorithms for Volume Reconstruction in PET
3.1 The problem of image reconstruction in PET
3.1.1 Solution of the 2D problem
3.1.2 Solution of the 3D problem
3.2 Analytic reconstruction algorithms
3.2.1 The reprojection algorithm (3DRP)
3.2.2 The Fast Volume Reconstruction (FAVOR) algorithm
3.2.3 Rebinning-based algorithms
3.3 Iterative reconstruction algorithms
3.3.1 Algebraic reconstruction algorithms
3.3.2 Statistical reconstruction algorithms
3.3.2.1 Maximum likelihood - expectation maximisation (ML-EM)
3.3.2.2 The Ordered Subsets EM (OSEM) algorithm
3.3.2.3 Regularisation for ML-EM reconstruction methods
3.3.2.4 Least square (LSQ) minimisation of the likelihood matrix
3.4 A modular, flexible and portable object-oriented library for 3D PET reconstruction
3.4.1 Data structure
3.4.2 The projection/backprojection operators
3.5 PARAPET project
3.5.1 COSEM : an iterative algorithm for fully 3D listmode data
3.5.2 OSEM with inter-update filtering
3.5.3 The mirror descent algorithm
3.5.4 Inverse Monte Carlo-based reconstruction
3.5.5 Parallelisation and scalability
4. Monte Carlo modelling in positron emission tomography
4.1 The Monte Carlo method
4.2 Computational methods
4.2.1 Random numbers generation
4.2.1.1 Linear Congruential Generators
4.2.1.2 Lagged-Fibonacci Generators
4.2.2 The source and positron emission
4.2.3 Modelling photon transport
4.2.4 Analogue sampling
4.2.4.1 Direct method
4.2.4.2 Rejection method
4.2.4.3 Mixed methods
4.2.5 Non-analogue sampling "Variance reduction techniques"
4.2.5.1 Interaction forcing
4.2.5.2 Stratification
4.2.5.3 Exponential transform, Russian roulette and particle splitting
4.2.5.4 Correlated sampling
4.2.5.5 Use of geometry symmetry
4.3 Applications of the Monte Carlo method in positron emission tomography
4.3.1 Detector modelling
4.3.2 Imaging systems and collimators design
4.3.3 Image reconstruction algorithms
4.3.4 Attenuation and scatter correction techniques
4.3.5 Dosimetry and treatment planning
4.3.6 Pharmacokinetic modelling
4.4 Monte Carlo computer codes
5. Development of a Monte Carlo Simulator for 3D PET
5.1 Designing object-oriented projects
5.1.1 Object-oriented programming concepts
5.1.2 Organising object-oriented projects
5.2 An object-oriented Monte Carlo simulator for 3D positron emission tomography
5.2.1 A simulation model for 3D PET
5.2.2 Software design
5.2.3 Graphical user interface
5.2.4 Monte Carlo code features
5.2.5 Validation of the simulation model
5.2.5.1 Spatial resolution
5.2.5.2 Energy spectra
5.2.5.3 Scatter fraction
5.2.5.4 Phantom studies
5.2.5.5 Clinical studies
5.3 Object model and software phantoms
5.3.1 Object modelling
5.3.2 Anthropomorphic phantoms
6. Improvement of the performance and efficiency of PET Monte Carlo simulations
6.1 Parallel implementation of the simulator
6.1.1 Parallel computing platforms
6.1.1.1 Single Instruction Single Data stream (SISD) machines
6.1.1.2 Single Instruction Multiple Data streams (SIMD) machines
6.1.1.3 Multiple Instructions Single Data stream (MISD) machines
6.1.1.4 Multiple Instructions Multiple Data streams (MIMD) machines
6.1.2 Parallelisation strategies for Monte Carlo codes
6.1.3 The Parsytec-CC system
6.1.4. Porting the software on the parallel platform
6.1.5 Distribution of random number sequences
6.1.6 Performance and timing results
6.2 Improvement of the precision and accuracy of PET Monte Carlo simulations
6.2.1 Photon cross section libraries and parametrizations
6.2.1.1 XCOM
6.2.1.2 PHOTX
6.2.1.3 GEANT
6.2.1.4 PETSIM
6.2.1.5 EPDL97
6.2.2 Comparative evaluation
7. Scatter Correction in 3D PET
7.1 The problem of Compton scatter
7.2 Scatter components in 3D PET
7.3 Scatter modelling in 3D PET
7.3.1 Scatter distribution functions
7.3.2 Scatter fractions
7.4 Overview of scatter correction approaches
7.4.1 Energy window-based approaches
7.4.2 Convolution-deconvolution based approaches
7.4.3 Approaches based on direct calculation of scatter distribution
7.4.4 Iterative reconstruction-based scatter correction approaches
7.5 Proposed scatter correction techniques
7.5.1 Monte Carlo-based scatter correction (MCBSC)
7.5.2 Statistical reconstruction-based scatter correction (SRBSC)
7.6 Evaluation of scatter correction techniques
7.6.1 Phantom simulation studies
7.6.1.1 The digital Utah multi-compartment phantom
7.6.1.2 The digital Hoffman 3D brain phantom
7.6.2 Experimental phantom studies
7.6.2.1 The physical Utah multi-compartment phantom
7.6.2.2 The physical Hoffman 3D brain phantom
7.6.3 Clinical studies
7.6.3.1 Brain scan study
7.6.3.2 Clinical oncology study
8. Concluding Remarks and Future Work
8.1 Key conclusions
8.2 Future aspects of quantitative 3D PET
Bibliography
Note(s)