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A Thesis for the Degree of PHILOSOPHIAE DOCTOR

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A Thesis for the Degree of PHILOSOPHIAE DOCTOR A Study of the Imaging of Contrast Agents for use in Computerised Tomography. A thesis for the degree of PHILOSOPHIAE DOCTOR Presented to DUBLIN CITY UNIVERSITY By Neil John O'Hare B.Sc. The School of Physical Sciences Dublin City University Research Supervisor Joseph Fryar B.Sc. Ph.D August 1991 This thesis is dedicated to all my friends who, in one form or another, enabled me to finally finish school. Of these, four deserve special mention. Firstly my parents, John and Lucy, who , through times good and bad, offered continued support and encouragement. Secondly Jonie, the woman in my life, thanks for listening. Finally Joe Fryar, my supervisor. His enthusiasm for the subject made me start and his guidance enabled me to finish. No more could I ask for. Domo Arigato. He who krvama otheriA Lb wl&e He who. knomtx hlm&eig ¿6. entbqhtened He who. canqueria atherux atruaru}. He who. canquesux hlm&ei£ io. mlqhty He mho. knauM, contentm ent ¿a nich He w ha keep& on hl& cauAAe with enenqy. haA. uuM He wha dae& not deAsiate pxom h ia paapea p la c e wiM long, endarve He wha may die but not perdAh haci ¿cmqeAsity. Tao Te Ching Declaration This thesis is based on my own work. Table of Contents. C h a p te r I Introduction to Computerised Tomography and its applications. 1.1 Introduction 1 1.2 Principles and History of Computed Tomography. 2 1.3 Commercial Scanner Developments. 7 1.4 Computerised Tomography Applications. 1.4.1 Medical 11 1.4.2 Industrial 13 1.5 Other Forms of Computerised Tomography 1.5.1 Gamma-ray CT. 14 1.5.2 Neutron CT 15 1.5.3 Electrical Impedance CT. 15 1.6 Summary 16 References 17 C h a p te r I I Basic X-ray physics, Differential Absorptiometry and Reconstruction Algorithms. 2.1 Introduction to X-rays. 2.1.1 Production of X-rays. 20 2.1.2 Interaction of X-rays with matter. 24 2.1.3 Detection of X-rays. 28 2.1.4 Biological Effects of Radiation 29 2.1.5 Radiation Units. 30 2.2 Differential X-Ray Absorptiometry 2.2.1 Introduction to Differential X-Ray Absorptiometry. 33. 2.2.2 Theory of Differential X-Ray Absorptiometry. 34. 2.2.3 Techniques to correct for matrix effects. 36 2.3 Reconstruction Algorithms. 2.3.1 Introduction to Reconstruction Algorithms. 37 2.3.2 Filtered Backprojection. 38 2.4 Errors Inherent in CT Systems. 46 References 49 Chapter III Sensitivities of Contrast Agents for use in Computerised Tomography of the Myocardium. 3.1 Introduction 51 3.1.1 Various Methods for Imaging the Heart. 52 3.1.2 Reasons for the Study. 60 3.2 Theory. 3.2.1 Introduction. 62 3.2.2 Monochromatic Beams. 63 3.2.3 Polychromatic Beams. 69 3.3 Simulations. 3.3.1 Introduction. 70 3.3.2 Dummy Data. 70 3.3.3 Poisson Noise. 73 3.3.4 Image Subtraction. 75 3.3.5 Perception of Images. 76 3.3.6 Visibility Criterion. 78 3.3.7 Single Energy Simulations. 80 3.3.8 Dual-Energy Simulations. 81 3.3.9 Number of Incident Photons / Number of Steps Scaling. 83 3.3.10 Polychromatic Spectra Simulations for full Disc Case. 83 3.3.11 Polychromatic Spectra Simulations for Thorax/Myocardium Phantom: No Subtraction. 87 3.3.12 Polychromatic Spectra Simulations for Thorax Myocardium Phantom: Subtraction. 9 0 3.4 Experimental Results. 3.4.1 Determination of the Number of Incident Photons and the Detector Efficiency. 91 3.4.2 Determination of the Number of Steps / Projections performed on the Somatom-2 Scanner. 94 3.4.3 Scaled Simulation Results 95 3.4.4 Experimental Phantom. 95 3.4.5 Preparation of Chemicals. 96 3.4.6 Results. 97 3.5 Discussion. 3.5.1 Introduction. 9 8 3.5.2 Fixed Mono-Energy Scans with Image Subtraction. 98 3.5.3 Monochromatic-Energy scans above and below the K-edge (K-edge subtraction). 98 3.5.4 Single Polychromatic Scan 99 3.5.5 Two Fixed-Voltage Polychromatic Scans with Image Subtraction 99 3.5.6 Gd-DTPA. 99 3.6 Conclusion. 101 References 103 C h a p te r I V Determination of the Sensitivity of CT to contrast agents in cylinders. 4.1 Introduction 109 4.2 Theory 1 1 1 4.2.1 The case where the analyte can be added to the matrix. 1 1 1 4.2.2 Determination of Concentration. 117 4.2.3 Multi-element compounds. 118 4.2.4 The case where the analyte cannot be added to the matrix (K-edge). 1 2 0 4.2.5 Theoretical results. 127 4.3 Computer simulations. 4.3.1 Introduction 137 4.3.2 Visibility parameter. 137 4.3.3 No. of incident photons scaling. 138 4.3.4 No. of projections scaling. 138 4.3.5 Min. Cone. vs. F simulations. 140 4.3.6 No. of mean free path dependence. 14 3 4.3.7 Determination of the Q value. 143 4.4 Summary 145 References. 147 C h apter V Experimental results on the sensitivity of CT to contrast agents in cylinders. 5.1 Introduction. 148 5.2 Apparatus. 148 5.2.1 Overview of Apparatus. 148 5.2.2 X-Ray Source / Shielding. 148 5.2.3 Si(Li) Detector. 151 5.2.4 Multichannel Analyser. 151 5.2.5 NIM Modules. 153 5.2.6 Pulse Shaping. 154 5.2.7 Counting Systems. 157 5.2.8 Scan Table / Stepper - motor interface. 159 5.2.9 Experimental Phantom. 160 5.2.10 Filtering the X-ray beam. 161 5.3 Software. 5.3.1 Scanning Program. 163 5.3.2 Transferring Data. 164 5.3.3 Reconstruct / Shift Data Routine. 164 5.3.4 Display Program. 167 5.4 Experimental Results. 5.4.1 Monochromatic results. 172 5.4.2 K-edge results 178 5.5 Summary. 183 References. 184 C h apter VI Conclusion and future work. 185 Acknowledgments. List of appendices. Appendices. Table of Figures. I Motion tomography 3 First generation scanner 5 Reconstruction grid with one beam shown. 5 Second generation scanner 7 Third generation scanner 8 Fourth generation scanner 9 Rotating anode X-ray tube. 21 Electron energy levels and transitions. 23 Photoelectric effect. 25 Compton scattering. 26 Relative effect of interaction mechanisms. 27 Variation of mass attenuation coefficient with energy. 35 Parallel data collection. 38 Process of backprojection. 39 Backprojections of a delta function. 41 Continuous and discrete form of the Ram-Lak filter. 43 Filtering the backprojection data. 44 I l l CVCT scanner. 60 Cases studied and by which method. 61 Diagram of the phantom used. 62 Ajut/fim vs. No. of mean free paths. 64 Min. Cone. vs. Energy: single monochromatic beam. 65 Min. Cone. vs. atomic number: single monochromatic beam. 65 Min. Cone. vs. atomic number: dual- energy case. 68 Scan geometry used for simulations. 71 Results from noise generation algorithm. 74 Images made from different number of pixels. 77 Min. Cone. vs. atomic number: initial results of simulations. 79 Variation of visibility parameter with increasing concentration. 80 Min. Cone. vs. energy: results of single energy simulations. 81 Theoretical and simulated results of Min. Cone, vs atomic number for single energy beams. 82 Theoretical and simulated results of Min. Cone, vs atomic number for dual energy beams. 82 Min. Cone. vs. No. incident photons. 84 Min. Cone. vs. No. of projections. 84 Incident 120 kVp filtered spectrum used in simulations. 85 3.19 Simulated image of water only phantom. 86 3.20 Sim. image of water & analyte phantom. 86 3.21 Subtracted sim. image of 3.19 & 3.20 86 3.22 Min. Cone, vs atomic number: subtraction case, homogeneous dispersion of the analyte. 88 3.23 Min. Cone. vs. atomic number: No subtraction, analyte in ring. 88 3.24 Min. Cone. vs. atomic number: Subtraction case, analyte in ring. 89 3.25 Incident 120 kVp spectrum. 92 3.26 Exposure rate vs. energy. 92 3.27 Undetected photons vs. energy for Csl crystal. 94 3.28 Scaled simulated and actual experimental results. 95 3.29 Gd-DTPA 101 C hapter 4.01 Geometry of the studied phantom. 110 4.02 3-D graph: dU/U vs. X v s . f. Monochromatic case. 128 4.03 As 4.02 except data logged. 128 4.04 3-D graph: Ca v s . f vs. X. K-edge case (Iodine in water). 129 4.05 As 4.04 except data logged. 129 4.06 3-D graph: Ca v s . f vs. X. K-edge case (Gadolinium in tissue). 130 4.07 As 4.06 except data logged. 130 4.08 dU/U vs. S, the number of projections. Monochromatic case. 131 4.09 Ln (Not) vs. Ln (dU/U) Monochromatic case. 132 4.10 dU/U vs. S: graph showing the quantisation effect of f. 132 4.11 Atomic number vs. Min. conc. (Mono) Three graphs at different f values. 133 4.12 Atomic number vs. Min conc. (K-edge) Three graphs at different f values. 133 4.13 Theoretical and simulated results: dU/U vs. Not. (Monochromatic case). 139 4.14 Theoretical and simulated results: Min. conc. vs. S. (K-edge case). 139 4.15 Theoretical and simulated results: Min. conc. vs. f (K-edge). 140 4.16 Theoretical and simulated results: dU/U vs. f. (Monochromatic case). 140 4.17 Two simulated images at f=0.1 and f=0.9. 141 4.18 Theoretical and simulated results: dU vs.
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